theory Why2 use array.Array as A use unit_inf.Unit use int.Int use int.ComputerDivision use real.Real use bool_inf.Bool predicate eq_unit Unit.unit Unit.unit predicate neq_unit Unit.unit Unit.unit predicate eq_bool Bool.bool Bool.bool predicate neq_bool Bool.bool Bool.bool predicate lt_int int int predicate le_int int int predicate gt_int int int predicate ge_int int int predicate eq_int int int predicate neq_int int int function add_int int int : int function sub_int int int : int function mul_int int int : int function div_int int int : int function mod_int int int : int function neg_int int : int predicate zwf_zero (a : int) (b : int) = ((Int.(<=) 0 b) /\ (Int.(<) a b)) function bw_compl int : int function bw_and int int : int function bw_xor int int : int function bw_or int int : int function lsl int int : int function lsr int int : int type pointer 'z type addr 'z type alloc_table function block_length alloc_table (pointer 'a1) : int function base_addr (pointer 'a1) : (addr 'a1) function offset (pointer 'a1) : int function shift (pointer 'a1) int : (pointer 'a1) function sub_pointer (pointer 'a1) (pointer 'a1) : int predicate lt_pointer (p1 : (pointer 'a1)) (p2 : (pointer 'a1)) = (((base_addr p1 : (addr 'a1)) = (base_addr p2 : (addr 'a1))) /\ (Int.(<) (offset p1 : int) (offset p2 : int))) predicate le_pointer (p1 : (pointer 'a1)) (p2 : (pointer 'a1)) = (((base_addr p1 : (addr 'a1)) = (base_addr p2 : (addr 'a1))) /\ (Int.(<=) (offset p1 : int) (offset p2 : int))) predicate gt_pointer (p1 : (pointer 'a1)) (p2 : (pointer 'a1)) = (((base_addr p1 : (addr 'a1)) = (base_addr p2 : (addr 'a1))) /\ (Int.(>) (offset p1 : int) (offset p2 : int))) predicate ge_pointer (p1 : (pointer 'a1)) (p2 : (pointer 'a1)) = (((base_addr p1 : (addr 'a1)) = (base_addr p2 : (addr 'a1))) /\ (Int.(>=) (offset p1 : int) (offset p2 : int))) predicate valid (a : alloc_table) (p : (pointer 'a1)) = ((Int.(<=) 0 (offset p : int)) /\ (Int.(<) (offset p : int) (block_length a p : int))) predicate valid_index (a : alloc_table) (p : (pointer 'a1)) (i : int) = ((Int.(<=) 0 (Int.(+) (offset p : int) i : int)) /\ (Int.(<) (Int.(+) (offset p : int) i : int) (block_length a p : int))) predicate valid_range (a : alloc_table) (p : (pointer 'a1)) (i : int) (j : int) = ((Int.(<=) 0 (Int.(+) (offset p : int) i : int)) /\ (Int.(<) (Int.(+) (offset p : int) j : int) (block_length a p : int))) axiom Offset_shift: (forall p:(pointer 'a1). (forall i:int [(offset (shift p i : (pointer 'a1)) : int)]. ((offset (shift p i : (pointer 'a1)) : int) = (Int.(+) (offset p : int) i : int)))) axiom Shift_zero: (forall p:(pointer 'a1) [(shift p 0 : (pointer 'a1))]. ((shift p 0 : (pointer 'a1)) = p)) axiom Shift_shift: (forall p:(pointer 'a1). (forall i:int. (forall j:int [(shift (shift p i : (pointer 'a1)) j : (pointer 'a1))]. ((shift (shift p i : (pointer 'a1)) j : (pointer 'a1)) = (shift p (Int.(+) i j : int) : (pointer 'a1)))))) axiom Base_addr_shift: (forall p:(pointer 'a1). (forall i:int [(base_addr (shift p i : (pointer 'a1)) : (addr 'a1))]. ((base_addr (shift p i : (pointer 'a1)) : (addr 'a1)) = (base_addr p : (addr 'a1))))) axiom Block_length_shift: (forall a:alloc_table. (forall p:(pointer 'a1). (forall i:int [(block_length a (shift p i : (pointer 'a1)) : int)]. ((block_length a (shift p i : (pointer 'a1)) : int) = (block_length a p : int))))) axiom Base_addr_block_length: (forall a:alloc_table. (forall p1:(pointer 'a1). (forall p2:(pointer 'a1). (((base_addr p1 : (addr 'a1)) = (base_addr p2 : (addr 'a1))) -> ((block_length a p1 : int) = (block_length a p2 : int)))))) axiom Pointer_pair_1: (forall p1:(pointer 'a1). (forall p2:(pointer 'a1). ((((base_addr p1 : (addr 'a1)) = (base_addr p2 : (addr 'a1))) /\ ((offset p1 : int) = (offset p2 : int))) -> (p1 = p2)))) axiom Pointer_pair_2: (forall p1:(pointer 'a1). (forall p2:(pointer 'a1). ((p1 = p2) -> (((base_addr p1 : (addr 'a1)) = (base_addr p2 : (addr 'a1))) /\ ((offset p1 : int) = (offset p2 : int)))))) axiom Neq_base_addr_neq_shift: (forall p1:(pointer 'a1). (forall p2:(pointer 'a1). (forall i:int. (forall j:int. (((base_addr p1 : (addr 'a1)) <> (base_addr p2 : (addr 'a1))) -> ((shift p1 i : (pointer 'a1)) <> (shift p2 j : (pointer 'a1)))))))) axiom Neq_offset_neq_shift: (forall p1:(pointer 'a1). (forall p2:(pointer 'a1). (forall i:int. (forall j:int. (((Int.(+) (offset p1 : int) i : int) <> (Int.(+) (offset p2 : int) j : int)) -> ((shift p1 i : (pointer 'a1)) <> (shift p2 j : (pointer 'a1)))))))) axiom Eq_offset_eq_shift: (forall p1:(pointer 'a1). (forall p2:(pointer 'a1). (forall i:int. (forall j:int. (((base_addr p1 : (addr 'a1)) = (base_addr p2 : (addr 'a1))) -> (((Int.(+) (offset p1 : int) i : int) = (Int.(+) (offset p2 : int) j : int)) -> ((shift p1 i : (pointer 'a1)) = (shift p2 j : (pointer 'a1))))))))) axiom Valid_index_valid_shift: (forall a:alloc_table. (forall p:(pointer 'a1). (forall i:int. ((valid_index a p i) -> (valid a (shift p i : (pointer 'a1))))))) axiom Valid_range_valid_shift: (forall a:alloc_table. (forall p:(pointer 'a1). (forall i:int. (forall j:int. (forall k:int. ((valid_range a p i j) -> (((Int.(<=) i k) /\ (Int.(<=) k j)) -> (valid a (shift p k : (pointer 'a1)))))))))) axiom Valid_range_valid: (forall a:alloc_table. (forall p:(pointer 'a1). (forall i:int. (forall j:int. ((valid_range a p i j) -> (((Int.(<=) i 0) /\ (Int.(<=) 0 j)) -> (valid a p))))))) axiom Valid_range_valid_index: (forall a:alloc_table. (forall p:(pointer 'a1). (forall i:int. (forall j:int. (forall k:int. ((valid_range a p i j) -> (((Int.(<=) i k) /\ (Int.(<=) k j)) -> (valid_index a p k)))))))) axiom Sub_pointer_def: (forall p1:(pointer 'a1). (forall p2:(pointer 'a1). (((base_addr p1 : (addr 'a1)) = (base_addr p2 : (addr 'a1))) -> ((sub_pointer p1 p2 : int) = (Int.(-) (offset p1 : int) (offset p2 : int) : int))))) type memory 'a 'z = A.t (pointer 'z) 'a function acc (m:memory 'a1 'a2) (k:pointer 'a2) : 'a1 = A.get m k function upd (m:memory 'a1 'a2) (k:pointer 'a2) (v:'a1) : (memory 'a1 'a2) = A.set m k v type pset 'z function pset_empty : (pset 'a1) function pset_singleton (pointer 'a1) : (pset 'a1) function pset_star (pset 'a2) (memory (pointer 'a1) 'a2) : (pset 'a1) function pset_all (pset 'a1) : (pset 'a1) function pset_range (pset 'a1) int int : (pset 'a1) function pset_range_left (pset 'a1) int : (pset 'a1) function pset_range_right (pset 'a1) int : (pset 'a1) function pset_acc_all (pset 'a2) (memory (pointer 'a1) 'a2) : (pset 'a1) function pset_acc_range (pset 'a2) (memory (pointer 'a1) 'a2) int int : (pset 'a1) function pset_acc_range_left (pset 'a2) (memory (pointer 'a1) 'a2) int : (pset 'a1) function pset_acc_range_right (pset 'a2) (memory (pointer 'a1) 'a2) int : (pset 'a1) function pset_union (pset 'a1) (pset 'a1) : (pset 'a1) predicate not_in_pset (pointer 'a1) (pset 'a1) predicate not_assigns (a : alloc_table) (m1 : (memory 'a1 'a2)) (m2 : (memory 'a1 'a2)) (l : (pset 'a2)) = (forall p:(pointer 'a2). ((valid a p) -> ((not_in_pset p l) -> ((acc m2 p : 'a1) = (acc m1 p : 'a1))))) axiom Pset_empty_intro: (forall p:(pointer 'a1). (not_in_pset p (pset_empty : (pset 'a1)))) axiom Pset_singleton_intro: (forall p1:(pointer 'a1). (forall p2:(pointer 'a1) [(not_in_pset p1 (pset_singleton p2 : (pset 'a1)))]. ((p1 <> p2) -> (not_in_pset p1 (pset_singleton p2 : (pset 'a1)))))) axiom Pset_singleton_elim: (forall p1:(pointer 'a1). (forall p2:(pointer 'a1) [(not_in_pset p1 (pset_singleton p2 : (pset 'a1)))]. ((not_in_pset p1 (pset_singleton p2 : (pset 'a1))) -> (p1 <> p2)))) axiom Not_not_in_singleton: (forall p:(pointer 'a1). (not (not_in_pset p (pset_singleton p : (pset 'a1))))) axiom Pset_union_intro: (forall l1:(pset 'a1). (forall l2:(pset 'a1). (forall p:(pointer 'a1) [(not_in_pset p (pset_union l1 l2 : (pset 'a1)))]. (((not_in_pset p l1) /\ (not_in_pset p l2)) -> (not_in_pset p (pset_union l1 l2 : (pset 'a1))))))) axiom Pset_union_elim1: (forall l1:(pset 'a1). (forall l2:(pset 'a1). (forall p:(pointer 'a1) [(not_in_pset p (pset_union l1 l2 : (pset 'a1)))]. ((not_in_pset p (pset_union l1 l2 : (pset 'a1))) -> (not_in_pset p l1))))) axiom Pset_union_elim2: (forall l1:(pset 'a1). (forall l2:(pset 'a1). (forall p:(pointer 'a1) [(not_in_pset p (pset_union l1 l2 : (pset 'a1)))]. ((not_in_pset p (pset_union l1 l2 : (pset 'a1))) -> (not_in_pset p l2))))) axiom Pset_star_intro: (forall l:(pset 'a1). (forall m:(memory (pointer 'a2) 'a1). (forall p:(pointer 'a2) [(not_in_pset p (pset_star l m : (pset 'a2)))]. ((forall p1:(pointer 'a1). ((p = (acc m p1 : (pointer 'a2))) -> (not_in_pset p1 l))) -> (not_in_pset p (pset_star l m : (pset 'a2))))))) axiom Pset_star_elim: (forall l:(pset 'a1). (forall m:(memory (pointer 'a2) 'a1). (forall p:(pointer 'a2) [(not_in_pset p (pset_star l m : (pset 'a2)))]. ((not_in_pset p (pset_star l m : (pset 'a2))) -> (forall p1:(pointer 'a1). ((p = (acc m p1 : (pointer 'a2))) -> (not_in_pset p1 l))))))) axiom Pset_all_intro: (forall p:(pointer 'a1). (forall l:(pset 'a1) [(not_in_pset p (pset_all l : (pset 'a1)))]. ((forall p1:(pointer 'a1). ((not (not_in_pset p1 l)) -> ((base_addr p : (addr 'a1)) <> (base_addr p1 : (addr 'a1))))) -> (not_in_pset p (pset_all l : (pset 'a1)))))) axiom Pset_all_elim: (forall p:(pointer 'a1). (forall l:(pset 'a1) [(not_in_pset p (pset_all l : (pset 'a1)))]. ((not_in_pset p (pset_all l : (pset 'a1))) -> (forall p1:(pointer 'a1). ((not (not_in_pset p1 l)) -> ((base_addr p : (addr 'a1)) <> (base_addr p1 : (addr 'a1)))))))) axiom Pset_range_intro: (forall p:(pointer 'a1). (forall l:(pset 'a1). (forall a:int. (forall b:int [(not_in_pset p (pset_range l a b : (pset 'a1)))]. ((forall p1:(pointer 'a1). ((not_in_pset p1 l) \/ (forall i:int. (((Int.(<=) a i) /\ (Int.(<=) i b)) -> (p <> (shift p1 i : (pointer 'a1))))))) -> (not_in_pset p (pset_range l a b : (pset 'a1)))))))) axiom Pset_range_elim: (forall p:(pointer 'a1). (forall l:(pset 'a1). (forall a:int. (forall b:int [(not_in_pset p (pset_range l a b : (pset 'a1)))]. ((not_in_pset p (pset_range l a b : (pset 'a1))) -> (forall p1:(pointer 'a1). ((not (not_in_pset p1 l)) -> (forall i:int. (((Int.(<=) a i) /\ (Int.(<=) i b)) -> ((shift p1 i : (pointer 'a1)) <> p)))))))))) axiom Pset_range_left_intro: (forall p:(pointer 'a1). (forall l:(pset 'a1). (forall a:int [(not_in_pset p (pset_range_left l a : (pset 'a1)))]. ((forall p1:(pointer 'a1). ((not_in_pset p1 l) \/ (forall i:int. ((Int.(<=) i a) -> (p <> (shift p1 i : (pointer 'a1))))))) -> (not_in_pset p (pset_range_left l a : (pset 'a1))))))) axiom Pset_range_left_elim: (forall p:(pointer 'a1). (forall l:(pset 'a1). (forall a:int [(not_in_pset p (pset_range_left l a : (pset 'a1)))]. ((not_in_pset p (pset_range_left l a : (pset 'a1))) -> (forall p1:(pointer 'a1). ((not (not_in_pset p1 l)) -> (forall i:int. ((Int.(<=) i a) -> ((shift p1 i : (pointer 'a1)) <> p))))))))) axiom Pset_range_right_intro: (forall p:(pointer 'a1). (forall l:(pset 'a1). (forall a:int [(not_in_pset p (pset_range_right l a : (pset 'a1)))]. ((forall p1:(pointer 'a1). ((not_in_pset p1 l) \/ (forall i:int. ((Int.(<=) a i) -> (p <> (shift p1 i : (pointer 'a1))))))) -> (not_in_pset p (pset_range_right l a : (pset 'a1))))))) axiom Pset_range_right_elim: (forall p:(pointer 'a1). (forall l:(pset 'a1). (forall a:int [(not_in_pset p (pset_range_right l a : (pset 'a1)))]. ((not_in_pset p (pset_range_right l a : (pset 'a1))) -> (forall p1:(pointer 'a1). ((not (not_in_pset p1 l)) -> (forall i:int. ((Int.(<=) a i) -> ((shift p1 i : (pointer 'a1)) <> p))))))))) axiom Pset_acc_all_intro: (forall p:(pointer 'a1). (forall l:(pset 'a2). (forall m:(memory (pointer 'a1) 'a2) [(not_in_pset p (pset_acc_all l m : (pset 'a1)))]. ((forall p1:(pointer 'a2). ((not (not_in_pset p1 l)) -> (forall i:int. (p <> (acc m (shift p1 i : (pointer 'a2)) : (pointer 'a1)))))) -> (not_in_pset p (pset_acc_all l m : (pset 'a1))))))) axiom Pset_acc_all_elim: (forall p:(pointer 'a1). (forall l:(pset 'a2). (forall m:(memory (pointer 'a1) 'a2) [(not_in_pset p (pset_acc_all l m : (pset 'a1)))]. ((not_in_pset p (pset_acc_all l m : (pset 'a1))) -> (forall p1:(pointer 'a2). ((not (not_in_pset p1 l)) -> (forall i:int. ((acc m (shift p1 i : (pointer 'a2)) : (pointer 'a1)) <> p)))))))) axiom Pset_acc_range_intro: (forall p:(pointer 'a1). (forall l:(pset 'a2). (forall m:(memory (pointer 'a1) 'a2). (forall a:int. (forall b:int [(not_in_pset p (pset_acc_range l m a b : (pset 'a1)))]. ((forall p1:(pointer 'a2). ((not (not_in_pset p1 l)) -> (forall i:int. (((Int.(<=) a i) /\ (Int.(<=) i b)) -> (p <> (acc m (shift p1 i : (pointer 'a2)) : (pointer 'a1))))))) -> (not_in_pset p (pset_acc_range l m a b : (pset 'a1))))))))) axiom Pset_acc_range_elim: (forall p:(pointer 'a1). (forall l:(pset 'a2). (forall m:(memory (pointer 'a1) 'a2). (forall a:int. (forall b:int. ((not_in_pset p (pset_acc_range l m a b : (pset 'a1))) -> (forall p1:(pointer 'a2). ((not (not_in_pset p1 l)) -> (forall i:int. (((Int.(<=) a i) /\ (Int.(<=) i b)) -> ((acc m (shift p1 i : (pointer 'a2)) : (pointer 'a1)) <> p))))))))))) axiom Pset_acc_range_left_intro: (forall p:(pointer 'a1). (forall l:(pset 'a2). (forall m:(memory (pointer 'a1) 'a2). (forall a:int [(not_in_pset p (pset_acc_range_left l m a : (pset 'a1)))]. ((forall p1:(pointer 'a2). ((not (not_in_pset p1 l)) -> (forall i:int. ((Int.(<=) i a) -> (p <> (acc m (shift p1 i : (pointer 'a2)) : (pointer 'a1))))))) -> (not_in_pset p (pset_acc_range_left l m a : (pset 'a1)))))))) axiom Pset_acc_range_left_elim: (forall p:(pointer 'a1). (forall l:(pset 'a2). (forall m:(memory (pointer 'a1) 'a2). (forall a:int [(not_in_pset p (pset_acc_range_left l m a : (pset 'a1)))]. ((not_in_pset p (pset_acc_range_left l m a : (pset 'a1))) -> (forall p1:(pointer 'a2). ((not (not_in_pset p1 l)) -> (forall i:int. ((Int.(<=) i a) -> ((acc m (shift p1 i : (pointer 'a2)) : (pointer 'a1)) <> p)))))))))) axiom Pset_acc_range_right_intro: (forall p:(pointer 'a1). (forall l:(pset 'a2). (forall m:(memory (pointer 'a1) 'a2). (forall a:int [(not_in_pset p (pset_acc_range_right l m a : (pset 'a1)))]. ((forall p1:(pointer 'a2). ((not (not_in_pset p1 l)) -> (forall i:int. ((Int.(<=) a i) -> (p <> (acc m (shift p1 i : (pointer 'a2)) : (pointer 'a1))))))) -> (not_in_pset p (pset_acc_range_right l m a : (pset 'a1)))))))) axiom Pset_acc_range_right_elim: (forall p:(pointer 'a1). (forall l:(pset 'a2). (forall m:(memory (pointer 'a1) 'a2). (forall a:int [(not_in_pset p (pset_acc_range_right l m a : (pset 'a1)))]. ((not_in_pset p (pset_acc_range_right l m a : (pset 'a1))) -> (forall p1:(pointer 'a2). ((not (not_in_pset p1 l)) -> (forall i:int. ((Int.(<=) a i) -> ((acc m (shift p1 i : (pointer 'a2)) : (pointer 'a1)) <> p)))))))))) axiom Not_assigns_trans: (forall a:alloc_table. (forall l:(pset 'a1). (forall m1:(memory 'a2 'a1). (forall m2:(memory 'a2 'a1). (forall m3:(memory 'a2 'a1). ((not_assigns a m1 m2 l) -> ((not_assigns a m2 m3 l) -> (not_assigns a m1 m3 l)))))))) axiom Not_assigns_refl: (forall a:alloc_table. (forall l:(pset 'a1). (forall m:(memory 'a2 'a1). (not_assigns a m m l)))) predicate valid_acc (m1 : (memory (pointer 'a1) 'a2)) = (forall p:(pointer 'a2). (forall a:alloc_table. ((valid a p) -> (valid a (acc m1 p : (pointer 'a1)))))) predicate valid_acc_range (m1 : (memory (pointer 'a1) 'a2)) (size : int) = (forall p:(pointer 'a2). (forall a:alloc_table. ((valid a p) -> (valid_range a (acc m1 p : (pointer 'a1)) 0 (Int.(-) size 1 : int))))) axiom Valid_acc_range_valid: (forall m1:(memory (pointer 'a1) 'a2). (forall size:int. (forall p:(pointer 'a2). (forall a:alloc_table. ((valid_acc_range m1 size) -> ((valid a p) -> (valid a (acc m1 p : (pointer 'a1))))))))) predicate separation1 (m1 : (memory (pointer 'a1) 'a2)) (m2 : (memory (pointer 'a1) 'a2)) = (forall p:(pointer 'a2). (forall a:alloc_table. ((valid a p) -> ((base_addr (acc m1 p : (pointer 'a1)) : (addr 'a1)) <> (base_addr (acc m2 p : (pointer 'a1)) : (addr 'a1)))))) predicate separation1_range1 (m1 : (memory (pointer 'a1) 'a2)) (m2 : (memory (pointer 'a1) 'a2)) (size : int) = (forall p:(pointer 'a2). (forall a:alloc_table. ((valid a p) -> (forall i1:int. (forall i2:int. (((Int.(<=) 0 i1) /\ (Int.(<) i1 size)) -> (((Int.(<=) 0 i2) /\ (Int.(<) i2 size)) -> ((base_addr (acc m1 (shift p i1 : (pointer 'a2)) : (pointer 'a1)) : (addr 'a1)) <> (base_addr (acc m2 (shift p i2 : (pointer 'a2)) : (pointer 'a1)) : (addr 'a1)))))))))) predicate separation1_range (m : (memory (pointer 'a1) 'a2)) (size : int) = (forall p:(pointer 'a2). (forall a:alloc_table. ((valid a p) -> (forall i1:int. (((Int.(<=) 0 i1) /\ (Int.(<) i1 size)) -> ((base_addr (acc m (shift p i1 : (pointer 'a2)) : (pointer 'a1)) : (addr 'a1)) <> (base_addr (acc m p : (pointer 'a1)) : (addr 'a1)))))))) predicate separation2 (m1 : (memory (pointer 'a1) 'a2)) (m2 : (memory (pointer 'a1) 'a2)) = (forall p1:(pointer 'a2). (forall p2:(pointer 'a2). ((p1 <> p2) -> ((base_addr (acc m1 p1 : (pointer 'a1)) : (addr 'a1)) <> (base_addr (acc m2 p2 : (pointer 'a1)) : (addr 'a1)))))) predicate separation2_range1 (m1 : (memory (pointer 'a1) 'a2)) (m2 : (memory (pointer 'a1) 'a2)) (size : int) = (forall p:(pointer 'a2). (forall q:(pointer 'a2). (forall a:alloc_table. (forall i:int. (((Int.(<=) 0 i) /\ (Int.(<) i size)) -> ((base_addr (acc m1 (shift p i : (pointer 'a2)) : (pointer 'a1)) : (addr 'a1)) <> (base_addr (acc m2 q : (pointer 'a1)) : (addr 'a1)))))))) predicate on_heap alloc_table (pointer 'a1) predicate on_stack alloc_table (pointer 'a1) predicate fresh alloc_table (pointer 'a1) axiom Fresh_not_valid: (forall a:alloc_table. (forall p:(pointer 'a1). ((fresh a p) -> (not (valid a p))))) axiom Fresh_not_valid_shift: (forall a:alloc_table. (forall p:(pointer 'a1). ((fresh a p) -> (forall i:int. (not (valid a (shift p i : (pointer 'a1)))))))) predicate alloc_extends alloc_table alloc_table axiom Alloc_extends_valid: (forall a1:alloc_table. (forall a2:alloc_table. ((alloc_extends a1 a2) -> (forall q:(pointer 'a1). ((valid a1 q) -> (valid a2 q)))))) axiom Alloc_extends_valid_index: (forall a1:alloc_table. (forall a2:alloc_table. ((alloc_extends a1 a2) -> (forall q:(pointer 'a1). (forall i:int. ((valid_index a1 q i) -> (valid_index a2 q i))))))) axiom Alloc_extends_valid_range: (forall a1:alloc_table. (forall a2:alloc_table. ((alloc_extends a1 a2) -> (forall q:(pointer 'a1). (forall i:int. (forall j:int. ((valid_range a1 q i j) -> (valid_range a2 q i j)))))))) axiom Alloc_extends_refl: (forall a:alloc_table. (alloc_extends a a)) axiom Alloc_extends_trans: (forall a1:alloc_table. (forall a2:alloc_table. (forall a3:alloc_table [(alloc_extends a1 a2), (alloc_extends a2 a3)]. ((alloc_extends a1 a2) -> ((alloc_extends a2 a3) -> (alloc_extends a1 a3)))))) predicate free_stack alloc_table alloc_table alloc_table axiom Free_stack_heap: (forall a1:alloc_table. (forall a2:alloc_table. (forall a3:alloc_table. ((free_stack a1 a2 a3) -> (forall p:(pointer 'a1). ((valid a2 p) -> ((on_heap a2 p) -> (valid a3 p)))))))) axiom Free_stack_stack: (forall a1:alloc_table. (forall a2:alloc_table. (forall a3:alloc_table. ((free_stack a1 a2 a3) -> (forall p:(pointer 'a1). ((valid a1 p) -> ((on_stack a1 p) -> (valid a3 p)))))))) function null : (pointer 'a1) axiom Null_not_valid: (forall a:alloc_table. (not (valid a (null : (pointer 'a1))))) type data_0 type index_1_14 type d_3 type indata_2 type d_7 type indata_6 type key_4 type key_8 type key_9 type index_0_13 type data_0_15 type data_0_16 type outdata_1 type outdata_5 type d_10 type indata_11 type outdata_12 axiom Valid_range_ax1a: ("CADUCEUS_1" (forall k:int. ((Int.(>=) k 0) -> ((Int.(<=) 0 (lsr k 3 : int)) /\ (Int.(<=) (lsr k 3 : int) k))))) axiom Valid_range_ax1b: ("CADUCEUS_2" (forall k:int. ((Int.(>=) k 0) -> ((Int.(<=) 0 (Int.(*) (lsr k 3 : int) 8 : int)) /\ (Int.(<=) (Int.(*) (lsr k 3 : int) 8 : int) k))))) axiom Valid_range_ax1c: ("CADUCEUS_3" (forall k:int. ((Int.(>=) k 0) -> ((Int.(<=) 0 (bw_and k 7 : int)) /\ (Int.(<=) (bw_and k 7 : int) 7))))) axiom Valid_range_ax1d: ("CADUCEUS_4" (forall k:int. ((Int.(>=) k 0) -> ((Int.(+) (Int.(*) (lsr k 3 : int) 8 : int) (bw_and k 7 : int) : int) = k)))) axiom Valid_range_ax2: ("CADUCEUS_5" (forall k:int. ((Int.(<=) 0 (bw_and k 255 : int)) /\ (Int.(<) (bw_and k 255 : int) 256)))) axiom Valid_range_ax4: ("CADUCEUS_6" (forall inp:int. (forall k:int. (forall out:int. ((out = (bw_xor k inp : int)) -> ((Int.(<=) 0 out) /\ (Int.(<) out 256))))))) goal RC4_impl_po_1: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> (valid alloc key)))))))) goal RC4_impl_po_2: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> ("CADUCEUS_61" (Int.(>) i 0)))))))))))))))))))))))) goal RC4_impl_po_3: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> ("CADUCEUS_61" (Int.(<=) i len)))))))))))))))))))))))) goal RC4_impl_po_4: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> ("CADUCEUS_61" (valid_range alloc indata 0 7)))))))))))))))))))))))) goal RC4_impl_po_5: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> ("CADUCEUS_61" (valid_range alloc outdata 0 7)))))))))))))))))))))))) goal RC4_impl_po_6: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> ("CADUCEUS_61" (indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i : int) 8 : int) : (pointer 'a3)))))))))))))))))))))))))) goal RC4_impl_po_7: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> ("CADUCEUS_61" (outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i : int) 8 : int) : (pointer 'a4)))))))))))))))))))))))))) goal RC4_impl_po_8: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> (valid alloc result1))))))))))))))))))))))))))))))))) goal RC4_impl_po_9: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ( (y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> (valid alloc result4)))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_10: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ( (y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> (valid alloc result3))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_11: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ( (y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> (valid alloc result6)))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_12: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ( (y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> (valid alloc result8))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_13: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ( (y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> (valid alloc result10)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_14: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> (valid alloc result7)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_15: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> (valid alloc result12)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_16: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> (valid alloc result15))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_17: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> (valid alloc result14)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_18: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> (valid alloc result17))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_19: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> (valid alloc result19)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_20: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> (valid alloc result21))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_21: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> (valid alloc result18)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_22: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> (valid alloc result23))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_23: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> (valid alloc result26)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_24: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> (valid alloc result25))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_25: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> (valid alloc result28)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_26: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> (valid alloc result30))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_27: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> (valid alloc result32)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_28: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> (valid alloc result29))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_29: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> (valid alloc result34)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_30: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> (valid alloc result37))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_31: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> (valid alloc result36)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_32: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> (valid alloc result39))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_33: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> (valid alloc result41)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_34: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> (valid alloc result43))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_35: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> (valid alloc result40)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_36: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> (valid alloc result45))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_37: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> (valid alloc result48)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_38: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> (valid alloc result47))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_39: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> (valid alloc result50)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_40: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> (valid alloc result52))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_41: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result52) -> (forall result53:int. ((result53 = (acc intM_d_10_10 result52 : int)) -> (forall result54:(pointer 'a3). ((result54 = (shift mutable_indata 4 : (pointer 'a3))) -> (valid alloc result54)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_42: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result52) -> (forall result53:int. ((result53 = (acc intM_d_10_10 result52 : int)) -> (forall result54:(pointer 'a3). ((result54 = (shift mutable_indata 4 : (pointer 'a3))) -> ((valid alloc result54) -> (forall result55:int. ((result55 = (acc intM_indata_11 result54 : int)) -> (valid alloc result51))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_43: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result52) -> (forall result53:int. ((result53 = (acc intM_d_10_10 result52 : int)) -> (forall result54:(pointer 'a3). ((result54 = (shift mutable_indata 4 : (pointer 'a3))) -> ((valid alloc result54) -> (forall result55:int. ((result55 = (acc intM_indata_11 result54 : int)) -> ((valid alloc result51) -> (forall intM_outdata_12_5:(memory int 'a4). ((intM_outdata_12_5 = (upd intM_outdata_12_4 result51 (bw_xor result53 result55 : int) : (memory int 'a4))) -> (forall x_0_6:int. ((x_0_6 = (bw_and (Int.(+) x_0_5 1 : int) 255 : int)) -> (forall result56:(pointer 'a2). ((result56 = (shift d x_0_6 : (pointer 'a2))) -> (valid alloc result56)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_44: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result52) -> (forall result53:int. ((result53 = (acc intM_d_10_10 result52 : int)) -> (forall result54:(pointer 'a3). ((result54 = (shift mutable_indata 4 : (pointer 'a3))) -> ((valid alloc result54) -> (forall result55:int. ((result55 = (acc intM_indata_11 result54 : int)) -> ((valid alloc result51) -> (forall intM_outdata_12_5:(memory int 'a4). ((intM_outdata_12_5 = (upd intM_outdata_12_4 result51 (bw_xor result53 result55 : int) : (memory int 'a4))) -> (forall x_0_6:int. ((x_0_6 = (bw_and (Int.(+) x_0_5 1 : int) 255 : int)) -> (forall result56:(pointer 'a2). ((result56 = (shift d x_0_6 : (pointer 'a2))) -> ((valid alloc result56) -> (forall result57:int. ((result57 = (acc intM_d_10_10 result56 : int)) -> (forall tx4:int. ((tx4 = result57) -> (forall y_0_6:int. ((y_0_6 = (bw_and (Int.(+) tx4 y_0_5 : int) 255 : int)) -> (forall result58:(pointer 'a2). ((result58 = (shift d x_0_6 : (pointer 'a2))) -> (forall result59:(pointer 'a2). ((result59 = (shift d y_0_6 : (pointer 'a2))) -> (valid alloc result59))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_45: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result52) -> (forall result53:int. ((result53 = (acc intM_d_10_10 result52 : int)) -> (forall result54:(pointer 'a3). ((result54 = (shift mutable_indata 4 : (pointer 'a3))) -> ((valid alloc result54) -> (forall result55:int. ((result55 = (acc intM_indata_11 result54 : int)) -> ((valid alloc result51) -> (forall intM_outdata_12_5:(memory int 'a4). ((intM_outdata_12_5 = (upd intM_outdata_12_4 result51 (bw_xor result53 result55 : int) : (memory int 'a4))) -> (forall x_0_6:int. ((x_0_6 = (bw_and (Int.(+) x_0_5 1 : int) 255 : int)) -> (forall result56:(pointer 'a2). ((result56 = (shift d x_0_6 : (pointer 'a2))) -> ((valid alloc result56) -> (forall result57:int. ((result57 = (acc intM_d_10_10 result56 : int)) -> (forall tx4:int. ((tx4 = result57) -> (forall y_0_6:int. ((y_0_6 = (bw_and (Int.(+) tx4 y_0_5 : int) 255 : int)) -> (forall result58:(pointer 'a2). ((result58 = (shift d x_0_6 : (pointer 'a2))) -> (forall result59:(pointer 'a2). ((result59 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result59) -> (forall result60:int. ((result60 = (acc intM_d_10_10 result59 : int)) -> (forall ty4:int. ((ty4 = result60) -> (valid alloc result58)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_46: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result52) -> (forall result53:int. ((result53 = (acc intM_d_10_10 result52 : int)) -> (forall result54:(pointer 'a3). ((result54 = (shift mutable_indata 4 : (pointer 'a3))) -> ((valid alloc result54) -> (forall result55:int. ((result55 = (acc intM_indata_11 result54 : int)) -> ((valid alloc result51) -> (forall intM_outdata_12_5:(memory int 'a4). ((intM_outdata_12_5 = (upd intM_outdata_12_4 result51 (bw_xor result53 result55 : int) : (memory int 'a4))) -> (forall x_0_6:int. ((x_0_6 = (bw_and (Int.(+) x_0_5 1 : int) 255 : int)) -> (forall result56:(pointer 'a2). ((result56 = (shift d x_0_6 : (pointer 'a2))) -> ((valid alloc result56) -> (forall result57:int. ((result57 = (acc intM_d_10_10 result56 : int)) -> (forall tx4:int. ((tx4 = result57) -> (forall y_0_6:int. ((y_0_6 = (bw_and (Int.(+) tx4 y_0_5 : int) 255 : int)) -> (forall result58:(pointer 'a2). ((result58 = (shift d x_0_6 : (pointer 'a2))) -> (forall result59:(pointer 'a2). ((result59 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result59) -> (forall result60:int. ((result60 = (acc intM_d_10_10 result59 : int)) -> (forall ty4:int. ((ty4 = result60) -> ((valid alloc result58) -> (forall intM_d_10_11:(memory int 'a2). ((intM_d_10_11 = (upd intM_d_10_10 result58 ty4 : (memory int 'a2))) -> (forall result61:(pointer 'a2). ((result61 = (shift d y_0_6 : (pointer 'a2))) -> (valid alloc result61))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_47: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result52) -> (forall result53:int. ((result53 = (acc intM_d_10_10 result52 : int)) -> (forall result54:(pointer 'a3). ((result54 = (shift mutable_indata 4 : (pointer 'a3))) -> ((valid alloc result54) -> (forall result55:int. ((result55 = (acc intM_indata_11 result54 : int)) -> ((valid alloc result51) -> (forall intM_outdata_12_5:(memory int 'a4). ((intM_outdata_12_5 = (upd intM_outdata_12_4 result51 (bw_xor result53 result55 : int) : (memory int 'a4))) -> (forall x_0_6:int. ((x_0_6 = (bw_and (Int.(+) x_0_5 1 : int) 255 : int)) -> (forall result56:(pointer 'a2). ((result56 = (shift d x_0_6 : (pointer 'a2))) -> ((valid alloc result56) -> (forall result57:int. ((result57 = (acc intM_d_10_10 result56 : int)) -> (forall tx4:int. ((tx4 = result57) -> (forall y_0_6:int. ((y_0_6 = (bw_and (Int.(+) tx4 y_0_5 : int) 255 : int)) -> (forall result58:(pointer 'a2). ((result58 = (shift d x_0_6 : (pointer 'a2))) -> (forall result59:(pointer 'a2). ((result59 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result59) -> (forall result60:int. ((result60 = (acc intM_d_10_10 result59 : int)) -> (forall ty4:int. ((ty4 = result60) -> ((valid alloc result58) -> (forall intM_d_10_11:(memory int 'a2). ((intM_d_10_11 = (upd intM_d_10_10 result58 ty4 : (memory int 'a2))) -> (forall result61:(pointer 'a2). ((result61 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result61) -> (forall intM_d_10_12:(memory int 'a2). ((intM_d_10_12 = (upd intM_d_10_11 result61 tx4 : (memory int 'a2))) -> (forall result62:(pointer 'a4). ((result62 = (shift mutable_outdata 5 : (pointer 'a4))) -> (forall result63:(pointer 'a2). ((result63 = (shift d (bw_and (Int.(+) tx4 ty4 : int) 255 : int) : (pointer 'a2))) -> (valid alloc result63)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_48: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result52) -> (forall result53:int. ((result53 = (acc intM_d_10_10 result52 : int)) -> (forall result54:(pointer 'a3). ((result54 = (shift mutable_indata 4 : (pointer 'a3))) -> ((valid alloc result54) -> (forall result55:int. ((result55 = (acc intM_indata_11 result54 : int)) -> ((valid alloc result51) -> (forall intM_outdata_12_5:(memory int 'a4). ((intM_outdata_12_5 = (upd intM_outdata_12_4 result51 (bw_xor result53 result55 : int) : (memory int 'a4))) -> (forall x_0_6:int. ((x_0_6 = (bw_and (Int.(+) x_0_5 1 : int) 255 : int)) -> (forall result56:(pointer 'a2). ((result56 = (shift d x_0_6 : (pointer 'a2))) -> ((valid alloc result56) -> (forall result57:int. ((result57 = (acc intM_d_10_10 result56 : int)) -> (forall tx4:int. ((tx4 = result57) -> (forall y_0_6:int. ((y_0_6 = (bw_and (Int.(+) tx4 y_0_5 : int) 255 : int)) -> (forall result58:(pointer 'a2). ((result58 = (shift d x_0_6 : (pointer 'a2))) -> (forall result59:(pointer 'a2). ((result59 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result59) -> (forall result60:int. ((result60 = (acc intM_d_10_10 result59 : int)) -> (forall ty4:int. ((ty4 = result60) -> ((valid alloc result58) -> (forall intM_d_10_11:(memory int 'a2). ((intM_d_10_11 = (upd intM_d_10_10 result58 ty4 : (memory int 'a2))) -> (forall result61:(pointer 'a2). ((result61 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result61) -> (forall intM_d_10_12:(memory int 'a2). ((intM_d_10_12 = (upd intM_d_10_11 result61 tx4 : (memory int 'a2))) -> (forall result62:(pointer 'a4). ((result62 = (shift mutable_outdata 5 : (pointer 'a4))) -> (forall result63:(pointer 'a2). ((result63 = (shift d (bw_and (Int.(+) tx4 ty4 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result63) -> (forall result64:int. ((result64 = (acc intM_d_10_12 result63 : int)) -> (forall result65:(pointer 'a3). ((result65 = (shift mutable_indata 5 : (pointer 'a3))) -> (valid alloc result65))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_49: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result52) -> (forall result53:int. ((result53 = (acc intM_d_10_10 result52 : int)) -> (forall result54:(pointer 'a3). ((result54 = (shift mutable_indata 4 : (pointer 'a3))) -> ((valid alloc result54) -> (forall result55:int. ((result55 = (acc intM_indata_11 result54 : int)) -> ((valid alloc result51) -> (forall intM_outdata_12_5:(memory int 'a4). ((intM_outdata_12_5 = (upd intM_outdata_12_4 result51 (bw_xor result53 result55 : int) : (memory int 'a4))) -> (forall x_0_6:int. ((x_0_6 = (bw_and (Int.(+) x_0_5 1 : int) 255 : int)) -> (forall result56:(pointer 'a2). ((result56 = (shift d x_0_6 : (pointer 'a2))) -> ((valid alloc result56) -> (forall result57:int. ((result57 = (acc intM_d_10_10 result56 : int)) -> (forall tx4:int. ((tx4 = result57) -> (forall y_0_6:int. ((y_0_6 = (bw_and (Int.(+) tx4 y_0_5 : int) 255 : int)) -> (forall result58:(pointer 'a2). ((result58 = (shift d x_0_6 : (pointer 'a2))) -> (forall result59:(pointer 'a2). ((result59 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result59) -> (forall result60:int. ((result60 = (acc intM_d_10_10 result59 : int)) -> (forall ty4:int. ((ty4 = result60) -> ((valid alloc result58) -> (forall intM_d_10_11:(memory int 'a2). ((intM_d_10_11 = (upd intM_d_10_10 result58 ty4 : (memory int 'a2))) -> (forall result61:(pointer 'a2). ((result61 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result61) -> (forall intM_d_10_12:(memory int 'a2). ((intM_d_10_12 = (upd intM_d_10_11 result61 tx4 : (memory int 'a2))) -> (forall result62:(pointer 'a4). ((result62 = (shift mutable_outdata 5 : (pointer 'a4))) -> (forall result63:(pointer 'a2). ((result63 = (shift d (bw_and (Int.(+) tx4 ty4 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result63) -> (forall result64:int. ((result64 = (acc intM_d_10_12 result63 : int)) -> (forall result65:(pointer 'a3). ((result65 = (shift mutable_indata 5 : (pointer 'a3))) -> ((valid alloc result65) -> (forall result66:int. ((result66 = (acc intM_indata_11 result65 : int)) -> (valid alloc result62)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_50: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result52) -> (forall result53:int. ((result53 = (acc intM_d_10_10 result52 : int)) -> (forall result54:(pointer 'a3). ((result54 = (shift mutable_indata 4 : (pointer 'a3))) -> ((valid alloc result54) -> (forall result55:int. ((result55 = (acc intM_indata_11 result54 : int)) -> ((valid alloc result51) -> (forall intM_outdata_12_5:(memory int 'a4). ((intM_outdata_12_5 = (upd intM_outdata_12_4 result51 (bw_xor result53 result55 : int) : (memory int 'a4))) -> (forall x_0_6:int. ((x_0_6 = (bw_and (Int.(+) x_0_5 1 : int) 255 : int)) -> (forall result56:(pointer 'a2). ((result56 = (shift d x_0_6 : (pointer 'a2))) -> ((valid alloc result56) -> (forall result57:int. ((result57 = (acc intM_d_10_10 result56 : int)) -> (forall tx4:int. ((tx4 = result57) -> (forall y_0_6:int. ((y_0_6 = (bw_and (Int.(+) tx4 y_0_5 : int) 255 : int)) -> (forall result58:(pointer 'a2). ((result58 = (shift d x_0_6 : (pointer 'a2))) -> (forall result59:(pointer 'a2). ((result59 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result59) -> (forall result60:int. ((result60 = (acc intM_d_10_10 result59 : int)) -> (forall ty4:int. ((ty4 = result60) -> ((valid alloc result58) -> (forall intM_d_10_11:(memory int 'a2). ((intM_d_10_11 = (upd intM_d_10_10 result58 ty4 : (memory int 'a2))) -> (forall result61:(pointer 'a2). ((result61 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result61) -> (forall intM_d_10_12:(memory int 'a2). ((intM_d_10_12 = (upd intM_d_10_11 result61 tx4 : (memory int 'a2))) -> (forall result62:(pointer 'a4). ((result62 = (shift mutable_outdata 5 : (pointer 'a4))) -> (forall result63:(pointer 'a2). ((result63 = (shift d (bw_and (Int.(+) tx4 ty4 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result63) -> (forall result64:int. ((result64 = (acc intM_d_10_12 result63 : int)) -> (forall result65:(pointer 'a3). ((result65 = (shift mutable_indata 5 : (pointer 'a3))) -> ((valid alloc result65) -> (forall result66:int. ((result66 = (acc intM_indata_11 result65 : int)) -> ((valid alloc result62) -> (forall intM_outdata_12_6:(memory int 'a4). ((intM_outdata_12_6 = (upd intM_outdata_12_5 result62 (bw_xor result64 result66 : int) : (memory int 'a4))) -> (forall x_0_7:int. ((x_0_7 = (bw_and (Int.(+) x_0_6 1 : int) 255 : int)) -> (forall result67:(pointer 'a2). ((result67 = (shift d x_0_7 : (pointer 'a2))) -> (valid alloc result67))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_51: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result52) -> (forall result53:int. ((result53 = (acc intM_d_10_10 result52 : int)) -> (forall result54:(pointer 'a3). ((result54 = (shift mutable_indata 4 : (pointer 'a3))) -> ((valid alloc result54) -> (forall result55:int. ((result55 = (acc intM_indata_11 result54 : int)) -> ((valid alloc result51) -> (forall intM_outdata_12_5:(memory int 'a4). ((intM_outdata_12_5 = (upd intM_outdata_12_4 result51 (bw_xor result53 result55 : int) : (memory int 'a4))) -> (forall x_0_6:int. ((x_0_6 = (bw_and (Int.(+) x_0_5 1 : int) 255 : int)) -> (forall result56:(pointer 'a2). ((result56 = (shift d x_0_6 : (pointer 'a2))) -> ((valid alloc result56) -> (forall result57:int. ((result57 = (acc intM_d_10_10 result56 : int)) -> (forall tx4:int. ((tx4 = result57) -> (forall y_0_6:int. ((y_0_6 = (bw_and (Int.(+) tx4 y_0_5 : int) 255 : int)) -> (forall result58:(pointer 'a2). ((result58 = (shift d x_0_6 : (pointer 'a2))) -> (forall result59:(pointer 'a2). ((result59 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result59) -> (forall result60:int. ((result60 = (acc intM_d_10_10 result59 : int)) -> (forall ty4:int. ((ty4 = result60) -> ((valid alloc result58) -> (forall intM_d_10_11:(memory int 'a2). ((intM_d_10_11 = (upd intM_d_10_10 result58 ty4 : (memory int 'a2))) -> (forall result61:(pointer 'a2). ((result61 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result61) -> (forall intM_d_10_12:(memory int 'a2). ((intM_d_10_12 = (upd intM_d_10_11 result61 tx4 : (memory int 'a2))) -> (forall result62:(pointer 'a4). ((result62 = (shift mutable_outdata 5 : (pointer 'a4))) -> (forall result63:(pointer 'a2). ((result63 = (shift d (bw_and (Int.(+) tx4 ty4 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result63) -> (forall result64:int. ((result64 = (acc intM_d_10_12 result63 : int)) -> (forall result65:(pointer 'a3). ((result65 = (shift mutable_indata 5 : (pointer 'a3))) -> ((valid alloc result65) -> (forall result66:int. ((result66 = (acc intM_indata_11 result65 : int)) -> ((valid alloc result62) -> (forall intM_outdata_12_6:(memory int 'a4). ((intM_outdata_12_6 = (upd intM_outdata_12_5 result62 (bw_xor result64 result66 : int) : (memory int 'a4))) -> (forall x_0_7:int. ((x_0_7 = (bw_and (Int.(+) x_0_6 1 : int) 255 : int)) -> (forall result67:(pointer 'a2). ((result67 = (shift d x_0_7 : (pointer 'a2))) -> ((valid alloc result67) -> (forall result68:int. ((result68 = (acc intM_d_10_12 result67 : int)) -> (forall tx5:int. ((tx5 = result68) -> (forall y_0_7:int. ((y_0_7 = (bw_and (Int.(+) tx5 y_0_6 : int) 255 : int)) -> (forall result69:(pointer 'a2). ((result69 = (shift d x_0_7 : (pointer 'a2))) -> (forall result70:(pointer 'a2). ((result70 = (shift d y_0_7 : (pointer 'a2))) -> (valid alloc result70)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_52: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result52) -> (forall result53:int. ((result53 = (acc intM_d_10_10 result52 : int)) -> (forall result54:(pointer 'a3). ((result54 = (shift mutable_indata 4 : (pointer 'a3))) -> ((valid alloc result54) -> (forall result55:int. ((result55 = (acc intM_indata_11 result54 : int)) -> ((valid alloc result51) -> (forall intM_outdata_12_5:(memory int 'a4). ((intM_outdata_12_5 = (upd intM_outdata_12_4 result51 (bw_xor result53 result55 : int) : (memory int 'a4))) -> (forall x_0_6:int. ((x_0_6 = (bw_and (Int.(+) x_0_5 1 : int) 255 : int)) -> (forall result56:(pointer 'a2). ((result56 = (shift d x_0_6 : (pointer 'a2))) -> ((valid alloc result56) -> (forall result57:int. ((result57 = (acc intM_d_10_10 result56 : int)) -> (forall tx4:int. ((tx4 = result57) -> (forall y_0_6:int. ((y_0_6 = (bw_and (Int.(+) tx4 y_0_5 : int) 255 : int)) -> (forall result58:(pointer 'a2). ((result58 = (shift d x_0_6 : (pointer 'a2))) -> (forall result59:(pointer 'a2). ((result59 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result59) -> (forall result60:int. ((result60 = (acc intM_d_10_10 result59 : int)) -> (forall ty4:int. ((ty4 = result60) -> ((valid alloc result58) -> (forall intM_d_10_11:(memory int 'a2). ((intM_d_10_11 = (upd intM_d_10_10 result58 ty4 : (memory int 'a2))) -> (forall result61:(pointer 'a2). ((result61 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result61) -> (forall intM_d_10_12:(memory int 'a2). ((intM_d_10_12 = (upd intM_d_10_11 result61 tx4 : (memory int 'a2))) -> (forall result62:(pointer 'a4). ((result62 = (shift mutable_outdata 5 : (pointer 'a4))) -> (forall result63:(pointer 'a2). ((result63 = (shift d (bw_and (Int.(+) tx4 ty4 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result63) -> (forall result64:int. ((result64 = (acc intM_d_10_12 result63 : int)) -> (forall result65:(pointer 'a3). ((result65 = (shift mutable_indata 5 : (pointer 'a3))) -> ((valid alloc result65) -> (forall result66:int. ((result66 = (acc intM_indata_11 result65 : int)) -> ((valid alloc result62) -> (forall intM_outdata_12_6:(memory int 'a4). ((intM_outdata_12_6 = (upd intM_outdata_12_5 result62 (bw_xor result64 result66 : int) : (memory int 'a4))) -> (forall x_0_7:int. ((x_0_7 = (bw_and (Int.(+) x_0_6 1 : int) 255 : int)) -> (forall result67:(pointer 'a2). ((result67 = (shift d x_0_7 : (pointer 'a2))) -> ((valid alloc result67) -> (forall result68:int. ((result68 = (acc intM_d_10_12 result67 : int)) -> (forall tx5:int. ((tx5 = result68) -> (forall y_0_7:int. ((y_0_7 = (bw_and (Int.(+) tx5 y_0_6 : int) 255 : int)) -> (forall result69:(pointer 'a2). ((result69 = (shift d x_0_7 : (pointer 'a2))) -> (forall result70:(pointer 'a2). ((result70 = (shift d y_0_7 : (pointer 'a2))) -> ((valid alloc result70) -> (forall result71:int. ((result71 = (acc intM_d_10_12 result70 : int)) -> (forall ty5:int. ((ty5 = result71) -> (valid alloc result69))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_53: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result52) -> (forall result53:int. ((result53 = (acc intM_d_10_10 result52 : int)) -> (forall result54:(pointer 'a3). ((result54 = (shift mutable_indata 4 : (pointer 'a3))) -> ((valid alloc result54) -> (forall result55:int. ((result55 = (acc intM_indata_11 result54 : int)) -> ((valid alloc result51) -> (forall intM_outdata_12_5:(memory int 'a4). ((intM_outdata_12_5 = (upd intM_outdata_12_4 result51 (bw_xor result53 result55 : int) : (memory int 'a4))) -> (forall x_0_6:int. ((x_0_6 = (bw_and (Int.(+) x_0_5 1 : int) 255 : int)) -> (forall result56:(pointer 'a2). ((result56 = (shift d x_0_6 : (pointer 'a2))) -> ((valid alloc result56) -> (forall result57:int. ((result57 = (acc intM_d_10_10 result56 : int)) -> (forall tx4:int. ((tx4 = result57) -> (forall y_0_6:int. ((y_0_6 = (bw_and (Int.(+) tx4 y_0_5 : int) 255 : int)) -> (forall result58:(pointer 'a2). ((result58 = (shift d x_0_6 : (pointer 'a2))) -> (forall result59:(pointer 'a2). ((result59 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result59) -> (forall result60:int. ((result60 = (acc intM_d_10_10 result59 : int)) -> (forall ty4:int. ((ty4 = result60) -> ((valid alloc result58) -> (forall intM_d_10_11:(memory int 'a2). ((intM_d_10_11 = (upd intM_d_10_10 result58 ty4 : (memory int 'a2))) -> (forall result61:(pointer 'a2). ((result61 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result61) -> (forall intM_d_10_12:(memory int 'a2). ((intM_d_10_12 = (upd intM_d_10_11 result61 tx4 : (memory int 'a2))) -> (forall result62:(pointer 'a4). ((result62 = (shift mutable_outdata 5 : (pointer 'a4))) -> (forall result63:(pointer 'a2). ((result63 = (shift d (bw_and (Int.(+) tx4 ty4 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result63) -> (forall result64:int. ((result64 = (acc intM_d_10_12 result63 : int)) -> (forall result65:(pointer 'a3). ((result65 = (shift mutable_indata 5 : (pointer 'a3))) -> ((valid alloc result65) -> (forall result66:int. ((result66 = (acc intM_indata_11 result65 : int)) -> ((valid alloc result62) -> (forall intM_outdata_12_6:(memory int 'a4). ((intM_outdata_12_6 = (upd intM_outdata_12_5 result62 (bw_xor result64 result66 : int) : (memory int 'a4))) -> (forall x_0_7:int. ((x_0_7 = (bw_and (Int.(+) x_0_6 1 : int) 255 : int)) -> (forall result67:(pointer 'a2). ((result67 = (shift d x_0_7 : (pointer 'a2))) -> ((valid alloc result67) -> (forall result68:int. ((result68 = (acc intM_d_10_12 result67 : int)) -> (forall tx5:int. ((tx5 = result68) -> (forall y_0_7:int. ((y_0_7 = (bw_and (Int.(+) tx5 y_0_6 : int) 255 : int)) -> (forall result69:(pointer 'a2). ((result69 = (shift d x_0_7 : (pointer 'a2))) -> (forall result70:(pointer 'a2). ((result70 = (shift d y_0_7 : (pointer 'a2))) -> ((valid alloc result70) -> (forall result71:int. ((result71 = (acc intM_d_10_12 result70 : int)) -> (forall ty5:int. ((ty5 = result71) -> ((valid alloc result69) -> (forall intM_d_10_13:(memory int 'a2). ((intM_d_10_13 = (upd intM_d_10_12 result69 ty5 : (memory int 'a2))) -> (forall result72:(pointer 'a2). ((result72 = (shift d y_0_7 : (pointer 'a2))) -> (valid alloc result72)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_54: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result52) -> (forall result53:int. ((result53 = (acc intM_d_10_10 result52 : int)) -> (forall result54:(pointer 'a3). ((result54 = (shift mutable_indata 4 : (pointer 'a3))) -> ((valid alloc result54) -> (forall result55:int. ((result55 = (acc intM_indata_11 result54 : int)) -> ((valid alloc result51) -> (forall intM_outdata_12_5:(memory int 'a4). ((intM_outdata_12_5 = (upd intM_outdata_12_4 result51 (bw_xor result53 result55 : int) : (memory int 'a4))) -> (forall x_0_6:int. ((x_0_6 = (bw_and (Int.(+) x_0_5 1 : int) 255 : int)) -> (forall result56:(pointer 'a2). ((result56 = (shift d x_0_6 : (pointer 'a2))) -> ((valid alloc result56) -> (forall result57:int. ((result57 = (acc intM_d_10_10 result56 : int)) -> (forall tx4:int. ((tx4 = result57) -> (forall y_0_6:int. ((y_0_6 = (bw_and (Int.(+) tx4 y_0_5 : int) 255 : int)) -> (forall result58:(pointer 'a2). ((result58 = (shift d x_0_6 : (pointer 'a2))) -> (forall result59:(pointer 'a2). ((result59 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result59) -> (forall result60:int. ((result60 = (acc intM_d_10_10 result59 : int)) -> (forall ty4:int. ((ty4 = result60) -> ((valid alloc result58) -> (forall intM_d_10_11:(memory int 'a2). ((intM_d_10_11 = (upd intM_d_10_10 result58 ty4 : (memory int 'a2))) -> (forall result61:(pointer 'a2). ((result61 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result61) -> (forall intM_d_10_12:(memory int 'a2). ((intM_d_10_12 = (upd intM_d_10_11 result61 tx4 : (memory int 'a2))) -> (forall result62:(pointer 'a4). ((result62 = (shift mutable_outdata 5 : (pointer 'a4))) -> (forall result63:(pointer 'a2). ((result63 = (shift d (bw_and (Int.(+) tx4 ty4 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result63) -> (forall result64:int. ((result64 = (acc intM_d_10_12 result63 : int)) -> (forall result65:(pointer 'a3). ((result65 = (shift mutable_indata 5 : (pointer 'a3))) -> ((valid alloc result65) -> (forall result66:int. ((result66 = (acc intM_indata_11 result65 : int)) -> ((valid alloc result62) -> (forall intM_outdata_12_6:(memory int 'a4). ((intM_outdata_12_6 = (upd intM_outdata_12_5 result62 (bw_xor result64 result66 : int) : (memory int 'a4))) -> (forall x_0_7:int. ((x_0_7 = (bw_and (Int.(+) x_0_6 1 : int) 255 : int)) -> (forall result67:(pointer 'a2). ((result67 = (shift d x_0_7 : (pointer 'a2))) -> ((valid alloc result67) -> (forall result68:int. ((result68 = (acc intM_d_10_12 result67 : int)) -> (forall tx5:int. ((tx5 = result68) -> (forall y_0_7:int. ((y_0_7 = (bw_and (Int.(+) tx5 y_0_6 : int) 255 : int)) -> (forall result69:(pointer 'a2). ((result69 = (shift d x_0_7 : (pointer 'a2))) -> (forall result70:(pointer 'a2). ((result70 = (shift d y_0_7 : (pointer 'a2))) -> ((valid alloc result70) -> (forall result71:int. ((result71 = (acc intM_d_10_12 result70 : int)) -> (forall ty5:int. ((ty5 = result71) -> ((valid alloc result69) -> (forall intM_d_10_13:(memory int 'a2). ((intM_d_10_13 = (upd intM_d_10_12 result69 ty5 : (memory int 'a2))) -> (forall result72:(pointer 'a2). ((result72 = (shift d y_0_7 : (pointer 'a2))) -> ((valid alloc result72) -> (forall intM_d_10_14:(memory int 'a2). ((intM_d_10_14 = (upd intM_d_10_13 result72 tx5 : (memory int 'a2))) -> (forall result73:(pointer 'a4). ((result73 = (shift mutable_outdata 6 : (pointer 'a4))) -> (forall result74:(pointer 'a2). ((result74 = (shift d (bw_and (Int.(+) tx5 ty5 : int) 255 : int) : (pointer 'a2))) -> (valid alloc result74))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_55: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result52) -> (forall result53:int. ((result53 = (acc intM_d_10_10 result52 : int)) -> (forall result54:(pointer 'a3). ((result54 = (shift mutable_indata 4 : (pointer 'a3))) -> ((valid alloc result54) -> (forall result55:int. ((result55 = (acc intM_indata_11 result54 : int)) -> ((valid alloc result51) -> (forall intM_outdata_12_5:(memory int 'a4). ((intM_outdata_12_5 = (upd intM_outdata_12_4 result51 (bw_xor result53 result55 : int) : (memory int 'a4))) -> (forall x_0_6:int. ((x_0_6 = (bw_and (Int.(+) x_0_5 1 : int) 255 : int)) -> (forall result56:(pointer 'a2). ((result56 = (shift d x_0_6 : (pointer 'a2))) -> ((valid alloc result56) -> (forall result57:int. ((result57 = (acc intM_d_10_10 result56 : int)) -> (forall tx4:int. ((tx4 = result57) -> (forall y_0_6:int. ((y_0_6 = (bw_and (Int.(+) tx4 y_0_5 : int) 255 : int)) -> (forall result58:(pointer 'a2). ((result58 = (shift d x_0_6 : (pointer 'a2))) -> (forall result59:(pointer 'a2). ((result59 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result59) -> (forall result60:int. ((result60 = (acc intM_d_10_10 result59 : int)) -> (forall ty4:int. ((ty4 = result60) -> ((valid alloc result58) -> (forall intM_d_10_11:(memory int 'a2). ((intM_d_10_11 = (upd intM_d_10_10 result58 ty4 : (memory int 'a2))) -> (forall result61:(pointer 'a2). ((result61 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result61) -> (forall intM_d_10_12:(memory int 'a2). ((intM_d_10_12 = (upd intM_d_10_11 result61 tx4 : (memory int 'a2))) -> (forall result62:(pointer 'a4). ((result62 = (shift mutable_outdata 5 : (pointer 'a4))) -> (forall result63:(pointer 'a2). ((result63 = (shift d (bw_and (Int.(+) tx4 ty4 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result63) -> (forall result64:int. ((result64 = (acc intM_d_10_12 result63 : int)) -> (forall result65:(pointer 'a3). ((result65 = (shift mutable_indata 5 : (pointer 'a3))) -> ((valid alloc result65) -> (forall result66:int. ((result66 = (acc intM_indata_11 result65 : int)) -> ((valid alloc result62) -> (forall intM_outdata_12_6:(memory int 'a4). ((intM_outdata_12_6 = (upd intM_outdata_12_5 result62 (bw_xor result64 result66 : int) : (memory int 'a4))) -> (forall x_0_7:int. ((x_0_7 = (bw_and (Int.(+) x_0_6 1 : int) 255 : int)) -> (forall result67:(pointer 'a2). ((result67 = (shift d x_0_7 : (pointer 'a2))) -> ((valid alloc result67) -> (forall result68:int. ((result68 = (acc intM_d_10_12 result67 : int)) -> (forall tx5:int. ((tx5 = result68) -> (forall y_0_7:int. ((y_0_7 = (bw_and (Int.(+) tx5 y_0_6 : int) 255 : int)) -> (forall result69:(pointer 'a2). ((result69 = (shift d x_0_7 : (pointer 'a2))) -> (forall result70:(pointer 'a2). ((result70 = (shift d y_0_7 : (pointer 'a2))) -> ((valid alloc result70) -> (forall result71:int. ((result71 = (acc intM_d_10_12 result70 : int)) -> (forall ty5:int. ((ty5 = result71) -> ((valid alloc result69) -> (forall intM_d_10_13:(memory int 'a2). ((intM_d_10_13 = (upd intM_d_10_12 result69 ty5 : (memory int 'a2))) -> (forall result72:(pointer 'a2). ((result72 = (shift d y_0_7 : (pointer 'a2))) -> ((valid alloc result72) -> (forall intM_d_10_14:(memory int 'a2). ((intM_d_10_14 = (upd intM_d_10_13 result72 tx5 : (memory int 'a2))) -> (forall result73:(pointer 'a4). ((result73 = (shift mutable_outdata 6 : (pointer 'a4))) -> (forall result74:(pointer 'a2). ((result74 = (shift d (bw_and (Int.(+) tx5 ty5 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result74) -> (forall result75:int. ((result75 = (acc intM_d_10_14 result74 : int)) -> (forall result76:(pointer 'a3). ((result76 = (shift mutable_indata 6 : (pointer 'a3))) -> (valid alloc result76)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_56: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result52) -> (forall result53:int. ((result53 = (acc intM_d_10_10 result52 : int)) -> (forall result54:(pointer 'a3). ((result54 = (shift mutable_indata 4 : (pointer 'a3))) -> ((valid alloc result54) -> (forall result55:int. ((result55 = (acc intM_indata_11 result54 : int)) -> ((valid alloc result51) -> (forall intM_outdata_12_5:(memory int 'a4). ((intM_outdata_12_5 = (upd intM_outdata_12_4 result51 (bw_xor result53 result55 : int) : (memory int 'a4))) -> (forall x_0_6:int. ((x_0_6 = (bw_and (Int.(+) x_0_5 1 : int) 255 : int)) -> (forall result56:(pointer 'a2). ((result56 = (shift d x_0_6 : (pointer 'a2))) -> ((valid alloc result56) -> (forall result57:int. ((result57 = (acc intM_d_10_10 result56 : int)) -> (forall tx4:int. ((tx4 = result57) -> (forall y_0_6:int. ((y_0_6 = (bw_and (Int.(+) tx4 y_0_5 : int) 255 : int)) -> (forall result58:(pointer 'a2). ((result58 = (shift d x_0_6 : (pointer 'a2))) -> (forall result59:(pointer 'a2). ((result59 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result59) -> (forall result60:int. ((result60 = (acc intM_d_10_10 result59 : int)) -> (forall ty4:int. ((ty4 = result60) -> ((valid alloc result58) -> (forall intM_d_10_11:(memory int 'a2). ((intM_d_10_11 = (upd intM_d_10_10 result58 ty4 : (memory int 'a2))) -> (forall result61:(pointer 'a2). ((result61 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result61) -> (forall intM_d_10_12:(memory int 'a2). ((intM_d_10_12 = (upd intM_d_10_11 result61 tx4 : (memory int 'a2))) -> (forall result62:(pointer 'a4). ((result62 = (shift mutable_outdata 5 : (pointer 'a4))) -> (forall result63:(pointer 'a2). ((result63 = (shift d (bw_and (Int.(+) tx4 ty4 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result63) -> (forall result64:int. ((result64 = (acc intM_d_10_12 result63 : int)) -> (forall result65:(pointer 'a3). ((result65 = (shift mutable_indata 5 : (pointer 'a3))) -> ((valid alloc result65) -> (forall result66:int. ((result66 = (acc intM_indata_11 result65 : int)) -> ((valid alloc result62) -> (forall intM_outdata_12_6:(memory int 'a4). ((intM_outdata_12_6 = (upd intM_outdata_12_5 result62 (bw_xor result64 result66 : int) : (memory int 'a4))) -> (forall x_0_7:int. ((x_0_7 = (bw_and (Int.(+) x_0_6 1 : int) 255 : int)) -> (forall result67:(pointer 'a2). ((result67 = (shift d x_0_7 : (pointer 'a2))) -> ((valid alloc result67) -> (forall result68:int. ((result68 = (acc intM_d_10_12 result67 : int)) -> (forall tx5:int. ((tx5 = result68) -> (forall y_0_7:int. ((y_0_7 = (bw_and (Int.(+) tx5 y_0_6 : int) 255 : int)) -> (forall result69:(pointer 'a2). ((result69 = (shift d x_0_7 : (pointer 'a2))) -> (forall result70:(pointer 'a2). ((result70 = (shift d y_0_7 : (pointer 'a2))) -> ((valid alloc result70) -> (forall result71:int. ((result71 = (acc intM_d_10_12 result70 : int)) -> (forall ty5:int. ((ty5 = result71) -> ((valid alloc result69) -> (forall intM_d_10_13:(memory int 'a2). ((intM_d_10_13 = (upd intM_d_10_12 result69 ty5 : (memory int 'a2))) -> (forall result72:(pointer 'a2). ((result72 = (shift d y_0_7 : (pointer 'a2))) -> ((valid alloc result72) -> (forall intM_d_10_14:(memory int 'a2). ((intM_d_10_14 = (upd intM_d_10_13 result72 tx5 : (memory int 'a2))) -> (forall result73:(pointer 'a4). ((result73 = (shift mutable_outdata 6 : (pointer 'a4))) -> (forall result74:(pointer 'a2). ((result74 = (shift d (bw_and (Int.(+) tx5 ty5 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result74) -> (forall result75:int. ((result75 = (acc intM_d_10_14 result74 : int)) -> (forall result76:(pointer 'a3). ((result76 = (shift mutable_indata 6 : (pointer 'a3))) -> ((valid alloc result76) -> (forall result77:int. ((result77 = (acc intM_indata_11 result76 : int)) -> (valid alloc result73))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_57: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result52) -> (forall result53:int. ((result53 = (acc intM_d_10_10 result52 : int)) -> (forall result54:(pointer 'a3). ((result54 = (shift mutable_indata 4 : (pointer 'a3))) -> ((valid alloc result54) -> (forall result55:int. ((result55 = (acc intM_indata_11 result54 : int)) -> ((valid alloc result51) -> (forall intM_outdata_12_5:(memory int 'a4). ((intM_outdata_12_5 = (upd intM_outdata_12_4 result51 (bw_xor result53 result55 : int) : (memory int 'a4))) -> (forall x_0_6:int. ((x_0_6 = (bw_and (Int.(+) x_0_5 1 : int) 255 : int)) -> (forall result56:(pointer 'a2). ((result56 = (shift d x_0_6 : (pointer 'a2))) -> ((valid alloc result56) -> (forall result57:int. ((result57 = (acc intM_d_10_10 result56 : int)) -> (forall tx4:int. ((tx4 = result57) -> (forall y_0_6:int. ((y_0_6 = (bw_and (Int.(+) tx4 y_0_5 : int) 255 : int)) -> (forall result58:(pointer 'a2). ((result58 = (shift d x_0_6 : (pointer 'a2))) -> (forall result59:(pointer 'a2). ((result59 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result59) -> (forall result60:int. ((result60 = (acc intM_d_10_10 result59 : int)) -> (forall ty4:int. ((ty4 = result60) -> ((valid alloc result58) -> (forall intM_d_10_11:(memory int 'a2). ((intM_d_10_11 = (upd intM_d_10_10 result58 ty4 : (memory int 'a2))) -> (forall result61:(pointer 'a2). ((result61 = (shift d y_0_6 : (pointer 'a2))) -> ((valid alloc result61) -> (forall intM_d_10_12:(memory int 'a2). ((intM_d_10_12 = (upd intM_d_10_11 result61 tx4 : (memory int 'a2))) -> (forall result62:(pointer 'a4). ((result62 = (shift mutable_outdata 5 : (pointer 'a4))) -> (forall result63:(pointer 'a2). ((result63 = (shift d (bw_and (Int.(+) tx4 ty4 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result63) -> (forall result64:int. ((result64 = (acc intM_d_10_12 result63 : int)) -> (forall result65:(pointer 'a3). ((result65 = (shift mutable_indata 5 : (pointer 'a3))) -> ((valid alloc result65) -> (forall result66:int. ((result66 = (acc intM_indata_11 result65 : int)) -> ((valid alloc result62) -> (forall intM_outdata_12_6:(memory int 'a4). ((intM_outdata_12_6 = (upd intM_outdata_12_5 result62 (bw_xor result64 result66 : int) : (memory int 'a4))) -> (forall x_0_7:int. ((x_0_7 = (bw_and (Int.(+) x_0_6 1 : int) 255 : int)) -> (forall result67:(pointer 'a2). ((result67 = (shift d x_0_7 : (pointer 'a2))) -> ((valid alloc result67) -> (forall result68:int. ((result68 = (acc intM_d_10_12 result67 : int)) -> (forall tx5:int. ((tx5 = result68) -> (forall y_0_7:int. ((y_0_7 = (bw_and (Int.(+) tx5 y_0_6 : int) 255 : int)) -> (forall result69:(pointer 'a2). ((result69 = (shift d x_0_7 : (pointer 'a2))) -> (forall result70:(pointer 'a2). ((result70 = (shift d y_0_7 : (pointer 'a2))) -> ((valid alloc result70) -> (forall result71:int. ((result71 = (acc intM_d_10_12 result70 : int)) -> (forall ty5:int. ((ty5 = result71) -> ((valid alloc result69) -> (forall intM_d_10_13:(memory int 'a2). ((intM_d_10_13 = (upd intM_d_10_12 result69 ty5 : (memory int 'a2))) -> (forall result72:(pointer 'a2). ((result72 = (shift d y_0_7 : (pointer 'a2))) -> ((valid alloc result72) -> (forall intM_d_10_14:(memory int 'a2). ((intM_d_10_14 = (upd intM_d_10_13 result72 tx5 : (memory int 'a2))) -> (forall result73:(pointer 'a4). ((result73 = (shift mutable_outdata 6 : (pointer 'a4))) -> (forall result74:(pointer 'a2). ((result74 = (shift d (bw_and (Int.(+) tx5 ty5 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result74) -> (forall result75:int. ((result75 = (acc intM_d_10_14 result74 : int)) -> (forall result76:(pointer 'a3). ((result76 = (shift mutable_indata 6 : (pointer 'a3))) -> ((valid alloc result76) -> (forall result77:int. ((result77 = (acc intM_indata_11 result76 : int)) -> ((valid alloc result73) -> (forall intM_outdata_12_7:(memory int 'a4). ((intM_outdata_12_7 = (upd intM_outdata_12_6 result73 (bw_xor result75 result77 : int) : (memory int 'a4))) -> (forall x_0_8:int. ((x_0_8 = (bw_and (Int.(+) x_0_7 1 : int) 255 : int)) -> (forall result78:(pointer 'a2). ((result78 = (shift d x_0_8 : (pointer 'a2))) -> (valid alloc result78)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) goal RC4_impl_po_58: (forall key:(pointer 'a1). (forall d:(pointer 'a2). (forall len:int. (forall indata:(pointer 'a3). (forall outdata:(pointer 'a4). (forall alloc:alloc_table. (forall intM_indata_11:(memory int 'a3). (forall x_key_9:(memory int 'a1). (forall y_key_9:(memory int 'a1). (("CADUCEUS_7" (((((Int.(>=) len 0) /\ (valid alloc key)) /\ (valid_range alloc d 0 255)) /\ (valid_range alloc indata 0 (Int.(-) len 1 : int))) /\ (valid_range alloc outdata 0 (Int.(-) len 1 : int)))) -> ((valid alloc key) -> (forall result:int. ((result = (acc x_key_9 key : int)) -> (forall x_0:int. ((x_0 = result) -> ((valid alloc key) -> (forall result0:int. ((result0 = (acc y_key_9 key : int)) -> (forall y_0:int. ((y_0 = result0) -> (forall i:int. ((i = (lsr len 3 : int)) -> ((i <> 0) -> (forall i0:int. (forall intM_d_10_0:(memory int 'a2). (forall intM_outdata_12_0:(memory int 'a4). (forall mutable_indata:(pointer 'a3). (forall mutable_outdata:(pointer 'a4). (forall x_0_0:int. (forall y_0_0:int. (("CADUCEUS_61" ((((((Int.(>) i0 0) /\ (Int.(<=) i0 len)) /\ (valid_range alloc mutable_indata 0 7)) /\ (valid_range alloc mutable_outdata 0 7)) /\ (mutable_indata = (shift indata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a3)))) /\ (mutable_outdata = (shift outdata (Int.(*) (Int.(-) (lsr len 3 : int) i0 : int) 8 : int) : (pointer 'a4))))) -> ((1 <> 0) -> (forall x_0_1:int. ((x_0_1 = (bw_and (Int.(+) x_0_0 1 : int) 255 : int)) -> (forall result1:(pointer 'a2). ((result1 = (shift d x_0_1 : (pointer 'a2))) -> ((valid alloc result1) -> (forall result2:int. ((result2 = (acc intM_d_10_0 result1 : int)) -> (forall tx:int. ((tx = result2) -> (forall y_0_1:int. ((y_0_1 = (bw_and (Int.(+) tx y_0_0 : int) 255 : int)) -> (forall result3:(pointer 'a2). ((result3 = (shift d x_0_1 : (pointer 'a2))) -> (forall result4:(pointer 'a2). ((result4 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result4) -> (forall result5:int. ((result5 = (acc intM_d_10_0 result4 : int)) -> (forall ty:int. ((ty = result5) -> ((valid alloc result3) -> (forall intM_d_10_1:(memory int 'a2). ((intM_d_10_1 = (upd intM_d_10_0 result3 ty : (memory int 'a2))) -> (forall result6:(pointer 'a2). ((result6 = (shift d y_0_1 : (pointer 'a2))) -> ((valid alloc result6) -> (forall intM_d_10_2:(memory int 'a2). ((intM_d_10_2 = (upd intM_d_10_1 result6 tx : (memory int 'a2))) -> (forall result7:(pointer 'a4). ((result7 = (shift mutable_outdata 0 : (pointer 'a4))) -> (forall result8:(pointer 'a2). ((result8 = (shift d (bw_and (Int.(+) tx ty : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result8) -> (forall result9:int. ((result9 = (acc intM_d_10_2 result8 : int)) -> (forall result10:(pointer 'a3). ((result10 = (shift mutable_indata 0 : (pointer 'a3))) -> ((valid alloc result10) -> (forall result11:int. ((result11 = (acc intM_indata_11 result10 : int)) -> ((valid alloc result7) -> (forall intM_outdata_12_1:(memory int 'a4). ((intM_outdata_12_1 = (upd intM_outdata_12_0 result7 (bw_xor result9 result11 : int) : (memory int 'a4))) -> (forall x_0_2:int. ((x_0_2 = (bw_and (Int.(+) x_0_1 1 : int) 255 : int)) -> (forall result12:(pointer 'a2). ((result12 = (shift d x_0_2 : (pointer 'a2))) -> ((valid alloc result12) -> (forall result13:int. ((result13 = (acc intM_d_10_2 result12 : int)) -> (forall tx0:int. ((tx0 = result13) -> (forall y_0_2:int. ((y_0_2 = (bw_and (Int.(+) tx0 y_0_1 : int) 255 : int)) -> (forall result14:(pointer 'a2). ((result14 = (shift d x_0_2 : (pointer 'a2))) -> (forall result15:(pointer 'a2). ((result15 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result15) -> (forall result16:int. ((result16 = (acc intM_d_10_2 result15 : int)) -> (forall ty0:int. ((ty0 = result16) -> ((valid alloc result14) -> (forall intM_d_10_3:(memory int 'a2). ((intM_d_10_3 = (upd intM_d_10_2 result14 ty0 : (memory int 'a2))) -> (forall result17:(pointer 'a2). ((result17 = (shift d y_0_2 : (pointer 'a2))) -> ((valid alloc result17) -> (forall intM_d_10_4:(memory int 'a2). ((intM_d_10_4 = (upd intM_d_10_3 result17 tx0 : (memory int 'a2))) -> (forall result18:(pointer 'a4). ((result18 = (shift mutable_outdata 1 : (pointer 'a4))) -> (forall result19:(pointer 'a2). ((result19 = (shift d (bw_and (Int.(+) tx0 ty0 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result19) -> (forall result20:int. ((result20 = (acc intM_d_10_4 result19 : int)) -> (forall result21:(pointer 'a3). ((result21 = (shift mutable_indata 1 : (pointer 'a3))) -> ((valid alloc result21) -> (forall result22:int. ((result22 = (acc intM_indata_11 result21 : int)) -> ((valid alloc result18) -> (forall intM_outdata_12_2:(memory int 'a4). ((intM_outdata_12_2 = (upd intM_outdata_12_1 result18 (bw_xor result20 result22 : int) : (memory int 'a4))) -> (forall x_0_3:int. ((x_0_3 = (bw_and (Int.(+) x_0_2 1 : int) 255 : int)) -> (forall result23:(pointer 'a2). ((result23 = (shift d x_0_3 : (pointer 'a2))) -> ((valid alloc result23) -> (forall result24:int. ((result24 = (acc intM_d_10_4 result23 : int)) -> (forall tx1:int. ((tx1 = result24) -> (forall y_0_3:int. ((y_0_3 = (bw_and (Int.(+) tx1 y_0_2 : int) 255 : int)) -> (forall result25:(pointer 'a2). ((result25 = (shift d x_0_3 : (pointer 'a2))) -> (forall result26:(pointer 'a2). ((result26 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result26) -> (forall result27:int. ((result27 = (acc intM_d_10_4 result26 : int)) -> (forall ty1:int. ((ty1 = result27) -> ((valid alloc result25) -> (forall intM_d_10_5:(memory int 'a2). ((intM_d_10_5 = (upd intM_d_10_4 result25 ty1 : (memory int 'a2))) -> (forall result28:(pointer 'a2). ((result28 = (shift d y_0_3 : (pointer 'a2))) -> ((valid alloc result28) -> (forall intM_d_10_6:(memory int 'a2). ((intM_d_10_6 = (upd intM_d_10_5 result28 tx1 : (memory int 'a2))) -> (forall result29:(pointer 'a4). ((result29 = (shift mutable_outdata 2 : (pointer 'a4))) -> (forall result30:(pointer 'a2). ((result30 = (shift d (bw_and (Int.(+) tx1 ty1 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result30) -> (forall result31:int. ((result31 = (acc intM_d_10_6 result30 : int)) -> (forall result32:(pointer 'a3). ((result32 = (shift mutable_indata 2 : (pointer 'a3))) -> ((valid alloc result32) -> (forall result33:int. ((result33 = (acc intM_indata_11 result32 : int)) -> ((valid alloc result29) -> (forall intM_outdata_12_3:(memory int 'a4). ((intM_outdata_12_3 = (upd intM_outdata_12_2 result29 (bw_xor result31 result33 : int) : (memory int 'a4))) -> (forall x_0_4:int. ((x_0_4 = (bw_and (Int.(+) x_0_3 1 : int) 255 : int)) -> (forall result34:(pointer 'a2). ((result34 = (shift d x_0_4 : (pointer 'a2))) -> ((valid alloc result34) -> (forall result35:int. ((result35 = (acc intM_d_10_6 result34 : int)) -> (forall tx2:int. ((tx2 = result35) -> (forall y_0_4:int. ((y_0_4 = (bw_and (Int.(+) tx2 y_0_3 : int) 255 : int)) -> (forall result36:(pointer 'a2). ((result36 = (shift d x_0_4 : (pointer 'a2))) -> (forall result37:(pointer 'a2). ((result37 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result37) -> (forall result38:int. ((result38 = (acc intM_d_10_6 result37 : int)) -> (forall ty2:int. ((ty2 = result38) -> ((valid alloc result36) -> (forall intM_d_10_7:(memory int 'a2). ((intM_d_10_7 = (upd intM_d_10_6 result36 ty2 : (memory int 'a2))) -> (forall result39:(pointer 'a2). ((result39 = (shift d y_0_4 : (pointer 'a2))) -> ((valid alloc result39) -> (forall intM_d_10_8:(memory int 'a2). ((intM_d_10_8 = (upd intM_d_10_7 result39 tx2 : (memory int 'a2))) -> (forall result40:(pointer 'a4). ((result40 = (shift mutable_outdata 3 : (pointer 'a4))) -> (forall result41:(pointer 'a2). ((result41 = (shift d (bw_and (Int.(+) tx2 ty2 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result41) -> (forall result42:int. ((result42 = (acc intM_d_10_8 result41 : int)) -> (forall result43:(pointer 'a3). ((result43 = (shift mutable_indata 3 : (pointer 'a3))) -> ((valid alloc result43) -> (forall result44:int. ((result44 = (acc intM_indata_11 result43 : int)) -> ((valid alloc result40) -> (forall intM_outdata_12_4:(memory int 'a4). ((intM_outdata_12_4 = (upd intM_outdata_12_3 result40 (bw_xor result42 result44 : int) : (memory int 'a4))) -> (forall x_0_5:int. ((x_0_5 = (bw_and (Int.(+) x_0_4 1 : int) 255 : int)) -> (forall result45:(pointer 'a2). ((result45 = (shift d x_0_5 : (pointer 'a2))) -> ((valid alloc result45) -> (forall result46:int. ((result46 = (acc intM_d_10_8 result45 : int)) -> (forall tx3:int. ((tx3 = result46) -> (forall y_0_5:int. ((y_0_5 = (bw_and (Int.(+) tx3 y_0_4 : int) 255 : int)) -> (forall result47:(pointer 'a2). ((result47 = (shift d x_0_5 : (pointer 'a2))) -> (forall result48:(pointer 'a2). ((result48 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result48) -> (forall result49:int. ((result49 = (acc intM_d_10_8 result48 : int)) -> (forall ty3:int. ((ty3 = result49) -> ((valid alloc result47) -> (forall intM_d_10_9:(memory int 'a2). ((intM_d_10_9 = (upd intM_d_10_8 result47 ty3 : (memory int 'a2))) -> (forall result50:(pointer 'a2). ((result50 = (shift d y_0_5 : (pointer 'a2))) -> ((valid alloc result50) -> (forall intM_d_10_10:(memory int 'a2). ((intM_d_10_10 = (upd intM_d_10_9 result50 tx3 : (memory int 'a2))) -> (forall result51:(pointer 'a4). ((result51 = (shift mutable_outdata 4 : (pointer 'a4))) -> (forall result52:(pointer 'a2). ((result52 = (shift d (bw_and (Int.(+) tx3 ty3 : int) 255 : int) : (pointer 'a2))) -> ((valid alloc result52) -> (forall result53:int. ((result53 = (acc intM_d_10_10 result52 : int)) -> (forall result54:(pointer 'a3). ((result54 = (shift mutable_indata 4 : (pointer 'a3))) -> ((valid alloc result54) -> (forall result55:int. ((result55 = (acc intM_indata_11 result54 : int)) -> ((valid alloc result51) ->