%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SWV236+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:06:32 PM UTC 2026
% Result : Theorem 161.82s 20.68s
% Output : Proof 161.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV236+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n026.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 10:17:26 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 161.82/20.68 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 161.82/20.68
% 161.82/20.68 % SZS status Theorem
% 161.82/20.68
% 161.82/20.68 % SZS output start Proof
% 161.82/20.68 Axiom 1 (initial_knowledge_of_intruder_9): p(exp) = true.
% 161.82/20.68 Axiom 2 (initial_knowledge_of_intruder_1): p(kp) = true.
% 161.82/20.68 Axiom 3 (xor_rules_2): xor(X, X) = id.
% 161.82/20.68 Axiom 4 (xor_commutative): xor(X, Y) = xor(Y, X).
% 161.82/20.68 Axiom 5 (xor_rules_1): xor(X, id) = X.
% 161.82/20.68 Axiom 6 (xor_associative): xor(X, xor(Y, Z)) = xor(xor(X, Y), Z).
% 161.82/20.68 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 161.82/20.68 Axiom 8 (combine_with_XOR): ifeq(p(X), true, ifeq(p(Y), true, p(xor(Y, X)), true), true) = true.
% 161.82/20.68 Axiom 9 (key_part_import___part_1): ifeq(p(X), true, ifeq(p(Y), true, p(crypt(xor(km, xor(kp, X)), Y)), true), true) = true.
% 161.82/20.69
% 161.82/20.69 Goal 1 (find_known_exporter): tuple(p(X), p(crypt(xor(km, exp), X))) = tuple(true, true).
% 161.82/20.69 The goal is true when:
% 161.82/20.69 X = exp
% 161.82/20.69
% 161.82/20.69 Proof:
% 161.82/20.69 tuple(p(exp), p(crypt(xor(km, exp), exp)))
% 161.82/20.69 = { by axiom 4 (xor_commutative) R->L }
% 161.82/20.69 tuple(p(exp), p(crypt(xor(exp, km), exp)))
% 161.82/20.69 = { by axiom 5 (xor_rules_1) R->L }
% 161.82/20.69 tuple(p(exp), p(crypt(xor(exp, xor(km, id)), exp)))
% 161.82/20.69 = { by axiom 4 (xor_commutative) }
% 161.82/20.69 tuple(p(exp), p(crypt(xor(exp, xor(id, km)), exp)))
% 161.82/20.69 = { by axiom 3 (xor_rules_2) R->L }
% 161.82/20.69 tuple(p(exp), p(crypt(xor(exp, xor(xor(kp, kp), km)), exp)))
% 161.82/20.69 = { by axiom 6 (xor_associative) R->L }
% 161.82/20.69 tuple(p(exp), p(crypt(xor(exp, xor(kp, xor(kp, km))), exp)))
% 161.82/20.69 = { by axiom 4 (xor_commutative) }
% 161.82/20.69 tuple(p(exp), p(crypt(xor(exp, xor(kp, xor(km, kp))), exp)))
% 161.82/20.69 = { by axiom 6 (xor_associative) }
% 161.82/20.69 tuple(p(exp), p(crypt(xor(xor(exp, kp), xor(km, kp)), exp)))
% 161.82/20.69 = { by axiom 7 (ifeq_axiom) R->L }
% 161.82/20.69 tuple(p(exp), ifeq(true, true, p(crypt(xor(xor(exp, kp), xor(km, kp)), exp)), true))
% 161.82/20.69 = { by axiom 8 (combine_with_XOR) R->L }
% 161.82/20.69 tuple(p(exp), ifeq(ifeq(p(exp), true, ifeq(p(kp), true, p(xor(kp, exp)), true), true), true, p(crypt(xor(xor(exp, kp), xor(km, kp)), exp)), true))
% 161.82/20.69 = { by axiom 1 (initial_knowledge_of_intruder_9) }
% 161.82/20.69 tuple(p(exp), ifeq(ifeq(true, true, ifeq(p(kp), true, p(xor(kp, exp)), true), true), true, p(crypt(xor(xor(exp, kp), xor(km, kp)), exp)), true))
% 161.82/20.69 = { by axiom 7 (ifeq_axiom) }
% 161.82/20.69 tuple(p(exp), ifeq(ifeq(p(kp), true, p(xor(kp, exp)), true), true, p(crypt(xor(xor(exp, kp), xor(km, kp)), exp)), true))
% 161.82/20.69 = { by axiom 2 (initial_knowledge_of_intruder_1) }
% 161.82/20.69 tuple(p(exp), ifeq(ifeq(true, true, p(xor(kp, exp)), true), true, p(crypt(xor(xor(exp, kp), xor(km, kp)), exp)), true))
% 161.82/20.69 = { by axiom 7 (ifeq_axiom) }
% 161.82/20.69 tuple(p(exp), ifeq(p(xor(kp, exp)), true, p(crypt(xor(xor(exp, kp), xor(km, kp)), exp)), true))
% 161.82/20.69 = { by axiom 4 (xor_commutative) }
% 161.82/20.69 tuple(p(exp), ifeq(p(xor(exp, kp)), true, p(crypt(xor(xor(exp, kp), xor(km, kp)), exp)), true))
% 161.82/20.69 = { by axiom 4 (xor_commutative) R->L }
% 161.82/20.69 tuple(p(exp), ifeq(p(xor(exp, kp)), true, p(crypt(xor(xor(km, kp), xor(exp, kp)), exp)), true))
% 161.82/20.69 = { by axiom 6 (xor_associative) R->L }
% 161.82/20.69 tuple(p(exp), ifeq(p(xor(exp, kp)), true, p(crypt(xor(km, xor(kp, xor(exp, kp))), exp)), true))
% 161.82/20.69 = { by axiom 7 (ifeq_axiom) R->L }
% 161.82/20.69 tuple(p(exp), ifeq(p(xor(exp, kp)), true, ifeq(true, true, p(crypt(xor(km, xor(kp, xor(exp, kp))), exp)), true), true))
% 161.82/20.69 = { by axiom 1 (initial_knowledge_of_intruder_9) R->L }
% 161.82/20.69 tuple(p(exp), ifeq(p(xor(exp, kp)), true, ifeq(p(exp), true, p(crypt(xor(km, xor(kp, xor(exp, kp))), exp)), true), true))
% 161.82/20.69 = { by axiom 9 (key_part_import___part_1) }
% 161.82/20.69 tuple(p(exp), true)
% 161.82/20.69 = { by axiom 1 (initial_knowledge_of_intruder_9) }
% 161.82/20.69 tuple(true, true)
% 161.82/20.69 % SZS output end Proof
% 161.82/20.69
% 161.82/20.69 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------