%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL678+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 11:50:20 AM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL678+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n005.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 16:33:31 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.44 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.11/0.44
% 0.11/0.44 % SZS status Theorem
% 0.11/0.44
% 0.11/0.44 % SZS output start Proof
% 0.11/0.44 Axiom 1 (reflexivity): r1(X, X) = true.
% 0.11/0.44 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.11/0.44 Axiom 3 (main_1): ifeq(r1(x2, X), true, r1(x(X), y(X)), true) = true.
% 0.11/0.44 Axiom 4 (main_2): ifeq(r1(x(X), Y), true, ifeq(r1(x2, X), true, p1(Y), true), true) = true.
% 0.11/0.44
% 0.11/0.44 Goal 1 (main_3): tuple(r1(x2, X), p1(y(X))) = tuple(true, true).
% 0.11/0.44 The goal is true when:
% 0.11/0.44 X = x2
% 0.11/0.44
% 0.11/0.44 Proof:
% 0.11/0.44 tuple(r1(x2, x2), p1(y(x2)))
% 0.11/0.44 = { by axiom 2 (ifeq_axiom) R->L }
% 0.11/0.44 tuple(r1(x2, x2), ifeq(true, true, p1(y(x2)), true))
% 0.11/0.44 = { by axiom 1 (reflexivity) R->L }
% 0.11/0.44 tuple(r1(x2, x2), ifeq(r1(x2, x2), true, p1(y(x2)), true))
% 0.11/0.44 = { by axiom 2 (ifeq_axiom) R->L }
% 0.11/0.44 tuple(r1(x2, x2), ifeq(true, true, ifeq(r1(x2, x2), true, p1(y(x2)), true), true))
% 0.11/0.44 = { by axiom 3 (main_1) R->L }
% 0.11/0.44 tuple(r1(x2, x2), ifeq(ifeq(r1(x2, x2), true, r1(x(x2), y(x2)), true), true, ifeq(r1(x2, x2), true, p1(y(x2)), true), true))
% 0.11/0.44 = { by axiom 1 (reflexivity) }
% 0.11/0.44 tuple(r1(x2, x2), ifeq(ifeq(true, true, r1(x(x2), y(x2)), true), true, ifeq(r1(x2, x2), true, p1(y(x2)), true), true))
% 0.11/0.44 = { by axiom 2 (ifeq_axiom) }
% 0.11/0.44 tuple(r1(x2, x2), ifeq(r1(x(x2), y(x2)), true, ifeq(r1(x2, x2), true, p1(y(x2)), true), true))
% 0.11/0.44 = { by axiom 4 (main_2) }
% 0.11/0.44 tuple(r1(x2, x2), true)
% 0.11/0.44 = { by axiom 1 (reflexivity) }
% 0.11/0.44 tuple(true, true)
% 0.11/0.44 % SZS output end Proof
% 0.11/0.44
% 0.11/0.44 RESULT: Theorem (the conjecture is true).
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