%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL684+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 11:50:23 AM UTC 2026
% Result : Theorem 0.09s 0.43s
% Output : Proof 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL684+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 16:39:25 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.43 Command-line arguments: --flatten --complete-subsets
% 0.09/0.43
% 0.09/0.43 % SZS status Theorem
% 0.09/0.43
% 0.09/0.43 % SZS output start Proof
% 0.09/0.43 Axiom 1 (main_1): p101(x) = true.
% 0.09/0.43 Axiom 2 (main): p201(x) = true.
% 0.09/0.43 Axiom 3 (reflexivity): r1(X, X) = true.
% 0.09/0.43
% 0.09/0.43 Lemma 4: p201(x) = p101(x).
% 0.09/0.43 Proof:
% 0.09/0.43 p201(x)
% 0.09/0.43 = { by axiom 2 (main) }
% 0.09/0.43 true
% 0.09/0.43 = { by axiom 1 (main_1) R->L }
% 0.09/0.43 p101(x)
% 0.09/0.43
% 0.09/0.43 Lemma 5: r1(X, X) = p201(x).
% 0.09/0.43 Proof:
% 0.09/0.43 r1(X, X)
% 0.09/0.43 = { by axiom 3 (reflexivity) }
% 0.09/0.43 true
% 0.09/0.43 = { by axiom 1 (main_1) R->L }
% 0.09/0.43 p101(x)
% 0.09/0.43 = { by lemma 4 R->L }
% 0.09/0.43 p201(x)
% 0.09/0.43
% 0.09/0.43 Goal 1 (main_2): tuple(r1(X, Y), r1(x, X), p201(Y), p101(Y)) = tuple(true, true, true, true).
% 0.09/0.43 The goal is true when:
% 0.09/0.43 X = x
% 0.09/0.43 Y = x
% 0.09/0.43
% 0.09/0.43 Proof:
% 0.09/0.43 tuple(r1(x, x), r1(x, x), p201(x), p101(x))
% 0.09/0.43 = { by lemma 5 }
% 0.09/0.43 tuple(p201(x), r1(x, x), p201(x), p101(x))
% 0.09/0.43 = { by lemma 5 }
% 0.09/0.43 tuple(p201(x), p201(x), p201(x), p101(x))
% 0.09/0.43 = { by lemma 4 R->L }
% 0.09/0.43 tuple(p201(x), p201(x), p201(x), p201(x))
% 0.09/0.43 = { by lemma 4 }
% 0.09/0.43 tuple(p101(x), p201(x), p201(x), p201(x))
% 0.09/0.44 = { by lemma 4 }
% 0.09/0.44 tuple(p101(x), p101(x), p201(x), p201(x))
% 0.09/0.44 = { by lemma 4 }
% 0.09/0.44 tuple(p101(x), p101(x), p101(x), p201(x))
% 0.09/0.44 = { by lemma 4 }
% 0.09/0.44 tuple(p101(x), p101(x), p101(x), p101(x))
% 0.09/0.44 = { by axiom 1 (main_1) }
% 0.09/0.44 tuple(true, p101(x), p101(x), p101(x))
% 0.09/0.44 = { by axiom 1 (main_1) }
% 0.09/0.44 tuple(true, true, p101(x), p101(x))
% 0.09/0.44 = { by axiom 1 (main_1) }
% 0.09/0.44 tuple(true, true, true, p101(x))
% 0.09/0.44 = { by axiom 1 (main_1) }
% 0.09/0.44 tuple(true, true, true, true)
% 0.09/0.44 % SZS output end Proof
% 0.09/0.44
% 0.09/0.44 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------