%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP657+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 10:11:35 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 : GRP657+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 10:30:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.43 Command-line arguments: --no-flatten-goal
% 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 (f02): ld(X, mult(X, Y)) = Y.
% 0.09/0.43 Axiom 2 (f04): rd(mult(X, Y), Y) = X.
% 0.09/0.43 Axiom 3 (f01): mult(X, ld(X, Y)) = Y.
% 0.09/0.43 Axiom 4 (f03): mult(rd(X, Y), Y) = X.
% 0.09/0.43 Axiom 5 (f05): mult(mult(X, Y), mult(Z, X)) = mult(X, mult(mult(Y, Z), X)).
% 0.09/0.43
% 0.09/0.43 Lemma 6: mult(ld(X, X), Y) = Y.
% 0.09/0.43 Proof:
% 0.09/0.43 mult(ld(X, X), Y)
% 0.09/0.43 = { by axiom 2 (f04) R->L }
% 0.09/0.43 rd(mult(mult(ld(X, X), Y), X), X)
% 0.09/0.43 = { by axiom 1 (f02) R->L }
% 0.09/0.43 rd(ld(X, mult(X, mult(mult(ld(X, X), Y), X))), X)
% 0.09/0.43 = { by axiom 5 (f05) R->L }
% 0.09/0.43 rd(ld(X, mult(mult(X, ld(X, X)), mult(Y, X))), X)
% 0.09/0.43 = { by axiom 3 (f01) }
% 0.09/0.43 rd(ld(X, mult(X, mult(Y, X))), X)
% 0.09/0.43 = { by axiom 1 (f02) }
% 0.09/0.43 rd(mult(Y, X), X)
% 0.09/0.43 = { by axiom 2 (f04) }
% 0.09/0.43 Y
% 0.09/0.43
% 0.09/0.43 Goal 1 (goals): tuple(mult(X, x1(X)), mult(x1_2(X), X)) = tuple(x1(X), x1_2(X)).
% 0.09/0.43 The goal is true when:
% 0.09/0.43 X = ld(X, X)
% 0.09/0.43
% 0.09/0.43 Proof:
% 0.09/0.43 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), ld(X, X)))
% 0.09/0.43 = { by axiom 2 (f04) R->L }
% 0.09/0.43 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), rd(mult(ld(X, X), rd(Y, x1_2(ld(X, X)))), rd(Y, x1_2(ld(X, X))))))
% 0.09/0.44 = { by lemma 6 }
% 0.09/0.44 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), rd(rd(Y, x1_2(ld(X, X))), rd(Y, x1_2(ld(X, X))))))
% 0.09/0.44 = { by axiom 2 (f04) R->L }
% 0.09/0.44 tuple(mult(ld(X, X), x1(ld(X, X))), rd(mult(mult(x1_2(ld(X, X)), rd(rd(Y, x1_2(ld(X, X))), rd(Y, x1_2(ld(X, X))))), Y), Y))
% 0.09/0.44 = { by axiom 4 (f03) R->L }
% 0.09/0.44 tuple(mult(ld(X, X), x1(ld(X, X))), rd(mult(mult(x1_2(ld(X, X)), rd(rd(Y, x1_2(ld(X, X))), rd(Y, x1_2(ld(X, X))))), mult(rd(Y, x1_2(ld(X, X))), x1_2(ld(X, X)))), Y))
% 0.09/0.44 = { by axiom 5 (f05) }
% 0.09/0.44 tuple(mult(ld(X, X), x1(ld(X, X))), rd(mult(x1_2(ld(X, X)), mult(mult(rd(rd(Y, x1_2(ld(X, X))), rd(Y, x1_2(ld(X, X)))), rd(Y, x1_2(ld(X, X)))), x1_2(ld(X, X)))), Y))
% 0.09/0.44 = { by axiom 4 (f03) }
% 0.09/0.44 tuple(mult(ld(X, X), x1(ld(X, X))), rd(mult(x1_2(ld(X, X)), mult(rd(Y, x1_2(ld(X, X))), x1_2(ld(X, X)))), Y))
% 0.09/0.44 = { by axiom 4 (f03) }
% 0.09/0.44 tuple(mult(ld(X, X), x1(ld(X, X))), rd(mult(x1_2(ld(X, X)), Y), Y))
% 0.09/0.44 = { by axiom 2 (f04) }
% 0.09/0.44 tuple(mult(ld(X, X), x1(ld(X, X))), x1_2(ld(X, X)))
% 0.09/0.44 = { by lemma 6 }
% 0.09/0.44 tuple(x1(ld(X, X)), x1_2(ld(X, X)))
% 0.09/0.44 % SZS output end Proof
% 0.09/0.44
% 0.09/0.44 RESULT: Theorem (the conjecture is true).
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