%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP656+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 0.12s 0.41s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP656+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n018.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 27 10:34:37 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.41 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.12/0.41
% 0.12/0.41 % SZS status Theorem
% 0.12/0.41
% 0.12/0.42 % SZS output start Proof
% 0.12/0.42 Axiom 1 (f03): mult(rd(X, Y), Y) = X.
% 0.12/0.42 Axiom 2 (f02): ld(X, mult(X, Y)) = Y.
% 0.12/0.42 Axiom 3 (f04): rd(mult(X, Y), Y) = X.
% 0.12/0.42 Axiom 4 (f05): mult(mult(X, Y), mult(Z, X)) = mult(mult(X, mult(Y, Z)), X).
% 0.12/0.42
% 0.12/0.42 Lemma 5: mult(X, rd(Y, Y)) = X.
% 0.12/0.42 Proof:
% 0.12/0.42 mult(X, rd(Y, Y))
% 0.12/0.42 = { by axiom 2 (f02) R->L }
% 0.12/0.42 ld(Y, mult(Y, mult(X, rd(Y, Y))))
% 0.12/0.42 = { by axiom 3 (f04) R->L }
% 0.12/0.42 ld(Y, rd(mult(mult(Y, mult(X, rd(Y, Y))), Y), Y))
% 0.12/0.42 = { by axiom 4 (f05) R->L }
% 0.12/0.42 ld(Y, rd(mult(mult(Y, X), mult(rd(Y, Y), Y)), Y))
% 0.12/0.42 = { by axiom 1 (f03) }
% 0.12/0.42 ld(Y, rd(mult(mult(Y, X), Y), Y))
% 0.12/0.42 = { by axiom 3 (f04) }
% 0.12/0.42 ld(Y, mult(Y, X))
% 0.12/0.42 = { by axiom 2 (f02) }
% 0.12/0.42 X
% 0.12/0.42
% 0.12/0.42 Lemma 6: rd(X, X) = ld(Y, Y).
% 0.12/0.42 Proof:
% 0.12/0.42 rd(X, X)
% 0.12/0.42 = { by axiom 2 (f02) R->L }
% 0.12/0.42 ld(Y, mult(Y, rd(X, X)))
% 0.12/0.42 = { by lemma 5 }
% 0.12/0.42 ld(Y, Y)
% 0.12/0.42
% 0.12/0.42 Goal 1 (goals): tuple(mult(X, x1(X)), mult(x1_2(X), X)) = tuple(x1(X), x1_2(X)).
% 0.12/0.42 The goal is true when:
% 0.12/0.42 X = ld(X, X)
% 0.12/0.42
% 0.12/0.42 Proof:
% 0.12/0.42 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), ld(X, X)))
% 0.12/0.42 = { by lemma 6 R->L }
% 0.12/0.42 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), rd(Y, Y)))
% 0.12/0.42 = { by lemma 5 }
% 0.12/0.42 tuple(mult(ld(X, X), x1(ld(X, X))), x1_2(ld(X, X)))
% 0.12/0.42 = { by lemma 6 R->L }
% 0.12/0.42 tuple(mult(rd(x1(ld(X, X)), x1(ld(X, X))), x1(ld(X, X))), x1_2(ld(X, X)))
% 0.12/0.42 = { by axiom 1 (f03) }
% 0.12/0.42 tuple(x1(ld(X, X)), x1_2(ld(X, X)))
% 0.12/0.42 % SZS output end Proof
% 0.12/0.42
% 0.12/0.42 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------