%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP659+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 10:11:36 AM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP659+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n026.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sun Sep 27 10:35:26 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.44 Command-line arguments: --flatten --complete-subsets
% 0.13/0.44
% 0.13/0.44 % SZS status Theorem
% 0.13/0.44
% 0.13/0.46 % SZS output start Proof
% 0.13/0.46 Axiom 1 (f02): ld(X, mult(X, Y)) = Y.
% 0.13/0.46 Axiom 2 (f04): rd(mult(X, Y), Y) = X.
% 0.13/0.46 Axiom 3 (f01): mult(X, ld(X, Y)) = Y.
% 0.13/0.46 Axiom 4 (f03): mult(rd(X, Y), Y) = X.
% 0.13/0.46 Axiom 5 (f05): mult(mult(X, mult(Y, Z)), Y) = mult(mult(X, Y), mult(Z, Y)).
% 0.13/0.46
% 0.13/0.46 Lemma 6: mult(mult(X, Y), mult(ld(Y, Z), Y)) = mult(mult(X, Z), Y).
% 0.13/0.46 Proof:
% 0.13/0.46 mult(mult(X, Y), mult(ld(Y, Z), Y))
% 0.13/0.46 = { by axiom 5 (f05) R->L }
% 0.13/0.46 mult(mult(X, mult(Y, ld(Y, Z))), Y)
% 0.13/0.46 = { by axiom 3 (f01) }
% 0.13/0.46 mult(mult(X, Z), Y)
% 0.13/0.46
% 0.13/0.46 Lemma 7: mult(X, mult(ld(Y, Y), Y)) = mult(X, Y).
% 0.13/0.46 Proof:
% 0.13/0.46 mult(X, mult(ld(Y, Y), Y))
% 0.13/0.46 = { by axiom 4 (f03) R->L }
% 0.13/0.46 mult(mult(rd(X, Y), Y), mult(ld(Y, Y), Y))
% 0.13/0.46 = { by lemma 6 }
% 0.13/0.46 mult(mult(rd(X, Y), Y), Y)
% 0.13/0.46 = { by axiom 4 (f03) }
% 0.13/0.46 mult(X, Y)
% 0.13/0.46
% 0.13/0.46 Lemma 8: mult(ld(X, X), X) = X.
% 0.13/0.46 Proof:
% 0.13/0.46 mult(ld(X, X), X)
% 0.13/0.46 = { by axiom 1 (f02) R->L }
% 0.13/0.46 ld(Y, mult(Y, mult(ld(X, X), X)))
% 0.13/0.46 = { by lemma 7 }
% 0.13/0.46 ld(Y, mult(Y, X))
% 0.13/0.46 = { by axiom 1 (f02) }
% 0.13/0.46 X
% 0.13/0.46
% 0.13/0.46 Lemma 9: rd(X, X) = ld(X, X).
% 0.13/0.46 Proof:
% 0.13/0.46 rd(X, X)
% 0.13/0.46 = { by lemma 8 R->L }
% 0.13/0.46 rd(mult(ld(X, X), X), X)
% 0.13/0.46 = { by axiom 2 (f04) }
% 0.13/0.46 ld(X, X)
% 0.13/0.46
% 0.13/0.46 Lemma 10: rd(mult(mult(X, Y), mult(Z, Y)), Y) = mult(X, mult(Y, Z)).
% 0.13/0.46 Proof:
% 0.13/0.46 rd(mult(mult(X, Y), mult(Z, Y)), Y)
% 0.13/0.46 = { by axiom 5 (f05) R->L }
% 0.13/0.46 rd(mult(mult(X, mult(Y, Z)), Y), Y)
% 0.13/0.46 = { by axiom 2 (f04) }
% 0.13/0.46 mult(X, mult(Y, Z))
% 0.13/0.46
% 0.13/0.46 Lemma 11: rd(X, ld(Y, X)) = Y.
% 0.13/0.46 Proof:
% 0.13/0.46 rd(X, ld(Y, X))
% 0.13/0.46 = { by axiom 3 (f01) R->L }
% 0.13/0.46 rd(mult(Y, ld(Y, X)), ld(Y, X))
% 0.13/0.46 = { by axiom 2 (f04) }
% 0.13/0.46 Y
% 0.13/0.46
% 0.13/0.46 Lemma 12: ld(ld(X, X), ld(X, X)) = ld(X, X).
% 0.13/0.46 Proof:
% 0.13/0.46 ld(ld(X, X), ld(X, X))
% 0.13/0.46 = { by axiom 2 (f04) R->L }
% 0.13/0.46 rd(mult(ld(ld(X, X), ld(X, X)), X), X)
% 0.13/0.46 = { by lemma 9 R->L }
% 0.13/0.46 rd(mult(rd(ld(X, X), ld(X, X)), X), X)
% 0.13/0.46 = { by lemma 7 R->L }
% 0.13/0.46 rd(mult(rd(ld(X, X), ld(X, X)), mult(ld(X, X), X)), X)
% 0.13/0.46 = { by lemma 10 R->L }
% 0.13/0.46 rd(rd(mult(mult(rd(ld(X, X), ld(X, X)), ld(X, X)), mult(X, ld(X, X))), ld(X, X)), X)
% 0.13/0.46 = { by axiom 4 (f03) }
% 0.13/0.46 rd(rd(mult(ld(X, X), mult(X, ld(X, X))), ld(X, X)), X)
% 0.13/0.46 = { by axiom 3 (f01) }
% 0.13/0.46 rd(rd(mult(ld(X, X), X), ld(X, X)), X)
% 0.13/0.46 = { by lemma 8 }
% 0.13/0.46 rd(rd(X, ld(X, X)), X)
% 0.13/0.46 = { by lemma 11 }
% 0.13/0.46 rd(X, X)
% 0.13/0.46 = { by lemma 9 }
% 0.13/0.46 ld(X, X)
% 0.13/0.46
% 0.13/0.46 Lemma 13: mult(X, ld(Y, Y)) = X.
% 0.13/0.46 Proof:
% 0.13/0.46 mult(X, ld(Y, Y))
% 0.13/0.46 = { by axiom 4 (f03) R->L }
% 0.13/0.46 mult(X, ld(Y, mult(rd(Y, X), X)))
% 0.13/0.46 = { by axiom 4 (f03) R->L }
% 0.13/0.46 mult(X, ld(mult(rd(Y, X), X), mult(rd(Y, X), X)))
% 0.13/0.46 = { by axiom 3 (f01) R->L }
% 0.13/0.46 mult(X, ld(mult(rd(Y, X), X), mult(mult(rd(Y, X), ld(rd(Y, X), rd(Y, X))), X)))
% 0.13/0.46 = { by lemma 6 R->L }
% 0.13/0.46 mult(X, ld(mult(rd(Y, X), X), mult(mult(rd(Y, X), X), mult(ld(X, ld(rd(Y, X), rd(Y, X))), X))))
% 0.13/0.46 = { by axiom 1 (f02) }
% 0.13/0.46 mult(X, mult(ld(X, ld(rd(Y, X), rd(Y, X))), X))
% 0.13/0.46 = { by lemma 10 R->L }
% 0.13/0.46 rd(mult(mult(X, ld(X, ld(rd(Y, X), rd(Y, X)))), mult(X, ld(X, ld(rd(Y, X), rd(Y, X))))), ld(X, ld(rd(Y, X), rd(Y, X))))
% 0.13/0.46 = { by axiom 3 (f01) }
% 0.13/0.46 rd(mult(ld(rd(Y, X), rd(Y, X)), mult(X, ld(X, ld(rd(Y, X), rd(Y, X))))), ld(X, ld(rd(Y, X), rd(Y, X))))
% 0.13/0.46 = { by axiom 3 (f01) }
% 0.13/0.46 rd(mult(ld(rd(Y, X), rd(Y, X)), ld(rd(Y, X), rd(Y, X))), ld(X, ld(rd(Y, X), rd(Y, X))))
% 0.13/0.46 = { by lemma 12 R->L }
% 0.13/0.46 rd(mult(ld(rd(Y, X), rd(Y, X)), ld(ld(rd(Y, X), rd(Y, X)), ld(rd(Y, X), rd(Y, X)))), ld(X, ld(rd(Y, X), rd(Y, X))))
% 0.13/0.46 = { by axiom 3 (f01) }
% 0.13/0.46 rd(ld(rd(Y, X), rd(Y, X)), ld(X, ld(rd(Y, X), rd(Y, X))))
% 0.13/0.46 = { by lemma 11 }
% 0.13/0.46 X
% 0.13/0.46
% 0.13/0.46 Goal 1 (goals): tuple(mult(X, x1(X)), mult(x1_2(X), X)) = tuple(x1(X), x1_2(X)).
% 0.13/0.46 The goal is true when:
% 0.13/0.46 X = ld(X, X)
% 0.13/0.46
% 0.13/0.46 Proof:
% 0.13/0.46 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), ld(X, X)))
% 0.13/0.46 = { by lemma 12 R->L }
% 0.13/0.46 tuple(mult(ld(ld(X, X), ld(X, X)), x1(ld(X, X))), mult(x1_2(ld(X, X)), ld(X, X)))
% 0.13/0.46 = { by lemma 13 R->L }
% 0.13/0.46 tuple(mult(mult(ld(ld(X, X), ld(X, X)), x1(ld(X, X))), ld(X, X)), mult(x1_2(ld(X, X)), ld(X, X)))
% 0.13/0.46 = { by lemma 6 R->L }
% 0.13/0.46 tuple(mult(mult(ld(ld(X, X), ld(X, X)), ld(X, X)), mult(ld(ld(X, X), x1(ld(X, X))), ld(X, X))), mult(x1_2(ld(X, X)), ld(X, X)))
% 0.13/0.46 = { by lemma 8 }
% 0.13/0.46 tuple(mult(ld(X, X), mult(ld(ld(X, X), x1(ld(X, X))), ld(X, X))), mult(x1_2(ld(X, X)), ld(X, X)))
% 0.13/0.46 = { by lemma 13 }
% 0.13/0.46 tuple(mult(ld(X, X), ld(ld(X, X), x1(ld(X, X)))), mult(x1_2(ld(X, X)), ld(X, X)))
% 0.13/0.46 = { by axiom 3 (f01) }
% 0.13/0.46 tuple(x1(ld(X, X)), mult(x1_2(ld(X, X)), ld(X, X)))
% 0.13/0.46 = { by lemma 13 }
% 0.13/0.46 tuple(x1(ld(X, X)), x1_2(ld(X, X)))
% 0.13/0.46 % SZS output end Proof
% 0.13/0.46
% 0.13/0.46 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------