%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP660+2 : 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 10:11:37 AM UTC 2026
% Result : Theorem 0.64s 0.52s
% Output : Proof 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP660+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:35:08 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.64/0.52 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.64/0.52
% 0.64/0.52 % SZS status Theorem
% 0.64/0.52
% 0.64/0.53 % SZS output start Proof
% 0.64/0.53 Axiom 1 (f01): mult(X, ld(X, Y)) = Y.
% 0.64/0.53 Axiom 2 (f03): mult(rd(X, Y), Y) = X.
% 0.64/0.53 Axiom 3 (f04): rd(mult(X, Y), Y) = X.
% 0.64/0.53 Axiom 4 (f02): ld(X, mult(X, Y)) = Y.
% 0.64/0.53 Axiom 5 (f05): mult(mult(mult(X, Y), Z), X) = mult(X, mult(Y, mult(Z, X))).
% 0.64/0.53
% 0.64/0.53 Lemma 6: ld(rd(X, Y), X) = Y.
% 0.64/0.53 Proof:
% 0.64/0.53 ld(rd(X, Y), X)
% 0.64/0.53 = { by axiom 2 (f03) R->L }
% 0.64/0.53 ld(rd(X, Y), mult(rd(X, Y), Y))
% 0.64/0.53 = { by axiom 4 (f02) }
% 0.64/0.53 Y
% 0.64/0.53
% 0.64/0.53 Lemma 7: rd(mult(X, mult(Y, mult(Z, X))), X) = mult(mult(X, Y), Z).
% 0.64/0.53 Proof:
% 0.64/0.53 rd(mult(X, mult(Y, mult(Z, X))), X)
% 0.64/0.53 = { by axiom 5 (f05) R->L }
% 0.64/0.53 rd(mult(mult(mult(X, Y), Z), X), X)
% 0.64/0.53 = { by axiom 3 (f04) }
% 0.64/0.53 mult(mult(X, Y), Z)
% 0.64/0.53
% 0.64/0.53 Lemma 8: mult(mult(X, rd(Y, mult(Z, X))), Z) = rd(mult(X, Y), X).
% 0.64/0.53 Proof:
% 0.64/0.53 mult(mult(X, rd(Y, mult(Z, X))), Z)
% 0.64/0.53 = { by lemma 7 R->L }
% 0.64/0.53 rd(mult(X, mult(rd(Y, mult(Z, X)), mult(Z, X))), X)
% 0.64/0.53 = { by axiom 2 (f03) }
% 0.64/0.53 rd(mult(X, Y), X)
% 0.64/0.53
% 0.64/0.53 Lemma 9: mult(rd(X, Y), mult(Y, mult(Z, rd(X, Y)))) = mult(mult(X, Z), rd(X, Y)).
% 0.64/0.53 Proof:
% 0.64/0.53 mult(rd(X, Y), mult(Y, mult(Z, rd(X, Y))))
% 0.64/0.53 = { by axiom 5 (f05) R->L }
% 0.64/0.53 mult(mult(mult(rd(X, Y), Y), Z), rd(X, Y))
% 0.64/0.53 = { by axiom 2 (f03) }
% 0.64/0.53 mult(mult(X, Z), rd(X, Y))
% 0.64/0.53
% 0.64/0.53 Lemma 10: ld(rd(Y, X), mult(Z, rd(Y, X))) = mult(X, mult(ld(Y, Z), rd(Y, X))).
% 0.64/0.53 Proof:
% 0.64/0.53 ld(rd(Y, X), mult(Z, rd(Y, X)))
% 0.64/0.53 = { by axiom 1 (f01) R->L }
% 0.64/0.53 ld(rd(Y, X), mult(mult(Y, ld(Y, Z)), rd(Y, X)))
% 0.64/0.53 = { by lemma 9 R->L }
% 0.64/0.53 ld(rd(Y, X), mult(rd(Y, X), mult(X, mult(ld(Y, Z), rd(Y, X)))))
% 0.64/0.53 = { by axiom 4 (f02) }
% 0.64/0.53 mult(X, mult(ld(Y, Z), rd(Y, X)))
% 0.64/0.53
% 0.64/0.53 Lemma 11: rd(mult(X, mult(Y, Z)), X) = mult(mult(X, Y), rd(Z, X)).
% 0.64/0.53 Proof:
% 0.64/0.53 rd(mult(X, mult(Y, Z)), X)
% 0.64/0.53 = { by axiom 2 (f03) R->L }
% 0.64/0.53 rd(mult(X, mult(Y, mult(rd(Z, X), X))), X)
% 0.64/0.53 = { by lemma 7 }
% 0.64/0.53 mult(mult(X, Y), rd(Z, X))
% 0.64/0.53
% 0.64/0.53 Lemma 12: mult(X, rd(X, X)) = X.
% 0.64/0.53 Proof:
% 0.64/0.53 mult(X, rd(X, X))
% 0.64/0.53 = { by lemma 6 R->L }
% 0.64/0.53 ld(rd(rd(X, X), mult(X, rd(X, X))), rd(X, X))
% 0.64/0.53 = { by axiom 4 (f02) R->L }
% 0.64/0.53 ld(ld(rd(X, X), mult(rd(X, X), rd(rd(X, X), mult(X, rd(X, X))))), rd(X, X))
% 0.64/0.53 = { by axiom 3 (f04) R->L }
% 0.64/0.53 ld(ld(rd(X, X), rd(mult(mult(rd(X, X), rd(rd(X, X), mult(X, rd(X, X)))), X), X)), rd(X, X))
% 0.64/0.53 = { by lemma 8 }
% 0.64/0.53 ld(ld(rd(X, X), rd(rd(mult(rd(X, X), rd(X, X)), rd(X, X)), X)), rd(X, X))
% 0.64/0.53 = { by axiom 3 (f04) }
% 0.64/0.53 ld(ld(rd(X, X), rd(rd(X, X), X)), rd(X, X))
% 0.64/0.53 = { by axiom 4 (f02) R->L }
% 0.64/0.53 ld(ld(rd(X, X), rd(ld(rd(X, X), mult(rd(X, X), rd(X, X))), X)), rd(X, X))
% 0.64/0.53 = { by lemma 10 }
% 0.64/0.53 ld(ld(rd(X, X), rd(mult(X, mult(ld(X, rd(X, X)), rd(X, X))), X)), rd(X, X))
% 0.64/0.53 = { by lemma 11 }
% 0.64/0.53 ld(ld(rd(X, X), mult(mult(X, ld(X, rd(X, X))), rd(rd(X, X), X))), rd(X, X))
% 0.64/0.53 = { by axiom 1 (f01) }
% 0.64/0.53 ld(ld(rd(X, X), mult(rd(X, X), rd(rd(X, X), X))), rd(X, X))
% 0.64/0.53 = { by axiom 4 (f02) }
% 0.64/0.53 ld(rd(rd(X, X), X), rd(X, X))
% 0.64/0.53 = { by lemma 6 }
% 0.64/0.53 X
% 0.64/0.53
% 0.64/0.53 Lemma 13: ld(X, X) = rd(X, X).
% 0.64/0.53 Proof:
% 0.64/0.53 ld(X, X)
% 0.64/0.53 = { by lemma 12 R->L }
% 0.64/0.53 ld(X, mult(X, rd(X, X)))
% 0.64/0.53 = { by axiom 4 (f02) }
% 0.64/0.53 rd(X, X)
% 0.64/0.53
% 0.64/0.53 Lemma 14: mult(mult(X, rd(Y, rd(X, Z))), rd(X, Z)) = mult(rd(X, Z), mult(Z, Y)).
% 0.64/0.53 Proof:
% 0.64/0.53 mult(mult(X, rd(Y, rd(X, Z))), rd(X, Z))
% 0.64/0.53 = { by lemma 9 R->L }
% 0.64/0.53 mult(rd(X, Z), mult(Z, mult(rd(Y, rd(X, Z)), rd(X, Z))))
% 0.64/0.53 = { by axiom 2 (f03) }
% 0.64/0.53 mult(rd(X, Z), mult(Z, Y))
% 0.64/0.53
% 0.64/0.53 Lemma 15: rd(ld(X, X), rd(X, X)) = rd(X, X).
% 0.64/0.54 Proof:
% 0.64/0.54 rd(ld(X, X), rd(X, X))
% 0.64/0.54 = { by axiom 3 (f04) R->L }
% 0.64/0.54 rd(mult(rd(ld(X, X), rd(X, X)), X), X)
% 0.64/0.54 = { by axiom 4 (f02) R->L }
% 0.64/0.54 rd(mult(ld(X, mult(X, rd(ld(X, X), rd(X, X)))), X), X)
% 0.64/0.54 = { by axiom 3 (f04) R->L }
% 0.64/0.54 rd(mult(ld(X, rd(mult(mult(X, rd(ld(X, X), rd(X, X))), rd(X, X)), rd(X, X))), X), X)
% 0.64/0.54 = { by lemma 14 }
% 0.64/0.54 rd(mult(ld(X, rd(mult(rd(X, X), mult(X, ld(X, X))), rd(X, X))), X), X)
% 0.64/0.54 = { by axiom 1 (f01) }
% 0.64/0.54 rd(mult(ld(X, rd(mult(rd(X, X), X), rd(X, X))), X), X)
% 0.64/0.54 = { by axiom 2 (f03) }
% 0.64/0.54 rd(mult(ld(X, rd(X, rd(X, X))), X), X)
% 0.64/0.54 = { by axiom 4 (f02) R->L }
% 0.64/0.54 rd(ld(X, mult(X, mult(ld(X, rd(X, rd(X, X))), X))), X)
% 0.64/0.54 = { by axiom 3 (f04) R->L }
% 0.64/0.54 rd(ld(X, mult(X, mult(rd(mult(ld(X, rd(X, rd(X, X))), rd(X, X)), rd(X, X)), X))), X)
% 0.64/0.54 = { by axiom 2 (f03) R->L }
% 0.64/0.54 rd(ld(X, mult(X, mult(rd(mult(ld(X, rd(X, rd(X, X))), rd(X, X)), rd(X, X)), mult(rd(X, X), X)))), X)
% 0.64/0.54 = { by axiom 5 (f05) R->L }
% 0.64/0.54 rd(ld(X, mult(mult(mult(X, rd(mult(ld(X, rd(X, rd(X, X))), rd(X, X)), rd(X, X))), rd(X, X)), X)), X)
% 0.64/0.54 = { by lemma 14 }
% 0.64/0.54 rd(ld(X, mult(mult(rd(X, X), mult(X, mult(ld(X, rd(X, rd(X, X))), rd(X, X)))), X)), X)
% 0.64/0.54 = { by lemma 10 R->L }
% 0.64/0.54 rd(ld(X, mult(mult(rd(X, X), ld(rd(X, X), mult(rd(X, rd(X, X)), rd(X, X)))), X)), X)
% 0.64/0.54 = { by axiom 1 (f01) }
% 0.64/0.54 rd(ld(X, mult(mult(rd(X, rd(X, X)), rd(X, X)), X)), X)
% 0.64/0.54 = { by axiom 2 (f03) }
% 0.64/0.54 rd(ld(X, mult(X, X)), X)
% 0.64/0.54 = { by axiom 4 (f02) }
% 0.64/0.54 rd(X, X)
% 0.64/0.54
% 0.64/0.54 Lemma 16: mult(X, mult(ld(X, Y), mult(Z, X))) = mult(mult(Y, Z), X).
% 0.64/0.54 Proof:
% 0.64/0.54 mult(X, mult(ld(X, Y), mult(Z, X)))
% 0.64/0.54 = { by axiom 5 (f05) R->L }
% 0.64/0.54 mult(mult(mult(X, ld(X, Y)), Z), X)
% 0.64/0.54 = { by axiom 1 (f01) }
% 0.64/0.54 mult(mult(Y, Z), X)
% 0.64/0.54
% 0.64/0.54 Lemma 17: ld(rd(X, X), rd(X, X)) = rd(X, X).
% 0.64/0.54 Proof:
% 0.64/0.54 ld(rd(X, X), rd(X, X))
% 0.64/0.54 = { by axiom 3 (f04) R->L }
% 0.64/0.54 rd(mult(ld(rd(X, X), rd(X, X)), mult(X, rd(X, X))), mult(X, rd(X, X)))
% 0.64/0.54 = { by axiom 4 (f02) R->L }
% 0.64/0.54 rd(ld(rd(X, X), mult(rd(X, X), mult(ld(rd(X, X), rd(X, X)), mult(X, rd(X, X))))), mult(X, rd(X, X)))
% 0.64/0.54 = { by lemma 16 }
% 0.64/0.54 rd(ld(rd(X, X), mult(mult(rd(X, X), X), rd(X, X))), mult(X, rd(X, X)))
% 0.64/0.54 = { by axiom 2 (f03) }
% 0.64/0.54 rd(ld(rd(X, X), mult(X, rd(X, X))), mult(X, rd(X, X)))
% 0.64/0.54 = { by lemma 12 }
% 0.64/0.54 rd(ld(rd(X, X), X), mult(X, rd(X, X)))
% 0.64/0.54 = { by lemma 6 }
% 0.64/0.54 rd(X, mult(X, rd(X, X)))
% 0.64/0.54 = { by lemma 12 }
% 0.64/0.54 rd(X, X)
% 0.64/0.54
% 0.64/0.54 Lemma 18: rd(mult(rd(X, X), Y), rd(X, X)) = mult(rd(X, X), mult(rd(X, X), Y)).
% 0.64/0.54 Proof:
% 0.64/0.54 rd(mult(rd(X, X), Y), rd(X, X))
% 0.64/0.54 = { by lemma 8 R->L }
% 0.64/0.54 mult(mult(rd(X, X), rd(Y, mult(rd(X, X), rd(X, X)))), rd(X, X))
% 0.64/0.54 = { by lemma 15 R->L }
% 0.64/0.54 mult(mult(rd(X, X), rd(Y, mult(rd(ld(X, X), rd(X, X)), rd(X, X)))), rd(X, X))
% 0.64/0.54 = { by axiom 2 (f03) }
% 0.64/0.54 mult(mult(rd(X, X), rd(Y, ld(X, X))), rd(X, X))
% 0.64/0.54 = { by lemma 13 }
% 0.64/0.54 mult(mult(rd(X, X), rd(Y, rd(X, X))), rd(X, X))
% 0.64/0.54 = { by lemma 16 R->L }
% 0.64/0.54 mult(rd(X, X), mult(ld(rd(X, X), rd(X, X)), mult(rd(Y, rd(X, X)), rd(X, X))))
% 0.64/0.54 = { by axiom 2 (f03) }
% 0.64/0.54 mult(rd(X, X), mult(ld(rd(X, X), rd(X, X)), Y))
% 0.64/0.54 = { by lemma 17 }
% 0.64/0.54 mult(rd(X, X), mult(rd(X, X), Y))
% 0.64/0.54
% 0.64/0.54 Lemma 19: rd(X, rd(Y, Y)) = mult(rd(Y, Y), X).
% 0.64/0.54 Proof:
% 0.64/0.54 rd(X, rd(Y, Y))
% 0.64/0.54 = { by axiom 1 (f01) R->L }
% 0.64/0.54 rd(mult(rd(Y, Y), ld(rd(Y, Y), X)), rd(Y, Y))
% 0.64/0.54 = { by lemma 18 }
% 0.64/0.54 mult(rd(Y, Y), mult(rd(Y, Y), ld(rd(Y, Y), X)))
% 0.64/0.54 = { by axiom 1 (f01) }
% 0.64/0.54 mult(rd(Y, Y), X)
% 0.64/0.54
% 0.64/0.54 Lemma 20: mult(rd(X, X), mult(Y, rd(X, X))) = Y.
% 0.64/0.54 Proof:
% 0.64/0.54 mult(rd(X, X), mult(Y, rd(X, X)))
% 0.64/0.54 = { by lemma 19 R->L }
% 0.64/0.54 rd(mult(Y, rd(X, X)), rd(X, X))
% 0.64/0.54 = { by axiom 3 (f04) }
% 0.64/0.54 Y
% 0.64/0.54
% 0.64/0.54 Lemma 21: mult(rd(X, X), Y) = Y.
% 0.64/0.54 Proof:
% 0.64/0.54 mult(rd(X, X), Y)
% 0.64/0.54 = { by lemma 20 R->L }
% 0.64/0.54 mult(rd(X, X), mult(rd(X, X), mult(Y, rd(X, X))))
% 0.64/0.54 = { by lemma 17 R->L }
% 0.64/0.54 mult(rd(X, X), mult(ld(rd(X, X), rd(X, X)), mult(Y, rd(X, X))))
% 0.64/0.54 = { by lemma 16 }
% 0.64/0.54 mult(mult(rd(X, X), Y), rd(X, X))
% 0.64/0.54 = { by lemma 19 R->L }
% 0.64/0.54 mult(rd(Y, rd(X, X)), rd(X, X))
% 0.64/0.54 = { by axiom 2 (f03) }
% 0.64/0.54 Y
% 0.64/0.54
% 0.64/0.54 Goal 1 (goals): tuple(mult(rd(x1, x1), x0), mult(x0_2, rd(x1_2, x1_2))) = tuple(x0, x0_2).
% 0.64/0.54 Proof:
% 0.64/0.54 tuple(mult(rd(x1, x1), x0), mult(x0_2, rd(x1_2, x1_2)))
% 0.64/0.54 = { by lemma 21 }
% 0.64/0.54 tuple(x0, mult(x0_2, rd(x1_2, x1_2)))
% 0.64/0.54 = { by lemma 15 R->L }
% 0.64/0.54 tuple(x0, mult(x0_2, rd(ld(x1_2, x1_2), rd(x1_2, x1_2))))
% 0.64/0.54 = { by lemma 13 }
% 0.64/0.54 tuple(x0, mult(x0_2, rd(rd(x1_2, x1_2), rd(x1_2, x1_2))))
% 0.64/0.54 = { by lemma 21 R->L }
% 0.64/0.54 tuple(x0, mult(mult(rd(x1_2, x1_2), x0_2), rd(rd(x1_2, x1_2), rd(x1_2, x1_2))))
% 0.64/0.54 = { by lemma 11 R->L }
% 0.64/0.54 tuple(x0, rd(mult(rd(x1_2, x1_2), mult(x0_2, rd(x1_2, x1_2))), rd(x1_2, x1_2)))
% 0.64/0.54 = { by lemma 18 }
% 0.64/0.54 tuple(x0, mult(rd(x1_2, x1_2), mult(rd(x1_2, x1_2), mult(x0_2, rd(x1_2, x1_2)))))
% 0.64/0.54 = { by lemma 20 }
% 0.64/0.54 tuple(x0, mult(rd(x1_2, x1_2), x0_2))
% 0.64/0.54 = { by lemma 21 }
% 0.64/0.54 tuple(x0, x0_2)
% 0.64/0.54 % SZS output end Proof
% 0.64/0.54
% 0.64/0.54 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------