%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP658+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 0.49s
% Output : Proof 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP658+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n004.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
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 10:32:37 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.49 Command-line arguments: --flatten-regeneralise
% 0.13/0.49
% 0.13/0.49 % SZS status Theorem
% 0.13/0.49
% 0.64/0.53 % SZS output start Proof
% 0.64/0.53 Axiom 1 (f02): ld(X, mult(X, Y)) = Y.
% 0.64/0.53 Axiom 2 (f04): rd(mult(X, Y), Y) = X.
% 0.64/0.53 Axiom 3 (f01): mult(X, ld(X, Y)) = Y.
% 0.64/0.53 Axiom 4 (f03): mult(rd(X, Y), Y) = X.
% 0.64/0.53 Axiom 5 (f05): mult(mult(X, mult(Y, Y)), Z) = mult(mult(X, Y), mult(Y, Z)).
% 0.64/0.53
% 0.64/0.53 Lemma 6: rd(mult(mult(X, Y), mult(Y, Z)), Z) = mult(X, mult(Y, Y)).
% 0.64/0.53 Proof:
% 0.64/0.53 rd(mult(mult(X, Y), mult(Y, Z)), Z)
% 0.64/0.53 = { by axiom 5 (f05) R->L }
% 0.64/0.53 rd(mult(mult(X, mult(Y, Y)), Z), Z)
% 0.64/0.53 = { by axiom 2 (f04) }
% 0.64/0.53 mult(X, mult(Y, Y))
% 0.64/0.53
% 0.64/0.53 Lemma 7: rd(mult(X, mult(Y, W)), W) = rd(mult(X, mult(Y, Z)), Z).
% 0.64/0.53 Proof:
% 0.64/0.53 rd(mult(X, mult(Y, W)), W)
% 0.64/0.53 = { by axiom 4 (f03) R->L }
% 0.64/0.53 rd(mult(mult(rd(X, Y), Y), mult(Y, W)), W)
% 0.64/0.53 = { by lemma 6 }
% 0.64/0.53 mult(rd(X, Y), mult(Y, Y))
% 0.64/0.53 = { by lemma 6 R->L }
% 0.64/0.53 rd(mult(mult(rd(X, Y), Y), mult(Y, Z)), Z)
% 0.64/0.53 = { by axiom 4 (f03) }
% 0.64/0.53 rd(mult(X, mult(Y, Z)), Z)
% 0.64/0.53
% 0.64/0.53 Lemma 8: rd(mult(X, mult(Y, Z)), Z) = rd(mult(X, W), ld(Y, W)).
% 0.64/0.53 Proof:
% 0.64/0.53 rd(mult(X, mult(Y, Z)), Z)
% 0.64/0.53 = { by lemma 7 }
% 0.64/0.53 rd(mult(X, mult(Y, ld(Y, W))), ld(Y, W))
% 0.64/0.53 = { by axiom 3 (f01) }
% 0.64/0.53 rd(mult(X, W), ld(Y, W))
% 0.64/0.53
% 0.64/0.53 Lemma 9: rd(mult(X, Y), ld(Z, Y)) = rd(W, ld(Z, ld(X, W))).
% 0.64/0.53 Proof:
% 0.64/0.53 rd(mult(X, Y), ld(Z, Y))
% 0.64/0.53 = { by axiom 3 (f01) R->L }
% 0.64/0.53 rd(mult(X, mult(Z, ld(Z, Y))), ld(Z, Y))
% 0.64/0.53 = { by lemma 7 R->L }
% 0.64/0.53 rd(mult(X, mult(Z, ld(Z, ld(X, W)))), ld(Z, ld(X, W)))
% 0.64/0.53 = { by axiom 3 (f01) }
% 0.64/0.53 rd(mult(X, ld(X, W)), ld(Z, ld(X, W)))
% 0.64/0.53 = { by axiom 3 (f01) }
% 0.64/0.53 rd(W, ld(Z, ld(X, W)))
% 0.64/0.53
% 0.64/0.53 Lemma 10: 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 4 (f03) R->L }
% 0.64/0.53 ld(rd(X, Y), mult(rd(X, Y), Y))
% 0.64/0.53 = { by axiom 1 (f02) }
% 0.64/0.53 Y
% 0.64/0.53
% 0.64/0.53 Lemma 11: rd(X, ld(Y, X)) = Y.
% 0.64/0.53 Proof:
% 0.64/0.53 rd(X, ld(Y, X))
% 0.64/0.53 = { by axiom 3 (f01) R->L }
% 0.64/0.53 rd(mult(Y, ld(Y, X)), ld(Y, X))
% 0.64/0.53 = { by axiom 2 (f04) }
% 0.64/0.53 Y
% 0.64/0.53
% 0.64/0.53 Lemma 12: mult(rd(X, X), Y) = Y.
% 0.64/0.53 Proof:
% 0.64/0.53 mult(rd(X, X), Y)
% 0.64/0.53 = { by axiom 3 (f01) R->L }
% 0.64/0.53 mult(rd(X, X), mult(Z, ld(Z, Y)))
% 0.64/0.53 = { by axiom 4 (f03) R->L }
% 0.64/0.53 mult(mult(rd(rd(X, X), Z), Z), mult(Z, ld(Z, Y)))
% 0.64/0.53 = { by axiom 5 (f05) R->L }
% 0.64/0.53 mult(mult(rd(rd(X, X), Z), mult(Z, Z)), ld(Z, Y))
% 0.64/0.53 = { by lemma 6 R->L }
% 0.64/0.53 mult(rd(mult(mult(rd(rd(X, X), Z), Z), mult(Z, W)), W), ld(Z, Y))
% 0.64/0.53 = { by axiom 4 (f03) }
% 0.64/0.53 mult(rd(mult(rd(X, X), mult(Z, W)), W), ld(Z, Y))
% 0.64/0.53 = { by lemma 8 }
% 0.64/0.53 mult(rd(mult(rd(X, X), V), ld(Z, V)), ld(Z, Y))
% 0.64/0.53 = { by lemma 9 }
% 0.64/0.53 mult(rd(X, ld(Z, ld(rd(X, X), X))), ld(Z, Y))
% 0.64/0.53 = { by lemma 10 }
% 0.64/0.53 mult(rd(X, ld(Z, X)), ld(Z, Y))
% 0.64/0.53 = { by lemma 11 }
% 0.64/0.53 mult(Z, ld(Z, Y))
% 0.64/0.53 = { by axiom 3 (f01) }
% 0.64/0.53 Y
% 0.64/0.53
% 0.64/0.53 Lemma 13: ld(rd(X, X), Y) = Y.
% 0.64/0.53 Proof:
% 0.64/0.53 ld(rd(X, X), Y)
% 0.64/0.53 = { by lemma 12 R->L }
% 0.64/0.53 ld(rd(X, X), mult(rd(X, X), Y))
% 0.64/0.53 = { by axiom 1 (f02) }
% 0.64/0.53 Y
% 0.64/0.53
% 0.64/0.53 Lemma 14: ld(rd(mult(X, Y), Z), W) = ld(rd(Y, Z), ld(X, W)).
% 0.64/0.53 Proof:
% 0.64/0.53 ld(rd(mult(X, Y), Z), W)
% 0.64/0.53 = { by axiom 4 (f03) R->L }
% 0.64/0.53 ld(rd(mult(X, mult(rd(Y, Z), Z)), Z), W)
% 0.64/0.53 = { by lemma 8 }
% 0.64/0.53 ld(rd(mult(X, V), ld(rd(Y, Z), V)), W)
% 0.64/0.53 = { by lemma 9 }
% 0.64/0.53 ld(rd(W, ld(rd(Y, Z), ld(X, W))), W)
% 0.64/0.53 = { by lemma 10 }
% 0.64/0.53 ld(rd(Y, Z), ld(X, W))
% 0.64/0.53
% 0.64/0.53 Lemma 15: mult(mult(rd(X, mult(Y, Y)), Y), mult(Y, Z)) = mult(X, Z).
% 0.64/0.53 Proof:
% 0.64/0.53 mult(mult(rd(X, mult(Y, Y)), Y), mult(Y, Z))
% 0.64/0.53 = { by axiom 5 (f05) R->L }
% 0.64/0.53 mult(mult(rd(X, mult(Y, Y)), mult(Y, Y)), Z)
% 0.64/0.53 = { by axiom 4 (f03) }
% 0.64/0.53 mult(X, Z)
% 0.64/0.53
% 0.64/0.53 Lemma 16: ld(rd(X, mult(Y, X)), Z) = mult(Y, Z).
% 0.64/0.53 Proof:
% 0.64/0.53 ld(rd(X, mult(Y, X)), Z)
% 0.64/0.53 = { by axiom 1 (f02) R->L }
% 0.64/0.53 ld(rd(X, mult(Y, X)), ld(W, mult(W, Z)))
% 0.64/0.53 = { by lemma 14 R->L }
% 0.64/0.53 ld(rd(mult(W, X), mult(Y, X)), mult(W, Z))
% 0.64/0.53 = { by lemma 15 R->L }
% 0.64/0.53 ld(rd(mult(mult(rd(W, mult(Y, Y)), Y), mult(Y, X)), mult(Y, X)), mult(W, Z))
% 0.64/0.53 = { by axiom 2 (f04) }
% 0.64/0.53 ld(mult(rd(W, mult(Y, Y)), Y), mult(W, Z))
% 0.64/0.53 = { by axiom 2 (f04) R->L }
% 0.64/0.53 ld(rd(mult(mult(rd(W, mult(Y, Y)), Y), mult(Y, Z)), mult(Y, Z)), mult(W, Z))
% 0.64/0.53 = { by lemma 15 }
% 0.64/0.53 ld(rd(mult(W, Z), mult(Y, Z)), mult(W, Z))
% 0.64/0.53 = { by lemma 10 }
% 0.64/0.54 mult(Y, Z)
% 0.64/0.54
% 0.64/0.54 Lemma 17: mult(rd(X, Y), Z) = ld(rd(Y, X), Z).
% 0.64/0.54 Proof:
% 0.64/0.54 mult(rd(X, Y), Z)
% 0.64/0.54 = { by lemma 16 R->L }
% 0.64/0.54 ld(rd(Y, mult(rd(X, Y), Y)), Z)
% 0.64/0.54 = { by axiom 4 (f03) }
% 0.64/0.54 ld(rd(Y, X), Z)
% 0.64/0.54
% 0.64/0.54 Lemma 18: mult(rd(X, mult(Y, Y)), Y) = rd(mult(X, Z), mult(Y, Z)).
% 0.64/0.54 Proof:
% 0.64/0.54 mult(rd(X, mult(Y, Y)), Y)
% 0.64/0.54 = { by axiom 2 (f04) R->L }
% 0.64/0.54 rd(mult(mult(rd(X, mult(Y, Y)), Y), mult(Y, Z)), mult(Y, Z))
% 0.64/0.54 = { by lemma 15 }
% 0.64/0.54 rd(mult(X, Z), mult(Y, Z))
% 0.64/0.54
% 0.64/0.54 Goal 1 (goals): tuple(mult(X, x1(X)), mult(x1_2(X), X)) = tuple(x1(X), x1_2(X)).
% 0.64/0.54 The goal is true when:
% 0.64/0.54 X = ld(X, X)
% 0.64/0.54
% 0.64/0.54 Proof:
% 0.64/0.54 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), ld(X, X)))
% 0.64/0.54 = { by lemma 13 R->L }
% 0.64/0.54 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), ld(rd(X, X), ld(X, X))))
% 0.64/0.54 = { by lemma 14 R->L }
% 0.64/0.54 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), ld(rd(mult(X, X), X), X)))
% 0.64/0.54 = { by lemma 17 R->L }
% 0.64/0.54 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), mult(rd(X, mult(X, X)), X)))
% 0.64/0.54 = { by lemma 18 }
% 0.64/0.54 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), rd(mult(X, ld(X, mult(x1_2(ld(X, X)), W))), mult(X, ld(X, mult(x1_2(ld(X, X)), W))))))
% 0.64/0.54 = { by axiom 3 (f01) }
% 0.64/0.54 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), rd(mult(x1_2(ld(X, X)), W), mult(X, ld(X, mult(x1_2(ld(X, X)), W))))))
% 0.64/0.54 = { by axiom 3 (f01) }
% 0.64/0.54 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), rd(mult(x1_2(ld(X, X)), W), mult(x1_2(ld(X, X)), W))))
% 0.64/0.54 = { by lemma 18 R->L }
% 0.64/0.54 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), mult(rd(x1_2(ld(X, X)), mult(x1_2(ld(X, X)), x1_2(ld(X, X)))), x1_2(ld(X, X)))))
% 0.64/0.54 = { by lemma 17 }
% 0.64/0.54 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), ld(rd(mult(x1_2(ld(X, X)), x1_2(ld(X, X))), x1_2(ld(X, X))), x1_2(ld(X, X)))))
% 0.64/0.54 = { by lemma 14 }
% 0.64/0.54 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), ld(rd(x1_2(ld(X, X)), x1_2(ld(X, X))), ld(x1_2(ld(X, X)), x1_2(ld(X, X))))))
% 0.64/0.54 = { by lemma 13 }
% 0.64/0.54 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), ld(x1_2(ld(X, X)), x1_2(ld(X, X)))))
% 0.64/0.54 = { by axiom 3 (f01) }
% 0.64/0.54 tuple(mult(ld(X, X), x1(ld(X, X))), x1_2(ld(X, X)))
% 0.64/0.54 = { by axiom 2 (f04) R->L }
% 0.64/0.54 tuple(mult(ld(rd(mult(X, X), X), X), x1(ld(X, X))), x1_2(ld(X, X)))
% 0.64/0.54 = { by axiom 2 (f04) R->L }
% 0.64/0.54 tuple(mult(ld(rd(mult(rd(mult(X, X), X), Z), Z), X), x1(ld(X, X))), x1_2(ld(X, X)))
% 0.64/0.54 = { by lemma 17 }
% 0.64/0.54 tuple(mult(ld(rd(ld(rd(X, mult(X, X)), Z), Z), X), x1(ld(X, X))), x1_2(ld(X, X)))
% 0.64/0.54 = { by axiom 3 (f01) R->L }
% 0.64/0.54 tuple(mult(ld(rd(ld(rd(X, mult(X, X)), Z), mult(rd(X, mult(X, X)), ld(rd(X, mult(X, X)), Z))), X), x1(ld(X, X))), x1_2(ld(X, X)))
% 0.64/0.54 = { by lemma 16 R->L }
% 0.64/0.54 tuple(mult(ld(rd(ld(rd(X, mult(X, X)), Z), ld(rd(X, mult(rd(X, mult(X, X)), X)), ld(rd(X, mult(X, X)), Z))), X), x1(ld(X, X))), x1_2(ld(X, X)))
% 0.64/0.54 = { by lemma 11 }
% 0.64/0.54 tuple(mult(ld(rd(X, mult(rd(X, mult(X, X)), X)), X), x1(ld(X, X))), x1_2(ld(X, X)))
% 0.64/0.54 = { by lemma 18 }
% 0.64/0.54 tuple(mult(ld(rd(X, rd(mult(X, Y), mult(X, Y))), X), x1(ld(X, X))), x1_2(ld(X, X)))
% 0.64/0.54 = { by lemma 10 }
% 0.64/0.54 tuple(mult(rd(mult(X, Y), mult(X, Y)), x1(ld(X, X))), x1_2(ld(X, X)))
% 0.64/0.54 = { by lemma 12 }
% 0.64/0.54 tuple(x1(ld(X, X)), x1_2(ld(X, X)))
% 0.64/0.54 % SZS output end Proof
% 0.64/0.54
% 0.64/0.54 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------