TSTP Solution File: GRP683-10 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP683-10 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:19:41 EDT 2023
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP683-10 : TPTP v8.1.2. Released v8.1.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 21:47:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.42 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.42
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 Axiom 1 (f01): ld(X, mult(X, X)) = X.
% 0.19/0.43 Axiom 2 (f03): mult(X, ld(X, Y)) = ld(X, mult(X, Y)).
% 0.19/0.43 Axiom 3 (f02): rd(mult(X, X), X) = X.
% 0.19/0.43 Axiom 4 (f04): mult(rd(X, Y), Y) = rd(mult(X, Y), Y).
% 0.19/0.43 Axiom 5 (f05): ld(ld(X, Y), mult(ld(X, Y), mult(Z, W))) = mult(ld(X, mult(X, Z)), W).
% 0.19/0.43 Axiom 6 (f06): rd(mult(mult(X, Y), rd(Z, W)), rd(Z, W)) = mult(X, rd(mult(Y, W), W)).
% 0.19/0.43
% 0.19/0.43 Lemma 7: mult(X, ld(X, X)) = X.
% 0.19/0.43 Proof:
% 0.19/0.43 mult(X, ld(X, X))
% 0.19/0.43 = { by axiom 2 (f03) }
% 0.19/0.43 ld(X, mult(X, X))
% 0.19/0.43 = { by axiom 1 (f01) }
% 0.19/0.43 X
% 0.19/0.43
% 0.19/0.43 Lemma 8: mult(ld(X, Y), ld(ld(X, Y), mult(Z, W))) = mult(mult(X, ld(X, Z)), W).
% 0.19/0.43 Proof:
% 0.19/0.43 mult(ld(X, Y), ld(ld(X, Y), mult(Z, W)))
% 0.19/0.43 = { by axiom 2 (f03) }
% 0.19/0.43 ld(ld(X, Y), mult(ld(X, Y), mult(Z, W)))
% 0.19/0.43 = { by axiom 5 (f05) }
% 0.19/0.43 mult(ld(X, mult(X, Z)), W)
% 0.19/0.43 = { by axiom 2 (f03) R->L }
% 0.19/0.43 mult(mult(X, ld(X, Z)), W)
% 0.19/0.43
% 0.19/0.43 Lemma 9: mult(mult(X, ld(X, Y)), Z) = mult(X, ld(X, mult(Y, Z))).
% 0.19/0.43 Proof:
% 0.19/0.43 mult(mult(X, ld(X, Y)), Z)
% 0.19/0.43 = { by lemma 8 R->L }
% 0.19/0.43 mult(ld(X, mult(X, X)), ld(ld(X, mult(X, X)), mult(Y, Z)))
% 0.19/0.43 = { by axiom 1 (f01) }
% 0.19/0.43 mult(X, ld(ld(X, mult(X, X)), mult(Y, Z)))
% 0.19/0.43 = { by axiom 1 (f01) }
% 0.19/0.43 mult(X, ld(X, mult(Y, Z)))
% 0.19/0.43
% 0.19/0.43 Lemma 10: mult(X, mult(X, ld(X, Y))) = mult(X, Y).
% 0.19/0.43 Proof:
% 0.19/0.43 mult(X, mult(X, ld(X, Y)))
% 0.19/0.43 = { by axiom 2 (f03) }
% 0.19/0.43 mult(X, ld(X, mult(X, Y)))
% 0.19/0.43 = { by lemma 9 R->L }
% 0.19/0.43 mult(mult(X, ld(X, X)), Y)
% 0.19/0.43 = { by lemma 7 }
% 0.19/0.43 mult(X, Y)
% 0.19/0.43
% 0.19/0.43 Lemma 11: mult(X, ld(X, mult(X, Y))) = mult(X, Y).
% 0.19/0.43 Proof:
% 0.19/0.43 mult(X, ld(X, mult(X, Y)))
% 0.19/0.43 = { by axiom 2 (f03) R->L }
% 0.19/0.43 mult(X, mult(X, ld(X, Y)))
% 0.19/0.43 = { by lemma 10 }
% 0.19/0.43 mult(X, Y)
% 0.19/0.43
% 0.19/0.43 Lemma 12: mult(ld(X, mult(X, Y)), Z) = mult(X, ld(X, mult(Y, Z))).
% 0.19/0.43 Proof:
% 0.19/0.43 mult(ld(X, mult(X, Y)), Z)
% 0.19/0.43 = { by axiom 2 (f03) R->L }
% 0.19/0.43 mult(mult(X, ld(X, Y)), Z)
% 0.19/0.43 = { by lemma 9 }
% 0.19/0.43 mult(X, ld(X, mult(Y, Z)))
% 0.19/0.43
% 0.19/0.43 Lemma 13: mult(rd(X, ld(X, X)), ld(X, X)) = X.
% 0.19/0.43 Proof:
% 0.19/0.43 mult(rd(X, ld(X, X)), ld(X, X))
% 0.19/0.43 = { by lemma 7 R->L }
% 0.19/0.43 mult(rd(mult(X, ld(X, X)), ld(X, X)), ld(X, X))
% 0.19/0.43 = { by axiom 3 (f02) R->L }
% 0.19/0.43 mult(rd(mult(X, ld(X, X)), ld(X, X)), rd(mult(ld(X, X), ld(X, X)), ld(X, X)))
% 0.19/0.43 = { by axiom 3 (f02) R->L }
% 0.19/0.43 mult(rd(mult(X, ld(X, X)), rd(mult(ld(X, X), ld(X, X)), ld(X, X))), rd(mult(ld(X, X), ld(X, X)), ld(X, X)))
% 0.19/0.43 = { by axiom 4 (f04) }
% 0.19/0.43 rd(mult(mult(X, ld(X, X)), rd(mult(ld(X, X), ld(X, X)), ld(X, X))), rd(mult(ld(X, X), ld(X, X)), ld(X, X)))
% 0.19/0.43 = { by axiom 6 (f06) }
% 0.19/0.43 mult(X, rd(mult(ld(X, X), ld(X, X)), ld(X, X)))
% 0.19/0.43 = { by axiom 3 (f02) }
% 0.19/0.43 mult(X, ld(X, X))
% 0.19/0.43 = { by lemma 7 }
% 0.19/0.43 X
% 0.19/0.43
% 0.19/0.43 Lemma 14: mult(ld(X, Y), ld(ld(X, Y), Z)) = mult(X, ld(X, Z)).
% 0.19/0.43 Proof:
% 0.19/0.43 mult(ld(X, Y), ld(ld(X, Y), Z))
% 0.19/0.43 = { by lemma 13 R->L }
% 0.19/0.43 mult(ld(X, Y), ld(ld(X, Y), mult(rd(Z, ld(Z, Z)), ld(Z, Z))))
% 0.19/0.43 = { by lemma 8 }
% 0.19/0.43 mult(mult(X, ld(X, rd(Z, ld(Z, Z)))), ld(Z, Z))
% 0.19/0.43 = { by lemma 9 }
% 0.19/0.43 mult(X, ld(X, mult(rd(Z, ld(Z, Z)), ld(Z, Z))))
% 0.19/0.43 = { by lemma 13 }
% 0.19/0.43 mult(X, ld(X, Z))
% 0.19/0.43
% 0.19/0.43 Goal 1 (goal): mult(x3, ld(x4, mult(x4, x5))) = mult(x3, x5).
% 0.19/0.43 Proof:
% 0.19/0.43 mult(x3, ld(x4, mult(x4, x5)))
% 0.19/0.43 = { by lemma 11 R->L }
% 0.19/0.43 mult(x3, ld(x3, mult(x3, ld(x4, mult(x4, x5)))))
% 0.19/0.43 = { by axiom 2 (f03) R->L }
% 0.19/0.43 mult(x3, mult(x3, ld(x3, ld(x4, mult(x4, x5)))))
% 0.19/0.43 = { by lemma 14 R->L }
% 0.19/0.43 mult(x3, mult(ld(x3, mult(x3, ld(x4, X))), ld(ld(x3, mult(x3, ld(x4, X))), ld(x4, mult(x4, x5)))))
% 0.19/0.43 = { by axiom 2 (f03) }
% 0.19/0.43 mult(x3, ld(ld(x3, mult(x3, ld(x4, X))), mult(ld(x3, mult(x3, ld(x4, X))), ld(x4, mult(x4, x5)))))
% 0.19/0.43 = { by lemma 12 }
% 0.19/0.43 mult(x3, ld(ld(x3, mult(x3, ld(x4, X))), mult(x3, ld(x3, mult(ld(x4, X), ld(x4, mult(x4, x5)))))))
% 0.19/0.43 = { by axiom 2 (f03) R->L }
% 0.19/0.43 mult(x3, ld(ld(x3, mult(x3, ld(x4, X))), mult(x3, ld(x3, mult(ld(x4, X), mult(x4, ld(x4, x5)))))))
% 0.19/0.43 = { by lemma 14 R->L }
% 0.19/0.43 mult(x3, ld(ld(x3, mult(x3, ld(x4, X))), mult(x3, ld(x3, mult(ld(x4, X), mult(ld(x4, X), ld(ld(x4, X), x5)))))))
% 0.19/0.44 = { by lemma 10 }
% 0.19/0.44 mult(x3, ld(ld(x3, mult(x3, ld(x4, X))), mult(x3, ld(x3, mult(ld(x4, X), x5)))))
% 0.19/0.44 = { by lemma 12 R->L }
% 0.19/0.44 mult(x3, ld(ld(x3, mult(x3, ld(x4, X))), mult(ld(x3, mult(x3, ld(x4, X))), x5)))
% 0.19/0.44 = { by axiom 2 (f03) R->L }
% 0.19/0.44 mult(x3, mult(ld(x3, mult(x3, ld(x4, X))), ld(ld(x3, mult(x3, ld(x4, X))), x5)))
% 0.19/0.44 = { by lemma 14 }
% 0.19/0.44 mult(x3, mult(x3, ld(x3, x5)))
% 0.19/0.44 = { by axiom 2 (f03) }
% 0.19/0.44 mult(x3, ld(x3, mult(x3, x5)))
% 0.19/0.44 = { by lemma 11 }
% 0.19/0.44 mult(x3, x5)
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44
% 0.19/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
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