TSTP Solution File: GRP660-13 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP660-13 : 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 : n018.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 01:19:32 EDT 2023
% Result : Unsatisfiable 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP660-13 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 20:51:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.48 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.19/0.48
% 0.19/0.48 % SZS status Unsatisfiable
% 0.19/0.48
% 0.19/0.50 % SZS output start Proof
% 0.19/0.50 Axiom 1 (f01): mult(X, ld(X, Y)) = Y.
% 0.19/0.50 Axiom 2 (f03): mult(rd(X, Y), Y) = X.
% 0.19/0.50 Axiom 3 (f02): ld(X, mult(X, Y)) = Y.
% 0.19/0.50 Axiom 4 (f04): rd(mult(X, Y), Y) = X.
% 0.19/0.50 Axiom 5 (f05): mult(mult(mult(X, Y), Z), X) = mult(X, mult(Y, mult(Z, X))).
% 0.19/0.50
% 0.19/0.50 Lemma 6: mult(X, mult(ld(X, Y), mult(Z, X))) = mult(mult(Y, Z), X).
% 0.19/0.50 Proof:
% 0.19/0.50 mult(X, mult(ld(X, Y), mult(Z, X)))
% 0.19/0.50 = { by axiom 5 (f05) R->L }
% 0.19/0.50 mult(mult(mult(X, ld(X, Y)), Z), X)
% 0.19/0.50 = { by axiom 1 (f01) }
% 0.19/0.50 mult(mult(Y, Z), X)
% 0.19/0.50
% 0.19/0.50 Lemma 7: ld(X, mult(mult(Y, Z), X)) = mult(ld(X, Y), mult(Z, X)).
% 0.19/0.50 Proof:
% 0.19/0.50 ld(X, mult(mult(Y, Z), X))
% 0.19/0.50 = { by lemma 6 R->L }
% 0.19/0.50 ld(X, mult(X, mult(ld(X, Y), mult(Z, X))))
% 0.19/0.50 = { by axiom 3 (f02) }
% 0.19/0.50 mult(ld(X, Y), mult(Z, X))
% 0.19/0.50
% 0.19/0.50 Lemma 8: mult(ld(mult(X, Y), X), mult(Y, mult(X, Y))) = mult(X, Y).
% 0.19/0.50 Proof:
% 0.19/0.50 mult(ld(mult(X, Y), X), mult(Y, mult(X, Y)))
% 0.19/0.50 = { by lemma 7 R->L }
% 0.19/0.50 ld(mult(X, Y), mult(mult(X, Y), mult(X, Y)))
% 0.19/0.50 = { by axiom 3 (f02) }
% 0.19/0.50 mult(X, Y)
% 0.19/0.50
% 0.19/0.50 Lemma 9: ld(ld(X, Y), X) = mult(ld(Y, X), X).
% 0.19/0.50 Proof:
% 0.19/0.50 ld(ld(X, Y), X)
% 0.19/0.50 = { by axiom 1 (f01) R->L }
% 0.19/0.50 ld(ld(X, Y), mult(Y, ld(Y, X)))
% 0.19/0.50 = { by lemma 8 R->L }
% 0.19/0.50 ld(ld(X, Y), mult(ld(mult(Y, ld(Y, X)), Y), mult(ld(Y, X), mult(Y, ld(Y, X)))))
% 0.19/0.50 = { by axiom 1 (f01) }
% 0.19/0.50 ld(ld(X, Y), mult(ld(X, Y), mult(ld(Y, X), mult(Y, ld(Y, X)))))
% 0.19/0.50 = { by axiom 1 (f01) }
% 0.19/0.50 ld(ld(X, Y), mult(ld(X, Y), mult(ld(Y, X), X)))
% 0.19/0.50 = { by axiom 3 (f02) }
% 0.19/0.50 mult(ld(Y, X), X)
% 0.19/0.50
% 0.19/0.50 Lemma 10: ld(ld(X, ld(X, X)), ld(X, X)) = mult(ld(X, X), X).
% 0.19/0.50 Proof:
% 0.19/0.50 ld(ld(X, ld(X, X)), ld(X, X))
% 0.19/0.50 = { by axiom 2 (f03) R->L }
% 0.19/0.50 ld(ld(X, ld(X, X)), ld(X, mult(rd(X, X), X)))
% 0.19/0.50 = { by axiom 1 (f01) R->L }
% 0.19/0.50 ld(ld(X, ld(X, X)), ld(X, mult(mult(ld(X, X), ld(ld(X, X), rd(X, X))), X)))
% 0.19/0.50 = { by axiom 4 (f04) R->L }
% 0.19/0.50 ld(ld(X, ld(X, X)), ld(X, mult(mult(ld(X, X), rd(mult(ld(ld(X, X), rd(X, X)), X), X)), X)))
% 0.19/0.50 = { by axiom 3 (f02) R->L }
% 0.19/0.50 ld(ld(X, ld(X, X)), ld(X, mult(mult(ld(X, X), rd(ld(ld(X, X), mult(ld(X, X), mult(ld(ld(X, X), rd(X, X)), X))), X)), X)))
% 0.19/0.50 = { by axiom 1 (f01) R->L }
% 0.19/0.50 ld(ld(X, ld(X, X)), ld(X, mult(mult(ld(X, X), rd(ld(ld(X, X), mult(ld(X, X), mult(ld(ld(X, X), rd(X, X)), mult(X, ld(X, X))))), X)), X)))
% 0.19/0.50 = { by lemma 6 }
% 0.19/0.50 ld(ld(X, ld(X, X)), ld(X, mult(mult(ld(X, X), rd(ld(ld(X, X), mult(mult(rd(X, X), X), ld(X, X))), X)), X)))
% 0.19/0.50 = { by axiom 2 (f03) }
% 0.19/0.50 ld(ld(X, ld(X, X)), ld(X, mult(mult(ld(X, X), rd(ld(ld(X, X), mult(X, ld(X, X))), X)), X)))
% 0.19/0.50 = { by axiom 1 (f01) }
% 0.19/0.50 ld(ld(X, ld(X, X)), ld(X, mult(mult(ld(X, X), rd(ld(ld(X, X), X), X)), X)))
% 0.19/0.50 = { by lemma 9 }
% 0.19/0.50 ld(ld(X, ld(X, X)), ld(X, mult(mult(ld(X, X), rd(mult(ld(X, X), X), X)), X)))
% 0.19/0.50 = { by axiom 4 (f04) }
% 0.19/0.50 ld(ld(X, ld(X, X)), ld(X, mult(mult(ld(X, X), ld(X, X)), X)))
% 0.19/0.50 = { by lemma 7 }
% 0.19/0.50 ld(ld(X, ld(X, X)), mult(ld(X, ld(X, X)), mult(ld(X, X), X)))
% 0.19/0.50 = { by axiom 3 (f02) }
% 0.19/0.50 mult(ld(X, X), X)
% 0.19/0.50
% 0.19/0.50 Lemma 11: mult(ld(mult(X, Y), X), X) = ld(Y, X).
% 0.19/0.50 Proof:
% 0.19/0.50 mult(ld(mult(X, Y), X), X)
% 0.19/0.50 = { by lemma 9 R->L }
% 0.19/0.50 ld(ld(X, mult(X, Y)), X)
% 0.19/0.50 = { by axiom 3 (f02) }
% 0.19/0.51 ld(Y, X)
% 0.19/0.51
% 0.19/0.51 Lemma 12: mult(mult(ld(X, ld(X, X)), ld(X, X)), ld(X, X)) = ld(X, ld(X, X)).
% 0.19/0.51 Proof:
% 0.19/0.51 mult(mult(ld(X, ld(X, X)), ld(X, X)), ld(X, X))
% 0.19/0.51 = { by lemma 9 R->L }
% 0.19/0.51 mult(ld(ld(ld(X, X), X), ld(X, X)), ld(X, X))
% 0.19/0.51 = { by lemma 9 }
% 0.19/0.51 mult(ld(mult(ld(X, X), X), ld(X, X)), ld(X, X))
% 0.19/0.51 = { by lemma 11 }
% 0.19/0.51 ld(X, ld(X, X))
% 0.19/0.51
% 0.19/0.51 Lemma 13: mult(ld(X, X), ld(X, X)) = ld(X, X).
% 0.19/0.51 Proof:
% 0.19/0.51 mult(ld(X, X), ld(X, X))
% 0.19/0.51 = { by axiom 3 (f02) R->L }
% 0.19/0.51 ld(X, mult(X, mult(ld(X, X), ld(X, X))))
% 0.19/0.51 = { by axiom 3 (f02) R->L }
% 0.19/0.51 ld(X, ld(ld(X, X), mult(ld(X, X), mult(X, mult(ld(X, X), ld(X, X))))))
% 0.19/0.51 = { by axiom 5 (f05) R->L }
% 0.19/0.51 ld(X, ld(ld(X, X), mult(mult(mult(ld(X, X), X), ld(X, X)), ld(X, X))))
% 0.19/0.51 = { by lemma 10 R->L }
% 0.19/0.51 ld(X, ld(ld(X, X), mult(mult(ld(ld(X, ld(X, X)), ld(X, X)), ld(X, X)), ld(X, X))))
% 0.19/0.51 = { by lemma 12 R->L }
% 0.19/0.51 ld(X, ld(ld(X, X), mult(mult(ld(mult(mult(ld(X, ld(X, X)), ld(X, X)), ld(X, X)), ld(X, X)), ld(X, X)), ld(X, X))))
% 0.19/0.51 = { by lemma 8 R->L }
% 0.19/0.51 ld(X, ld(ld(X, X), mult(mult(ld(mult(ld(mult(mult(ld(X, ld(X, X)), ld(X, X)), ld(X, X)), mult(ld(X, ld(X, X)), ld(X, X))), mult(ld(X, X), mult(mult(ld(X, ld(X, X)), ld(X, X)), ld(X, X)))), ld(X, X)), ld(X, X)), ld(X, X))))
% 0.19/0.51 = { by lemma 12 }
% 0.19/0.51 ld(X, ld(ld(X, X), mult(mult(ld(mult(ld(ld(X, ld(X, X)), mult(ld(X, ld(X, X)), ld(X, X))), mult(ld(X, X), mult(mult(ld(X, ld(X, X)), ld(X, X)), ld(X, X)))), ld(X, X)), ld(X, X)), ld(X, X))))
% 0.19/0.51 = { by axiom 3 (f02) }
% 0.19/0.51 ld(X, ld(ld(X, X), mult(mult(ld(mult(ld(X, X), mult(ld(X, X), mult(mult(ld(X, ld(X, X)), ld(X, X)), ld(X, X)))), ld(X, X)), ld(X, X)), ld(X, X))))
% 0.19/0.51 = { by lemma 12 }
% 0.19/0.51 ld(X, ld(ld(X, X), mult(mult(ld(mult(ld(X, X), mult(ld(X, X), ld(X, ld(X, X)))), ld(X, X)), ld(X, X)), ld(X, X))))
% 0.19/0.51 = { by lemma 11 }
% 0.19/0.51 ld(X, ld(ld(X, X), mult(ld(mult(ld(X, X), ld(X, ld(X, X))), ld(X, X)), ld(X, X))))
% 0.19/0.51 = { by lemma 11 }
% 0.19/0.51 ld(X, ld(ld(X, X), ld(ld(X, ld(X, X)), ld(X, X))))
% 0.19/0.51 = { by lemma 10 }
% 0.19/0.51 ld(X, ld(ld(X, X), mult(ld(X, X), X)))
% 0.19/0.51 = { by axiom 3 (f02) }
% 0.19/0.51 ld(X, X)
% 0.19/0.51
% 0.19/0.51 Lemma 14: mult(X, mult(Y, mult(ld(mult(X, Y), Z), X))) = mult(Z, X).
% 0.19/0.51 Proof:
% 0.19/0.51 mult(X, mult(Y, mult(ld(mult(X, Y), Z), X)))
% 0.19/0.51 = { by axiom 5 (f05) R->L }
% 0.19/0.51 mult(mult(mult(X, Y), ld(mult(X, Y), Z)), X)
% 0.19/0.51 = { by axiom 1 (f01) }
% 0.19/0.51 mult(Z, X)
% 0.19/0.51
% 0.19/0.51 Goal 1 (goal): mult(x0, ld(x1, x1)) = x0.
% 0.19/0.51 Proof:
% 0.19/0.51 mult(x0, ld(x1, x1))
% 0.19/0.51 = { by lemma 14 R->L }
% 0.19/0.51 mult(ld(x1, x1), mult(ld(x1, x1), mult(ld(mult(ld(x1, x1), ld(x1, x1)), x0), ld(x1, x1))))
% 0.19/0.51 = { by axiom 2 (f03) R->L }
% 0.19/0.51 mult(ld(x1, x1), mult(ld(x1, x1), mult(mult(rd(ld(mult(ld(x1, x1), ld(x1, x1)), x0), ld(x1, x1)), ld(x1, x1)), ld(x1, x1))))
% 0.19/0.51 = { by lemma 6 R->L }
% 0.19/0.51 mult(ld(x1, x1), mult(ld(x1, x1), mult(ld(x1, x1), mult(ld(ld(x1, x1), rd(ld(mult(ld(x1, x1), ld(x1, x1)), x0), ld(x1, x1))), mult(ld(x1, x1), ld(x1, x1))))))
% 0.19/0.51 = { by lemma 13 }
% 0.19/0.51 mult(ld(x1, x1), mult(ld(x1, x1), mult(ld(x1, x1), mult(ld(ld(x1, x1), rd(ld(mult(ld(x1, x1), ld(x1, x1)), x0), ld(x1, x1))), ld(x1, x1)))))
% 0.19/0.51 = { by lemma 13 R->L }
% 0.19/0.51 mult(ld(x1, x1), mult(ld(x1, x1), mult(ld(x1, x1), mult(ld(mult(ld(x1, x1), ld(x1, x1)), rd(ld(mult(ld(x1, x1), ld(x1, x1)), x0), ld(x1, x1))), ld(x1, x1)))))
% 0.19/0.51 = { by lemma 14 }
% 0.19/0.51 mult(ld(x1, x1), mult(rd(ld(mult(ld(x1, x1), ld(x1, x1)), x0), ld(x1, x1)), ld(x1, x1)))
% 0.19/0.51 = { by axiom 2 (f03) }
% 0.19/0.51 mult(ld(x1, x1), ld(mult(ld(x1, x1), ld(x1, x1)), x0))
% 0.19/0.51 = { by lemma 13 }
% 0.19/0.51 mult(ld(x1, x1), ld(ld(x1, x1), x0))
% 0.19/0.51 = { by axiom 1 (f01) }
% 0.19/0.51 x0
% 0.19/0.51 % SZS output end Proof
% 0.19/0.51
% 0.19/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------