TSTP Solution File: GRP660-14 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP660-14 : 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 : n022.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 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP660-14 : TPTP v8.1.2. Released v8.1.0.
% 0.07/0.13 % 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 : n022.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 23:25:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.45 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.45
% 0.19/0.45 % SZS status Unsatisfiable
% 0.19/0.45
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 Axiom 1 (f01): mult(X, ld(X, Y)) = Y.
% 0.19/0.48 Axiom 2 (f03): mult(rd(X, Y), Y) = X.
% 0.19/0.48 Axiom 3 (f02): ld(X, mult(X, Y)) = Y.
% 0.19/0.48 Axiom 4 (f04): rd(mult(X, Y), Y) = X.
% 0.19/0.48 Axiom 5 (f05): mult(mult(mult(X, Y), Z), X) = mult(X, mult(Y, mult(Z, X))).
% 0.19/0.48
% 0.19/0.48 Lemma 6: rd(X, ld(Y, X)) = Y.
% 0.19/0.48 Proof:
% 0.19/0.48 rd(X, ld(Y, X))
% 0.19/0.48 = { by axiom 1 (f01) R->L }
% 0.19/0.48 rd(mult(Y, ld(Y, X)), ld(Y, X))
% 0.19/0.48 = { by axiom 4 (f04) }
% 0.19/0.48 Y
% 0.19/0.48
% 0.19/0.48 Lemma 7: mult(X, mult(ld(X, Y), mult(Z, X))) = mult(mult(Y, Z), X).
% 0.19/0.48 Proof:
% 0.19/0.48 mult(X, mult(ld(X, Y), mult(Z, X)))
% 0.19/0.48 = { by axiom 5 (f05) R->L }
% 0.19/0.48 mult(mult(mult(X, ld(X, Y)), Z), X)
% 0.19/0.48 = { by axiom 1 (f01) }
% 0.19/0.48 mult(mult(Y, Z), X)
% 0.19/0.48
% 0.19/0.48 Lemma 8: mult(mult(X, rd(Y, Z)), Z) = mult(Z, mult(ld(Z, X), Y)).
% 0.19/0.48 Proof:
% 0.19/0.48 mult(mult(X, rd(Y, Z)), Z)
% 0.19/0.48 = { by lemma 7 R->L }
% 0.19/0.48 mult(Z, mult(ld(Z, X), mult(rd(Y, Z), Z)))
% 0.19/0.48 = { by axiom 2 (f03) }
% 0.19/0.48 mult(Z, mult(ld(Z, X), Y))
% 0.19/0.48
% 0.19/0.48 Lemma 9: ld(X, mult(mult(Y, Z), X)) = mult(ld(X, Y), mult(Z, X)).
% 0.19/0.48 Proof:
% 0.19/0.48 ld(X, mult(mult(Y, Z), X))
% 0.19/0.48 = { by lemma 7 R->L }
% 0.19/0.48 ld(X, mult(X, mult(ld(X, Y), mult(Z, X))))
% 0.19/0.48 = { by axiom 3 (f02) }
% 0.19/0.48 mult(ld(X, Y), mult(Z, X))
% 0.19/0.48
% 0.19/0.48 Lemma 10: mult(ld(X, Y), mult(ld(Y, Z), X)) = ld(X, mult(Z, X)).
% 0.19/0.48 Proof:
% 0.19/0.48 mult(ld(X, Y), mult(ld(Y, Z), X))
% 0.19/0.48 = { by lemma 9 R->L }
% 0.19/0.48 ld(X, mult(mult(Y, ld(Y, Z)), X))
% 0.19/0.48 = { by axiom 1 (f01) }
% 0.19/0.48 ld(X, mult(Z, X))
% 0.19/0.48
% 0.19/0.48 Lemma 11: rd(mult(X, mult(Y, mult(Z, X))), X) = mult(mult(X, Y), Z).
% 0.19/0.48 Proof:
% 0.19/0.48 rd(mult(X, mult(Y, mult(Z, X))), X)
% 0.19/0.48 = { by axiom 5 (f05) R->L }
% 0.19/0.48 rd(mult(mult(mult(X, Y), Z), X), X)
% 0.19/0.48 = { by axiom 4 (f04) }
% 0.19/0.48 mult(mult(X, Y), Z)
% 0.19/0.48
% 0.19/0.48 Lemma 12: rd(mult(X, mult(Y, Z)), X) = mult(mult(X, Y), rd(Z, X)).
% 0.19/0.48 Proof:
% 0.19/0.48 rd(mult(X, mult(Y, Z)), X)
% 0.19/0.48 = { by axiom 2 (f03) R->L }
% 0.19/0.48 rd(mult(X, mult(Y, mult(rd(Z, X), X))), X)
% 0.19/0.48 = { by lemma 11 }
% 0.19/0.48 mult(mult(X, Y), rd(Z, X))
% 0.19/0.48
% 0.19/0.48 Lemma 13: rd(rd(mult(X, Y), X), Z) = mult(X, rd(Y, mult(Z, X))).
% 0.19/0.48 Proof:
% 0.19/0.48 rd(rd(mult(X, Y), X), Z)
% 0.19/0.48 = { by axiom 2 (f03) R->L }
% 0.19/0.48 rd(rd(mult(X, mult(rd(Y, mult(Z, X)), mult(Z, X))), X), Z)
% 0.19/0.48 = { by lemma 11 }
% 0.19/0.48 rd(mult(mult(X, rd(Y, mult(Z, X))), Z), Z)
% 0.19/0.48 = { by axiom 4 (f04) }
% 0.19/0.48 mult(X, rd(Y, mult(Z, X)))
% 0.19/0.48
% 0.19/0.48 Lemma 14: mult(ld(X, X), X) = X.
% 0.19/0.48 Proof:
% 0.19/0.48 mult(ld(X, X), X)
% 0.19/0.48 = { by lemma 6 R->L }
% 0.19/0.48 mult(ld(X, X), rd(ld(X, X), ld(X, ld(X, X))))
% 0.19/0.48 = { by axiom 4 (f04) R->L }
% 0.19/0.48 mult(ld(X, X), rd(ld(X, X), ld(X, rd(mult(ld(X, X), ld(X, X)), ld(X, X)))))
% 0.19/0.48 = { by axiom 3 (f02) R->L }
% 0.19/0.48 mult(ld(X, X), rd(ld(X, X), ld(X, rd(ld(X, mult(X, mult(ld(X, X), ld(X, X)))), ld(X, X)))))
% 0.19/0.48 = { by lemma 8 R->L }
% 0.19/0.48 mult(ld(X, X), rd(ld(X, X), ld(X, rd(ld(X, mult(mult(X, rd(ld(X, X), X)), X)), ld(X, X)))))
% 0.19/0.48 = { by lemma 10 R->L }
% 0.19/0.48 mult(ld(X, X), rd(ld(X, X), ld(X, rd(mult(ld(X, X), mult(ld(X, mult(X, rd(ld(X, X), X))), X)), ld(X, X)))))
% 0.19/0.48 = { by lemma 12 }
% 0.19/0.48 mult(ld(X, X), rd(ld(X, X), ld(X, mult(mult(ld(X, X), ld(X, mult(X, rd(ld(X, X), X)))), rd(X, ld(X, X))))))
% 0.19/0.48 = { by lemma 6 }
% 0.19/0.48 mult(ld(X, X), rd(ld(X, X), ld(X, mult(mult(ld(X, X), ld(X, mult(X, rd(ld(X, X), X)))), X))))
% 0.19/0.48 = { by axiom 3 (f02) }
% 0.19/0.48 mult(ld(X, X), rd(ld(X, X), ld(X, mult(mult(ld(X, X), rd(ld(X, X), X)), X))))
% 0.19/0.48 = { by lemma 8 }
% 0.19/0.48 mult(ld(X, X), rd(ld(X, X), ld(X, mult(X, mult(ld(X, ld(X, X)), ld(X, X))))))
% 0.19/0.48 = { by axiom 3 (f02) }
% 0.19/0.48 mult(ld(X, X), rd(ld(X, X), mult(ld(X, ld(X, X)), ld(X, X))))
% 0.19/0.48 = { by lemma 13 R->L }
% 0.19/0.48 rd(rd(mult(ld(X, X), ld(X, X)), ld(X, X)), ld(X, ld(X, X)))
% 0.19/0.48 = { by axiom 4 (f04) }
% 0.19/0.48 rd(ld(X, X), ld(X, ld(X, X)))
% 0.19/0.48 = { by lemma 6 }
% 0.19/0.48 X
% 0.19/0.48
% 0.19/0.48 Lemma 15: rd(X, X) = ld(X, X).
% 0.19/0.48 Proof:
% 0.19/0.48 rd(X, X)
% 0.19/0.48 = { by lemma 14 R->L }
% 0.19/0.48 rd(mult(ld(X, X), X), X)
% 0.19/0.48 = { by axiom 4 (f04) }
% 0.19/0.48 ld(X, X)
% 0.19/0.48
% 0.19/0.48 Lemma 16: ld(ld(X, Y), X) = mult(ld(Y, X), X).
% 0.19/0.48 Proof:
% 0.19/0.48 ld(ld(X, Y), X)
% 0.19/0.48 = { by axiom 3 (f02) R->L }
% 0.19/0.48 ld(ld(X, Y), ld(X, mult(X, X)))
% 0.19/0.48 = { by axiom 1 (f01) R->L }
% 0.19/0.48 ld(ld(X, Y), ld(X, mult(mult(Y, ld(Y, X)), X)))
% 0.19/0.48 = { by lemma 9 }
% 0.19/0.48 ld(ld(X, Y), mult(ld(X, Y), mult(ld(Y, X), X)))
% 0.19/0.48 = { by axiom 3 (f02) }
% 0.19/0.48 mult(ld(Y, X), X)
% 0.19/0.48
% 0.19/0.48 Lemma 17: mult(ld(X, X), ld(X, X)) = ld(X, X).
% 0.19/0.48 Proof:
% 0.19/0.48 mult(ld(X, X), ld(X, X))
% 0.19/0.48 = { by axiom 3 (f02) R->L }
% 0.19/0.48 ld(mult(ld(X, X), X), mult(mult(ld(X, X), X), mult(ld(X, X), ld(X, X))))
% 0.19/0.48 = { by lemma 16 R->L }
% 0.19/0.48 ld(mult(ld(X, X), X), mult(ld(ld(X, X), X), mult(ld(X, X), ld(X, X))))
% 0.19/0.48 = { by lemma 10 }
% 0.19/0.48 ld(mult(ld(X, X), X), ld(ld(X, X), mult(X, ld(X, X))))
% 0.19/0.48 = { by axiom 1 (f01) }
% 0.19/0.48 ld(mult(ld(X, X), X), ld(ld(X, X), X))
% 0.19/0.48 = { by lemma 16 }
% 0.19/0.48 ld(mult(ld(X, X), X), mult(ld(X, X), X))
% 0.19/0.48 = { by lemma 14 }
% 0.19/0.48 ld(X, mult(ld(X, X), X))
% 0.19/0.48 = { by lemma 14 }
% 0.19/0.48 ld(X, X)
% 0.19/0.48
% 0.19/0.48 Lemma 18: ld(ld(X, X), ld(X, X)) = ld(X, X).
% 0.19/0.48 Proof:
% 0.19/0.48 ld(ld(X, X), ld(X, X))
% 0.19/0.48 = { by lemma 17 R->L }
% 0.19/0.48 ld(ld(X, X), mult(ld(X, X), ld(X, X)))
% 0.19/0.48 = { by axiom 3 (f02) }
% 0.19/0.48 ld(X, X)
% 0.19/0.48
% 0.19/0.48 Lemma 19: rd(mult(ld(X, X), Y), ld(X, X)) = mult(ld(X, X), mult(ld(X, X), Y)).
% 0.19/0.48 Proof:
% 0.19/0.48 rd(mult(ld(X, X), Y), ld(X, X))
% 0.19/0.48 = { by axiom 2 (f03) R->L }
% 0.19/0.48 mult(rd(rd(mult(ld(X, X), Y), ld(X, X)), ld(X, X)), ld(X, X))
% 0.19/0.48 = { by lemma 13 }
% 0.19/0.48 mult(mult(ld(X, X), rd(Y, mult(ld(X, X), ld(X, X)))), ld(X, X))
% 0.19/0.48 = { by lemma 17 }
% 0.19/0.48 mult(mult(ld(X, X), rd(Y, ld(X, X))), ld(X, X))
% 0.19/0.48 = { by lemma 8 }
% 0.19/0.48 mult(ld(X, X), mult(ld(ld(X, X), ld(X, X)), Y))
% 0.19/0.48 = { by lemma 18 }
% 0.19/0.48 mult(ld(X, X), mult(ld(X, X), Y))
% 0.19/0.49
% 0.19/0.49 Lemma 20: mult(ld(X, X), mult(mult(ld(X, X), Y), ld(X, X))) = Y.
% 0.19/0.49 Proof:
% 0.19/0.49 mult(ld(X, X), mult(mult(ld(X, X), Y), ld(X, X)))
% 0.19/0.49 = { by lemma 18 R->L }
% 0.19/0.49 mult(ld(ld(X, X), ld(X, X)), mult(mult(ld(X, X), Y), ld(X, X)))
% 0.19/0.49 = { by axiom 4 (f04) R->L }
% 0.19/0.49 mult(ld(ld(X, X), rd(mult(ld(X, X), mult(ld(X, X), Y)), mult(ld(X, X), Y))), mult(mult(ld(X, X), Y), ld(X, X)))
% 0.19/0.49 = { by lemma 19 R->L }
% 0.19/0.49 mult(ld(ld(X, X), rd(rd(mult(ld(X, X), Y), ld(X, X)), mult(ld(X, X), Y))), mult(mult(ld(X, X), Y), ld(X, X)))
% 0.19/0.49 = { by lemma 13 }
% 0.19/0.49 mult(ld(ld(X, X), mult(ld(X, X), rd(Y, mult(mult(ld(X, X), Y), ld(X, X))))), mult(mult(ld(X, X), Y), ld(X, X)))
% 0.19/0.49 = { by axiom 3 (f02) }
% 0.19/0.49 mult(rd(Y, mult(mult(ld(X, X), Y), ld(X, X))), mult(mult(ld(X, X), Y), ld(X, X)))
% 0.19/0.49 = { by axiom 2 (f03) }
% 0.19/0.49 Y
% 0.19/0.49
% 0.19/0.49 Goal 1 (goal): mult(ld(x1, x1), x0) = x0.
% 0.19/0.49 Proof:
% 0.19/0.49 mult(ld(x1, x1), x0)
% 0.19/0.49 = { by axiom 2 (f03) R->L }
% 0.19/0.49 mult(ld(x1, x1), mult(rd(x0, ld(x1, x1)), ld(x1, x1)))
% 0.19/0.49 = { by lemma 20 R->L }
% 0.19/0.49 mult(ld(x1, x1), mult(rd(mult(ld(x1, x1), mult(mult(ld(x1, x1), x0), ld(x1, x1))), ld(x1, x1)), ld(x1, x1)))
% 0.19/0.49 = { by lemma 12 }
% 0.19/0.49 mult(ld(x1, x1), mult(mult(mult(ld(x1, x1), mult(ld(x1, x1), x0)), rd(ld(x1, x1), ld(x1, x1))), ld(x1, x1)))
% 0.19/0.49 = { by lemma 15 R->L }
% 0.19/0.49 mult(ld(x1, x1), mult(mult(mult(ld(x1, x1), mult(ld(x1, x1), x0)), rd(ld(x1, x1), rd(x1, x1))), ld(x1, x1)))
% 0.19/0.49 = { by axiom 3 (f02) R->L }
% 0.19/0.49 mult(ld(x1, x1), mult(mult(mult(ld(x1, x1), mult(ld(x1, x1), x0)), ld(mult(rd(x1, x1), x1), mult(mult(rd(x1, x1), x1), rd(ld(x1, x1), rd(x1, x1))))), ld(x1, x1)))
% 0.19/0.49 = { by lemma 12 R->L }
% 0.19/0.49 mult(ld(x1, x1), mult(mult(mult(ld(x1, x1), mult(ld(x1, x1), x0)), ld(mult(rd(x1, x1), x1), rd(mult(rd(x1, x1), mult(x1, ld(x1, x1))), rd(x1, x1)))), ld(x1, x1)))
% 0.19/0.49 = { by axiom 1 (f01) }
% 0.19/0.49 mult(ld(x1, x1), mult(mult(mult(ld(x1, x1), mult(ld(x1, x1), x0)), ld(mult(rd(x1, x1), x1), rd(mult(rd(x1, x1), x1), rd(x1, x1)))), ld(x1, x1)))
% 0.19/0.49 = { by axiom 2 (f03) }
% 0.19/0.49 mult(ld(x1, x1), mult(mult(mult(ld(x1, x1), mult(ld(x1, x1), x0)), ld(x1, rd(mult(rd(x1, x1), x1), rd(x1, x1)))), ld(x1, x1)))
% 0.19/0.49 = { by axiom 2 (f03) }
% 0.19/0.49 mult(ld(x1, x1), mult(mult(mult(ld(x1, x1), mult(ld(x1, x1), x0)), ld(x1, rd(x1, rd(x1, x1)))), ld(x1, x1)))
% 0.19/0.49 = { by lemma 15 }
% 0.19/0.49 mult(ld(x1, x1), mult(mult(mult(ld(x1, x1), mult(ld(x1, x1), x0)), ld(x1, rd(x1, ld(x1, x1)))), ld(x1, x1)))
% 0.19/0.49 = { by lemma 6 }
% 0.19/0.49 mult(ld(x1, x1), mult(mult(mult(ld(x1, x1), mult(ld(x1, x1), x0)), ld(x1, x1)), ld(x1, x1)))
% 0.19/0.49 = { by lemma 19 R->L }
% 0.19/0.49 mult(ld(x1, x1), mult(mult(rd(mult(ld(x1, x1), x0), ld(x1, x1)), ld(x1, x1)), ld(x1, x1)))
% 0.19/0.49 = { by axiom 2 (f03) }
% 0.19/0.49 mult(ld(x1, x1), mult(mult(ld(x1, x1), x0), ld(x1, x1)))
% 0.19/0.49 = { by lemma 20 }
% 0.19/0.49 x0
% 0.19/0.49 % SZS output end Proof
% 0.19/0.49
% 0.19/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------