TSTP Solution File: GRP515-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP515-1 : TPTP v8.1.2. Released v2.6.0.
% 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 : n009.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 01:18:44 EDT 2023
% Result : Unsatisfiable 0.14s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP515-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 23:11:35 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.41 Command-line arguments: --no-flatten-goal
% 0.14/0.41
% 0.14/0.41 % SZS status Unsatisfiable
% 0.14/0.41
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 Axiom 1 (single_axiom): multiply(X, multiply(multiply(Y, Z), inverse(multiply(X, Z)))) = Y.
% 0.20/0.42
% 0.20/0.42 Lemma 2: multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z))))))) = W.
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z)))))))
% 0.20/0.43 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.43 multiply(X, multiply(multiply(W, multiply(multiply(Y, Z), inverse(multiply(W, Z)))), inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z)))))))
% 0.20/0.43 = { by axiom 1 (single_axiom) }
% 0.20/0.43 W
% 0.20/0.43
% 0.20/0.43 Lemma 3: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(X, multiply(Y, inverse(Y)))
% 0.20/0.43 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.43 multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(X, Z)))))))
% 0.20/0.43 = { by lemma 2 }
% 0.20/0.43 X
% 0.20/0.43
% 0.20/0.43 Lemma 4: multiply(X, multiply(Y, inverse(X))) = Y.
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(X, multiply(Y, inverse(X)))
% 0.20/0.43 = { by lemma 3 R->L }
% 0.20/0.43 multiply(X, multiply(Y, inverse(multiply(X, multiply(Z, inverse(Z))))))
% 0.20/0.43 = { by lemma 3 R->L }
% 0.20/0.43 multiply(X, multiply(multiply(Y, multiply(Z, inverse(Z))), inverse(multiply(X, multiply(Z, inverse(Z))))))
% 0.20/0.43 = { by axiom 1 (single_axiom) }
% 0.20/0.43 Y
% 0.20/0.43
% 0.20/0.43 Lemma 5: multiply(multiply(X, Y), multiply(Z, inverse(X))) = multiply(Z, Y).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(multiply(X, Y), multiply(Z, inverse(X)))
% 0.20/0.43 = { by lemma 2 R->L }
% 0.20/0.43 multiply(multiply(X, Y), multiply(Z, inverse(multiply(multiply(X, Y), multiply(multiply(Z, Y), inverse(multiply(multiply(X, Y), multiply(multiply(multiply(Z, Y), Y), inverse(multiply(X, Y))))))))))
% 0.20/0.43 = { by lemma 4 }
% 0.20/0.43 multiply(multiply(X, Y), multiply(Z, inverse(multiply(multiply(X, Y), multiply(multiply(Z, Y), inverse(multiply(multiply(Z, Y), Y)))))))
% 0.20/0.43 = { by lemma 2 }
% 0.20/0.43 multiply(Z, Y)
% 0.20/0.43
% 0.20/0.43 Lemma 6: multiply(X, multiply(Y, inverse(Z))) = multiply(Y, multiply(X, inverse(Z))).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(X, multiply(Y, inverse(Z)))
% 0.20/0.43 = { by lemma 5 R->L }
% 0.20/0.43 multiply(multiply(Z, multiply(Y, inverse(Z))), multiply(X, inverse(Z)))
% 0.20/0.43 = { by lemma 4 }
% 0.20/0.43 multiply(Y, multiply(X, inverse(Z)))
% 0.20/0.43
% 0.20/0.43 Lemma 7: multiply(multiply(X, Y), Z) = multiply(multiply(X, Z), Y).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(multiply(X, Y), Z)
% 0.20/0.43 = { by lemma 5 R->L }
% 0.20/0.43 multiply(multiply(X, Z), multiply(multiply(X, Y), inverse(X)))
% 0.20/0.43 = { by lemma 6 R->L }
% 0.20/0.43 multiply(multiply(X, Y), multiply(multiply(X, Z), inverse(X)))
% 0.20/0.43 = { by lemma 5 }
% 0.20/0.43 multiply(multiply(X, Z), Y)
% 0.20/0.43
% 0.20/0.43 Lemma 8: multiply(X, multiply(multiply(Y, inverse(X)), Z)) = multiply(Y, Z).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(X, multiply(multiply(Y, inverse(X)), Z))
% 0.20/0.43 = { by lemma 7 R->L }
% 0.20/0.43 multiply(X, multiply(multiply(Y, Z), inverse(X)))
% 0.20/0.43 = { by lemma 4 }
% 0.20/0.43 multiply(Y, Z)
% 0.20/0.43
% 0.20/0.43 Lemma 9: multiply(X, inverse(multiply(Y, inverse(Y)))) = X.
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(X, inverse(multiply(Y, inverse(Y))))
% 0.20/0.43 = { by lemma 8 R->L }
% 0.20/0.43 multiply(Y, multiply(multiply(X, inverse(Y)), inverse(multiply(Y, inverse(Y)))))
% 0.20/0.43 = { by axiom 1 (single_axiom) }
% 0.20/0.43 X
% 0.20/0.43
% 0.20/0.43 Lemma 10: multiply(Y, X) = multiply(X, Y).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(Y, X)
% 0.20/0.43 = { by lemma 9 R->L }
% 0.20/0.43 multiply(Y, multiply(X, inverse(multiply(Z, inverse(Z)))))
% 0.20/0.43 = { by lemma 6 }
% 0.20/0.43 multiply(X, multiply(Y, inverse(multiply(Z, inverse(Z)))))
% 0.20/0.43 = { by lemma 9 }
% 0.20/0.43 multiply(X, Y)
% 0.20/0.43
% 0.20/0.43 Lemma 11: multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z)))) = multiply(X, multiply(Y, inverse(W))).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z))))
% 0.20/0.43 = { by lemma 2 R->L }
% 0.20/0.43 multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, multiply(V, inverse(V))), inverse(multiply(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z)))), multiply(V, inverse(V)))))))))
% 0.20/0.43 = { by lemma 3 }
% 0.20/0.43 multiply(X, multiply(Y, inverse(multiply(X, multiply(Y, inverse(multiply(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z)))), multiply(V, inverse(V)))))))))
% 0.20/0.43 = { by lemma 3 }
% 0.20/0.43 multiply(X, multiply(Y, inverse(multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z))))))))))
% 0.20/0.43 = { by lemma 2 }
% 0.20/0.43 multiply(X, multiply(Y, inverse(W)))
% 0.20/0.43
% 0.20/0.43 Lemma 12: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(inverse(X), multiply(X, Y))
% 0.20/0.43 = { by lemma 10 }
% 0.20/0.43 multiply(inverse(X), multiply(Y, X))
% 0.20/0.43 = { by lemma 10 }
% 0.20/0.43 multiply(multiply(Y, X), inverse(X))
% 0.20/0.43 = { by lemma 7 R->L }
% 0.20/0.43 multiply(multiply(Y, inverse(X)), X)
% 0.20/0.43 = { by lemma 2 R->L }
% 0.20/0.43 multiply(multiply(Y, inverse(X)), multiply(Z, multiply(multiply(multiply(Y, inverse(X)), inverse(Z)), inverse(multiply(Z, multiply(multiply(multiply(multiply(Y, inverse(X)), inverse(Z)), W), inverse(multiply(X, W))))))))
% 0.20/0.43 = { by lemma 8 }
% 0.20/0.43 multiply(multiply(Y, inverse(X)), multiply(multiply(Y, inverse(X)), inverse(multiply(Z, multiply(multiply(multiply(multiply(Y, inverse(X)), inverse(Z)), W), inverse(multiply(X, W)))))))
% 0.20/0.43 = { by lemma 11 }
% 0.20/0.43 multiply(multiply(Y, inverse(X)), multiply(multiply(Y, inverse(X)), inverse(multiply(Z, multiply(multiply(multiply(Y, inverse(X)), inverse(Z)), inverse(X))))))
% 0.20/0.43 = { by lemma 8 }
% 0.20/0.43 multiply(multiply(Y, inverse(X)), multiply(multiply(Y, inverse(X)), inverse(multiply(multiply(Y, inverse(X)), inverse(X)))))
% 0.20/0.43 = { by axiom 1 (single_axiom) }
% 0.20/0.43 Y
% 0.20/0.43
% 0.20/0.43 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(multiply(a3, b3), c3)
% 0.20/0.43 = { by lemma 7 R->L }
% 0.20/0.43 multiply(multiply(a3, c3), b3)
% 0.20/0.43 = { by lemma 10 R->L }
% 0.20/0.43 multiply(b3, multiply(a3, c3))
% 0.20/0.43 = { by lemma 10 }
% 0.20/0.43 multiply(b3, multiply(c3, a3))
% 0.20/0.43 = { by lemma 5 R->L }
% 0.20/0.43 multiply(multiply(inverse(c3), multiply(c3, a3)), multiply(b3, inverse(inverse(c3))))
% 0.20/0.43 = { by lemma 12 }
% 0.20/0.43 multiply(a3, multiply(b3, inverse(inverse(c3))))
% 0.20/0.43 = { by lemma 12 R->L }
% 0.20/0.43 multiply(a3, multiply(b3, inverse(multiply(inverse(X), multiply(X, inverse(c3))))))
% 0.20/0.43 = { by lemma 11 R->L }
% 0.20/0.43 multiply(a3, multiply(b3, inverse(multiply(inverse(X), multiply(multiply(X, Y), inverse(multiply(c3, Y)))))))
% 0.20/0.43 = { by lemma 12 R->L }
% 0.20/0.43 multiply(a3, multiply(b3, multiply(inverse(X), multiply(X, inverse(multiply(inverse(X), multiply(multiply(X, Y), inverse(multiply(c3, Y)))))))))
% 0.20/0.43 = { by lemma 2 }
% 0.20/0.44 multiply(a3, multiply(b3, c3))
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44
% 0.20/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------