TSTP Solution File: GRP513-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP513-1 : 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 01:18:43 EDT 2023
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP513-1 : TPTP v8.1.2. Released v2.6.0.
% 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 : n009.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 21:57:50 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.39 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.13/0.39
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 Axiom 1 (single_axiom): multiply(X, multiply(multiply(Y, Z), inverse(multiply(X, Z)))) = Y.
% 0.19/0.40
% 0.19/0.40 Lemma 2: multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z))))))) = W.
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z)))))))
% 0.19/0.40 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.40 multiply(X, multiply(multiply(W, multiply(multiply(Y, Z), inverse(multiply(W, Z)))), inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z)))))))
% 0.19/0.40 = { by axiom 1 (single_axiom) }
% 0.19/0.40 W
% 0.19/0.40
% 0.19/0.40 Lemma 3: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(X, multiply(Y, inverse(Y)))
% 0.19/0.40 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.40 multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(X, Z)))))))
% 0.19/0.40 = { by lemma 2 }
% 0.19/0.40 X
% 0.19/0.40
% 0.19/0.40 Lemma 4: multiply(X, multiply(multiply(Y, Z), inverse(Y))) = multiply(X, Z).
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(X, multiply(multiply(Y, Z), inverse(Y)))
% 0.19/0.40 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.40 multiply(X, multiply(multiply(Y, Z), inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(X, Z)))))))
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 multiply(X, multiply(multiply(Y, Z), inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(multiply(X, Z), multiply(W, inverse(W)))))))))
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 multiply(X, multiply(multiply(Y, Z), inverse(multiply(X, multiply(multiply(multiply(Y, Z), multiply(W, inverse(W))), inverse(multiply(multiply(X, Z), multiply(W, inverse(W)))))))))
% 0.19/0.40 = { by lemma 2 }
% 0.19/0.40 multiply(X, Z)
% 0.19/0.40
% 0.19/0.40 Lemma 5: multiply(X, multiply(Y, inverse(X))) = Y.
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(X, multiply(Y, inverse(X)))
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 multiply(X, multiply(Y, inverse(multiply(X, multiply(Z, inverse(Z))))))
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 multiply(X, multiply(multiply(Y, multiply(Z, inverse(Z))), inverse(multiply(X, multiply(Z, inverse(Z))))))
% 0.19/0.40 = { by axiom 1 (single_axiom) }
% 0.19/0.40 Y
% 0.19/0.40
% 0.19/0.40 Lemma 6: multiply(multiply(X, Y), multiply(Z, inverse(X))) = multiply(Z, Y).
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(multiply(X, Y), multiply(Z, inverse(X)))
% 0.19/0.40 = { by lemma 2 R->L }
% 0.19/0.40 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))))))))))
% 0.19/0.40 = { by lemma 5 }
% 0.19/0.40 multiply(multiply(X, Y), multiply(Z, inverse(multiply(multiply(X, Y), multiply(multiply(Z, Y), inverse(multiply(multiply(Z, Y), Y)))))))
% 0.19/0.40 = { by lemma 2 }
% 0.19/0.40 multiply(Z, Y)
% 0.19/0.40
% 0.19/0.40 Lemma 7: multiply(X, multiply(multiply(Y, inverse(X)), Z)) = multiply(Y, Z).
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(X, multiply(multiply(Y, inverse(X)), Z))
% 0.19/0.40 = { by lemma 4 R->L }
% 0.19/0.40 multiply(X, multiply(multiply(Y, inverse(X)), multiply(multiply(Y, Z), inverse(Y))))
% 0.19/0.40 = { by lemma 6 }
% 0.19/0.40 multiply(X, multiply(multiply(Y, Z), inverse(X)))
% 0.19/0.40 = { by lemma 5 }
% 0.19/0.40 multiply(Y, Z)
% 0.19/0.40
% 0.19/0.40 Lemma 8: multiply(X, inverse(multiply(Y, inverse(Y)))) = X.
% 0.19/0.40 Proof:
% 0.19/0.41 multiply(X, inverse(multiply(Y, inverse(Y))))
% 0.19/0.41 = { by lemma 7 R->L }
% 0.19/0.41 multiply(Y, multiply(multiply(X, inverse(Y)), inverse(multiply(Y, inverse(Y)))))
% 0.19/0.41 = { by axiom 1 (single_axiom) }
% 0.19/0.41 X
% 0.19/0.41
% 0.19/0.41 Lemma 9: multiply(Y, X) = multiply(X, Y).
% 0.19/0.41 Proof:
% 0.19/0.41 multiply(Y, X)
% 0.19/0.41 = { by lemma 8 R->L }
% 0.19/0.41 multiply(Y, multiply(X, inverse(multiply(Z, inverse(Z)))))
% 0.19/0.41 = { by lemma 6 R->L }
% 0.19/0.41 multiply(multiply(multiply(Z, inverse(Z)), multiply(X, inverse(multiply(Z, inverse(Z))))), multiply(Y, inverse(multiply(Z, inverse(Z)))))
% 0.19/0.41 = { by lemma 5 }
% 0.19/0.41 multiply(X, multiply(Y, inverse(multiply(Z, inverse(Z)))))
% 0.19/0.41 = { by lemma 8 }
% 0.19/0.41 multiply(X, Y)
% 0.19/0.41
% 0.19/0.41 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.19/0.41 Proof:
% 0.19/0.41 multiply(inverse(a1), a1)
% 0.19/0.41 = { by lemma 9 R->L }
% 0.19/0.41 multiply(a1, inverse(a1))
% 0.19/0.41 = { by lemma 7 R->L }
% 0.19/0.41 multiply(b1, multiply(multiply(a1, inverse(b1)), inverse(a1)))
% 0.19/0.41 = { by lemma 4 }
% 0.19/0.41 multiply(b1, inverse(b1))
% 0.19/0.41 = { by lemma 9 }
% 0.19/0.41 multiply(inverse(b1), b1)
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41
% 0.19/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------