TSTP Solution File: GRP567-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP567-1 : 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 : n003.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 01:18:56 EDT 2023
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP567-1 : TPTP v8.1.2. Released v2.6.0.
% 0.04/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.33 % Computer : n003.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon Aug 28 22:18:40 EDT 2023
% 0.14/0.33 % CPUTime :
% 0.20/0.42 Command-line arguments: --no-flatten-goal
% 0.20/0.42
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.20/0.45 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.20/0.45 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.20/0.45 Axiom 4 (single_axiom): double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(identity, Z))), double_divide(identity, identity)) = Y.
% 0.20/0.45
% 0.20/0.45 Lemma 5: double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(identity, Z))), inverse(identity)) = Y.
% 0.20/0.45 Proof:
% 0.20/0.45 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(identity, Z))), inverse(identity))
% 0.20/0.45 = { by axiom 1 (inverse) }
% 0.20/0.45 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(identity, Z))), double_divide(identity, identity))
% 0.20/0.45 = { by axiom 4 (single_axiom) }
% 0.20/0.45 Y
% 0.20/0.45
% 0.20/0.45 Lemma 6: double_divide(double_divide(X, double_divide(double_divide(Y, inverse(X)), inverse(identity))), inverse(identity)) = Y.
% 0.20/0.45 Proof:
% 0.20/0.45 double_divide(double_divide(X, double_divide(double_divide(Y, inverse(X)), inverse(identity))), inverse(identity))
% 0.20/0.45 = { by axiom 1 (inverse) }
% 0.20/0.45 double_divide(double_divide(X, double_divide(double_divide(Y, inverse(X)), double_divide(identity, identity))), inverse(identity))
% 0.20/0.45 = { by axiom 1 (inverse) }
% 0.20/0.45 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, identity)), double_divide(identity, identity))), inverse(identity))
% 0.20/0.45 = { by lemma 5 }
% 0.20/0.45 Y
% 0.20/0.45
% 0.20/0.45 Lemma 7: double_divide(inverse(X), inverse(identity)) = X.
% 0.20/0.45 Proof:
% 0.20/0.45 double_divide(inverse(X), inverse(identity))
% 0.20/0.45 = { by axiom 1 (inverse) }
% 0.20/0.45 double_divide(double_divide(X, identity), inverse(identity))
% 0.20/0.45 = { by axiom 2 (identity) }
% 0.20/0.45 double_divide(double_divide(X, double_divide(identity, inverse(identity))), inverse(identity))
% 0.20/0.45 = { by axiom 2 (identity) }
% 0.20/0.45 double_divide(double_divide(X, double_divide(double_divide(X, inverse(X)), inverse(identity))), inverse(identity))
% 0.20/0.45 = { by lemma 6 }
% 0.20/0.45 X
% 0.20/0.45
% 0.20/0.45 Lemma 8: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.20/0.45 Proof:
% 0.20/0.45 inverse(double_divide(X, Y))
% 0.20/0.45 = { by axiom 1 (inverse) }
% 0.20/0.45 double_divide(double_divide(X, Y), identity)
% 0.20/0.45 = { by axiom 3 (multiply) R->L }
% 0.20/0.45 multiply(Y, X)
% 0.20/0.45
% 0.20/0.45 Lemma 9: multiply(identity, X) = inverse(inverse(X)).
% 0.20/0.45 Proof:
% 0.20/0.45 multiply(identity, X)
% 0.20/0.45 = { by lemma 8 R->L }
% 0.20/0.45 inverse(double_divide(X, identity))
% 0.20/0.45 = { by axiom 1 (inverse) R->L }
% 0.20/0.45 inverse(inverse(X))
% 0.20/0.45
% 0.20/0.45 Lemma 10: double_divide(double_divide(X, multiply(double_divide(X, inverse(identity)), Y)), inverse(identity)) = Y.
% 0.20/0.45 Proof:
% 0.20/0.45 double_divide(double_divide(X, multiply(double_divide(X, inverse(identity)), Y)), inverse(identity))
% 0.20/0.45 = { by lemma 8 R->L }
% 0.20/0.45 double_divide(double_divide(X, inverse(double_divide(Y, double_divide(X, inverse(identity))))), inverse(identity))
% 0.20/0.45 = { by axiom 1 (inverse) }
% 0.20/0.45 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, inverse(identity))), identity)), inverse(identity))
% 0.20/0.45 = { by axiom 2 (identity) }
% 0.20/0.45 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, inverse(identity))), double_divide(identity, inverse(identity)))), inverse(identity))
% 0.20/0.45 = { by lemma 5 }
% 0.20/0.45 Y
% 0.20/0.45
% 0.20/0.45 Lemma 11: double_divide(double_divide(identity, inverse(inverse(X))), inverse(identity)) = X.
% 0.20/0.45 Proof:
% 0.20/0.45 double_divide(double_divide(identity, inverse(inverse(X))), inverse(identity))
% 0.20/0.45 = { by lemma 9 R->L }
% 0.20/0.45 double_divide(double_divide(identity, multiply(identity, X)), inverse(identity))
% 0.20/0.45 = { by axiom 2 (identity) }
% 0.20/0.45 double_divide(double_divide(identity, multiply(double_divide(identity, inverse(identity)), X)), inverse(identity))
% 0.20/0.45 = { by lemma 10 }
% 0.20/0.45 X
% 0.20/0.45
% 0.20/0.45 Lemma 12: double_divide(double_divide(inverse(X), X), inverse(identity)) = identity.
% 0.20/0.45 Proof:
% 0.20/0.45 double_divide(double_divide(inverse(X), X), inverse(identity))
% 0.20/0.45 = { by lemma 11 R->L }
% 0.20/0.45 double_divide(double_divide(inverse(X), double_divide(double_divide(identity, inverse(inverse(X))), inverse(identity))), inverse(identity))
% 0.20/0.45 = { by lemma 6 }
% 0.20/0.45 identity
% 0.20/0.45
% 0.20/0.45 Lemma 13: inverse(identity) = identity.
% 0.20/0.45 Proof:
% 0.20/0.45 inverse(identity)
% 0.20/0.45 = { by lemma 7 R->L }
% 0.20/0.45 double_divide(inverse(inverse(identity)), inverse(identity))
% 0.20/0.45 = { by axiom 1 (inverse) }
% 0.20/0.45 double_divide(double_divide(inverse(identity), identity), inverse(identity))
% 0.20/0.45 = { by lemma 12 }
% 0.20/0.45 identity
% 0.20/0.45
% 0.20/0.45 Lemma 14: inverse(inverse(X)) = X.
% 0.20/0.45 Proof:
% 0.20/0.45 inverse(inverse(X))
% 0.20/0.45 = { by lemma 6 R->L }
% 0.20/0.45 double_divide(double_divide(X, double_divide(double_divide(inverse(inverse(X)), inverse(X)), inverse(identity))), inverse(identity))
% 0.20/0.45 = { by lemma 12 }
% 0.20/0.45 double_divide(double_divide(X, identity), inverse(identity))
% 0.20/0.45 = { by axiom 1 (inverse) R->L }
% 0.20/0.45 double_divide(inverse(X), inverse(identity))
% 0.20/0.45 = { by lemma 7 }
% 0.20/0.45 X
% 0.20/0.45
% 0.20/0.45 Lemma 15: double_divide(identity, X) = inverse(X).
% 0.20/0.45 Proof:
% 0.20/0.45 double_divide(identity, X)
% 0.20/0.45 = { by lemma 14 R->L }
% 0.20/0.45 inverse(inverse(double_divide(identity, X)))
% 0.20/0.45 = { by lemma 9 R->L }
% 0.20/0.45 multiply(identity, double_divide(identity, X))
% 0.20/0.45 = { by lemma 13 R->L }
% 0.20/0.45 multiply(inverse(identity), double_divide(identity, X))
% 0.20/0.45 = { by lemma 14 R->L }
% 0.20/0.45 multiply(inverse(identity), double_divide(identity, inverse(inverse(X))))
% 0.20/0.45 = { by lemma 8 R->L }
% 0.20/0.45 inverse(double_divide(double_divide(identity, inverse(inverse(X))), inverse(identity)))
% 0.20/0.45 = { by lemma 11 }
% 0.20/0.45 inverse(X)
% 0.20/0.45
% 0.20/0.45 Lemma 16: inverse(multiply(X, Y)) = double_divide(Y, X).
% 0.20/0.45 Proof:
% 0.20/0.45 inverse(multiply(X, Y))
% 0.20/0.45 = { by axiom 1 (inverse) }
% 0.20/0.45 double_divide(multiply(X, Y), identity)
% 0.20/0.45 = { by lemma 13 R->L }
% 0.20/0.45 double_divide(multiply(X, Y), inverse(identity))
% 0.20/0.45 = { by lemma 8 R->L }
% 0.20/0.45 double_divide(inverse(double_divide(Y, X)), inverse(identity))
% 0.20/0.45 = { by lemma 7 }
% 0.20/0.45 double_divide(Y, X)
% 0.20/0.45
% 0.20/0.45 Lemma 17: multiply(multiply(X, Y), inverse(X)) = Y.
% 0.20/0.45 Proof:
% 0.20/0.45 multiply(multiply(X, Y), inverse(X))
% 0.20/0.45 = { by lemma 8 R->L }
% 0.20/0.45 multiply(inverse(double_divide(Y, X)), inverse(X))
% 0.20/0.45 = { by axiom 1 (inverse) }
% 0.20/0.45 multiply(double_divide(double_divide(Y, X), identity), inverse(X))
% 0.20/0.45 = { by lemma 8 R->L }
% 0.20/0.45 inverse(double_divide(inverse(X), double_divide(double_divide(Y, X), identity)))
% 0.20/0.45 = { by axiom 1 (inverse) }
% 0.20/0.45 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, X), identity)), identity)
% 0.20/0.45 = { by lemma 13 R->L }
% 0.20/0.45 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, X), inverse(identity))), identity)
% 0.20/0.45 = { by lemma 13 R->L }
% 0.20/0.45 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, X), inverse(identity))), inverse(identity))
% 0.20/0.45 = { by lemma 14 R->L }
% 0.20/0.45 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, inverse(inverse(X))), inverse(identity))), inverse(identity))
% 0.20/0.45 = { by lemma 6 }
% 0.20/0.45 Y
% 0.20/0.45
% 0.20/0.45 Lemma 18: multiply(X, double_divide(X, Y)) = inverse(Y).
% 0.20/0.45 Proof:
% 0.20/0.45 multiply(X, double_divide(X, Y))
% 0.20/0.45 = { by lemma 16 R->L }
% 0.20/0.45 multiply(X, inverse(multiply(Y, X)))
% 0.20/0.45 = { by lemma 17 R->L }
% 0.20/0.45 multiply(multiply(multiply(Y, X), inverse(Y)), inverse(multiply(Y, X)))
% 0.20/0.45 = { by lemma 17 }
% 0.20/0.45 inverse(Y)
% 0.20/0.45
% 0.20/0.45 Lemma 19: double_divide(X, inverse(Y)) = multiply(Y, inverse(X)).
% 0.20/0.45 Proof:
% 0.20/0.45 double_divide(X, inverse(Y))
% 0.20/0.45 = { by lemma 14 R->L }
% 0.20/0.45 inverse(inverse(double_divide(X, inverse(Y))))
% 0.20/0.45 = { by lemma 9 R->L }
% 0.20/0.45 multiply(identity, double_divide(X, inverse(Y)))
% 0.20/0.46 = { by lemma 13 R->L }
% 0.20/0.46 multiply(inverse(identity), double_divide(X, inverse(Y)))
% 0.20/0.46 = { by lemma 18 R->L }
% 0.20/0.46 multiply(inverse(identity), double_divide(X, multiply(double_divide(X, inverse(identity)), double_divide(double_divide(X, inverse(identity)), Y))))
% 0.20/0.46 = { by lemma 8 R->L }
% 0.20/0.46 inverse(double_divide(double_divide(X, multiply(double_divide(X, inverse(identity)), double_divide(double_divide(X, inverse(identity)), Y))), inverse(identity)))
% 0.20/0.46 = { by lemma 10 }
% 0.20/0.46 inverse(double_divide(double_divide(X, inverse(identity)), Y))
% 0.20/0.46 = { by lemma 8 }
% 0.20/0.46 multiply(Y, double_divide(X, inverse(identity)))
% 0.20/0.46 = { by lemma 13 }
% 0.20/0.46 multiply(Y, double_divide(X, identity))
% 0.20/0.46 = { by axiom 1 (inverse) R->L }
% 0.20/0.46 multiply(Y, inverse(X))
% 0.20/0.46
% 0.20/0.46 Lemma 20: multiply(Y, X) = multiply(X, Y).
% 0.20/0.46 Proof:
% 0.20/0.46 multiply(Y, X)
% 0.20/0.46 = { by lemma 8 R->L }
% 0.20/0.46 inverse(double_divide(X, Y))
% 0.20/0.46 = { by lemma 14 R->L }
% 0.20/0.46 inverse(inverse(inverse(double_divide(X, Y))))
% 0.20/0.46 = { by lemma 9 R->L }
% 0.20/0.46 multiply(identity, inverse(double_divide(X, Y)))
% 0.20/0.46 = { by lemma 19 R->L }
% 0.20/0.46 double_divide(double_divide(X, Y), inverse(identity))
% 0.20/0.46 = { by lemma 5 R->L }
% 0.20/0.46 double_divide(double_divide(X, double_divide(double_divide(identity, double_divide(double_divide(Y, double_divide(identity, double_divide(X, inverse(identity)))), double_divide(identity, double_divide(X, inverse(identity))))), inverse(identity))), inverse(identity))
% 0.20/0.46 = { by lemma 15 }
% 0.20/0.46 double_divide(double_divide(X, double_divide(inverse(double_divide(double_divide(Y, double_divide(identity, double_divide(X, inverse(identity)))), double_divide(identity, double_divide(X, inverse(identity))))), inverse(identity))), inverse(identity))
% 0.20/0.46 = { by lemma 7 }
% 0.20/0.46 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(identity, double_divide(X, inverse(identity)))), double_divide(identity, double_divide(X, inverse(identity))))), inverse(identity))
% 0.20/0.46 = { by lemma 15 }
% 0.20/0.46 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(identity, double_divide(X, inverse(identity)))), inverse(double_divide(X, inverse(identity))))), inverse(identity))
% 0.20/0.46 = { by lemma 15 }
% 0.20/0.46 double_divide(double_divide(X, double_divide(double_divide(Y, inverse(double_divide(X, inverse(identity)))), inverse(double_divide(X, inverse(identity))))), inverse(identity))
% 0.20/0.46 = { by lemma 19 }
% 0.20/0.46 double_divide(double_divide(X, multiply(double_divide(X, inverse(identity)), inverse(double_divide(Y, inverse(double_divide(X, inverse(identity))))))), inverse(identity))
% 0.20/0.46 = { by lemma 8 }
% 0.20/0.46 double_divide(double_divide(X, multiply(double_divide(X, inverse(identity)), multiply(inverse(double_divide(X, inverse(identity))), Y))), inverse(identity))
% 0.20/0.46 = { by lemma 10 }
% 0.20/0.46 multiply(inverse(double_divide(X, inverse(identity))), Y)
% 0.20/0.46 = { by lemma 8 }
% 0.20/0.46 multiply(multiply(inverse(identity), X), Y)
% 0.20/0.46 = { by lemma 13 }
% 0.20/0.46 multiply(multiply(identity, X), Y)
% 0.20/0.46 = { by lemma 9 }
% 0.20/0.46 multiply(inverse(inverse(X)), Y)
% 0.20/0.46 = { by lemma 14 }
% 0.20/0.46 multiply(X, Y)
% 0.20/0.46
% 0.20/0.46 Lemma 21: double_divide(double_divide(identity, inverse(multiply(X, Y))), inverse(identity)) = double_divide(Y, X).
% 0.20/0.46 Proof:
% 0.20/0.46 double_divide(double_divide(identity, inverse(multiply(X, Y))), inverse(identity))
% 0.20/0.46 = { by lemma 8 R->L }
% 0.20/0.46 double_divide(double_divide(identity, inverse(inverse(double_divide(Y, X)))), inverse(identity))
% 0.20/0.46 = { by lemma 11 }
% 0.20/0.46 double_divide(Y, X)
% 0.20/0.46
% 0.20/0.46 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.20/0.46 Proof:
% 0.20/0.46 multiply(multiply(a3, b3), c3)
% 0.20/0.46 = { by lemma 20 R->L }
% 0.20/0.46 multiply(c3, multiply(a3, b3))
% 0.20/0.46 = { by lemma 20 }
% 0.20/0.46 multiply(c3, multiply(b3, a3))
% 0.20/0.46 = { by lemma 20 }
% 0.20/0.46 multiply(multiply(b3, a3), c3)
% 0.20/0.46 = { by lemma 8 R->L }
% 0.20/0.46 multiply(inverse(double_divide(a3, b3)), c3)
% 0.20/0.46 = { by lemma 8 R->L }
% 0.20/0.46 inverse(double_divide(c3, inverse(double_divide(a3, b3))))
% 0.20/0.46 = { by axiom 1 (inverse) }
% 0.20/0.46 double_divide(double_divide(c3, inverse(double_divide(a3, b3))), identity)
% 0.20/0.46 = { by lemma 13 R->L }
% 0.20/0.46 double_divide(double_divide(c3, inverse(double_divide(a3, b3))), inverse(identity))
% 0.20/0.46 = { by lemma 18 R->L }
% 0.20/0.46 double_divide(double_divide(c3, multiply(double_divide(c3, inverse(identity)), double_divide(double_divide(c3, inverse(identity)), double_divide(a3, b3)))), inverse(identity))
% 0.20/0.46 = { by lemma 10 }
% 0.20/0.46 double_divide(double_divide(c3, inverse(identity)), double_divide(a3, b3))
% 0.20/0.46 = { by lemma 13 }
% 0.20/0.46 double_divide(double_divide(c3, identity), double_divide(a3, b3))
% 0.20/0.46 = { by axiom 1 (inverse) R->L }
% 0.20/0.46 double_divide(inverse(c3), double_divide(a3, b3))
% 0.20/0.46 = { by lemma 16 R->L }
% 0.20/0.46 inverse(multiply(double_divide(a3, b3), inverse(c3)))
% 0.20/0.46 = { by lemma 11 R->L }
% 0.20/0.46 double_divide(double_divide(identity, inverse(inverse(inverse(multiply(double_divide(a3, b3), inverse(c3)))))), inverse(identity))
% 0.20/0.46 = { by lemma 14 }
% 0.20/0.46 double_divide(double_divide(identity, inverse(multiply(double_divide(a3, b3), inverse(c3)))), inverse(identity))
% 0.20/0.46 = { by lemma 20 }
% 0.20/0.46 double_divide(double_divide(identity, inverse(multiply(inverse(c3), double_divide(a3, b3)))), inverse(identity))
% 0.20/0.46 = { by lemma 21 }
% 0.20/0.46 double_divide(double_divide(a3, b3), inverse(c3))
% 0.20/0.46 = { by lemma 5 R->L }
% 0.20/0.46 double_divide(double_divide(a3, double_divide(double_divide(double_divide(double_divide(a3, b3), inverse(c3)), double_divide(a3, b3)), double_divide(identity, b3))), inverse(identity))
% 0.20/0.46 = { by lemma 21 R->L }
% 0.20/0.46 double_divide(double_divide(a3, double_divide(double_divide(double_divide(identity, inverse(multiply(double_divide(a3, b3), double_divide(double_divide(a3, b3), inverse(c3))))), inverse(identity)), double_divide(identity, b3))), inverse(identity))
% 0.20/0.46 = { by lemma 18 }
% 0.20/0.46 double_divide(double_divide(a3, double_divide(double_divide(double_divide(identity, inverse(inverse(inverse(c3)))), inverse(identity)), double_divide(identity, b3))), inverse(identity))
% 0.20/0.46 = { by lemma 11 }
% 0.20/0.46 double_divide(double_divide(a3, double_divide(inverse(c3), double_divide(identity, b3))), inverse(identity))
% 0.20/0.46 = { by lemma 19 }
% 0.20/0.46 multiply(identity, inverse(double_divide(a3, double_divide(inverse(c3), double_divide(identity, b3)))))
% 0.20/0.46 = { by lemma 9 }
% 0.20/0.46 inverse(inverse(inverse(double_divide(a3, double_divide(inverse(c3), double_divide(identity, b3))))))
% 0.20/0.46 = { by lemma 14 }
% 0.20/0.46 inverse(double_divide(a3, double_divide(inverse(c3), double_divide(identity, b3))))
% 0.20/0.46 = { by lemma 8 }
% 0.20/0.46 multiply(double_divide(inverse(c3), double_divide(identity, b3)), a3)
% 0.20/0.46 = { by lemma 15 }
% 0.20/0.46 multiply(double_divide(inverse(c3), inverse(b3)), a3)
% 0.20/0.46 = { by lemma 19 }
% 0.20/0.46 multiply(multiply(b3, inverse(inverse(c3))), a3)
% 0.20/0.46 = { by lemma 20 R->L }
% 0.20/0.46 multiply(a3, multiply(b3, inverse(inverse(c3))))
% 0.20/0.46 = { by lemma 14 }
% 0.20/0.46 multiply(a3, multiply(b3, c3))
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46
% 0.20/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------