TSTP Solution File: GRP575-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP575-1 : 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 : n028.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 01:18:58 EDT 2023
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP575-1 : TPTP v8.1.2. Released v2.6.0.
% 0.10/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 01:03:25 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.44 Command-line arguments: --no-flatten-goal
% 0.19/0.44
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44
% 0.19/0.45 % SZS output start Proof
% 0.19/0.45 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.19/0.45 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.19/0.45 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.19/0.45 Axiom 4 (single_axiom): double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(Z, X)), double_divide(Z, identity))), double_divide(identity, identity)) = Y.
% 0.19/0.45
% 0.19/0.45 Lemma 5: double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(Z, X)), inverse(Z))), inverse(identity)) = Y.
% 0.19/0.45 Proof:
% 0.19/0.45 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(Z, X)), inverse(Z))), inverse(identity))
% 0.19/0.45 = { by axiom 1 (inverse) }
% 0.19/0.45 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(Z, X)), inverse(Z))), double_divide(identity, identity))
% 0.19/0.45 = { by axiom 1 (inverse) }
% 0.19/0.45 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(Z, X)), double_divide(Z, identity))), double_divide(identity, identity))
% 0.19/0.45 = { by axiom 4 (single_axiom) }
% 0.19/0.45 Y
% 0.19/0.45
% 0.19/0.45 Lemma 6: double_divide(double_divide(inverse(X), double_divide(inverse(Y), inverse(X))), inverse(identity)) = Y.
% 0.19/0.45 Proof:
% 0.19/0.45 double_divide(double_divide(inverse(X), double_divide(inverse(Y), inverse(X))), inverse(identity))
% 0.19/0.45 = { by axiom 1 (inverse) }
% 0.19/0.46 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, identity), inverse(X))), inverse(identity))
% 0.19/0.46 = { by axiom 2 (identity) }
% 0.19/0.46 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, double_divide(X, inverse(X))), inverse(X))), inverse(identity))
% 0.19/0.46 = { by lemma 5 }
% 0.19/0.46 Y
% 0.19/0.46
% 0.19/0.46 Lemma 7: double_divide(inverse(inverse(inverse(X))), inverse(identity)) = X.
% 0.19/0.46 Proof:
% 0.19/0.46 double_divide(inverse(inverse(inverse(X))), inverse(identity))
% 0.19/0.46 = { by axiom 1 (inverse) }
% 0.19/0.46 double_divide(double_divide(inverse(inverse(X)), identity), inverse(identity))
% 0.19/0.46 = { by axiom 2 (identity) }
% 0.19/0.46 double_divide(double_divide(inverse(inverse(X)), double_divide(inverse(X), inverse(inverse(X)))), inverse(identity))
% 0.19/0.46 = { by lemma 6 }
% 0.19/0.46 X
% 0.19/0.46
% 0.19/0.46 Lemma 8: double_divide(double_divide(inverse(identity), X), inverse(identity)) = inverse(inverse(X)).
% 0.19/0.46 Proof:
% 0.19/0.46 double_divide(double_divide(inverse(identity), X), inverse(identity))
% 0.19/0.46 = { by lemma 7 R->L }
% 0.19/0.46 double_divide(double_divide(inverse(identity), double_divide(inverse(inverse(inverse(X))), inverse(identity))), inverse(identity))
% 0.19/0.46 = { by lemma 6 }
% 0.19/0.46 inverse(inverse(X))
% 0.19/0.46
% 0.19/0.46 Lemma 9: inverse(identity) = identity.
% 0.19/0.46 Proof:
% 0.19/0.46 inverse(identity)
% 0.19/0.46 = { by lemma 7 R->L }
% 0.19/0.46 double_divide(inverse(inverse(inverse(inverse(identity)))), inverse(identity))
% 0.19/0.46 = { by lemma 8 R->L }
% 0.19/0.46 double_divide(double_divide(double_divide(inverse(identity), inverse(inverse(identity))), inverse(identity)), inverse(identity))
% 0.19/0.46 = { by axiom 2 (identity) R->L }
% 0.19/0.46 double_divide(double_divide(identity, inverse(identity)), inverse(identity))
% 0.19/0.46 = { by axiom 2 (identity) R->L }
% 0.19/0.46 double_divide(identity, inverse(identity))
% 0.19/0.46 = { by axiom 2 (identity) R->L }
% 0.19/0.46 identity
% 0.19/0.46
% 0.19/0.46 Lemma 10: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.19/0.46 Proof:
% 0.19/0.46 inverse(double_divide(X, Y))
% 0.19/0.46 = { by axiom 1 (inverse) }
% 0.19/0.46 double_divide(double_divide(X, Y), identity)
% 0.19/0.46 = { by axiom 3 (multiply) R->L }
% 0.19/0.46 multiply(Y, X)
% 0.19/0.46
% 0.19/0.46 Lemma 11: multiply(identity, X) = inverse(inverse(X)).
% 0.19/0.46 Proof:
% 0.19/0.46 multiply(identity, X)
% 0.19/0.46 = { by lemma 10 R->L }
% 0.19/0.46 inverse(double_divide(X, identity))
% 0.19/0.46 = { by axiom 1 (inverse) R->L }
% 0.19/0.46 inverse(inverse(X))
% 0.19/0.46
% 0.19/0.46 Lemma 12: inverse(inverse(inverse(inverse(X)))) = X.
% 0.19/0.46 Proof:
% 0.19/0.46 inverse(inverse(inverse(inverse(X))))
% 0.19/0.46 = { by lemma 11 R->L }
% 0.19/0.46 inverse(multiply(identity, inverse(X)))
% 0.19/0.46 = { by lemma 9 R->L }
% 0.19/0.46 inverse(multiply(inverse(identity), inverse(X)))
% 0.19/0.46 = { by lemma 10 R->L }
% 0.19/0.46 inverse(inverse(double_divide(inverse(X), inverse(identity))))
% 0.19/0.46 = { by lemma 8 R->L }
% 0.19/0.46 double_divide(double_divide(inverse(identity), double_divide(inverse(X), inverse(identity))), inverse(identity))
% 0.19/0.46 = { by lemma 6 }
% 0.19/0.46 X
% 0.19/0.46
% 0.19/0.46 Lemma 13: inverse(inverse(inverse(multiply(X, Y)))) = double_divide(Y, X).
% 0.19/0.46 Proof:
% 0.19/0.46 inverse(inverse(inverse(multiply(X, Y))))
% 0.19/0.46 = { by lemma 10 R->L }
% 0.19/0.46 inverse(inverse(inverse(inverse(double_divide(Y, X)))))
% 0.19/0.46 = { by lemma 12 }
% 0.19/0.46 double_divide(Y, X)
% 0.19/0.46
% 0.19/0.46 Lemma 14: double_divide(identity, X) = inverse(X).
% 0.19/0.46 Proof:
% 0.19/0.46 double_divide(identity, X)
% 0.19/0.46 = { by lemma 13 R->L }
% 0.19/0.46 inverse(inverse(inverse(multiply(X, identity))))
% 0.19/0.46 = { by lemma 10 R->L }
% 0.19/0.46 inverse(inverse(inverse(inverse(double_divide(identity, X)))))
% 0.19/0.46 = { by axiom 1 (inverse) }
% 0.19/0.46 inverse(inverse(inverse(double_divide(double_divide(identity, X), identity))))
% 0.19/0.46 = { by lemma 9 R->L }
% 0.19/0.46 inverse(inverse(inverse(double_divide(double_divide(identity, X), inverse(identity)))))
% 0.19/0.46 = { by lemma 9 R->L }
% 0.19/0.46 inverse(inverse(inverse(double_divide(double_divide(inverse(identity), X), inverse(identity)))))
% 0.19/0.46 = { by lemma 8 }
% 0.19/0.46 inverse(inverse(inverse(inverse(inverse(X)))))
% 0.19/0.46 = { by lemma 12 }
% 0.19/0.46 inverse(X)
% 0.19/0.46
% 0.19/0.46 Lemma 15: multiply(multiply(inverse(X), Y), X) = Y.
% 0.19/0.46 Proof:
% 0.19/0.46 multiply(multiply(inverse(X), Y), X)
% 0.19/0.46 = { by lemma 10 R->L }
% 0.19/0.46 inverse(double_divide(X, multiply(inverse(X), Y)))
% 0.19/0.46 = { by axiom 1 (inverse) }
% 0.19/0.46 double_divide(double_divide(X, multiply(inverse(X), Y)), identity)
% 0.19/0.46 = { by lemma 9 R->L }
% 0.19/0.46 double_divide(double_divide(X, multiply(inverse(X), Y)), inverse(identity))
% 0.19/0.46 = { by lemma 14 R->L }
% 0.19/0.46 double_divide(double_divide(X, multiply(double_divide(identity, X), Y)), inverse(identity))
% 0.19/0.46 = { by lemma 10 R->L }
% 0.19/0.46 double_divide(double_divide(X, inverse(double_divide(Y, double_divide(identity, X)))), inverse(identity))
% 0.19/0.46 = { by axiom 1 (inverse) }
% 0.19/0.46 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(identity, X)), identity)), inverse(identity))
% 0.19/0.46 = { by lemma 9 R->L }
% 0.19/0.46 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(identity, X)), inverse(identity))), inverse(identity))
% 0.19/0.46 = { by lemma 5 }
% 0.19/0.46 Y
% 0.19/0.46
% 0.19/0.46 Lemma 16: inverse(inverse(X)) = X.
% 0.19/0.46 Proof:
% 0.19/0.46 inverse(inverse(X))
% 0.19/0.46 = { by lemma 11 R->L }
% 0.19/0.46 multiply(identity, X)
% 0.19/0.46 = { by lemma 9 R->L }
% 0.19/0.46 multiply(inverse(identity), X)
% 0.19/0.46 = { by axiom 2 (identity) }
% 0.19/0.46 multiply(inverse(double_divide(X, inverse(X))), X)
% 0.19/0.46 = { by lemma 10 }
% 0.19/0.46 multiply(multiply(inverse(X), X), X)
% 0.19/0.46 = { by lemma 15 }
% 0.19/0.46 X
% 0.19/0.46
% 0.19/0.46 Lemma 17: multiply(X, Y) = multiply(Y, X).
% 0.19/0.46 Proof:
% 0.19/0.46 multiply(X, Y)
% 0.19/0.46 = { by lemma 10 R->L }
% 0.19/0.46 inverse(double_divide(Y, X))
% 0.19/0.46 = { by lemma 5 R->L }
% 0.19/0.46 double_divide(double_divide(X, double_divide(double_divide(inverse(double_divide(Y, X)), double_divide(Y, X)), inverse(Y))), inverse(identity))
% 0.19/0.46 = { by lemma 16 R->L }
% 0.19/0.46 double_divide(double_divide(X, double_divide(double_divide(inverse(double_divide(Y, X)), inverse(inverse(double_divide(Y, X)))), inverse(Y))), inverse(identity))
% 0.19/0.46 = { by axiom 2 (identity) R->L }
% 0.19/0.46 double_divide(double_divide(X, double_divide(identity, inverse(Y))), inverse(identity))
% 0.19/0.46 = { by lemma 14 }
% 0.19/0.46 double_divide(double_divide(X, inverse(inverse(Y))), inverse(identity))
% 0.19/0.46 = { by lemma 16 }
% 0.19/0.46 double_divide(double_divide(X, Y), inverse(identity))
% 0.19/0.46 = { by lemma 9 }
% 0.19/0.46 double_divide(double_divide(X, Y), identity)
% 0.19/0.46 = { by axiom 1 (inverse) R->L }
% 0.19/0.46 inverse(double_divide(X, Y))
% 0.19/0.46 = { by lemma 10 }
% 0.19/0.46 multiply(Y, X)
% 0.19/0.46
% 0.19/0.46 Lemma 18: multiply(double_divide(inverse(X), Y), Y) = X.
% 0.19/0.46 Proof:
% 0.19/0.46 multiply(double_divide(inverse(X), Y), Y)
% 0.19/0.46 = { by lemma 10 R->L }
% 0.19/0.46 inverse(double_divide(Y, double_divide(inverse(X), Y)))
% 0.19/0.46 = { by axiom 1 (inverse) }
% 0.19/0.46 double_divide(double_divide(Y, double_divide(inverse(X), Y)), identity)
% 0.19/0.46 = { by lemma 9 R->L }
% 0.19/0.46 double_divide(double_divide(Y, double_divide(inverse(X), Y)), inverse(identity))
% 0.19/0.46 = { by lemma 12 R->L }
% 0.19/0.46 double_divide(double_divide(Y, double_divide(inverse(X), inverse(inverse(inverse(inverse(Y)))))), inverse(identity))
% 0.19/0.46 = { by lemma 12 R->L }
% 0.19/0.46 double_divide(double_divide(inverse(inverse(inverse(inverse(Y)))), double_divide(inverse(X), inverse(inverse(inverse(inverse(Y)))))), inverse(identity))
% 0.19/0.46 = { by lemma 6 }
% 0.19/0.46 X
% 0.19/0.46
% 0.19/0.46 Lemma 19: double_divide(X, inverse(Y)) = multiply(Y, inverse(X)).
% 0.19/0.46 Proof:
% 0.19/0.46 double_divide(X, inverse(Y))
% 0.19/0.46 = { by lemma 16 R->L }
% 0.19/0.46 double_divide(X, inverse(inverse(inverse(Y))))
% 0.19/0.46 = { by lemma 18 R->L }
% 0.19/0.46 double_divide(X, multiply(double_divide(inverse(inverse(inverse(inverse(Y)))), inverse(X)), inverse(X)))
% 0.19/0.46 = { by lemma 12 }
% 0.19/0.46 double_divide(X, multiply(double_divide(Y, inverse(X)), inverse(X)))
% 0.19/0.46 = { by lemma 17 R->L }
% 0.19/0.46 double_divide(X, multiply(inverse(X), double_divide(Y, inverse(X))))
% 0.19/0.46 = { by lemma 13 R->L }
% 0.19/0.46 inverse(inverse(inverse(multiply(multiply(inverse(X), double_divide(Y, inverse(X))), X))))
% 0.19/0.46 = { by lemma 15 }
% 0.19/0.46 inverse(inverse(inverse(double_divide(Y, inverse(X)))))
% 0.19/0.46 = { by lemma 16 }
% 0.19/0.46 inverse(double_divide(Y, inverse(X)))
% 0.19/0.46 = { by lemma 10 }
% 0.19/0.46 multiply(inverse(X), Y)
% 0.19/0.46 = { by lemma 17 }
% 0.19/0.46 multiply(Y, inverse(X))
% 0.19/0.46
% 0.19/0.46 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.19/0.46 Proof:
% 0.19/0.46 multiply(multiply(a3, b3), c3)
% 0.19/0.46 = { by lemma 17 }
% 0.19/0.46 multiply(c3, multiply(a3, b3))
% 0.19/0.46 = { by lemma 10 R->L }
% 0.19/0.46 multiply(c3, inverse(double_divide(b3, a3)))
% 0.19/0.46 = { by lemma 19 R->L }
% 0.19/0.46 double_divide(double_divide(b3, a3), inverse(c3))
% 0.19/0.46 = { by lemma 13 R->L }
% 0.19/0.46 inverse(inverse(inverse(multiply(inverse(c3), double_divide(b3, a3)))))
% 0.19/0.46 = { by lemma 17 R->L }
% 0.19/0.46 inverse(inverse(inverse(multiply(double_divide(b3, a3), inverse(c3)))))
% 0.19/0.46 = { by lemma 10 R->L }
% 0.19/0.46 inverse(inverse(inverse(inverse(double_divide(inverse(c3), double_divide(b3, a3))))))
% 0.19/0.46 = { by lemma 16 }
% 0.19/0.46 inverse(inverse(double_divide(inverse(c3), double_divide(b3, a3))))
% 0.19/0.46 = { by lemma 16 }
% 0.19/0.46 double_divide(inverse(c3), double_divide(b3, a3))
% 0.19/0.46 = { by lemma 5 R->L }
% 0.19/0.46 double_divide(double_divide(a3, double_divide(double_divide(double_divide(inverse(c3), double_divide(b3, a3)), double_divide(b3, a3)), inverse(b3))), inverse(identity))
% 0.19/0.46 = { by lemma 9 }
% 0.19/0.46 double_divide(double_divide(a3, double_divide(double_divide(double_divide(inverse(c3), double_divide(b3, a3)), double_divide(b3, a3)), inverse(b3))), identity)
% 0.19/0.46 = { by axiom 1 (inverse) R->L }
% 0.19/0.46 inverse(double_divide(a3, double_divide(double_divide(double_divide(inverse(c3), double_divide(b3, a3)), double_divide(b3, a3)), inverse(b3))))
% 0.19/0.46 = { by lemma 10 }
% 0.19/0.46 multiply(double_divide(double_divide(double_divide(inverse(c3), double_divide(b3, a3)), double_divide(b3, a3)), inverse(b3)), a3)
% 0.19/0.46 = { by lemma 19 }
% 0.19/0.46 multiply(multiply(b3, inverse(double_divide(double_divide(inverse(c3), double_divide(b3, a3)), double_divide(b3, a3)))), a3)
% 0.19/0.46 = { by lemma 10 }
% 0.19/0.46 multiply(multiply(b3, multiply(double_divide(b3, a3), double_divide(inverse(c3), double_divide(b3, a3)))), a3)
% 0.19/0.46 = { by lemma 17 }
% 0.19/0.46 multiply(a3, multiply(b3, multiply(double_divide(b3, a3), double_divide(inverse(c3), double_divide(b3, a3)))))
% 0.19/0.46 = { by lemma 17 }
% 0.19/0.46 multiply(a3, multiply(b3, multiply(double_divide(inverse(c3), double_divide(b3, a3)), double_divide(b3, a3))))
% 0.19/0.46 = { by lemma 18 }
% 0.19/0.46 multiply(a3, multiply(b3, c3))
% 0.19/0.46 % SZS output end Proof
% 0.19/0.46
% 0.19/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------