TSTP Solution File: GRP571-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP571-1 : 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 : n026.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 01:18:57 EDT 2023
% Result : Unsatisfiable 0.22s 0.43s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP571-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n026.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Aug 28 21:35:05 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.43 Command-line arguments: --no-flatten-goal
% 0.22/0.43
% 0.22/0.43 % SZS status Unsatisfiable
% 0.22/0.43
% 0.22/0.46 % SZS output start Proof
% 0.22/0.46 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.22/0.46 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.22/0.46 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.22/0.46 Axiom 4 (single_axiom): double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(Z, identity))), double_divide(identity, identity)) = Y.
% 0.22/0.46
% 0.22/0.46 Lemma 5: double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), inverse(Z))), inverse(identity)) = Y.
% 0.22/0.46 Proof:
% 0.22/0.46 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), inverse(Z))), inverse(identity))
% 0.22/0.46 = { by axiom 1 (inverse) }
% 0.22/0.46 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), inverse(Z))), double_divide(identity, identity))
% 0.22/0.46 = { by axiom 1 (inverse) }
% 0.22/0.46 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(Z, identity))), double_divide(identity, identity))
% 0.22/0.46 = { by axiom 4 (single_axiom) }
% 0.22/0.46 Y
% 0.22/0.46
% 0.22/0.46 Lemma 6: double_divide(double_divide(X, double_divide(double_divide(Y, inverse(X)), inverse(identity))), inverse(identity)) = Y.
% 0.22/0.46 Proof:
% 0.22/0.46 double_divide(double_divide(X, double_divide(double_divide(Y, inverse(X)), inverse(identity))), inverse(identity))
% 0.22/0.46 = { by axiom 1 (inverse) }
% 0.22/0.46 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, identity)), inverse(identity))), inverse(identity))
% 0.22/0.46 = { by lemma 5 }
% 0.22/0.46 Y
% 0.22/0.46
% 0.22/0.46 Lemma 7: double_divide(inverse(X), inverse(identity)) = X.
% 0.22/0.46 Proof:
% 0.22/0.46 double_divide(inverse(X), inverse(identity))
% 0.22/0.46 = { by axiom 1 (inverse) }
% 0.22/0.46 double_divide(double_divide(X, identity), inverse(identity))
% 0.22/0.46 = { by axiom 2 (identity) }
% 0.22/0.46 double_divide(double_divide(X, double_divide(identity, inverse(identity))), inverse(identity))
% 0.22/0.46 = { by axiom 2 (identity) }
% 0.22/0.46 double_divide(double_divide(X, double_divide(double_divide(X, inverse(X)), inverse(identity))), inverse(identity))
% 0.22/0.46 = { by lemma 6 }
% 0.22/0.46 X
% 0.22/0.46
% 0.22/0.46 Lemma 8: double_divide(double_divide(identity, double_divide(X, inverse(identity))), inverse(identity)) = inverse(X).
% 0.22/0.46 Proof:
% 0.22/0.46 double_divide(double_divide(identity, double_divide(X, inverse(identity))), inverse(identity))
% 0.22/0.46 = { by lemma 7 R->L }
% 0.22/0.46 double_divide(double_divide(identity, double_divide(double_divide(inverse(X), inverse(identity)), inverse(identity))), inverse(identity))
% 0.22/0.46 = { by lemma 6 }
% 0.22/0.46 inverse(X)
% 0.22/0.46
% 0.22/0.46 Lemma 9: inverse(identity) = identity.
% 0.22/0.46 Proof:
% 0.22/0.46 inverse(identity)
% 0.22/0.46 = { by lemma 8 R->L }
% 0.22/0.46 double_divide(double_divide(identity, double_divide(identity, inverse(identity))), inverse(identity))
% 0.22/0.46 = { by axiom 2 (identity) R->L }
% 0.22/0.46 double_divide(double_divide(identity, identity), inverse(identity))
% 0.22/0.46 = { by axiom 1 (inverse) R->L }
% 0.22/0.46 double_divide(inverse(identity), inverse(identity))
% 0.22/0.46 = { by lemma 7 }
% 0.22/0.46 identity
% 0.22/0.46
% 0.22/0.46 Lemma 10: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.22/0.46 Proof:
% 0.22/0.46 inverse(double_divide(X, Y))
% 0.22/0.46 = { by axiom 1 (inverse) }
% 0.22/0.46 double_divide(double_divide(X, Y), identity)
% 0.22/0.46 = { by axiom 3 (multiply) R->L }
% 0.22/0.46 multiply(Y, X)
% 0.22/0.46
% 0.22/0.46 Lemma 11: double_divide(multiply(X, Y), inverse(identity)) = double_divide(Y, X).
% 0.22/0.46 Proof:
% 0.22/0.46 double_divide(multiply(X, Y), inverse(identity))
% 0.22/0.46 = { by lemma 10 R->L }
% 0.22/0.46 double_divide(inverse(double_divide(Y, X)), inverse(identity))
% 0.22/0.46 = { by lemma 7 }
% 0.22/0.46 double_divide(Y, X)
% 0.22/0.46
% 0.22/0.46 Lemma 12: inverse(multiply(X, Y)) = double_divide(Y, X).
% 0.22/0.46 Proof:
% 0.22/0.46 inverse(multiply(X, Y))
% 0.22/0.46 = { by axiom 1 (inverse) }
% 0.22/0.46 double_divide(multiply(X, Y), identity)
% 0.22/0.46 = { by lemma 9 R->L }
% 0.22/0.46 double_divide(multiply(X, Y), inverse(identity))
% 0.22/0.46 = { by lemma 11 }
% 0.22/0.46 double_divide(Y, X)
% 0.22/0.46
% 0.22/0.46 Lemma 13: multiply(identity, X) = inverse(inverse(X)).
% 0.22/0.46 Proof:
% 0.22/0.46 multiply(identity, X)
% 0.22/0.46 = { by lemma 10 R->L }
% 0.22/0.46 inverse(double_divide(X, identity))
% 0.22/0.46 = { by axiom 1 (inverse) R->L }
% 0.22/0.46 inverse(inverse(X))
% 0.22/0.46
% 0.22/0.46 Lemma 14: inverse(inverse(X)) = X.
% 0.22/0.46 Proof:
% 0.22/0.46 inverse(inverse(X))
% 0.22/0.46 = { by lemma 13 R->L }
% 0.22/0.46 multiply(identity, X)
% 0.22/0.46 = { by lemma 10 R->L }
% 0.22/0.46 inverse(double_divide(X, identity))
% 0.22/0.46 = { by lemma 8 R->L }
% 0.22/0.46 double_divide(double_divide(identity, double_divide(double_divide(X, identity), inverse(identity))), inverse(identity))
% 0.22/0.46 = { by lemma 9 R->L }
% 0.22/0.46 double_divide(double_divide(identity, double_divide(double_divide(X, inverse(identity)), inverse(identity))), inverse(identity))
% 0.22/0.46 = { by lemma 6 }
% 0.22/0.46 X
% 0.22/0.46
% 0.22/0.46 Lemma 15: multiply(multiply(X, Y), inverse(X)) = Y.
% 0.22/0.46 Proof:
% 0.22/0.47 multiply(multiply(X, Y), inverse(X))
% 0.22/0.47 = { by lemma 10 R->L }
% 0.22/0.47 multiply(inverse(double_divide(Y, X)), inverse(X))
% 0.22/0.47 = { by axiom 1 (inverse) }
% 0.22/0.47 multiply(double_divide(double_divide(Y, X), identity), inverse(X))
% 0.22/0.47 = { by lemma 10 R->L }
% 0.22/0.47 inverse(double_divide(inverse(X), double_divide(double_divide(Y, X), identity)))
% 0.22/0.47 = { by axiom 1 (inverse) }
% 0.22/0.47 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, X), identity)), identity)
% 0.22/0.47 = { by lemma 9 R->L }
% 0.22/0.47 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, X), inverse(identity))), identity)
% 0.22/0.47 = { by lemma 9 R->L }
% 0.22/0.47 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, X), inverse(identity))), inverse(identity))
% 0.22/0.47 = { by lemma 14 R->L }
% 0.22/0.47 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, inverse(inverse(X))), inverse(identity))), inverse(identity))
% 0.22/0.47 = { by lemma 6 }
% 0.22/0.47 Y
% 0.22/0.47
% 0.22/0.47 Lemma 16: multiply(X, double_divide(X, Y)) = inverse(Y).
% 0.22/0.47 Proof:
% 0.22/0.47 multiply(X, double_divide(X, Y))
% 0.22/0.47 = { by lemma 12 R->L }
% 0.22/0.47 multiply(X, inverse(multiply(Y, X)))
% 0.22/0.47 = { by lemma 15 R->L }
% 0.22/0.47 multiply(multiply(multiply(Y, X), inverse(Y)), inverse(multiply(Y, X)))
% 0.22/0.47 = { by lemma 15 }
% 0.22/0.47 inverse(Y)
% 0.22/0.47
% 0.22/0.47 Lemma 17: double_divide(double_divide(X, Y), X) = Y.
% 0.22/0.47 Proof:
% 0.22/0.47 double_divide(double_divide(X, Y), X)
% 0.22/0.47 = { by lemma 11 R->L }
% 0.22/0.47 double_divide(multiply(X, double_divide(X, Y)), inverse(identity))
% 0.22/0.47 = { by lemma 16 }
% 0.22/0.47 double_divide(inverse(Y), inverse(identity))
% 0.22/0.47 = { by lemma 7 }
% 0.22/0.47 Y
% 0.22/0.47
% 0.22/0.47 Lemma 18: multiply(multiply(inverse(X), Y), X) = Y.
% 0.22/0.47 Proof:
% 0.22/0.47 multiply(multiply(inverse(X), Y), X)
% 0.22/0.47 = { by lemma 10 R->L }
% 0.22/0.47 inverse(double_divide(X, multiply(inverse(X), Y)))
% 0.22/0.47 = { by axiom 1 (inverse) }
% 0.22/0.47 double_divide(double_divide(X, multiply(inverse(X), Y)), identity)
% 0.22/0.47 = { by lemma 9 R->L }
% 0.22/0.47 double_divide(double_divide(X, multiply(inverse(X), Y)), inverse(identity))
% 0.22/0.47 = { by axiom 1 (inverse) }
% 0.22/0.47 double_divide(double_divide(X, multiply(double_divide(X, identity), Y)), inverse(identity))
% 0.22/0.47 = { by lemma 10 R->L }
% 0.22/0.47 double_divide(double_divide(X, inverse(double_divide(Y, double_divide(X, identity)))), inverse(identity))
% 0.22/0.47 = { by axiom 1 (inverse) }
% 0.22/0.47 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, identity)), identity)), inverse(identity))
% 0.22/0.48 = { by lemma 9 R->L }
% 0.22/0.48 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, identity)), inverse(identity))), inverse(identity))
% 0.22/0.48 = { by lemma 5 }
% 0.22/0.48 Y
% 0.22/0.48
% 0.22/0.48 Lemma 19: double_divide(X, multiply(inverse(X), Y)) = inverse(Y).
% 0.22/0.48 Proof:
% 0.22/0.48 double_divide(X, multiply(inverse(X), Y))
% 0.22/0.48 = { by lemma 11 R->L }
% 0.22/0.48 double_divide(multiply(multiply(inverse(X), Y), X), inverse(identity))
% 0.22/0.48 = { by lemma 18 }
% 0.22/0.48 double_divide(Y, inverse(identity))
% 0.22/0.48 = { by lemma 9 }
% 0.22/0.48 double_divide(Y, identity)
% 0.22/0.48 = { by axiom 1 (inverse) R->L }
% 0.22/0.48 inverse(Y)
% 0.22/0.48
% 0.22/0.48 Lemma 20: double_divide(X, inverse(Y)) = multiply(Y, inverse(X)).
% 0.22/0.48 Proof:
% 0.22/0.48 double_divide(X, inverse(Y))
% 0.22/0.48 = { by lemma 16 R->L }
% 0.22/0.48 double_divide(X, multiply(inverse(X), double_divide(inverse(X), Y)))
% 0.22/0.48 = { by lemma 19 }
% 0.22/0.48 inverse(double_divide(inverse(X), Y))
% 0.22/0.48 = { by lemma 10 }
% 0.22/0.48 multiply(Y, inverse(X))
% 0.22/0.48
% 0.22/0.48 Lemma 21: double_divide(inverse(X), Y) = multiply(inverse(Y), X).
% 0.22/0.48 Proof:
% 0.22/0.48 double_divide(inverse(X), Y)
% 0.22/0.48 = { by lemma 18 R->L }
% 0.22/0.48 multiply(multiply(inverse(X), double_divide(inverse(X), Y)), X)
% 0.22/0.48 = { by lemma 16 }
% 0.22/0.48 multiply(inverse(Y), X)
% 0.22/0.48
% 0.22/0.48 Lemma 22: multiply(X, Y) = multiply(Y, X).
% 0.22/0.48 Proof:
% 0.22/0.48 multiply(X, Y)
% 0.22/0.48 = { by lemma 10 R->L }
% 0.22/0.48 inverse(double_divide(Y, X))
% 0.22/0.48 = { by lemma 5 R->L }
% 0.22/0.48 double_divide(double_divide(X, double_divide(double_divide(inverse(double_divide(Y, X)), double_divide(X, double_divide(Y, X))), inverse(double_divide(Y, X)))), inverse(identity))
% 0.22/0.48 = { by lemma 17 }
% 0.22/0.48 double_divide(double_divide(X, double_divide(X, double_divide(Y, X))), inverse(identity))
% 0.22/0.48 = { by lemma 20 }
% 0.22/0.48 multiply(identity, inverse(double_divide(X, double_divide(X, double_divide(Y, X)))))
% 0.22/0.48 = { by lemma 13 }
% 0.22/0.48 inverse(inverse(inverse(double_divide(X, double_divide(X, double_divide(Y, X))))))
% 0.22/0.48 = { by lemma 14 }
% 0.22/0.48 inverse(double_divide(X, double_divide(X, double_divide(Y, X))))
% 0.22/0.48 = { by lemma 10 }
% 0.22/0.48 multiply(double_divide(X, double_divide(Y, X)), X)
% 0.22/0.48 = { by lemma 11 R->L }
% 0.22/0.48 multiply(double_divide(multiply(double_divide(Y, X), X), inverse(identity)), X)
% 0.22/0.48 = { by lemma 12 R->L }
% 0.22/0.48 multiply(double_divide(multiply(inverse(multiply(X, Y)), X), inverse(identity)), X)
% 0.22/0.49 = { by lemma 21 R->L }
% 0.22/0.49 multiply(double_divide(double_divide(inverse(X), multiply(X, Y)), inverse(identity)), X)
% 0.22/0.49 = { by lemma 14 R->L }
% 0.22/0.49 multiply(double_divide(double_divide(inverse(X), multiply(inverse(inverse(X)), Y)), inverse(identity)), X)
% 0.22/0.49 = { by lemma 19 }
% 0.22/0.49 multiply(double_divide(inverse(Y), inverse(identity)), X)
% 0.22/0.49 = { by lemma 7 }
% 0.22/0.49 multiply(Y, X)
% 0.22/0.49
% 0.22/0.49 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.22/0.49 Proof:
% 0.22/0.49 multiply(multiply(a3, b3), c3)
% 0.22/0.49 = { by lemma 22 }
% 0.22/0.49 multiply(c3, multiply(a3, b3))
% 0.22/0.49 = { by lemma 22 R->L }
% 0.22/0.49 multiply(c3, multiply(b3, a3))
% 0.22/0.49 = { by lemma 22 R->L }
% 0.22/0.49 multiply(multiply(b3, a3), c3)
% 0.22/0.49 = { by lemma 10 R->L }
% 0.22/0.49 multiply(inverse(double_divide(a3, b3)), c3)
% 0.22/0.49 = { by lemma 21 R->L }
% 0.22/0.49 double_divide(inverse(c3), double_divide(a3, b3))
% 0.22/0.49 = { by lemma 12 R->L }
% 0.22/0.49 inverse(multiply(double_divide(a3, b3), inverse(c3)))
% 0.22/0.49 = { by lemma 14 R->L }
% 0.22/0.49 inverse(inverse(inverse(multiply(double_divide(a3, b3), inverse(c3)))))
% 0.22/0.49 = { by lemma 13 R->L }
% 0.22/0.49 multiply(identity, inverse(multiply(double_divide(a3, b3), inverse(c3))))
% 0.22/0.49 = { by lemma 20 R->L }
% 0.22/0.49 double_divide(multiply(double_divide(a3, b3), inverse(c3)), inverse(identity))
% 0.22/0.49 = { by lemma 22 R->L }
% 0.22/0.49 double_divide(multiply(inverse(c3), double_divide(a3, b3)), inverse(identity))
% 0.22/0.49 = { by lemma 11 }
% 0.22/0.49 double_divide(double_divide(a3, b3), inverse(c3))
% 0.22/0.49 = { by lemma 5 R->L }
% 0.22/0.49 double_divide(double_divide(a3, double_divide(double_divide(double_divide(double_divide(a3, b3), inverse(c3)), double_divide(a3, b3)), inverse(b3))), inverse(identity))
% 0.22/0.49 = { by lemma 17 }
% 0.22/0.49 double_divide(double_divide(a3, double_divide(inverse(c3), inverse(b3))), inverse(identity))
% 0.22/0.49 = { by lemma 20 }
% 0.22/0.49 multiply(identity, inverse(double_divide(a3, double_divide(inverse(c3), inverse(b3)))))
% 0.22/0.49 = { by lemma 13 }
% 0.22/0.49 inverse(inverse(inverse(double_divide(a3, double_divide(inverse(c3), inverse(b3))))))
% 0.22/0.49 = { by lemma 14 }
% 0.22/0.49 inverse(double_divide(a3, double_divide(inverse(c3), inverse(b3))))
% 0.22/0.49 = { by lemma 10 }
% 0.22/0.49 multiply(double_divide(inverse(c3), inverse(b3)), a3)
% 0.22/0.49 = { by lemma 20 }
% 0.22/0.49 multiply(multiply(b3, inverse(inverse(c3))), a3)
% 0.22/0.49 = { by lemma 22 }
% 0.22/0.49 multiply(a3, multiply(b3, inverse(inverse(c3))))
% 0.22/0.49 = { by lemma 14 }
% 0.22/0.49 multiply(a3, multiply(b3, c3))
% 0.22/0.49 % SZS output end Proof
% 0.22/0.49
% 0.22/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------