TSTP Solution File: GRP599-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP599-1 : 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 : n011.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 01:19:04 EDT 2023
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP599-1 : TPTP v8.1.2. Released v2.6.0.
% 0.13/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 20:29:10 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.45 Command-line arguments: --no-flatten-goal
% 0.20/0.45
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.20/0.47 Axiom 2 (single_axiom): double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(double_divide(inverse(Z), Y))))) = Z.
% 0.20/0.47
% 0.20/0.47 Lemma 3: double_divide(double_divide(X, Y), multiply(multiply(Y, inverse(Z)), X)) = Z.
% 0.20/0.47 Proof:
% 0.20/0.47 double_divide(double_divide(X, Y), multiply(multiply(Y, inverse(Z)), X))
% 0.20/0.47 = { by axiom 1 (multiply) }
% 0.20/0.47 double_divide(double_divide(X, Y), multiply(inverse(double_divide(inverse(Z), Y)), X))
% 0.20/0.47 = { by axiom 1 (multiply) }
% 0.20/0.47 double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(double_divide(inverse(Z), Y)))))
% 0.20/0.47 = { by axiom 2 (single_axiom) }
% 0.20/0.47 Z
% 0.20/0.47
% 0.20/0.47 Lemma 4: multiply(multiply(multiply(X, inverse(Y)), Z), double_divide(Z, X)) = inverse(Y).
% 0.20/0.47 Proof:
% 0.20/0.47 multiply(multiply(multiply(X, inverse(Y)), Z), double_divide(Z, X))
% 0.20/0.47 = { by axiom 1 (multiply) }
% 0.20/0.47 inverse(double_divide(double_divide(Z, X), multiply(multiply(X, inverse(Y)), Z)))
% 0.20/0.48 = { by lemma 3 }
% 0.20/0.48 inverse(Y)
% 0.20/0.48
% 0.20/0.48 Lemma 5: multiply(multiply(multiply(multiply(multiply(X, inverse(Y)), Z), inverse(W)), double_divide(Z, X)), Y) = inverse(W).
% 0.20/0.48 Proof:
% 0.20/0.48 multiply(multiply(multiply(multiply(multiply(X, inverse(Y)), Z), inverse(W)), double_divide(Z, X)), Y)
% 0.20/0.48 = { by lemma 3 R->L }
% 0.20/0.48 multiply(multiply(multiply(multiply(multiply(X, inverse(Y)), Z), inverse(W)), double_divide(Z, X)), double_divide(double_divide(Z, X), multiply(multiply(X, inverse(Y)), Z)))
% 0.20/0.48 = { by lemma 4 }
% 0.20/0.48 inverse(W)
% 0.20/0.48
% 0.20/0.48 Lemma 6: multiply(multiply(inverse(X), inverse(Y)), X) = inverse(Y).
% 0.20/0.48 Proof:
% 0.20/0.48 multiply(multiply(inverse(X), inverse(Y)), X)
% 0.20/0.48 = { by lemma 3 R->L }
% 0.20/0.48 multiply(multiply(inverse(X), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))), X)
% 0.20/0.48 = { by lemma 5 R->L }
% 0.20/0.48 multiply(multiply(multiply(multiply(multiply(multiply(multiply(W, inverse(inverse(Y))), Z), inverse(X)), double_divide(Z, W)), inverse(Y)), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))), X)
% 0.20/0.48 = { by lemma 5 }
% 0.20/0.48 inverse(Y)
% 0.20/0.48
% 0.20/0.48 Lemma 7: double_divide(double_divide(X, inverse(X)), multiply(Y, Z)) = double_divide(Z, Y).
% 0.20/0.48 Proof:
% 0.20/0.48 double_divide(double_divide(X, inverse(X)), multiply(Y, Z))
% 0.20/0.48 = { by axiom 1 (multiply) }
% 0.20/0.48 double_divide(double_divide(X, inverse(X)), inverse(double_divide(Z, Y)))
% 0.20/0.48 = { by lemma 6 R->L }
% 0.20/0.48 double_divide(double_divide(X, inverse(X)), multiply(multiply(inverse(X), inverse(double_divide(Z, Y))), X))
% 0.20/0.48 = { by lemma 3 }
% 0.20/0.48 double_divide(Z, Y)
% 0.20/0.48
% 0.20/0.48 Lemma 8: double_divide(X, multiply(inverse(X), inverse(Y))) = Y.
% 0.20/0.48 Proof:
% 0.20/0.48 double_divide(X, multiply(inverse(X), inverse(Y)))
% 0.20/0.48 = { by lemma 3 R->L }
% 0.20/0.48 double_divide(X, multiply(inverse(X), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))))
% 0.20/0.48 = { by lemma 5 R->L }
% 0.20/0.48 double_divide(X, multiply(multiply(multiply(multiply(multiply(multiply(W, inverse(inverse(Y))), Z), inverse(X)), double_divide(Z, W)), inverse(Y)), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))))
% 0.20/0.48 = { by lemma 3 R->L }
% 0.20/0.48 double_divide(double_divide(double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z)), multiply(multiply(multiply(multiply(W, inverse(inverse(Y))), Z), inverse(X)), double_divide(Z, W))), multiply(multiply(multiply(multiply(multiply(multiply(W, inverse(inverse(Y))), Z), inverse(X)), double_divide(Z, W)), inverse(Y)), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))))
% 0.20/0.48 = { by lemma 3 }
% 0.20/0.48 Y
% 0.20/0.48
% 0.20/0.48 Lemma 9: double_divide(inverse(X), multiply(inverse(Y), Y)) = X.
% 0.20/0.48 Proof:
% 0.20/0.48 double_divide(inverse(X), multiply(inverse(Y), Y))
% 0.20/0.48 = { by axiom 1 (multiply) }
% 0.20/0.48 double_divide(inverse(X), inverse(double_divide(Y, inverse(Y))))
% 0.20/0.48 = { by lemma 7 R->L }
% 0.20/0.48 double_divide(double_divide(Y, inverse(Y)), multiply(inverse(double_divide(Y, inverse(Y))), inverse(X)))
% 0.20/0.48 = { by lemma 8 }
% 0.20/0.48 X
% 0.20/0.48
% 0.20/0.48 Lemma 10: multiply(multiply(inverse(X), X), inverse(Y)) = inverse(Y).
% 0.20/0.48 Proof:
% 0.20/0.48 multiply(multiply(inverse(X), X), inverse(Y))
% 0.20/0.48 = { by axiom 1 (multiply) }
% 0.20/0.48 multiply(inverse(double_divide(X, inverse(X))), inverse(Y))
% 0.20/0.48 = { by axiom 1 (multiply) }
% 0.20/0.48 inverse(double_divide(inverse(Y), inverse(double_divide(X, inverse(X)))))
% 0.20/0.48 = { by lemma 4 R->L }
% 0.20/0.48 multiply(multiply(multiply(inverse(X), inverse(double_divide(inverse(Y), inverse(double_divide(X, inverse(X)))))), X), double_divide(X, inverse(X)))
% 0.20/0.48 = { by lemma 6 }
% 0.20/0.48 multiply(inverse(double_divide(inverse(Y), inverse(double_divide(X, inverse(X))))), double_divide(X, inverse(X)))
% 0.20/0.48 = { by axiom 1 (multiply) R->L }
% 0.20/0.48 multiply(multiply(inverse(double_divide(X, inverse(X))), inverse(Y)), double_divide(X, inverse(X)))
% 0.20/0.48 = { by lemma 6 }
% 0.20/0.48 inverse(Y)
% 0.20/0.48
% 0.20/0.48 Lemma 11: double_divide(double_divide(double_divide(inverse(X), Y), multiply(Y, inverse(Z))), inverse(Z)) = X.
% 0.20/0.48 Proof:
% 0.20/0.48 double_divide(double_divide(double_divide(inverse(X), Y), multiply(Y, inverse(Z))), inverse(Z))
% 0.20/0.48 = { by lemma 4 R->L }
% 0.20/0.48 double_divide(double_divide(double_divide(inverse(X), Y), multiply(Y, inverse(Z))), multiply(multiply(multiply(Y, inverse(Z)), inverse(X)), double_divide(inverse(X), Y)))
% 0.20/0.48 = { by lemma 3 }
% 0.20/0.48 X
% 0.20/0.48
% 0.20/0.48 Lemma 12: double_divide(double_divide(X, inverse(Y)), inverse(Y)) = X.
% 0.20/0.48 Proof:
% 0.20/0.48 double_divide(double_divide(X, inverse(Y)), inverse(Y))
% 0.20/0.48 = { by lemma 9 R->L }
% 0.20/0.48 double_divide(double_divide(double_divide(inverse(X), multiply(inverse(Z), Z)), inverse(Y)), inverse(Y))
% 0.20/0.48 = { by lemma 10 R->L }
% 0.20/0.48 double_divide(double_divide(double_divide(inverse(X), multiply(inverse(Z), Z)), multiply(multiply(inverse(Z), Z), inverse(Y))), inverse(Y))
% 0.20/0.48 = { by lemma 11 }
% 0.20/0.48 X
% 0.20/0.48
% 0.20/0.48 Lemma 13: double_divide(double_divide(inverse(X), inverse(inverse(Y))), inverse(X)) = Y.
% 0.20/0.48 Proof:
% 0.20/0.48 double_divide(double_divide(inverse(X), inverse(inverse(Y))), inverse(X))
% 0.20/0.48 = { by lemma 7 R->L }
% 0.20/0.48 double_divide(double_divide(double_divide(inverse(Y), inverse(inverse(Y))), multiply(inverse(inverse(Y)), inverse(X))), inverse(X))
% 0.20/0.48 = { by lemma 11 }
% 0.20/0.48 Y
% 0.20/0.48
% 0.20/0.48 Lemma 14: inverse(inverse(X)) = X.
% 0.20/0.48 Proof:
% 0.20/0.48 inverse(inverse(X))
% 0.20/0.48 = { by lemma 12 R->L }
% 0.20/0.48 double_divide(double_divide(inverse(inverse(X)), inverse(inverse(X))), inverse(inverse(X)))
% 0.20/0.48 = { by lemma 13 }
% 0.20/0.48 X
% 0.20/0.48
% 0.20/0.48 Lemma 15: double_divide(double_divide(X, Y), X) = Y.
% 0.20/0.48 Proof:
% 0.20/0.48 double_divide(double_divide(X, Y), X)
% 0.20/0.48 = { by lemma 14 R->L }
% 0.20/0.48 double_divide(double_divide(X, Y), inverse(inverse(X)))
% 0.20/0.48 = { by lemma 14 R->L }
% 0.20/0.48 double_divide(double_divide(X, inverse(inverse(Y))), inverse(inverse(X)))
% 0.20/0.48 = { by lemma 14 R->L }
% 0.20/0.48 double_divide(double_divide(inverse(inverse(X)), inverse(inverse(Y))), inverse(inverse(X)))
% 0.20/0.48 = { by lemma 13 }
% 0.20/0.48 Y
% 0.20/0.48
% 0.20/0.48 Lemma 16: double_divide(Y, X) = double_divide(X, Y).
% 0.20/0.48 Proof:
% 0.20/0.48 double_divide(Y, X)
% 0.20/0.48 = { by lemma 15 R->L }
% 0.20/0.48 double_divide(double_divide(double_divide(X, Y), X), X)
% 0.20/0.48 = { by lemma 14 R->L }
% 0.20/0.48 double_divide(double_divide(double_divide(X, Y), X), inverse(inverse(X)))
% 0.20/0.48 = { by lemma 14 R->L }
% 0.20/0.48 double_divide(double_divide(double_divide(X, Y), inverse(inverse(X))), inverse(inverse(X)))
% 0.20/0.48 = { by lemma 12 }
% 0.20/0.48 double_divide(X, Y)
% 0.20/0.48
% 0.20/0.48 Lemma 17: multiply(Y, X) = multiply(X, Y).
% 0.20/0.48 Proof:
% 0.20/0.48 multiply(Y, X)
% 0.20/0.48 = { by axiom 1 (multiply) }
% 0.20/0.48 inverse(double_divide(X, Y))
% 0.20/0.48 = { by lemma 16 }
% 0.20/0.48 inverse(double_divide(Y, X))
% 0.20/0.48 = { by axiom 1 (multiply) R->L }
% 0.20/0.48 multiply(X, Y)
% 0.20/0.48
% 0.20/0.48 Lemma 18: inverse(multiply(X, Y)) = double_divide(Y, X).
% 0.20/0.48 Proof:
% 0.20/0.48 inverse(multiply(X, Y))
% 0.20/0.48 = { by axiom 1 (multiply) }
% 0.20/0.48 inverse(inverse(double_divide(Y, X)))
% 0.20/0.48 = { by lemma 14 }
% 0.20/0.48 double_divide(Y, X)
% 0.20/0.48
% 0.20/0.48 Lemma 19: multiply(X, inverse(Y)) = double_divide(Y, inverse(X)).
% 0.20/0.48 Proof:
% 0.20/0.48 multiply(X, inverse(Y))
% 0.20/0.48 = { by lemma 14 R->L }
% 0.20/0.48 multiply(inverse(inverse(X)), inverse(Y))
% 0.20/0.48 = { by lemma 17 }
% 0.20/0.48 multiply(inverse(Y), inverse(inverse(X)))
% 0.20/0.48 = { by lemma 15 R->L }
% 0.20/0.48 double_divide(double_divide(Y, multiply(inverse(Y), inverse(inverse(X)))), Y)
% 0.20/0.48 = { by lemma 8 }
% 0.20/0.48 double_divide(inverse(X), Y)
% 0.20/0.48 = { by lemma 16 R->L }
% 0.20/0.48 double_divide(Y, inverse(X))
% 0.20/0.48
% 0.20/0.48 Lemma 20: multiply(X, double_divide(X, Y)) = inverse(Y).
% 0.20/0.48 Proof:
% 0.20/0.48 multiply(X, double_divide(X, Y))
% 0.20/0.48 = { by lemma 16 }
% 0.20/0.48 multiply(X, double_divide(Y, X))
% 0.20/0.48 = { by lemma 14 R->L }
% 0.20/0.48 multiply(X, double_divide(Y, inverse(inverse(X))))
% 0.20/0.48 = { by lemma 14 R->L }
% 0.20/0.48 multiply(inverse(inverse(X)), double_divide(Y, inverse(inverse(X))))
% 0.20/0.48 = { by lemma 9 R->L }
% 0.20/0.48 multiply(inverse(inverse(X)), double_divide(double_divide(inverse(Y), multiply(inverse(Z), Z)), inverse(inverse(X))))
% 0.20/0.48 = { by lemma 10 R->L }
% 0.20/0.48 multiply(inverse(inverse(X)), double_divide(double_divide(inverse(Y), multiply(inverse(Z), Z)), multiply(multiply(inverse(Z), Z), inverse(inverse(X)))))
% 0.20/0.48 = { by lemma 4 R->L }
% 0.20/0.48 multiply(multiply(multiply(multiply(multiply(inverse(Z), Z), inverse(inverse(X))), inverse(Y)), double_divide(inverse(Y), multiply(inverse(Z), Z))), double_divide(double_divide(inverse(Y), multiply(inverse(Z), Z)), multiply(multiply(inverse(Z), Z), inverse(inverse(X)))))
% 0.20/0.48 = { by lemma 4 }
% 0.20/0.48 inverse(Y)
% 0.20/0.48
% 0.20/0.48 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.20/0.48 Proof:
% 0.20/0.48 multiply(multiply(a3, b3), c3)
% 0.20/0.48 = { by axiom 1 (multiply) }
% 0.20/0.48 inverse(double_divide(c3, multiply(a3, b3)))
% 0.20/0.48 = { by lemma 17 }
% 0.20/0.48 inverse(double_divide(c3, multiply(b3, a3)))
% 0.20/0.48 = { by lemma 8 R->L }
% 0.20/0.48 inverse(double_divide(c3, multiply(b3, double_divide(b3, multiply(inverse(b3), inverse(a3))))))
% 0.20/0.48 = { by lemma 20 }
% 0.20/0.48 inverse(double_divide(c3, inverse(multiply(inverse(b3), inverse(a3)))))
% 0.20/0.48 = { by lemma 18 }
% 0.20/0.48 inverse(double_divide(c3, double_divide(inverse(a3), inverse(b3))))
% 0.20/0.48 = { by lemma 19 R->L }
% 0.20/0.48 inverse(double_divide(c3, multiply(b3, inverse(inverse(a3)))))
% 0.20/0.48 = { by lemma 18 R->L }
% 0.20/0.48 inverse(inverse(multiply(multiply(b3, inverse(inverse(a3))), c3)))
% 0.20/0.48 = { by lemma 20 R->L }
% 0.20/0.48 inverse(multiply(double_divide(c3, b3), double_divide(double_divide(c3, b3), multiply(multiply(b3, inverse(inverse(a3))), c3))))
% 0.20/0.48 = { by lemma 3 }
% 0.20/0.48 inverse(multiply(double_divide(c3, b3), inverse(a3)))
% 0.20/0.48 = { by lemma 19 }
% 0.20/0.48 inverse(double_divide(a3, inverse(double_divide(c3, b3))))
% 0.20/0.48 = { by axiom 1 (multiply) R->L }
% 0.20/0.48 inverse(double_divide(a3, multiply(b3, c3)))
% 0.20/0.48 = { by lemma 17 R->L }
% 0.20/0.48 inverse(double_divide(a3, multiply(c3, b3)))
% 0.20/0.48 = { by axiom 1 (multiply) R->L }
% 0.20/0.48 multiply(multiply(c3, b3), a3)
% 0.20/0.48 = { by lemma 17 R->L }
% 0.20/0.48 multiply(a3, multiply(c3, b3))
% 0.20/0.48 = { by lemma 17 R->L }
% 0.20/0.48 multiply(a3, multiply(b3, c3))
% 0.20/0.48 % SZS output end Proof
% 0.20/0.48
% 0.20/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------