TSTP Solution File: GRP588-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP588-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 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 : n023.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 01:19:01 EDT 2023
% Result : Unsatisfiable 0.18s 0.41s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP588-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.03/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 23:39:40 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.41 Command-line arguments: --no-flatten-goal
% 0.18/0.41
% 0.18/0.41 % SZS status Unsatisfiable
% 0.18/0.41
% 0.18/0.44 % SZS output start Proof
% 0.18/0.44 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.18/0.44 Axiom 2 (single_axiom): double_divide(X, inverse(double_divide(inverse(double_divide(double_divide(X, Y), inverse(Z))), Y))) = Z.
% 0.18/0.44
% 0.18/0.44 Lemma 3: double_divide(X, multiply(Y, multiply(inverse(Z), double_divide(X, Y)))) = Z.
% 0.18/0.44 Proof:
% 0.18/0.44 double_divide(X, multiply(Y, multiply(inverse(Z), double_divide(X, Y))))
% 0.18/0.44 = { by axiom 1 (multiply) }
% 0.18/0.44 double_divide(X, multiply(Y, inverse(double_divide(double_divide(X, Y), inverse(Z)))))
% 0.18/0.44 = { by axiom 1 (multiply) }
% 0.18/0.44 double_divide(X, inverse(double_divide(inverse(double_divide(double_divide(X, Y), inverse(Z))), Y)))
% 0.18/0.44 = { by axiom 2 (single_axiom) }
% 0.18/0.44 Z
% 0.18/0.44
% 0.18/0.44 Lemma 4: multiply(multiply(X, multiply(inverse(Y), double_divide(Z, X))), Z) = inverse(Y).
% 0.18/0.44 Proof:
% 0.18/0.44 multiply(multiply(X, multiply(inverse(Y), double_divide(Z, X))), Z)
% 0.18/0.44 = { by axiom 1 (multiply) }
% 0.18/0.44 inverse(double_divide(Z, multiply(X, multiply(inverse(Y), double_divide(Z, X)))))
% 0.18/0.44 = { by lemma 3 }
% 0.18/0.44 inverse(Y)
% 0.18/0.44
% 0.18/0.44 Lemma 5: multiply(multiply(X, multiply(multiply(Y, Z), double_divide(W, X))), W) = multiply(Y, Z).
% 0.18/0.44 Proof:
% 0.18/0.44 multiply(multiply(X, multiply(multiply(Y, Z), double_divide(W, X))), W)
% 0.18/0.44 = { by axiom 1 (multiply) }
% 0.18/0.44 multiply(multiply(X, multiply(inverse(double_divide(Z, Y)), double_divide(W, X))), W)
% 0.18/0.44 = { by lemma 4 }
% 0.18/0.44 inverse(double_divide(Z, Y))
% 0.18/0.44 = { by axiom 1 (multiply) R->L }
% 0.18/0.44 multiply(Y, Z)
% 0.18/0.44
% 0.18/0.44 Lemma 6: multiply(X, multiply(multiply(Y, Z), double_divide(double_divide(W, V), X))) = multiply(multiply(V, multiply(Y, Z)), W).
% 0.18/0.44 Proof:
% 0.18/0.44 multiply(X, multiply(multiply(Y, Z), double_divide(double_divide(W, V), X)))
% 0.18/0.44 = { by lemma 5 R->L }
% 0.18/0.44 multiply(multiply(V, multiply(multiply(X, multiply(multiply(Y, Z), double_divide(double_divide(W, V), X))), double_divide(W, V))), W)
% 0.18/0.44 = { by lemma 5 }
% 0.18/0.44 multiply(multiply(V, multiply(Y, Z)), W)
% 0.18/0.44
% 0.18/0.44 Lemma 7: multiply(multiply(multiply(X, multiply(Y, Z)), W), double_divide(W, X)) = multiply(Y, Z).
% 0.18/0.44 Proof:
% 0.18/0.44 multiply(multiply(multiply(X, multiply(Y, Z)), W), double_divide(W, X))
% 0.18/0.44 = { by lemma 6 R->L }
% 0.18/0.44 multiply(multiply(V, multiply(multiply(Y, Z), double_divide(double_divide(W, X), V))), double_divide(W, X))
% 0.18/0.44 = { by lemma 5 }
% 0.18/0.44 multiply(Y, Z)
% 0.18/0.44
% 0.18/0.44 Lemma 8: double_divide(X, multiply(Y, multiply(multiply(Z, W), double_divide(X, Y)))) = double_divide(W, Z).
% 0.18/0.44 Proof:
% 0.18/0.44 double_divide(X, multiply(Y, multiply(multiply(Z, W), double_divide(X, Y))))
% 0.18/0.44 = { by axiom 1 (multiply) }
% 0.18/0.44 double_divide(X, multiply(Y, multiply(inverse(double_divide(W, Z)), double_divide(X, Y))))
% 0.18/0.44 = { by lemma 3 }
% 0.18/0.44 double_divide(W, Z)
% 0.18/0.44
% 0.18/0.44 Lemma 9: multiply(X, multiply(inverse(Y), double_divide(double_divide(Z, W), X))) = multiply(multiply(W, inverse(Y)), Z).
% 0.18/0.44 Proof:
% 0.18/0.44 multiply(X, multiply(inverse(Y), double_divide(double_divide(Z, W), X)))
% 0.18/0.44 = { by axiom 1 (multiply) }
% 0.18/0.44 inverse(double_divide(multiply(inverse(Y), double_divide(double_divide(Z, W), X)), X))
% 0.18/0.44 = { by lemma 8 R->L }
% 0.18/0.44 inverse(double_divide(Z, multiply(W, multiply(multiply(X, multiply(inverse(Y), double_divide(double_divide(Z, W), X))), double_divide(Z, W)))))
% 0.18/0.44 = { by lemma 4 }
% 0.18/0.44 inverse(double_divide(Z, multiply(W, inverse(Y))))
% 0.18/0.44 = { by axiom 1 (multiply) R->L }
% 0.18/0.44 multiply(multiply(W, inverse(Y)), Z)
% 0.18/0.44
% 0.18/0.44 Lemma 10: multiply(multiply(inverse(X), double_divide(double_divide(inverse(Y), Z), Z)), X) = inverse(Y).
% 0.18/0.44 Proof:
% 0.18/0.44 multiply(multiply(inverse(X), double_divide(double_divide(inverse(Y), Z), Z)), X)
% 0.18/0.44 = { by lemma 3 R->L }
% 0.18/0.44 multiply(multiply(inverse(X), double_divide(double_divide(inverse(Y), Z), Z)), double_divide(double_divide(inverse(Y), Z), multiply(Z, multiply(inverse(X), double_divide(double_divide(inverse(Y), Z), Z)))))
% 0.18/0.44 = { by lemma 7 R->L }
% 0.18/0.44 multiply(multiply(multiply(multiply(Z, multiply(inverse(X), double_divide(double_divide(inverse(Y), Z), Z))), inverse(Y)), double_divide(inverse(Y), Z)), double_divide(double_divide(inverse(Y), Z), multiply(Z, multiply(inverse(X), double_divide(double_divide(inverse(Y), Z), Z)))))
% 0.18/0.44 = { by lemma 9 R->L }
% 0.18/0.44 multiply(multiply(W, multiply(inverse(Y), double_divide(double_divide(double_divide(inverse(Y), Z), multiply(Z, multiply(inverse(X), double_divide(double_divide(inverse(Y), Z), Z)))), W))), double_divide(double_divide(inverse(Y), Z), multiply(Z, multiply(inverse(X), double_divide(double_divide(inverse(Y), Z), Z)))))
% 0.18/0.44 = { by lemma 4 }
% 0.18/0.44 inverse(Y)
% 0.18/0.44
% 0.18/0.44 Lemma 11: double_divide(double_divide(X, Y), multiply(multiply(Y, multiply(Z, W)), X)) = double_divide(W, Z).
% 0.18/0.44 Proof:
% 0.18/0.44 double_divide(double_divide(X, Y), multiply(multiply(Y, multiply(Z, W)), X))
% 0.18/0.44 = { by lemma 6 R->L }
% 0.18/0.44 double_divide(double_divide(X, Y), multiply(V, multiply(multiply(Z, W), double_divide(double_divide(X, Y), V))))
% 0.18/0.44 = { by lemma 8 }
% 0.18/0.44 double_divide(W, Z)
% 0.18/0.44
% 0.18/0.44 Lemma 12: multiply(multiply(X, multiply(Y, Z)), inverse(W)) = multiply(X, multiply(multiply(Y, inverse(W)), Z)).
% 0.18/0.44 Proof:
% 0.18/0.44 multiply(multiply(X, multiply(Y, Z)), inverse(W))
% 0.18/0.44 = { by lemma 6 R->L }
% 0.18/0.44 multiply(X, multiply(multiply(Y, Z), double_divide(double_divide(inverse(W), X), X)))
% 0.18/0.44 = { by axiom 1 (multiply) }
% 0.18/0.44 multiply(X, multiply(inverse(double_divide(Z, Y)), double_divide(double_divide(inverse(W), X), X)))
% 0.18/0.44 = { by lemma 5 R->L }
% 0.18/0.44 multiply(X, multiply(multiply(Y, multiply(multiply(inverse(double_divide(Z, Y)), double_divide(double_divide(inverse(W), X), X)), double_divide(Z, Y))), Z))
% 0.18/0.44 = { by lemma 10 }
% 0.18/0.44 multiply(X, multiply(multiply(Y, inverse(W)), Z))
% 0.18/0.44
% 0.18/0.44 Lemma 13: multiply(X, multiply(multiply(Y, inverse(W)), Z)) = multiply(X, multiply(multiply(Y, Z), inverse(W))).
% 0.18/0.44 Proof:
% 0.18/0.44 multiply(X, multiply(multiply(Y, inverse(W)), Z))
% 0.18/0.44 = { by lemma 12 R->L }
% 0.18/0.44 multiply(multiply(X, multiply(Y, Z)), inverse(W))
% 0.18/0.44 = { by lemma 5 R->L }
% 0.18/0.44 multiply(multiply(X, multiply(multiply(V, multiply(multiply(Y, Z), double_divide(U, V))), U)), inverse(W))
% 0.18/0.44 = { by lemma 12 }
% 0.18/0.44 multiply(X, multiply(multiply(multiply(V, multiply(multiply(Y, Z), double_divide(U, V))), inverse(W)), U))
% 0.18/0.44 = { by lemma 12 }
% 0.18/0.44 multiply(X, multiply(multiply(V, multiply(multiply(multiply(Y, Z), inverse(W)), double_divide(U, V))), U))
% 0.18/0.44 = { by lemma 5 }
% 0.18/0.44 multiply(X, multiply(multiply(Y, Z), inverse(W)))
% 0.18/0.45
% 0.18/0.45 Lemma 14: double_divide(inverse(X), multiply(Y, Z)) = double_divide(Z, multiply(Y, inverse(X))).
% 0.18/0.45 Proof:
% 0.18/0.45 double_divide(inverse(X), multiply(Y, Z))
% 0.18/0.45 = { by lemma 11 R->L }
% 0.18/0.45 double_divide(double_divide(W, V), multiply(multiply(V, multiply(multiply(Y, Z), inverse(X))), W))
% 0.18/0.45 = { by lemma 13 R->L }
% 0.18/0.45 double_divide(double_divide(W, V), multiply(multiply(V, multiply(multiply(Y, inverse(X)), Z)), W))
% 0.18/0.45 = { by lemma 11 }
% 0.18/0.45 double_divide(Z, multiply(Y, inverse(X)))
% 0.18/0.45
% 0.18/0.45 Lemma 15: double_divide(inverse(X), multiply(inverse(inverse(X)), inverse(Y))) = Y.
% 0.18/0.45 Proof:
% 0.18/0.45 double_divide(inverse(X), multiply(inverse(inverse(X)), inverse(Y)))
% 0.18/0.45 = { by lemma 10 R->L }
% 0.18/0.45 double_divide(inverse(X), multiply(inverse(inverse(X)), multiply(multiply(inverse(double_divide(inverse(X), inverse(inverse(X)))), double_divide(double_divide(inverse(Y), Z), Z)), double_divide(inverse(X), inverse(inverse(X))))))
% 0.18/0.45 = { by lemma 8 }
% 0.18/0.45 double_divide(double_divide(double_divide(inverse(Y), Z), Z), inverse(double_divide(inverse(X), inverse(inverse(X)))))
% 0.18/0.45 = { by axiom 1 (multiply) R->L }
% 0.18/0.45 double_divide(double_divide(double_divide(inverse(Y), Z), Z), multiply(inverse(inverse(X)), inverse(X)))
% 0.18/0.45 = { by lemma 14 R->L }
% 0.18/0.45 double_divide(inverse(X), multiply(inverse(inverse(X)), double_divide(double_divide(inverse(Y), Z), Z)))
% 0.18/0.45 = { by lemma 3 R->L }
% 0.18/0.45 double_divide(double_divide(double_divide(inverse(Y), Z), multiply(Z, multiply(inverse(inverse(X)), double_divide(double_divide(inverse(Y), Z), Z)))), multiply(inverse(inverse(X)), double_divide(double_divide(inverse(Y), Z), Z)))
% 0.18/0.45 = { by lemma 7 R->L }
% 0.18/0.45 double_divide(double_divide(double_divide(inverse(Y), Z), multiply(Z, multiply(inverse(inverse(X)), double_divide(double_divide(inverse(Y), Z), Z)))), multiply(multiply(multiply(Z, multiply(inverse(inverse(X)), double_divide(double_divide(inverse(Y), Z), Z))), inverse(Y)), double_divide(inverse(Y), Z)))
% 0.18/0.45 = { by lemma 9 R->L }
% 0.18/0.45 double_divide(double_divide(double_divide(inverse(Y), Z), multiply(Z, multiply(inverse(inverse(X)), double_divide(double_divide(inverse(Y), Z), Z)))), multiply(W, multiply(inverse(Y), double_divide(double_divide(double_divide(inverse(Y), Z), multiply(Z, multiply(inverse(inverse(X)), double_divide(double_divide(inverse(Y), Z), Z)))), W))))
% 0.18/0.45 = { by lemma 3 }
% 0.18/0.45 Y
% 0.18/0.45
% 0.18/0.45 Lemma 16: multiply(multiply(X, inverse(Y)), inverse(Z)) = multiply(X, multiply(inverse(Y), inverse(Z))).
% 0.18/0.45 Proof:
% 0.18/0.45 multiply(multiply(X, inverse(Y)), inverse(Z))
% 0.18/0.45 = { by lemma 4 R->L }
% 0.18/0.45 multiply(multiply(X, multiply(multiply(W, multiply(inverse(Y), double_divide(V, W))), V)), inverse(Z))
% 0.18/0.45 = { by lemma 12 }
% 0.18/0.45 multiply(X, multiply(multiply(multiply(W, multiply(inverse(Y), double_divide(V, W))), inverse(Z)), V))
% 0.18/0.45 = { by lemma 12 }
% 0.18/0.45 multiply(X, multiply(multiply(W, multiply(multiply(inverse(Y), inverse(Z)), double_divide(V, W))), V))
% 0.18/0.45 = { by lemma 5 }
% 0.18/0.45 multiply(X, multiply(inverse(Y), inverse(Z)))
% 0.18/0.45
% 0.18/0.45 Lemma 17: multiply(X, multiply(inverse(Z), inverse(Y))) = multiply(X, multiply(inverse(Y), inverse(Z))).
% 0.18/0.45 Proof:
% 0.18/0.45 multiply(X, multiply(inverse(Z), inverse(Y)))
% 0.18/0.45 = { by lemma 16 R->L }
% 0.18/0.45 multiply(multiply(X, inverse(Z)), inverse(Y))
% 0.18/0.45 = { by lemma 7 R->L }
% 0.18/0.45 multiply(multiply(multiply(W, multiply(multiply(X, inverse(Z)), inverse(Y))), V), double_divide(V, W))
% 0.18/0.45 = { by lemma 13 }
% 0.18/0.45 multiply(multiply(multiply(W, multiply(multiply(X, inverse(Y)), inverse(Z))), V), double_divide(V, W))
% 0.18/0.45 = { by lemma 7 }
% 0.18/0.45 multiply(multiply(X, inverse(Y)), inverse(Z))
% 0.18/0.45 = { by lemma 16 }
% 0.18/0.45 multiply(X, multiply(inverse(Y), inverse(Z)))
% 0.18/0.45
% 0.18/0.45 Lemma 18: inverse(inverse(X)) = X.
% 0.18/0.45 Proof:
% 0.18/0.45 inverse(inverse(X))
% 0.18/0.45 = { by lemma 15 R->L }
% 0.18/0.45 double_divide(inverse(X), multiply(inverse(inverse(X)), inverse(inverse(inverse(X)))))
% 0.18/0.45 = { by lemma 7 R->L }
% 0.18/0.45 double_divide(inverse(X), multiply(multiply(multiply(Y, multiply(inverse(inverse(X)), inverse(inverse(inverse(X))))), Z), double_divide(Z, Y)))
% 0.18/0.45 = { by lemma 17 }
% 0.18/0.45 double_divide(inverse(X), multiply(multiply(multiply(Y, multiply(inverse(inverse(inverse(X))), inverse(inverse(X)))), Z), double_divide(Z, Y)))
% 0.18/0.45 = { by lemma 7 }
% 0.18/0.45 double_divide(inverse(X), multiply(inverse(inverse(inverse(X))), inverse(inverse(X))))
% 0.18/0.45 = { by lemma 14 R->L }
% 0.18/0.45 double_divide(inverse(inverse(X)), multiply(inverse(inverse(inverse(X))), inverse(X)))
% 0.18/0.45 = { by lemma 15 }
% 0.18/0.45 X
% 0.18/0.45
% 0.18/0.45 Goal 1 (prove_these_axioms_4): multiply(a, b) = multiply(b, a).
% 0.18/0.45 Proof:
% 0.18/0.45 multiply(a, b)
% 0.18/0.45 = { by axiom 1 (multiply) }
% 0.18/0.45 inverse(double_divide(b, a))
% 0.18/0.45 = { by lemma 18 R->L }
% 0.18/0.45 inverse(double_divide(inverse(inverse(b)), a))
% 0.18/0.45 = { by lemma 18 R->L }
% 0.18/0.45 inverse(double_divide(inverse(inverse(b)), inverse(inverse(a))))
% 0.18/0.45 = { by lemma 11 R->L }
% 0.18/0.45 inverse(double_divide(double_divide(X, Y), multiply(multiply(Y, multiply(inverse(inverse(a)), inverse(inverse(b)))), X)))
% 0.18/0.45 = { by lemma 17 }
% 0.18/0.45 inverse(double_divide(double_divide(X, Y), multiply(multiply(Y, multiply(inverse(inverse(b)), inverse(inverse(a)))), X)))
% 0.18/0.45 = { by lemma 11 }
% 0.18/0.45 inverse(double_divide(inverse(inverse(a)), inverse(inverse(b))))
% 0.18/0.45 = { by lemma 18 }
% 0.18/0.45 inverse(double_divide(a, inverse(inverse(b))))
% 0.18/0.45 = { by lemma 18 }
% 0.18/0.45 inverse(double_divide(a, b))
% 0.18/0.45 = { by axiom 1 (multiply) R->L }
% 0.18/0.45 multiply(b, a)
% 0.18/0.45 % SZS output end Proof
% 0.18/0.45
% 0.18/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------