TSTP Solution File: GRP591-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP591-1 : 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 : 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 01:19:02 EDT 2023
% Result : Unsatisfiable 0.18s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP591-1 : TPTP v8.1.2. Released v2.6.0.
% 0.03/0.13 % 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 : n023.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 01:12:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.18/0.40 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.18/0.40
% 0.18/0.40 % SZS status Unsatisfiable
% 0.18/0.40
% 0.18/0.42 % SZS output start Proof
% 0.18/0.42 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.18/0.42 Axiom 2 (single_axiom): double_divide(inverse(double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(Z))))), Y) = Z.
% 0.18/0.42
% 0.18/0.42 Lemma 3: double_divide(multiply(multiply(inverse(X), Y), double_divide(Y, Z)), Z) = X.
% 0.18/0.42 Proof:
% 0.18/0.42 double_divide(multiply(multiply(inverse(X), Y), double_divide(Y, Z)), Z)
% 0.18/0.42 = { by axiom 1 (multiply) }
% 0.18/0.42 double_divide(multiply(inverse(double_divide(Y, inverse(X))), double_divide(Y, Z)), Z)
% 0.18/0.42 = { by axiom 1 (multiply) }
% 0.18/0.42 double_divide(inverse(double_divide(double_divide(Y, Z), inverse(double_divide(Y, inverse(X))))), Z)
% 0.18/0.42 = { by axiom 2 (single_axiom) }
% 0.18/0.42 X
% 0.18/0.42
% 0.18/0.42 Lemma 4: multiply(X, multiply(multiply(inverse(Y), Z), double_divide(Z, X))) = inverse(Y).
% 0.18/0.42 Proof:
% 0.18/0.42 multiply(X, multiply(multiply(inverse(Y), Z), double_divide(Z, X)))
% 0.18/0.42 = { by axiom 1 (multiply) }
% 0.18/0.42 inverse(double_divide(multiply(multiply(inverse(Y), Z), double_divide(Z, X)), X))
% 0.18/0.42 = { by lemma 3 }
% 0.18/0.42 inverse(Y)
% 0.18/0.42
% 0.18/0.42 Lemma 5: multiply(inverse(X), multiply(inverse(Y), Y)) = inverse(X).
% 0.18/0.42 Proof:
% 0.18/0.42 multiply(inverse(X), multiply(inverse(Y), Y))
% 0.18/0.42 = { by lemma 3 R->L }
% 0.18/0.42 multiply(inverse(X), multiply(inverse(Y), double_divide(multiply(multiply(inverse(Y), Z), double_divide(Z, inverse(X))), inverse(X))))
% 0.18/0.42 = { by lemma 4 R->L }
% 0.18/0.42 multiply(inverse(X), multiply(multiply(inverse(X), multiply(multiply(inverse(Y), Z), double_divide(Z, inverse(X)))), double_divide(multiply(multiply(inverse(Y), Z), double_divide(Z, inverse(X))), inverse(X))))
% 0.18/0.42 = { by lemma 4 }
% 0.18/0.42 inverse(X)
% 0.18/0.42
% 0.18/0.42 Lemma 6: double_divide(multiply(multiply(multiply(X, Y), Z), double_divide(Z, W)), W) = double_divide(Y, X).
% 0.18/0.42 Proof:
% 0.18/0.42 double_divide(multiply(multiply(multiply(X, Y), Z), double_divide(Z, W)), W)
% 0.18/0.42 = { by axiom 1 (multiply) }
% 0.18/0.42 double_divide(multiply(multiply(inverse(double_divide(Y, X)), Z), double_divide(Z, W)), W)
% 0.18/0.42 = { by lemma 3 }
% 0.18/0.42 double_divide(Y, X)
% 0.18/0.42
% 0.18/0.42 Lemma 7: double_divide(multiply(inverse(X), X), inverse(Y)) = Y.
% 0.18/0.42 Proof:
% 0.18/0.42 double_divide(multiply(inverse(X), X), inverse(Y))
% 0.18/0.42 = { by lemma 6 R->L }
% 0.18/0.42 double_divide(multiply(multiply(multiply(inverse(Y), multiply(inverse(X), X)), Z), double_divide(Z, W)), W)
% 0.18/0.42 = { by lemma 5 }
% 0.18/0.42 double_divide(multiply(multiply(inverse(Y), Z), double_divide(Z, W)), W)
% 0.18/0.42 = { by lemma 3 }
% 0.18/0.42 Y
% 0.18/0.42
% 0.18/0.42 Lemma 8: multiply(inverse(X), multiply(multiply(Y, Z), X)) = multiply(Y, Z).
% 0.18/0.42 Proof:
% 0.18/0.42 multiply(inverse(X), multiply(multiply(Y, Z), X))
% 0.18/0.42 = { by axiom 1 (multiply) }
% 0.18/0.42 multiply(inverse(X), multiply(inverse(double_divide(Z, Y)), X))
% 0.18/0.42 = { by lemma 5 R->L }
% 0.18/0.42 multiply(inverse(X), multiply(multiply(inverse(double_divide(Z, Y)), multiply(inverse(W), W)), X))
% 0.18/0.42 = { by axiom 1 (multiply) R->L }
% 0.18/0.42 multiply(inverse(X), multiply(multiply(multiply(Y, Z), multiply(inverse(W), W)), X))
% 0.18/0.42 = { by lemma 7 R->L }
% 0.18/0.42 multiply(inverse(X), multiply(multiply(multiply(Y, Z), multiply(inverse(W), W)), double_divide(multiply(inverse(W), W), inverse(X))))
% 0.18/0.42 = { by axiom 1 (multiply) }
% 0.18/0.42 inverse(double_divide(multiply(multiply(multiply(Y, Z), multiply(inverse(W), W)), double_divide(multiply(inverse(W), W), inverse(X))), inverse(X)))
% 0.18/0.42 = { by lemma 6 }
% 0.18/0.42 inverse(double_divide(Z, Y))
% 0.18/0.42 = { by axiom 1 (multiply) R->L }
% 0.18/0.42 multiply(Y, Z)
% 0.18/0.42
% 0.18/0.42 Lemma 9: multiply(inverse(multiply(multiply(X, Y), Z)), multiply(X, Y)) = inverse(Z).
% 0.18/0.42 Proof:
% 0.18/0.42 multiply(inverse(multiply(multiply(X, Y), Z)), multiply(X, Y))
% 0.18/0.43 = { by lemma 8 R->L }
% 0.18/0.43 multiply(inverse(multiply(multiply(X, Y), Z)), multiply(inverse(Z), multiply(multiply(X, Y), Z)))
% 0.18/0.43 = { by lemma 5 R->L }
% 0.18/0.43 multiply(inverse(multiply(multiply(X, Y), Z)), multiply(multiply(inverse(Z), multiply(inverse(W), W)), multiply(multiply(X, Y), Z)))
% 0.18/0.43 = { by lemma 7 R->L }
% 0.18/0.43 multiply(inverse(multiply(multiply(X, Y), Z)), multiply(multiply(inverse(Z), multiply(inverse(W), W)), double_divide(multiply(inverse(W), W), inverse(multiply(multiply(X, Y), Z)))))
% 0.18/0.43 = { by lemma 4 }
% 0.18/0.43 inverse(Z)
% 0.18/0.43
% 0.18/0.43 Lemma 10: multiply(multiply(inverse(X), X), Y) = Y.
% 0.18/0.43 Proof:
% 0.18/0.43 multiply(multiply(inverse(X), X), Y)
% 0.18/0.43 = { by lemma 3 R->L }
% 0.18/0.43 double_divide(multiply(multiply(inverse(multiply(multiply(inverse(X), X), Y)), Z), double_divide(Z, W)), W)
% 0.18/0.43 = { by lemma 5 R->L }
% 0.18/0.43 double_divide(multiply(multiply(multiply(inverse(multiply(multiply(inverse(X), X), Y)), multiply(inverse(X), X)), Z), double_divide(Z, W)), W)
% 0.18/0.43 = { by lemma 9 }
% 0.18/0.43 double_divide(multiply(multiply(inverse(Y), Z), double_divide(Z, W)), W)
% 0.18/0.43 = { by lemma 3 }
% 0.18/0.43 Y
% 0.18/0.43
% 0.18/0.43 Lemma 11: multiply(multiply(X, Y), Z) = multiply(X, multiply(Z, Y)).
% 0.18/0.43 Proof:
% 0.18/0.43 multiply(multiply(X, Y), Z)
% 0.18/0.43 = { by axiom 1 (multiply) }
% 0.18/0.43 multiply(inverse(double_divide(Y, X)), Z)
% 0.18/0.43 = { by lemma 3 R->L }
% 0.18/0.43 multiply(inverse(double_divide(double_divide(multiply(multiply(inverse(Y), multiply(multiply(multiply(inverse(W), W), Z), Y)), double_divide(multiply(multiply(multiply(inverse(W), W), Z), Y), X)), X), X)), Z)
% 0.18/0.43 = { by lemma 8 }
% 0.18/0.43 multiply(inverse(double_divide(double_divide(multiply(multiply(multiply(inverse(W), W), Z), double_divide(multiply(multiply(multiply(inverse(W), W), Z), Y), X)), X), X)), Z)
% 0.18/0.43 = { by lemma 10 }
% 0.18/0.43 multiply(inverse(double_divide(double_divide(multiply(Z, double_divide(multiply(multiply(multiply(inverse(W), W), Z), Y), X)), X), X)), Z)
% 0.18/0.43 = { by lemma 10 }
% 0.18/0.43 multiply(inverse(double_divide(double_divide(multiply(Z, double_divide(multiply(Z, Y), X)), X), X)), Z)
% 0.18/0.43 = { by lemma 10 R->L }
% 0.18/0.43 multiply(inverse(double_divide(multiply(multiply(inverse(multiply(Z, double_divide(multiply(Z, Y), X))), multiply(Z, double_divide(multiply(Z, Y), X))), double_divide(multiply(Z, double_divide(multiply(Z, Y), X)), X)), X)), Z)
% 0.18/0.43 = { by lemma 3 }
% 0.18/0.43 multiply(inverse(multiply(Z, double_divide(multiply(Z, Y), X))), Z)
% 0.18/0.43 = { by lemma 10 R->L }
% 0.18/0.43 multiply(inverse(multiply(Z, double_divide(multiply(Z, Y), X))), multiply(multiply(inverse(V), V), Z))
% 0.18/0.43 = { by lemma 10 R->L }
% 0.18/0.43 multiply(inverse(multiply(multiply(multiply(inverse(V), V), Z), double_divide(multiply(Z, Y), X))), multiply(multiply(inverse(V), V), Z))
% 0.18/0.43 = { by lemma 9 }
% 0.18/0.43 inverse(double_divide(multiply(Z, Y), X))
% 0.18/0.43 = { by axiom 1 (multiply) R->L }
% 0.18/0.43 multiply(X, multiply(Z, Y))
% 0.18/0.43
% 0.18/0.43 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.18/0.43 Proof:
% 0.18/0.43 multiply(multiply(a3, b3), c3)
% 0.18/0.43 = { by lemma 11 }
% 0.18/0.43 multiply(a3, multiply(c3, b3))
% 0.18/0.43 = { by lemma 10 R->L }
% 0.18/0.43 multiply(a3, multiply(multiply(inverse(X), X), multiply(c3, b3)))
% 0.18/0.43 = { by lemma 11 R->L }
% 0.18/0.43 multiply(a3, multiply(multiply(multiply(inverse(X), X), b3), c3))
% 0.18/0.43 = { by lemma 10 }
% 0.18/0.43 multiply(a3, multiply(b3, c3))
% 0.18/0.43 % SZS output end Proof
% 0.18/0.43
% 0.18/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
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