TSTP Solution File: GRP605-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP605-1 : 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 : n029.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 01:19:05 EDT 2023
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP605-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.13 % 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 : n029.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 20:36:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.39 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.12/0.39
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.19/0.40 Axiom 2 (single_axiom): double_divide(inverse(double_divide(X, inverse(double_divide(inverse(Y), double_divide(X, Z))))), Z) = Y.
% 0.19/0.40
% 0.19/0.40 Lemma 3: double_divide(multiply(multiply(double_divide(X, Y), inverse(Z)), X), Y) = Z.
% 0.19/0.40 Proof:
% 0.19/0.40 double_divide(multiply(multiply(double_divide(X, Y), inverse(Z)), X), Y)
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 double_divide(multiply(inverse(double_divide(inverse(Z), double_divide(X, Y))), X), Y)
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 double_divide(inverse(double_divide(X, inverse(double_divide(inverse(Z), double_divide(X, Y))))), Y)
% 0.19/0.40 = { by axiom 2 (single_axiom) }
% 0.19/0.40 Z
% 0.19/0.40
% 0.19/0.40 Lemma 4: multiply(multiply(X, inverse(Y)), inverse(X)) = inverse(Y).
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(multiply(X, inverse(Y)), inverse(X))
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 inverse(double_divide(inverse(X), multiply(X, inverse(Y))))
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 inverse(double_divide(inverse(double_divide(multiply(multiply(double_divide(Z, multiply(X, inverse(Y))), inverse(X)), Z), multiply(X, inverse(Y)))), multiply(X, inverse(Y))))
% 0.19/0.40 = { by axiom 1 (multiply) R->L }
% 0.19/0.40 inverse(double_divide(multiply(multiply(X, inverse(Y)), multiply(multiply(double_divide(Z, multiply(X, inverse(Y))), inverse(X)), Z)), multiply(X, inverse(Y))))
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 inverse(double_divide(multiply(multiply(double_divide(multiply(multiply(double_divide(Z, multiply(X, inverse(Y))), inverse(X)), Z), multiply(X, inverse(Y))), inverse(Y)), multiply(multiply(double_divide(Z, multiply(X, inverse(Y))), inverse(X)), Z)), multiply(X, inverse(Y))))
% 0.19/0.40 = { by lemma 3 }
% 0.19/0.40 inverse(Y)
% 0.19/0.40
% 0.19/0.40 Lemma 5: multiply(inverse(X), inverse(multiply(Y, inverse(X)))) = inverse(Y).
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(inverse(X), inverse(multiply(Y, inverse(X))))
% 0.19/0.40 = { by lemma 4 R->L }
% 0.19/0.40 multiply(multiply(multiply(Y, inverse(X)), inverse(Y)), inverse(multiply(Y, inverse(X))))
% 0.19/0.40 = { by lemma 4 }
% 0.19/0.40 inverse(Y)
% 0.19/0.40
% 0.19/0.40 Lemma 6: multiply(multiply(X, multiply(Y, Z)), inverse(X)) = multiply(Y, Z).
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(multiply(X, multiply(Y, Z)), inverse(X))
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 multiply(multiply(X, inverse(double_divide(Z, Y))), inverse(X))
% 0.19/0.40 = { by lemma 4 }
% 0.19/0.40 inverse(double_divide(Z, Y))
% 0.19/0.40 = { by axiom 1 (multiply) R->L }
% 0.19/0.40 multiply(Y, Z)
% 0.19/0.40
% 0.19/0.40 Lemma 7: multiply(X, multiply(Y, inverse(X))) = Y.
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(X, multiply(Y, inverse(X)))
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 double_divide(multiply(multiply(double_divide(Z, W), inverse(multiply(X, multiply(Y, inverse(X))))), Z), W)
% 0.19/0.40 = { by lemma 5 R->L }
% 0.19/0.40 double_divide(multiply(multiply(double_divide(Z, W), multiply(inverse(X), inverse(multiply(multiply(X, multiply(Y, inverse(X))), inverse(X))))), Z), W)
% 0.19/0.40 = { by lemma 6 }
% 0.19/0.40 double_divide(multiply(multiply(double_divide(Z, W), multiply(inverse(X), inverse(multiply(Y, inverse(X))))), Z), W)
% 0.19/0.40 = { by lemma 5 }
% 0.19/0.40 double_divide(multiply(multiply(double_divide(Z, W), inverse(Y)), Z), W)
% 0.19/0.40 = { by lemma 3 }
% 0.19/0.40 Y
% 0.19/0.40
% 0.19/0.40 Lemma 8: multiply(Y, multiply(X, Z)) = multiply(X, multiply(Y, Z)).
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(Y, multiply(X, Z))
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 inverse(double_divide(multiply(X, Z), Y))
% 0.19/0.40 = { by lemma 7 R->L }
% 0.19/0.40 inverse(double_divide(multiply(multiply(double_divide(Z, Y), multiply(X, inverse(double_divide(Z, Y)))), Z), Y))
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 inverse(double_divide(multiply(multiply(double_divide(Z, Y), inverse(double_divide(inverse(double_divide(Z, Y)), X))), Z), Y))
% 0.19/0.40 = { by lemma 3 }
% 0.19/0.40 inverse(double_divide(inverse(double_divide(Z, Y)), X))
% 0.19/0.40 = { by axiom 1 (multiply) R->L }
% 0.19/0.40 inverse(double_divide(multiply(Y, Z), X))
% 0.19/0.40 = { by axiom 1 (multiply) R->L }
% 0.19/0.40 multiply(X, multiply(Y, Z))
% 0.19/0.40
% 0.19/0.40 Lemma 9: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(X, multiply(Y, inverse(Y)))
% 0.19/0.40 = { by lemma 8 }
% 0.19/0.40 multiply(Y, multiply(X, inverse(Y)))
% 0.19/0.40 = { by lemma 7 }
% 0.19/0.40 X
% 0.19/0.40
% 0.19/0.40 Lemma 10: multiply(Y, X) = multiply(X, Y).
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(Y, X)
% 0.19/0.40 = { by lemma 9 R->L }
% 0.19/0.40 multiply(Y, multiply(X, multiply(Z, inverse(Z))))
% 0.19/0.40 = { by lemma 8 R->L }
% 0.19/0.40 multiply(X, multiply(Y, multiply(Z, inverse(Z))))
% 0.19/0.40 = { by lemma 9 }
% 0.19/0.40 multiply(X, Y)
% 0.19/0.40
% 0.19/0.40 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(inverse(a1), a1)
% 0.19/0.40 = { by lemma 10 R->L }
% 0.19/0.40 multiply(a1, inverse(a1))
% 0.19/0.40 = { by lemma 9 R->L }
% 0.19/0.40 multiply(multiply(a1, multiply(b1, inverse(b1))), inverse(a1))
% 0.19/0.40 = { by lemma 6 }
% 0.19/0.40 multiply(b1, inverse(b1))
% 0.19/0.40 = { by lemma 10 }
% 0.19/0.40 multiply(inverse(b1), b1)
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40
% 0.19/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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