TSTP Solution File: GRP589-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP589-1 : 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 : n001.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 0.19s 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
% 0.00/0.12 % Problem : GRP589-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Mon Aug 28 22:04:20 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.39 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.39
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39
% 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(double_divide(X, Y), inverse(double_divide(X, inverse(Z))))), Y) = Z.
% 0.19/0.40
% 0.19/0.40 Lemma 3: double_divide(multiply(multiply(inverse(X), Y), double_divide(Y, Z)), Z) = X.
% 0.19/0.40 Proof:
% 0.19/0.40 double_divide(multiply(multiply(inverse(X), Y), double_divide(Y, Z)), Z)
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 double_divide(multiply(inverse(double_divide(Y, inverse(X))), double_divide(Y, Z)), Z)
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 double_divide(inverse(double_divide(double_divide(Y, Z), inverse(double_divide(Y, inverse(X))))), Z)
% 0.19/0.40 = { by axiom 2 (single_axiom) }
% 0.19/0.40 X
% 0.19/0.40
% 0.19/0.40 Lemma 4: multiply(X, multiply(multiply(inverse(Y), Z), double_divide(Z, X))) = inverse(Y).
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(X, multiply(multiply(inverse(Y), Z), double_divide(Z, X)))
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 inverse(double_divide(multiply(multiply(inverse(Y), Z), double_divide(Z, X)), X))
% 0.19/0.40 = { by lemma 3 }
% 0.19/0.40 inverse(Y)
% 0.19/0.40
% 0.19/0.40 Lemma 5: double_divide(multiply(inverse(X), X), inverse(Y)) = Y.
% 0.19/0.40 Proof:
% 0.19/0.40 double_divide(multiply(inverse(X), X), inverse(Y))
% 0.19/0.40 = { by lemma 4 R->L }
% 0.19/0.40 double_divide(multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), double_divide(Z, inverse(Y)))), X), inverse(Y))
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 double_divide(multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), double_divide(Z, inverse(Y)))), double_divide(multiply(multiply(inverse(X), Z), double_divide(Z, inverse(Y))), inverse(Y))), inverse(Y))
% 0.19/0.40 = { by lemma 3 }
% 0.19/0.40 Y
% 0.19/0.40
% 0.19/0.40 Lemma 6: multiply(inverse(X), multiply(inverse(Y), Y)) = inverse(X).
% 0.19/0.41 Proof:
% 0.19/0.41 multiply(inverse(X), multiply(inverse(Y), Y))
% 0.19/0.41 = { by axiom 1 (multiply) }
% 0.19/0.41 inverse(double_divide(multiply(inverse(Y), Y), inverse(X)))
% 0.19/0.41 = { by lemma 5 }
% 0.19/0.41 inverse(X)
% 0.19/0.41
% 0.19/0.41 Lemma 7: multiply(inverse(X), multiply(inverse(Y), X)) = inverse(Y).
% 0.19/0.41 Proof:
% 0.19/0.41 multiply(inverse(X), multiply(inverse(Y), X))
% 0.19/0.41 = { by axiom 1 (multiply) }
% 0.19/0.41 inverse(double_divide(multiply(inverse(Y), X), inverse(X)))
% 0.19/0.41 = { by lemma 4 R->L }
% 0.19/0.41 inverse(double_divide(multiply(inverse(Y), X), multiply(Z, multiply(multiply(inverse(X), W), double_divide(W, Z)))))
% 0.19/0.41 = { by lemma 3 R->L }
% 0.19/0.41 inverse(double_divide(multiply(inverse(Y), double_divide(multiply(multiply(inverse(X), W), double_divide(W, Z)), Z)), multiply(Z, multiply(multiply(inverse(X), W), double_divide(W, Z)))))
% 0.19/0.41 = { by lemma 6 R->L }
% 0.19/0.41 inverse(double_divide(multiply(multiply(inverse(Y), multiply(inverse(V), V)), double_divide(multiply(multiply(inverse(X), W), double_divide(W, Z)), Z)), multiply(Z, multiply(multiply(inverse(X), W), double_divide(W, Z)))))
% 0.19/0.41 = { by lemma 5 R->L }
% 0.19/0.41 inverse(double_divide(multiply(multiply(inverse(Y), multiply(inverse(V), V)), double_divide(multiply(inverse(V), V), inverse(double_divide(multiply(multiply(inverse(X), W), double_divide(W, Z)), Z)))), multiply(Z, multiply(multiply(inverse(X), W), double_divide(W, Z)))))
% 0.19/0.41 = { by axiom 1 (multiply) R->L }
% 0.19/0.41 inverse(double_divide(multiply(multiply(inverse(Y), multiply(inverse(V), V)), double_divide(multiply(inverse(V), V), multiply(Z, multiply(multiply(inverse(X), W), double_divide(W, Z))))), multiply(Z, multiply(multiply(inverse(X), W), double_divide(W, Z)))))
% 0.19/0.41 = { by lemma 3 }
% 0.19/0.41 inverse(Y)
% 0.19/0.41
% 0.19/0.41 Lemma 8: multiply(inverse(multiply(inverse(X), X)), Y) = Y.
% 0.19/0.41 Proof:
% 0.19/0.41 multiply(inverse(multiply(inverse(X), X)), Y)
% 0.19/0.41 = { by lemma 3 R->L }
% 0.19/0.41 double_divide(multiply(multiply(inverse(multiply(inverse(multiply(inverse(X), X)), Y)), Z), double_divide(Z, W)), W)
% 0.19/0.41 = { by lemma 6 R->L }
% 0.19/0.41 double_divide(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(X), X)), Y)), multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X))), Z), double_divide(Z, W)), W)
% 0.19/0.41 = { by lemma 6 }
% 0.19/0.41 double_divide(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(X), X)), Y)), inverse(multiply(inverse(X), X))), Z), double_divide(Z, W)), W)
% 0.19/0.41 = { by lemma 7 R->L }
% 0.19/0.41 double_divide(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(X), X)), Y)), multiply(inverse(Y), multiply(inverse(multiply(inverse(X), X)), Y))), Z), double_divide(Z, W)), W)
% 0.19/0.41 = { by lemma 7 }
% 0.19/0.41 double_divide(multiply(multiply(inverse(Y), Z), double_divide(Z, W)), W)
% 0.19/0.41 = { by lemma 3 }
% 0.19/0.41 Y
% 0.19/0.41
% 0.19/0.41 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.19/0.41 Proof:
% 0.19/0.41 multiply(inverse(a1), a1)
% 0.19/0.41 = { by lemma 8 R->L }
% 0.19/0.41 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(a1), a1))
% 0.19/0.41 = { by lemma 6 }
% 0.19/0.41 inverse(multiply(inverse(X), X))
% 0.19/0.41 = { by lemma 6 R->L }
% 0.19/0.41 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(b1), b1))
% 0.19/0.41 = { by lemma 8 }
% 0.19/0.41 multiply(inverse(b1), b1)
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41
% 0.19/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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