TSTP Solution File: GRP452-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP452-1 : 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 : n014.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 01:18:29 EDT 2023
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP452-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 22:38:01 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.39 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.13/0.39
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.40
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 Axiom 1 (inverse): inverse(X) = divide(divide(Y, Y), X).
% 0.20/0.41 Axiom 2 (multiply): multiply(X, Y) = divide(X, divide(divide(Z, Z), Y)).
% 0.20/0.41 Axiom 3 (single_axiom): divide(divide(divide(X, X), divide(X, divide(Y, divide(divide(divide(X, X), X), Z)))), Z) = Y.
% 0.20/0.41
% 0.20/0.41 Lemma 4: divide(inverse(divide(X, divide(Y, divide(inverse(X), Z)))), Z) = Y.
% 0.20/0.41 Proof:
% 0.20/0.41 divide(inverse(divide(X, divide(Y, divide(inverse(X), Z)))), Z)
% 0.20/0.41 = { by axiom 1 (inverse) }
% 0.20/0.41 divide(inverse(divide(X, divide(Y, divide(divide(divide(X, X), X), Z)))), Z)
% 0.20/0.41 = { by axiom 1 (inverse) }
% 0.20/0.41 divide(divide(divide(X, X), divide(X, divide(Y, divide(divide(divide(X, X), X), Z)))), Z)
% 0.20/0.41 = { by axiom 3 (single_axiom) }
% 0.20/0.41 Y
% 0.20/0.41
% 0.20/0.41 Lemma 5: divide(Y, Y) = divide(X, X).
% 0.20/0.41 Proof:
% 0.20/0.41 divide(Y, Y)
% 0.20/0.41 = { by lemma 4 R->L }
% 0.20/0.41 divide(inverse(divide(Z, divide(divide(Y, Y), divide(inverse(Z), W)))), W)
% 0.20/0.41 = { by axiom 1 (inverse) R->L }
% 0.20/0.41 divide(inverse(divide(Z, inverse(divide(inverse(Z), W)))), W)
% 0.20/0.41 = { by axiom 1 (inverse) }
% 0.20/0.41 divide(inverse(divide(Z, divide(divide(X, X), divide(inverse(Z), W)))), W)
% 0.20/0.41 = { by lemma 4 }
% 0.20/0.41 divide(X, X)
% 0.20/0.41
% 0.20/0.41 Lemma 6: divide(X, inverse(Y)) = multiply(X, Y).
% 0.20/0.41 Proof:
% 0.20/0.41 divide(X, inverse(Y))
% 0.20/0.41 = { by axiom 1 (inverse) }
% 0.20/0.41 divide(X, divide(divide(Z, Z), Y))
% 0.20/0.41 = { by axiom 2 (multiply) R->L }
% 0.20/0.41 multiply(X, Y)
% 0.20/0.41
% 0.20/0.41 Lemma 7: inverse(divide(X, X)) = divide(Y, Y).
% 0.20/0.41 Proof:
% 0.20/0.41 inverse(divide(X, X))
% 0.20/0.41 = { by axiom 1 (inverse) }
% 0.20/0.41 divide(divide(X, X), divide(X, X))
% 0.20/0.41 = { by lemma 5 R->L }
% 0.20/0.41 divide(Y, Y)
% 0.20/0.41
% 0.20/0.41 Lemma 8: divide(inverse(divide(X, X)), Y) = inverse(Y).
% 0.20/0.41 Proof:
% 0.20/0.41 divide(inverse(divide(X, X)), Y)
% 0.20/0.41 = { by axiom 1 (inverse) }
% 0.20/0.41 divide(divide(divide(X, X), divide(X, X)), Y)
% 0.20/0.41 = { by axiom 1 (inverse) R->L }
% 0.20/0.41 inverse(Y)
% 0.20/0.41
% 0.20/0.41 Lemma 9: divide(inverse(inverse(multiply(X, Y))), Y) = X.
% 0.20/0.41 Proof:
% 0.20/0.41 divide(inverse(inverse(multiply(X, Y))), Y)
% 0.20/0.41 = { by lemma 6 R->L }
% 0.20/0.41 divide(inverse(inverse(divide(X, inverse(Y)))), Y)
% 0.20/0.41 = { by axiom 1 (inverse) }
% 0.20/0.41 divide(inverse(divide(divide(Z, Z), divide(X, inverse(Y)))), Y)
% 0.20/0.41 = { by lemma 8 R->L }
% 0.20/0.41 divide(inverse(divide(divide(Z, Z), divide(X, divide(inverse(divide(Z, Z)), Y)))), Y)
% 0.20/0.41 = { by lemma 4 }
% 0.20/0.41 X
% 0.20/0.41
% 0.20/0.41 Lemma 10: inverse(multiply(X, divide(Y, Y))) = inverse(X).
% 0.20/0.41 Proof:
% 0.20/0.41 inverse(multiply(X, divide(Y, Y)))
% 0.20/0.41 = { by lemma 9 R->L }
% 0.20/0.41 divide(inverse(inverse(multiply(inverse(multiply(X, divide(Y, Y))), X))), X)
% 0.20/0.41 = { by lemma 6 R->L }
% 0.20/0.41 divide(inverse(inverse(divide(inverse(multiply(X, divide(Y, Y))), inverse(X)))), X)
% 0.20/0.41 = { by lemma 5 }
% 0.20/0.41 divide(inverse(inverse(divide(inverse(multiply(X, divide(inverse(X), inverse(X)))), inverse(X)))), X)
% 0.20/0.41 = { by lemma 6 R->L }
% 0.20/0.41 divide(inverse(inverse(divide(inverse(divide(X, inverse(divide(inverse(X), inverse(X))))), inverse(X)))), X)
% 0.20/0.41 = { by axiom 1 (inverse) }
% 0.20/0.41 divide(inverse(inverse(divide(inverse(divide(X, divide(divide(Z, Z), divide(inverse(X), inverse(X))))), inverse(X)))), X)
% 0.20/0.41 = { by lemma 4 }
% 0.20/0.41 divide(inverse(inverse(divide(Z, Z))), X)
% 0.20/0.41 = { by lemma 7 }
% 0.20/0.41 divide(inverse(divide(W, W)), X)
% 0.20/0.41 = { by lemma 8 }
% 0.20/0.41 inverse(X)
% 0.20/0.41
% 0.20/0.41 Lemma 11: multiply(inverse(inverse(multiply(X, inverse(Y)))), Y) = X.
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(inverse(inverse(multiply(X, inverse(Y)))), Y)
% 0.20/0.41 = { by lemma 6 R->L }
% 0.20/0.41 divide(inverse(inverse(multiply(X, inverse(Y)))), inverse(Y))
% 0.20/0.41 = { by lemma 9 }
% 0.20/0.41 X
% 0.20/0.41
% 0.20/0.41 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(multiply(inverse(b2), b2), a2)
% 0.20/0.41 = { by lemma 6 R->L }
% 0.20/0.41 divide(multiply(inverse(b2), b2), inverse(a2))
% 0.20/0.41 = { by lemma 6 R->L }
% 0.20/0.41 divide(divide(inverse(b2), inverse(b2)), inverse(a2))
% 0.20/0.41 = { by axiom 1 (inverse) R->L }
% 0.20/0.41 inverse(inverse(a2))
% 0.20/0.41 = { by lemma 9 R->L }
% 0.20/0.41 divide(inverse(inverse(multiply(inverse(inverse(a2)), X))), X)
% 0.20/0.41 = { by lemma 6 R->L }
% 0.20/0.41 divide(inverse(inverse(divide(inverse(inverse(a2)), inverse(X)))), X)
% 0.20/0.42 = { by lemma 9 R->L }
% 0.20/0.42 divide(inverse(inverse(divide(inverse(inverse(divide(inverse(inverse(multiply(a2, inverse(inverse(X))))), inverse(inverse(X))))), inverse(X)))), X)
% 0.20/0.42 = { by lemma 10 R->L }
% 0.20/0.42 divide(inverse(inverse(divide(inverse(inverse(divide(inverse(inverse(multiply(a2, inverse(inverse(multiply(X, divide(Y, Y))))))), inverse(inverse(X))))), inverse(X)))), X)
% 0.20/0.42 = { by lemma 7 R->L }
% 0.20/0.42 divide(inverse(inverse(divide(inverse(inverse(divide(inverse(inverse(multiply(a2, inverse(inverse(multiply(X, inverse(divide(Z, Z)))))))), inverse(inverse(X))))), inverse(X)))), X)
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 divide(inverse(inverse(divide(inverse(inverse(divide(inverse(inverse(divide(a2, inverse(inverse(inverse(multiply(X, inverse(divide(Z, Z))))))))), inverse(inverse(X))))), inverse(X)))), X)
% 0.20/0.42 = { by lemma 10 R->L }
% 0.20/0.42 divide(inverse(inverse(divide(inverse(inverse(divide(inverse(inverse(divide(a2, inverse(multiply(inverse(inverse(multiply(X, inverse(divide(Z, Z))))), divide(Z, Z)))))), inverse(inverse(X))))), inverse(X)))), X)
% 0.20/0.42 = { by lemma 6 }
% 0.20/0.42 divide(inverse(inverse(divide(inverse(inverse(divide(inverse(inverse(multiply(a2, multiply(inverse(inverse(multiply(X, inverse(divide(Z, Z))))), divide(Z, Z))))), inverse(inverse(X))))), inverse(X)))), X)
% 0.20/0.42 = { by lemma 11 }
% 0.20/0.42 divide(inverse(inverse(divide(inverse(inverse(divide(inverse(inverse(multiply(a2, X))), inverse(inverse(X))))), inverse(X)))), X)
% 0.20/0.42 = { by lemma 6 }
% 0.20/0.42 divide(inverse(inverse(divide(inverse(inverse(multiply(inverse(inverse(multiply(a2, X))), inverse(X)))), inverse(X)))), X)
% 0.20/0.42 = { by lemma 9 }
% 0.20/0.42 divide(inverse(inverse(inverse(inverse(multiply(a2, X))))), X)
% 0.20/0.42 = { by lemma 10 R->L }
% 0.20/0.42 divide(inverse(inverse(inverse(multiply(inverse(multiply(a2, X)), divide(W, W))))), X)
% 0.20/0.42 = { by lemma 7 R->L }
% 0.20/0.42 divide(inverse(inverse(inverse(multiply(inverse(multiply(a2, X)), inverse(divide(V, V)))))), X)
% 0.20/0.42 = { by lemma 10 R->L }
% 0.20/0.42 divide(inverse(multiply(inverse(inverse(multiply(inverse(multiply(a2, X)), inverse(divide(V, V))))), divide(V, V))), X)
% 0.20/0.42 = { by lemma 11 }
% 0.20/0.42 divide(inverse(inverse(multiply(a2, X))), X)
% 0.20/0.42 = { by lemma 9 }
% 0.20/0.42 a2
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42
% 0.20/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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