TSTP Solution File: GRP559-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP559-1 : 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 : n008.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 01:18:54 EDT 2023
% Result : Unsatisfiable 0.20s 0.38s
% 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
% 0.00/0.12 % Problem : GRP559-1 : 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
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 00:31:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.38 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.38
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38
% 0.20/0.40 % SZS output start Proof
% 0.20/0.41 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.20/0.41 Axiom 2 (single_axiom): divide(X, inverse(divide(divide(Y, Z), divide(X, Z)))) = Y.
% 0.20/0.41
% 0.20/0.41 Lemma 3: multiply(X, divide(multiply(Y, Z), multiply(X, Z))) = Y.
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(X, divide(multiply(Y, Z), multiply(X, Z)))
% 0.20/0.41 = { by axiom 1 (multiply) }
% 0.20/0.41 multiply(X, divide(multiply(Y, Z), divide(X, inverse(Z))))
% 0.20/0.41 = { by axiom 1 (multiply) }
% 0.20/0.41 multiply(X, divide(divide(Y, inverse(Z)), divide(X, inverse(Z))))
% 0.20/0.41 = { by axiom 1 (multiply) }
% 0.20/0.41 divide(X, inverse(divide(divide(Y, inverse(Z)), divide(X, inverse(Z)))))
% 0.20/0.41 = { by axiom 2 (single_axiom) }
% 0.20/0.41 Y
% 0.20/0.41
% 0.20/0.41 Lemma 4: multiply(X, divide(Y, multiply(X, divide(multiply(Y, Z), multiply(W, Z))))) = W.
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(X, divide(Y, multiply(X, divide(multiply(Y, Z), multiply(W, Z)))))
% 0.20/0.41 = { by lemma 3 R->L }
% 0.20/0.41 multiply(X, divide(multiply(W, divide(multiply(Y, Z), multiply(W, Z))), multiply(X, divide(multiply(Y, Z), multiply(W, Z)))))
% 0.20/0.41 = { by lemma 3 }
% 0.20/0.41 W
% 0.20/0.41
% 0.20/0.41 Lemma 5: multiply(X, divide(Y, Y)) = X.
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(X, divide(Y, Y))
% 0.20/0.41 = { by lemma 3 R->L }
% 0.20/0.41 multiply(X, divide(Y, multiply(X, divide(multiply(Y, Z), multiply(X, Z)))))
% 0.20/0.41 = { by lemma 4 }
% 0.20/0.41 X
% 0.20/0.41
% 0.20/0.41 Lemma 6: multiply(X, divide(Y, X)) = Y.
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(X, divide(Y, X))
% 0.20/0.41 = { by lemma 5 R->L }
% 0.20/0.41 multiply(X, divide(Y, multiply(X, divide(Z, Z))))
% 0.20/0.41 = { by lemma 5 R->L }
% 0.20/0.41 multiply(X, divide(multiply(Y, divide(Z, Z)), multiply(X, divide(Z, Z))))
% 0.20/0.41 = { by lemma 3 }
% 0.20/0.41 Y
% 0.20/0.41
% 0.20/0.41 Lemma 7: multiply(X, multiply(Y, Z)) = multiply(Y, multiply(X, Z)).
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(X, multiply(Y, Z))
% 0.20/0.41 = { by lemma 4 R->L }
% 0.20/0.41 multiply(multiply(inverse(Z), multiply(Y, Z)), divide(X, multiply(multiply(inverse(Z), multiply(Y, Z)), divide(multiply(X, multiply(Y, Z)), multiply(multiply(X, multiply(Y, Z)), multiply(Y, Z))))))
% 0.20/0.41 = { by lemma 6 R->L }
% 0.20/0.41 multiply(multiply(inverse(Z), multiply(Y, Z)), divide(X, multiply(multiply(inverse(Z), multiply(Y, Z)), divide(multiply(X, multiply(Y, Z)), multiply(multiply(inverse(Z), multiply(Y, Z)), divide(multiply(multiply(X, multiply(Y, Z)), multiply(Y, Z)), multiply(inverse(Z), multiply(Y, Z))))))))
% 0.20/0.41 = { by lemma 4 }
% 0.20/0.41 multiply(multiply(inverse(Z), multiply(Y, Z)), divide(X, inverse(Z)))
% 0.20/0.41 = { by axiom 1 (multiply) }
% 0.20/0.41 multiply(multiply(inverse(Z), divide(Y, inverse(Z))), divide(X, inverse(Z)))
% 0.20/0.41 = { by lemma 6 }
% 0.20/0.41 multiply(Y, divide(X, inverse(Z)))
% 0.20/0.41 = { by axiom 1 (multiply) R->L }
% 0.20/0.41 multiply(Y, multiply(X, Z))
% 0.20/0.41
% 0.20/0.41 Lemma 8: multiply(Y, X) = multiply(X, Y).
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(Y, X)
% 0.20/0.41 = { by lemma 5 R->L }
% 0.20/0.41 multiply(Y, multiply(X, divide(Z, Z)))
% 0.20/0.41 = { by lemma 7 }
% 0.20/0.41 multiply(X, multiply(Y, divide(Z, Z)))
% 0.20/0.41 = { by lemma 5 }
% 0.20/0.41 multiply(X, Y)
% 0.20/0.41
% 0.20/0.41 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(multiply(a3, b3), c3)
% 0.20/0.41 = { by lemma 8 R->L }
% 0.20/0.41 multiply(c3, multiply(a3, b3))
% 0.20/0.41 = { by lemma 7 }
% 0.20/0.41 multiply(a3, multiply(c3, b3))
% 0.20/0.41 = { by lemma 8 R->L }
% 0.20/0.41 multiply(a3, multiply(b3, c3))
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41
% 0.20/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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