TSTP Solution File: GRP558-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP558-1 : 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 : n007.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 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP558-1 : TPTP v8.1.2. Released v2.6.0.
% 0.11/0.12 % 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 : n007.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 21:53:58 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.37 Command-line arguments: --no-flatten-goal
% 0.12/0.37
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.12/0.38 Axiom 2 (single_axiom): divide(X, inverse(divide(divide(Y, Z), divide(X, Z)))) = Y.
% 0.12/0.38
% 0.12/0.38 Lemma 3: multiply(X, divide(divide(Y, Z), divide(X, Z))) = Y.
% 0.12/0.38 Proof:
% 0.12/0.38 multiply(X, divide(divide(Y, Z), divide(X, Z)))
% 0.12/0.38 = { by axiom 1 (multiply) }
% 0.12/0.38 divide(X, inverse(divide(divide(Y, Z), divide(X, Z))))
% 0.12/0.38 = { by axiom 2 (single_axiom) }
% 0.12/0.38 Y
% 0.12/0.38
% 0.12/0.38 Lemma 4: multiply(X, divide(multiply(Y, Z), multiply(X, Z))) = Y.
% 0.12/0.38 Proof:
% 0.12/0.38 multiply(X, divide(multiply(Y, Z), multiply(X, Z)))
% 0.12/0.38 = { by axiom 1 (multiply) }
% 0.12/0.38 multiply(X, divide(multiply(Y, Z), divide(X, inverse(Z))))
% 0.12/0.38 = { by axiom 1 (multiply) }
% 0.12/0.38 multiply(X, divide(divide(Y, inverse(Z)), divide(X, inverse(Z))))
% 0.12/0.38 = { by lemma 3 }
% 0.12/0.38 Y
% 0.12/0.38
% 0.12/0.38 Lemma 5: multiply(X, divide(Y, Y)) = X.
% 0.12/0.38 Proof:
% 0.12/0.38 multiply(X, divide(Y, Y))
% 0.12/0.38 = { by lemma 3 R->L }
% 0.12/0.38 multiply(X, divide(Y, multiply(X, divide(divide(Y, Z), divide(X, Z)))))
% 0.12/0.38 = { by lemma 3 R->L }
% 0.12/0.38 multiply(X, divide(multiply(X, divide(divide(Y, Z), divide(X, Z))), multiply(X, divide(divide(Y, Z), divide(X, Z)))))
% 0.12/0.38 = { by lemma 4 }
% 0.12/0.38 X
% 0.12/0.38
% 0.12/0.38 Lemma 6: multiply(X, divide(Y, X)) = Y.
% 0.12/0.38 Proof:
% 0.12/0.38 multiply(X, divide(Y, X))
% 0.12/0.38 = { by lemma 5 R->L }
% 0.12/0.38 multiply(X, divide(Y, multiply(X, divide(Z, Z))))
% 0.12/0.38 = { by lemma 5 R->L }
% 0.12/0.38 multiply(X, divide(multiply(Y, divide(Z, Z)), multiply(X, divide(Z, Z))))
% 0.12/0.38 = { by lemma 4 }
% 0.12/0.38 Y
% 0.12/0.38
% 0.12/0.38 Lemma 7: multiply(inverse(divide(X, X)), Y) = Y.
% 0.12/0.38 Proof:
% 0.12/0.38 multiply(inverse(divide(X, X)), Y)
% 0.12/0.38 = { by lemma 5 R->L }
% 0.12/0.38 multiply(inverse(divide(X, X)), multiply(Y, divide(X, X)))
% 0.12/0.38 = { by axiom 1 (multiply) }
% 0.12/0.38 multiply(inverse(divide(X, X)), divide(Y, inverse(divide(X, X))))
% 0.12/0.38 = { by lemma 6 }
% 0.12/0.38 Y
% 0.12/0.38
% 0.12/0.38 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.12/0.38 Proof:
% 0.12/0.38 multiply(multiply(inverse(b2), b2), a2)
% 0.12/0.38 = { by lemma 7 R->L }
% 0.12/0.38 multiply(multiply(inverse(divide(X, X)), multiply(inverse(b2), b2)), a2)
% 0.12/0.38 = { by axiom 1 (multiply) }
% 0.12/0.38 multiply(multiply(inverse(divide(X, X)), divide(inverse(b2), inverse(b2))), a2)
% 0.12/0.38 = { by lemma 7 }
% 0.12/0.38 multiply(divide(inverse(b2), inverse(b2)), a2)
% 0.12/0.38 = { by lemma 6 R->L }
% 0.12/0.38 multiply(a2, divide(multiply(divide(inverse(b2), inverse(b2)), a2), a2))
% 0.12/0.38 = { by lemma 7 R->L }
% 0.12/0.38 multiply(a2, divide(multiply(divide(inverse(b2), inverse(b2)), a2), multiply(inverse(divide(Y, Y)), a2)))
% 0.12/0.38 = { by lemma 7 R->L }
% 0.12/0.38 multiply(a2, multiply(inverse(divide(Y, Y)), divide(multiply(divide(inverse(b2), inverse(b2)), a2), multiply(inverse(divide(Y, Y)), a2))))
% 0.12/0.38 = { by lemma 4 }
% 0.12/0.38 multiply(a2, divide(inverse(b2), inverse(b2)))
% 0.12/0.38 = { by lemma 5 }
% 0.12/0.38 a2
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38
% 0.12/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
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