TSTP Solution File: GRP523-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP523-1 : 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 : n032.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 01:18:46 EDT 2023
% Result : Unsatisfiable 0.14s 0.33s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : GRP523-1 : TPTP v8.1.2. Released v2.6.0.
% 0.05/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Aug 29 01:51:16 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.33 Command-line arguments: --no-flatten-goal
% 0.14/0.33
% 0.14/0.33 % SZS status Unsatisfiable
% 0.14/0.33
% 0.14/0.34 % SZS output start Proof
% 0.14/0.34 Axiom 1 (inverse): inverse(X) = divide(divide(Y, Y), X).
% 0.14/0.34 Axiom 2 (multiply): multiply(X, Y) = divide(X, divide(divide(Z, Z), Y)).
% 0.14/0.34 Axiom 3 (single_axiom): divide(X, divide(Y, divide(Z, divide(X, Y)))) = Z.
% 0.14/0.34
% 0.14/0.34 Lemma 4: divide(X, inverse(Y)) = multiply(X, Y).
% 0.14/0.34 Proof:
% 0.14/0.34 divide(X, inverse(Y))
% 0.14/0.34 = { by axiom 1 (inverse) }
% 0.14/0.34 divide(X, divide(divide(Z, Z), Y))
% 0.14/0.34 = { by axiom 2 (multiply) R->L }
% 0.14/0.34 multiply(X, Y)
% 0.14/0.34
% 0.14/0.34 Lemma 5: inverse(divide(X, multiply(Y, X))) = Y.
% 0.14/0.34 Proof:
% 0.14/0.34 inverse(divide(X, multiply(Y, X)))
% 0.14/0.34 = { by lemma 4 R->L }
% 0.14/0.34 inverse(divide(X, divide(Y, inverse(X))))
% 0.14/0.34 = { by axiom 1 (inverse) }
% 0.14/0.34 inverse(divide(X, divide(Y, divide(divide(Z, Z), X))))
% 0.14/0.34 = { by axiom 1 (inverse) }
% 0.14/0.34 divide(divide(Z, Z), divide(X, divide(Y, divide(divide(Z, Z), X))))
% 0.14/0.34 = { by axiom 3 (single_axiom) }
% 0.14/0.34 Y
% 0.14/0.34
% 0.14/0.34 Lemma 6: inverse(inverse(multiply(X, divide(Y, Y)))) = X.
% 0.14/0.34 Proof:
% 0.14/0.34 inverse(inverse(multiply(X, divide(Y, Y))))
% 0.14/0.34 = { by axiom 1 (inverse) }
% 0.14/0.34 inverse(divide(divide(Y, Y), multiply(X, divide(Y, Y))))
% 0.14/0.34 = { by lemma 5 }
% 0.14/0.34 X
% 0.14/0.34
% 0.14/0.34 Lemma 7: multiply(divide(X, X), Y) = inverse(inverse(Y)).
% 0.14/0.34 Proof:
% 0.14/0.34 multiply(divide(X, X), Y)
% 0.14/0.34 = { by lemma 4 R->L }
% 0.14/0.34 divide(divide(X, X), inverse(Y))
% 0.14/0.34 = { by axiom 1 (inverse) R->L }
% 0.14/0.34 inverse(inverse(Y))
% 0.14/0.34
% 0.14/0.34 Lemma 8: divide(X, divide(Y, Y)) = multiply(X, divide(Z, Z)).
% 0.14/0.34 Proof:
% 0.14/0.34 divide(X, divide(Y, Y))
% 0.14/0.34 = { by lemma 5 R->L }
% 0.14/0.34 divide(X, inverse(divide(W, multiply(divide(Y, Y), W))))
% 0.14/0.34 = { by lemma 7 }
% 0.14/0.34 divide(X, inverse(divide(W, inverse(inverse(W)))))
% 0.14/0.34 = { by lemma 7 R->L }
% 0.14/0.34 divide(X, inverse(divide(W, multiply(divide(divide(Z, Z), divide(Z, Z)), W))))
% 0.14/0.34 = { by lemma 5 }
% 0.14/0.34 divide(X, divide(divide(Z, Z), divide(Z, Z)))
% 0.14/0.34 = { by axiom 1 (inverse) R->L }
% 0.14/0.34 divide(X, inverse(divide(Z, Z)))
% 0.14/0.34 = { by lemma 4 }
% 0.14/0.34 multiply(X, divide(Z, Z))
% 0.14/0.34
% 0.14/0.34 Lemma 9: multiply(X, divide(Y, Y)) = X.
% 0.14/0.34 Proof:
% 0.14/0.34 multiply(X, divide(Y, Y))
% 0.14/0.34 = { by lemma 6 R->L }
% 0.14/0.34 inverse(inverse(multiply(multiply(X, divide(Y, Y)), divide(Z, Z))))
% 0.14/0.34 = { by lemma 8 R->L }
% 0.14/0.34 inverse(inverse(divide(multiply(X, divide(Y, Y)), divide(inverse(multiply(X, divide(Y, Y))), inverse(multiply(X, divide(Y, Y)))))))
% 0.14/0.34 = { by lemma 4 }
% 0.14/0.34 inverse(inverse(divide(multiply(X, divide(Y, Y)), multiply(inverse(multiply(X, divide(Y, Y))), multiply(X, divide(Y, Y))))))
% 0.14/0.34 = { by lemma 5 }
% 0.14/0.34 inverse(inverse(multiply(X, divide(Y, Y))))
% 0.14/0.34 = { by lemma 6 }
% 0.14/0.34 X
% 0.14/0.34
% 0.14/0.34 Lemma 10: multiply(X, divide(Y, multiply(Z, Y))) = divide(X, Z).
% 0.14/0.34 Proof:
% 0.14/0.34 multiply(X, divide(Y, multiply(Z, Y)))
% 0.14/0.34 = { by lemma 4 R->L }
% 0.14/0.34 divide(X, inverse(divide(Y, multiply(Z, Y))))
% 0.14/0.34 = { by lemma 5 }
% 0.14/0.34 divide(X, Z)
% 0.14/0.34
% 0.14/0.34 Lemma 11: divide(X, divide(multiply(Y, X), Y)) = divide(Z, Z).
% 0.14/0.34 Proof:
% 0.14/0.34 divide(X, divide(multiply(Y, X), Y))
% 0.14/0.34 = { by lemma 10 R->L }
% 0.14/0.34 divide(X, multiply(multiply(Y, X), divide(X, multiply(Y, X))))
% 0.14/0.34 = { by lemma 4 R->L }
% 0.14/0.34 divide(X, divide(multiply(Y, X), inverse(divide(X, multiply(Y, X)))))
% 0.14/0.34 = { by axiom 1 (inverse) }
% 0.14/0.34 divide(X, divide(multiply(Y, X), divide(divide(Z, Z), divide(X, multiply(Y, X)))))
% 0.14/0.34 = { by axiom 3 (single_axiom) }
% 0.14/0.34 divide(Z, Z)
% 0.14/0.34
% 0.14/0.34 Lemma 12: divide(multiply(X, Y), X) = Y.
% 0.14/0.34 Proof:
% 0.14/0.34 divide(multiply(X, Y), X)
% 0.14/0.34 = { by lemma 9 R->L }
% 0.14/0.34 divide(multiply(X, Y), multiply(X, divide(Z, Z)))
% 0.14/0.34 = { by lemma 8 R->L }
% 0.14/0.34 divide(multiply(X, Y), divide(X, divide(W, W)))
% 0.14/0.34 = { by lemma 11 R->L }
% 0.14/0.34 divide(multiply(X, Y), divide(X, divide(Y, divide(multiply(X, Y), X))))
% 0.14/0.34 = { by axiom 3 (single_axiom) }
% 0.14/0.34 Y
% 0.14/0.34
% 0.14/0.34 Lemma 13: multiply(divide(X, Y), Y) = X.
% 0.14/0.34 Proof:
% 0.14/0.34 multiply(divide(X, Y), Y)
% 0.14/0.34 = { by axiom 3 (single_axiom) R->L }
% 0.14/0.34 divide(X, divide(Y, divide(multiply(divide(X, Y), Y), divide(X, Y))))
% 0.14/0.34 = { by lemma 11 }
% 0.14/0.34 divide(X, divide(Z, Z))
% 0.14/0.34 = { by lemma 8 }
% 0.14/0.34 multiply(X, divide(W, W))
% 0.14/0.34 = { by lemma 9 }
% 0.14/0.34 X
% 0.14/0.34
% 0.14/0.34 Lemma 14: multiply(Y, X) = multiply(X, Y).
% 0.14/0.34 Proof:
% 0.14/0.34 multiply(Y, X)
% 0.14/0.34 = { by lemma 12 R->L }
% 0.14/0.34 multiply(divide(multiply(X, Y), X), X)
% 0.14/0.34 = { by lemma 13 }
% 0.14/0.34 multiply(X, Y)
% 0.14/0.34
% 0.14/0.34 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.14/0.34 Proof:
% 0.14/0.34 multiply(multiply(a3, b3), c3)
% 0.14/0.35 = { by lemma 14 R->L }
% 0.14/0.35 multiply(c3, multiply(a3, b3))
% 0.14/0.35 = { by lemma 4 R->L }
% 0.14/0.35 multiply(c3, divide(a3, inverse(b3)))
% 0.14/0.35 = { by lemma 13 R->L }
% 0.14/0.35 multiply(c3, divide(a3, multiply(divide(inverse(b3), a3), a3)))
% 0.14/0.35 = { by lemma 10 }
% 0.14/0.35 divide(c3, divide(inverse(b3), a3))
% 0.14/0.35 = { by lemma 12 R->L }
% 0.14/0.35 divide(c3, divide(inverse(b3), divide(multiply(divide(c3, inverse(b3)), a3), divide(c3, inverse(b3)))))
% 0.14/0.35 = { by axiom 3 (single_axiom) }
% 0.14/0.35 multiply(divide(c3, inverse(b3)), a3)
% 0.14/0.35 = { by lemma 14 R->L }
% 0.14/0.35 multiply(a3, divide(c3, inverse(b3)))
% 0.14/0.35 = { by lemma 4 }
% 0.14/0.35 multiply(a3, multiply(c3, b3))
% 0.14/0.35 = { by lemma 14 R->L }
% 0.14/0.35 multiply(a3, multiply(b3, c3))
% 0.14/0.35 % SZS output end Proof
% 0.14/0.35
% 0.14/0.35 RESULT: Unsatisfiable (the axioms are contradictory).
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