TSTP Solution File: BOO025-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : BOO025-1 : TPTP v8.1.2. Released v2.2.0.
% 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 : n027.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 : Wed Aug 30 18:11:29 EDT 2023
% Result : Unsatisfiable 0.16s 0.43s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : BOO025-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.31 % Computer : n027.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sun Aug 27 08:15:35 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.43 Command-line arguments: --no-flatten-goal
% 0.16/0.43
% 0.16/0.43 % SZS status Unsatisfiable
% 0.16/0.43
% 0.16/0.45 % SZS output start Proof
% 0.16/0.45 Axiom 1 (pixley1): pixley(X, X, Y) = Y.
% 0.16/0.45 Axiom 2 (pixley2): pixley(X, Y, Y) = X.
% 0.16/0.45 Axiom 3 (additive_inverse): add(X, inverse(X)) = n1.
% 0.16/0.45 Axiom 4 (multiply_add): multiply(add(X, Y), Y) = Y.
% 0.16/0.45 Axiom 5 (multiply_add_property): multiply(X, add(Y, Z)) = add(multiply(Y, X), multiply(Z, X)).
% 0.16/0.45 Axiom 6 (pixley_defn): pixley(X, Y, Z) = add(multiply(X, inverse(Y)), add(multiply(X, Z), multiply(inverse(Y), Z))).
% 0.16/0.45
% 0.16/0.45 Lemma 7: multiply(n1, inverse(X)) = inverse(X).
% 0.16/0.45 Proof:
% 0.16/0.45 multiply(n1, inverse(X))
% 0.16/0.45 = { by axiom 3 (additive_inverse) R->L }
% 0.16/0.45 multiply(add(X, inverse(X)), inverse(X))
% 0.16/0.45 = { by axiom 4 (multiply_add) }
% 0.16/0.45 inverse(X)
% 0.16/0.45
% 0.16/0.45 Lemma 8: add(multiply(X, inverse(Y)), multiply(Z, add(X, inverse(Y)))) = pixley(X, Y, Z).
% 0.16/0.45 Proof:
% 0.16/0.45 add(multiply(X, inverse(Y)), multiply(Z, add(X, inverse(Y))))
% 0.16/0.45 = { by axiom 5 (multiply_add_property) }
% 0.16/0.45 add(multiply(X, inverse(Y)), add(multiply(X, Z), multiply(inverse(Y), Z)))
% 0.16/0.45 = { by axiom 6 (pixley_defn) R->L }
% 0.16/0.45 pixley(X, Y, Z)
% 0.16/0.45
% 0.16/0.45 Lemma 9: add(multiply(X, inverse(X)), multiply(Y, n1)) = Y.
% 0.16/0.45 Proof:
% 0.16/0.45 add(multiply(X, inverse(X)), multiply(Y, n1))
% 0.16/0.45 = { by axiom 3 (additive_inverse) R->L }
% 0.16/0.45 add(multiply(X, inverse(X)), multiply(Y, add(X, inverse(X))))
% 0.16/0.45 = { by lemma 8 }
% 0.16/0.45 pixley(X, X, Y)
% 0.16/0.45 = { by axiom 1 (pixley1) }
% 0.16/0.45 Y
% 0.16/0.45
% 0.16/0.45 Lemma 10: add(inverse(n1), multiply(X, n1)) = X.
% 0.16/0.45 Proof:
% 0.16/0.45 add(inverse(n1), multiply(X, n1))
% 0.16/0.45 = { by lemma 7 R->L }
% 0.16/0.45 add(multiply(n1, inverse(n1)), multiply(X, n1))
% 0.16/0.45 = { by lemma 9 }
% 0.16/0.45 X
% 0.16/0.45
% 0.16/0.45 Lemma 11: add(Y, n1) = add(X, n1).
% 0.16/0.45 Proof:
% 0.16/0.45 add(Y, n1)
% 0.16/0.45 = { by lemma 10 R->L }
% 0.16/0.45 add(inverse(n1), multiply(add(Y, n1), n1))
% 0.16/0.45 = { by axiom 4 (multiply_add) }
% 0.16/0.45 add(inverse(n1), n1)
% 0.16/0.45 = { by axiom 4 (multiply_add) R->L }
% 0.16/0.45 add(inverse(n1), multiply(add(X, n1), n1))
% 0.16/0.45 = { by lemma 10 }
% 0.16/0.45 add(X, n1)
% 0.16/0.45
% 0.16/0.45 Lemma 12: multiply(X, add(add(Y, X), Z)) = add(X, multiply(Z, X)).
% 0.16/0.45 Proof:
% 0.16/0.45 multiply(X, add(add(Y, X), Z))
% 0.16/0.45 = { by axiom 5 (multiply_add_property) }
% 0.16/0.45 add(multiply(add(Y, X), X), multiply(Z, X))
% 0.16/0.45 = { by axiom 4 (multiply_add) }
% 0.16/0.45 add(X, multiply(Z, X))
% 0.16/0.45
% 0.16/0.45 Lemma 13: multiply(add(X, X), add(Y, n1)) = X.
% 0.16/0.45 Proof:
% 0.16/0.45 multiply(add(X, X), add(Y, n1))
% 0.16/0.45 = { by lemma 11 }
% 0.16/0.45 multiply(add(X, X), add(multiply(Z, inverse(Z)), n1))
% 0.16/0.45 = { by axiom 5 (multiply_add_property) }
% 0.16/0.45 add(multiply(multiply(Z, inverse(Z)), add(X, X)), multiply(n1, add(X, X)))
% 0.16/0.45 = { by axiom 5 (multiply_add_property) }
% 0.16/0.45 add(multiply(multiply(Z, inverse(Z)), add(X, X)), add(multiply(X, n1), multiply(X, n1)))
% 0.16/0.45 = { by axiom 4 (multiply_add) R->L }
% 0.16/0.45 add(multiply(multiply(Z, inverse(Z)), add(X, X)), add(multiply(X, n1), multiply(add(multiply(W, inverse(W)), multiply(X, n1)), multiply(X, n1))))
% 0.16/0.45 = { by lemma 9 }
% 0.16/0.45 add(multiply(multiply(Z, inverse(Z)), add(X, X)), add(multiply(X, n1), multiply(X, multiply(X, n1))))
% 0.16/0.45 = { by lemma 12 R->L }
% 0.16/0.45 add(multiply(multiply(Z, inverse(Z)), add(X, X)), multiply(multiply(X, n1), add(add(multiply(V, inverse(V)), multiply(X, n1)), X)))
% 0.16/0.45 = { by lemma 9 }
% 0.16/0.45 add(multiply(multiply(Z, inverse(Z)), add(X, X)), multiply(multiply(X, n1), add(X, X)))
% 0.16/0.45 = { by axiom 5 (multiply_add_property) R->L }
% 0.16/0.45 multiply(add(X, X), add(multiply(Z, inverse(Z)), multiply(X, n1)))
% 0.16/0.45 = { by lemma 9 }
% 0.16/0.45 multiply(add(X, X), X)
% 0.16/0.45 = { by axiom 4 (multiply_add) }
% 0.16/0.46 X
% 0.16/0.46
% 0.16/0.46 Lemma 14: multiply(X, add(Y, n1)) = add(X, multiply(n1, X)).
% 0.16/0.46 Proof:
% 0.16/0.46 multiply(X, add(Y, n1))
% 0.16/0.46 = { by lemma 11 }
% 0.16/0.46 multiply(X, add(add(Z, X), n1))
% 0.16/0.46 = { by lemma 12 }
% 0.16/0.46 add(X, multiply(n1, X))
% 0.16/0.46
% 0.16/0.46 Lemma 15: multiply(add(X, X), n1) = X.
% 0.16/0.46 Proof:
% 0.16/0.46 multiply(add(X, X), n1)
% 0.16/0.46 = { by lemma 13 R->L }
% 0.16/0.46 multiply(add(X, X), multiply(add(n1, n1), add(multiply(Y, n1), n1)))
% 0.16/0.46 = { by axiom 4 (multiply_add) R->L }
% 0.16/0.46 multiply(add(X, X), multiply(multiply(add(Y, add(n1, n1)), add(n1, n1)), add(multiply(Y, n1), n1)))
% 0.16/0.46 = { by lemma 14 }
% 0.16/0.46 multiply(add(X, X), multiply(add(add(Y, add(n1, n1)), multiply(n1, add(Y, add(n1, n1)))), add(multiply(Y, n1), n1)))
% 0.16/0.46 = { by axiom 5 (multiply_add_property) }
% 0.16/0.46 multiply(add(X, X), multiply(add(add(Y, add(n1, n1)), add(multiply(Y, n1), multiply(add(n1, n1), n1))), add(multiply(Y, n1), n1)))
% 0.16/0.46 = { by axiom 4 (multiply_add) }
% 0.16/0.46 multiply(add(X, X), multiply(add(add(Y, add(n1, n1)), add(multiply(Y, n1), n1)), add(multiply(Y, n1), n1)))
% 0.16/0.46 = { by axiom 4 (multiply_add) }
% 0.16/0.46 multiply(add(X, X), add(multiply(Y, n1), n1))
% 0.16/0.46 = { by lemma 13 }
% 0.16/0.46 X
% 0.16/0.46
% 0.16/0.46 Lemma 16: multiply(n1, add(X, X)) = X.
% 0.16/0.46 Proof:
% 0.16/0.46 multiply(n1, add(X, X))
% 0.16/0.46 = { by axiom 5 (multiply_add_property) }
% 0.16/0.46 add(multiply(X, n1), multiply(X, n1))
% 0.16/0.46 = { by lemma 10 R->L }
% 0.16/0.46 add(inverse(n1), multiply(add(multiply(X, n1), multiply(X, n1)), n1))
% 0.16/0.46 = { by lemma 15 }
% 0.16/0.46 add(inverse(n1), multiply(X, n1))
% 0.16/0.46 = { by lemma 10 }
% 0.16/0.46 X
% 0.16/0.46
% 0.16/0.46 Lemma 17: multiply(X, X) = X.
% 0.16/0.46 Proof:
% 0.16/0.46 multiply(X, X)
% 0.16/0.46 = { by lemma 13 R->L }
% 0.16/0.46 multiply(multiply(add(X, X), add(Y, n1)), X)
% 0.16/0.46 = { by lemma 16 R->L }
% 0.16/0.46 multiply(multiply(add(X, X), add(Y, n1)), multiply(n1, add(X, X)))
% 0.16/0.46 = { by axiom 5 (multiply_add_property) }
% 0.16/0.46 multiply(add(multiply(Y, add(X, X)), multiply(n1, add(X, X))), multiply(n1, add(X, X)))
% 0.16/0.46 = { by axiom 4 (multiply_add) }
% 0.16/0.46 multiply(n1, add(X, X))
% 0.16/0.46 = { by lemma 16 }
% 0.16/0.46 X
% 0.16/0.46
% 0.16/0.46 Lemma 18: add(X, X) = X.
% 0.16/0.46 Proof:
% 0.16/0.46 add(X, X)
% 0.16/0.46 = { by lemma 17 R->L }
% 0.16/0.46 add(X, multiply(X, X))
% 0.16/0.46 = { by lemma 12 R->L }
% 0.16/0.46 multiply(X, add(add(X, X), X))
% 0.16/0.46 = { by lemma 16 R->L }
% 0.16/0.46 multiply(X, add(add(X, X), multiply(n1, add(X, X))))
% 0.16/0.46 = { by lemma 14 R->L }
% 0.16/0.46 multiply(X, multiply(add(X, X), add(Y, n1)))
% 0.16/0.46 = { by lemma 13 }
% 0.16/0.46 multiply(X, X)
% 0.16/0.46 = { by lemma 17 }
% 0.16/0.46 X
% 0.16/0.46
% 0.16/0.46 Lemma 19: add(inverse(n1), X) = X.
% 0.16/0.46 Proof:
% 0.16/0.46 add(inverse(n1), X)
% 0.16/0.46 = { by lemma 7 R->L }
% 0.16/0.46 add(multiply(n1, inverse(n1)), X)
% 0.16/0.46 = { by lemma 15 R->L }
% 0.16/0.46 add(multiply(n1, inverse(n1)), multiply(add(X, X), n1))
% 0.16/0.46 = { by lemma 9 }
% 0.16/0.46 add(X, X)
% 0.16/0.46 = { by lemma 18 }
% 0.16/0.46 X
% 0.16/0.46
% 0.16/0.46 Lemma 20: multiply(X, inverse(X)) = inverse(n1).
% 0.16/0.46 Proof:
% 0.16/0.46 multiply(X, inverse(X))
% 0.16/0.46 = { by lemma 18 R->L }
% 0.16/0.46 add(multiply(X, inverse(X)), multiply(X, inverse(X)))
% 0.16/0.46 = { by axiom 5 (multiply_add_property) R->L }
% 0.16/0.46 multiply(inverse(X), add(X, X))
% 0.16/0.46 = { by lemma 18 }
% 0.16/0.46 multiply(inverse(X), X)
% 0.16/0.46 = { by lemma 19 R->L }
% 0.16/0.46 multiply(inverse(X), add(inverse(n1), X))
% 0.16/0.46 = { by axiom 5 (multiply_add_property) }
% 0.16/0.46 add(multiply(inverse(n1), inverse(X)), multiply(X, inverse(X)))
% 0.16/0.46 = { by lemma 19 R->L }
% 0.16/0.46 add(multiply(inverse(n1), inverse(X)), multiply(X, add(inverse(n1), inverse(X))))
% 0.16/0.46 = { by lemma 8 }
% 0.16/0.46 pixley(inverse(n1), X, X)
% 0.16/0.46 = { by axiom 2 (pixley2) }
% 0.16/0.46 inverse(n1)
% 0.16/0.46
% 0.16/0.46 Goal 1 (prove_equal_identity): multiply(b, inverse(b)) = multiply(a, inverse(a)).
% 0.16/0.46 Proof:
% 0.16/0.46 multiply(b, inverse(b))
% 0.16/0.46 = { by lemma 20 }
% 0.16/0.46 inverse(n1)
% 0.16/0.46 = { by lemma 20 R->L }
% 0.16/0.46 multiply(a, inverse(a))
% 0.16/0.46 % SZS output end Proof
% 0.16/0.46
% 0.16/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
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