TSTP Solution File: BOO024-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : BOO024-1 : 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 : n025.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 18:11:28 EDT 2023
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : BOO024-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.35 % Computer : n025.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Sun Aug 27 08:27:23 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.20/0.41 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.41
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 Axiom 1 (pixley1): pixley(X, X, Y) = Y.
% 0.20/0.42 Axiom 2 (additive_inverse): add(X, inverse(X)) = n1.
% 0.20/0.42 Axiom 3 (multiply_add): multiply(add(X, Y), Y) = Y.
% 0.20/0.42 Axiom 4 (multiply_add_property): multiply(X, add(Y, Z)) = add(multiply(Y, X), multiply(Z, X)).
% 0.20/0.42 Axiom 5 (pixley_defn): pixley(X, Y, Z) = add(multiply(X, inverse(Y)), add(multiply(X, Z), multiply(inverse(Y), Z))).
% 0.20/0.42
% 0.20/0.42 Lemma 6: add(multiply(X, inverse(X)), multiply(Y, n1)) = Y.
% 0.20/0.42 Proof:
% 0.20/0.42 add(multiply(X, inverse(X)), multiply(Y, n1))
% 0.20/0.42 = { by axiom 2 (additive_inverse) R->L }
% 0.20/0.42 add(multiply(X, inverse(X)), multiply(Y, add(X, inverse(X))))
% 0.20/0.42 = { by axiom 4 (multiply_add_property) }
% 0.20/0.42 add(multiply(X, inverse(X)), add(multiply(X, Y), multiply(inverse(X), Y)))
% 0.20/0.42 = { by axiom 5 (pixley_defn) R->L }
% 0.20/0.42 pixley(X, X, Y)
% 0.20/0.42 = { by axiom 1 (pixley1) }
% 0.20/0.42 Y
% 0.20/0.42
% 0.20/0.42 Lemma 7: add(Y, n1) = add(X, n1).
% 0.20/0.42 Proof:
% 0.20/0.42 add(Y, n1)
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 add(multiply(Z, inverse(Z)), multiply(add(Y, n1), n1))
% 0.20/0.42 = { by axiom 3 (multiply_add) }
% 0.20/0.42 add(multiply(Z, inverse(Z)), n1)
% 0.20/0.42 = { by axiom 3 (multiply_add) R->L }
% 0.20/0.42 add(multiply(Z, inverse(Z)), multiply(add(X, n1), n1))
% 0.20/0.42 = { by lemma 6 }
% 0.20/0.42 add(X, n1)
% 0.20/0.42
% 0.20/0.42 Lemma 8: multiply(X, add(add(Y, X), Z)) = add(X, multiply(Z, X)).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(X, add(add(Y, X), Z))
% 0.20/0.42 = { by axiom 4 (multiply_add_property) }
% 0.20/0.42 add(multiply(add(Y, X), X), multiply(Z, X))
% 0.20/0.42 = { by axiom 3 (multiply_add) }
% 0.20/0.42 add(X, multiply(Z, X))
% 0.20/0.42
% 0.20/0.42 Lemma 9: multiply(add(X, X), add(Y, n1)) = X.
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(add(X, X), add(Y, n1))
% 0.20/0.42 = { by lemma 7 }
% 0.20/0.42 multiply(add(X, X), add(multiply(Z, inverse(Z)), n1))
% 0.20/0.42 = { by axiom 4 (multiply_add_property) }
% 0.20/0.42 add(multiply(multiply(Z, inverse(Z)), add(X, X)), multiply(n1, add(X, X)))
% 0.20/0.42 = { by axiom 4 (multiply_add_property) }
% 0.20/0.42 add(multiply(multiply(Z, inverse(Z)), add(X, X)), add(multiply(X, n1), multiply(X, n1)))
% 0.20/0.42 = { by axiom 3 (multiply_add) R->L }
% 0.20/0.42 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))))
% 0.20/0.42 = { by lemma 6 }
% 0.20/0.42 add(multiply(multiply(Z, inverse(Z)), add(X, X)), add(multiply(X, n1), multiply(X, multiply(X, n1))))
% 0.20/0.42 = { by lemma 8 R->L }
% 0.20/0.42 add(multiply(multiply(Z, inverse(Z)), add(X, X)), multiply(multiply(X, n1), add(add(multiply(V, inverse(V)), multiply(X, n1)), X)))
% 0.20/0.42 = { by lemma 6 }
% 0.20/0.42 add(multiply(multiply(Z, inverse(Z)), add(X, X)), multiply(multiply(X, n1), add(X, X)))
% 0.20/0.42 = { by axiom 4 (multiply_add_property) R->L }
% 0.20/0.42 multiply(add(X, X), add(multiply(Z, inverse(Z)), multiply(X, n1)))
% 0.20/0.42 = { by lemma 6 }
% 0.20/0.42 multiply(add(X, X), X)
% 0.20/0.42 = { by axiom 3 (multiply_add) }
% 0.20/0.42 X
% 0.20/0.42
% 0.20/0.42 Lemma 10: multiply(X, add(Y, add(Z, X))) = add(multiply(Y, X), X).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(X, add(Y, add(Z, X)))
% 0.20/0.42 = { by axiom 4 (multiply_add_property) }
% 0.20/0.42 add(multiply(Y, X), multiply(add(Z, X), X))
% 0.20/0.42 = { by axiom 3 (multiply_add) }
% 0.20/0.42 add(multiply(Y, X), X)
% 0.20/0.42
% 0.20/0.42 Lemma 11: multiply(add(X, X), n1) = X.
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(add(X, X), n1)
% 0.20/0.42 = { by lemma 9 R->L }
% 0.20/0.42 multiply(add(X, X), multiply(add(n1, n1), add(multiply(Y, n1), n1)))
% 0.20/0.42 = { by axiom 3 (multiply_add) R->L }
% 0.20/0.42 multiply(add(X, X), multiply(multiply(add(Y, add(n1, n1)), add(n1, n1)), add(multiply(Y, n1), n1)))
% 0.20/0.42 = { by lemma 7 }
% 0.20/0.42 multiply(add(X, X), multiply(multiply(add(Y, add(n1, n1)), add(add(Z, add(Y, add(n1, n1))), n1)), add(multiply(Y, n1), n1)))
% 0.20/0.42 = { by lemma 8 }
% 0.20/0.42 multiply(add(X, X), multiply(add(add(Y, add(n1, n1)), multiply(n1, add(Y, add(n1, n1)))), add(multiply(Y, n1), n1)))
% 0.20/0.42 = { by lemma 10 }
% 0.20/0.42 multiply(add(X, X), multiply(add(add(Y, add(n1, n1)), add(multiply(Y, n1), n1)), add(multiply(Y, n1), n1)))
% 0.20/0.42 = { by axiom 3 (multiply_add) }
% 0.20/0.42 multiply(add(X, X), add(multiply(Y, n1), n1))
% 0.20/0.42 = { by lemma 9 }
% 0.20/0.43 X
% 0.20/0.43
% 0.20/0.43 Goal 1 (prove_add_multiply): add(multiply(a, b), b) = b.
% 0.20/0.43 Proof:
% 0.20/0.43 add(multiply(a, b), b)
% 0.20/0.43 = { by lemma 10 R->L }
% 0.20/0.43 multiply(b, add(a, add(b, b)))
% 0.20/0.43 = { by lemma 11 R->L }
% 0.20/0.43 multiply(add(multiply(b, add(a, add(b, b))), multiply(b, add(a, add(b, b)))), n1)
% 0.20/0.43 = { by axiom 4 (multiply_add_property) R->L }
% 0.20/0.43 multiply(multiply(add(a, add(b, b)), add(b, b)), n1)
% 0.20/0.43 = { by axiom 3 (multiply_add) }
% 0.20/0.44 multiply(add(b, b), n1)
% 0.20/0.44 = { by lemma 11 }
% 0.20/0.44 b
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44
% 0.20/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------