TSTP Solution File: RNG018-6 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG018-6 : TPTP v8.1.2. Released v1.0.0.
% 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 : n005.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 13:58:50 EDT 2023
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG018-6 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 02:15:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.43 Command-line arguments: --ground-connectedness --complete-subsets
% 0.20/0.43
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 Axiom 1 (additive_inverse_additive_inverse): additive_inverse(additive_inverse(X)) = X.
% 0.20/0.44 Axiom 2 (commutativity_for_addition): add(X, Y) = add(Y, X).
% 0.20/0.44 Axiom 3 (right_additive_identity): add(X, additive_identity) = X.
% 0.20/0.44 Axiom 4 (left_additive_identity): add(additive_identity, X) = X.
% 0.20/0.44 Axiom 5 (right_multiplicative_zero): multiply(X, additive_identity) = additive_identity.
% 0.20/0.44 Axiom 6 (right_additive_inverse): add(X, additive_inverse(X)) = additive_identity.
% 0.20/0.44 Axiom 7 (associativity_for_addition): add(X, add(Y, Z)) = add(add(X, Y), Z).
% 0.20/0.44 Axiom 8 (distribute1): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
% 0.20/0.44 Axiom 9 (distribute2): multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)).
% 0.20/0.44
% 0.20/0.44 Lemma 10: add(X, add(Y, additive_inverse(X))) = Y.
% 0.20/0.44 Proof:
% 0.20/0.44 add(X, add(Y, additive_inverse(X)))
% 0.20/0.44 = { by axiom 2 (commutativity_for_addition) R->L }
% 0.20/0.44 add(X, add(additive_inverse(X), Y))
% 0.20/0.44 = { by axiom 7 (associativity_for_addition) }
% 0.20/0.44 add(add(X, additive_inverse(X)), Y)
% 0.20/0.44 = { by axiom 6 (right_additive_inverse) }
% 0.20/0.44 add(additive_identity, Y)
% 0.20/0.44 = { by axiom 4 (left_additive_identity) }
% 0.20/0.44 Y
% 0.20/0.44
% 0.20/0.44 Lemma 11: add(X, add(additive_inverse(X), Y)) = Y.
% 0.20/0.44 Proof:
% 0.20/0.44 add(X, add(additive_inverse(X), Y))
% 0.20/0.44 = { by axiom 2 (commutativity_for_addition) R->L }
% 0.20/0.44 add(X, add(Y, additive_inverse(X)))
% 0.20/0.44 = { by lemma 10 }
% 0.20/0.44 Y
% 0.20/0.44
% 0.20/0.44 Goal 1 (prove_distributivity): multiply(add(x, y), additive_inverse(z)) = add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))).
% 0.20/0.44 Proof:
% 0.20/0.44 multiply(add(x, y), additive_inverse(z))
% 0.20/0.45 = { by lemma 10 R->L }
% 0.20/0.45 add(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))), add(multiply(add(x, y), additive_inverse(z)), additive_inverse(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))))))
% 0.20/0.45 = { by lemma 11 R->L }
% 0.20/0.45 add(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))), add(multiply(add(x, y), additive_inverse(z)), add(multiply(x, z), add(additive_inverse(multiply(x, z)), additive_inverse(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))))))))
% 0.20/0.45 = { by axiom 3 (right_additive_identity) R->L }
% 0.20/0.45 add(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))), add(multiply(add(x, y), additive_inverse(z)), add(multiply(x, z), add(add(additive_inverse(multiply(x, z)), additive_identity), additive_inverse(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))))))))
% 0.20/0.45 = { by axiom 6 (right_additive_inverse) R->L }
% 0.20/0.45 add(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))), add(multiply(add(x, y), additive_inverse(z)), add(multiply(x, z), add(add(additive_inverse(multiply(x, z)), add(multiply(y, z), additive_inverse(multiply(y, z)))), additive_inverse(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))))))))
% 0.20/0.45 = { by axiom 2 (commutativity_for_addition) R->L }
% 0.20/0.45 add(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))), add(multiply(add(x, y), additive_inverse(z)), add(multiply(x, z), add(add(additive_inverse(multiply(x, z)), add(additive_inverse(multiply(y, z)), multiply(y, z))), additive_inverse(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))))))))
% 0.20/0.45 = { by axiom 7 (associativity_for_addition) }
% 0.20/0.45 add(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))), add(multiply(add(x, y), additive_inverse(z)), add(multiply(x, z), add(add(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))), multiply(y, z)), additive_inverse(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))))))))
% 0.20/0.45 = { by axiom 7 (associativity_for_addition) R->L }
% 0.20/0.45 add(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))), add(multiply(add(x, y), additive_inverse(z)), add(multiply(x, z), add(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))), add(multiply(y, z), additive_inverse(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z)))))))))
% 0.20/0.45 = { by axiom 2 (commutativity_for_addition) }
% 0.20/0.45 add(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))), add(multiply(add(x, y), additive_inverse(z)), add(multiply(x, z), add(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))), add(additive_inverse(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z)))), multiply(y, z))))))
% 0.20/0.45 = { by lemma 11 }
% 0.20/0.45 add(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))), add(multiply(add(x, y), additive_inverse(z)), add(multiply(x, z), multiply(y, z))))
% 0.20/0.45 = { by axiom 9 (distribute2) R->L }
% 0.20/0.45 add(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))), add(multiply(add(x, y), additive_inverse(z)), multiply(add(x, y), z)))
% 0.20/0.45 = { by axiom 1 (additive_inverse_additive_inverse) R->L }
% 0.20/0.45 add(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))), add(multiply(add(x, y), additive_inverse(z)), multiply(add(x, y), additive_inverse(additive_inverse(z)))))
% 0.20/0.45 = { by axiom 8 (distribute1) R->L }
% 0.20/0.45 add(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))), multiply(add(x, y), add(additive_inverse(z), additive_inverse(additive_inverse(z)))))
% 0.20/0.45 = { by axiom 6 (right_additive_inverse) }
% 0.20/0.45 add(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))), multiply(add(x, y), additive_identity))
% 0.20/0.45 = { by axiom 5 (right_multiplicative_zero) }
% 0.20/0.45 add(add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z))), additive_identity)
% 0.20/0.45 = { by axiom 3 (right_additive_identity) }
% 0.20/0.45 add(additive_inverse(multiply(x, z)), additive_inverse(multiply(y, z)))
% 0.20/0.45 % SZS output end Proof
% 0.20/0.45
% 0.20/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------