TSTP Solution File: RNG020-7 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG020-7 : 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 : n010.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 116.60s 15.29s
% Output : Proof 117.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG020-7 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 01:33:05 EDT 2023
% 0.14/0.34 % CPUTime :
% 116.60/15.29 Command-line arguments: --flatten
% 116.60/15.29
% 116.60/15.29 % SZS status Unsatisfiable
% 116.60/15.29
% 116.60/15.30 % SZS output start Proof
% 116.60/15.30 Axiom 1 (additive_inverse_additive_inverse): additive_inverse(additive_inverse(X)) = X.
% 116.60/15.30 Axiom 2 (commutativity_for_addition): add(X, Y) = add(Y, X).
% 116.60/15.30 Axiom 3 (right_additive_identity): add(X, additive_identity) = X.
% 116.60/15.30 Axiom 4 (left_additive_identity): add(additive_identity, X) = X.
% 116.60/15.30 Axiom 5 (right_additive_inverse): add(X, additive_inverse(X)) = additive_identity.
% 116.60/15.30 Axiom 6 (inverse_product2): multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y)).
% 116.60/15.30 Axiom 7 (associativity_for_addition): add(X, add(Y, Z)) = add(add(X, Y), Z).
% 116.60/15.30 Axiom 8 (distribute1): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
% 116.60/15.30 Axiom 9 (distribute2): multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)).
% 116.60/15.30 Axiom 10 (associator): associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))).
% 116.60/15.30
% 116.60/15.30 Lemma 11: add(X, add(Y, additive_inverse(X))) = Y.
% 116.60/15.30 Proof:
% 116.60/15.30 add(X, add(Y, additive_inverse(X)))
% 116.60/15.30 = { by axiom 2 (commutativity_for_addition) R->L }
% 116.60/15.30 add(X, add(additive_inverse(X), Y))
% 116.60/15.30 = { by axiom 7 (associativity_for_addition) }
% 116.60/15.30 add(add(X, additive_inverse(X)), Y)
% 116.60/15.30 = { by axiom 5 (right_additive_inverse) }
% 116.60/15.30 add(additive_identity, Y)
% 116.60/15.30 = { by axiom 4 (left_additive_identity) }
% 116.60/15.30 Y
% 116.60/15.30
% 116.60/15.30 Lemma 12: add(X, additive_inverse(add(X, Y))) = additive_inverse(Y).
% 116.60/15.30 Proof:
% 116.60/15.30 add(X, additive_inverse(add(X, Y)))
% 116.60/15.30 = { by axiom 1 (additive_inverse_additive_inverse) R->L }
% 116.60/15.30 add(X, additive_inverse(add(X, additive_inverse(additive_inverse(Y)))))
% 116.60/15.30 = { by axiom 2 (commutativity_for_addition) R->L }
% 116.60/15.30 add(X, additive_inverse(add(additive_inverse(additive_inverse(Y)), X)))
% 116.60/15.30 = { by lemma 11 R->L }
% 116.60/15.30 add(additive_inverse(Y), add(add(X, additive_inverse(add(additive_inverse(additive_inverse(Y)), X))), additive_inverse(additive_inverse(Y))))
% 116.60/15.30 = { by axiom 2 (commutativity_for_addition) }
% 116.60/15.30 add(additive_inverse(Y), add(additive_inverse(additive_inverse(Y)), add(X, additive_inverse(add(additive_inverse(additive_inverse(Y)), X)))))
% 116.60/15.30 = { by axiom 7 (associativity_for_addition) }
% 116.60/15.30 add(additive_inverse(Y), add(add(additive_inverse(additive_inverse(Y)), X), additive_inverse(add(additive_inverse(additive_inverse(Y)), X))))
% 116.60/15.30 = { by axiom 5 (right_additive_inverse) }
% 116.60/15.30 add(additive_inverse(Y), additive_identity)
% 116.60/15.30 = { by axiom 3 (right_additive_identity) }
% 116.60/15.30 additive_inverse(Y)
% 116.60/15.30
% 116.60/15.30 Lemma 13: additive_inverse(add(X, additive_inverse(Y))) = add(Y, additive_inverse(X)).
% 116.60/15.30 Proof:
% 116.60/15.30 additive_inverse(add(X, additive_inverse(Y)))
% 116.60/15.30 = { by lemma 12 R->L }
% 116.60/15.30 add(Y, additive_inverse(add(Y, add(X, additive_inverse(Y)))))
% 116.60/15.30 = { by lemma 11 }
% 116.60/15.30 add(Y, additive_inverse(X))
% 116.60/15.30
% 116.60/15.30 Lemma 14: add(associator(X, Y, Z), multiply(X, multiply(Y, Z))) = multiply(multiply(X, Y), Z).
% 116.60/15.30 Proof:
% 116.60/15.30 add(associator(X, Y, Z), multiply(X, multiply(Y, Z)))
% 116.60/15.30 = { by axiom 2 (commutativity_for_addition) R->L }
% 116.60/15.30 add(multiply(X, multiply(Y, Z)), associator(X, Y, Z))
% 116.60/15.30 = { by axiom 10 (associator) }
% 116.60/15.30 add(multiply(X, multiply(Y, Z)), add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))))
% 116.60/15.30 = { by lemma 11 }
% 117.22/15.30 multiply(multiply(X, Y), Z)
% 117.22/15.30
% 117.22/15.30 Lemma 15: add(multiply(X, multiply(Y, Z)), additive_inverse(multiply(multiply(X, Y), Z))) = associator(X, Y, additive_inverse(Z)).
% 117.22/15.30 Proof:
% 117.22/15.30 add(multiply(X, multiply(Y, Z)), additive_inverse(multiply(multiply(X, Y), Z)))
% 117.22/15.30 = { by lemma 13 R->L }
% 117.22/15.30 additive_inverse(add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))))
% 117.22/15.30 = { by axiom 6 (inverse_product2) R->L }
% 117.22/15.30 additive_inverse(add(multiply(multiply(X, Y), Z), multiply(X, additive_inverse(multiply(Y, Z)))))
% 117.22/15.30 = { by axiom 6 (inverse_product2) R->L }
% 117.22/15.30 additive_inverse(add(multiply(multiply(X, Y), Z), multiply(X, multiply(Y, additive_inverse(Z)))))
% 117.22/15.30 = { by axiom 1 (additive_inverse_additive_inverse) R->L }
% 117.22/15.30 additive_inverse(add(multiply(multiply(X, Y), Z), additive_inverse(additive_inverse(multiply(X, multiply(Y, additive_inverse(Z)))))))
% 117.22/15.30 = { by lemma 13 }
% 117.22/15.30 add(additive_inverse(multiply(X, multiply(Y, additive_inverse(Z)))), additive_inverse(multiply(multiply(X, Y), Z)))
% 117.22/15.30 = { by axiom 2 (commutativity_for_addition) }
% 117.22/15.30 add(additive_inverse(multiply(multiply(X, Y), Z)), additive_inverse(multiply(X, multiply(Y, additive_inverse(Z)))))
% 117.22/15.30 = { by axiom 6 (inverse_product2) R->L }
% 117.22/15.30 add(multiply(multiply(X, Y), additive_inverse(Z)), additive_inverse(multiply(X, multiply(Y, additive_inverse(Z)))))
% 117.22/15.30 = { by axiom 10 (associator) R->L }
% 117.22/15.30 associator(X, Y, additive_inverse(Z))
% 117.22/15.30
% 117.22/15.30 Goal 1 (prove_linearised_form2): associator(x, add(u, v), y) = add(associator(x, u, y), associator(x, v, y)).
% 117.22/15.30 Proof:
% 117.22/15.30 associator(x, add(u, v), y)
% 117.22/15.30 = { by axiom 1 (additive_inverse_additive_inverse) R->L }
% 117.22/15.30 additive_inverse(additive_inverse(associator(x, add(u, v), y)))
% 117.22/15.30 = { by axiom 10 (associator) }
% 117.22/15.30 additive_inverse(additive_inverse(add(multiply(multiply(x, add(u, v)), y), additive_inverse(multiply(x, multiply(add(u, v), y))))))
% 117.22/15.30 = { by lemma 13 R->L }
% 117.22/15.30 additive_inverse(additive_inverse(additive_inverse(add(multiply(x, multiply(add(u, v), y)), additive_inverse(multiply(multiply(x, add(u, v)), y))))))
% 117.22/15.30 = { by lemma 15 }
% 117.22/15.30 additive_inverse(additive_inverse(additive_inverse(associator(x, add(u, v), additive_inverse(y)))))
% 117.22/15.30 = { by axiom 1 (additive_inverse_additive_inverse) }
% 117.22/15.30 additive_inverse(associator(x, add(u, v), additive_inverse(y)))
% 117.22/15.30 = { by lemma 15 R->L }
% 117.22/15.30 additive_inverse(add(multiply(x, multiply(add(u, v), y)), additive_inverse(multiply(multiply(x, add(u, v)), y))))
% 117.22/15.30 = { by axiom 2 (commutativity_for_addition) R->L }
% 117.22/15.30 additive_inverse(add(multiply(x, multiply(add(u, v), y)), additive_inverse(multiply(multiply(x, add(v, u)), y))))
% 117.22/15.30 = { by axiom 8 (distribute1) }
% 117.22/15.30 additive_inverse(add(multiply(x, multiply(add(u, v), y)), additive_inverse(multiply(add(multiply(x, v), multiply(x, u)), y))))
% 117.22/15.30 = { by axiom 9 (distribute2) }
% 117.22/15.31 additive_inverse(add(multiply(x, multiply(add(u, v), y)), additive_inverse(add(multiply(multiply(x, v), y), multiply(multiply(x, u), y)))))
% 117.22/15.31 = { by axiom 2 (commutativity_for_addition) R->L }
% 117.22/15.31 additive_inverse(add(multiply(x, multiply(add(u, v), y)), additive_inverse(add(multiply(multiply(x, u), y), multiply(multiply(x, v), y)))))
% 117.22/15.31 = { by lemma 14 R->L }
% 117.22/15.31 additive_inverse(add(multiply(x, multiply(add(u, v), y)), additive_inverse(add(add(associator(x, u, y), multiply(x, multiply(u, y))), multiply(multiply(x, v), y)))))
% 117.22/15.31 = { by axiom 7 (associativity_for_addition) R->L }
% 117.22/15.31 additive_inverse(add(multiply(x, multiply(add(u, v), y)), additive_inverse(add(associator(x, u, y), add(multiply(x, multiply(u, y)), multiply(multiply(x, v), y))))))
% 117.22/15.31 = { by lemma 14 R->L }
% 117.22/15.31 additive_inverse(add(multiply(x, multiply(add(u, v), y)), additive_inverse(add(associator(x, u, y), add(multiply(x, multiply(u, y)), add(associator(x, v, y), multiply(x, multiply(v, y))))))))
% 117.22/15.31 = { by axiom 2 (commutativity_for_addition) R->L }
% 117.22/15.31 additive_inverse(add(multiply(x, multiply(add(u, v), y)), additive_inverse(add(associator(x, u, y), add(multiply(x, multiply(u, y)), add(multiply(x, multiply(v, y)), associator(x, v, y)))))))
% 117.22/15.31 = { by axiom 7 (associativity_for_addition) }
% 117.22/15.31 additive_inverse(add(multiply(x, multiply(add(u, v), y)), additive_inverse(add(associator(x, u, y), add(add(multiply(x, multiply(u, y)), multiply(x, multiply(v, y))), associator(x, v, y))))))
% 117.22/15.31 = { by axiom 8 (distribute1) R->L }
% 117.22/15.31 additive_inverse(add(multiply(x, multiply(add(u, v), y)), additive_inverse(add(associator(x, u, y), add(multiply(x, add(multiply(u, y), multiply(v, y))), associator(x, v, y))))))
% 117.22/15.31 = { by axiom 2 (commutativity_for_addition) R->L }
% 117.22/15.31 additive_inverse(add(multiply(x, multiply(add(u, v), y)), additive_inverse(add(associator(x, u, y), add(associator(x, v, y), multiply(x, add(multiply(u, y), multiply(v, y))))))))
% 117.22/15.31 = { by axiom 7 (associativity_for_addition) }
% 117.22/15.31 additive_inverse(add(multiply(x, multiply(add(u, v), y)), additive_inverse(add(add(associator(x, u, y), associator(x, v, y)), multiply(x, add(multiply(u, y), multiply(v, y)))))))
% 117.22/15.31 = { by axiom 2 (commutativity_for_addition) }
% 117.22/15.31 additive_inverse(add(multiply(x, multiply(add(u, v), y)), additive_inverse(add(multiply(x, add(multiply(u, y), multiply(v, y))), add(associator(x, u, y), associator(x, v, y))))))
% 117.22/15.31 = { by axiom 9 (distribute2) R->L }
% 117.22/15.31 additive_inverse(add(multiply(x, multiply(add(u, v), y)), additive_inverse(add(multiply(x, multiply(add(u, v), y)), add(associator(x, u, y), associator(x, v, y))))))
% 117.22/15.31 = { by lemma 12 }
% 117.22/15.31 additive_inverse(additive_inverse(add(associator(x, u, y), associator(x, v, y))))
% 117.22/15.31 = { by axiom 1 (additive_inverse_additive_inverse) }
% 117.22/15.31 add(associator(x, u, y), associator(x, v, y))
% 117.22/15.31 % SZS output end Proof
% 117.22/15.31
% 117.22/15.31 RESULT: Unsatisfiable (the axioms are contradictory).
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