TSTP Solution File: RNG025-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG025-1 : 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 : n017.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 13:58:52 EDT 2023
% Result : Unsatisfiable 34.57s 4.78s
% Output : Proof 34.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG025-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 01:21:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 34.57/4.78 Command-line arguments: --no-flatten-goal
% 34.57/4.78
% 34.57/4.78 % SZS status Unsatisfiable
% 34.57/4.78
% 34.57/4.79 % SZS output start Proof
% 34.57/4.79 Take the following subset of the input axioms:
% 34.57/4.79 fof(add_inverse, axiom, ![X]: add(additive_inverse(X), X)=additive_identity).
% 34.57/4.79 fof(additive_inverse_additive_inverse, axiom, ![X2]: additive_inverse(additive_inverse(X2))=X2).
% 34.57/4.79 fof(associativity_for_addition, axiom, ![Y, Z, X2]: add(X2, add(Y, Z))=add(add(X2, Y), Z)).
% 34.57/4.79 fof(commutativity_for_addition, axiom, ![X2, Y2]: add(X2, Y2)=add(Y2, X2)).
% 34.57/4.79 fof(inverse_product1, axiom, ![X2, Y2]: multiply(additive_inverse(X2), Y2)=additive_inverse(multiply(X2, Y2))).
% 34.57/4.79 fof(inverse_product2, axiom, ![X2, Y2]: multiply(X2, additive_inverse(Y2))=additive_inverse(multiply(X2, Y2))).
% 34.57/4.79 fof(left_additive_identity, axiom, ![X2]: add(additive_identity, X2)=X2).
% 34.57/4.79 fof(left_alternative, axiom, ![X2, Y2]: multiply(multiply(X2, X2), Y2)=multiply(X2, multiply(X2, Y2))).
% 34.57/4.79 fof(multiply_over_add1, axiom, ![X2, Y2, Z2]: multiply(X2, add(Y2, Z2))=add(multiply(X2, Y2), multiply(X2, Z2))).
% 34.57/4.79 fof(multiply_over_add2, axiom, ![X2, Y2, Z2]: multiply(add(X2, Y2), Z2)=add(multiply(X2, Z2), multiply(Y2, Z2))).
% 34.57/4.79 fof(prove_middle_law, negated_conjecture, multiply(multiply(cy, cx), cy)!=multiply(cy, multiply(cx, cy))).
% 34.57/4.79 fof(right_alternative, axiom, ![X2, Y2]: multiply(multiply(X2, Y2), Y2)=multiply(X2, multiply(Y2, Y2))).
% 34.57/4.79 fof(sum_of_inverses, axiom, ![X2, Y2]: additive_inverse(add(X2, Y2))=add(additive_inverse(X2), additive_inverse(Y2))).
% 34.57/4.79
% 34.57/4.79 Now clausify the problem and encode Horn clauses using encoding 3 of
% 34.57/4.79 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 34.57/4.79 We repeatedly replace C & s=t => u=v by the two clauses:
% 34.57/4.79 fresh(y, y, x1...xn) = u
% 34.57/4.79 C => fresh(s, t, x1...xn) = v
% 34.57/4.79 where fresh is a fresh function symbol and x1..xn are the free
% 34.57/4.79 variables of u and v.
% 34.57/4.79 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 34.57/4.79 input problem has no model of domain size 1).
% 34.57/4.79
% 34.57/4.79 The encoding turns the above axioms into the following unit equations and goals:
% 34.57/4.79
% 34.57/4.79 Axiom 1 (additive_inverse_additive_inverse): additive_inverse(additive_inverse(X)) = X.
% 34.57/4.79 Axiom 2 (commutativity_for_addition): add(X, Y) = add(Y, X).
% 34.57/4.79 Axiom 3 (left_additive_identity): add(additive_identity, X) = X.
% 34.57/4.79 Axiom 4 (add_inverse): add(additive_inverse(X), X) = additive_identity.
% 34.57/4.79 Axiom 5 (inverse_product2): multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y)).
% 34.57/4.79 Axiom 6 (inverse_product1): multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y)).
% 34.57/4.79 Axiom 7 (sum_of_inverses): additive_inverse(add(X, Y)) = add(additive_inverse(X), additive_inverse(Y)).
% 34.57/4.79 Axiom 8 (associativity_for_addition): add(X, add(Y, Z)) = add(add(X, Y), Z).
% 34.57/4.79 Axiom 9 (left_alternative): multiply(multiply(X, X), Y) = multiply(X, multiply(X, Y)).
% 34.57/4.79 Axiom 10 (right_alternative): multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y)).
% 34.57/4.79 Axiom 11 (multiply_over_add1): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
% 34.57/4.79 Axiom 12 (multiply_over_add2): multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)).
% 34.57/4.79
% 34.57/4.79 Lemma 13: add(X, additive_inverse(X)) = additive_identity.
% 34.57/4.79 Proof:
% 34.57/4.79 add(X, additive_inverse(X))
% 34.57/4.79 = { by axiom 2 (commutativity_for_addition) R->L }
% 34.57/4.79 add(additive_inverse(X), X)
% 34.57/4.79 = { by axiom 4 (add_inverse) }
% 34.57/4.79 additive_identity
% 34.57/4.79
% 34.57/4.79 Lemma 14: add(X, add(Y, additive_inverse(X))) = Y.
% 34.57/4.79 Proof:
% 34.57/4.79 add(X, add(Y, additive_inverse(X)))
% 34.57/4.79 = { by axiom 2 (commutativity_for_addition) R->L }
% 34.57/4.79 add(X, add(additive_inverse(X), Y))
% 34.57/4.79 = { by axiom 8 (associativity_for_addition) }
% 34.57/4.79 add(add(X, additive_inverse(X)), Y)
% 34.57/4.79 = { by lemma 13 }
% 34.57/4.79 add(additive_identity, Y)
% 34.57/4.79 = { by axiom 3 (left_additive_identity) }
% 34.57/4.79 Y
% 34.57/4.79
% 34.57/4.79 Goal 1 (prove_middle_law): multiply(multiply(cy, cx), cy) = multiply(cy, multiply(cx, cy)).
% 34.57/4.79 Proof:
% 34.57/4.79 multiply(multiply(cy, cx), cy)
% 34.57/4.79 = { by lemma 14 R->L }
% 34.57/4.79 multiply(multiply(cy, cx), add(cx, add(cy, additive_inverse(cx))))
% 34.57/4.79 = { by lemma 14 R->L }
% 34.57/4.79 multiply(multiply(add(cx, add(cy, additive_inverse(cx))), cx), add(cx, add(cy, additive_inverse(cx))))
% 34.57/4.79 = { by axiom 11 (multiply_over_add1) }
% 34.57/4.79 add(multiply(multiply(add(cx, add(cy, additive_inverse(cx))), cx), cx), multiply(multiply(add(cx, add(cy, additive_inverse(cx))), cx), add(cy, additive_inverse(cx))))
% 34.57/4.79 = { by axiom 10 (right_alternative) }
% 34.57/4.79 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), multiply(multiply(add(cx, add(cy, additive_inverse(cx))), cx), add(cy, additive_inverse(cx))))
% 34.57/4.79 = { by axiom 1 (additive_inverse_additive_inverse) R->L }
% 34.57/4.79 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), additive_inverse(additive_inverse(multiply(multiply(add(cx, add(cy, additive_inverse(cx))), cx), add(cy, additive_inverse(cx))))))
% 34.57/4.79 = { by axiom 6 (inverse_product1) R->L }
% 34.57/4.79 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), additive_inverse(multiply(additive_inverse(multiply(add(cx, add(cy, additive_inverse(cx))), cx)), add(cy, additive_inverse(cx)))))
% 34.57/4.79 = { by axiom 5 (inverse_product2) R->L }
% 34.57/4.79 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), additive_inverse(multiply(multiply(add(cx, add(cy, additive_inverse(cx))), additive_inverse(cx)), add(cy, additive_inverse(cx)))))
% 34.57/4.79 = { by axiom 6 (inverse_product1) R->L }
% 34.57/4.79 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), multiply(additive_inverse(multiply(add(cx, add(cy, additive_inverse(cx))), additive_inverse(cx))), add(cy, additive_inverse(cx))))
% 34.57/4.79 = { by axiom 6 (inverse_product1) R->L }
% 34.57/4.79 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), multiply(multiply(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), additive_inverse(cx)), add(cy, additive_inverse(cx))))
% 34.57/4.79 = { by lemma 14 R->L }
% 34.57/4.79 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), multiply(multiply(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), add(add(cy, additive_inverse(cx)), add(additive_inverse(cx), additive_inverse(add(cy, additive_inverse(cx)))))), add(cy, additive_inverse(cx))))
% 34.57/4.79 = { by axiom 7 (sum_of_inverses) R->L }
% 34.57/4.79 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), multiply(multiply(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), add(add(cy, additive_inverse(cx)), additive_inverse(add(cx, add(cy, additive_inverse(cx)))))), add(cy, additive_inverse(cx))))
% 34.57/4.79 = { by axiom 2 (commutativity_for_addition) R->L }
% 34.57/4.79 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), multiply(multiply(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), add(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), add(cy, additive_inverse(cx)))), add(cy, additive_inverse(cx))))
% 34.57/4.79 = { by axiom 11 (multiply_over_add1) }
% 34.57/4.79 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), multiply(add(multiply(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), additive_inverse(add(cx, add(cy, additive_inverse(cx))))), multiply(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), add(cy, additive_inverse(cx)))), add(cy, additive_inverse(cx))))
% 34.57/4.79 = { by axiom 12 (multiply_over_add2) }
% 34.57/4.79 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), add(multiply(multiply(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), additive_inverse(add(cx, add(cy, additive_inverse(cx))))), add(cy, additive_inverse(cx))), multiply(multiply(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), add(cy, additive_inverse(cx))), add(cy, additive_inverse(cx)))))
% 34.57/4.79 = { by axiom 9 (left_alternative) }
% 34.57/4.79 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), add(multiply(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), multiply(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), add(cy, additive_inverse(cx)))), multiply(multiply(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), add(cy, additive_inverse(cx))), add(cy, additive_inverse(cx)))))
% 34.57/4.79 = { by axiom 10 (right_alternative) }
% 34.57/4.79 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), add(multiply(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), multiply(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), add(cy, additive_inverse(cx)))), multiply(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), multiply(add(cy, additive_inverse(cx)), add(cy, additive_inverse(cx))))))
% 34.57/4.79 = { by axiom 11 (multiply_over_add1) R->L }
% 34.57/4.79 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), multiply(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), add(multiply(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), add(cy, additive_inverse(cx))), multiply(add(cy, additive_inverse(cx)), add(cy, additive_inverse(cx))))))
% 34.57/4.79 = { by axiom 12 (multiply_over_add2) R->L }
% 34.57/4.79 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), multiply(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), multiply(add(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), add(cy, additive_inverse(cx))), add(cy, additive_inverse(cx)))))
% 34.57/4.80 = { by axiom 6 (inverse_product1) }
% 34.57/4.80 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), additive_inverse(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(add(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), add(cy, additive_inverse(cx))), add(cy, additive_inverse(cx))))))
% 34.57/4.80 = { by axiom 2 (commutativity_for_addition) R->L }
% 34.57/4.80 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), additive_inverse(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(add(add(cy, additive_inverse(cx)), additive_inverse(add(cx, add(cy, additive_inverse(cx))))), add(cy, additive_inverse(cx))))))
% 34.57/4.80 = { by axiom 5 (inverse_product2) R->L }
% 34.57/4.80 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), multiply(add(cx, add(cy, additive_inverse(cx))), additive_inverse(multiply(add(add(cy, additive_inverse(cx)), additive_inverse(add(cx, add(cy, additive_inverse(cx))))), add(cy, additive_inverse(cx))))))
% 34.57/4.80 = { by axiom 6 (inverse_product1) R->L }
% 34.57/4.80 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), multiply(add(cx, add(cy, additive_inverse(cx))), multiply(additive_inverse(add(add(cy, additive_inverse(cx)), additive_inverse(add(cx, add(cy, additive_inverse(cx)))))), add(cy, additive_inverse(cx)))))
% 34.57/4.80 = { by axiom 2 (commutativity_for_addition) R->L }
% 34.57/4.80 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), multiply(add(cx, add(cy, additive_inverse(cx))), multiply(additive_inverse(add(additive_inverse(add(cx, add(cy, additive_inverse(cx)))), add(cy, additive_inverse(cx)))), add(cy, additive_inverse(cx)))))
% 34.57/4.80 = { by axiom 7 (sum_of_inverses) }
% 34.57/4.80 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), multiply(add(cx, add(cy, additive_inverse(cx))), multiply(add(additive_inverse(additive_inverse(add(cx, add(cy, additive_inverse(cx))))), additive_inverse(add(cy, additive_inverse(cx)))), add(cy, additive_inverse(cx)))))
% 34.57/4.80 = { by axiom 1 (additive_inverse_additive_inverse) }
% 34.57/4.80 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), multiply(add(cx, add(cy, additive_inverse(cx))), multiply(add(add(cx, add(cy, additive_inverse(cx))), additive_inverse(add(cy, additive_inverse(cx)))), add(cy, additive_inverse(cx)))))
% 34.57/4.80 = { by axiom 8 (associativity_for_addition) R->L }
% 34.57/4.80 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), multiply(add(cx, add(cy, additive_inverse(cx))), multiply(add(cx, add(add(cy, additive_inverse(cx)), additive_inverse(add(cy, additive_inverse(cx))))), add(cy, additive_inverse(cx)))))
% 34.57/4.80 = { by lemma 13 }
% 34.57/4.80 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), multiply(add(cx, add(cy, additive_inverse(cx))), multiply(add(cx, additive_identity), add(cy, additive_inverse(cx)))))
% 34.57/4.80 = { by axiom 2 (commutativity_for_addition) R->L }
% 34.57/4.80 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), multiply(add(cx, add(cy, additive_inverse(cx))), multiply(add(additive_identity, cx), add(cy, additive_inverse(cx)))))
% 34.57/4.80 = { by axiom 3 (left_additive_identity) }
% 34.57/4.80 add(multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, cx)), multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, add(cy, additive_inverse(cx)))))
% 34.57/4.80 = { by axiom 11 (multiply_over_add1) R->L }
% 34.57/4.80 multiply(add(cx, add(cy, additive_inverse(cx))), add(multiply(cx, cx), multiply(cx, add(cy, additive_inverse(cx)))))
% 34.57/4.80 = { by axiom 11 (multiply_over_add1) R->L }
% 34.57/4.80 multiply(add(cx, add(cy, additive_inverse(cx))), multiply(cx, add(cx, add(cy, additive_inverse(cx)))))
% 34.57/4.80 = { by lemma 14 }
% 34.57/4.80 multiply(cy, multiply(cx, add(cx, add(cy, additive_inverse(cx)))))
% 34.57/4.80 = { by lemma 14 }
% 34.57/4.80 multiply(cy, multiply(cx, cy))
% 34.57/4.80 % SZS output end Proof
% 34.57/4.80
% 34.57/4.80 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------