TSTP Solution File: RNG001-10 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG001-10 : TPTP v8.1.2. Released v7.3.0.
% 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 13:58:41 EDT 2023
% Result : Unsatisfiable 3.27s 0.79s
% Output : Proof 3.27s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG001-10 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 02:01:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.27/0.79 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 3.27/0.79
% 3.27/0.79 % SZS status Unsatisfiable
% 3.27/0.79
% 3.27/0.81 % SZS output start Proof
% 3.27/0.81 Axiom 1 (additive_identity2): sum(X, additive_identity, X) = true.
% 3.27/0.81 Axiom 2 (additive_identity1): sum(additive_identity, X, X) = true.
% 3.27/0.81 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 3.27/0.81 Axiom 4 (right_inverse): sum(X, additive_inverse(X), additive_identity) = true.
% 3.27/0.81 Axiom 5 (ifeq_axiom_001): ifeq(X, X, Y, Z) = Y.
% 3.27/0.81 Axiom 6 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 3.27/0.81 Axiom 7 (closure_of_addition): sum(X, Y, add(X, Y)) = true.
% 3.27/0.81 Axiom 8 (commutativity_of_addition): ifeq(sum(X, Y, Z), true, sum(Y, X, Z), true) = true.
% 3.27/0.81 Axiom 9 (multiplication_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 3.27/0.81 Axiom 10 (addition_is_well_defined): ifeq2(sum(X, Y, Z), true, ifeq2(sum(X, Y, W), true, W, Z), Z) = Z.
% 3.27/0.81 Axiom 11 (cancellation1): ifeq2(sum(X, Y, Z), true, ifeq2(sum(X, W, Z), true, W, Y), Y) = Y.
% 3.27/0.81 Axiom 12 (associativity_of_addition1): ifeq(sum(X, Y, Z), true, ifeq(sum(W, Y, V), true, ifeq(sum(U, W, X), true, sum(U, V, Z), true), true), true) = true.
% 3.27/0.81 Axiom 13 (distributivity2): ifeq(product(X, Y, Z), true, ifeq(product(X, W, V), true, ifeq(sum(V, Z, U), true, ifeq(sum(W, Y, T), true, product(X, T, U), true), true), true), true) = true.
% 3.27/0.81
% 3.27/0.81 Lemma 14: sum(X, Y, add(Y, X)) = true.
% 3.27/0.81 Proof:
% 3.27/0.81 sum(X, Y, add(Y, X))
% 3.27/0.81 = { by axiom 5 (ifeq_axiom_001) R->L }
% 3.27/0.81 ifeq(true, true, sum(X, Y, add(Y, X)), true)
% 3.27/0.81 = { by axiom 7 (closure_of_addition) R->L }
% 3.27/0.81 ifeq(sum(Y, X, add(Y, X)), true, sum(X, Y, add(Y, X)), true)
% 3.27/0.81 = { by axiom 8 (commutativity_of_addition) }
% 3.27/0.81 true
% 3.27/0.81
% 3.27/0.81 Lemma 15: add(X, Y) = add(Y, X).
% 3.27/0.81 Proof:
% 3.27/0.81 add(X, Y)
% 3.27/0.81 = { by axiom 10 (addition_is_well_defined) R->L }
% 3.27/0.81 ifeq2(sum(Y, X, add(X, Y)), true, ifeq2(sum(Y, X, add(Y, X)), true, add(Y, X), add(X, Y)), add(X, Y))
% 3.27/0.81 = { by axiom 7 (closure_of_addition) }
% 3.27/0.81 ifeq2(sum(Y, X, add(X, Y)), true, ifeq2(true, true, add(Y, X), add(X, Y)), add(X, Y))
% 3.27/0.81 = { by axiom 3 (ifeq_axiom) }
% 3.27/0.81 ifeq2(sum(Y, X, add(X, Y)), true, add(Y, X), add(X, Y))
% 3.27/0.81 = { by lemma 14 }
% 3.27/0.81 ifeq2(true, true, add(Y, X), add(X, Y))
% 3.27/0.81 = { by axiom 3 (ifeq_axiom) }
% 3.27/0.81 add(Y, X)
% 3.27/0.81
% 3.27/0.81 Goal 1 (prove_a_times_additive_id_is_additive_id): product(a, additive_identity, additive_identity) = true.
% 3.27/0.81 Proof:
% 3.27/0.81 product(a, additive_identity, additive_identity)
% 3.27/0.81 = { by axiom 3 (ifeq_axiom) R->L }
% 3.27/0.81 product(a, additive_identity, ifeq2(true, true, additive_identity, add(additive_inverse(multiply(a, X)), multiply(a, X))))
% 3.27/0.81 = { by lemma 14 R->L }
% 3.27/0.81 product(a, additive_identity, ifeq2(sum(multiply(a, X), additive_inverse(multiply(a, X)), add(additive_inverse(multiply(a, X)), multiply(a, X))), true, additive_identity, add(additive_inverse(multiply(a, X)), multiply(a, X))))
% 3.27/0.81 = { by axiom 3 (ifeq_axiom) R->L }
% 3.27/0.81 product(a, additive_identity, ifeq2(sum(multiply(a, X), additive_inverse(multiply(a, X)), add(additive_inverse(multiply(a, X)), multiply(a, X))), true, ifeq2(true, true, additive_identity, add(additive_inverse(multiply(a, X)), multiply(a, X))), add(additive_inverse(multiply(a, X)), multiply(a, X))))
% 3.27/0.81 = { by axiom 4 (right_inverse) R->L }
% 3.27/0.81 product(a, additive_identity, ifeq2(sum(multiply(a, X), additive_inverse(multiply(a, X)), add(additive_inverse(multiply(a, X)), multiply(a, X))), true, ifeq2(sum(multiply(a, X), additive_inverse(multiply(a, X)), additive_identity), true, additive_identity, add(additive_inverse(multiply(a, X)), multiply(a, X))), add(additive_inverse(multiply(a, X)), multiply(a, X))))
% 3.27/0.81 = { by axiom 10 (addition_is_well_defined) }
% 3.27/0.81 product(a, additive_identity, add(additive_inverse(multiply(a, X)), multiply(a, X)))
% 3.27/0.81 = { by axiom 3 (ifeq_axiom) R->L }
% 3.27/0.81 product(a, additive_identity, add(additive_inverse(multiply(a, X)), ifeq2(true, true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))))
% 3.27/0.81 = { by axiom 13 (distributivity2) R->L }
% 3.27/0.82 product(a, additive_identity, add(additive_inverse(multiply(a, X)), ifeq2(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, X, multiply(a, X)), true, ifeq(sum(multiply(a, X), multiply(a, additive_identity), add(multiply(a, X), multiply(a, additive_identity))), true, ifeq(sum(X, additive_identity, X), true, product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true), true), true), true), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))))
% 3.27/0.82 = { by axiom 1 (additive_identity2) }
% 3.27/0.82 product(a, additive_identity, add(additive_inverse(multiply(a, X)), ifeq2(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, X, multiply(a, X)), true, ifeq(sum(multiply(a, X), multiply(a, additive_identity), add(multiply(a, X), multiply(a, additive_identity))), true, ifeq(true, true, product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true), true), true), true), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))))
% 3.27/0.82 = { by axiom 5 (ifeq_axiom_001) }
% 3.27/0.82 product(a, additive_identity, add(additive_inverse(multiply(a, X)), ifeq2(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, X, multiply(a, X)), true, ifeq(sum(multiply(a, X), multiply(a, additive_identity), add(multiply(a, X), multiply(a, additive_identity))), true, product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true), true), true), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))))
% 3.27/0.82 = { by axiom 7 (closure_of_addition) }
% 3.27/0.82 product(a, additive_identity, add(additive_inverse(multiply(a, X)), ifeq2(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, X, multiply(a, X)), true, ifeq(true, true, product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true), true), true), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))))
% 3.27/0.82 = { by axiom 5 (ifeq_axiom_001) }
% 3.27/0.82 product(a, additive_identity, add(additive_inverse(multiply(a, X)), ifeq2(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, X, multiply(a, X)), true, product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true), true), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))))
% 3.27/0.82 = { by axiom 6 (closure_of_multiplication) }
% 3.27/0.82 product(a, additive_identity, add(additive_inverse(multiply(a, X)), ifeq2(ifeq(true, true, ifeq(product(a, X, multiply(a, X)), true, product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true), true), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))))
% 3.27/0.82 = { by axiom 5 (ifeq_axiom_001) }
% 3.27/0.82 product(a, additive_identity, add(additive_inverse(multiply(a, X)), ifeq2(ifeq(product(a, X, multiply(a, X)), true, product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))))
% 3.27/0.82 = { by axiom 6 (closure_of_multiplication) }
% 3.27/0.82 product(a, additive_identity, add(additive_inverse(multiply(a, X)), ifeq2(ifeq(true, true, product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))))
% 3.27/0.82 = { by axiom 5 (ifeq_axiom_001) }
% 3.27/0.82 product(a, additive_identity, add(additive_inverse(multiply(a, X)), ifeq2(product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))))
% 3.27/0.82 = { by axiom 3 (ifeq_axiom) R->L }
% 3.27/0.82 product(a, additive_identity, add(additive_inverse(multiply(a, X)), ifeq2(product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true, ifeq2(true, true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity))), add(multiply(a, X), multiply(a, additive_identity)))))
% 3.27/0.82 = { by axiom 6 (closure_of_multiplication) R->L }
% 3.27/0.82 product(a, additive_identity, add(additive_inverse(multiply(a, X)), ifeq2(product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true, ifeq2(product(a, X, multiply(a, X)), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity))), add(multiply(a, X), multiply(a, additive_identity)))))
% 3.27/0.82 = { by axiom 9 (multiplication_is_well_defined) }
% 3.27/0.82 product(a, additive_identity, add(additive_inverse(multiply(a, X)), add(multiply(a, X), multiply(a, additive_identity))))
% 3.27/0.82 = { by lemma 15 R->L }
% 3.27/0.82 product(a, additive_identity, add(add(multiply(a, X), multiply(a, additive_identity)), additive_inverse(multiply(a, X))))
% 3.27/0.82 = { by axiom 3 (ifeq_axiom) R->L }
% 3.27/0.82 product(a, additive_identity, ifeq2(true, true, add(add(multiply(a, X), multiply(a, additive_identity)), additive_inverse(multiply(a, X))), multiply(a, additive_identity)))
% 3.27/0.82 = { by axiom 12 (associativity_of_addition1) R->L }
% 3.27/0.82 product(a, additive_identity, ifeq2(ifeq(sum(additive_identity, add(multiply(a, X), multiply(a, additive_identity)), add(multiply(a, X), multiply(a, additive_identity))), true, ifeq(sum(additive_inverse(multiply(a, X)), add(multiply(a, X), multiply(a, additive_identity)), add(additive_inverse(multiply(a, X)), add(multiply(a, X), multiply(a, additive_identity)))), true, ifeq(sum(multiply(a, X), additive_inverse(multiply(a, X)), additive_identity), true, sum(multiply(a, X), add(additive_inverse(multiply(a, X)), add(multiply(a, X), multiply(a, additive_identity))), add(multiply(a, X), multiply(a, additive_identity))), true), true), true), true, add(add(multiply(a, X), multiply(a, additive_identity)), additive_inverse(multiply(a, X))), multiply(a, additive_identity)))
% 3.27/0.82 = { by axiom 2 (additive_identity1) }
% 3.27/0.82 product(a, additive_identity, ifeq2(ifeq(true, true, ifeq(sum(additive_inverse(multiply(a, X)), add(multiply(a, X), multiply(a, additive_identity)), add(additive_inverse(multiply(a, X)), add(multiply(a, X), multiply(a, additive_identity)))), true, ifeq(sum(multiply(a, X), additive_inverse(multiply(a, X)), additive_identity), true, sum(multiply(a, X), add(additive_inverse(multiply(a, X)), add(multiply(a, X), multiply(a, additive_identity))), add(multiply(a, X), multiply(a, additive_identity))), true), true), true), true, add(add(multiply(a, X), multiply(a, additive_identity)), additive_inverse(multiply(a, X))), multiply(a, additive_identity)))
% 3.27/0.82 = { by axiom 5 (ifeq_axiom_001) }
% 3.27/0.82 product(a, additive_identity, ifeq2(ifeq(sum(additive_inverse(multiply(a, X)), add(multiply(a, X), multiply(a, additive_identity)), add(additive_inverse(multiply(a, X)), add(multiply(a, X), multiply(a, additive_identity)))), true, ifeq(sum(multiply(a, X), additive_inverse(multiply(a, X)), additive_identity), true, sum(multiply(a, X), add(additive_inverse(multiply(a, X)), add(multiply(a, X), multiply(a, additive_identity))), add(multiply(a, X), multiply(a, additive_identity))), true), true), true, add(add(multiply(a, X), multiply(a, additive_identity)), additive_inverse(multiply(a, X))), multiply(a, additive_identity)))
% 3.27/0.82 = { by axiom 4 (right_inverse) }
% 3.27/0.82 product(a, additive_identity, ifeq2(ifeq(sum(additive_inverse(multiply(a, X)), add(multiply(a, X), multiply(a, additive_identity)), add(additive_inverse(multiply(a, X)), add(multiply(a, X), multiply(a, additive_identity)))), true, ifeq(true, true, sum(multiply(a, X), add(additive_inverse(multiply(a, X)), add(multiply(a, X), multiply(a, additive_identity))), add(multiply(a, X), multiply(a, additive_identity))), true), true), true, add(add(multiply(a, X), multiply(a, additive_identity)), additive_inverse(multiply(a, X))), multiply(a, additive_identity)))
% 3.27/0.82 = { by axiom 5 (ifeq_axiom_001) }
% 3.27/0.82 product(a, additive_identity, ifeq2(ifeq(sum(additive_inverse(multiply(a, X)), add(multiply(a, X), multiply(a, additive_identity)), add(additive_inverse(multiply(a, X)), add(multiply(a, X), multiply(a, additive_identity)))), true, sum(multiply(a, X), add(additive_inverse(multiply(a, X)), add(multiply(a, X), multiply(a, additive_identity))), add(multiply(a, X), multiply(a, additive_identity))), true), true, add(add(multiply(a, X), multiply(a, additive_identity)), additive_inverse(multiply(a, X))), multiply(a, additive_identity)))
% 3.27/0.82 = { by axiom 7 (closure_of_addition) }
% 3.27/0.82 product(a, additive_identity, ifeq2(ifeq(true, true, sum(multiply(a, X), add(additive_inverse(multiply(a, X)), add(multiply(a, X), multiply(a, additive_identity))), add(multiply(a, X), multiply(a, additive_identity))), true), true, add(add(multiply(a, X), multiply(a, additive_identity)), additive_inverse(multiply(a, X))), multiply(a, additive_identity)))
% 3.27/0.82 = { by axiom 5 (ifeq_axiom_001) }
% 3.27/0.82 product(a, additive_identity, ifeq2(sum(multiply(a, X), add(additive_inverse(multiply(a, X)), add(multiply(a, X), multiply(a, additive_identity))), add(multiply(a, X), multiply(a, additive_identity))), true, add(add(multiply(a, X), multiply(a, additive_identity)), additive_inverse(multiply(a, X))), multiply(a, additive_identity)))
% 3.27/0.82 = { by lemma 15 }
% 3.27/0.82 product(a, additive_identity, ifeq2(sum(multiply(a, X), add(add(multiply(a, X), multiply(a, additive_identity)), additive_inverse(multiply(a, X))), add(multiply(a, X), multiply(a, additive_identity))), true, add(add(multiply(a, X), multiply(a, additive_identity)), additive_inverse(multiply(a, X))), multiply(a, additive_identity)))
% 3.27/0.82 = { by axiom 3 (ifeq_axiom) R->L }
% 3.27/0.82 product(a, additive_identity, ifeq2(true, true, ifeq2(sum(multiply(a, X), add(add(multiply(a, X), multiply(a, additive_identity)), additive_inverse(multiply(a, X))), add(multiply(a, X), multiply(a, additive_identity))), true, add(add(multiply(a, X), multiply(a, additive_identity)), additive_inverse(multiply(a, X))), multiply(a, additive_identity)), multiply(a, additive_identity)))
% 3.27/0.82 = { by axiom 7 (closure_of_addition) R->L }
% 3.27/0.82 product(a, additive_identity, ifeq2(sum(multiply(a, X), multiply(a, additive_identity), add(multiply(a, X), multiply(a, additive_identity))), true, ifeq2(sum(multiply(a, X), add(add(multiply(a, X), multiply(a, additive_identity)), additive_inverse(multiply(a, X))), add(multiply(a, X), multiply(a, additive_identity))), true, add(add(multiply(a, X), multiply(a, additive_identity)), additive_inverse(multiply(a, X))), multiply(a, additive_identity)), multiply(a, additive_identity)))
% 3.27/0.82 = { by axiom 11 (cancellation1) }
% 3.27/0.82 product(a, additive_identity, multiply(a, additive_identity))
% 3.27/0.82 = { by axiom 6 (closure_of_multiplication) }
% 3.27/0.82 true
% 3.27/0.82 % SZS output end Proof
% 3.27/0.82
% 3.27/0.82 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------