%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:35:22 AM UTC 2026
% Result : Unsatisfiable 27.67s 3.76s
% Output : Proof 28.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n007.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 21:01:40 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.67/3.76 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 27.67/3.76
% 27.67/3.76 % SZS status Unsatisfiable
% 27.67/3.76
% 27.67/3.79 % SZS output start Proof
% 27.67/3.79 Axiom 1 (multiplicative_inverse2): product(X, inverse(X), additive_identity) = true.
% 27.67/3.79 Axiom 2 (additive_identity2): sum(X, additive_identity, X) = true.
% 27.67/3.79 Axiom 3 (additive_identity1): sum(additive_identity, X, X) = true.
% 27.67/3.79 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 27.67/3.79 Axiom 5 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 27.67/3.79 Axiom 6 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 27.67/3.79 Axiom 7 (closure_of_addition): sum(X, Y, add(X, Y)) = true.
% 27.67/3.79 Axiom 8 (commutativity_of_multiplication): ifeq(product(X, Y, Z), true, product(Y, X, Z), true) = true.
% 27.67/3.79 Axiom 9 (commutativity_of_addition): ifeq(sum(X, Y, Z), true, sum(Y, X, Z), true) = true.
% 27.67/3.80 Axiom 10 (multiplication_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 27.67/3.80 Axiom 11 (addition_is_well_defined): ifeq2(sum(X, Y, Z), true, ifeq2(sum(X, Y, W), true, W, Z), Z) = Z.
% 27.67/3.80 Axiom 12 (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.
% 27.67/3.80 Axiom 13 (distributivity8): ifeq(product(X, Y, Z), true, ifeq(product(W, V, U), true, ifeq(sum(V, T, Y), true, ifeq(sum(W, T, X), true, sum(U, T, Z), true), true), true), true) = true.
% 27.67/3.80
% 27.67/3.80 Lemma 14: multiply(X, additive_identity) = additive_identity.
% 27.67/3.80 Proof:
% 27.67/3.80 multiply(X, additive_identity)
% 27.67/3.80 = { by axiom 10 (multiplication_is_well_defined) R->L }
% 27.67/3.80 ifeq2(product(X, inverse(X), multiply(X, additive_identity)), true, ifeq2(product(X, inverse(X), additive_identity), true, additive_identity, multiply(X, additive_identity)), multiply(X, additive_identity))
% 27.67/3.80 = { by axiom 1 (multiplicative_inverse2) }
% 27.67/3.80 ifeq2(product(X, inverse(X), multiply(X, additive_identity)), true, ifeq2(true, true, additive_identity, multiply(X, additive_identity)), multiply(X, additive_identity))
% 27.67/3.80 = { by axiom 5 (ifeq_axiom) }
% 27.67/3.80 ifeq2(product(X, inverse(X), multiply(X, additive_identity)), true, additive_identity, multiply(X, additive_identity))
% 27.67/3.80 = { by axiom 4 (ifeq_axiom) R->L }
% 27.67/3.80 ifeq2(ifeq(true, true, product(X, inverse(X), multiply(X, additive_identity)), true), true, additive_identity, multiply(X, additive_identity))
% 27.67/3.80 = { by axiom 6 (closure_of_multiplication) R->L }
% 27.67/3.80 ifeq2(ifeq(product(X, additive_identity, multiply(X, additive_identity)), true, product(X, inverse(X), multiply(X, additive_identity)), true), true, additive_identity, multiply(X, additive_identity))
% 27.67/3.80 = { by axiom 4 (ifeq_axiom) R->L }
% 27.67/3.80 ifeq2(ifeq(true, true, ifeq(product(X, additive_identity, multiply(X, additive_identity)), true, product(X, inverse(X), multiply(X, additive_identity)), true), true), true, additive_identity, multiply(X, additive_identity))
% 27.67/3.80 = { by axiom 1 (multiplicative_inverse2) R->L }
% 27.67/3.80 ifeq2(ifeq(product(X, inverse(X), additive_identity), true, ifeq(product(X, additive_identity, multiply(X, additive_identity)), true, product(X, inverse(X), multiply(X, additive_identity)), true), true), true, additive_identity, multiply(X, additive_identity))
% 27.67/3.80 = { by axiom 4 (ifeq_axiom) R->L }
% 27.67/3.80 ifeq2(ifeq(product(X, inverse(X), additive_identity), true, ifeq(product(X, additive_identity, multiply(X, additive_identity)), true, ifeq(true, true, product(X, inverse(X), multiply(X, additive_identity)), true), true), true), true, additive_identity, multiply(X, additive_identity))
% 27.67/3.80 = { by axiom 3 (additive_identity1) R->L }
% 27.67/3.80 ifeq2(ifeq(product(X, inverse(X), additive_identity), true, ifeq(product(X, additive_identity, multiply(X, additive_identity)), true, ifeq(sum(additive_identity, inverse(X), inverse(X)), true, product(X, inverse(X), multiply(X, additive_identity)), true), true), true), true, additive_identity, multiply(X, additive_identity))
% 27.67/3.80 = { by axiom 4 (ifeq_axiom) R->L }
% 28.44/3.80 ifeq2(ifeq(product(X, inverse(X), additive_identity), true, ifeq(product(X, additive_identity, multiply(X, additive_identity)), true, ifeq(true, true, ifeq(sum(additive_identity, inverse(X), inverse(X)), true, product(X, inverse(X), multiply(X, additive_identity)), true), true), true), true), true, additive_identity, multiply(X, additive_identity))
% 28.44/3.80 = { by axiom 2 (additive_identity2) R->L }
% 28.44/3.80 ifeq2(ifeq(product(X, inverse(X), additive_identity), true, ifeq(product(X, additive_identity, multiply(X, additive_identity)), true, ifeq(sum(multiply(X, additive_identity), additive_identity, multiply(X, additive_identity)), true, ifeq(sum(additive_identity, inverse(X), inverse(X)), true, product(X, inverse(X), multiply(X, additive_identity)), true), true), true), true), true, additive_identity, multiply(X, additive_identity))
% 28.44/3.80 = { by axiom 12 (distributivity2) }
% 28.44/3.80 ifeq2(true, true, additive_identity, multiply(X, additive_identity))
% 28.44/3.80 = { by axiom 5 (ifeq_axiom) }
% 28.44/3.80 additive_identity
% 28.44/3.80
% 28.44/3.80 Goal 1 (prove_equations): product(x, add(x, y), x) = true.
% 28.44/3.80 Proof:
% 28.44/3.80 product(x, add(x, y), x)
% 28.44/3.80 = { by axiom 4 (ifeq_axiom) R->L }
% 28.44/3.80 ifeq(true, true, product(x, add(x, y), x), true)
% 28.44/3.80 = { by axiom 2 (additive_identity2) R->L }
% 28.44/3.80 ifeq(sum(x, additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.80 = { by axiom 11 (addition_is_well_defined) R->L }
% 28.44/3.80 ifeq(sum(ifeq2(sum(additive_identity, x, x), true, ifeq2(sum(additive_identity, x, multiply(x, add(x, y))), true, multiply(x, add(x, y)), x), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.80 = { by axiom 3 (additive_identity1) }
% 28.44/3.80 ifeq(sum(ifeq2(true, true, ifeq2(sum(additive_identity, x, multiply(x, add(x, y))), true, multiply(x, add(x, y)), x), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.80 = { by axiom 5 (ifeq_axiom) }
% 28.44/3.80 ifeq(sum(ifeq2(sum(additive_identity, x, multiply(x, add(x, y))), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.80 = { by axiom 4 (ifeq_axiom) R->L }
% 28.44/3.80 ifeq(sum(ifeq2(ifeq(true, true, sum(additive_identity, x, multiply(x, add(x, y))), true), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.80 = { by axiom 6 (closure_of_multiplication) R->L }
% 28.44/3.80 ifeq(sum(ifeq2(ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, sum(additive_identity, x, multiply(x, add(x, y))), true), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.80 = { by axiom 4 (ifeq_axiom) R->L }
% 28.44/3.80 ifeq(sum(ifeq2(ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(true, true, sum(additive_identity, x, multiply(x, add(x, y))), true), true), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.80 = { by axiom 9 (commutativity_of_addition) R->L }
% 28.44/3.80 ifeq(sum(ifeq2(ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(ifeq(sum(x, y, add(x, y)), true, sum(y, x, add(x, y)), true), true, sum(additive_identity, x, multiply(x, add(x, y))), true), true), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.80 = { by axiom 7 (closure_of_addition) }
% 28.44/3.80 ifeq(sum(ifeq2(ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(ifeq(true, true, sum(y, x, add(x, y)), true), true, sum(additive_identity, x, multiply(x, add(x, y))), true), true), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.80 = { by axiom 4 (ifeq_axiom) }
% 28.44/3.80 ifeq(sum(ifeq2(ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(sum(y, x, add(x, y)), true, sum(additive_identity, x, multiply(x, add(x, y))), true), true), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.81 = { by lemma 14 R->L }
% 28.44/3.81 ifeq(sum(ifeq2(ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(sum(y, x, add(x, y)), true, sum(multiply(y, additive_identity), x, multiply(x, add(x, y))), true), true), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.81 = { by axiom 10 (multiplication_is_well_defined) R->L }
% 28.44/3.81 ifeq(sum(ifeq2(ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(sum(y, x, add(x, y)), true, sum(ifeq2(product(additive_identity, y, multiply(y, additive_identity)), true, ifeq2(product(additive_identity, y, multiply(additive_identity, y)), true, multiply(additive_identity, y), multiply(y, additive_identity)), multiply(y, additive_identity)), x, multiply(x, add(x, y))), true), true), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.81 = { by axiom 6 (closure_of_multiplication) }
% 28.44/3.81 ifeq(sum(ifeq2(ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(sum(y, x, add(x, y)), true, sum(ifeq2(product(additive_identity, y, multiply(y, additive_identity)), true, ifeq2(true, true, multiply(additive_identity, y), multiply(y, additive_identity)), multiply(y, additive_identity)), x, multiply(x, add(x, y))), true), true), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.81 = { by axiom 5 (ifeq_axiom) }
% 28.44/3.81 ifeq(sum(ifeq2(ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(sum(y, x, add(x, y)), true, sum(ifeq2(product(additive_identity, y, multiply(y, additive_identity)), true, multiply(additive_identity, y), multiply(y, additive_identity)), x, multiply(x, add(x, y))), true), true), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.81 = { by axiom 4 (ifeq_axiom) R->L }
% 28.44/3.81 ifeq(sum(ifeq2(ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(sum(y, x, add(x, y)), true, sum(ifeq2(ifeq(true, true, product(additive_identity, y, multiply(y, additive_identity)), true), true, multiply(additive_identity, y), multiply(y, additive_identity)), x, multiply(x, add(x, y))), true), true), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.81 = { by axiom 6 (closure_of_multiplication) R->L }
% 28.44/3.81 ifeq(sum(ifeq2(ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(sum(y, x, add(x, y)), true, sum(ifeq2(ifeq(product(y, additive_identity, multiply(y, additive_identity)), true, product(additive_identity, y, multiply(y, additive_identity)), true), true, multiply(additive_identity, y), multiply(y, additive_identity)), x, multiply(x, add(x, y))), true), true), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.81 = { by axiom 8 (commutativity_of_multiplication) }
% 28.44/3.81 ifeq(sum(ifeq2(ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(sum(y, x, add(x, y)), true, sum(ifeq2(true, true, multiply(additive_identity, y), multiply(y, additive_identity)), x, multiply(x, add(x, y))), true), true), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.81 = { by axiom 5 (ifeq_axiom) }
% 28.44/3.81 ifeq(sum(ifeq2(ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(sum(y, x, add(x, y)), true, sum(multiply(additive_identity, y), x, multiply(x, add(x, y))), true), true), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.81 = { by axiom 4 (ifeq_axiom) R->L }
% 28.44/3.81 ifeq(sum(ifeq2(ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(true, true, ifeq(sum(y, x, add(x, y)), true, sum(multiply(additive_identity, y), x, multiply(x, add(x, y))), true), true), true), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.81 = { by axiom 6 (closure_of_multiplication) R->L }
% 28.44/3.81 ifeq(sum(ifeq2(ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(product(additive_identity, y, multiply(additive_identity, y)), true, ifeq(sum(y, x, add(x, y)), true, sum(multiply(additive_identity, y), x, multiply(x, add(x, y))), true), true), true), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.81 = { by axiom 4 (ifeq_axiom) R->L }
% 28.44/3.81 ifeq(sum(ifeq2(ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(product(additive_identity, y, multiply(additive_identity, y)), true, ifeq(sum(y, x, add(x, y)), true, ifeq(true, true, sum(multiply(additive_identity, y), x, multiply(x, add(x, y))), true), true), true), true), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.81 = { by axiom 3 (additive_identity1) R->L }
% 28.44/3.81 ifeq(sum(ifeq2(ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(product(additive_identity, y, multiply(additive_identity, y)), true, ifeq(sum(y, x, add(x, y)), true, ifeq(sum(additive_identity, x, x), true, sum(multiply(additive_identity, y), x, multiply(x, add(x, y))), true), true), true), true), true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.81 = { by axiom 13 (distributivity8) }
% 28.44/3.81 ifeq(sum(ifeq2(true, true, multiply(x, add(x, y)), x), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.81 = { by axiom 5 (ifeq_axiom) }
% 28.44/3.81 ifeq(sum(multiply(x, add(x, y)), additive_identity, x), true, product(x, add(x, y), x), true)
% 28.44/3.81 = { by axiom 4 (ifeq_axiom) R->L }
% 28.44/3.81 ifeq(true, true, ifeq(sum(multiply(x, add(x, y)), additive_identity, x), true, product(x, add(x, y), x), true), true)
% 28.44/3.81 = { by axiom 6 (closure_of_multiplication) R->L }
% 28.44/3.81 ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(sum(multiply(x, add(x, y)), additive_identity, x), true, product(x, add(x, y), x), true), true)
% 28.44/3.81 = { by lemma 14 R->L }
% 28.44/3.81 ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(sum(multiply(x, add(x, y)), multiply(x, additive_identity), x), true, product(x, add(x, y), x), true), true)
% 28.44/3.81 = { by axiom 4 (ifeq_axiom) R->L }
% 28.44/3.81 ifeq(true, true, ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(sum(multiply(x, add(x, y)), multiply(x, additive_identity), x), true, product(x, add(x, y), x), true), true), true)
% 28.44/3.81 = { by axiom 6 (closure_of_multiplication) R->L }
% 28.44/3.81 ifeq(product(x, additive_identity, multiply(x, additive_identity)), true, ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(sum(multiply(x, add(x, y)), multiply(x, additive_identity), x), true, product(x, add(x, y), x), true), true), true)
% 28.44/3.81 = { by axiom 4 (ifeq_axiom) R->L }
% 28.44/3.81 ifeq(product(x, additive_identity, multiply(x, additive_identity)), true, ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(sum(multiply(x, add(x, y)), multiply(x, additive_identity), x), true, ifeq(true, true, product(x, add(x, y), x), true), true), true), true)
% 28.44/3.81 = { by axiom 2 (additive_identity2) R->L }
% 28.44/3.81 ifeq(product(x, additive_identity, multiply(x, additive_identity)), true, ifeq(product(x, add(x, y), multiply(x, add(x, y))), true, ifeq(sum(multiply(x, add(x, y)), multiply(x, additive_identity), x), true, ifeq(sum(add(x, y), additive_identity, add(x, y)), true, product(x, add(x, y), x), true), true), true), true)
% 28.44/3.81 = { by axiom 12 (distributivity2) }
% 28.44/3.81 true
% 28.44/3.81 % SZS output end Proof
% 28.44/3.81
% 28.44/3.81 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------