%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO005-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 09:35:20 AM UTC 2026
% Result : Unsatisfiable 17.71s 2.51s
% Output : Proof 17.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n026.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 21:06:12 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.71/2.51 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
% 17.71/2.51
% 17.71/2.51 % SZS status Unsatisfiable
% 17.71/2.51
% 17.71/2.52 % SZS output start Proof
% 17.71/2.52 Axiom 1 (additive_inverse1): sum(inverse(X), X, multiplicative_identity) = true.
% 17.71/2.52 Axiom 2 (multiplicative_identity2): product(X, multiplicative_identity, X) = true.
% 17.71/2.52 Axiom 3 (multiplicative_identity1): product(multiplicative_identity, X, X) = true.
% 17.71/2.52 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 17.71/2.52 Axiom 5 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 17.71/2.52 Axiom 6 (closure_of_addition): sum(X, Y, add(X, Y)) = true.
% 17.71/2.52 Axiom 7 (commutativity_of_addition): ifeq(sum(X, Y, Z), true, sum(Y, X, Z), true) = true.
% 17.71/2.52 Axiom 8 (addition_is_well_defined): ifeq2(sum(X, Y, Z), true, ifeq2(sum(X, Y, W), true, W, Z), Z) = Z.
% 17.71/2.52 Axiom 9 (multiplication_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 17.71/2.52 Axiom 10 (distributivity7): ifeq(product(X, Y, Z), true, ifeq(sum(Z, W, V), true, ifeq(sum(Y, W, U), true, ifeq(sum(X, W, T), true, product(T, U, V), true), true), true), true) = true.
% 17.71/2.52
% 17.71/2.52 Goal 1 (prove_equations): sum(x, multiplicative_identity, multiplicative_identity) = true.
% 17.71/2.52 Proof:
% 17.71/2.52 sum(x, multiplicative_identity, multiplicative_identity)
% 17.71/2.52 = { by axiom 5 (ifeq_axiom) R->L }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(true, true, multiplicative_identity, add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 10 (distributivity7) R->L }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(ifeq(product(inverse(x), multiplicative_identity, inverse(x)), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, ifeq(sum(multiplicative_identity, x, add(multiplicative_identity, x)), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, product(multiplicative_identity, add(multiplicative_identity, x), multiplicative_identity), true), true), true), true), true, multiplicative_identity, add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 2 (multiplicative_identity2) }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(ifeq(true, true, ifeq(sum(inverse(x), x, multiplicative_identity), true, ifeq(sum(multiplicative_identity, x, add(multiplicative_identity, x)), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, product(multiplicative_identity, add(multiplicative_identity, x), multiplicative_identity), true), true), true), true), true, multiplicative_identity, add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 4 (ifeq_axiom) }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(ifeq(sum(inverse(x), x, multiplicative_identity), true, ifeq(sum(multiplicative_identity, x, add(multiplicative_identity, x)), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, product(multiplicative_identity, add(multiplicative_identity, x), multiplicative_identity), true), true), true), true, multiplicative_identity, add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 1 (additive_inverse1) }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(ifeq(true, true, ifeq(sum(multiplicative_identity, x, add(multiplicative_identity, x)), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, product(multiplicative_identity, add(multiplicative_identity, x), multiplicative_identity), true), true), true), true, multiplicative_identity, add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 4 (ifeq_axiom) }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(ifeq(sum(multiplicative_identity, x, add(multiplicative_identity, x)), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, product(multiplicative_identity, add(multiplicative_identity, x), multiplicative_identity), true), true), true, multiplicative_identity, add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 1 (additive_inverse1) }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(ifeq(sum(multiplicative_identity, x, add(multiplicative_identity, x)), true, ifeq(true, true, product(multiplicative_identity, add(multiplicative_identity, x), multiplicative_identity), true), true), true, multiplicative_identity, add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 4 (ifeq_axiom) }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(ifeq(sum(multiplicative_identity, x, add(multiplicative_identity, x)), true, product(multiplicative_identity, add(multiplicative_identity, x), multiplicative_identity), true), true, multiplicative_identity, add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 6 (closure_of_addition) }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(ifeq(true, true, product(multiplicative_identity, add(multiplicative_identity, x), multiplicative_identity), true), true, multiplicative_identity, add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 4 (ifeq_axiom) }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(product(multiplicative_identity, add(multiplicative_identity, x), multiplicative_identity), true, multiplicative_identity, add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 8 (addition_is_well_defined) R->L }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(product(multiplicative_identity, ifeq2(sum(x, multiplicative_identity, add(multiplicative_identity, x)), true, ifeq2(sum(x, multiplicative_identity, add(x, multiplicative_identity)), true, add(x, multiplicative_identity), add(multiplicative_identity, x)), add(multiplicative_identity, x)), multiplicative_identity), true, multiplicative_identity, add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 6 (closure_of_addition) }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(product(multiplicative_identity, ifeq2(sum(x, multiplicative_identity, add(multiplicative_identity, x)), true, ifeq2(true, true, add(x, multiplicative_identity), add(multiplicative_identity, x)), add(multiplicative_identity, x)), multiplicative_identity), true, multiplicative_identity, add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 5 (ifeq_axiom) }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(product(multiplicative_identity, ifeq2(sum(x, multiplicative_identity, add(multiplicative_identity, x)), true, add(x, multiplicative_identity), add(multiplicative_identity, x)), multiplicative_identity), true, multiplicative_identity, add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 4 (ifeq_axiom) R->L }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(product(multiplicative_identity, ifeq2(ifeq(true, true, sum(x, multiplicative_identity, add(multiplicative_identity, x)), true), true, add(x, multiplicative_identity), add(multiplicative_identity, x)), multiplicative_identity), true, multiplicative_identity, add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 6 (closure_of_addition) R->L }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(product(multiplicative_identity, ifeq2(ifeq(sum(multiplicative_identity, x, add(multiplicative_identity, x)), true, sum(x, multiplicative_identity, add(multiplicative_identity, x)), true), true, add(x, multiplicative_identity), add(multiplicative_identity, x)), multiplicative_identity), true, multiplicative_identity, add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 7 (commutativity_of_addition) }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(product(multiplicative_identity, ifeq2(true, true, add(x, multiplicative_identity), add(multiplicative_identity, x)), multiplicative_identity), true, multiplicative_identity, add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 5 (ifeq_axiom) }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(product(multiplicative_identity, add(x, multiplicative_identity), multiplicative_identity), true, multiplicative_identity, add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 5 (ifeq_axiom) R->L }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(true, true, ifeq2(product(multiplicative_identity, add(x, multiplicative_identity), multiplicative_identity), true, multiplicative_identity, add(x, multiplicative_identity)), add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 3 (multiplicative_identity1) R->L }
% 17.71/2.52 sum(x, multiplicative_identity, ifeq2(product(multiplicative_identity, add(x, multiplicative_identity), add(x, multiplicative_identity)), true, ifeq2(product(multiplicative_identity, add(x, multiplicative_identity), multiplicative_identity), true, multiplicative_identity, add(x, multiplicative_identity)), add(x, multiplicative_identity)))
% 17.71/2.52 = { by axiom 9 (multiplication_is_well_defined) }
% 17.71/2.52 sum(x, multiplicative_identity, add(x, multiplicative_identity))
% 17.71/2.52 = { by axiom 6 (closure_of_addition) }
% 17.71/2.52 true
% 17.71/2.52 % SZS output end Proof
% 17.71/2.52
% 17.71/2.52 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------