%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO003-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 2.14s 0.63s
% Output : Proof 2.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.22 % Computer : n003.cluster.edu
% 0.07/0.22 % Model : x86_64 x86_64
% 0.07/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.22 % Memory : 8046.5625MB
% 0.07/0.22 % OS : Linux 6.8.0-71-generic
% 0.07/0.22 % CPULimit : 300
% 0.07/0.22 % WCLimit : 300
% 0.07/0.22 % DateTime : Mon Sep 28 21:04:42 UTC 2026
% 0.07/0.23 % CPUTime :
% 0.07/0.23 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.14/0.63 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
% 2.14/0.63
% 2.14/0.63 % SZS status Unsatisfiable
% 2.14/0.63
% 2.14/0.63 % SZS output start Proof
% 2.14/0.63 Axiom 1 (multiplicative_identity2): product(X, multiplicative_identity, X) = true.
% 2.14/0.63 Axiom 2 (multiplicative_inverse2): product(X, inverse(X), additive_identity) = true.
% 2.14/0.63 Axiom 3 (additive_identity2): sum(X, additive_identity, X) = true.
% 2.14/0.63 Axiom 4 (additive_inverse2): sum(X, inverse(X), multiplicative_identity) = true.
% 2.14/0.63 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.14/0.63 Axiom 6 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 2.14/0.63 Axiom 7 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 2.14/0.63 Axiom 8 (multiplication_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 2.14/0.63 Axiom 9 (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.
% 2.14/0.63
% 2.14/0.63 Goal 1 (prove_both_equalities): product(x, x, x) = true.
% 2.14/0.63 Proof:
% 2.14/0.63 product(x, x, x)
% 2.14/0.63 = { by axiom 8 (multiplication_is_well_defined) R->L }
% 2.14/0.63 product(x, x, ifeq2(product(x, multiplicative_identity, x), true, ifeq2(product(x, multiplicative_identity, multiply(x, x)), true, multiply(x, x), x), x))
% 2.14/0.63 = { by axiom 1 (multiplicative_identity2) }
% 2.14/0.64 product(x, x, ifeq2(true, true, ifeq2(product(x, multiplicative_identity, multiply(x, x)), true, multiply(x, x), x), x))
% 2.14/0.64 = { by axiom 6 (ifeq_axiom) }
% 2.14/0.64 product(x, x, ifeq2(product(x, multiplicative_identity, multiply(x, x)), true, multiply(x, x), x))
% 2.14/0.64 = { by axiom 5 (ifeq_axiom) R->L }
% 2.14/0.64 product(x, x, ifeq2(ifeq(true, true, product(x, multiplicative_identity, multiply(x, x)), true), true, multiply(x, x), x))
% 2.14/0.64 = { by axiom 7 (closure_of_multiplication) R->L }
% 2.14/0.64 product(x, x, ifeq2(ifeq(product(x, x, multiply(x, x)), true, product(x, multiplicative_identity, multiply(x, x)), true), true, multiply(x, x), x))
% 2.14/0.64 = { by axiom 5 (ifeq_axiom) R->L }
% 2.14/0.64 product(x, x, ifeq2(ifeq(product(x, x, multiply(x, x)), true, ifeq(true, true, product(x, multiplicative_identity, multiply(x, x)), true), true), true, multiply(x, x), x))
% 2.14/0.64 = { by axiom 4 (additive_inverse2) R->L }
% 2.14/0.64 product(x, x, ifeq2(ifeq(product(x, x, multiply(x, x)), true, ifeq(sum(x, inverse(x), multiplicative_identity), true, product(x, multiplicative_identity, multiply(x, x)), true), true), true, multiply(x, x), x))
% 2.14/0.64 = { by axiom 5 (ifeq_axiom) R->L }
% 2.14/0.64 product(x, x, ifeq2(ifeq(true, true, ifeq(product(x, x, multiply(x, x)), true, ifeq(sum(x, inverse(x), multiplicative_identity), true, product(x, multiplicative_identity, multiply(x, x)), true), true), true), true, multiply(x, x), x))
% 2.14/0.64 = { by axiom 2 (multiplicative_inverse2) R->L }
% 2.14/0.64 product(x, x, ifeq2(ifeq(product(x, inverse(x), additive_identity), true, ifeq(product(x, x, multiply(x, x)), true, ifeq(sum(x, inverse(x), multiplicative_identity), true, product(x, multiplicative_identity, multiply(x, x)), true), true), true), true, multiply(x, x), x))
% 2.14/0.64 = { by axiom 5 (ifeq_axiom) R->L }
% 2.14/0.64 product(x, x, ifeq2(ifeq(product(x, inverse(x), additive_identity), true, ifeq(product(x, x, multiply(x, x)), true, ifeq(true, true, ifeq(sum(x, inverse(x), multiplicative_identity), true, product(x, multiplicative_identity, multiply(x, x)), true), true), true), true), true, multiply(x, x), x))
% 2.14/0.64 = { by axiom 3 (additive_identity2) R->L }
% 2.14/0.64 product(x, x, ifeq2(ifeq(product(x, inverse(x), additive_identity), true, ifeq(product(x, x, multiply(x, x)), true, ifeq(sum(multiply(x, x), additive_identity, multiply(x, x)), true, ifeq(sum(x, inverse(x), multiplicative_identity), true, product(x, multiplicative_identity, multiply(x, x)), true), true), true), true), true, multiply(x, x), x))
% 2.14/0.64 = { by axiom 9 (distributivity2) }
% 2.14/0.64 product(x, x, ifeq2(true, true, multiply(x, x), x))
% 2.14/0.64 = { by axiom 6 (ifeq_axiom) }
% 2.14/0.64 product(x, x, multiply(x, x))
% 2.14/0.64 = { by axiom 7 (closure_of_multiplication) }
% 2.14/0.64 true
% 2.14/0.64 % SZS output end Proof
% 2.14/0.64
% 2.14/0.64 RESULT: Unsatisfiable (the axioms are contradictory).
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