%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 09:35:21 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.22s
% Output : Proof 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : BOO006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Mon Sep 28 21:03:03 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.22 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
% 0.07/0.22
% 0.07/0.22 % SZS status Unsatisfiable
% 0.07/0.22
% 0.07/0.23 % SZS output start Proof
% 0.07/0.23 Axiom 1 (multiplicative_inverse2): product(X, inverse(X), additive_identity) = true.
% 0.07/0.23 Axiom 2 (additive_identity2): sum(X, additive_identity, X) = true.
% 0.07/0.23 Axiom 3 (additive_identity1): sum(additive_identity, X, X) = true.
% 0.07/0.23 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.07/0.23 Axiom 5 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.07/0.23 Axiom 6 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 0.07/0.23 Axiom 7 (multiplication_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 0.07/0.23 Axiom 8 (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.
% 0.07/0.23
% 0.07/0.23 Goal 1 (prove_equations): product(x, additive_identity, additive_identity) = true.
% 0.07/0.23 Proof:
% 0.07/0.23 product(x, additive_identity, additive_identity)
% 0.07/0.23 = { by axiom 5 (ifeq_axiom) R->L }
% 0.07/0.23 product(x, additive_identity, ifeq2(true, true, additive_identity, multiply(x, additive_identity)))
% 0.07/0.23 = { by axiom 8 (distributivity2) R->L }
% 0.07/0.23 product(x, additive_identity, 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)))
% 0.07/0.23 = { by axiom 2 (additive_identity2) }
% 0.07/0.23 product(x, additive_identity, 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)))
% 0.07/0.23 = { by axiom 4 (ifeq_axiom) }
% 0.07/0.23 product(x, additive_identity, 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)))
% 0.07/0.23 = { by axiom 3 (additive_identity1) }
% 0.07/0.23 product(x, additive_identity, 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)))
% 0.07/0.23 = { by axiom 4 (ifeq_axiom) }
% 0.07/0.23 product(x, additive_identity, 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)))
% 0.07/0.23 = { by axiom 1 (multiplicative_inverse2) }
% 0.07/0.23 product(x, additive_identity, 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)))
% 0.07/0.23 = { by axiom 4 (ifeq_axiom) }
% 0.07/0.23 product(x, additive_identity, 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)))
% 0.07/0.23 = { by axiom 6 (closure_of_multiplication) }
% 0.07/0.23 product(x, additive_identity, ifeq2(ifeq(true, true, product(x, inverse(x), multiply(x, additive_identity)), true), true, additive_identity, multiply(x, additive_identity)))
% 0.07/0.23 = { by axiom 4 (ifeq_axiom) }
% 0.07/0.23 product(x, additive_identity, ifeq2(product(x, inverse(x), multiply(x, additive_identity)), true, additive_identity, multiply(x, additive_identity)))
% 0.07/0.23 = { by axiom 5 (ifeq_axiom) R->L }
% 0.07/0.23 product(x, additive_identity, ifeq2(product(x, inverse(x), multiply(x, additive_identity)), true, ifeq2(true, true, additive_identity, multiply(x, additive_identity)), multiply(x, additive_identity)))
% 0.07/0.23 = { by axiom 1 (multiplicative_inverse2) R->L }
% 0.07/0.23 product(x, additive_identity, 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)))
% 0.07/0.23 = { by axiom 7 (multiplication_is_well_defined) }
% 0.07/0.23 product(x, additive_identity, multiply(x, additive_identity))
% 0.07/0.23 = { by axiom 6 (closure_of_multiplication) }
% 0.07/0.23 true
% 0.07/0.23 % SZS output end Proof
% 0.07/0.23
% 0.07/0.23 RESULT: Unsatisfiable (the axioms are contradictory).
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