%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP043-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 10:09:08 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.45s
% Output : Proof 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP043-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n014.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 09:16:01 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.45 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
% 0.09/0.45
% 0.09/0.45 % SZS status Unsatisfiable
% 0.09/0.45
% 0.09/0.45 % SZS output start Proof
% 0.09/0.45 Axiom 1 (a_equals_b): equalish(a, b) = true.
% 0.09/0.45 Axiom 2 (b_equals_c): equalish(b, c) = true.
% 0.09/0.45 Axiom 3 (left_identity): product(identity, X, X) = true.
% 0.09/0.45 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.09/0.45 Axiom 5 (product_substitution3): ifeq(equalish(X, Y), true, ifeq(product(Z, W, X), true, product(Z, W, Y), true), true) = true.
% 0.09/0.45 Axiom 6 (total_function2): ifeq(product(X, Y, Z), true, ifeq(product(X, Y, W), true, equalish(W, Z), true), true) = true.
% 0.09/0.45
% 0.09/0.45 Goal 1 (prove_transitivity): equalish(a, c) = true.
% 0.09/0.45 Proof:
% 0.09/0.45 equalish(a, c)
% 0.09/0.45 = { by axiom 4 (ifeq_axiom) R->L }
% 0.09/0.45 ifeq(true, true, equalish(a, c), true)
% 0.09/0.45 = { by axiom 5 (product_substitution3) R->L }
% 0.09/0.45 ifeq(ifeq(equalish(b, c), true, ifeq(product(identity, a, b), true, product(identity, a, c), true), true), true, equalish(a, c), true)
% 0.09/0.45 = { by axiom 2 (b_equals_c) }
% 0.09/0.45 ifeq(ifeq(true, true, ifeq(product(identity, a, b), true, product(identity, a, c), true), true), true, equalish(a, c), true)
% 0.09/0.45 = { by axiom 4 (ifeq_axiom) }
% 0.09/0.45 ifeq(ifeq(product(identity, a, b), true, product(identity, a, c), true), true, equalish(a, c), true)
% 0.09/0.45 = { by axiom 4 (ifeq_axiom) R->L }
% 0.09/0.45 ifeq(ifeq(ifeq(true, true, product(identity, a, b), true), true, product(identity, a, c), true), true, equalish(a, c), true)
% 0.09/0.45 = { by axiom 1 (a_equals_b) R->L }
% 0.09/0.45 ifeq(ifeq(ifeq(equalish(a, b), true, product(identity, a, b), true), true, product(identity, a, c), true), true, equalish(a, c), true)
% 0.09/0.45 = { by axiom 4 (ifeq_axiom) R->L }
% 0.09/0.45 ifeq(ifeq(ifeq(equalish(a, b), true, ifeq(true, true, product(identity, a, b), true), true), true, product(identity, a, c), true), true, equalish(a, c), true)
% 0.09/0.45 = { by axiom 3 (left_identity) R->L }
% 0.09/0.45 ifeq(ifeq(ifeq(equalish(a, b), true, ifeq(product(identity, a, a), true, product(identity, a, b), true), true), true, product(identity, a, c), true), true, equalish(a, c), true)
% 0.09/0.45 = { by axiom 5 (product_substitution3) }
% 0.09/0.45 ifeq(ifeq(true, true, product(identity, a, c), true), true, equalish(a, c), true)
% 0.09/0.45 = { by axiom 4 (ifeq_axiom) }
% 0.09/0.45 ifeq(product(identity, a, c), true, equalish(a, c), true)
% 0.09/0.45 = { by axiom 4 (ifeq_axiom) R->L }
% 0.09/0.45 ifeq(product(identity, a, c), true, ifeq(true, true, equalish(a, c), true), true)
% 0.09/0.45 = { by axiom 3 (left_identity) R->L }
% 0.09/0.45 ifeq(product(identity, a, c), true, ifeq(product(identity, a, a), true, equalish(a, c), true), true)
% 0.09/0.45 = { by axiom 6 (total_function2) }
% 0.09/0.45 true
% 0.09/0.45 % SZS output end Proof
% 0.09/0.45
% 0.09/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
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