%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : CAT004-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 09:36:21 AM UTC 2026
% Result : Unsatisfiable 2.18s 0.69s
% Output : Proof 2.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.27 % Computer : n017.cluster.edu
% 0.12/0.27 % Model : x86_64 x86_64
% 0.12/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.27 % Memory : 8046.5625MB
% 0.12/0.27 % OS : Linux 6.8.0-71-generic
% 0.12/0.27 % CPULimit : 300
% 0.12/0.27 % WCLimit : 300
% 0.12/0.27 % DateTime : Mon Sep 28 21:08:21 UTC 2026
% 0.12/0.27 % CPUTime :
% 0.12/0.27 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.18/0.69 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
% 2.18/0.69
% 2.18/0.69 % SZS status Unsatisfiable
% 2.18/0.69
% 2.67/0.71 % SZS output start Proof
% 2.67/0.71 Axiom 1 (codomain_of_a_equals_domain_of_b): codomain(a) = domain(b).
% 2.67/0.71 Axiom 2 (codomain_of_ab_equals_domain_of_h): codomain(compose(a, b)) = domain(h).
% 2.67/0.71 Axiom 3 (codomain_of_ab_equals_domain_of_g): codomain(compose(a, b)) = domain(g).
% 2.67/0.71 Axiom 4 (ab_h_equals_ab_g): compose(compose(a, b), h) = compose(compose(a, b), g).
% 2.67/0.71 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.67/0.71 Axiom 6 (codomain_domain1): ifeq(codomain(X), domain(Y), domain(compose(X, Y)), domain(X)) = domain(X).
% 2.67/0.71 Axiom 7 (codomain_domain2): ifeq(codomain(X), domain(Y), codomain(compose(X, Y)), codomain(Y)) = codomain(Y).
% 2.67/0.71 Axiom 8 (star_property): ifeq(codomain(X), domain(Y), ifeq(codomain(Z), domain(X), compose(Z, compose(X, Y)), compose(compose(Z, X), Y)), compose(compose(Z, X), Y)) = compose(compose(Z, X), Y).
% 2.67/0.71 Axiom 9 (epimorphism1): ifeq(codomain(a), domain(X), ifeq(codomain(a), domain(Y), ifeq(compose(a, X), Z, ifeq(compose(a, Y), Z, Y, X), X), X), X) = X.
% 2.67/0.71 Axiom 10 (epimorphism2): ifeq(codomain(b), domain(X), ifeq(codomain(b), domain(Y), ifeq(compose(b, X), Z, ifeq(compose(b, Y), Z, Y, X), X), X), X) = X.
% 2.67/0.71
% 2.67/0.71 Lemma 11: domain(g) = domain(h).
% 2.67/0.71 Proof:
% 2.67/0.71 domain(g)
% 2.67/0.71 = { by axiom 3 (codomain_of_ab_equals_domain_of_g) R->L }
% 2.67/0.71 codomain(compose(a, b))
% 2.67/0.71 = { by axiom 2 (codomain_of_ab_equals_domain_of_h) }
% 2.67/0.71 domain(h)
% 2.67/0.71
% 2.67/0.71 Lemma 12: codomain(b) = domain(h).
% 2.67/0.71 Proof:
% 2.67/0.71 codomain(b)
% 2.67/0.71 = { by axiom 7 (codomain_domain2) R->L }
% 2.67/0.71 ifeq(codomain(a), domain(b), codomain(compose(a, b)), codomain(b))
% 2.67/0.71 = { by axiom 2 (codomain_of_ab_equals_domain_of_h) }
% 2.67/0.71 ifeq(codomain(a), domain(b), domain(h), codomain(b))
% 2.67/0.71 = { by axiom 1 (codomain_of_a_equals_domain_of_b) }
% 2.67/0.71 ifeq(domain(b), domain(b), domain(h), codomain(b))
% 2.67/0.71 = { by axiom 5 (ifeq_axiom) }
% 2.67/0.71 domain(h)
% 2.67/0.71
% 2.67/0.71 Lemma 13: compose(compose(a, b), h) = compose(a, compose(b, g)).
% 2.67/0.71 Proof:
% 2.67/0.71 compose(compose(a, b), h)
% 2.67/0.71 = { by axiom 4 (ab_h_equals_ab_g) }
% 2.67/0.71 compose(compose(a, b), g)
% 2.67/0.71 = { by axiom 8 (star_property) R->L }
% 2.67/0.71 ifeq(codomain(b), domain(g), ifeq(codomain(a), domain(b), compose(a, compose(b, g)), compose(compose(a, b), g)), compose(compose(a, b), g))
% 2.67/0.71 = { by axiom 4 (ab_h_equals_ab_g) R->L }
% 2.67/0.71 ifeq(codomain(b), domain(g), ifeq(codomain(a), domain(b), compose(a, compose(b, g)), compose(compose(a, b), h)), compose(compose(a, b), g))
% 2.67/0.71 = { by lemma 12 }
% 2.67/0.71 ifeq(domain(h), domain(g), ifeq(codomain(a), domain(b), compose(a, compose(b, g)), compose(compose(a, b), h)), compose(compose(a, b), g))
% 2.67/0.71 = { by lemma 11 }
% 2.67/0.71 ifeq(domain(h), domain(h), ifeq(codomain(a), domain(b), compose(a, compose(b, g)), compose(compose(a, b), h)), compose(compose(a, b), g))
% 2.67/0.71 = { by axiom 5 (ifeq_axiom) }
% 2.67/0.71 ifeq(codomain(a), domain(b), compose(a, compose(b, g)), compose(compose(a, b), h))
% 2.67/0.71 = { by axiom 1 (codomain_of_a_equals_domain_of_b) }
% 2.67/0.71 ifeq(domain(b), domain(b), compose(a, compose(b, g)), compose(compose(a, b), h))
% 2.67/0.71 = { by axiom 5 (ifeq_axiom) }
% 2.67/0.71 compose(a, compose(b, g))
% 2.67/0.71
% 2.67/0.71 Lemma 14: ifeq(domain(h), domain(X), domain(compose(b, X)), domain(b)) = domain(b).
% 2.67/0.71 Proof:
% 2.67/0.71 ifeq(domain(h), domain(X), domain(compose(b, X)), domain(b))
% 2.67/0.71 = { by lemma 12 R->L }
% 2.67/0.71 ifeq(codomain(b), domain(X), domain(compose(b, X)), domain(b))
% 2.67/0.71 = { by axiom 6 (codomain_domain1) }
% 2.67/0.71 domain(b)
% 2.67/0.71
% 2.67/0.71 Goal 1 (prove_h_equals_g): h = g.
% 2.67/0.71 Proof:
% 2.67/0.71 h
% 2.67/0.71 = { by axiom 5 (ifeq_axiom) R->L }
% 2.67/0.71 ifeq(compose(b, h), compose(b, h), h, g)
% 2.67/0.71 = { by axiom 5 (ifeq_axiom) R->L }
% 2.67/0.71 ifeq(domain(h), domain(h), ifeq(compose(b, h), compose(b, h), h, g), g)
% 2.67/0.71 = { by lemma 11 R->L }
% 2.67/0.71 ifeq(domain(h), domain(g), ifeq(compose(b, h), compose(b, h), h, g), g)
% 2.67/0.71 = { by axiom 5 (ifeq_axiom) R->L }
% 2.67/0.71 ifeq(domain(h), domain(g), ifeq(compose(b, h), ifeq(compose(a, compose(b, h)), compose(a, compose(b, h)), compose(b, h), compose(b, g)), h, g), g)
% 2.67/0.71 = { by axiom 5 (ifeq_axiom) R->L }
% 2.67/0.71 ifeq(domain(h), domain(g), ifeq(compose(b, h), ifeq(domain(b), domain(b), ifeq(compose(a, compose(b, h)), compose(a, compose(b, h)), compose(b, h), compose(b, g)), compose(b, g)), h, g), g)
% 2.67/0.71 = { by lemma 14 R->L }
% 2.67/0.71 ifeq(domain(h), domain(g), ifeq(compose(b, h), ifeq(domain(b), ifeq(domain(h), domain(g), domain(compose(b, g)), domain(b)), ifeq(compose(a, compose(b, h)), compose(a, compose(b, h)), compose(b, h), compose(b, g)), compose(b, g)), h, g), g)
% 2.67/0.71 = { by lemma 11 }
% 2.67/0.71 ifeq(domain(h), domain(g), ifeq(compose(b, h), ifeq(domain(b), ifeq(domain(h), domain(h), domain(compose(b, g)), domain(b)), ifeq(compose(a, compose(b, h)), compose(a, compose(b, h)), compose(b, h), compose(b, g)), compose(b, g)), h, g), g)
% 2.67/0.71 = { by axiom 5 (ifeq_axiom) }
% 2.67/0.71 ifeq(domain(h), domain(g), ifeq(compose(b, h), ifeq(domain(b), domain(compose(b, g)), ifeq(compose(a, compose(b, h)), compose(a, compose(b, h)), compose(b, h), compose(b, g)), compose(b, g)), h, g), g)
% 2.67/0.71 = { by axiom 5 (ifeq_axiom) R->L }
% 2.67/0.71 ifeq(domain(h), domain(g), ifeq(compose(b, h), ifeq(domain(b), domain(compose(b, g)), ifeq(compose(a, compose(b, h)), ifeq(domain(b), domain(b), compose(a, compose(b, h)), compose(a, compose(b, g))), compose(b, h), compose(b, g)), compose(b, g)), h, g), g)
% 2.67/0.71 = { by axiom 1 (codomain_of_a_equals_domain_of_b) R->L }
% 2.67/0.71 ifeq(domain(h), domain(g), ifeq(compose(b, h), ifeq(domain(b), domain(compose(b, g)), ifeq(compose(a, compose(b, h)), ifeq(codomain(a), domain(b), compose(a, compose(b, h)), compose(a, compose(b, g))), compose(b, h), compose(b, g)), compose(b, g)), h, g), g)
% 2.67/0.71 = { by axiom 5 (ifeq_axiom) R->L }
% 2.67/0.71 ifeq(domain(h), domain(g), ifeq(compose(b, h), ifeq(domain(b), domain(compose(b, g)), ifeq(compose(a, compose(b, h)), ifeq(domain(h), domain(h), ifeq(codomain(a), domain(b), compose(a, compose(b, h)), compose(a, compose(b, g))), compose(compose(a, b), h)), compose(b, h), compose(b, g)), compose(b, g)), h, g), g)
% 2.67/0.71 = { by lemma 12 R->L }
% 2.67/0.71 ifeq(domain(h), domain(g), ifeq(compose(b, h), ifeq(domain(b), domain(compose(b, g)), ifeq(compose(a, compose(b, h)), ifeq(codomain(b), domain(h), ifeq(codomain(a), domain(b), compose(a, compose(b, h)), compose(a, compose(b, g))), compose(compose(a, b), h)), compose(b, h), compose(b, g)), compose(b, g)), h, g), g)
% 2.67/0.71 = { by lemma 13 R->L }
% 2.67/0.71 ifeq(domain(h), domain(g), ifeq(compose(b, h), ifeq(domain(b), domain(compose(b, g)), ifeq(compose(a, compose(b, h)), ifeq(codomain(b), domain(h), ifeq(codomain(a), domain(b), compose(a, compose(b, h)), compose(compose(a, b), h)), compose(compose(a, b), h)), compose(b, h), compose(b, g)), compose(b, g)), h, g), g)
% 2.67/0.71 = { by axiom 8 (star_property) }
% 2.67/0.71 ifeq(domain(h), domain(g), ifeq(compose(b, h), ifeq(domain(b), domain(compose(b, g)), ifeq(compose(a, compose(b, h)), compose(compose(a, b), h), compose(b, h), compose(b, g)), compose(b, g)), h, g), g)
% 2.67/0.71 = { by lemma 13 }
% 2.67/0.71 ifeq(domain(h), domain(g), ifeq(compose(b, h), ifeq(domain(b), domain(compose(b, g)), ifeq(compose(a, compose(b, h)), compose(a, compose(b, g)), compose(b, h), compose(b, g)), compose(b, g)), h, g), g)
% 2.67/0.71 = { by axiom 5 (ifeq_axiom) R->L }
% 2.67/0.71 ifeq(domain(h), domain(g), ifeq(compose(b, h), ifeq(domain(b), domain(compose(b, g)), ifeq(domain(b), domain(b), ifeq(compose(a, compose(b, h)), compose(a, compose(b, g)), compose(b, h), compose(b, g)), compose(b, g)), compose(b, g)), h, g), g)
% 2.67/0.71 = { by lemma 14 R->L }
% 2.67/0.72 ifeq(domain(h), domain(g), ifeq(compose(b, h), ifeq(domain(b), domain(compose(b, g)), ifeq(domain(b), ifeq(domain(h), domain(h), domain(compose(b, h)), domain(b)), ifeq(compose(a, compose(b, h)), compose(a, compose(b, g)), compose(b, h), compose(b, g)), compose(b, g)), compose(b, g)), h, g), g)
% 2.67/0.72 = { by axiom 5 (ifeq_axiom) }
% 2.67/0.72 ifeq(domain(h), domain(g), ifeq(compose(b, h), ifeq(domain(b), domain(compose(b, g)), ifeq(domain(b), domain(compose(b, h)), ifeq(compose(a, compose(b, h)), compose(a, compose(b, g)), compose(b, h), compose(b, g)), compose(b, g)), compose(b, g)), h, g), g)
% 2.67/0.72 = { by axiom 5 (ifeq_axiom) R->L }
% 2.67/0.72 ifeq(domain(h), domain(g), ifeq(compose(b, h), ifeq(domain(b), domain(compose(b, g)), ifeq(domain(b), domain(compose(b, h)), ifeq(compose(a, compose(b, g)), compose(a, compose(b, g)), ifeq(compose(a, compose(b, h)), compose(a, compose(b, g)), compose(b, h), compose(b, g)), compose(b, g)), compose(b, g)), compose(b, g)), h, g), g)
% 2.67/0.72 = { by axiom 1 (codomain_of_a_equals_domain_of_b) R->L }
% 2.67/0.72 ifeq(domain(h), domain(g), ifeq(compose(b, h), ifeq(codomain(a), domain(compose(b, g)), ifeq(domain(b), domain(compose(b, h)), ifeq(compose(a, compose(b, g)), compose(a, compose(b, g)), ifeq(compose(a, compose(b, h)), compose(a, compose(b, g)), compose(b, h), compose(b, g)), compose(b, g)), compose(b, g)), compose(b, g)), h, g), g)
% 2.67/0.72 = { by axiom 1 (codomain_of_a_equals_domain_of_b) R->L }
% 2.67/0.72 ifeq(domain(h), domain(g), ifeq(compose(b, h), ifeq(codomain(a), domain(compose(b, g)), ifeq(codomain(a), domain(compose(b, h)), ifeq(compose(a, compose(b, g)), compose(a, compose(b, g)), ifeq(compose(a, compose(b, h)), compose(a, compose(b, g)), compose(b, h), compose(b, g)), compose(b, g)), compose(b, g)), compose(b, g)), h, g), g)
% 2.67/0.72 = { by axiom 9 (epimorphism1) }
% 2.67/0.72 ifeq(domain(h), domain(g), ifeq(compose(b, h), compose(b, g), h, g), g)
% 2.67/0.72 = { by axiom 5 (ifeq_axiom) R->L }
% 2.67/0.72 ifeq(domain(h), domain(g), ifeq(domain(h), domain(h), ifeq(compose(b, h), compose(b, g), h, g), g), g)
% 2.67/0.72 = { by lemma 12 R->L }
% 2.67/0.72 ifeq(codomain(b), domain(g), ifeq(domain(h), domain(h), ifeq(compose(b, h), compose(b, g), h, g), g), g)
% 2.67/0.72 = { by lemma 12 R->L }
% 2.67/0.72 ifeq(codomain(b), domain(g), ifeq(codomain(b), domain(h), ifeq(compose(b, h), compose(b, g), h, g), g), g)
% 2.67/0.72 = { by axiom 5 (ifeq_axiom) R->L }
% 2.67/0.72 ifeq(codomain(b), domain(g), ifeq(codomain(b), domain(h), ifeq(compose(b, g), compose(b, g), ifeq(compose(b, h), compose(b, g), h, g), g), g), g)
% 2.67/0.72 = { by axiom 10 (epimorphism2) }
% 2.67/0.72 g
% 2.67/0.72 % SZS output end Proof
% 2.67/0.72
% 2.67/0.72 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------