%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : CAT003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 2.15s 0.54s
% Output : Proof 2.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.17 % Computer : n017.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Mon Sep 28 21:08:21 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.15/0.54 Command-line arguments: --flatten --complete-subsets
% 2.15/0.54
% 2.15/0.54 % SZS status Unsatisfiable
% 2.15/0.54
% 2.15/0.54 % SZS output start Proof
% 2.15/0.54 Axiom 1 (codomain_of_a_equals_domain_of_b): codomain(a) = domain(b).
% 2.15/0.54 Axiom 2 (codomain_of_b_equals_domain_of_h): codomain(b) = domain(h).
% 2.15/0.54 Axiom 3 (codomain_of_b_equals_domain_of_g): codomain(b) = domain(g).
% 2.15/0.54 Axiom 4 (bh_equals_bg): compose(b, h) = compose(b, g).
% 2.15/0.54 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.15/0.54 Axiom 6 (codomain_domain2): ifeq(codomain(X), domain(Y), codomain(compose(X, Y)), codomain(Y)) = codomain(Y).
% 2.15/0.54 Axiom 7 (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).
% 2.15/0.54 Axiom 8 (endomorphism): ifeq(codomain(compose(a, b)), domain(X), ifeq(codomain(compose(a, b)), domain(Y), ifeq(compose(compose(a, b), X), Z, ifeq(compose(compose(a, b), Y), Z, Y, X), X), X), X) = X.
% 2.15/0.54
% 2.15/0.54 Lemma 9: codomain(compose(a, b)) = codomain(b).
% 2.15/0.54 Proof:
% 2.15/0.54 codomain(compose(a, b))
% 2.15/0.54 = { by axiom 5 (ifeq_axiom) R->L }
% 2.15/0.54 ifeq(codomain(a), codomain(a), codomain(compose(a, b)), codomain(b))
% 2.15/0.54 = { by axiom 1 (codomain_of_a_equals_domain_of_b) }
% 2.15/0.54 ifeq(codomain(a), domain(b), codomain(compose(a, b)), codomain(b))
% 2.15/0.54 = { by axiom 6 (codomain_domain2) }
% 2.15/0.54 codomain(b)
% 2.15/0.54
% 2.15/0.54 Lemma 10: ifeq(codomain(compose(a, b)), domain(X), compose(a, compose(b, X)), compose(compose(a, b), X)) = compose(compose(a, b), X).
% 2.15/0.54 Proof:
% 2.15/0.54 ifeq(codomain(compose(a, b)), domain(X), compose(a, compose(b, X)), compose(compose(a, b), X))
% 2.15/0.54 = { by axiom 5 (ifeq_axiom) R->L }
% 2.15/0.54 ifeq(codomain(compose(a, b)), domain(X), ifeq(codomain(a), codomain(a), compose(a, compose(b, X)), compose(compose(a, b), X)), compose(compose(a, b), X))
% 2.15/0.54 = { by axiom 1 (codomain_of_a_equals_domain_of_b) }
% 2.15/0.54 ifeq(codomain(compose(a, b)), domain(X), ifeq(codomain(a), domain(b), compose(a, compose(b, X)), compose(compose(a, b), X)), compose(compose(a, b), X))
% 2.15/0.54 = { by lemma 9 }
% 2.15/0.54 ifeq(codomain(b), domain(X), ifeq(codomain(a), domain(b), compose(a, compose(b, X)), compose(compose(a, b), X)), compose(compose(a, b), X))
% 2.15/0.54 = { by axiom 7 (star_property) }
% 2.15/0.54 compose(compose(a, b), X)
% 2.15/0.54
% 2.15/0.54 Goal 1 (prove_g_equals_h): g = h.
% 2.15/0.54 Proof:
% 2.15/0.54 g
% 2.15/0.54 = { by axiom 8 (endomorphism) R->L }
% 2.15/0.54 ifeq(codomain(compose(a, b)), domain(g), ifeq(codomain(compose(a, b)), domain(h), ifeq(compose(compose(a, b), g), compose(compose(a, b), g), ifeq(compose(compose(a, b), h), compose(compose(a, b), g), h, g), g), g), g)
% 2.15/0.54 = { by axiom 5 (ifeq_axiom) }
% 2.15/0.54 ifeq(codomain(compose(a, b)), domain(g), ifeq(codomain(compose(a, b)), domain(h), ifeq(compose(compose(a, b), h), compose(compose(a, b), g), h, g), g), g)
% 2.15/0.54 = { by axiom 2 (codomain_of_b_equals_domain_of_h) R->L }
% 2.15/0.54 ifeq(codomain(compose(a, b)), domain(g), ifeq(codomain(compose(a, b)), codomain(b), ifeq(compose(compose(a, b), h), compose(compose(a, b), g), h, g), g), g)
% 2.15/0.54 = { by lemma 9 R->L }
% 2.15/0.54 ifeq(codomain(compose(a, b)), domain(g), ifeq(codomain(compose(a, b)), codomain(compose(a, b)), ifeq(compose(compose(a, b), h), compose(compose(a, b), g), h, g), g), g)
% 2.15/0.54 = { by axiom 5 (ifeq_axiom) }
% 2.15/0.54 ifeq(codomain(compose(a, b)), domain(g), ifeq(compose(compose(a, b), h), compose(compose(a, b), g), h, g), g)
% 2.15/0.54 = { by axiom 3 (codomain_of_b_equals_domain_of_g) R->L }
% 2.15/0.54 ifeq(codomain(compose(a, b)), codomain(b), ifeq(compose(compose(a, b), h), compose(compose(a, b), g), h, g), g)
% 2.15/0.54 = { by lemma 9 R->L }
% 2.15/0.54 ifeq(codomain(compose(a, b)), codomain(compose(a, b)), ifeq(compose(compose(a, b), h), compose(compose(a, b), g), h, g), g)
% 2.15/0.55 = { by axiom 5 (ifeq_axiom) }
% 2.15/0.55 ifeq(compose(compose(a, b), h), compose(compose(a, b), g), h, g)
% 2.15/0.55 = { by lemma 10 R->L }
% 2.15/0.55 ifeq(compose(compose(a, b), h), ifeq(codomain(compose(a, b)), domain(g), compose(a, compose(b, g)), compose(compose(a, b), g)), h, g)
% 2.15/0.55 = { by axiom 3 (codomain_of_b_equals_domain_of_g) R->L }
% 2.15/0.55 ifeq(compose(compose(a, b), h), ifeq(codomain(compose(a, b)), codomain(b), compose(a, compose(b, g)), compose(compose(a, b), g)), h, g)
% 2.15/0.55 = { by lemma 9 R->L }
% 2.15/0.55 ifeq(compose(compose(a, b), h), ifeq(codomain(compose(a, b)), codomain(compose(a, b)), compose(a, compose(b, g)), compose(compose(a, b), g)), h, g)
% 2.15/0.55 = { by axiom 5 (ifeq_axiom) }
% 2.15/0.55 ifeq(compose(compose(a, b), h), compose(a, compose(b, g)), h, g)
% 2.15/0.55 = { by axiom 4 (bh_equals_bg) R->L }
% 2.15/0.55 ifeq(compose(compose(a, b), h), compose(a, compose(b, h)), h, g)
% 2.15/0.55 = { by axiom 5 (ifeq_axiom) R->L }
% 2.15/0.55 ifeq(compose(compose(a, b), h), ifeq(codomain(compose(a, b)), codomain(compose(a, b)), compose(a, compose(b, h)), compose(compose(a, b), h)), h, g)
% 2.15/0.55 = { by lemma 9 }
% 2.15/0.55 ifeq(compose(compose(a, b), h), ifeq(codomain(compose(a, b)), codomain(b), compose(a, compose(b, h)), compose(compose(a, b), h)), h, g)
% 2.15/0.55 = { by axiom 2 (codomain_of_b_equals_domain_of_h) }
% 2.15/0.55 ifeq(compose(compose(a, b), h), ifeq(codomain(compose(a, b)), domain(h), compose(a, compose(b, h)), compose(compose(a, b), h)), h, g)
% 2.15/0.55 = { by lemma 10 }
% 2.15/0.55 ifeq(compose(compose(a, b), h), compose(compose(a, b), h), h, g)
% 2.15/0.55 = { by axiom 5 (ifeq_axiom) }
% 2.15/0.55 h
% 2.15/0.55 % SZS output end Proof
% 2.15/0.55
% 2.15/0.55 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------