%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : CAT010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 09:36:23 AM UTC 2026
% Result : Unsatisfiable 0.43s 0.31s
% Output : Proof 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n007.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 21:11:10 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.43/0.31 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.43/0.31
% 0.43/0.31 % SZS status Unsatisfiable
% 0.43/0.31
% 0.43/0.33 % SZS output start Proof
% 0.43/0.33 Axiom 1 (codomain_is_an_identity_map): identity_map(codomain(X)) = true.
% 0.43/0.33 Axiom 2 (ba_defined): defined(b, a) = true.
% 0.43/0.33 Axiom 3 (mapping_from_codomain_of_x_to_x): defined(codomain(X), X) = true.
% 0.43/0.33 Axiom 4 (product_on_codomain): product(codomain(X), X, X) = true.
% 0.43/0.33 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.43/0.33 Axiom 6 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.43/0.33 Axiom 7 (closure_of_composition): ifeq(defined(X, Y), true, product(X, Y, compose(X, Y)), true) = true.
% 0.43/0.33 Axiom 8 (identity1): ifeq(identity_map(X), true, ifeq(defined(X, Y), true, product(X, Y, Y), true), true) = true.
% 0.43/0.33 Axiom 9 (identity2): ifeq(identity_map(X), true, ifeq(defined(Y, X), true, product(Y, X, Y), true), true) = true.
% 0.43/0.33 Axiom 10 (composition_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 0.43/0.34 Axiom 11 (category_theory_axiom3): ifeq(product(X, Y, Z), true, ifeq(defined(W, Z), true, defined(W, X), true), true) = true.
% 0.43/0.34
% 0.43/0.34 Goal 1 (prove_codomain_of_ba_equals_codomain_of_b): codomain(compose(b, a)) = codomain(b).
% 0.43/0.34 Proof:
% 0.43/0.34 codomain(compose(b, a))
% 0.43/0.34 = { by axiom 10 (composition_is_well_defined) R->L }
% 0.43/0.34 ifeq2(product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true, ifeq2(product(codomain(compose(b, a)), codomain(b), codomain(b)), true, codomain(b), codomain(compose(b, a))), codomain(compose(b, a)))
% 0.43/0.34 = { by axiom 5 (ifeq_axiom) R->L }
% 0.43/0.34 ifeq2(product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true, ifeq2(ifeq(true, true, product(codomain(compose(b, a)), codomain(b), codomain(b)), true), true, codomain(b), codomain(compose(b, a))), codomain(compose(b, a)))
% 0.43/0.34 = { by axiom 5 (ifeq_axiom) R->L }
% 0.43/0.34 ifeq2(product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true, ifeq2(ifeq(true, true, ifeq(true, true, product(codomain(compose(b, a)), codomain(b), codomain(b)), true), true), true, codomain(b), codomain(compose(b, a))), codomain(compose(b, a)))
% 0.43/0.34 = { by axiom 1 (codomain_is_an_identity_map) R->L }
% 0.43/0.34 ifeq2(product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true, ifeq2(ifeq(identity_map(codomain(compose(b, a))), true, ifeq(true, true, product(codomain(compose(b, a)), codomain(b), codomain(b)), true), true), true, codomain(b), codomain(compose(b, a))), codomain(compose(b, a)))
% 0.43/0.34 = { by axiom 11 (category_theory_axiom3) R->L }
% 0.43/0.34 ifeq2(product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true, ifeq2(ifeq(identity_map(codomain(compose(b, a))), true, ifeq(ifeq(product(codomain(b), b, b), true, ifeq(defined(codomain(compose(b, a)), b), true, defined(codomain(compose(b, a)), codomain(b)), true), true), true, product(codomain(compose(b, a)), codomain(b), codomain(b)), true), true), true, codomain(b), codomain(compose(b, a))), codomain(compose(b, a)))
% 0.43/0.34 = { by axiom 4 (product_on_codomain) }
% 0.43/0.34 ifeq2(product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true, ifeq2(ifeq(identity_map(codomain(compose(b, a))), true, ifeq(ifeq(true, true, ifeq(defined(codomain(compose(b, a)), b), true, defined(codomain(compose(b, a)), codomain(b)), true), true), true, product(codomain(compose(b, a)), codomain(b), codomain(b)), true), true), true, codomain(b), codomain(compose(b, a))), codomain(compose(b, a)))
% 0.43/0.34 = { by axiom 5 (ifeq_axiom) }
% 0.43/0.34 ifeq2(product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true, ifeq2(ifeq(identity_map(codomain(compose(b, a))), true, ifeq(ifeq(defined(codomain(compose(b, a)), b), true, defined(codomain(compose(b, a)), codomain(b)), true), true, product(codomain(compose(b, a)), codomain(b), codomain(b)), true), true), true, codomain(b), codomain(compose(b, a))), codomain(compose(b, a)))
% 0.43/0.34 = { by axiom 5 (ifeq_axiom) R->L }
% 0.43/0.34 ifeq2(product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true, ifeq2(ifeq(identity_map(codomain(compose(b, a))), true, ifeq(ifeq(ifeq(true, true, defined(codomain(compose(b, a)), b), true), true, defined(codomain(compose(b, a)), codomain(b)), true), true, product(codomain(compose(b, a)), codomain(b), codomain(b)), true), true), true, codomain(b), codomain(compose(b, a))), codomain(compose(b, a)))
% 0.43/0.34 = { by axiom 3 (mapping_from_codomain_of_x_to_x) R->L }
% 0.43/0.34 ifeq2(product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true, ifeq2(ifeq(identity_map(codomain(compose(b, a))), true, ifeq(ifeq(ifeq(defined(codomain(compose(b, a)), compose(b, a)), true, defined(codomain(compose(b, a)), b), true), true, defined(codomain(compose(b, a)), codomain(b)), true), true, product(codomain(compose(b, a)), codomain(b), codomain(b)), true), true), true, codomain(b), codomain(compose(b, a))), codomain(compose(b, a)))
% 0.43/0.34 = { by axiom 5 (ifeq_axiom) R->L }
% 0.43/0.34 ifeq2(product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true, ifeq2(ifeq(identity_map(codomain(compose(b, a))), true, ifeq(ifeq(ifeq(true, true, ifeq(defined(codomain(compose(b, a)), compose(b, a)), true, defined(codomain(compose(b, a)), b), true), true), true, defined(codomain(compose(b, a)), codomain(b)), true), true, product(codomain(compose(b, a)), codomain(b), codomain(b)), true), true), true, codomain(b), codomain(compose(b, a))), codomain(compose(b, a)))
% 0.43/0.34 = { by axiom 7 (closure_of_composition) R->L }
% 0.43/0.34 ifeq2(product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true, ifeq2(ifeq(identity_map(codomain(compose(b, a))), true, ifeq(ifeq(ifeq(ifeq(defined(b, a), true, product(b, a, compose(b, a)), true), true, ifeq(defined(codomain(compose(b, a)), compose(b, a)), true, defined(codomain(compose(b, a)), b), true), true), true, defined(codomain(compose(b, a)), codomain(b)), true), true, product(codomain(compose(b, a)), codomain(b), codomain(b)), true), true), true, codomain(b), codomain(compose(b, a))), codomain(compose(b, a)))
% 0.43/0.34 = { by axiom 2 (ba_defined) }
% 0.43/0.34 ifeq2(product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true, ifeq2(ifeq(identity_map(codomain(compose(b, a))), true, ifeq(ifeq(ifeq(ifeq(true, true, product(b, a, compose(b, a)), true), true, ifeq(defined(codomain(compose(b, a)), compose(b, a)), true, defined(codomain(compose(b, a)), b), true), true), true, defined(codomain(compose(b, a)), codomain(b)), true), true, product(codomain(compose(b, a)), codomain(b), codomain(b)), true), true), true, codomain(b), codomain(compose(b, a))), codomain(compose(b, a)))
% 0.43/0.34 = { by axiom 5 (ifeq_axiom) }
% 0.43/0.35 ifeq2(product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true, ifeq2(ifeq(identity_map(codomain(compose(b, a))), true, ifeq(ifeq(ifeq(product(b, a, compose(b, a)), true, ifeq(defined(codomain(compose(b, a)), compose(b, a)), true, defined(codomain(compose(b, a)), b), true), true), true, defined(codomain(compose(b, a)), codomain(b)), true), true, product(codomain(compose(b, a)), codomain(b), codomain(b)), true), true), true, codomain(b), codomain(compose(b, a))), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 11 (category_theory_axiom3) }
% 0.43/0.35 ifeq2(product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true, ifeq2(ifeq(identity_map(codomain(compose(b, a))), true, ifeq(ifeq(true, true, defined(codomain(compose(b, a)), codomain(b)), true), true, product(codomain(compose(b, a)), codomain(b), codomain(b)), true), true), true, codomain(b), codomain(compose(b, a))), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 5 (ifeq_axiom) }
% 0.43/0.35 ifeq2(product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true, ifeq2(ifeq(identity_map(codomain(compose(b, a))), true, ifeq(defined(codomain(compose(b, a)), codomain(b)), true, product(codomain(compose(b, a)), codomain(b), codomain(b)), true), true), true, codomain(b), codomain(compose(b, a))), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 8 (identity1) }
% 0.43/0.35 ifeq2(product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true, ifeq2(true, true, codomain(b), codomain(compose(b, a))), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 6 (ifeq_axiom) }
% 0.43/0.35 ifeq2(product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true, codomain(b), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 5 (ifeq_axiom) R->L }
% 0.43/0.35 ifeq2(ifeq(true, true, product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true), true, codomain(b), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 5 (ifeq_axiom) R->L }
% 0.43/0.35 ifeq2(ifeq(true, true, ifeq(true, true, product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true), true), true, codomain(b), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 1 (codomain_is_an_identity_map) R->L }
% 0.43/0.35 ifeq2(ifeq(identity_map(codomain(b)), true, ifeq(true, true, product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true), true), true, codomain(b), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 11 (category_theory_axiom3) R->L }
% 0.43/0.35 ifeq2(ifeq(identity_map(codomain(b)), true, ifeq(ifeq(product(codomain(b), b, b), true, ifeq(defined(codomain(compose(b, a)), b), true, defined(codomain(compose(b, a)), codomain(b)), true), true), true, product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true), true), true, codomain(b), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 4 (product_on_codomain) }
% 0.43/0.35 ifeq2(ifeq(identity_map(codomain(b)), true, ifeq(ifeq(true, true, ifeq(defined(codomain(compose(b, a)), b), true, defined(codomain(compose(b, a)), codomain(b)), true), true), true, product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true), true), true, codomain(b), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 5 (ifeq_axiom) }
% 0.43/0.35 ifeq2(ifeq(identity_map(codomain(b)), true, ifeq(ifeq(defined(codomain(compose(b, a)), b), true, defined(codomain(compose(b, a)), codomain(b)), true), true, product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true), true), true, codomain(b), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 5 (ifeq_axiom) R->L }
% 0.43/0.35 ifeq2(ifeq(identity_map(codomain(b)), true, ifeq(ifeq(ifeq(true, true, defined(codomain(compose(b, a)), b), true), true, defined(codomain(compose(b, a)), codomain(b)), true), true, product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true), true), true, codomain(b), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 3 (mapping_from_codomain_of_x_to_x) R->L }
% 0.43/0.35 ifeq2(ifeq(identity_map(codomain(b)), true, ifeq(ifeq(ifeq(defined(codomain(compose(b, a)), compose(b, a)), true, defined(codomain(compose(b, a)), b), true), true, defined(codomain(compose(b, a)), codomain(b)), true), true, product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true), true), true, codomain(b), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 5 (ifeq_axiom) R->L }
% 0.43/0.35 ifeq2(ifeq(identity_map(codomain(b)), true, ifeq(ifeq(ifeq(true, true, ifeq(defined(codomain(compose(b, a)), compose(b, a)), true, defined(codomain(compose(b, a)), b), true), true), true, defined(codomain(compose(b, a)), codomain(b)), true), true, product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true), true), true, codomain(b), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 7 (closure_of_composition) R->L }
% 0.43/0.35 ifeq2(ifeq(identity_map(codomain(b)), true, ifeq(ifeq(ifeq(ifeq(defined(b, a), true, product(b, a, compose(b, a)), true), true, ifeq(defined(codomain(compose(b, a)), compose(b, a)), true, defined(codomain(compose(b, a)), b), true), true), true, defined(codomain(compose(b, a)), codomain(b)), true), true, product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true), true), true, codomain(b), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 2 (ba_defined) }
% 0.43/0.35 ifeq2(ifeq(identity_map(codomain(b)), true, ifeq(ifeq(ifeq(ifeq(true, true, product(b, a, compose(b, a)), true), true, ifeq(defined(codomain(compose(b, a)), compose(b, a)), true, defined(codomain(compose(b, a)), b), true), true), true, defined(codomain(compose(b, a)), codomain(b)), true), true, product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true), true), true, codomain(b), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 5 (ifeq_axiom) }
% 0.43/0.35 ifeq2(ifeq(identity_map(codomain(b)), true, ifeq(ifeq(ifeq(product(b, a, compose(b, a)), true, ifeq(defined(codomain(compose(b, a)), compose(b, a)), true, defined(codomain(compose(b, a)), b), true), true), true, defined(codomain(compose(b, a)), codomain(b)), true), true, product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true), true), true, codomain(b), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 11 (category_theory_axiom3) }
% 0.43/0.35 ifeq2(ifeq(identity_map(codomain(b)), true, ifeq(ifeq(true, true, defined(codomain(compose(b, a)), codomain(b)), true), true, product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true), true), true, codomain(b), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 5 (ifeq_axiom) }
% 0.43/0.35 ifeq2(ifeq(identity_map(codomain(b)), true, ifeq(defined(codomain(compose(b, a)), codomain(b)), true, product(codomain(compose(b, a)), codomain(b), codomain(compose(b, a))), true), true), true, codomain(b), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 9 (identity2) }
% 0.43/0.35 ifeq2(true, true, codomain(b), codomain(compose(b, a)))
% 0.43/0.35 = { by axiom 6 (ifeq_axiom) }
% 0.43/0.35 codomain(b)
% 0.43/0.35 % SZS output end Proof
% 0.43/0.35
% 0.43/0.35 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------