%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : CAT018-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 09:36:25 AM UTC 2026
% Result : Unsatisfiable 0.51s 0.33s
% Output : Proof 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT018-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.16 % Computer : n016.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Mon Sep 28 21:18:33 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.51/0.33 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
% 0.51/0.33
% 0.51/0.33 % SZS status Unsatisfiable
% 0.51/0.33
% 0.51/0.34 % SZS output start Proof
% 0.51/0.34 Axiom 1 (codomain_is_an_identity_map): identity_map(codomain(X)) = true.
% 0.51/0.34 Axiom 2 (assume_bc_exists): defined(b, c) = true.
% 0.51/0.34 Axiom 3 (assume_ab_exists): defined(a, b) = true.
% 0.51/0.34 Axiom 4 (mapping_from_codomain_of_x_to_x): defined(codomain(X), X) = true.
% 0.51/0.34 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.51/0.34 Axiom 6 (closure_of_composition): ifeq(defined(X, Y), true, product(X, Y, compose(X, Y)), true) = true.
% 0.51/0.34 Axiom 7 (identity1): ifeq(identity_map(X), true, ifeq(defined(X, Y), true, product(X, Y, Y), true), true) = true.
% 0.51/0.34 Axiom 8 (category_theory_axiom3): ifeq(product(X, Y, Z), true, ifeq(defined(W, Z), true, defined(W, X), true), true) = true.
% 0.51/0.34 Axiom 9 (category_theory_axiom6): ifeq(identity_map(X), true, ifeq(defined(X, Y), true, ifeq(defined(Z, X), true, defined(Z, Y), true), true), true) = true.
% 0.51/0.34
% 0.51/0.34 Goal 1 (prove_a_bc_exists): defined(a, compose(b, c)) = true.
% 0.51/0.34 Proof:
% 0.51/0.34 defined(a, compose(b, c))
% 0.51/0.34 = { by axiom 5 (ifeq_axiom) R->L }
% 0.51/0.34 ifeq(true, true, defined(a, compose(b, c)), true)
% 0.51/0.34 = { by axiom 8 (category_theory_axiom3) R->L }
% 0.51/0.34 ifeq(ifeq(product(codomain(compose(b, c)), b, b), true, ifeq(defined(a, b), true, defined(a, codomain(compose(b, c))), true), true), true, defined(a, compose(b, c)), true)
% 0.51/0.34 = { by axiom 3 (assume_ab_exists) }
% 0.51/0.34 ifeq(ifeq(product(codomain(compose(b, c)), b, b), true, ifeq(true, true, defined(a, codomain(compose(b, c))), true), true), true, defined(a, compose(b, c)), true)
% 0.51/0.34 = { by axiom 5 (ifeq_axiom) }
% 0.51/0.34 ifeq(ifeq(product(codomain(compose(b, c)), b, b), true, defined(a, codomain(compose(b, c))), true), true, defined(a, compose(b, c)), true)
% 0.51/0.34 = { by axiom 5 (ifeq_axiom) R->L }
% 0.51/0.34 ifeq(ifeq(ifeq(true, true, product(codomain(compose(b, c)), b, b), true), true, defined(a, codomain(compose(b, c))), true), true, defined(a, compose(b, c)), true)
% 0.51/0.34 = { by axiom 5 (ifeq_axiom) R->L }
% 0.51/0.34 ifeq(ifeq(ifeq(true, true, ifeq(true, true, product(codomain(compose(b, c)), b, b), true), true), true, defined(a, codomain(compose(b, c))), true), true, defined(a, compose(b, c)), true)
% 0.51/0.34 = { by axiom 1 (codomain_is_an_identity_map) R->L }
% 0.51/0.34 ifeq(ifeq(ifeq(identity_map(codomain(compose(b, c))), true, ifeq(true, true, product(codomain(compose(b, c)), b, b), true), true), true, defined(a, codomain(compose(b, c))), true), true, defined(a, compose(b, c)), true)
% 0.51/0.34 = { by axiom 8 (category_theory_axiom3) R->L }
% 0.51/0.34 ifeq(ifeq(ifeq(identity_map(codomain(compose(b, c))), true, ifeq(ifeq(product(b, c, compose(b, c)), true, ifeq(defined(codomain(compose(b, c)), compose(b, c)), true, defined(codomain(compose(b, c)), b), true), true), true, product(codomain(compose(b, c)), b, b), true), true), true, defined(a, codomain(compose(b, c))), true), true, defined(a, compose(b, c)), true)
% 0.51/0.34 = { by axiom 4 (mapping_from_codomain_of_x_to_x) }
% 0.51/0.34 ifeq(ifeq(ifeq(identity_map(codomain(compose(b, c))), true, ifeq(ifeq(product(b, c, compose(b, c)), true, ifeq(true, true, defined(codomain(compose(b, c)), b), true), true), true, product(codomain(compose(b, c)), b, b), true), true), true, defined(a, codomain(compose(b, c))), true), true, defined(a, compose(b, c)), true)
% 0.51/0.34 = { by axiom 5 (ifeq_axiom) }
% 0.51/0.34 ifeq(ifeq(ifeq(identity_map(codomain(compose(b, c))), true, ifeq(ifeq(product(b, c, compose(b, c)), true, defined(codomain(compose(b, c)), b), true), true, product(codomain(compose(b, c)), b, b), true), true), true, defined(a, codomain(compose(b, c))), true), true, defined(a, compose(b, c)), true)
% 0.51/0.34 = { by axiom 5 (ifeq_axiom) R->L }
% 0.51/0.35 ifeq(ifeq(ifeq(identity_map(codomain(compose(b, c))), true, ifeq(ifeq(ifeq(true, true, product(b, c, compose(b, c)), true), true, defined(codomain(compose(b, c)), b), true), true, product(codomain(compose(b, c)), b, b), true), true), true, defined(a, codomain(compose(b, c))), true), true, defined(a, compose(b, c)), true)
% 0.51/0.35 = { by axiom 2 (assume_bc_exists) R->L }
% 0.51/0.35 ifeq(ifeq(ifeq(identity_map(codomain(compose(b, c))), true, ifeq(ifeq(ifeq(defined(b, c), true, product(b, c, compose(b, c)), true), true, defined(codomain(compose(b, c)), b), true), true, product(codomain(compose(b, c)), b, b), true), true), true, defined(a, codomain(compose(b, c))), true), true, defined(a, compose(b, c)), true)
% 0.51/0.35 = { by axiom 6 (closure_of_composition) }
% 0.51/0.35 ifeq(ifeq(ifeq(identity_map(codomain(compose(b, c))), true, ifeq(ifeq(true, true, defined(codomain(compose(b, c)), b), true), true, product(codomain(compose(b, c)), b, b), true), true), true, defined(a, codomain(compose(b, c))), true), true, defined(a, compose(b, c)), true)
% 0.51/0.35 = { by axiom 5 (ifeq_axiom) }
% 0.51/0.35 ifeq(ifeq(ifeq(identity_map(codomain(compose(b, c))), true, ifeq(defined(codomain(compose(b, c)), b), true, product(codomain(compose(b, c)), b, b), true), true), true, defined(a, codomain(compose(b, c))), true), true, defined(a, compose(b, c)), true)
% 0.51/0.35 = { by axiom 7 (identity1) }
% 0.51/0.35 ifeq(ifeq(true, true, defined(a, codomain(compose(b, c))), true), true, defined(a, compose(b, c)), true)
% 0.51/0.35 = { by axiom 5 (ifeq_axiom) }
% 0.51/0.35 ifeq(defined(a, codomain(compose(b, c))), true, defined(a, compose(b, c)), true)
% 0.51/0.35 = { by axiom 5 (ifeq_axiom) R->L }
% 0.51/0.35 ifeq(true, true, ifeq(defined(a, codomain(compose(b, c))), true, defined(a, compose(b, c)), true), true)
% 0.51/0.35 = { by axiom 5 (ifeq_axiom) R->L }
% 0.51/0.35 ifeq(true, true, ifeq(true, true, ifeq(defined(a, codomain(compose(b, c))), true, defined(a, compose(b, c)), true), true), true)
% 0.51/0.35 = { by axiom 1 (codomain_is_an_identity_map) R->L }
% 0.51/0.35 ifeq(identity_map(codomain(compose(b, c))), true, ifeq(true, true, ifeq(defined(a, codomain(compose(b, c))), true, defined(a, compose(b, c)), true), true), true)
% 0.51/0.35 = { by axiom 4 (mapping_from_codomain_of_x_to_x) R->L }
% 0.51/0.35 ifeq(identity_map(codomain(compose(b, c))), true, ifeq(defined(codomain(compose(b, c)), compose(b, c)), true, ifeq(defined(a, codomain(compose(b, c))), true, defined(a, compose(b, c)), true), true), true)
% 0.51/0.35 = { by axiom 9 (category_theory_axiom6) }
% 0.51/0.35 true
% 0.51/0.35 % SZS output end Proof
% 0.51/0.35
% 0.51/0.35 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------