%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : CAT006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 09:36:22 AM UTC 2026
% Result : Unsatisfiable 0.22s 0.30s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n013.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 21:12:21 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.30 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.22/0.30
% 0.22/0.30 % SZS status Unsatisfiable
% 0.22/0.30
% 0.22/0.31 % SZS output start Proof
% 0.22/0.31 Axiom 1 (h_is_the_identity_map): identity_map(h) = true.
% 0.22/0.31 Axiom 2 (codomain_is_an_identity_map): identity_map(codomain(X)) = true.
% 0.22/0.31 Axiom 3 (ha_defined): defined(h, a) = true.
% 0.22/0.31 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.22/0.31 Axiom 5 (product_on_codomain): product(codomain(X), X, X) = true.
% 0.22/0.31 Axiom 6 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.22/0.31 Axiom 7 (identity1): ifeq(identity_map(X), true, ifeq(defined(X, Y), true, product(X, Y, Y), true), true) = true.
% 0.22/0.31 Axiom 8 (identity2): ifeq(identity_map(X), true, ifeq(defined(Y, X), true, product(Y, X, Y), true), true) = true.
% 0.22/0.31 Axiom 9 (composition_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 0.22/0.31 Axiom 10 (category_theory_axiom3): ifeq(product(X, Y, Z), true, ifeq(defined(W, Z), true, defined(W, X), true), true) = true.
% 0.22/0.31
% 0.22/0.31 Goal 1 (prove_codomain_of_a_is_h): codomain(a) = h.
% 0.22/0.31 Proof:
% 0.22/0.31 codomain(a)
% 0.22/0.31 = { by axiom 6 (ifeq_axiom) R->L }
% 0.22/0.31 ifeq2(true, true, codomain(a), h)
% 0.22/0.31 = { by axiom 8 (identity2) R->L }
% 0.22/0.31 ifeq2(ifeq(identity_map(codomain(a)), true, ifeq(defined(h, codomain(a)), true, product(h, codomain(a), h), true), true), true, codomain(a), h)
% 0.22/0.31 = { by axiom 4 (ifeq_axiom) R->L }
% 0.22/0.31 ifeq2(ifeq(identity_map(codomain(a)), true, ifeq(ifeq(true, true, defined(h, codomain(a)), true), true, product(h, codomain(a), h), true), true), true, codomain(a), h)
% 0.22/0.31 = { by axiom 3 (ha_defined) R->L }
% 0.22/0.31 ifeq2(ifeq(identity_map(codomain(a)), true, ifeq(ifeq(defined(h, a), true, defined(h, codomain(a)), true), true, product(h, codomain(a), h), true), true), true, codomain(a), h)
% 0.22/0.31 = { by axiom 4 (ifeq_axiom) R->L }
% 0.22/0.31 ifeq2(ifeq(identity_map(codomain(a)), true, ifeq(ifeq(true, true, ifeq(defined(h, a), true, defined(h, codomain(a)), true), true), true, product(h, codomain(a), h), true), true), true, codomain(a), h)
% 0.22/0.31 = { by axiom 5 (product_on_codomain) R->L }
% 0.22/0.31 ifeq2(ifeq(identity_map(codomain(a)), true, ifeq(ifeq(product(codomain(a), a, a), true, ifeq(defined(h, a), true, defined(h, codomain(a)), true), true), true, product(h, codomain(a), h), true), true), true, codomain(a), h)
% 0.22/0.31 = { by axiom 10 (category_theory_axiom3) }
% 0.22/0.31 ifeq2(ifeq(identity_map(codomain(a)), true, ifeq(true, true, product(h, codomain(a), h), true), true), true, codomain(a), h)
% 0.22/0.31 = { by axiom 2 (codomain_is_an_identity_map) }
% 0.22/0.31 ifeq2(ifeq(true, true, ifeq(true, true, product(h, codomain(a), h), true), true), true, codomain(a), h)
% 0.22/0.31 = { by axiom 4 (ifeq_axiom) }
% 0.22/0.31 ifeq2(ifeq(true, true, product(h, codomain(a), h), true), true, codomain(a), h)
% 0.22/0.31 = { by axiom 4 (ifeq_axiom) }
% 0.22/0.31 ifeq2(product(h, codomain(a), h), true, codomain(a), h)
% 0.22/0.31 = { by axiom 6 (ifeq_axiom) R->L }
% 0.22/0.31 ifeq2(product(h, codomain(a), h), true, ifeq2(true, true, codomain(a), h), h)
% 0.22/0.31 = { by axiom 7 (identity1) R->L }
% 0.22/0.31 ifeq2(product(h, codomain(a), h), true, ifeq2(ifeq(identity_map(h), true, ifeq(defined(h, codomain(a)), true, product(h, codomain(a), codomain(a)), true), true), true, codomain(a), h), h)
% 0.22/0.31 = { by axiom 4 (ifeq_axiom) R->L }
% 0.22/0.31 ifeq2(product(h, codomain(a), h), true, ifeq2(ifeq(identity_map(h), true, ifeq(ifeq(true, true, defined(h, codomain(a)), true), true, product(h, codomain(a), codomain(a)), true), true), true, codomain(a), h), h)
% 0.22/0.31 = { by axiom 3 (ha_defined) R->L }
% 0.22/0.31 ifeq2(product(h, codomain(a), h), true, ifeq2(ifeq(identity_map(h), true, ifeq(ifeq(defined(h, a), true, defined(h, codomain(a)), true), true, product(h, codomain(a), codomain(a)), true), true), true, codomain(a), h), h)
% 0.22/0.31 = { by axiom 4 (ifeq_axiom) R->L }
% 0.22/0.31 ifeq2(product(h, codomain(a), h), true, ifeq2(ifeq(identity_map(h), true, ifeq(ifeq(true, true, ifeq(defined(h, a), true, defined(h, codomain(a)), true), true), true, product(h, codomain(a), codomain(a)), true), true), true, codomain(a), h), h)
% 0.22/0.31 = { by axiom 5 (product_on_codomain) R->L }
% 0.22/0.31 ifeq2(product(h, codomain(a), h), true, ifeq2(ifeq(identity_map(h), true, ifeq(ifeq(product(codomain(a), a, a), true, ifeq(defined(h, a), true, defined(h, codomain(a)), true), true), true, product(h, codomain(a), codomain(a)), true), true), true, codomain(a), h), h)
% 0.22/0.31 = { by axiom 10 (category_theory_axiom3) }
% 0.22/0.31 ifeq2(product(h, codomain(a), h), true, ifeq2(ifeq(identity_map(h), true, ifeq(true, true, product(h, codomain(a), codomain(a)), true), true), true, codomain(a), h), h)
% 0.22/0.31 = { by axiom 1 (h_is_the_identity_map) }
% 0.22/0.31 ifeq2(product(h, codomain(a), h), true, ifeq2(ifeq(true, true, ifeq(true, true, product(h, codomain(a), codomain(a)), true), true), true, codomain(a), h), h)
% 0.22/0.31 = { by axiom 4 (ifeq_axiom) }
% 0.22/0.31 ifeq2(product(h, codomain(a), h), true, ifeq2(ifeq(true, true, product(h, codomain(a), codomain(a)), true), true, codomain(a), h), h)
% 0.22/0.31 = { by axiom 4 (ifeq_axiom) }
% 0.22/0.31 ifeq2(product(h, codomain(a), h), true, ifeq2(product(h, codomain(a), codomain(a)), true, codomain(a), h), h)
% 0.22/0.31 = { by axiom 9 (composition_is_well_defined) }
% 0.22/0.31 h
% 0.22/0.31 % SZS output end Proof
% 0.22/0.31
% 0.22/0.31 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------