%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : CAT001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 09:36:20 AM UTC 2026
% Result : Unsatisfiable 42.27s 5.65s
% Output : Proof 43.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n019.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 21:11:18 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 42.27/5.65 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
% 42.27/5.65
% 42.27/5.65 % SZS status Unsatisfiable
% 42.27/5.65
% 43.03/5.71 % SZS output start Proof
% 43.03/5.71 Axiom 1 (domain_is_an_identity_map): identity_map(domain(X)) = true.
% 43.03/5.71 Axiom 2 (bh_equals_d): product(b, h, d) = true.
% 43.03/5.71 Axiom 3 (bg_equals_d): product(b, g, d) = true.
% 43.03/5.71 Axiom 4 (ab_equals_c): product(a, b, c) = true.
% 43.03/5.71 Axiom 5 (mapping_from_x_to_its_domain): defined(X, domain(X)) = true.
% 43.03/5.71 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 43.03/5.71 Axiom 7 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 43.03/5.71 Axiom 8 (associative_property1): ifeq(product(X, Y, Z), true, defined(X, Y), true) = true.
% 43.03/5.71 Axiom 9 (closure_of_composition): ifeq(defined(X, Y), true, product(X, Y, compose(X, Y)), true) = true.
% 43.03/5.71 Axiom 10 (identity2): ifeq(identity_map(X), true, ifeq(defined(Y, X), true, product(Y, X, Y), true), true) = true.
% 43.03/5.71 Axiom 11 (cancellation_for_product): ifeq2(product(c, X, Y), true, ifeq2(product(c, Z, Y), true, Z, X), X) = X.
% 43.03/5.71 Axiom 12 (associative_property2): ifeq(product(X, Y, Z), true, ifeq(defined(Z, W), true, defined(Y, W), true), true) = true.
% 43.03/5.71 Axiom 13 (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.
% 43.03/5.71 Axiom 14 (category_theory_axiom5): ifeq(product(X, Y, Z), true, ifeq(product(X, W, V), true, ifeq(product(W, U, Y), true, product(V, U, Z), true), true), true) = true.
% 43.03/5.71 Axiom 15 (category_theory_axiom2): ifeq(product(X, Y, Z), true, ifeq(product(W, Y, V), true, ifeq(product(U, W, X), true, product(U, V, Z), true), true), true) = true.
% 43.03/5.71
% 43.03/5.71 Goal 1 (prove_h_equals_g): h = g.
% 43.03/5.71 Proof:
% 43.03/5.71 h
% 43.03/5.71 = { by axiom 7 (ifeq_axiom) R->L }
% 43.03/5.71 ifeq2(true, true, h, g)
% 43.03/5.71 = { by axiom 14 (category_theory_axiom5) R->L }
% 43.03/5.71 ifeq2(ifeq(product(a, d, compose(c, h)), true, ifeq(product(a, b, c), true, ifeq(product(b, g, d), true, product(c, g, compose(c, h)), true), true), true), true, h, g)
% 43.03/5.71 = { by axiom 3 (bg_equals_d) }
% 43.03/5.71 ifeq2(ifeq(product(a, d, compose(c, h)), true, ifeq(product(a, b, c), true, ifeq(true, true, product(c, g, compose(c, h)), true), true), true), true, h, g)
% 43.03/5.71 = { by axiom 6 (ifeq_axiom) }
% 43.03/5.71 ifeq2(ifeq(product(a, d, compose(c, h)), true, ifeq(product(a, b, c), true, product(c, g, compose(c, h)), true), true), true, h, g)
% 43.03/5.71 = { by axiom 4 (ab_equals_c) }
% 43.03/5.71 ifeq2(ifeq(product(a, d, compose(c, h)), true, ifeq(true, true, product(c, g, compose(c, h)), true), true), true, h, g)
% 43.03/5.72 = { by axiom 6 (ifeq_axiom) }
% 43.03/5.72 ifeq2(ifeq(product(a, d, compose(c, h)), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 6 (ifeq_axiom) R->L }
% 43.03/5.72 ifeq2(ifeq(ifeq(true, true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 9 (closure_of_composition) R->L }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(defined(c, h), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 6 (ifeq_axiom) R->L }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(true, true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 12 (associative_property2) R->L }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(product(b, domain(c), b), true, ifeq(defined(b, h), true, defined(domain(c), h), true), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 6 (ifeq_axiom) R->L }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(product(b, domain(c), b), true, ifeq(ifeq(true, true, defined(b, h), true), true, defined(domain(c), h), true), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 2 (bh_equals_d) R->L }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(product(b, domain(c), b), true, ifeq(ifeq(product(b, h, d), true, defined(b, h), true), true, defined(domain(c), h), true), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 8 (associative_property1) }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(product(b, domain(c), b), true, ifeq(true, true, defined(domain(c), h), true), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 6 (ifeq_axiom) }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(product(b, domain(c), b), true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 6 (ifeq_axiom) R->L }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, product(b, domain(c), b), true), true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 6 (ifeq_axiom) R->L }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(true, true, product(b, domain(c), b), true), true), true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 1 (domain_is_an_identity_map) R->L }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(identity_map(domain(c)), true, ifeq(true, true, product(b, domain(c), b), true), true), true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 12 (associative_property2) R->L }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(identity_map(domain(c)), true, ifeq(ifeq(product(a, b, c), true, ifeq(defined(c, domain(c)), true, defined(b, domain(c)), true), true), true, product(b, domain(c), b), true), true), true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 4 (ab_equals_c) }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(identity_map(domain(c)), true, ifeq(ifeq(true, true, ifeq(defined(c, domain(c)), true, defined(b, domain(c)), true), true), true, product(b, domain(c), b), true), true), true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 6 (ifeq_axiom) }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(identity_map(domain(c)), true, ifeq(ifeq(defined(c, domain(c)), true, defined(b, domain(c)), true), true, product(b, domain(c), b), true), true), true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 5 (mapping_from_x_to_its_domain) }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(identity_map(domain(c)), true, ifeq(ifeq(true, true, defined(b, domain(c)), true), true, product(b, domain(c), b), true), true), true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 6 (ifeq_axiom) }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(identity_map(domain(c)), true, ifeq(defined(b, domain(c)), true, product(b, domain(c), b), true), true), true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 10 (identity2) }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 6 (ifeq_axiom) }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(defined(domain(c), h), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 6 (ifeq_axiom) R->L }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(defined(domain(c), h), true, ifeq(true, true, defined(c, h), true), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 6 (ifeq_axiom) R->L }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(defined(domain(c), h), true, ifeq(true, true, defined(c, h), true), true), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 1 (domain_is_an_identity_map) R->L }
% 43.03/5.72 ifeq2(ifeq(ifeq(ifeq(ifeq(identity_map(domain(c)), true, ifeq(defined(domain(c), h), true, ifeq(true, true, defined(c, h), true), true), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.72 = { by axiom 5 (mapping_from_x_to_its_domain) R->L }
% 43.03/5.73 ifeq2(ifeq(ifeq(ifeq(ifeq(identity_map(domain(c)), true, ifeq(defined(domain(c), h), true, ifeq(defined(c, domain(c)), true, defined(c, h), true), true), true), true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.73 = { by axiom 13 (category_theory_axiom6) }
% 43.03/5.73 ifeq2(ifeq(ifeq(ifeq(true, true, product(c, h, compose(c, h)), true), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.73 = { by axiom 6 (ifeq_axiom) }
% 43.03/5.73 ifeq2(ifeq(ifeq(product(c, h, compose(c, h)), true, product(a, d, compose(c, h)), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.73 = { by axiom 6 (ifeq_axiom) R->L }
% 43.03/5.73 ifeq2(ifeq(ifeq(product(c, h, compose(c, h)), true, ifeq(true, true, product(a, d, compose(c, h)), true), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.73 = { by axiom 4 (ab_equals_c) R->L }
% 43.03/5.73 ifeq2(ifeq(ifeq(product(c, h, compose(c, h)), true, ifeq(product(a, b, c), true, product(a, d, compose(c, h)), true), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.73 = { by axiom 6 (ifeq_axiom) R->L }
% 43.03/5.73 ifeq2(ifeq(ifeq(product(c, h, compose(c, h)), true, ifeq(true, true, ifeq(product(a, b, c), true, product(a, d, compose(c, h)), true), true), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.73 = { by axiom 2 (bh_equals_d) R->L }
% 43.03/5.73 ifeq2(ifeq(ifeq(product(c, h, compose(c, h)), true, ifeq(product(b, h, d), true, ifeq(product(a, b, c), true, product(a, d, compose(c, h)), true), true), true), true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.73 = { by axiom 15 (category_theory_axiom2) }
% 43.03/5.73 ifeq2(ifeq(true, true, product(c, g, compose(c, h)), true), true, h, g)
% 43.03/5.73 = { by axiom 6 (ifeq_axiom) }
% 43.03/5.73 ifeq2(product(c, g, compose(c, h)), true, h, g)
% 43.03/5.73 = { by axiom 7 (ifeq_axiom) R->L }
% 43.03/5.73 ifeq2(product(c, g, compose(c, h)), true, ifeq2(true, true, h, g), g)
% 43.03/5.73 = { by axiom 9 (closure_of_composition) R->L }
% 43.03/5.73 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(defined(c, h), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.73 = { by axiom 6 (ifeq_axiom) R->L }
% 43.03/5.73 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(true, true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.73 = { by axiom 12 (associative_property2) R->L }
% 43.03/5.73 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(ifeq(product(b, domain(c), b), true, ifeq(defined(b, h), true, defined(domain(c), h), true), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.73 = { by axiom 6 (ifeq_axiom) R->L }
% 43.03/5.73 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(ifeq(product(b, domain(c), b), true, ifeq(ifeq(true, true, defined(b, h), true), true, defined(domain(c), h), true), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.73 = { by axiom 2 (bh_equals_d) R->L }
% 43.03/5.73 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(ifeq(product(b, domain(c), b), true, ifeq(ifeq(product(b, h, d), true, defined(b, h), true), true, defined(domain(c), h), true), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.73 = { by axiom 8 (associative_property1) }
% 43.03/5.73 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(ifeq(product(b, domain(c), b), true, ifeq(true, true, defined(domain(c), h), true), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.73 = { by axiom 6 (ifeq_axiom) }
% 43.03/5.73 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(ifeq(product(b, domain(c), b), true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.73 = { by axiom 6 (ifeq_axiom) R->L }
% 43.03/5.73 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(ifeq(ifeq(true, true, product(b, domain(c), b), true), true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.73 = { by axiom 6 (ifeq_axiom) R->L }
% 43.03/5.73 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(true, true, product(b, domain(c), b), true), true), true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.74 = { by axiom 1 (domain_is_an_identity_map) R->L }
% 43.03/5.74 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(ifeq(ifeq(identity_map(domain(c)), true, ifeq(true, true, product(b, domain(c), b), true), true), true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.74 = { by axiom 12 (associative_property2) R->L }
% 43.03/5.74 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(ifeq(ifeq(identity_map(domain(c)), true, ifeq(ifeq(product(a, b, c), true, ifeq(defined(c, domain(c)), true, defined(b, domain(c)), true), true), true, product(b, domain(c), b), true), true), true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.74 = { by axiom 4 (ab_equals_c) }
% 43.03/5.74 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(ifeq(ifeq(identity_map(domain(c)), true, ifeq(ifeq(true, true, ifeq(defined(c, domain(c)), true, defined(b, domain(c)), true), true), true, product(b, domain(c), b), true), true), true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.74 = { by axiom 6 (ifeq_axiom) }
% 43.03/5.74 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(ifeq(ifeq(identity_map(domain(c)), true, ifeq(ifeq(defined(c, domain(c)), true, defined(b, domain(c)), true), true, product(b, domain(c), b), true), true), true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.74 = { by axiom 5 (mapping_from_x_to_its_domain) }
% 43.03/5.74 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(ifeq(ifeq(identity_map(domain(c)), true, ifeq(ifeq(true, true, defined(b, domain(c)), true), true, product(b, domain(c), b), true), true), true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.74 = { by axiom 6 (ifeq_axiom) }
% 43.03/5.74 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(ifeq(ifeq(identity_map(domain(c)), true, ifeq(defined(b, domain(c)), true, product(b, domain(c), b), true), true), true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.74 = { by axiom 10 (identity2) }
% 43.03/5.74 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(ifeq(true, true, defined(domain(c), h), true), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.74 = { by axiom 6 (ifeq_axiom) }
% 43.03/5.74 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(defined(domain(c), h), true, defined(c, h), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.74 = { by axiom 6 (ifeq_axiom) R->L }
% 43.03/5.74 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(defined(domain(c), h), true, ifeq(true, true, defined(c, h), true), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.74 = { by axiom 6 (ifeq_axiom) R->L }
% 43.03/5.74 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(true, true, ifeq(defined(domain(c), h), true, ifeq(true, true, defined(c, h), true), true), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.74 = { by axiom 1 (domain_is_an_identity_map) R->L }
% 43.03/5.74 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(identity_map(domain(c)), true, ifeq(defined(domain(c), h), true, ifeq(true, true, defined(c, h), true), true), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.74 = { by axiom 5 (mapping_from_x_to_its_domain) R->L }
% 43.03/5.74 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(ifeq(identity_map(domain(c)), true, ifeq(defined(domain(c), h), true, ifeq(defined(c, domain(c)), true, defined(c, h), true), true), true), true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.74 = { by axiom 13 (category_theory_axiom6) }
% 43.03/5.74 ifeq2(product(c, g, compose(c, h)), true, ifeq2(ifeq(true, true, product(c, h, compose(c, h)), true), true, h, g), g)
% 43.03/5.74 = { by axiom 6 (ifeq_axiom) }
% 43.03/5.74 ifeq2(product(c, g, compose(c, h)), true, ifeq2(product(c, h, compose(c, h)), true, h, g), g)
% 43.03/5.74 = { by axiom 11 (cancellation_for_product) }
% 43.03/5.74 g
% 43.03/5.74 % SZS output end Proof
% 43.03/5.74
% 43.03/5.74 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------