%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : CAT003-1 : 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 09:36:21 AM UTC 2026
% Result : Unsatisfiable 32.81s 4.49s
% Output : Proof 33.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n016.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 21:17:48 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.81/4.49 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
% 32.81/4.49
% 32.81/4.49 % SZS status Unsatisfiable
% 32.81/4.49
% 33.62/4.55 % SZS output start Proof
% 33.62/4.55 Axiom 1 (codomain_is_an_identity_map): identity_map(codomain(X)) = true.
% 33.62/4.55 Axiom 2 (ab_equals_c): product(a, b, c) = true.
% 33.62/4.55 Axiom 3 (ha_equals_d): product(h, a, d) = true.
% 33.62/4.55 Axiom 4 (ga_equals_d): product(g, a, d) = true.
% 33.62/4.55 Axiom 5 (mapping_from_codomain_of_x_to_x): defined(codomain(X), X) = true.
% 33.62/4.55 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 33.62/4.55 Axiom 7 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 33.62/4.55 Axiom 8 (associative_property1): ifeq(product(X, Y, Z), true, defined(X, Y), true) = true.
% 33.62/4.55 Axiom 9 (closure_of_composition): ifeq(defined(X, Y), true, product(X, Y, compose(X, Y)), true) = true.
% 33.62/4.55 Axiom 10 (identity1): ifeq(identity_map(X), true, ifeq(defined(X, Y), true, product(X, Y, Y), true), true) = true.
% 33.62/4.55 Axiom 11 (cancellation_for_product): ifeq2(product(X, c, Y), true, ifeq2(product(Z, c, Y), true, Z, X), X) = X.
% 33.62/4.55 Axiom 12 (category_theory_axiom3): ifeq(product(X, Y, Z), true, ifeq(defined(W, Z), true, defined(W, X), true), true) = true.
% 33.62/4.55 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.
% 33.62/4.55 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.
% 33.62/4.55 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.
% 33.62/4.55
% 33.62/4.55 Goal 1 (prove_h_equals_g): h = g.
% 33.62/4.55 Proof:
% 33.62/4.55 h
% 33.62/4.55 = { by axiom 7 (ifeq_axiom) R->L }
% 33.62/4.55 ifeq2(true, true, h, g)
% 33.62/4.55 = { by axiom 15 (category_theory_axiom2) R->L }
% 33.62/4.55 ifeq2(ifeq(product(d, b, compose(h, c)), true, ifeq(product(a, b, c), true, ifeq(product(g, a, d), true, product(g, c, compose(h, c)), true), true), true), true, h, g)
% 33.62/4.55 = { by axiom 2 (ab_equals_c) }
% 33.62/4.55 ifeq2(ifeq(product(d, b, compose(h, c)), true, ifeq(true, true, ifeq(product(g, a, d), true, product(g, c, compose(h, c)), true), true), true), true, h, g)
% 33.62/4.55 = { by axiom 6 (ifeq_axiom) }
% 33.62/4.55 ifeq2(ifeq(product(d, b, compose(h, c)), true, ifeq(product(g, a, d), true, product(g, c, compose(h, c)), true), true), true, h, g)
% 33.62/4.55 = { by axiom 4 (ga_equals_d) }
% 33.62/4.55 ifeq2(ifeq(product(d, b, compose(h, c)), true, ifeq(true, true, product(g, c, compose(h, c)), true), true), true, h, g)
% 33.62/4.55 = { by axiom 6 (ifeq_axiom) }
% 33.62/4.55 ifeq2(ifeq(product(d, b, compose(h, c)), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.55 = { by axiom 6 (ifeq_axiom) R->L }
% 33.62/4.55 ifeq2(ifeq(ifeq(true, true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.55 = { by axiom 9 (closure_of_composition) R->L }
% 33.62/4.55 ifeq2(ifeq(ifeq(ifeq(defined(h, c), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.55 = { by axiom 6 (ifeq_axiom) R->L }
% 33.62/4.55 ifeq2(ifeq(ifeq(ifeq(ifeq(true, true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.55 = { by axiom 12 (category_theory_axiom3) R->L }
% 33.62/4.55 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(product(codomain(c), a, a), true, ifeq(defined(h, a), true, defined(h, codomain(c)), true), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.55 = { by axiom 6 (ifeq_axiom) R->L }
% 33.62/4.55 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(product(codomain(c), a, a), true, ifeq(ifeq(true, true, defined(h, a), true), true, defined(h, codomain(c)), true), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.55 = { by axiom 3 (ha_equals_d) R->L }
% 33.62/4.55 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(product(codomain(c), a, a), true, ifeq(ifeq(product(h, a, d), true, defined(h, a), true), true, defined(h, codomain(c)), true), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.55 = { by axiom 8 (associative_property1) }
% 33.62/4.55 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(product(codomain(c), a, a), true, ifeq(true, true, defined(h, codomain(c)), true), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.55 = { by axiom 6 (ifeq_axiom) }
% 33.62/4.56 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(product(codomain(c), a, a), true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 6 (ifeq_axiom) R->L }
% 33.62/4.56 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, product(codomain(c), a, a), true), true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 6 (ifeq_axiom) R->L }
% 33.62/4.56 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(true, true, product(codomain(c), a, a), true), true), true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 1 (codomain_is_an_identity_map) R->L }
% 33.62/4.56 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(identity_map(codomain(c)), true, ifeq(true, true, product(codomain(c), a, a), true), true), true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 12 (category_theory_axiom3) R->L }
% 33.62/4.56 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(identity_map(codomain(c)), true, ifeq(ifeq(product(a, b, c), true, ifeq(defined(codomain(c), c), true, defined(codomain(c), a), true), true), true, product(codomain(c), a, a), true), true), true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 2 (ab_equals_c) }
% 33.62/4.56 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(identity_map(codomain(c)), true, ifeq(ifeq(true, true, ifeq(defined(codomain(c), c), true, defined(codomain(c), a), true), true), true, product(codomain(c), a, a), true), true), true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 6 (ifeq_axiom) }
% 33.62/4.56 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(identity_map(codomain(c)), true, ifeq(ifeq(defined(codomain(c), c), true, defined(codomain(c), a), true), true, product(codomain(c), a, a), true), true), true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 5 (mapping_from_codomain_of_x_to_x) }
% 33.62/4.56 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(identity_map(codomain(c)), true, ifeq(ifeq(true, true, defined(codomain(c), a), true), true, product(codomain(c), a, a), true), true), true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 6 (ifeq_axiom) }
% 33.62/4.56 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(identity_map(codomain(c)), true, ifeq(defined(codomain(c), a), true, product(codomain(c), a, a), true), true), true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 10 (identity1) }
% 33.62/4.56 ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 6 (ifeq_axiom) }
% 33.62/4.56 ifeq2(ifeq(ifeq(ifeq(ifeq(defined(h, codomain(c)), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 6 (ifeq_axiom) R->L }
% 33.62/4.56 ifeq2(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(defined(h, codomain(c)), true, defined(h, c), true), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 6 (ifeq_axiom) R->L }
% 33.62/4.56 ifeq2(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(true, true, ifeq(defined(h, codomain(c)), true, defined(h, c), true), true), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 1 (codomain_is_an_identity_map) R->L }
% 33.62/4.56 ifeq2(ifeq(ifeq(ifeq(ifeq(identity_map(codomain(c)), true, ifeq(true, true, ifeq(defined(h, codomain(c)), true, defined(h, c), true), true), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 5 (mapping_from_codomain_of_x_to_x) R->L }
% 33.62/4.56 ifeq2(ifeq(ifeq(ifeq(ifeq(identity_map(codomain(c)), true, ifeq(defined(codomain(c), c), true, ifeq(defined(h, codomain(c)), true, defined(h, c), true), true), true), true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 13 (category_theory_axiom6) }
% 33.62/4.56 ifeq2(ifeq(ifeq(ifeq(true, true, product(h, c, compose(h, c)), true), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 6 (ifeq_axiom) }
% 33.62/4.56 ifeq2(ifeq(ifeq(product(h, c, compose(h, c)), true, product(d, b, compose(h, c)), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 6 (ifeq_axiom) R->L }
% 33.62/4.56 ifeq2(ifeq(ifeq(product(h, c, compose(h, c)), true, ifeq(true, true, product(d, b, compose(h, c)), true), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 3 (ha_equals_d) R->L }
% 33.62/4.56 ifeq2(ifeq(ifeq(product(h, c, compose(h, c)), true, ifeq(product(h, a, d), true, product(d, b, compose(h, c)), true), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 6 (ifeq_axiom) R->L }
% 33.62/4.56 ifeq2(ifeq(ifeq(product(h, c, compose(h, c)), true, ifeq(product(h, a, d), true, ifeq(true, true, product(d, b, compose(h, c)), true), true), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 2 (ab_equals_c) R->L }
% 33.62/4.56 ifeq2(ifeq(ifeq(product(h, c, compose(h, c)), true, ifeq(product(h, a, d), true, ifeq(product(a, b, c), true, product(d, b, compose(h, c)), true), true), true), true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 14 (category_theory_axiom5) }
% 33.62/4.56 ifeq2(ifeq(true, true, product(g, c, compose(h, c)), true), true, h, g)
% 33.62/4.56 = { by axiom 6 (ifeq_axiom) }
% 33.62/4.56 ifeq2(product(g, c, compose(h, c)), true, h, g)
% 33.62/4.56 = { by axiom 7 (ifeq_axiom) R->L }
% 33.62/4.56 ifeq2(product(g, c, compose(h, c)), true, ifeq2(true, true, h, g), g)
% 33.62/4.56 = { by axiom 9 (closure_of_composition) R->L }
% 33.62/4.56 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(defined(h, c), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.56 = { by axiom 6 (ifeq_axiom) R->L }
% 33.62/4.56 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(true, true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.56 = { by axiom 12 (category_theory_axiom3) R->L }
% 33.62/4.56 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(ifeq(product(codomain(c), a, a), true, ifeq(defined(h, a), true, defined(h, codomain(c)), true), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.56 = { by axiom 6 (ifeq_axiom) R->L }
% 33.62/4.56 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(ifeq(product(codomain(c), a, a), true, ifeq(ifeq(true, true, defined(h, a), true), true, defined(h, codomain(c)), true), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.56 = { by axiom 3 (ha_equals_d) R->L }
% 33.62/4.56 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(ifeq(product(codomain(c), a, a), true, ifeq(ifeq(product(h, a, d), true, defined(h, a), true), true, defined(h, codomain(c)), true), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.56 = { by axiom 8 (associative_property1) }
% 33.62/4.57 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(ifeq(product(codomain(c), a, a), true, ifeq(true, true, defined(h, codomain(c)), true), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.57 = { by axiom 6 (ifeq_axiom) }
% 33.62/4.57 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(ifeq(product(codomain(c), a, a), true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.57 = { by axiom 6 (ifeq_axiom) R->L }
% 33.62/4.57 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(ifeq(ifeq(true, true, product(codomain(c), a, a), true), true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.57 = { by axiom 6 (ifeq_axiom) R->L }
% 33.62/4.57 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(true, true, product(codomain(c), a, a), true), true), true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.57 = { by axiom 1 (codomain_is_an_identity_map) R->L }
% 33.62/4.57 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(ifeq(ifeq(identity_map(codomain(c)), true, ifeq(true, true, product(codomain(c), a, a), true), true), true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.57 = { by axiom 12 (category_theory_axiom3) R->L }
% 33.62/4.57 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(ifeq(ifeq(identity_map(codomain(c)), true, ifeq(ifeq(product(a, b, c), true, ifeq(defined(codomain(c), c), true, defined(codomain(c), a), true), true), true, product(codomain(c), a, a), true), true), true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.57 = { by axiom 2 (ab_equals_c) }
% 33.62/4.57 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(ifeq(ifeq(identity_map(codomain(c)), true, ifeq(ifeq(true, true, ifeq(defined(codomain(c), c), true, defined(codomain(c), a), true), true), true, product(codomain(c), a, a), true), true), true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.57 = { by axiom 6 (ifeq_axiom) }
% 33.62/4.57 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(ifeq(ifeq(identity_map(codomain(c)), true, ifeq(ifeq(defined(codomain(c), c), true, defined(codomain(c), a), true), true, product(codomain(c), a, a), true), true), true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.57 = { by axiom 5 (mapping_from_codomain_of_x_to_x) }
% 33.62/4.57 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(ifeq(ifeq(identity_map(codomain(c)), true, ifeq(ifeq(true, true, defined(codomain(c), a), true), true, product(codomain(c), a, a), true), true), true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.57 = { by axiom 6 (ifeq_axiom) }
% 33.62/4.57 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(ifeq(ifeq(identity_map(codomain(c)), true, ifeq(defined(codomain(c), a), true, product(codomain(c), a, a), true), true), true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.57 = { by axiom 10 (identity1) }
% 33.62/4.57 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(ifeq(true, true, defined(h, codomain(c)), true), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.57 = { by axiom 6 (ifeq_axiom) }
% 33.62/4.57 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(defined(h, codomain(c)), true, defined(h, c), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.57 = { by axiom 6 (ifeq_axiom) R->L }
% 33.62/4.57 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(true, true, ifeq(defined(h, codomain(c)), true, defined(h, c), true), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.57 = { by axiom 6 (ifeq_axiom) R->L }
% 33.62/4.57 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(true, true, ifeq(true, true, ifeq(defined(h, codomain(c)), true, defined(h, c), true), true), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.57 = { by axiom 1 (codomain_is_an_identity_map) R->L }
% 33.62/4.57 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(identity_map(codomain(c)), true, ifeq(true, true, ifeq(defined(h, codomain(c)), true, defined(h, c), true), true), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.57 = { by axiom 5 (mapping_from_codomain_of_x_to_x) R->L }
% 33.62/4.57 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(ifeq(identity_map(codomain(c)), true, ifeq(defined(codomain(c), c), true, ifeq(defined(h, codomain(c)), true, defined(h, c), true), true), true), true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.57 = { by axiom 13 (category_theory_axiom6) }
% 33.62/4.57 ifeq2(product(g, c, compose(h, c)), true, ifeq2(ifeq(true, true, product(h, c, compose(h, c)), true), true, h, g), g)
% 33.62/4.57 = { by axiom 6 (ifeq_axiom) }
% 33.62/4.57 ifeq2(product(g, c, compose(h, c)), true, ifeq2(product(h, c, compose(h, c)), true, h, g), g)
% 33.62/4.57 = { by axiom 11 (cancellation_for_product) }
% 33.62/4.57 g
% 33.62/4.57 % SZS output end Proof
% 33.62/4.57
% 33.62/4.57 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------