%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : CAT013-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 09:36:24 AM UTC 2026
% Result : Unsatisfiable 0.22s 0.29s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n004.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 21:13:22 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.19 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.29 Command-line arguments: --flatten --complete-subsets
% 0.22/0.29
% 0.22/0.29 % SZS status Unsatisfiable
% 0.22/0.29
% 0.22/0.29 % SZS output start Proof
% 0.22/0.29 Axiom 1 (codomain_is_an_identity_map): identity_map(codomain(X)) = true.
% 0.22/0.29 Axiom 2 (mapping_from_x_to_its_domain): defined(X, domain(X)) = true.
% 0.22/0.29 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.22/0.29 Axiom 4 (product_on_domain): product(X, domain(X), X) = true.
% 0.22/0.29 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.22/0.29 Axiom 6 (composition_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 0.22/0.29 Axiom 7 (identity1): ifeq(identity_map(X), true, ifeq(defined(X, Y), true, product(X, Y, Y), true), true) = true.
% 0.22/0.29
% 0.22/0.29 Goal 1 (prove_domain_of_codomain_is_codomain): domain(codomain(a)) = codomain(a).
% 0.22/0.29 Proof:
% 0.22/0.29 domain(codomain(a))
% 0.22/0.29 = { by axiom 6 (composition_is_well_defined) R->L }
% 0.22/0.29 ifeq2(product(codomain(a), domain(codomain(a)), domain(codomain(a))), true, ifeq2(product(codomain(a), domain(codomain(a)), codomain(a)), true, codomain(a), domain(codomain(a))), domain(codomain(a)))
% 0.22/0.29 = { by axiom 4 (product_on_domain) }
% 0.22/0.29 ifeq2(product(codomain(a), domain(codomain(a)), domain(codomain(a))), true, ifeq2(true, true, codomain(a), domain(codomain(a))), domain(codomain(a)))
% 0.22/0.29 = { by axiom 3 (ifeq_axiom) }
% 0.22/0.29 ifeq2(product(codomain(a), domain(codomain(a)), domain(codomain(a))), true, codomain(a), domain(codomain(a)))
% 0.22/0.29 = { by axiom 5 (ifeq_axiom) R->L }
% 0.22/0.29 ifeq2(ifeq(true, true, product(codomain(a), domain(codomain(a)), domain(codomain(a))), true), true, codomain(a), domain(codomain(a)))
% 0.22/0.30 = { by axiom 5 (ifeq_axiom) R->L }
% 0.22/0.30 ifeq2(ifeq(true, true, ifeq(true, true, product(codomain(a), domain(codomain(a)), domain(codomain(a))), true), true), true, codomain(a), domain(codomain(a)))
% 0.22/0.30 = { by axiom 1 (codomain_is_an_identity_map) R->L }
% 0.22/0.30 ifeq2(ifeq(identity_map(codomain(a)), true, ifeq(true, true, product(codomain(a), domain(codomain(a)), domain(codomain(a))), true), true), true, codomain(a), domain(codomain(a)))
% 0.22/0.30 = { by axiom 2 (mapping_from_x_to_its_domain) R->L }
% 0.22/0.30 ifeq2(ifeq(identity_map(codomain(a)), true, ifeq(defined(codomain(a), domain(codomain(a))), true, product(codomain(a), domain(codomain(a)), domain(codomain(a))), true), true), true, codomain(a), domain(codomain(a)))
% 0.22/0.30 = { by axiom 7 (identity1) }
% 0.22/0.30 ifeq2(true, true, codomain(a), domain(codomain(a)))
% 0.22/0.30 = { by axiom 3 (ifeq_axiom) }
% 0.22/0.30 codomain(a)
% 0.22/0.30 % SZS output end Proof
% 0.22/0.30
% 0.22/0.30 RESULT: Unsatisfiable (the axioms are contradictory).
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