%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : CAT012-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 0.21s 0.28s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT012-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n010.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 21:13:47 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.28 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
% 0.21/0.28
% 0.21/0.28 % SZS status Unsatisfiable
% 0.21/0.28
% 0.21/0.28 % SZS output start Proof
% 0.21/0.28 Axiom 1 (domain_is_an_identity_map): identity_map(domain(X)) = true.
% 0.21/0.28 Axiom 2 (mapping_from_codomain_of_x_to_x): defined(codomain(X), X) = true.
% 0.21/0.28 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.21/0.28 Axiom 4 (product_on_codomain): product(codomain(X), X, X) = true.
% 0.21/0.28 Axiom 5 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.21/0.28 Axiom 6 (identity2): ifeq(identity_map(X), true, ifeq(defined(Y, X), true, product(Y, X, Y), true), true) = true.
% 0.21/0.28 Axiom 7 (composition_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 0.21/0.28
% 0.21/0.28 Goal 1 (prove_codomain_of_domain_is_domain): codomain(domain(a)) = domain(a).
% 0.21/0.28 Proof:
% 0.21/0.28 codomain(domain(a))
% 0.21/0.28 = { by axiom 5 (ifeq_axiom) R->L }
% 0.21/0.28 ifeq2(true, true, codomain(domain(a)), domain(a))
% 0.21/0.28 = { by axiom 6 (identity2) R->L }
% 0.21/0.28 ifeq2(ifeq(identity_map(domain(a)), true, ifeq(defined(codomain(domain(a)), domain(a)), true, product(codomain(domain(a)), domain(a), codomain(domain(a))), true), true), true, codomain(domain(a)), domain(a))
% 0.21/0.28 = { by axiom 2 (mapping_from_codomain_of_x_to_x) }
% 0.21/0.28 ifeq2(ifeq(identity_map(domain(a)), true, ifeq(true, true, product(codomain(domain(a)), domain(a), codomain(domain(a))), true), true), true, codomain(domain(a)), domain(a))
% 0.21/0.28 = { by axiom 3 (ifeq_axiom) }
% 0.21/0.28 ifeq2(ifeq(identity_map(domain(a)), true, product(codomain(domain(a)), domain(a), codomain(domain(a))), true), true, codomain(domain(a)), domain(a))
% 0.21/0.28 = { by axiom 1 (domain_is_an_identity_map) }
% 0.21/0.28 ifeq2(ifeq(true, true, product(codomain(domain(a)), domain(a), codomain(domain(a))), true), true, codomain(domain(a)), domain(a))
% 0.21/0.28 = { by axiom 3 (ifeq_axiom) }
% 0.21/0.28 ifeq2(product(codomain(domain(a)), domain(a), codomain(domain(a))), true, codomain(domain(a)), domain(a))
% 0.21/0.28 = { by axiom 5 (ifeq_axiom) R->L }
% 0.21/0.28 ifeq2(true, true, ifeq2(product(codomain(domain(a)), domain(a), codomain(domain(a))), true, codomain(domain(a)), domain(a)), domain(a))
% 0.21/0.28 = { by axiom 4 (product_on_codomain) R->L }
% 0.21/0.28 ifeq2(product(codomain(domain(a)), domain(a), domain(a)), true, ifeq2(product(codomain(domain(a)), domain(a), codomain(domain(a))), true, codomain(domain(a)), domain(a)), domain(a))
% 0.21/0.28 = { by axiom 7 (composition_is_well_defined) }
% 0.21/0.28 domain(a)
% 0.21/0.28 % SZS output end Proof
% 0.21/0.28
% 0.21/0.28 RESULT: Unsatisfiable (the axioms are contradictory).
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