%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : CAT005-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 0.20s 0.27s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT005-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n001.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 21:18:48 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.27 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
% 0.20/0.27
% 0.20/0.27 % SZS status Unsatisfiable
% 0.20/0.27
% 0.20/0.28 % SZS output start Proof
% 0.20/0.28 Axiom 1 (ad_exists): there_exists(compose(a, d)) = true.
% 0.20/0.28 Axiom 2 (compose_codomain): compose(codomain(X), X) = X.
% 0.20/0.28 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.20/0.28 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.20/0.28 Axiom 5 (codomain_has_elements): ifeq(there_exists(codomain(X)), true, there_exists(X), true) = true.
% 0.20/0.28 Axiom 6 (composition_implies_domain): ifeq(there_exists(compose(X, Y)), true, there_exists(domain(X)), true) = true.
% 0.20/0.28 Axiom 7 (domain_codomain_composition1): ifeq2(there_exists(compose(X, Y)), true, domain(X), codomain(Y)) = codomain(Y).
% 0.20/0.28 Axiom 8 (xd_equals_x): ifeq2(there_exists(compose(X, d)), true, compose(X, d), X) = X.
% 0.20/0.28
% 0.20/0.28 Lemma 9: codomain(d) = domain(a).
% 0.20/0.28 Proof:
% 0.20/0.28 codomain(d)
% 0.20/0.28 = { by axiom 7 (domain_codomain_composition1) R->L }
% 0.20/0.28 ifeq2(there_exists(compose(a, d)), true, domain(a), codomain(d))
% 0.20/0.28 = { by axiom 1 (ad_exists) }
% 0.20/0.28 ifeq2(true, true, domain(a), codomain(d))
% 0.20/0.28 = { by axiom 4 (ifeq_axiom) }
% 0.20/0.28 domain(a)
% 0.20/0.28
% 0.20/0.28 Lemma 10: compose(domain(a), d) = d.
% 0.20/0.28 Proof:
% 0.20/0.28 compose(domain(a), d)
% 0.20/0.28 = { by lemma 9 R->L }
% 0.20/0.28 compose(codomain(d), d)
% 0.20/0.28 = { by axiom 2 (compose_codomain) }
% 0.20/0.28 d
% 0.20/0.28
% 0.20/0.28 Goal 1 (prove_domain_of_a_is_d): domain(a) = d.
% 0.20/0.28 Proof:
% 0.20/0.28 domain(a)
% 0.20/0.28 = { by axiom 8 (xd_equals_x) R->L }
% 0.20/0.28 ifeq2(there_exists(compose(domain(a), d)), true, compose(domain(a), d), domain(a))
% 0.20/0.28 = { by lemma 10 }
% 0.20/0.28 ifeq2(there_exists(d), true, compose(domain(a), d), domain(a))
% 0.20/0.28 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.28 ifeq2(ifeq(true, true, there_exists(d), true), true, compose(domain(a), d), domain(a))
% 0.20/0.28 = { by axiom 6 (composition_implies_domain) R->L }
% 0.20/0.28 ifeq2(ifeq(ifeq(there_exists(compose(a, d)), true, there_exists(domain(a)), true), true, there_exists(d), true), true, compose(domain(a), d), domain(a))
% 0.20/0.28 = { by axiom 1 (ad_exists) }
% 0.20/0.28 ifeq2(ifeq(ifeq(true, true, there_exists(domain(a)), true), true, there_exists(d), true), true, compose(domain(a), d), domain(a))
% 0.20/0.28 = { by axiom 3 (ifeq_axiom) }
% 0.20/0.28 ifeq2(ifeq(there_exists(domain(a)), true, there_exists(d), true), true, compose(domain(a), d), domain(a))
% 0.20/0.28 = { by lemma 9 R->L }
% 0.20/0.28 ifeq2(ifeq(there_exists(codomain(d)), true, there_exists(d), true), true, compose(domain(a), d), domain(a))
% 0.20/0.28 = { by axiom 5 (codomain_has_elements) }
% 0.20/0.28 ifeq2(true, true, compose(domain(a), d), domain(a))
% 0.20/0.28 = { by axiom 4 (ifeq_axiom) }
% 0.20/0.28 compose(domain(a), d)
% 0.20/0.28 = { by lemma 10 }
% 0.20/0.28 d
% 0.20/0.28 % SZS output end Proof
% 0.20/0.28
% 0.20/0.28 RESULT: Unsatisfiable (the axioms are contradictory).
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