%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : CAT014-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 0.08s 0.25s
% Output : Proof 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT014-4 : 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 : n020.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
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 21:14:34 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.25 Command-line arguments: --flatten --complete-subsets
% 0.08/0.25
% 0.08/0.25 % SZS status Unsatisfiable
% 0.08/0.25
% 0.08/0.25 % SZS output start Proof
% 0.08/0.25 Axiom 1 (assume_codomain_exists): there_exists(codomain(a)) = true.
% 0.08/0.25 Axiom 2 (compose_codomain): compose(codomain(X), X) = X.
% 0.08/0.25 Axiom 3 (compose_domain): compose(X, domain(X)) = X.
% 0.08/0.25 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.08/0.25 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.08/0.25 Axiom 6 (codomain_has_elements): ifeq(there_exists(codomain(X)), true, there_exists(X), true) = true.
% 0.08/0.25 Axiom 7 (domain_codomain_composition1): ifeq2(there_exists(compose(X, Y)), true, domain(X), codomain(Y)) = codomain(Y).
% 0.08/0.25
% 0.08/0.25 Lemma 8: ifeq2(there_exists(compose(X, Y)), there_exists(codomain(a)), domain(X), codomain(Y)) = codomain(Y).
% 0.08/0.25 Proof:
% 0.08/0.25 ifeq2(there_exists(compose(X, Y)), there_exists(codomain(a)), domain(X), codomain(Y))
% 0.08/0.25 = { by axiom 1 (assume_codomain_exists) }
% 0.08/0.25 ifeq2(there_exists(compose(X, Y)), true, domain(X), codomain(Y))
% 0.08/0.25 = { by axiom 7 (domain_codomain_composition1) }
% 0.08/0.25 codomain(Y)
% 0.08/0.25
% 0.08/0.25 Lemma 9: domain(codomain(a)) = codomain(a).
% 0.08/0.25 Proof:
% 0.08/0.25 domain(codomain(a))
% 0.08/0.25 = { by axiom 4 (ifeq_axiom) R->L }
% 0.08/0.25 ifeq2(there_exists(codomain(a)), there_exists(codomain(a)), domain(codomain(a)), codomain(a))
% 0.08/0.25 = { by axiom 1 (assume_codomain_exists) }
% 0.08/0.25 ifeq2(true, there_exists(codomain(a)), domain(codomain(a)), codomain(a))
% 0.08/0.25 = { by axiom 6 (codomain_has_elements) R->L }
% 0.08/0.25 ifeq2(ifeq(there_exists(codomain(a)), true, there_exists(a), true), there_exists(codomain(a)), domain(codomain(a)), codomain(a))
% 0.08/0.25 = { by axiom 1 (assume_codomain_exists) R->L }
% 0.08/0.25 ifeq2(ifeq(there_exists(codomain(a)), true, there_exists(a), there_exists(codomain(a))), there_exists(codomain(a)), domain(codomain(a)), codomain(a))
% 0.08/0.25 = { by axiom 1 (assume_codomain_exists) R->L }
% 0.08/0.25 ifeq2(ifeq(there_exists(codomain(a)), there_exists(codomain(a)), there_exists(a), there_exists(codomain(a))), there_exists(codomain(a)), domain(codomain(a)), codomain(a))
% 0.08/0.25 = { by axiom 5 (ifeq_axiom) }
% 0.08/0.25 ifeq2(there_exists(a), there_exists(codomain(a)), domain(codomain(a)), codomain(a))
% 0.08/0.25 = { by axiom 2 (compose_codomain) R->L }
% 0.08/0.25 ifeq2(there_exists(compose(codomain(a), a)), there_exists(codomain(a)), domain(codomain(a)), codomain(a))
% 0.08/0.25 = { by lemma 8 }
% 0.08/0.25 codomain(a)
% 0.08/0.25
% 0.08/0.25 Goal 1 (prove_codomain_is_idempotent): codomain(codomain(a)) = codomain(a).
% 0.08/0.25 Proof:
% 0.08/0.25 codomain(codomain(a))
% 0.08/0.25 = { by lemma 8 R->L }
% 0.08/0.25 ifeq2(there_exists(compose(codomain(a), codomain(a))), there_exists(codomain(a)), domain(codomain(a)), codomain(codomain(a)))
% 0.08/0.25 = { by lemma 9 R->L }
% 0.08/0.25 ifeq2(there_exists(compose(codomain(a), domain(codomain(a)))), there_exists(codomain(a)), domain(codomain(a)), codomain(codomain(a)))
% 0.08/0.25 = { by axiom 3 (compose_domain) }
% 0.08/0.25 ifeq2(there_exists(codomain(a)), there_exists(codomain(a)), domain(codomain(a)), codomain(codomain(a)))
% 0.08/0.25 = { by axiom 4 (ifeq_axiom) }
% 0.08/0.25 domain(codomain(a))
% 0.08/0.25 = { by lemma 9 }
% 0.08/0.25 codomain(a)
% 0.08/0.25 % SZS output end Proof
% 0.08/0.25
% 0.08/0.25 RESULT: Unsatisfiable (the axioms are contradictory).
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