%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : CAT006-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 0.22s 0.27s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT006-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n008.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 21:13:54 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.27 Command-line arguments: --no-flatten-goal
% 0.22/0.27
% 0.22/0.27 % SZS status Unsatisfiable
% 0.22/0.27
% 0.22/0.28 % SZS output start Proof
% 0.22/0.28 Axiom 1 (da_exists): there_exists(compose(d, a)) = true.
% 0.22/0.28 Axiom 2 (compose_domain): compose(X, domain(X)) = X.
% 0.22/0.28 Axiom 3 (compose_codomain): compose(codomain(X), X) = X.
% 0.22/0.28 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.22/0.28 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.22/0.28 Axiom 6 (associativity_of_compose): compose(X, compose(Y, Z)) = compose(compose(X, Y), Z).
% 0.22/0.28 Axiom 7 (domain_has_elements): ifeq(there_exists(domain(X)), true, there_exists(X), true) = true.
% 0.22/0.28 Axiom 8 (composition_implies_domain): ifeq(there_exists(compose(X, Y)), true, there_exists(domain(X)), true) = true.
% 0.22/0.28 Axiom 9 (domain_codomain_composition1): ifeq2(there_exists(compose(X, Y)), true, domain(X), codomain(Y)) = codomain(Y).
% 0.22/0.28 Axiom 10 (dx_equals_x): ifeq2(there_exists(compose(d, X)), true, compose(d, X), X) = X.
% 0.22/0.28
% 0.22/0.28 Lemma 11: compose(X, domain(domain(X))) = X.
% 0.22/0.28 Proof:
% 0.22/0.28 compose(X, domain(domain(X)))
% 0.22/0.28 = { by axiom 2 (compose_domain) R->L }
% 0.22/0.28 compose(compose(X, domain(X)), domain(domain(X)))
% 0.22/0.28 = { by axiom 6 (associativity_of_compose) R->L }
% 0.22/0.28 compose(X, compose(domain(X), domain(domain(X))))
% 0.22/0.28 = { by axiom 2 (compose_domain) }
% 0.22/0.28 compose(X, domain(X))
% 0.22/0.28 = { by axiom 2 (compose_domain) }
% 0.22/0.28 X
% 0.22/0.28
% 0.22/0.28 Goal 1 (prove_codomain_of_a_is_d): codomain(a) = d.
% 0.22/0.28 Proof:
% 0.22/0.28 codomain(a)
% 0.22/0.28 = { by axiom 9 (domain_codomain_composition1) R->L }
% 0.22/0.28 ifeq2(there_exists(compose(domain(d), a)), true, domain(domain(d)), codomain(a))
% 0.22/0.28 = { by axiom 4 (ifeq_axiom) R->L }
% 0.22/0.28 ifeq2(there_exists(compose(ifeq2(true, true, domain(d), codomain(a)), a)), true, domain(domain(d)), codomain(a))
% 0.22/0.28 = { by axiom 1 (da_exists) R->L }
% 0.22/0.28 ifeq2(there_exists(compose(ifeq2(there_exists(compose(d, a)), true, domain(d), codomain(a)), a)), true, domain(domain(d)), codomain(a))
% 0.22/0.28 = { by axiom 9 (domain_codomain_composition1) }
% 0.22/0.28 ifeq2(there_exists(compose(codomain(a), a)), true, domain(domain(d)), codomain(a))
% 0.22/0.28 = { by axiom 3 (compose_codomain) }
% 0.22/0.28 ifeq2(there_exists(a), true, domain(domain(d)), codomain(a))
% 0.22/0.28 = { by axiom 10 (dx_equals_x) R->L }
% 0.22/0.28 ifeq2(there_exists(ifeq2(there_exists(compose(d, a)), true, compose(d, a), a)), true, domain(domain(d)), codomain(a))
% 0.22/0.28 = { by axiom 1 (da_exists) }
% 0.22/0.28 ifeq2(there_exists(ifeq2(true, true, compose(d, a), a)), true, domain(domain(d)), codomain(a))
% 0.22/0.28 = { by axiom 4 (ifeq_axiom) }
% 0.22/0.28 ifeq2(there_exists(compose(d, a)), true, domain(domain(d)), codomain(a))
% 0.22/0.28 = { by axiom 1 (da_exists) }
% 0.22/0.28 ifeq2(true, true, domain(domain(d)), codomain(a))
% 0.22/0.28 = { by axiom 4 (ifeq_axiom) }
% 0.22/0.28 domain(domain(d))
% 0.22/0.28 = { by axiom 10 (dx_equals_x) R->L }
% 0.22/0.28 ifeq2(there_exists(compose(d, domain(domain(d)))), true, compose(d, domain(domain(d))), domain(domain(d)))
% 0.22/0.28 = { by lemma 11 }
% 0.22/0.28 ifeq2(there_exists(d), true, compose(d, domain(domain(d))), domain(domain(d)))
% 0.22/0.28 = { by axiom 5 (ifeq_axiom) R->L }
% 0.22/0.28 ifeq2(ifeq(true, true, there_exists(d), true), true, compose(d, domain(domain(d))), domain(domain(d)))
% 0.22/0.28 = { by axiom 8 (composition_implies_domain) R->L }
% 0.22/0.28 ifeq2(ifeq(ifeq(there_exists(compose(d, a)), true, there_exists(domain(d)), true), true, there_exists(d), true), true, compose(d, domain(domain(d))), domain(domain(d)))
% 0.22/0.28 = { by axiom 1 (da_exists) }
% 0.22/0.28 ifeq2(ifeq(ifeq(true, true, there_exists(domain(d)), true), true, there_exists(d), true), true, compose(d, domain(domain(d))), domain(domain(d)))
% 0.22/0.28 = { by axiom 5 (ifeq_axiom) }
% 0.22/0.28 ifeq2(ifeq(there_exists(domain(d)), true, there_exists(d), true), true, compose(d, domain(domain(d))), domain(domain(d)))
% 0.22/0.28 = { by axiom 7 (domain_has_elements) }
% 0.22/0.28 ifeq2(true, true, compose(d, domain(domain(d))), domain(domain(d)))
% 0.22/0.28 = { by axiom 4 (ifeq_axiom) }
% 0.22/0.28 compose(d, domain(domain(d)))
% 0.22/0.28 = { by lemma 11 }
% 0.22/0.28 d
% 0.22/0.28 % SZS output end Proof
% 0.22/0.28
% 0.22/0.28 RESULT: Unsatisfiable (the axioms are contradictory).
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