%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : CAT009-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 09:36:23 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.29s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT009-4 : 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 : n006.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 21:12:54 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.29 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
% 0.23/0.29
% 0.23/0.29 % SZS status Unsatisfiable
% 0.23/0.29
% 0.23/0.29 % SZS output start Proof
% 0.23/0.29 Axiom 1 (ab_exists): there_exists(compose(a, b)) = true.
% 0.23/0.29 Axiom 2 (compose_domain): compose(X, domain(X)) = X.
% 0.23/0.29 Axiom 3 (associativity_of_compose): compose(X, compose(Y, Z)) = compose(compose(X, Y), Z).
% 0.23/0.29 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.23/0.29 Axiom 5 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.23/0.29 Axiom 6 (codomain_has_elements): ifeq(there_exists(codomain(X)), true, there_exists(X), true) = true.
% 0.23/0.29 Axiom 7 (composition_implies_domain): ifeq(there_exists(compose(X, Y)), true, there_exists(domain(X)), true) = true.
% 0.23/0.29 Axiom 8 (domain_codomain_composition1): ifeq2(there_exists(compose(X, Y)), true, domain(X), codomain(Y)) = codomain(Y).
% 0.23/0.29
% 0.23/0.29 Lemma 9: compose(X, domain(domain(X))) = X.
% 0.23/0.29 Proof:
% 0.23/0.29 compose(X, domain(domain(X)))
% 0.23/0.29 = { by axiom 2 (compose_domain) R->L }
% 0.23/0.29 compose(compose(X, domain(X)), domain(domain(X)))
% 0.23/0.29 = { by axiom 3 (associativity_of_compose) R->L }
% 0.23/0.29 compose(X, compose(domain(X), domain(domain(X))))
% 0.23/0.29 = { by axiom 2 (compose_domain) }
% 0.23/0.29 compose(X, domain(X))
% 0.23/0.29 = { by axiom 2 (compose_domain) }
% 0.23/0.29 X
% 0.23/0.29
% 0.23/0.29 Goal 1 (prove_domain_of_ab_equals_domain_of_b): domain(compose(a, b)) = domain(b).
% 0.23/0.29 Proof:
% 0.23/0.29 domain(compose(a, b))
% 0.23/0.29 = { by axiom 5 (ifeq_axiom) R->L }
% 0.23/0.29 ifeq2(true, true, domain(compose(a, b)), codomain(domain(domain(b))))
% 0.23/0.29 = { by axiom 1 (ab_exists) R->L }
% 0.23/0.29 ifeq2(there_exists(compose(a, b)), true, domain(compose(a, b)), codomain(domain(domain(b))))
% 0.23/0.29 = { by lemma 9 R->L }
% 0.23/0.29 ifeq2(there_exists(compose(a, compose(b, domain(domain(b))))), true, domain(compose(a, b)), codomain(domain(domain(b))))
% 0.23/0.29 = { by axiom 3 (associativity_of_compose) }
% 0.23/0.29 ifeq2(there_exists(compose(compose(a, b), domain(domain(b)))), true, domain(compose(a, b)), codomain(domain(domain(b))))
% 0.23/0.29 = { by axiom 8 (domain_codomain_composition1) }
% 0.23/0.29 codomain(domain(domain(b)))
% 0.23/0.29 = { by axiom 8 (domain_codomain_composition1) R->L }
% 0.23/0.29 ifeq2(there_exists(compose(b, domain(domain(b)))), true, domain(b), codomain(domain(domain(b))))
% 0.23/0.29 = { by lemma 9 }
% 0.23/0.29 ifeq2(there_exists(b), true, domain(b), codomain(domain(domain(b))))
% 0.23/0.29 = { by axiom 4 (ifeq_axiom) R->L }
% 0.23/0.29 ifeq2(ifeq(true, true, there_exists(b), true), true, domain(b), codomain(domain(domain(b))))
% 0.23/0.29 = { by axiom 7 (composition_implies_domain) R->L }
% 0.23/0.29 ifeq2(ifeq(ifeq(there_exists(compose(a, b)), true, there_exists(domain(a)), true), true, there_exists(b), true), true, domain(b), codomain(domain(domain(b))))
% 0.23/0.29 = { by axiom 1 (ab_exists) }
% 0.23/0.29 ifeq2(ifeq(ifeq(true, true, there_exists(domain(a)), true), true, there_exists(b), true), true, domain(b), codomain(domain(domain(b))))
% 0.23/0.29 = { by axiom 4 (ifeq_axiom) }
% 0.23/0.29 ifeq2(ifeq(there_exists(domain(a)), true, there_exists(b), true), true, domain(b), codomain(domain(domain(b))))
% 0.23/0.29 = { by axiom 5 (ifeq_axiom) R->L }
% 0.23/0.29 ifeq2(ifeq(there_exists(ifeq2(true, true, domain(a), codomain(b))), true, there_exists(b), true), true, domain(b), codomain(domain(domain(b))))
% 0.23/0.29 = { by axiom 1 (ab_exists) R->L }
% 0.23/0.29 ifeq2(ifeq(there_exists(ifeq2(there_exists(compose(a, b)), true, domain(a), codomain(b))), true, there_exists(b), true), true, domain(b), codomain(domain(domain(b))))
% 0.23/0.29 = { by axiom 8 (domain_codomain_composition1) }
% 0.23/0.29 ifeq2(ifeq(there_exists(codomain(b)), true, there_exists(b), true), true, domain(b), codomain(domain(domain(b))))
% 0.23/0.29 = { by axiom 6 (codomain_has_elements) }
% 0.23/0.29 ifeq2(true, true, domain(b), codomain(domain(domain(b))))
% 0.23/0.29 = { by axiom 5 (ifeq_axiom) }
% 0.23/0.29 domain(b)
% 0.23/0.29 % SZS output end Proof
% 0.23/0.29
% 0.23/0.29 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------