%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : CAT018-4 : 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 09:36:25 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.27s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT018-4 : 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 : n006.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 21:13:24 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.27 Command-line arguments: --flatten --complete-subsets
% 0.19/0.27
% 0.19/0.27 % SZS status Unsatisfiable
% 0.19/0.27
% 0.19/0.28 % SZS output start Proof
% 0.19/0.28 Axiom 1 (assume_ab_exists): there_exists(compose(a, b)) = true.
% 0.19/0.28 Axiom 2 (assume_bc_exists): there_exists(compose(b, c)) = true.
% 0.19/0.28 Axiom 3 (compose_domain): compose(X, domain(X)) = X.
% 0.19/0.28 Axiom 4 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 0.19/0.28 Axiom 5 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.19/0.28 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.19/0.28 Axiom 7 (associativity_of_compose): compose(X, compose(Y, Z)) = compose(compose(X, Y), Z).
% 0.19/0.28 Axiom 8 (codomain_has_elements): ifeq(there_exists(codomain(X)), true, there_exists(X), true) = true.
% 0.19/0.28 Axiom 9 (composition_implies_domain): ifeq(there_exists(compose(X, Y)), true, there_exists(domain(X)), true) = true.
% 0.19/0.28 Axiom 10 (domain_codomain_composition1): ifeq2(there_exists(compose(X, Y)), true, domain(X), codomain(Y)) = codomain(Y).
% 0.19/0.28 Axiom 11 (domain_codomain_composition2): ifeq(there_exists(domain(X)), true, ifeq3(domain(X), codomain(Y), there_exists(compose(X, Y)), true), true) = true.
% 0.19/0.28
% 0.19/0.28 Lemma 12: there_exists(compose(b, c)) = there_exists(compose(a, b)).
% 0.19/0.28 Proof:
% 0.19/0.28 there_exists(compose(b, c))
% 0.19/0.28 = { by axiom 2 (assume_bc_exists) }
% 0.19/0.28 true
% 0.19/0.28 = { by axiom 1 (assume_ab_exists) R->L }
% 0.19/0.28 there_exists(compose(a, b))
% 0.19/0.28
% 0.19/0.28 Lemma 13: ifeq2(there_exists(compose(X, Y)), there_exists(compose(a, b)), domain(X), codomain(Y)) = codomain(Y).
% 0.19/0.28 Proof:
% 0.19/0.28 ifeq2(there_exists(compose(X, Y)), there_exists(compose(a, b)), domain(X), codomain(Y))
% 0.19/0.28 = { by axiom 1 (assume_ab_exists) }
% 0.19/0.28 ifeq2(there_exists(compose(X, Y)), true, domain(X), codomain(Y))
% 0.19/0.28 = { by axiom 10 (domain_codomain_composition1) }
% 0.19/0.28 codomain(Y)
% 0.19/0.28
% 0.19/0.28 Lemma 14: domain(b) = codomain(c).
% 0.19/0.28 Proof:
% 0.19/0.28 domain(b)
% 0.19/0.28 = { by axiom 5 (ifeq_axiom) R->L }
% 0.19/0.28 ifeq2(there_exists(compose(a, b)), there_exists(compose(a, b)), domain(b), codomain(c))
% 0.19/0.28 = { by lemma 12 R->L }
% 0.19/0.28 ifeq2(there_exists(compose(b, c)), there_exists(compose(a, b)), domain(b), codomain(c))
% 0.19/0.28 = { by lemma 13 }
% 0.19/0.28 codomain(c)
% 0.19/0.28
% 0.19/0.28 Lemma 15: ifeq(there_exists(compose(X, Y)), there_exists(compose(a, b)), there_exists(domain(X)), there_exists(compose(a, b))) = there_exists(compose(a, b)).
% 0.19/0.28 Proof:
% 0.19/0.28 ifeq(there_exists(compose(X, Y)), there_exists(compose(a, b)), there_exists(domain(X)), there_exists(compose(a, b)))
% 0.19/0.28 = { by axiom 1 (assume_ab_exists) }
% 0.19/0.28 ifeq(there_exists(compose(X, Y)), true, there_exists(domain(X)), there_exists(compose(a, b)))
% 0.19/0.28 = { by axiom 1 (assume_ab_exists) }
% 0.19/0.28 ifeq(there_exists(compose(X, Y)), true, there_exists(domain(X)), true)
% 0.19/0.28 = { by axiom 9 (composition_implies_domain) }
% 0.19/0.28 true
% 0.19/0.28 = { by axiom 1 (assume_ab_exists) R->L }
% 0.19/0.28 there_exists(compose(a, b))
% 0.19/0.28
% 0.19/0.28 Lemma 16: domain(compose(a, b)) = codomain(c).
% 0.19/0.28 Proof:
% 0.19/0.28 domain(compose(a, b))
% 0.19/0.28 = { by axiom 5 (ifeq_axiom) R->L }
% 0.19/0.28 ifeq2(there_exists(compose(a, b)), there_exists(compose(a, b)), domain(compose(a, b)), codomain(codomain(c)))
% 0.19/0.28 = { by axiom 3 (compose_domain) R->L }
% 0.19/0.28 ifeq2(there_exists(compose(a, compose(b, domain(b)))), there_exists(compose(a, b)), domain(compose(a, b)), codomain(codomain(c)))
% 0.19/0.28 = { by axiom 7 (associativity_of_compose) }
% 0.19/0.28 ifeq2(there_exists(compose(compose(a, b), domain(b))), there_exists(compose(a, b)), domain(compose(a, b)), codomain(codomain(c)))
% 0.19/0.28 = { by lemma 14 }
% 0.19/0.28 ifeq2(there_exists(compose(compose(a, b), codomain(c))), there_exists(compose(a, b)), domain(compose(a, b)), codomain(codomain(c)))
% 0.19/0.28 = { by lemma 13 }
% 0.19/0.28 codomain(codomain(c))
% 0.19/0.28 = { by lemma 13 R->L }
% 0.19/0.28 ifeq2(there_exists(compose(b, codomain(c))), there_exists(compose(a, b)), domain(b), codomain(codomain(c)))
% 0.19/0.28 = { by lemma 14 R->L }
% 0.19/0.28 ifeq2(there_exists(compose(b, domain(b))), there_exists(compose(a, b)), domain(b), codomain(codomain(c)))
% 0.19/0.28 = { by axiom 3 (compose_domain) }
% 0.19/0.28 ifeq2(there_exists(b), there_exists(compose(a, b)), domain(b), codomain(codomain(c)))
% 0.19/0.28 = { by axiom 6 (ifeq_axiom) R->L }
% 0.19/0.28 ifeq2(ifeq(there_exists(compose(a, b)), there_exists(compose(a, b)), there_exists(b), there_exists(compose(a, b))), there_exists(compose(a, b)), domain(b), codomain(codomain(c)))
% 0.19/0.28 = { by lemma 15 R->L }
% 0.19/0.28 ifeq2(ifeq(ifeq(there_exists(compose(a, b)), there_exists(compose(a, b)), there_exists(domain(a)), there_exists(compose(a, b))), there_exists(compose(a, b)), there_exists(b), there_exists(compose(a, b))), there_exists(compose(a, b)), domain(b), codomain(codomain(c)))
% 0.19/0.28 = { by axiom 6 (ifeq_axiom) }
% 0.19/0.28 ifeq2(ifeq(there_exists(domain(a)), there_exists(compose(a, b)), there_exists(b), there_exists(compose(a, b))), there_exists(compose(a, b)), domain(b), codomain(codomain(c)))
% 0.19/0.28 = { by axiom 5 (ifeq_axiom) R->L }
% 0.19/0.28 ifeq2(ifeq(there_exists(ifeq2(there_exists(compose(a, b)), there_exists(compose(a, b)), domain(a), codomain(b))), there_exists(compose(a, b)), there_exists(b), there_exists(compose(a, b))), there_exists(compose(a, b)), domain(b), codomain(codomain(c)))
% 0.19/0.28 = { by lemma 13 }
% 0.19/0.28 ifeq2(ifeq(there_exists(codomain(b)), there_exists(compose(a, b)), there_exists(b), there_exists(compose(a, b))), there_exists(compose(a, b)), domain(b), codomain(codomain(c)))
% 0.19/0.28 = { by axiom 1 (assume_ab_exists) }
% 0.19/0.28 ifeq2(ifeq(there_exists(codomain(b)), true, there_exists(b), there_exists(compose(a, b))), there_exists(compose(a, b)), domain(b), codomain(codomain(c)))
% 0.19/0.28 = { by axiom 1 (assume_ab_exists) }
% 0.19/0.28 ifeq2(ifeq(there_exists(codomain(b)), true, there_exists(b), true), there_exists(compose(a, b)), domain(b), codomain(codomain(c)))
% 0.19/0.28 = { by axiom 8 (codomain_has_elements) }
% 0.19/0.28 ifeq2(true, there_exists(compose(a, b)), domain(b), codomain(codomain(c)))
% 0.19/0.28 = { by axiom 1 (assume_ab_exists) R->L }
% 0.19/0.28 ifeq2(there_exists(compose(a, b)), there_exists(compose(a, b)), domain(b), codomain(codomain(c)))
% 0.19/0.28 = { by axiom 5 (ifeq_axiom) }
% 0.19/0.28 domain(b)
% 0.19/0.28 = { by lemma 14 }
% 0.19/0.28 codomain(c)
% 0.19/0.28
% 0.19/0.28 Goal 1 (prove_a_bc_exists): there_exists(compose(a, compose(b, c))) = true.
% 0.19/0.28 Proof:
% 0.19/0.28 there_exists(compose(a, compose(b, c)))
% 0.19/0.28 = { by axiom 7 (associativity_of_compose) }
% 0.19/0.28 there_exists(compose(compose(a, b), c))
% 0.19/0.28 = { by axiom 4 (ifeq_axiom) R->L }
% 0.19/0.28 ifeq3(codomain(c), codomain(c), there_exists(compose(compose(a, b), c)), there_exists(compose(a, b)))
% 0.19/0.28 = { by lemma 16 R->L }
% 0.19/0.28 ifeq3(domain(compose(a, b)), codomain(c), there_exists(compose(compose(a, b), c)), there_exists(compose(a, b)))
% 0.19/0.28 = { by axiom 6 (ifeq_axiom) R->L }
% 0.19/0.28 ifeq(there_exists(compose(a, b)), there_exists(compose(a, b)), ifeq3(domain(compose(a, b)), codomain(c), there_exists(compose(compose(a, b), c)), there_exists(compose(a, b))), there_exists(compose(a, b)))
% 0.19/0.28 = { by lemma 15 R->L }
% 0.19/0.28 ifeq(ifeq(there_exists(compose(b, c)), there_exists(compose(a, b)), there_exists(domain(b)), there_exists(compose(a, b))), there_exists(compose(a, b)), ifeq3(domain(compose(a, b)), codomain(c), there_exists(compose(compose(a, b), c)), there_exists(compose(a, b))), there_exists(compose(a, b)))
% 0.19/0.28 = { by lemma 12 }
% 0.19/0.28 ifeq(ifeq(there_exists(compose(a, b)), there_exists(compose(a, b)), there_exists(domain(b)), there_exists(compose(a, b))), there_exists(compose(a, b)), ifeq3(domain(compose(a, b)), codomain(c), there_exists(compose(compose(a, b), c)), there_exists(compose(a, b))), there_exists(compose(a, b)))
% 0.19/0.28 = { by axiom 6 (ifeq_axiom) }
% 0.19/0.28 ifeq(there_exists(domain(b)), there_exists(compose(a, b)), ifeq3(domain(compose(a, b)), codomain(c), there_exists(compose(compose(a, b), c)), there_exists(compose(a, b))), there_exists(compose(a, b)))
% 0.19/0.28 = { by lemma 14 }
% 0.19/0.28 ifeq(there_exists(codomain(c)), there_exists(compose(a, b)), ifeq3(domain(compose(a, b)), codomain(c), there_exists(compose(compose(a, b), c)), there_exists(compose(a, b))), there_exists(compose(a, b)))
% 0.19/0.28 = { by lemma 16 R->L }
% 0.19/0.28 ifeq(there_exists(domain(compose(a, b))), there_exists(compose(a, b)), ifeq3(domain(compose(a, b)), codomain(c), there_exists(compose(compose(a, b), c)), there_exists(compose(a, b))), there_exists(compose(a, b)))
% 0.19/0.28 = { by axiom 1 (assume_ab_exists) }
% 0.19/0.28 ifeq(there_exists(domain(compose(a, b))), true, ifeq3(domain(compose(a, b)), codomain(c), there_exists(compose(compose(a, b), c)), there_exists(compose(a, b))), there_exists(compose(a, b)))
% 0.19/0.28 = { by axiom 1 (assume_ab_exists) }
% 0.19/0.28 ifeq(there_exists(domain(compose(a, b))), true, ifeq3(domain(compose(a, b)), codomain(c), there_exists(compose(compose(a, b), c)), true), there_exists(compose(a, b)))
% 0.19/0.28 = { by axiom 1 (assume_ab_exists) }
% 0.19/0.28 ifeq(there_exists(domain(compose(a, b))), true, ifeq3(domain(compose(a, b)), codomain(c), there_exists(compose(compose(a, b), c)), true), true)
% 0.19/0.28 = { by axiom 11 (domain_codomain_composition2) }
% 0.19/0.28 true
% 0.19/0.28 % SZS output end Proof
% 0.19/0.28
% 0.19/0.28 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------