%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : CAT009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 0.45s 0.36s
% Output : Proof 1.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.15 % Computer : n017.cluster.edu
% 0.10/0.15 % Model : x86_64 x86_64
% 0.10/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.15 % Memory : 8046.5625MB
% 0.10/0.15 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Mon Sep 28 21:08:36 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.45/0.36 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.45/0.36
% 0.45/0.36 % SZS status Unsatisfiable
% 0.45/0.36
% 1.25/0.39 % SZS output start Proof
% 1.25/0.39 Axiom 1 (domain_is_an_identity_map): identity_map(domain(X)) = true.
% 1.25/0.39 Axiom 2 (mapping_from_x_to_its_domain): defined(X, domain(X)) = true.
% 1.25/0.39 Axiom 3 (ba_defined): defined(b, a) = true.
% 1.25/0.39 Axiom 4 (product_on_domain): product(X, domain(X), X) = true.
% 1.25/0.39 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 1.25/0.39 Axiom 6 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 1.25/0.39 Axiom 7 (closure_of_composition): ifeq(defined(X, Y), true, product(X, Y, compose(X, Y)), true) = true.
% 1.25/0.39 Axiom 8 (identity1): ifeq(identity_map(X), true, ifeq(defined(X, Y), true, product(X, Y, Y), true), true) = true.
% 1.25/0.39 Axiom 9 (identity2): ifeq(identity_map(X), true, ifeq(defined(Y, X), true, product(Y, X, Y), true), true) = true.
% 1.25/0.39 Axiom 10 (composition_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 1.25/0.39 Axiom 11 (associative_property2): ifeq(product(X, Y, Z), true, ifeq(defined(Z, W), true, defined(Y, W), true), true) = true.
% 1.25/0.39
% 1.25/0.39 Goal 1 (prove_domain_of_ba_equals_domain_of_a): domain(compose(b, a)) = domain(a).
% 1.25/0.39 Proof:
% 1.25/0.39 domain(compose(b, a))
% 1.25/0.39 = { by axiom 6 (ifeq_axiom) R->L }
% 1.25/0.39 ifeq2(true, true, domain(compose(b, a)), domain(a))
% 1.25/0.39 = { by axiom 9 (identity2) R->L }
% 1.25/0.39 ifeq2(ifeq(identity_map(domain(compose(b, a))), true, ifeq(defined(domain(a), domain(compose(b, a))), true, product(domain(a), domain(compose(b, a)), domain(a)), true), true), true, domain(compose(b, a)), domain(a))
% 1.25/0.39 = { by axiom 5 (ifeq_axiom) R->L }
% 1.25/0.39 ifeq2(ifeq(identity_map(domain(compose(b, a))), true, ifeq(ifeq(true, true, defined(domain(a), domain(compose(b, a))), true), true, product(domain(a), domain(compose(b, a)), domain(a)), true), true), true, domain(compose(b, a)), domain(a))
% 1.25/0.39 = { by axiom 11 (associative_property2) R->L }
% 1.25/0.39 ifeq2(ifeq(identity_map(domain(compose(b, a))), true, ifeq(ifeq(ifeq(product(b, a, compose(b, a)), true, ifeq(defined(compose(b, a), domain(compose(b, a))), true, defined(a, domain(compose(b, a))), true), true), true, defined(domain(a), domain(compose(b, a))), true), true, product(domain(a), domain(compose(b, a)), domain(a)), true), true), true, domain(compose(b, a)), domain(a))
% 1.25/0.39 = { by axiom 5 (ifeq_axiom) R->L }
% 1.25/0.39 ifeq2(ifeq(identity_map(domain(compose(b, a))), true, ifeq(ifeq(ifeq(ifeq(true, true, product(b, a, compose(b, a)), true), true, ifeq(defined(compose(b, a), domain(compose(b, a))), true, defined(a, domain(compose(b, a))), true), true), true, defined(domain(a), domain(compose(b, a))), true), true, product(domain(a), domain(compose(b, a)), domain(a)), true), true), true, domain(compose(b, a)), domain(a))
% 1.25/0.39 = { by axiom 3 (ba_defined) R->L }
% 1.25/0.39 ifeq2(ifeq(identity_map(domain(compose(b, a))), true, ifeq(ifeq(ifeq(ifeq(defined(b, a), true, product(b, a, compose(b, a)), true), true, ifeq(defined(compose(b, a), domain(compose(b, a))), true, defined(a, domain(compose(b, a))), true), true), true, defined(domain(a), domain(compose(b, a))), true), true, product(domain(a), domain(compose(b, a)), domain(a)), true), true), true, domain(compose(b, a)), domain(a))
% 1.25/0.39 = { by axiom 7 (closure_of_composition) }
% 1.25/0.39 ifeq2(ifeq(identity_map(domain(compose(b, a))), true, ifeq(ifeq(ifeq(true, true, ifeq(defined(compose(b, a), domain(compose(b, a))), true, defined(a, domain(compose(b, a))), true), true), true, defined(domain(a), domain(compose(b, a))), true), true, product(domain(a), domain(compose(b, a)), domain(a)), true), true), true, domain(compose(b, a)), domain(a))
% 1.25/0.39 = { by axiom 5 (ifeq_axiom) }
% 1.25/0.39 ifeq2(ifeq(identity_map(domain(compose(b, a))), true, ifeq(ifeq(ifeq(defined(compose(b, a), domain(compose(b, a))), true, defined(a, domain(compose(b, a))), true), true, defined(domain(a), domain(compose(b, a))), true), true, product(domain(a), domain(compose(b, a)), domain(a)), true), true), true, domain(compose(b, a)), domain(a))
% 1.25/0.39 = { by axiom 2 (mapping_from_x_to_its_domain) }
% 1.25/0.40 ifeq2(ifeq(identity_map(domain(compose(b, a))), true, ifeq(ifeq(ifeq(true, true, defined(a, domain(compose(b, a))), true), true, defined(domain(a), domain(compose(b, a))), true), true, product(domain(a), domain(compose(b, a)), domain(a)), true), true), true, domain(compose(b, a)), domain(a))
% 1.25/0.40 = { by axiom 5 (ifeq_axiom) }
% 1.25/0.40 ifeq2(ifeq(identity_map(domain(compose(b, a))), true, ifeq(ifeq(defined(a, domain(compose(b, a))), true, defined(domain(a), domain(compose(b, a))), true), true, product(domain(a), domain(compose(b, a)), domain(a)), true), true), true, domain(compose(b, a)), domain(a))
% 1.25/0.40 = { by axiom 5 (ifeq_axiom) R->L }
% 1.25/0.40 ifeq2(ifeq(identity_map(domain(compose(b, a))), true, ifeq(ifeq(true, true, ifeq(defined(a, domain(compose(b, a))), true, defined(domain(a), domain(compose(b, a))), true), true), true, product(domain(a), domain(compose(b, a)), domain(a)), true), true), true, domain(compose(b, a)), domain(a))
% 1.25/0.40 = { by axiom 4 (product_on_domain) R->L }
% 1.25/0.40 ifeq2(ifeq(identity_map(domain(compose(b, a))), true, ifeq(ifeq(product(a, domain(a), a), true, ifeq(defined(a, domain(compose(b, a))), true, defined(domain(a), domain(compose(b, a))), true), true), true, product(domain(a), domain(compose(b, a)), domain(a)), true), true), true, domain(compose(b, a)), domain(a))
% 1.25/0.40 = { by axiom 11 (associative_property2) }
% 1.25/0.40 ifeq2(ifeq(identity_map(domain(compose(b, a))), true, ifeq(true, true, product(domain(a), domain(compose(b, a)), domain(a)), true), true), true, domain(compose(b, a)), domain(a))
% 1.25/0.40 = { by axiom 1 (domain_is_an_identity_map) }
% 1.25/0.40 ifeq2(ifeq(true, true, ifeq(true, true, product(domain(a), domain(compose(b, a)), domain(a)), true), true), true, domain(compose(b, a)), domain(a))
% 1.25/0.40 = { by axiom 5 (ifeq_axiom) }
% 1.25/0.40 ifeq2(ifeq(true, true, product(domain(a), domain(compose(b, a)), domain(a)), true), true, domain(compose(b, a)), domain(a))
% 1.25/0.40 = { by axiom 5 (ifeq_axiom) }
% 1.25/0.40 ifeq2(product(domain(a), domain(compose(b, a)), domain(a)), true, domain(compose(b, a)), domain(a))
% 1.25/0.40 = { by axiom 6 (ifeq_axiom) R->L }
% 1.25/0.40 ifeq2(product(domain(a), domain(compose(b, a)), domain(a)), true, ifeq2(true, true, domain(compose(b, a)), domain(a)), domain(a))
% 1.25/0.40 = { by axiom 8 (identity1) R->L }
% 1.25/0.40 ifeq2(product(domain(a), domain(compose(b, a)), domain(a)), true, ifeq2(ifeq(identity_map(domain(a)), true, ifeq(defined(domain(a), domain(compose(b, a))), true, product(domain(a), domain(compose(b, a)), domain(compose(b, a))), true), true), true, domain(compose(b, a)), domain(a)), domain(a))
% 1.25/0.40 = { by axiom 5 (ifeq_axiom) R->L }
% 1.25/0.40 ifeq2(product(domain(a), domain(compose(b, a)), domain(a)), true, ifeq2(ifeq(identity_map(domain(a)), true, ifeq(ifeq(true, true, defined(domain(a), domain(compose(b, a))), true), true, product(domain(a), domain(compose(b, a)), domain(compose(b, a))), true), true), true, domain(compose(b, a)), domain(a)), domain(a))
% 1.25/0.40 = { by axiom 11 (associative_property2) R->L }
% 1.25/0.40 ifeq2(product(domain(a), domain(compose(b, a)), domain(a)), true, ifeq2(ifeq(identity_map(domain(a)), true, ifeq(ifeq(ifeq(product(b, a, compose(b, a)), true, ifeq(defined(compose(b, a), domain(compose(b, a))), true, defined(a, domain(compose(b, a))), true), true), true, defined(domain(a), domain(compose(b, a))), true), true, product(domain(a), domain(compose(b, a)), domain(compose(b, a))), true), true), true, domain(compose(b, a)), domain(a)), domain(a))
% 1.25/0.41 = { by axiom 5 (ifeq_axiom) R->L }
% 1.25/0.41 ifeq2(product(domain(a), domain(compose(b, a)), domain(a)), true, ifeq2(ifeq(identity_map(domain(a)), true, ifeq(ifeq(ifeq(ifeq(true, true, product(b, a, compose(b, a)), true), true, ifeq(defined(compose(b, a), domain(compose(b, a))), true, defined(a, domain(compose(b, a))), true), true), true, defined(domain(a), domain(compose(b, a))), true), true, product(domain(a), domain(compose(b, a)), domain(compose(b, a))), true), true), true, domain(compose(b, a)), domain(a)), domain(a))
% 1.25/0.41 = { by axiom 3 (ba_defined) R->L }
% 1.25/0.41 ifeq2(product(domain(a), domain(compose(b, a)), domain(a)), true, ifeq2(ifeq(identity_map(domain(a)), true, ifeq(ifeq(ifeq(ifeq(defined(b, a), true, product(b, a, compose(b, a)), true), true, ifeq(defined(compose(b, a), domain(compose(b, a))), true, defined(a, domain(compose(b, a))), true), true), true, defined(domain(a), domain(compose(b, a))), true), true, product(domain(a), domain(compose(b, a)), domain(compose(b, a))), true), true), true, domain(compose(b, a)), domain(a)), domain(a))
% 1.25/0.41 = { by axiom 7 (closure_of_composition) }
% 1.25/0.41 ifeq2(product(domain(a), domain(compose(b, a)), domain(a)), true, ifeq2(ifeq(identity_map(domain(a)), true, ifeq(ifeq(ifeq(true, true, ifeq(defined(compose(b, a), domain(compose(b, a))), true, defined(a, domain(compose(b, a))), true), true), true, defined(domain(a), domain(compose(b, a))), true), true, product(domain(a), domain(compose(b, a)), domain(compose(b, a))), true), true), true, domain(compose(b, a)), domain(a)), domain(a))
% 1.25/0.41 = { by axiom 5 (ifeq_axiom) }
% 1.25/0.41 ifeq2(product(domain(a), domain(compose(b, a)), domain(a)), true, ifeq2(ifeq(identity_map(domain(a)), true, ifeq(ifeq(ifeq(defined(compose(b, a), domain(compose(b, a))), true, defined(a, domain(compose(b, a))), true), true, defined(domain(a), domain(compose(b, a))), true), true, product(domain(a), domain(compose(b, a)), domain(compose(b, a))), true), true), true, domain(compose(b, a)), domain(a)), domain(a))
% 1.25/0.41 = { by axiom 2 (mapping_from_x_to_its_domain) }
% 1.25/0.41 ifeq2(product(domain(a), domain(compose(b, a)), domain(a)), true, ifeq2(ifeq(identity_map(domain(a)), true, ifeq(ifeq(ifeq(true, true, defined(a, domain(compose(b, a))), true), true, defined(domain(a), domain(compose(b, a))), true), true, product(domain(a), domain(compose(b, a)), domain(compose(b, a))), true), true), true, domain(compose(b, a)), domain(a)), domain(a))
% 1.25/0.41 = { by axiom 5 (ifeq_axiom) }
% 1.25/0.41 ifeq2(product(domain(a), domain(compose(b, a)), domain(a)), true, ifeq2(ifeq(identity_map(domain(a)), true, ifeq(ifeq(defined(a, domain(compose(b, a))), true, defined(domain(a), domain(compose(b, a))), true), true, product(domain(a), domain(compose(b, a)), domain(compose(b, a))), true), true), true, domain(compose(b, a)), domain(a)), domain(a))
% 1.25/0.41 = { by axiom 5 (ifeq_axiom) R->L }
% 1.25/0.41 ifeq2(product(domain(a), domain(compose(b, a)), domain(a)), true, ifeq2(ifeq(identity_map(domain(a)), true, ifeq(ifeq(true, true, ifeq(defined(a, domain(compose(b, a))), true, defined(domain(a), domain(compose(b, a))), true), true), true, product(domain(a), domain(compose(b, a)), domain(compose(b, a))), true), true), true, domain(compose(b, a)), domain(a)), domain(a))
% 1.25/0.41 = { by axiom 4 (product_on_domain) R->L }
% 1.25/0.41 ifeq2(product(domain(a), domain(compose(b, a)), domain(a)), true, ifeq2(ifeq(identity_map(domain(a)), true, ifeq(ifeq(product(a, domain(a), a), true, ifeq(defined(a, domain(compose(b, a))), true, defined(domain(a), domain(compose(b, a))), true), true), true, product(domain(a), domain(compose(b, a)), domain(compose(b, a))), true), true), true, domain(compose(b, a)), domain(a)), domain(a))
% 1.25/0.41 = { by axiom 11 (associative_property2) }
% 1.25/0.41 ifeq2(product(domain(a), domain(compose(b, a)), domain(a)), true, ifeq2(ifeq(identity_map(domain(a)), true, ifeq(true, true, product(domain(a), domain(compose(b, a)), domain(compose(b, a))), true), true), true, domain(compose(b, a)), domain(a)), domain(a))
% 1.25/0.41 = { by axiom 1 (domain_is_an_identity_map) }
% 1.25/0.41 ifeq2(product(domain(a), domain(compose(b, a)), domain(a)), true, ifeq2(ifeq(true, true, ifeq(true, true, product(domain(a), domain(compose(b, a)), domain(compose(b, a))), true), true), true, domain(compose(b, a)), domain(a)), domain(a))
% 1.25/0.41 = { by axiom 5 (ifeq_axiom) }
% 1.25/0.41 ifeq2(product(domain(a), domain(compose(b, a)), domain(a)), true, ifeq2(ifeq(true, true, product(domain(a), domain(compose(b, a)), domain(compose(b, a))), true), true, domain(compose(b, a)), domain(a)), domain(a))
% 1.25/0.41 = { by axiom 5 (ifeq_axiom) }
% 1.25/0.41 ifeq2(product(domain(a), domain(compose(b, a)), domain(a)), true, ifeq2(product(domain(a), domain(compose(b, a)), domain(compose(b, a))), true, domain(compose(b, a)), domain(a)), domain(a))
% 1.25/0.41 = { by axiom 10 (composition_is_well_defined) }
% 1.25/0.41 domain(a)
% 1.25/0.41 % SZS output end Proof
% 1.25/0.41
% 1.25/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------