%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SEU263+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:45:37 PM UTC 2026
% Result : Theorem 53.95s 7.26s
% Output : Proof 53.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU263+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 28 04:23:15 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 53.95/7.26 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
% 53.95/7.26
% 53.95/7.26 % SZS status Theorem
% 53.95/7.26
% 53.95/7.27 % SZS output start Proof
% 53.95/7.27 Axiom 1 (reflexivity_r1_tarski): subset(X, X) = true.
% 53.95/7.27 Axiom 2 (t14_relset_1): subset(relation_rng(d), b) = true.
% 53.95/7.27 Axiom 3 (t14_relset_1_1): relation_of2_as_subset(d, c, a) = true.
% 53.95/7.27 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 53.95/7.27 Axiom 5 (cc1_relset_1): ifeq(element(X, powerset(cartesian_product2(Y, Z))), true, relation(X), true) = true.
% 53.95/7.27 Axiom 6 (t12_relset_1): ifeq(relation_of2_as_subset(X, Y, Z), true, subset(relation_dom(X), Y), true) = true.
% 53.95/7.27 Axiom 7 (redefinition_m2_relset_1): ifeq(relation_of2(X, Y, Z), true, relation_of2_as_subset(X, Y, Z), true) = true.
% 53.95/7.27 Axiom 8 (t21_relat_1): ifeq(relation(X), true, subset(X, cartesian_product2(relation_dom(X), relation_rng(X))), true) = true.
% 53.95/7.27 Axiom 9 (dt_m2_relset_1): ifeq(relation_of2_as_subset(X, Y, Z), true, element(X, powerset(cartesian_product2(Y, Z))), true) = true.
% 53.95/7.27 Axiom 10 (d1_relset_1_1): ifeq(subset(X, cartesian_product2(Y, Z)), true, relation_of2(X, Y, Z), true) = true.
% 53.95/7.27 Axiom 11 (t1_xboole_1): ifeq(subset(X, Y), true, ifeq(subset(Z, X), true, subset(Z, Y), true), true) = true.
% 53.95/7.27 Axiom 12 (t119_zfmisc_1): ifeq(subset(X, Y), true, ifeq(subset(Z, W), true, subset(cartesian_product2(Z, X), cartesian_product2(W, Y)), true), true) = true.
% 53.95/7.28
% 53.95/7.28 Goal 1 (t14_relset_1_2): relation_of2_as_subset(d, c, b) = true.
% 53.95/7.28 Proof:
% 53.95/7.28 relation_of2_as_subset(d, c, b)
% 53.95/7.28 = { by axiom 4 (ifeq_axiom) R->L }
% 53.95/7.28 ifeq(true, true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 10 (d1_relset_1_1) R->L }
% 53.95/7.28 ifeq(ifeq(subset(d, cartesian_product2(c, b)), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 4 (ifeq_axiom) R->L }
% 53.95/7.28 ifeq(ifeq(ifeq(true, true, subset(d, cartesian_product2(c, b)), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 11 (t1_xboole_1) R->L }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(subset(cartesian_product2(relation_dom(d), relation_rng(d)), cartesian_product2(c, relation_rng(d))), true, ifeq(subset(d, cartesian_product2(relation_dom(d), relation_rng(d))), true, subset(d, cartesian_product2(c, relation_rng(d))), true), true), true, subset(d, cartesian_product2(c, b)), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 4 (ifeq_axiom) R->L }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, subset(cartesian_product2(relation_dom(d), relation_rng(d)), cartesian_product2(c, relation_rng(d))), true), true, ifeq(subset(d, cartesian_product2(relation_dom(d), relation_rng(d))), true, subset(d, cartesian_product2(c, relation_rng(d))), true), true), true, subset(d, cartesian_product2(c, b)), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 6 (t12_relset_1) R->L }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(relation_of2_as_subset(d, c, a), true, subset(relation_dom(d), c), true), true, subset(cartesian_product2(relation_dom(d), relation_rng(d)), cartesian_product2(c, relation_rng(d))), true), true, ifeq(subset(d, cartesian_product2(relation_dom(d), relation_rng(d))), true, subset(d, cartesian_product2(c, relation_rng(d))), true), true), true, subset(d, cartesian_product2(c, b)), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 3 (t14_relset_1_1) }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, subset(relation_dom(d), c), true), true, subset(cartesian_product2(relation_dom(d), relation_rng(d)), cartesian_product2(c, relation_rng(d))), true), true, ifeq(subset(d, cartesian_product2(relation_dom(d), relation_rng(d))), true, subset(d, cartesian_product2(c, relation_rng(d))), true), true), true, subset(d, cartesian_product2(c, b)), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 4 (ifeq_axiom) }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(ifeq(subset(relation_dom(d), c), true, subset(cartesian_product2(relation_dom(d), relation_rng(d)), cartesian_product2(c, relation_rng(d))), true), true, ifeq(subset(d, cartesian_product2(relation_dom(d), relation_rng(d))), true, subset(d, cartesian_product2(c, relation_rng(d))), true), true), true, subset(d, cartesian_product2(c, b)), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 4 (ifeq_axiom) R->L }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(subset(relation_dom(d), c), true, subset(cartesian_product2(relation_dom(d), relation_rng(d)), cartesian_product2(c, relation_rng(d))), true), true), true, ifeq(subset(d, cartesian_product2(relation_dom(d), relation_rng(d))), true, subset(d, cartesian_product2(c, relation_rng(d))), true), true), true, subset(d, cartesian_product2(c, b)), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 1 (reflexivity_r1_tarski) R->L }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(ifeq(subset(relation_rng(d), relation_rng(d)), true, ifeq(subset(relation_dom(d), c), true, subset(cartesian_product2(relation_dom(d), relation_rng(d)), cartesian_product2(c, relation_rng(d))), true), true), true, ifeq(subset(d, cartesian_product2(relation_dom(d), relation_rng(d))), true, subset(d, cartesian_product2(c, relation_rng(d))), true), true), true, subset(d, cartesian_product2(c, b)), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 12 (t119_zfmisc_1) }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(subset(d, cartesian_product2(relation_dom(d), relation_rng(d))), true, subset(d, cartesian_product2(c, relation_rng(d))), true), true), true, subset(d, cartesian_product2(c, b)), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 4 (ifeq_axiom) }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(subset(d, cartesian_product2(relation_dom(d), relation_rng(d))), true, subset(d, cartesian_product2(c, relation_rng(d))), true), true, subset(d, cartesian_product2(c, b)), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 4 (ifeq_axiom) R->L }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, subset(d, cartesian_product2(relation_dom(d), relation_rng(d))), true), true, subset(d, cartesian_product2(c, relation_rng(d))), true), true, subset(d, cartesian_product2(c, b)), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 5 (cc1_relset_1) R->L }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(element(d, powerset(cartesian_product2(c, a))), true, relation(d), true), true, subset(d, cartesian_product2(relation_dom(d), relation_rng(d))), true), true, subset(d, cartesian_product2(c, relation_rng(d))), true), true, subset(d, cartesian_product2(c, b)), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 4 (ifeq_axiom) R->L }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, element(d, powerset(cartesian_product2(c, a))), true), true, relation(d), true), true, subset(d, cartesian_product2(relation_dom(d), relation_rng(d))), true), true, subset(d, cartesian_product2(c, relation_rng(d))), true), true, subset(d, cartesian_product2(c, b)), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 3 (t14_relset_1_1) R->L }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(relation_of2_as_subset(d, c, a), true, element(d, powerset(cartesian_product2(c, a))), true), true, relation(d), true), true, subset(d, cartesian_product2(relation_dom(d), relation_rng(d))), true), true, subset(d, cartesian_product2(c, relation_rng(d))), true), true, subset(d, cartesian_product2(c, b)), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 9 (dt_m2_relset_1) }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, relation(d), true), true, subset(d, cartesian_product2(relation_dom(d), relation_rng(d))), true), true, subset(d, cartesian_product2(c, relation_rng(d))), true), true, subset(d, cartesian_product2(c, b)), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 4 (ifeq_axiom) }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(ifeq(relation(d), true, subset(d, cartesian_product2(relation_dom(d), relation_rng(d))), true), true, subset(d, cartesian_product2(c, relation_rng(d))), true), true, subset(d, cartesian_product2(c, b)), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 8 (t21_relat_1) }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(true, true, subset(d, cartesian_product2(c, relation_rng(d))), true), true, subset(d, cartesian_product2(c, b)), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 4 (ifeq_axiom) }
% 53.95/7.28 ifeq(ifeq(ifeq(subset(d, cartesian_product2(c, relation_rng(d))), true, subset(d, cartesian_product2(c, b)), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 4 (ifeq_axiom) R->L }
% 53.95/7.28 ifeq(ifeq(ifeq(true, true, ifeq(subset(d, cartesian_product2(c, relation_rng(d))), true, subset(d, cartesian_product2(c, b)), true), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 12 (t119_zfmisc_1) R->L }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(subset(relation_rng(d), b), true, ifeq(subset(c, c), true, subset(cartesian_product2(c, relation_rng(d)), cartesian_product2(c, b)), true), true), true, ifeq(subset(d, cartesian_product2(c, relation_rng(d))), true, subset(d, cartesian_product2(c, b)), true), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 1 (reflexivity_r1_tarski) }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(subset(relation_rng(d), b), true, ifeq(true, true, subset(cartesian_product2(c, relation_rng(d)), cartesian_product2(c, b)), true), true), true, ifeq(subset(d, cartesian_product2(c, relation_rng(d))), true, subset(d, cartesian_product2(c, b)), true), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 4 (ifeq_axiom) }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(subset(relation_rng(d), b), true, subset(cartesian_product2(c, relation_rng(d)), cartesian_product2(c, b)), true), true, ifeq(subset(d, cartesian_product2(c, relation_rng(d))), true, subset(d, cartesian_product2(c, b)), true), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 2 (t14_relset_1) }
% 53.95/7.28 ifeq(ifeq(ifeq(ifeq(true, true, subset(cartesian_product2(c, relation_rng(d)), cartesian_product2(c, b)), true), true, ifeq(subset(d, cartesian_product2(c, relation_rng(d))), true, subset(d, cartesian_product2(c, b)), true), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 4 (ifeq_axiom) }
% 53.95/7.28 ifeq(ifeq(ifeq(subset(cartesian_product2(c, relation_rng(d)), cartesian_product2(c, b)), true, ifeq(subset(d, cartesian_product2(c, relation_rng(d))), true, subset(d, cartesian_product2(c, b)), true), true), true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 11 (t1_xboole_1) }
% 53.95/7.28 ifeq(ifeq(true, true, relation_of2(d, c, b), true), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 4 (ifeq_axiom) }
% 53.95/7.28 ifeq(relation_of2(d, c, b), true, relation_of2_as_subset(d, c, b), true)
% 53.95/7.28 = { by axiom 7 (redefinition_m2_relset_1) }
% 53.95/7.28 true
% 53.95/7.28 % SZS output end Proof
% 53.95/7.28
% 53.95/7.28 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------