%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SEU264+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 12:45:38 PM UTC 2026
% Result : Theorem 0.11s 0.46s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU264+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 28 04:23:00 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.46 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
% 0.11/0.46
% 0.11/0.46 % SZS status Theorem
% 0.11/0.46
% 0.11/0.46 % SZS output start Proof
% 0.11/0.46 Axiom 1 (t16_relset_1_1): subset(a, b) = true.
% 0.11/0.46 Axiom 2 (t16_relset_1): relation_of2_as_subset(d, c, a) = true.
% 0.11/0.46 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.11/0.46 Axiom 4 (t12_relset_1_1): ifeq(relation_of2_as_subset(X, Y, Z), true, subset(relation_rng(X), Z), true) = true.
% 0.11/0.47 Axiom 5 (t1_xboole_1): ifeq(subset(X, Y), true, ifeq(subset(Z, X), true, subset(Z, Y), true), true) = true.
% 0.11/0.47 Axiom 6 (t14_relset_1): ifeq(subset(relation_rng(X), Y), true, ifeq(relation_of2_as_subset(X, Z, W), true, relation_of2_as_subset(X, Z, Y), true), true) = true.
% 0.11/0.47
% 0.11/0.47 Goal 1 (t16_relset_1_2): relation_of2_as_subset(d, c, b) = true.
% 0.11/0.47 Proof:
% 0.11/0.47 relation_of2_as_subset(d, c, b)
% 0.11/0.47 = { by axiom 3 (ifeq_axiom) R->L }
% 0.11/0.47 ifeq(true, true, relation_of2_as_subset(d, c, b), true)
% 0.11/0.47 = { by axiom 5 (t1_xboole_1) R->L }
% 0.11/0.47 ifeq(ifeq(subset(a, b), true, ifeq(subset(relation_rng(d), a), true, subset(relation_rng(d), b), true), true), true, relation_of2_as_subset(d, c, b), true)
% 0.11/0.47 = { by axiom 1 (t16_relset_1_1) }
% 0.11/0.47 ifeq(ifeq(true, true, ifeq(subset(relation_rng(d), a), true, subset(relation_rng(d), b), true), true), true, relation_of2_as_subset(d, c, b), true)
% 0.11/0.47 = { by axiom 3 (ifeq_axiom) }
% 0.11/0.47 ifeq(ifeq(subset(relation_rng(d), a), true, subset(relation_rng(d), b), true), true, relation_of2_as_subset(d, c, b), true)
% 0.11/0.47 = { by axiom 3 (ifeq_axiom) R->L }
% 0.11/0.47 ifeq(ifeq(ifeq(true, true, subset(relation_rng(d), a), true), true, subset(relation_rng(d), b), true), true, relation_of2_as_subset(d, c, b), true)
% 0.11/0.47 = { by axiom 2 (t16_relset_1) R->L }
% 0.11/0.47 ifeq(ifeq(ifeq(relation_of2_as_subset(d, c, a), true, subset(relation_rng(d), a), true), true, subset(relation_rng(d), b), true), true, relation_of2_as_subset(d, c, b), true)
% 0.11/0.47 = { by axiom 4 (t12_relset_1_1) }
% 0.11/0.47 ifeq(ifeq(true, true, subset(relation_rng(d), b), true), true, relation_of2_as_subset(d, c, b), true)
% 0.11/0.47 = { by axiom 3 (ifeq_axiom) }
% 0.11/0.47 ifeq(subset(relation_rng(d), b), true, relation_of2_as_subset(d, c, b), true)
% 0.11/0.47 = { by axiom 3 (ifeq_axiom) R->L }
% 0.11/0.47 ifeq(subset(relation_rng(d), b), true, ifeq(true, true, relation_of2_as_subset(d, c, b), true), true)
% 0.11/0.47 = { by axiom 2 (t16_relset_1) R->L }
% 0.11/0.47 ifeq(subset(relation_rng(d), b), true, ifeq(relation_of2_as_subset(d, c, a), true, relation_of2_as_subset(d, c, b), true), true)
% 0.11/0.47 = { by axiom 6 (t14_relset_1) }
% 0.11/0.47 true
% 0.11/0.47 % SZS output end Proof
% 0.11/0.47
% 0.11/0.47 RESULT: Theorem (the conjecture is true).
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