%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SEU275+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:45:39 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU275+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n026.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 04:29:41 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.45 Command-line arguments: --no-flatten-goal
% 0.11/0.45
% 0.11/0.45 % SZS status Theorem
% 0.11/0.45
% 0.11/0.45 % SZS output start Proof
% 0.11/0.45 Axiom 1 (t2_wellord2): reflexive(inclusion_relation(X)) = true.
% 0.11/0.45 Axiom 2 (t3_wellord2): transitive(inclusion_relation(X)) = true.
% 0.11/0.45 Axiom 3 (t5_wellord2): antisymmetric(inclusion_relation(X)) = true.
% 0.11/0.45 Axiom 4 (t7_wellord2): ordinal(a) = true.
% 0.11/0.45 Axiom 5 (dt_k1_wellord2): relation(inclusion_relation(X)) = true.
% 0.11/0.45 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.11/0.45 Axiom 7 (t4_wellord2): ifeq(ordinal(X), true, connected(inclusion_relation(X)), true) = true.
% 0.11/0.45 Axiom 8 (t6_wellord2): ifeq(ordinal(X), true, well_founded_relation(inclusion_relation(X)), true) = true.
% 0.11/0.45 Axiom 9 (d4_wellord1_5): ifeq(well_founded_relation(X), true, ifeq(connected(X), true, ifeq(antisymmetric(X), true, ifeq(transitive(X), true, ifeq(reflexive(X), true, ifeq(relation(X), true, well_ordering(X), true), true), true), true), true), true) = true.
% 0.11/0.45
% 0.11/0.45 Goal 1 (t7_wellord2_1): well_ordering(inclusion_relation(a)) = true.
% 0.11/0.45 Proof:
% 0.11/0.45 well_ordering(inclusion_relation(a))
% 0.11/0.45 = { by axiom 6 (ifeq_axiom) R->L }
% 0.11/0.45 ifeq(true, true, well_ordering(inclusion_relation(a)), true)
% 0.11/0.45 = { by axiom 5 (dt_k1_wellord2) R->L }
% 0.11/0.45 ifeq(relation(inclusion_relation(a)), true, well_ordering(inclusion_relation(a)), true)
% 0.11/0.45 = { by axiom 6 (ifeq_axiom) R->L }
% 0.11/0.45 ifeq(true, true, ifeq(relation(inclusion_relation(a)), true, well_ordering(inclusion_relation(a)), true), true)
% 0.11/0.45 = { by axiom 1 (t2_wellord2) R->L }
% 0.11/0.45 ifeq(reflexive(inclusion_relation(a)), true, ifeq(relation(inclusion_relation(a)), true, well_ordering(inclusion_relation(a)), true), true)
% 0.11/0.45 = { by axiom 6 (ifeq_axiom) R->L }
% 0.11/0.45 ifeq(true, true, ifeq(reflexive(inclusion_relation(a)), true, ifeq(relation(inclusion_relation(a)), true, well_ordering(inclusion_relation(a)), true), true), true)
% 0.11/0.45 = { by axiom 2 (t3_wellord2) R->L }
% 0.11/0.45 ifeq(transitive(inclusion_relation(a)), true, ifeq(reflexive(inclusion_relation(a)), true, ifeq(relation(inclusion_relation(a)), true, well_ordering(inclusion_relation(a)), true), true), true)
% 0.11/0.45 = { by axiom 6 (ifeq_axiom) R->L }
% 0.11/0.45 ifeq(true, true, ifeq(transitive(inclusion_relation(a)), true, ifeq(reflexive(inclusion_relation(a)), true, ifeq(relation(inclusion_relation(a)), true, well_ordering(inclusion_relation(a)), true), true), true), true)
% 0.11/0.45 = { by axiom 3 (t5_wellord2) R->L }
% 0.11/0.45 ifeq(antisymmetric(inclusion_relation(a)), true, ifeq(transitive(inclusion_relation(a)), true, ifeq(reflexive(inclusion_relation(a)), true, ifeq(relation(inclusion_relation(a)), true, well_ordering(inclusion_relation(a)), true), true), true), true)
% 0.11/0.45 = { by axiom 6 (ifeq_axiom) R->L }
% 0.11/0.45 ifeq(true, true, ifeq(antisymmetric(inclusion_relation(a)), true, ifeq(transitive(inclusion_relation(a)), true, ifeq(reflexive(inclusion_relation(a)), true, ifeq(relation(inclusion_relation(a)), true, well_ordering(inclusion_relation(a)), true), true), true), true), true)
% 0.11/0.45 = { by axiom 7 (t4_wellord2) R->L }
% 0.11/0.45 ifeq(ifeq(ordinal(a), true, connected(inclusion_relation(a)), true), true, ifeq(antisymmetric(inclusion_relation(a)), true, ifeq(transitive(inclusion_relation(a)), true, ifeq(reflexive(inclusion_relation(a)), true, ifeq(relation(inclusion_relation(a)), true, well_ordering(inclusion_relation(a)), true), true), true), true), true)
% 0.11/0.45 = { by axiom 4 (t7_wellord2) }
% 0.11/0.45 ifeq(ifeq(true, true, connected(inclusion_relation(a)), true), true, ifeq(antisymmetric(inclusion_relation(a)), true, ifeq(transitive(inclusion_relation(a)), true, ifeq(reflexive(inclusion_relation(a)), true, ifeq(relation(inclusion_relation(a)), true, well_ordering(inclusion_relation(a)), true), true), true), true), true)
% 0.11/0.45 = { by axiom 6 (ifeq_axiom) }
% 0.11/0.45 ifeq(connected(inclusion_relation(a)), true, ifeq(antisymmetric(inclusion_relation(a)), true, ifeq(transitive(inclusion_relation(a)), true, ifeq(reflexive(inclusion_relation(a)), true, ifeq(relation(inclusion_relation(a)), true, well_ordering(inclusion_relation(a)), true), true), true), true), true)
% 0.11/0.45 = { by axiom 6 (ifeq_axiom) R->L }
% 0.11/0.45 ifeq(true, true, ifeq(connected(inclusion_relation(a)), true, ifeq(antisymmetric(inclusion_relation(a)), true, ifeq(transitive(inclusion_relation(a)), true, ifeq(reflexive(inclusion_relation(a)), true, ifeq(relation(inclusion_relation(a)), true, well_ordering(inclusion_relation(a)), true), true), true), true), true), true)
% 0.11/0.45 = { by axiom 8 (t6_wellord2) R->L }
% 0.11/0.45 ifeq(ifeq(ordinal(a), true, well_founded_relation(inclusion_relation(a)), true), true, ifeq(connected(inclusion_relation(a)), true, ifeq(antisymmetric(inclusion_relation(a)), true, ifeq(transitive(inclusion_relation(a)), true, ifeq(reflexive(inclusion_relation(a)), true, ifeq(relation(inclusion_relation(a)), true, well_ordering(inclusion_relation(a)), true), true), true), true), true), true)
% 0.11/0.45 = { by axiom 4 (t7_wellord2) }
% 0.11/0.45 ifeq(ifeq(true, true, well_founded_relation(inclusion_relation(a)), true), true, ifeq(connected(inclusion_relation(a)), true, ifeq(antisymmetric(inclusion_relation(a)), true, ifeq(transitive(inclusion_relation(a)), true, ifeq(reflexive(inclusion_relation(a)), true, ifeq(relation(inclusion_relation(a)), true, well_ordering(inclusion_relation(a)), true), true), true), true), true), true)
% 0.11/0.45 = { by axiom 6 (ifeq_axiom) }
% 0.11/0.45 ifeq(well_founded_relation(inclusion_relation(a)), true, ifeq(connected(inclusion_relation(a)), true, ifeq(antisymmetric(inclusion_relation(a)), true, ifeq(transitive(inclusion_relation(a)), true, ifeq(reflexive(inclusion_relation(a)), true, ifeq(relation(inclusion_relation(a)), true, well_ordering(inclusion_relation(a)), true), true), true), true), true), true)
% 0.11/0.45 = { by axiom 9 (d4_wellord1_5) }
% 0.11/0.45 true
% 0.11/0.45 % SZS output end Proof
% 0.11/0.45
% 0.11/0.45 RESULT: Theorem (the conjecture is true).
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