%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SEU261+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 12:45:37 PM UTC 2026
% Result : Theorem 0.11s 0.43s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU261+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n026.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 28 04:25:11 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.43 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
% 0.11/0.43
% 0.11/0.43 % SZS status Theorem
% 0.11/0.43
% 0.11/0.45 % SZS output start Proof
% 0.11/0.45 Axiom 1 (t54_wellord1_1): relation(b) = true.
% 0.11/0.45 Axiom 2 (t54_wellord1): relation(a) = true.
% 0.11/0.45 Axiom 3 (t54_wellord1_2): relation(c) = true.
% 0.11/0.45 Axiom 4 (t54_wellord1_3): well_ordering(a) = true.
% 0.11/0.45 Axiom 5 (t54_wellord1_4): function(c) = true.
% 0.11/0.45 Axiom 6 (t54_wellord1_5): relation_isomorphism(a, b, c) = true.
% 0.11/0.45 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.11/0.45 Axiom 8 (d4_wellord1): ifeq(well_ordering(X), true, ifeq(relation(X), true, reflexive(X), true), true) = true.
% 0.11/0.45 Axiom 9 (d4_wellord1_1): ifeq(well_ordering(X), true, ifeq(relation(X), true, transitive(X), true), true) = true.
% 0.11/0.45 Axiom 10 (d4_wellord1_2): ifeq(well_ordering(X), true, ifeq(relation(X), true, antisymmetric(X), true), true) = true.
% 0.11/0.45 Axiom 11 (d4_wellord1_3): ifeq(well_ordering(X), true, ifeq(relation(X), true, connected(X), true), true) = true.
% 0.11/0.45 Axiom 12 (d4_wellord1_4): ifeq(well_ordering(X), true, ifeq(relation(X), true, well_founded_relation(X), true), true) = true.
% 0.11/0.45 Axiom 13 (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 Axiom 14 (t53_wellord1): ifeq(relation_isomorphism(X, Y, Z), true, ifeq(function(Z), true, ifeq(reflexive(X), true, ifeq(relation(Z), true, ifeq(relation(Y), true, ifeq(relation(X), true, reflexive(Y), true), true), true), true), true), true) = true.
% 0.11/0.45 Axiom 15 (t53_wellord1_1): ifeq(relation_isomorphism(X, Y, Z), true, ifeq(function(Z), true, ifeq(transitive(X), true, ifeq(relation(Z), true, ifeq(relation(Y), true, ifeq(relation(X), true, transitive(Y), true), true), true), true), true), true) = true.
% 0.11/0.45 Axiom 16 (t53_wellord1_2): ifeq(relation_isomorphism(X, Y, Z), true, ifeq(function(Z), true, ifeq(antisymmetric(X), true, ifeq(relation(Z), true, ifeq(relation(Y), true, ifeq(relation(X), true, antisymmetric(Y), true), true), true), true), true), true) = true.
% 0.11/0.45 Axiom 17 (t53_wellord1_3): ifeq(relation_isomorphism(X, Y, Z), true, ifeq(function(Z), true, ifeq(connected(X), true, ifeq(relation(Z), true, ifeq(relation(Y), true, ifeq(relation(X), true, connected(Y), true), true), true), true), true), true) = true.
% 0.11/0.45 Axiom 18 (t53_wellord1_4): ifeq(relation_isomorphism(X, Y, Z), true, ifeq(function(Z), true, ifeq(well_founded_relation(X), true, ifeq(relation(Z), true, ifeq(relation(Y), true, ifeq(relation(X), true, well_founded_relation(Y), true), true), true), true), true), true) = true.
% 0.11/0.45
% 0.11/0.45 Goal 1 (t54_wellord1_6): well_ordering(b) = true.
% 0.11/0.45 Proof:
% 0.11/0.45 well_ordering(b)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) R->L }
% 0.11/0.46 ifeq(true, true, well_ordering(b), true)
% 0.11/0.46 = { by axiom 1 (t54_wellord1_1) R->L }
% 0.11/0.46 ifeq(relation(b), true, well_ordering(b), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) R->L }
% 0.11/0.46 ifeq(true, true, ifeq(relation(b), true, well_ordering(b), true), true)
% 0.11/0.46 = { by axiom 14 (t53_wellord1) R->L }
% 0.11/0.46 ifeq(ifeq(relation_isomorphism(a, b, c), true, ifeq(function(c), true, ifeq(reflexive(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, reflexive(b), true), true), true), true), true), true), true, ifeq(relation(b), true, well_ordering(b), true), true)
% 0.11/0.46 = { by axiom 6 (t54_wellord1_5) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(function(c), true, ifeq(reflexive(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, reflexive(b), true), true), true), true), true), true), true, ifeq(relation(b), true, well_ordering(b), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(function(c), true, ifeq(reflexive(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, reflexive(b), true), true), true), true), true), true, ifeq(relation(b), true, well_ordering(b), true), true)
% 0.11/0.46 = { by axiom 5 (t54_wellord1_4) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(reflexive(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, reflexive(b), true), true), true), true), true), true, ifeq(relation(b), true, well_ordering(b), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(reflexive(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, reflexive(b), true), true), true), true), true, ifeq(relation(b), true, well_ordering(b), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) R->L }
% 0.11/0.46 ifeq(ifeq(ifeq(true, true, reflexive(a), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, reflexive(b), true), true), true), true), true, ifeq(relation(b), true, well_ordering(b), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) R->L }
% 0.11/0.46 ifeq(ifeq(ifeq(true, true, ifeq(true, true, reflexive(a), true), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, reflexive(b), true), true), true), true), true, ifeq(relation(b), true, well_ordering(b), true), true)
% 0.11/0.46 = { by axiom 4 (t54_wellord1_3) R->L }
% 0.11/0.46 ifeq(ifeq(ifeq(well_ordering(a), true, ifeq(true, true, reflexive(a), true), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, reflexive(b), true), true), true), true), true, ifeq(relation(b), true, well_ordering(b), true), true)
% 0.11/0.46 = { by axiom 2 (t54_wellord1) R->L }
% 0.11/0.46 ifeq(ifeq(ifeq(well_ordering(a), true, ifeq(relation(a), true, reflexive(a), true), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, reflexive(b), true), true), true), true), true, ifeq(relation(b), true, well_ordering(b), true), true)
% 0.11/0.46 = { by axiom 8 (d4_wellord1) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, reflexive(b), true), true), true), true), true, ifeq(relation(b), true, well_ordering(b), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, reflexive(b), true), true), true), true, ifeq(relation(b), true, well_ordering(b), true), true)
% 0.11/0.46 = { by axiom 3 (t54_wellord1_2) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(relation(b), true, ifeq(relation(a), true, reflexive(b), true), true), true), true, ifeq(relation(b), true, well_ordering(b), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(relation(b), true, ifeq(relation(a), true, reflexive(b), true), true), true, ifeq(relation(b), true, well_ordering(b), true), true)
% 0.11/0.46 = { by axiom 1 (t54_wellord1_1) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(relation(a), true, reflexive(b), true), true), true, ifeq(relation(b), true, well_ordering(b), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(relation(a), true, reflexive(b), true), true, ifeq(relation(b), true, well_ordering(b), true), true)
% 0.11/0.46 = { by axiom 2 (t54_wellord1) }
% 0.11/0.46 ifeq(ifeq(true, true, reflexive(b), true), true, ifeq(relation(b), true, well_ordering(b), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) R->L }
% 0.11/0.46 ifeq(true, true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true)
% 0.11/0.46 = { by axiom 15 (t53_wellord1_1) R->L }
% 0.11/0.46 ifeq(ifeq(relation_isomorphism(a, b, c), true, ifeq(function(c), true, ifeq(transitive(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, transitive(b), true), true), true), true), true), true), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true)
% 0.11/0.46 = { by axiom 6 (t54_wellord1_5) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(function(c), true, ifeq(transitive(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, transitive(b), true), true), true), true), true), true), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(function(c), true, ifeq(transitive(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, transitive(b), true), true), true), true), true), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true)
% 0.11/0.46 = { by axiom 5 (t54_wellord1_4) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(transitive(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, transitive(b), true), true), true), true), true), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(transitive(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, transitive(b), true), true), true), true), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) R->L }
% 0.11/0.46 ifeq(ifeq(ifeq(true, true, transitive(a), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, transitive(b), true), true), true), true), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) R->L }
% 0.11/0.46 ifeq(ifeq(ifeq(true, true, ifeq(true, true, transitive(a), true), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, transitive(b), true), true), true), true), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true)
% 0.11/0.46 = { by axiom 4 (t54_wellord1_3) R->L }
% 0.11/0.46 ifeq(ifeq(ifeq(well_ordering(a), true, ifeq(true, true, transitive(a), true), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, transitive(b), true), true), true), true), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true)
% 0.11/0.46 = { by axiom 2 (t54_wellord1) R->L }
% 0.11/0.46 ifeq(ifeq(ifeq(well_ordering(a), true, ifeq(relation(a), true, transitive(a), true), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, transitive(b), true), true), true), true), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true)
% 0.11/0.46 = { by axiom 9 (d4_wellord1_1) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, transitive(b), true), true), true), true), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, transitive(b), true), true), true), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true)
% 0.11/0.46 = { by axiom 3 (t54_wellord1_2) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(relation(b), true, ifeq(relation(a), true, transitive(b), true), true), true), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(relation(b), true, ifeq(relation(a), true, transitive(b), true), true), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true)
% 0.11/0.46 = { by axiom 1 (t54_wellord1_1) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(relation(a), true, transitive(b), true), true), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(relation(a), true, transitive(b), true), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true)
% 0.11/0.46 = { by axiom 2 (t54_wellord1) }
% 0.11/0.46 ifeq(ifeq(true, true, transitive(b), true), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) R->L }
% 0.11/0.46 ifeq(true, true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true)
% 0.11/0.46 = { by axiom 16 (t53_wellord1_2) R->L }
% 0.11/0.46 ifeq(ifeq(relation_isomorphism(a, b, c), true, ifeq(function(c), true, ifeq(antisymmetric(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, antisymmetric(b), true), true), true), true), true), true), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true)
% 0.11/0.46 = { by axiom 6 (t54_wellord1_5) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(function(c), true, ifeq(antisymmetric(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, antisymmetric(b), true), true), true), true), true), true), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(function(c), true, ifeq(antisymmetric(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, antisymmetric(b), true), true), true), true), true), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true)
% 0.11/0.46 = { by axiom 5 (t54_wellord1_4) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(antisymmetric(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, antisymmetric(b), true), true), true), true), true), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(antisymmetric(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, antisymmetric(b), true), true), true), true), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) R->L }
% 0.11/0.46 ifeq(ifeq(ifeq(true, true, antisymmetric(a), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, antisymmetric(b), true), true), true), true), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) R->L }
% 0.11/0.46 ifeq(ifeq(ifeq(true, true, ifeq(true, true, antisymmetric(a), true), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, antisymmetric(b), true), true), true), true), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true)
% 0.11/0.46 = { by axiom 4 (t54_wellord1_3) R->L }
% 0.11/0.46 ifeq(ifeq(ifeq(well_ordering(a), true, ifeq(true, true, antisymmetric(a), true), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, antisymmetric(b), true), true), true), true), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true)
% 0.11/0.46 = { by axiom 2 (t54_wellord1) R->L }
% 0.11/0.46 ifeq(ifeq(ifeq(well_ordering(a), true, ifeq(relation(a), true, antisymmetric(a), true), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, antisymmetric(b), true), true), true), true), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true)
% 0.11/0.46 = { by axiom 10 (d4_wellord1_2) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, antisymmetric(b), true), true), true), true), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, antisymmetric(b), true), true), true), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true)
% 0.11/0.46 = { by axiom 3 (t54_wellord1_2) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(relation(b), true, ifeq(relation(a), true, antisymmetric(b), true), true), true), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(relation(b), true, ifeq(relation(a), true, antisymmetric(b), true), true), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true)
% 0.11/0.46 = { by axiom 1 (t54_wellord1_1) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(relation(a), true, antisymmetric(b), true), true), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(relation(a), true, antisymmetric(b), true), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true)
% 0.11/0.46 = { by axiom 2 (t54_wellord1) }
% 0.11/0.46 ifeq(ifeq(true, true, antisymmetric(b), true), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) R->L }
% 0.11/0.46 ifeq(true, true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true)
% 0.11/0.46 = { by axiom 17 (t53_wellord1_3) R->L }
% 0.11/0.46 ifeq(ifeq(relation_isomorphism(a, b, c), true, ifeq(function(c), true, ifeq(connected(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, connected(b), true), true), true), true), true), true), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true)
% 0.11/0.46 = { by axiom 6 (t54_wellord1_5) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(function(c), true, ifeq(connected(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, connected(b), true), true), true), true), true), true), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(function(c), true, ifeq(connected(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, connected(b), true), true), true), true), true), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true)
% 0.11/0.46 = { by axiom 5 (t54_wellord1_4) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(connected(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, connected(b), true), true), true), true), true), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(connected(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, connected(b), true), true), true), true), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) R->L }
% 0.11/0.46 ifeq(ifeq(ifeq(true, true, connected(a), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, connected(b), true), true), true), true), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) R->L }
% 0.11/0.46 ifeq(ifeq(ifeq(true, true, ifeq(true, true, connected(a), true), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, connected(b), true), true), true), true), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true)
% 0.11/0.46 = { by axiom 4 (t54_wellord1_3) R->L }
% 0.11/0.46 ifeq(ifeq(ifeq(well_ordering(a), true, ifeq(true, true, connected(a), true), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, connected(b), true), true), true), true), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true)
% 0.11/0.46 = { by axiom 2 (t54_wellord1) R->L }
% 0.11/0.46 ifeq(ifeq(ifeq(well_ordering(a), true, ifeq(relation(a), true, connected(a), true), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, connected(b), true), true), true), true), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true)
% 0.11/0.46 = { by axiom 11 (d4_wellord1_3) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, connected(b), true), true), true), true), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, connected(b), true), true), true), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true)
% 0.11/0.46 = { by axiom 3 (t54_wellord1_2) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(relation(b), true, ifeq(relation(a), true, connected(b), true), true), true), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(relation(b), true, ifeq(relation(a), true, connected(b), true), true), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true)
% 0.11/0.46 = { by axiom 1 (t54_wellord1_1) }
% 0.11/0.46 ifeq(ifeq(true, true, ifeq(relation(a), true, connected(b), true), true), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(ifeq(relation(a), true, connected(b), true), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true)
% 0.11/0.46 = { by axiom 2 (t54_wellord1) }
% 0.11/0.46 ifeq(ifeq(true, true, connected(b), true), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.46 ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true)
% 0.11/0.46 = { by axiom 7 (ifeq_axiom) R->L }
% 0.11/0.46 ifeq(true, true, ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true), true)
% 0.11/0.46 = { by axiom 18 (t53_wellord1_4) R->L }
% 0.11/0.46 ifeq(ifeq(relation_isomorphism(a, b, c), true, ifeq(function(c), true, ifeq(well_founded_relation(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, well_founded_relation(b), true), true), true), true), true), true), true, ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true), true)
% 0.11/0.46 = { by axiom 6 (t54_wellord1_5) }
% 0.11/0.47 ifeq(ifeq(true, true, ifeq(function(c), true, ifeq(well_founded_relation(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, well_founded_relation(b), true), true), true), true), true), true), true, ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true), true)
% 0.11/0.47 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.47 ifeq(ifeq(function(c), true, ifeq(well_founded_relation(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, well_founded_relation(b), true), true), true), true), true), true, ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true), true)
% 0.11/0.47 = { by axiom 5 (t54_wellord1_4) }
% 0.11/0.47 ifeq(ifeq(true, true, ifeq(well_founded_relation(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, well_founded_relation(b), true), true), true), true), true), true, ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true), true)
% 0.11/0.47 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.47 ifeq(ifeq(well_founded_relation(a), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, well_founded_relation(b), true), true), true), true), true, ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true), true)
% 0.11/0.47 = { by axiom 7 (ifeq_axiom) R->L }
% 0.11/0.47 ifeq(ifeq(ifeq(true, true, well_founded_relation(a), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, well_founded_relation(b), true), true), true), true), true, ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true), true)
% 0.11/0.47 = { by axiom 7 (ifeq_axiom) R->L }
% 0.11/0.47 ifeq(ifeq(ifeq(true, true, ifeq(true, true, well_founded_relation(a), true), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, well_founded_relation(b), true), true), true), true), true, ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true), true)
% 0.11/0.47 = { by axiom 4 (t54_wellord1_3) R->L }
% 0.11/0.47 ifeq(ifeq(ifeq(well_ordering(a), true, ifeq(true, true, well_founded_relation(a), true), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, well_founded_relation(b), true), true), true), true), true, ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true), true)
% 0.11/0.47 = { by axiom 2 (t54_wellord1) R->L }
% 0.11/0.47 ifeq(ifeq(ifeq(well_ordering(a), true, ifeq(relation(a), true, well_founded_relation(a), true), true), true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, well_founded_relation(b), true), true), true), true), true, ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true), true)
% 0.11/0.47 = { by axiom 12 (d4_wellord1_4) }
% 0.11/0.47 ifeq(ifeq(true, true, ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, well_founded_relation(b), true), true), true), true), true, ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true), true)
% 0.11/0.47 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.47 ifeq(ifeq(relation(c), true, ifeq(relation(b), true, ifeq(relation(a), true, well_founded_relation(b), true), true), true), true, ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true), true)
% 0.11/0.47 = { by axiom 3 (t54_wellord1_2) }
% 0.11/0.47 ifeq(ifeq(true, true, ifeq(relation(b), true, ifeq(relation(a), true, well_founded_relation(b), true), true), true), true, ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true), true)
% 0.11/0.47 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.47 ifeq(ifeq(relation(b), true, ifeq(relation(a), true, well_founded_relation(b), true), true), true, ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true), true)
% 0.11/0.47 = { by axiom 1 (t54_wellord1_1) }
% 0.11/0.47 ifeq(ifeq(true, true, ifeq(relation(a), true, well_founded_relation(b), true), true), true, ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true), true)
% 0.11/0.47 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.47 ifeq(ifeq(relation(a), true, well_founded_relation(b), true), true, ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true), true)
% 0.11/0.47 = { by axiom 2 (t54_wellord1) }
% 0.11/0.47 ifeq(ifeq(true, true, well_founded_relation(b), true), true, ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true), true)
% 0.11/0.47 = { by axiom 7 (ifeq_axiom) }
% 0.11/0.47 ifeq(well_founded_relation(b), true, ifeq(connected(b), true, ifeq(antisymmetric(b), true, ifeq(transitive(b), true, ifeq(reflexive(b), true, ifeq(relation(b), true, well_ordering(b), true), true), true), true), true), true)
% 0.11/0.47 = { by axiom 13 (d4_wellord1_5) }
% 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).
%------------------------------------------------------------------------------