%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SEU257+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 12:45:37 PM UTC 2026
% Result : Theorem 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU257+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n017.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 04:16:35 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47 Command-line arguments: --no-flatten-goal
% 0.19/0.47
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 Axiom 1 (t32_wellord1): relation(b) = true.
% 0.19/0.48 Axiom 2 (t32_wellord1_1): well_ordering(b) = true.
% 0.19/0.48 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.19/0.48 Axiom 4 (dt_k2_wellord1): ifeq(relation(X), true, relation(relation_restriction(X, Y)), true) = true.
% 0.19/0.48 Axiom 5 (d4_wellord1): ifeq(well_ordering(X), true, ifeq(relation(X), true, reflexive(X), true), true) = true.
% 0.19/0.48 Axiom 6 (d4_wellord1_1): ifeq(well_ordering(X), true, ifeq(relation(X), true, transitive(X), true), true) = true.
% 0.19/0.48 Axiom 7 (d4_wellord1_2): ifeq(well_ordering(X), true, ifeq(relation(X), true, antisymmetric(X), true), true) = true.
% 0.19/0.48 Axiom 8 (d4_wellord1_3): ifeq(well_ordering(X), true, ifeq(relation(X), true, connected(X), true), true) = true.
% 0.19/0.48 Axiom 9 (d4_wellord1_4): ifeq(well_ordering(X), true, ifeq(relation(X), true, well_founded_relation(X), true), true) = true.
% 0.19/0.48 Axiom 10 (t22_wellord1): ifeq(reflexive(X), true, ifeq(relation(X), true, reflexive(relation_restriction(X, Y)), true), true) = true.
% 0.19/0.48 Axiom 11 (t24_wellord1): ifeq(transitive(X), true, ifeq(relation(X), true, transitive(relation_restriction(X, Y)), true), true) = true.
% 0.19/0.48 Axiom 12 (t25_wellord1): ifeq(antisymmetric(X), true, ifeq(relation(X), true, antisymmetric(relation_restriction(X, Y)), true), true) = true.
% 0.19/0.48 Axiom 13 (t23_wellord1): ifeq(connected(X), true, ifeq(relation(X), true, connected(relation_restriction(X, Y)), true), true) = true.
% 0.19/0.48 Axiom 14 (t31_wellord1): ifeq(well_founded_relation(X), true, ifeq(relation(X), true, well_founded_relation(relation_restriction(X, Y)), true), true) = true.
% 0.19/0.48 Axiom 15 (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.
% 0.19/0.48
% 0.19/0.48 Goal 1 (t32_wellord1_2): well_ordering(relation_restriction(b, a)) = true.
% 0.19/0.48 Proof:
% 0.19/0.48 well_ordering(relation_restriction(b, a))
% 0.19/0.48 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.48 ifeq(true, true, well_ordering(relation_restriction(b, a)), true)
% 0.19/0.48 = { by axiom 4 (dt_k2_wellord1) R->L }
% 0.19/0.48 ifeq(ifeq(relation(b), true, relation(relation_restriction(b, a)), true), true, well_ordering(relation_restriction(b, a)), true)
% 0.19/0.48 = { by axiom 1 (t32_wellord1) }
% 0.19/0.48 ifeq(ifeq(true, true, relation(relation_restriction(b, a)), true), true, well_ordering(relation_restriction(b, a)), true)
% 0.19/0.48 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.48 ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 ifeq(true, true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true)
% 0.19/0.49 = { by axiom 10 (t22_wellord1) R->L }
% 0.19/0.49 ifeq(ifeq(reflexive(b), true, ifeq(relation(b), true, reflexive(relation_restriction(b, a)), true), true), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(true, true, reflexive(b), true), true, ifeq(relation(b), true, reflexive(relation_restriction(b, a)), true), true), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(true, true, ifeq(true, true, reflexive(b), true), true), true, ifeq(relation(b), true, reflexive(relation_restriction(b, a)), true), true), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true)
% 0.19/0.49 = { by axiom 2 (t32_wellord1_1) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(well_ordering(b), true, ifeq(true, true, reflexive(b), true), true), true, ifeq(relation(b), true, reflexive(relation_restriction(b, a)), true), true), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true)
% 0.19/0.49 = { by axiom 1 (t32_wellord1) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(well_ordering(b), true, ifeq(relation(b), true, reflexive(b), true), true), true, ifeq(relation(b), true, reflexive(relation_restriction(b, a)), true), true), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true)
% 0.19/0.49 = { by axiom 5 (d4_wellord1) }
% 0.19/0.49 ifeq(ifeq(true, true, ifeq(relation(b), true, reflexive(relation_restriction(b, a)), true), true), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.49 ifeq(ifeq(relation(b), true, reflexive(relation_restriction(b, a)), true), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true)
% 0.19/0.49 = { by axiom 1 (t32_wellord1) }
% 0.19/0.49 ifeq(ifeq(true, true, reflexive(relation_restriction(b, a)), true), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.49 ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 ifeq(true, true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true)
% 0.19/0.49 = { by axiom 11 (t24_wellord1) R->L }
% 0.19/0.49 ifeq(ifeq(transitive(b), true, ifeq(relation(b), true, transitive(relation_restriction(b, a)), true), true), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(true, true, transitive(b), true), true, ifeq(relation(b), true, transitive(relation_restriction(b, a)), true), true), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(true, true, ifeq(true, true, transitive(b), true), true), true, ifeq(relation(b), true, transitive(relation_restriction(b, a)), true), true), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true)
% 0.19/0.49 = { by axiom 2 (t32_wellord1_1) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(well_ordering(b), true, ifeq(true, true, transitive(b), true), true), true, ifeq(relation(b), true, transitive(relation_restriction(b, a)), true), true), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true)
% 0.19/0.49 = { by axiom 1 (t32_wellord1) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(well_ordering(b), true, ifeq(relation(b), true, transitive(b), true), true), true, ifeq(relation(b), true, transitive(relation_restriction(b, a)), true), true), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true)
% 0.19/0.49 = { by axiom 6 (d4_wellord1_1) }
% 0.19/0.49 ifeq(ifeq(true, true, ifeq(relation(b), true, transitive(relation_restriction(b, a)), true), true), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.49 ifeq(ifeq(relation(b), true, transitive(relation_restriction(b, a)), true), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true)
% 0.19/0.49 = { by axiom 1 (t32_wellord1) }
% 0.19/0.49 ifeq(ifeq(true, true, transitive(relation_restriction(b, a)), true), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.49 ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 ifeq(true, true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true)
% 0.19/0.49 = { by axiom 12 (t25_wellord1) R->L }
% 0.19/0.49 ifeq(ifeq(antisymmetric(b), true, ifeq(relation(b), true, antisymmetric(relation_restriction(b, a)), true), true), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(true, true, antisymmetric(b), true), true, ifeq(relation(b), true, antisymmetric(relation_restriction(b, a)), true), true), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(true, true, ifeq(true, true, antisymmetric(b), true), true), true, ifeq(relation(b), true, antisymmetric(relation_restriction(b, a)), true), true), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true)
% 0.19/0.49 = { by axiom 2 (t32_wellord1_1) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(well_ordering(b), true, ifeq(true, true, antisymmetric(b), true), true), true, ifeq(relation(b), true, antisymmetric(relation_restriction(b, a)), true), true), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true)
% 0.19/0.49 = { by axiom 1 (t32_wellord1) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(well_ordering(b), true, ifeq(relation(b), true, antisymmetric(b), true), true), true, ifeq(relation(b), true, antisymmetric(relation_restriction(b, a)), true), true), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true)
% 0.19/0.49 = { by axiom 7 (d4_wellord1_2) }
% 0.19/0.49 ifeq(ifeq(true, true, ifeq(relation(b), true, antisymmetric(relation_restriction(b, a)), true), true), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.49 ifeq(ifeq(relation(b), true, antisymmetric(relation_restriction(b, a)), true), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true)
% 0.19/0.49 = { by axiom 1 (t32_wellord1) }
% 0.19/0.49 ifeq(ifeq(true, true, antisymmetric(relation_restriction(b, a)), true), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.49 ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 ifeq(true, true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true)
% 0.19/0.49 = { by axiom 13 (t23_wellord1) R->L }
% 0.19/0.49 ifeq(ifeq(connected(b), true, ifeq(relation(b), true, connected(relation_restriction(b, a)), true), true), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(true, true, connected(b), true), true, ifeq(relation(b), true, connected(relation_restriction(b, a)), true), true), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(true, true, ifeq(true, true, connected(b), true), true), true, ifeq(relation(b), true, connected(relation_restriction(b, a)), true), true), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true)
% 0.19/0.49 = { by axiom 2 (t32_wellord1_1) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(well_ordering(b), true, ifeq(true, true, connected(b), true), true), true, ifeq(relation(b), true, connected(relation_restriction(b, a)), true), true), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true)
% 0.19/0.49 = { by axiom 1 (t32_wellord1) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(well_ordering(b), true, ifeq(relation(b), true, connected(b), true), true), true, ifeq(relation(b), true, connected(relation_restriction(b, a)), true), true), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true)
% 0.19/0.49 = { by axiom 8 (d4_wellord1_3) }
% 0.19/0.49 ifeq(ifeq(true, true, ifeq(relation(b), true, connected(relation_restriction(b, a)), true), true), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.49 ifeq(ifeq(relation(b), true, connected(relation_restriction(b, a)), true), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true)
% 0.19/0.49 = { by axiom 1 (t32_wellord1) }
% 0.19/0.49 ifeq(ifeq(true, true, connected(relation_restriction(b, a)), true), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.49 ifeq(connected(relation_restriction(b, a)), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 ifeq(true, true, ifeq(connected(relation_restriction(b, a)), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true), true)
% 0.19/0.49 = { by axiom 14 (t31_wellord1) R->L }
% 0.19/0.49 ifeq(ifeq(well_founded_relation(b), true, ifeq(relation(b), true, well_founded_relation(relation_restriction(b, a)), true), true), true, ifeq(connected(relation_restriction(b, a)), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(true, true, well_founded_relation(b), true), true, ifeq(relation(b), true, well_founded_relation(relation_restriction(b, a)), true), true), true, ifeq(connected(relation_restriction(b, a)), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(true, true, ifeq(true, true, well_founded_relation(b), true), true), true, ifeq(relation(b), true, well_founded_relation(relation_restriction(b, a)), true), true), true, ifeq(connected(relation_restriction(b, a)), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true), true)
% 0.19/0.49 = { by axiom 2 (t32_wellord1_1) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(well_ordering(b), true, ifeq(true, true, well_founded_relation(b), true), true), true, ifeq(relation(b), true, well_founded_relation(relation_restriction(b, a)), true), true), true, ifeq(connected(relation_restriction(b, a)), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true), true)
% 0.19/0.49 = { by axiom 1 (t32_wellord1) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(well_ordering(b), true, ifeq(relation(b), true, well_founded_relation(b), true), true), true, ifeq(relation(b), true, well_founded_relation(relation_restriction(b, a)), true), true), true, ifeq(connected(relation_restriction(b, a)), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true), true)
% 0.19/0.49 = { by axiom 9 (d4_wellord1_4) }
% 0.19/0.49 ifeq(ifeq(true, true, ifeq(relation(b), true, well_founded_relation(relation_restriction(b, a)), true), true), true, ifeq(connected(relation_restriction(b, a)), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.49 ifeq(ifeq(relation(b), true, well_founded_relation(relation_restriction(b, a)), true), true, ifeq(connected(relation_restriction(b, a)), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true), true)
% 0.19/0.49 = { by axiom 1 (t32_wellord1) }
% 0.19/0.49 ifeq(ifeq(true, true, well_founded_relation(relation_restriction(b, a)), true), true, ifeq(connected(relation_restriction(b, a)), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true), true)
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.49 ifeq(well_founded_relation(relation_restriction(b, a)), true, ifeq(connected(relation_restriction(b, a)), true, ifeq(antisymmetric(relation_restriction(b, a)), true, ifeq(transitive(relation_restriction(b, a)), true, ifeq(reflexive(relation_restriction(b, a)), true, ifeq(relation(relation_restriction(b, a)), true, well_ordering(relation_restriction(b, a)), true), true), true), true), true), true)
% 0.19/0.49 = { by axiom 15 (d4_wellord1_5) }
% 0.19/0.49 true
% 0.19/0.49 % SZS output end Proof
% 0.19/0.49
% 0.19/0.49 RESULT: Theorem (the conjecture is true).
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