%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU275+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:28 AM UTC 2025
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU275+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 06:38:20 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(well_ordering_type, type, (
% 0.13/0.39 well_ordering: $i > $o)).
% 0.13/0.39 tff(inclusion_relation_type, type, (
% 0.13/0.39 inclusion_relation: $i > $i)).
% 0.13/0.39 tff(tptp_fun_A_1_type, type, (
% 0.13/0.39 tptp_fun_A_1: $i)).
% 0.13/0.39 tff(well_founded_relation_type, type, (
% 0.13/0.39 well_founded_relation: $i > $o)).
% 0.13/0.39 tff(connected_type, type, (
% 0.13/0.39 connected: $i > $o)).
% 0.13/0.39 tff(antisymmetric_type, type, (
% 0.13/0.39 antisymmetric: $i > $o)).
% 0.13/0.39 tff(transitive_type, type, (
% 0.13/0.39 transitive: $i > $o)).
% 0.13/0.39 tff(reflexive_type, type, (
% 0.13/0.39 reflexive: $i > $o)).
% 0.13/0.39 tff(relation_type, type, (
% 0.13/0.39 relation: $i > $o)).
% 0.13/0.39 tff(ordinal_type, type, (
% 0.13/0.39 ordinal: $i > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[A: $i] : refl(relation(inclusion_relation(A)) <=> relation(inclusion_relation(A)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![A: $i] : relation(inclusion_relation(A)) <=> ![A: $i] : relation(inclusion_relation(A))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![A: $i] : relation(inclusion_relation(A)) <=> ![A: $i] : relation(inclusion_relation(A))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,axiom,(![A: $i] : relation(inclusion_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_wellord2')).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![A: $i] : relation(inclusion_relation(A))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.39 tff(6,plain,(
% 0.13/0.39 ![A: $i] : relation(inclusion_relation(A))),
% 0.13/0.39 inference(skolemize,[status(sab)],[5])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![A: $i] : relation(inclusion_relation(A))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 ((~![A: $i] : relation(inclusion_relation(A))) | relation(inclusion_relation(A!1))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (relation(inclusion_relation(A!1))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (^[A: $i] : refl(((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A)))) <=> ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A)))) <=> ![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (^[A: $i] : rewrite(((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))) <=> ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))) <=> ![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))) <=> ![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (^[A: $i] : trans(monotonicity(rewrite((well_ordering(A) <=> ((((reflexive(A) & transitive(A)) & antisymmetric(A)) & connected(A)) & well_founded_relation(A))) <=> (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))), ((relation(A) => (well_ordering(A) <=> ((((reflexive(A) & transitive(A)) & antisymmetric(A)) & connected(A)) & well_founded_relation(A)))) <=> (relation(A) => (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))))), rewrite((relation(A) => (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A)))) <=> ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))), ((relation(A) => (well_ordering(A) <=> ((((reflexive(A) & transitive(A)) & antisymmetric(A)) & connected(A)) & well_founded_relation(A)))) <=> ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (![A: $i] : (relation(A) => (well_ordering(A) <=> ((((reflexive(A) & transitive(A)) & antisymmetric(A)) & connected(A)) & well_founded_relation(A)))) <=> ![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.13/0.39 tff(17,axiom,(![A: $i] : (relation(A) => (well_ordering(A) <=> ((((reflexive(A) & transitive(A)) & antisymmetric(A)) & connected(A)) & well_founded_relation(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_wellord1')).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.13/0.39 tff(20,plain,(
% 0.13/0.39 ![A: $i] : ((~relation(A)) | (well_ordering(A) <=> (reflexive(A) & transitive(A) & antisymmetric(A) & connected(A) & well_founded_relation(A))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[19])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(inclusion_relation(A!1))) | (~(((~reflexive(inclusion_relation(A!1))) | (~transitive(inclusion_relation(A!1))) | (~antisymmetric(inclusion_relation(A!1))) | (~connected(inclusion_relation(A!1))) | (~well_founded_relation(inclusion_relation(A!1)))) <=> well_ordering(inclusion_relation(A!1)))))) <=> ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(inclusion_relation(A!1))) | (~(((~reflexive(inclusion_relation(A!1))) | (~transitive(inclusion_relation(A!1))) | (~antisymmetric(inclusion_relation(A!1))) | (~connected(inclusion_relation(A!1))) | (~well_founded_relation(inclusion_relation(A!1)))) <=> well_ordering(inclusion_relation(A!1)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | ((~relation(inclusion_relation(A!1))) | (~(((~reflexive(inclusion_relation(A!1))) | (~transitive(inclusion_relation(A!1))) | (~antisymmetric(inclusion_relation(A!1))) | (~connected(inclusion_relation(A!1))) | (~well_founded_relation(inclusion_relation(A!1)))) <=> well_ordering(inclusion_relation(A!1)))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 ((~![A: $i] : ((~relation(A)) | (~(((~reflexive(A)) | (~transitive(A)) | (~antisymmetric(A)) | (~connected(A)) | (~well_founded_relation(A))) <=> well_ordering(A))))) | (~relation(inclusion_relation(A!1))) | (~(((~reflexive(inclusion_relation(A!1))) | (~transitive(inclusion_relation(A!1))) | (~antisymmetric(inclusion_relation(A!1))) | (~connected(inclusion_relation(A!1))) | (~well_founded_relation(inclusion_relation(A!1)))) <=> well_ordering(inclusion_relation(A!1))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 ((~relation(inclusion_relation(A!1))) | (~(((~reflexive(inclusion_relation(A!1))) | (~transitive(inclusion_relation(A!1))) | (~antisymmetric(inclusion_relation(A!1))) | (~connected(inclusion_relation(A!1))) | (~well_founded_relation(inclusion_relation(A!1)))) <=> well_ordering(inclusion_relation(A!1))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[25, 22])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (~(((~reflexive(inclusion_relation(A!1))) | (~transitive(inclusion_relation(A!1))) | (~antisymmetric(inclusion_relation(A!1))) | (~connected(inclusion_relation(A!1))) | (~well_founded_relation(inclusion_relation(A!1)))) <=> well_ordering(inclusion_relation(A!1)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[26, 9])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (^[A: $i] : refl(transitive(inclusion_relation(A)) <=> transitive(inclusion_relation(A)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (![A: $i] : transitive(inclusion_relation(A)) <=> ![A: $i] : transitive(inclusion_relation(A))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[28])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (![A: $i] : transitive(inclusion_relation(A)) <=> ![A: $i] : transitive(inclusion_relation(A))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(31,axiom,(![A: $i] : transitive(inclusion_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_wellord2')).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (![A: $i] : transitive(inclusion_relation(A))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.13/0.40 tff(33,plain,(
% 0.13/0.40 ![A: $i] : transitive(inclusion_relation(A))),
% 0.13/0.40 inference(skolemize,[status(sab)],[32])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (![A: $i] : transitive(inclusion_relation(A))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 ((~![A: $i] : transitive(inclusion_relation(A))) | transitive(inclusion_relation(A!1))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (transitive(inclusion_relation(A!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (^[A: $i] : refl(antisymmetric(inclusion_relation(A)) <=> antisymmetric(inclusion_relation(A)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (![A: $i] : antisymmetric(inclusion_relation(A)) <=> ![A: $i] : antisymmetric(inclusion_relation(A))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[37])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (![A: $i] : antisymmetric(inclusion_relation(A)) <=> ![A: $i] : antisymmetric(inclusion_relation(A))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(40,axiom,(![A: $i] : antisymmetric(inclusion_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t5_wellord2')).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 (![A: $i] : antisymmetric(inclusion_relation(A))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.13/0.40 tff(42,plain,(
% 0.13/0.40 ![A: $i] : antisymmetric(inclusion_relation(A))),
% 0.13/0.40 inference(skolemize,[status(sab)],[41])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 (![A: $i] : antisymmetric(inclusion_relation(A))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 ((~![A: $i] : antisymmetric(inclusion_relation(A))) | antisymmetric(inclusion_relation(A!1))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 (antisymmetric(inclusion_relation(A!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 (^[A: $i] : refl(reflexive(inclusion_relation(A)) <=> reflexive(inclusion_relation(A)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 (![A: $i] : reflexive(inclusion_relation(A)) <=> ![A: $i] : reflexive(inclusion_relation(A))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[46])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 (![A: $i] : reflexive(inclusion_relation(A)) <=> ![A: $i] : reflexive(inclusion_relation(A))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(49,axiom,(![A: $i] : reflexive(inclusion_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_wellord2')).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 (![A: $i] : reflexive(inclusion_relation(A))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.13/0.40 tff(51,plain,(
% 0.13/0.40 ![A: $i] : reflexive(inclusion_relation(A))),
% 0.13/0.40 inference(skolemize,[status(sab)],[50])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 (![A: $i] : reflexive(inclusion_relation(A))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 ((~![A: $i] : reflexive(inclusion_relation(A))) | reflexive(inclusion_relation(A!1))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 (reflexive(inclusion_relation(A!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 ((~![A: $i] : ((~ordinal(A)) | well_ordering(inclusion_relation(A)))) <=> (~![A: $i] : ((~ordinal(A)) | well_ordering(inclusion_relation(A))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 ((~![A: $i] : (ordinal(A) => well_ordering(inclusion_relation(A)))) <=> (~![A: $i] : ((~ordinal(A)) | well_ordering(inclusion_relation(A))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(57,axiom,(~![A: $i] : (ordinal(A) => well_ordering(inclusion_relation(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_wellord2')).
% 0.13/0.40 tff(58,plain,
% 0.13/0.40 (~![A: $i] : ((~ordinal(A)) | well_ordering(inclusion_relation(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 (~![A: $i] : ((~ordinal(A)) | well_ordering(inclusion_relation(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 (~![A: $i] : ((~ordinal(A)) | well_ordering(inclusion_relation(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.13/0.40 tff(61,plain,
% 0.13/0.40 (~![A: $i] : ((~ordinal(A)) | well_ordering(inclusion_relation(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[60, 55])).
% 0.13/0.40 tff(62,plain,(
% 0.13/0.40 ~((~ordinal(A!1)) | well_ordering(inclusion_relation(A!1)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[61])).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 (ordinal(A!1)),
% 0.13/0.40 inference(or_elim,[status(thm)],[62])).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 (^[A: $i] : refl((connected(inclusion_relation(A)) | (~ordinal(A))) <=> (connected(inclusion_relation(A)) | (~ordinal(A))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 (![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A))) <=> ![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.13/0.40 tff(66,plain,
% 0.13/0.40 (![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A))) <=> ![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(67,plain,
% 0.13/0.40 (^[A: $i] : rewrite((ordinal(A) => connected(inclusion_relation(A))) <=> (connected(inclusion_relation(A)) | (~ordinal(A))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 (![A: $i] : (ordinal(A) => connected(inclusion_relation(A))) <=> ![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[67])).
% 0.13/0.40 tff(69,axiom,(![A: $i] : (ordinal(A) => connected(inclusion_relation(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t4_wellord2')).
% 0.13/0.40 tff(70,plain,
% 0.13/0.40 (![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.13/0.40 tff(71,plain,
% 0.13/0.40 (![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.13/0.40 tff(72,plain,(
% 0.13/0.40 ![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[71])).
% 0.13/0.40 tff(73,plain,
% 0.13/0.40 (![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.13/0.40 tff(74,plain,
% 0.13/0.40 (((~![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A)))) | (connected(inclusion_relation(A!1)) | (~ordinal(A!1)))) <=> ((~![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A)))) | connected(inclusion_relation(A!1)) | (~ordinal(A!1)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(75,plain,
% 0.13/0.40 ((~![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A)))) | (connected(inclusion_relation(A!1)) | (~ordinal(A!1)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(76,plain,
% 0.13/0.40 ((~![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A)))) | connected(inclusion_relation(A!1)) | (~ordinal(A!1))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.13/0.40 tff(77,plain,
% 0.13/0.40 (connected(inclusion_relation(A!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[76, 73, 63])).
% 0.13/0.40 tff(78,plain,
% 0.13/0.40 (^[A: $i] : refl(((~ordinal(A)) | well_founded_relation(inclusion_relation(A))) <=> ((~ordinal(A)) | well_founded_relation(inclusion_relation(A))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(79,plain,
% 0.13/0.40 (![A: $i] : ((~ordinal(A)) | well_founded_relation(inclusion_relation(A))) <=> ![A: $i] : ((~ordinal(A)) | well_founded_relation(inclusion_relation(A)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[78])).
% 0.13/0.40 tff(80,plain,
% 0.13/0.40 (![A: $i] : ((~ordinal(A)) | well_founded_relation(inclusion_relation(A))) <=> ![A: $i] : ((~ordinal(A)) | well_founded_relation(inclusion_relation(A)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(81,plain,
% 0.13/0.40 (^[A: $i] : rewrite((ordinal(A) => well_founded_relation(inclusion_relation(A))) <=> ((~ordinal(A)) | well_founded_relation(inclusion_relation(A))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(82,plain,
% 0.13/0.40 (![A: $i] : (ordinal(A) => well_founded_relation(inclusion_relation(A))) <=> ![A: $i] : ((~ordinal(A)) | well_founded_relation(inclusion_relation(A)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[81])).
% 0.13/0.40 tff(83,axiom,(![A: $i] : (ordinal(A) => well_founded_relation(inclusion_relation(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t6_wellord2')).
% 0.13/0.40 tff(84,plain,
% 0.13/0.40 (![A: $i] : ((~ordinal(A)) | well_founded_relation(inclusion_relation(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.13/0.40 tff(85,plain,
% 0.13/0.40 (![A: $i] : ((~ordinal(A)) | well_founded_relation(inclusion_relation(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.13/0.40 tff(86,plain,(
% 0.13/0.40 ![A: $i] : ((~ordinal(A)) | well_founded_relation(inclusion_relation(A)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[85])).
% 0.13/0.40 tff(87,plain,
% 0.13/0.40 (![A: $i] : ((~ordinal(A)) | well_founded_relation(inclusion_relation(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.13/0.40 tff(88,plain,
% 0.13/0.40 (((~![A: $i] : ((~ordinal(A)) | well_founded_relation(inclusion_relation(A)))) | ((~ordinal(A!1)) | well_founded_relation(inclusion_relation(A!1)))) <=> ((~![A: $i] : ((~ordinal(A)) | well_founded_relation(inclusion_relation(A)))) | (~ordinal(A!1)) | well_founded_relation(inclusion_relation(A!1)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(89,plain,
% 0.13/0.40 ((~![A: $i] : ((~ordinal(A)) | well_founded_relation(inclusion_relation(A)))) | ((~ordinal(A!1)) | well_founded_relation(inclusion_relation(A!1)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(90,plain,
% 0.13/0.40 ((~![A: $i] : ((~ordinal(A)) | well_founded_relation(inclusion_relation(A)))) | (~ordinal(A!1)) | well_founded_relation(inclusion_relation(A!1))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.13/0.40 tff(91,plain,
% 0.13/0.40 (well_founded_relation(inclusion_relation(A!1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[90, 87, 63])).
% 0.13/0.40 tff(92,plain,
% 0.13/0.40 ((~((~reflexive(inclusion_relation(A!1))) | (~transitive(inclusion_relation(A!1))) | (~antisymmetric(inclusion_relation(A!1))) | (~connected(inclusion_relation(A!1))) | (~well_founded_relation(inclusion_relation(A!1))))) | (~reflexive(inclusion_relation(A!1))) | (~transitive(inclusion_relation(A!1))) | (~antisymmetric(inclusion_relation(A!1))) | (~connected(inclusion_relation(A!1))) | (~well_founded_relation(inclusion_relation(A!1)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(93,plain,
% 0.13/0.40 ((~((~reflexive(inclusion_relation(A!1))) | (~transitive(inclusion_relation(A!1))) | (~antisymmetric(inclusion_relation(A!1))) | (~connected(inclusion_relation(A!1))) | (~well_founded_relation(inclusion_relation(A!1))))) | (~reflexive(inclusion_relation(A!1))) | (~transitive(inclusion_relation(A!1))) | (~antisymmetric(inclusion_relation(A!1)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[92, 91, 77])).
% 0.13/0.41 tff(94,plain,
% 0.13/0.41 (~((~reflexive(inclusion_relation(A!1))) | (~transitive(inclusion_relation(A!1))) | (~antisymmetric(inclusion_relation(A!1))) | (~connected(inclusion_relation(A!1))) | (~well_founded_relation(inclusion_relation(A!1))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[93, 54, 45, 36])).
% 0.13/0.41 tff(95,plain,
% 0.13/0.41 (~well_ordering(inclusion_relation(A!1))),
% 0.13/0.41 inference(or_elim,[status(thm)],[62])).
% 0.13/0.41 tff(96,plain,
% 0.13/0.41 ((((~reflexive(inclusion_relation(A!1))) | (~transitive(inclusion_relation(A!1))) | (~antisymmetric(inclusion_relation(A!1))) | (~connected(inclusion_relation(A!1))) | (~well_founded_relation(inclusion_relation(A!1)))) <=> well_ordering(inclusion_relation(A!1))) | ((~reflexive(inclusion_relation(A!1))) | (~transitive(inclusion_relation(A!1))) | (~antisymmetric(inclusion_relation(A!1))) | (~connected(inclusion_relation(A!1))) | (~well_founded_relation(inclusion_relation(A!1)))) | well_ordering(inclusion_relation(A!1))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(97,plain,
% 0.13/0.41 ((((~reflexive(inclusion_relation(A!1))) | (~transitive(inclusion_relation(A!1))) | (~antisymmetric(inclusion_relation(A!1))) | (~connected(inclusion_relation(A!1))) | (~well_founded_relation(inclusion_relation(A!1)))) <=> well_ordering(inclusion_relation(A!1))) | ((~reflexive(inclusion_relation(A!1))) | (~transitive(inclusion_relation(A!1))) | (~antisymmetric(inclusion_relation(A!1))) | (~connected(inclusion_relation(A!1))) | (~well_founded_relation(inclusion_relation(A!1))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.13/0.41 tff(98,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[97, 94, 27])).
% 0.13/0.41 % SZS output end Proof
% 0.13/0.41 % E exiting
%------------------------------------------------------------------------------