%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU555^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 : Wed Sep 30 08:26:42 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU555^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n015.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 13:53:17 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.23 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p
% 0.22/0.27 % Version: 3.5.1-ho
% 0.22/0.27 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.27 % Starting sh5l with 300s (1) cores
% 0.22/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.22/0.27 % new_bool_2 with pid 3559090 completed with status 0
% 0.22/0.27 % Result found by new_bool_2
% 0.22/0.27 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.27 % Starting sh5l with 300s (1) cores
% 0.22/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.22/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.27 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.22/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.27 % SubtermCWHack with pid 3559091 completed with status 0
% 0.22/0.27 % Result found by SubtermCWHack
% 0.22/0.27 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.27 % Starting sh5l with 300s (1) cores
% 0.22/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.22/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.27 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.22/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.27 % Preprocessing time : 0.004 s
% 0.22/0.27
% 0.22/0.27 % Proof found!
% 0.22/0.27 % SZS status Theorem
% 0.22/0.27 % SZS output start CNFRefutation
% 0.22/0.27 thf(decl_23, type, in: $i > $i > $o).
% 0.22/0.27 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.22/0.27 thf(decl_25, type, setextAx: $o).
% 0.22/0.27 thf(decl_26, type, emptyset: $i).
% 0.22/0.27 thf(decl_27, type, emptysetAx: $o).
% 0.22/0.27 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.22/0.27 thf(decl_29, type, setadjoinAx: $o).
% 0.22/0.27 thf(decl_30, type, powerset: $i > $i).
% 0.22/0.27 thf(decl_31, type, powersetAx: $o).
% 0.22/0.27 thf(decl_32, type, setunion: $i > $i).
% 0.22/0.27 thf(decl_33, type, setunionAx: $o).
% 0.22/0.27 thf(decl_34, type, omega: $i).
% 0.22/0.27 thf(decl_35, type, omega0Ax: $o).
% 0.22/0.27 thf(decl_36, type, omegaSAx: $o).
% 0.22/0.27 thf(decl_37, type, omegaIndAx: $o).
% 0.22/0.27 thf(decl_38, type, replAx: $o).
% 0.22/0.27 thf(decl_39, type, foundationAx: $o).
% 0.22/0.27 thf(decl_40, type, wellorderingAx: $o).
% 0.22/0.27 thf(decl_42, type, descrp: $o).
% 0.22/0.27 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.22/0.27 thf(decl_44, type, dsetconstrI: $o).
% 0.22/0.27 thf(decl_45, type, dsetconstrEL: $o).
% 0.22/0.27 thf(decl_46, type, dsetconstrER: $o).
% 0.22/0.27 thf(decl_47, type, exuE1: $o).
% 0.22/0.27 thf(decl_48, type, prop2set: $o > $i).
% 0.22/0.27 thf(decl_49, type, prop2setE: $o).
% 0.22/0.27 thf(decl_50, type, emptysetE: $o).
% 0.22/0.27 thf(decl_51, type, emptysetimpfalse: $o).
% 0.22/0.27 thf(decl_52, type, notinemptyset: $o).
% 0.22/0.27 thf(decl_53, type, exuE3e: $o).
% 0.22/0.27 thf(decl_54, type, setext: $o).
% 0.22/0.27 thf(decl_55, type, emptyI: $o).
% 0.22/0.27 thf(decl_56, type, noeltsimpempty: $o).
% 0.22/0.27 thf(decl_57, type, setbeta: $o).
% 0.22/0.27 thf(decl_58, type, nonempty: $i > $o).
% 0.22/0.27 thf(decl_59, type, nonemptyE1: $o).
% 0.22/0.27 thf(decl_60, type, nonemptyI: $o).
% 0.22/0.27 thf(decl_61, type, nonemptyI1: $o).
% 0.22/0.27 thf(decl_62, type, setadjoinIL: $o).
% 0.22/0.27 thf(decl_63, type, emptyinunitempty: $o).
% 0.22/0.27 thf(decl_64, type, setadjoinIR: $o).
% 0.22/0.27 thf(decl_65, type, setadjoinE: $o).
% 0.22/0.27 thf(decl_66, type, setadjoinOr: $o).
% 0.22/0.27 thf(decl_67, type, setoftrueEq: $o).
% 0.22/0.27 thf(decl_68, type, powersetI: $o).
% 0.22/0.27 thf(decl_69, type, emptyinPowerset: $o).
% 0.22/0.27 thf(decl_70, type, emptyInPowerset: $o).
% 0.22/0.27 thf(decl_71, type, powersetE: $o).
% 0.22/0.27 thf(decl_72, type, setunionI: $o).
% 0.22/0.27 thf(decl_73, type, setunionE: $o).
% 0.22/0.27 thf(decl_74, type, subPowSU: $o).
% 0.22/0.27 thf(decl_75, type, exuE2: $o).
% 0.22/0.27 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.22/0.27 thf(decl_77, type, uniqinunit: $o).
% 0.22/0.27 thf(decl_78, type, notinsingleton: $o).
% 0.22/0.27 thf(decl_79, type, eqinunit: $o).
% 0.22/0.27 thf(decl_80, type, singletonsswitch: $o).
% 0.22/0.27 thf(decl_81, type, upairsetE: $o).
% 0.22/0.27 thf(decl_82, type, upairsetIL: $o).
% 0.22/0.27 thf(decl_83, type, upairsetIR: $o).
% 0.22/0.27 thf(decl_84, type, emptyE1: $o).
% 0.22/0.27 thf(decl_85, type, vacuousDall: $o).
% 0.22/0.27 thf(decl_86, type, quantDeMorgan1: $o).
% 0.22/0.27 thf(decl_87, type, quantDeMorgan2: $o).
% 0.22/0.27 thf(decl_88, type, quantDeMorgan3: $o).
% 0.22/0.27 thf(decl_89, type, quantDeMorgan4: $o).
% 0.22/0.27 thf(decl_90, type, prop2setI: $o).
% 0.22/0.27 thf(decl_92, type, prop2set2propI: $o).
% 0.22/0.27 thf(decl_93, type, notdexE: $o).
% 0.22/0.27 thf(decl_94, type, notdallE: $o).
% 0.22/0.27 thf(decl_95, type, exuI1: $o).
% 0.22/0.27 thf(decl_96, type, exuI3: $o).
% 0.22/0.27 thf(decl_97, type, exuI2: $o).
% 0.22/0.27 thf(decl_98, type, inCongP: $o).
% 0.22/0.27 thf(decl_99, type, in__Cong: $o).
% 0.22/0.27 thf(decl_100, type, exuE3u: $o).
% 0.22/0.27 thf(decl_101, type, exu__Cong: $o).
% 0.22/0.27 thf(decl_102, type, emptyset__Cong: $o).
% 0.22/0.27 thf(decl_103, type, setadjoin__Cong: $o).
% 0.22/0.27 thf(decl_104, type, powerset__Cong: $o).
% 0.22/0.27 thf(decl_105, type, setunion__Cong: $o).
% 0.22/0.27 thf(decl_106, type, epred1_0: $o).
% 0.22/0.27 thf(decl_107, type, esk1_2: $i > $i > $i).
% 0.22/0.27 thf(decl_108, type, esk2_2: $i > $i > $i).
% 0.22/0.27 thf(decl_109, type, esk3_2: $i > $i > $i).
% 0.22/0.27 thf(decl_110, type, esk4_1: $i > $i).
% 0.22/0.27 thf(decl_111, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.22/0.27 thf(decl_112, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.27 thf(decl_113, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.22/0.27 thf(decl_114, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.27 thf(decl_115, type, esk9_1: $i > $i).
% 0.22/0.27 thf(decl_116, type, esk10_2: ($i > $o) > $i > $i).
% 0.22/0.27 thf(decl_117, type, esk11_1: ($i > $o) > $i).
% 0.22/0.27 thf(decl_118, type, esk12_2: ($i > $o) > $i > $i).
% 0.22/0.27 thf(decl_119, type, esk13_1: ($i > $o) > $i).
% 0.22/0.27 thf(decl_120, type, esk14_2: $i > $i > $i).
% 0.22/0.27 thf(decl_121, type, esk15_2: $i > $i > $i).
% 0.22/0.27 thf(decl_122, type, esk16_1: $i > $i).
% 0.22/0.27 thf(decl_123, type, esk17_1: $i > $i).
% 0.22/0.27 thf(decl_124, type, esk18_1: $i > $i).
% 0.22/0.27 thf(decl_125, type, esk19_2: $i > $i > $i).
% 0.22/0.27 thf(decl_126, type, esk20_3: $i > $i > $o > $i).
% 0.22/0.27 thf(decl_127, type, esk21_2: ($i > $o) > $i > $i).
% 0.22/0.27 thf(decl_128, type, esk22_1: ($i > $o) > $i).
% 0.22/0.27 thf(decl_129, type, esk23_1: $i > $i).
% 0.22/0.27 thf(decl_130, type, esk24_2: $i > ($i > $o) > $i).
% 0.22/0.27 thf(decl_131, type, esk25_2: $i > ($i > $o) > $i).
% 0.22/0.27 thf(decl_132, type, esk26_2: $i > ($i > $o) > $i).
% 0.22/0.27 thf(decl_133, type, esk27_2: $i > ($i > $o) > $i).
% 0.22/0.27 thf(decl_134, type, esk28_2: $i > ($i > $o) > $i).
% 0.22/0.27 thf(decl_135, type, esk29_2: $i > ($i > $o) > $i).
% 0.22/0.27 thf(decl_136, type, esk30_2: ($i > $o) > $i > $i).
% 0.22/0.27 thf(decl_137, type, esk31_1: ($i > $o) > $i).
% 0.22/0.27 thf(decl_138, type, esk32_1: ($i > $o) > $i).
% 0.22/0.27 thf(decl_139, type, esk33_1: ($i > $o) > $i).
% 0.22/0.27 thf(decl_140, type, esk34_1: ($i > $o) > $i).
% 0.22/0.27 thf(decl_141, type, esk35_2: ($i > $o) > $i > $i).
% 0.22/0.27 thf(decl_142, type, esk36_1: ($i > $o) > $i).
% 0.22/0.27 thf(decl_143, type, esk37_2: ($i > $o) > $i > $i).
% 0.22/0.27 thf(decl_144, type, esk38_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.27 thf(decl_145, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.27 thf(decl_146, type, esk40_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.27 thf(decl_147, type, esk41_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.27 thf(decl_148, type, esk42_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.27 thf(decl_149, type, esk43_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.27 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', exuI1)).
% 0.22/0.27 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', exu)).
% 0.22/0.27 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', exuI3)).
% 0.22/0.27 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', exuI2)).
% 0.22/0.27 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', exuE3u)).
% 0.22/0.27 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', exu__Cong)).
% 0.22/0.27 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', replAx)).
% 0.22/0.27 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', exuE1)).
% 0.22/0.27 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', nonempty)).
% 0.22/0.27 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', exuE3e)).
% 0.22/0.27 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', nonemptyI)).
% 0.22/0.27 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', exuE2)).
% 0.22/0.27 thf(omega__Cong, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega)=(omega))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', omega__Cong)).
% 0.22/0.27 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', dsetconstrEL)).
% 0.22/0.27 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', dsetconstrER)).
% 0.22/0.27 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', dsetconstrI)).
% 0.22/0.27 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', nonemptyE1)).
% 0.22/0.27 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', setbeta)).
% 0.22/0.27 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', setoftrueEq)).
% 0.22/0.27 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', nonemptyI1)).
% 0.22/0.27 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', nonemptyImpWitness)).
% 0.22/0.27 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', emptyE1)).
% 0.22/0.27 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', prop2setI)).
% 0.22/0.27 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', quantDeMorgan4)).
% 0.22/0.27 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', notdexE)).
% 0.22/0.27 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', notdallE)).
% 0.22/0.27 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', inCongP)).
% 0.22/0.27 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', in__Cong)).
% 0.22/0.27 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', emptyset__Cong)).
% 0.22/0.27 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', setadjoin__Cong)).
% 0.22/0.27 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', powerset__Cong)).
% 0.22/0.27 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', setunion__Cong)).
% 0.22/0.27 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', emptysetE)).
% 0.22/0.27 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', prop2setE)).
% 0.22/0.27 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', emptyinunitempty)).
% 0.22/0.27 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', setadjoinIL)).
% 0.22/0.27 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', wellorderingAx)).
% 0.22/0.27 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', emptysetimpfalse)).
% 0.22/0.27 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', noeltsimpempty)).
% 0.22/0.27 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', emptyI)).
% 0.22/0.27 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', setext)).
% 0.22/0.27 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', notinemptyset)).
% 0.22/0.27 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', setadjoinOr)).
% 0.22/0.27 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', setadjoinE)).
% 0.22/0.27 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', setadjoinIR)).
% 0.22/0.27 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', powersetI)).
% 0.22/0.27 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', subPowSU)).
% 0.22/0.27 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', setunionE)).
% 0.22/0.27 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', setunionI)).
% 0.22/0.27 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', powersetE)).
% 0.22/0.27 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', emptyInPowerset)).
% 0.22/0.27 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', emptyinPowerset)).
% 0.22/0.27 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', upairsetIR)).
% 0.22/0.27 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', upairsetIL)).
% 0.22/0.27 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', upairsetE)).
% 0.22/0.27 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', singletonsswitch)).
% 0.22/0.27 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', eqinunit)).
% 0.22/0.27 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', foundationAx)).
% 0.22/0.27 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', notinsingleton)).
% 0.22/0.27 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', uniqinunit)).
% 0.22/0.27 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', vacuousDall)).
% 0.22/0.27 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', quantDeMorgan1)).
% 0.22/0.27 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', quantDeMorgan2)).
% 0.22/0.27 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', quantDeMorgan3)).
% 0.22/0.27 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', omegaIndAx)).
% 0.22/0.27 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', omegaSAx)).
% 0.22/0.27 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', omega0Ax)).
% 0.22/0.27 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', setunionAx)).
% 0.22/0.27 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', powersetAx)).
% 0.22/0.27 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', setadjoinAx)).
% 0.22/0.27 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', emptysetAx)).
% 0.22/0.27 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.ecargI6Yrg/E---3.1_3559074.p', setextAx)).
% 0.22/0.27 thf(c_0_72, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.22/0.27 thf(c_0_73, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.22/0.27 thf(c_0_74, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.22/0.27 thf(c_0_75, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.22/0.27 thf(c_0_76, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.22/0.27 thf(c_0_77, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.22/0.27 thf(c_0_78, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.22/0.27 thf(c_0_79, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.22/0.27 thf(c_0_80, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.22/0.27 thf(c_0_81, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.22/0.27 thf(c_0_82, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.22/0.27 thf(c_0_83, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.22/0.27 thf(c_0_84, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega)=(omega)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[omega__Cong])).
% 0.22/0.27 thf(c_0_85, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.22/0.27 thf(c_0_86, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X224:$i]:(((((X1 @ X224)))&(![X225:$i]:(((((X1 @ X225)))=>(((X224)=(X225)))))))))))))), inference(apply_def,[status(thm)],[c_0_72, c_0_73])).
% 0.22/0.27 thf(c_0_87, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X226:$i]:(((((X1 @ X226)))&(![X227:$i]:(((((X1 @ X227)))=>(((X226)=(X227)))))))))))))))), inference(apply_def,[status(thm)],[c_0_74, c_0_73])).
% 0.22/0.27 thf(c_0_88, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X228:$i]:(((((X1 @ X228)))&(![X229:$i]:(((((X1 @ X229)))=>(((X228)=(X229)))))))))))))), inference(apply_def,[status(thm)],[c_0_75, c_0_73])).
% 0.22/0.27 thf(c_0_89, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X230:$i]:(((((X1 @ X230)))&(![X231:$i]:(((((X1 @ X231)))=>(((X230)=(X231))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_76, c_0_73])).
% 0.22/0.27 thf(c_0_90, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X232:$i]:(((((X1 @ X232)))&(![X233:$i]:(((((X1 @ X233)))=>(((X232)=(X233))))))))))<=>((?[X234:$i]:(((((X17 @ X234)))&(![X235:$i]:(((((X17 @ X235)))=>(((X234)=(X235)))))))))))))))), inference(apply_def,[status(thm)],[c_0_77, c_0_73])).
% 0.22/0.27 thf(c_0_91, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X216:$i]:(((((X6 @ X2 @ X216)))&(![X217:$i]:(((((X6 @ X2 @ X217)))=>(((X216)=(X217)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_78, c_0_73])).
% 0.22/0.27 thf(c_0_92, plain, ((exuE1)=(![X1:$i > $o]:((((?[X218:$i]:(((((X1 @ X218)))&(![X219:$i]:(((((X1 @ X219)))=>(((X218)=(X219))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_79, c_0_73])).
% 0.22/0.27 thf(c_0_93, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.22/0.27 thf(c_0_94, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.22/0.27 thf(c_0_95, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_80])).
% 0.22/0.27 thf(c_0_96, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.22/0.27 thf(c_0_97, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X220:$i]:(((((X1 @ X220)))&(![X221:$i]:(((((X1 @ X221)))=>(((X220)=(X221))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_81, c_0_73])).
% 0.22/0.27 thf(c_0_98, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_82, c_0_80])).
% 0.22/0.27 thf(c_0_99, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.22/0.27 thf(c_0_100, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_80])).
% 0.22/0.27 thf(c_0_101, plain, ((exuE2)=(![X1:$i > $o]:((((?[X222:$i]:(((((X1 @ X222)))&(![X223:$i]:(((((X1 @ X223)))=>(((X222)=(X223))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_83, c_0_73])).
% 0.22/0.27 thf(c_0_102, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_80])).
% 0.22/0.27 thf(c_0_103, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 0.22/0.27 thf(c_0_104, plain, ((epred1_0)<=>![X265:$i]:(?[X266:$i]:((((![X267:$i]:(((in @ X267 @ X266)=>![X268:$i]:(((in @ X268 @ X267)=>(in @ X268 @ X265)))))&![X269:$i, X270:$i]:((((in @ X269 @ X265)&(in @ X270 @ X265))=>(![X271:$i]:(((in @ X271 @ X266)=>((in @ X269 @ X271)<=>(in @ X270 @ X271))))=>((X269)=(X270))))))&![X272:$i, X273:$i]:((((in @ X272 @ X266)&(in @ X273 @ X266))=>(![X274:$i]:(((in @ X274 @ X272)=>(in @ X274 @ X273)))|![X275:$i]:(((in @ X275 @ X273)=>(in @ X275 @ X272)))))))&![X276:$i]:(((![X277:$i]:(((in @ X277 @ X276)=>(in @ X277 @ X265)))&?[X278:$i]:((in @ X278 @ X276)))=>?[X279:$i, X280:$i]:(((((in @ X279 @ X266)&(in @ X280 @ X276))&~(?[X281:$i]:(((in @ X281 @ X279)&(in @ X281 @ X276)))))&![X282:$i]:(((in @ X282 @ X266)=>(![X283:$i]:(((in @ X283 @ X282)=>(in @ X283 @ X279)))|(in @ X280 @ X282)))))))))))), introduced(definition)).
% 0.22/0.27 thf(c_0_105, negated_conjecture, ~((![X236:$i, X237:$i]:((![X238:$i]:(((in @ X238 @ X236)<=>(in @ X238 @ X237)))=>((X236)=(X237))))=>(![X239:$i]:(~(in @ X239 @ emptyset))=>(![X240:$i, X241:$i, X242:$i]:(((in @ X242 @ (setadjoin @ X240 @ X241))<=>(((X242)=(X240))|(in @ X242 @ X241))))=>(![X243:$i, X244:$i]:(((in @ X244 @ (powerset @ X243))<=>![X245:$i]:(((in @ X245 @ X244)=>(in @ X245 @ X243)))))=>(![X246:$i, X247:$i]:(((in @ X247 @ (setunion @ X246))<=>?[X248:$i]:(((in @ X247 @ X248)&(in @ X248 @ X246)))))=>((in @ emptyset @ omega)=>(![X249:$i]:(((in @ X249 @ omega)=>(in @ (setadjoin @ X249 @ X249) @ omega)))=>(![X250:$i]:((((in @ emptyset @ X250)&![X251:$i]:((((in @ X251 @ omega)&(in @ X251 @ X250))=>(in @ (setadjoin @ X251 @ X251) @ X250))))=>![X252:$i]:(((in @ X252 @ omega)=>(in @ X252 @ X250)))))=>(![X253:$i > $i > $o, X254:$i]:((![X255:$i]:(((in @ X255 @ X254)=>?[X256:$i]:(((X253 @ X255 @ X256)&![X257:$i]:(((X253 @ X255 @ X257)=>((X256)=(X257))))))))=>?[X258:$i]:(![X259:$i]:(((in @ X259 @ X258)<=>?[X260:$i]:(((in @ X260 @ X254)&(X253 @ X260 @ X259))))))))=>(![X261:$i]:((?[X262:$i]:((in @ X262 @ X261))=>?[X263:$i]:(((in @ X263 @ X261)&~(?[X264:$i]:(((in @ X264 @ X263)&(in @ X264 @ X261))))))))=>((epred1_0)=>((descrp)=>(![X284:$i, X285:$i > $o, X286:$i]:(((in @ X286 @ X284)=>((X285 @ X286)=>(in @ X286 @ (dsetconstr @ X284 @ (^[Z0:$i]:((X285 @ Z0))))))))=>(![X287:$i, X288:$i > $o, X289:$i]:(((in @ X289 @ (dsetconstr @ X287 @ (^[Z0:$i]:((X288 @ Z0)))))=>(in @ X289 @ X287)))=>(![X290:$i, X291:$i > $o, X292:$i]:(((in @ X292 @ (dsetconstr @ X290 @ (^[Z0:$i]:((X291 @ Z0)))))=>(X291 @ X292)))=>(![X293:$i > $o]:((?[X294:$i]:(((X293 @ X294)&![X295:$i]:(((X293 @ X295)=>((X294)=(X295))))))=>?[X296:$i]:(((X293 @ X296)&![X297:$i]:(((X293 @ X297)=>((X296)=(X297))))))))=>(![X298:$o, X299:$i]:(((in @ X299 @ (prop2set @ ((X298))))=>(X298)))=>(![X300:$i]:(((in @ X300 @ emptyset)=>![X301:$o]:((X301))))=>(![X302:$i]:(~(in @ X302 @ emptyset))=>(![X303:$i]:(~(in @ X303 @ emptyset))=>(![X304:$i > $o]:((?[X305:$i]:(((X304 @ X305)&![X306:$i]:(((X304 @ X306)=>((X305)=(X306))))))=>?[X307:$i]:((X304 @ X307))))=>(![X308:$i, X309:$i]:((![X310:$i]:(((in @ X310 @ X308)=>(in @ X310 @ X309)))=>(![X311:$i]:(((in @ X311 @ X309)=>(in @ X311 @ X308)))=>((X308)=(X309)))))=>(![X312:$i]:((![X313:$i]:(~(in @ X313 @ X312))=>((X312)=(emptyset))))=>(![X314:$i]:((![X315:$i]:(~(in @ X315 @ X314))=>((X314)=(emptyset))))=>(![X316:$i, X317:$i > $o, X318:$i]:(((in @ X318 @ X316)=>((in @ X318 @ (dsetconstr @ X316 @ (^[Z0:$i]:((X317 @ Z0)))))<=>(X317 @ X318))))=>(![X319:$i]:((((X319)!=(emptyset))=>?[X320:$i]:((in @ X320 @ X319))))=>(![X321:$i, X322:$i > $o, X323:$i]:(((in @ X323 @ X321)=>((X322 @ X323)=>((dsetconstr @ X321 @ (^[Z0:$i]:((X322 @ Z0))))!=(emptyset)))))=>(![X324:$i]:((?[X325:$i]:((in @ X325 @ X324))=>((X324)!=(emptyset))))=>(![X326:$i, X327:$i]:((in @ X326 @ (setadjoin @ X326 @ X327)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X328:$i, X329:$i, X330:$i]:(((in @ X330 @ X329)=>(in @ X330 @ (setadjoin @ X328 @ X329))))=>(![X331:$i, X332:$i, X333:$i]:(((in @ X333 @ (setadjoin @ X331 @ X332))=>![X334:$o]:(((((X333)=(X331))=>(X334))=>(((in @ X333 @ X332)=>(X334))=>(X334))))))=>(![X335:$i, X336:$i, X337:$i]:(((in @ X337 @ (setadjoin @ X335 @ X336))=>(((X337)=(X335))|(in @ X337 @ X336))))=>(![X338:$i]:(((dsetconstr @ X338 @ (^[Z0:$i]:(($true))))=(X338)))=>(![X339:$i, X340:$i]:((![X341:$i]:(((in @ X341 @ X340)=>(in @ X341 @ X339)))=>(in @ X340 @ (powerset @ X339))))=>(![X342:$i]:((in @ emptyset @ (powerset @ X342)))=>(![X343:$i]:((in @ emptyset @ (powerset @ X343)))=>(![X344:$i, X345:$i, X346:$i]:(((in @ X345 @ (powerset @ X344))=>((in @ X346 @ X345)=>(in @ X346 @ X344))))=>(![X347:$i, X348:$i, X349:$i]:(((in @ X348 @ X349)=>((in @ X349 @ X347)=>(in @ X348 @ (setunion @ X347)))))=>(![X350:$i, X351:$i]:(((in @ X351 @ (setunion @ X350))=>![X352:$o]:((![X353:$i]:(((in @ X351 @ X353)=>((in @ X353 @ X350)=>(X352))))=>(X352)))))=>(![X354:$i, X355:$i]:(((in @ X355 @ X354)=>(in @ X355 @ (powerset @ (setunion @ X354)))))=>(![X356:$i > $o]:((?[X357:$i]:(((X356 @ X357)&![X358:$i]:(((X356 @ X358)=>((X357)=(X358))))))=>?[X359:$i]:(![X360:$i]:(((X356 @ X360)<=>((X360)=(X359)))))))=>(![X361:$i]:((((X361)!=(emptyset))=>?[X362:$i]:((in @ X362 @ X361))))=>(![X363:$i, X364:$i]:(((in @ X363 @ (setadjoin @ X364 @ emptyset))=>((X363)=(X364))))=>(![X365:$i, X366:$i]:((((X365)!=(X366))=>~(in @ X366 @ (setadjoin @ X365 @ emptyset))))=>(![X367:$i, X368:$i]:((((X367)=(X368))=>(in @ X367 @ (setadjoin @ X368 @ emptyset))))=>(![X369:$i, X370:$i]:(((in @ X369 @ (setadjoin @ X370 @ emptyset))=>(in @ X370 @ (setadjoin @ X369 @ emptyset))))=>(![X371:$i, X372:$i, X373:$i]:(((in @ X373 @ (setadjoin @ X371 @ (setadjoin @ X372 @ emptyset)))=>(((X373)=(X371))|((X373)=(X372)))))=>(![X374:$i, X375:$i]:((in @ X374 @ (setadjoin @ X374 @ (setadjoin @ X375 @ emptyset))))=>(![X376:$i, X377:$i]:((in @ X377 @ (setadjoin @ X376 @ (setadjoin @ X377 @ emptyset))))=>(![X378:$i, X379:$i > $o]:((?[X380:$i]:(((in @ X380 @ X378)&(X379 @ X380)))=>((dsetconstr @ X378 @ (^[Z0:$i]:((X379 @ Z0))))!=(emptyset))))=>(![X381:$i > $o, X382:$i]:(((in @ X382 @ emptyset)=>(X381 @ X382)))=>(![X383:$i, X384:$i > $o]:((~(![X385:$i]:(((in @ X385 @ X383)=>(X384 @ X385))))=>?[X386:$i]:(((in @ X386 @ X383)&~(X384 @ X386)))))=>(![X387:$i, X388:$i > $o]:((![X389:$i]:(((in @ X389 @ X387)=>~(X388 @ X389)))=>~(?[X390:$i]:(((in @ X390 @ X387)&(X388 @ X390))))))=>(![X391:$i, X392:$i > $o]:((~(?[X393:$i]:(((in @ X393 @ X391)&(X392 @ X393))))=>![X394:$i]:(((in @ X394 @ X391)=>~(X392 @ X394)))))=>(![X395:$i, X396:$i > $o]:((?[X397:$i]:(((in @ X397 @ X395)&~(X396 @ X397)))=>~(![X398:$i]:(((in @ X398 @ X395)=>(X396 @ X398))))))=>(![X399:$o]:(((X399)=>(in @ emptyset @ (prop2set @ ((X399))))))=>((prop2set2propI)=>(![X400:$i, X401:$i > $o]:((~(?[X402:$i]:(((in @ X402 @ X400)&(X401 @ X402))))=>![X403:$i]:(((in @ X403 @ X400)=>~(X401 @ X403)))))=>(![X404:$i, X405:$i > $o]:((~(![X406:$i]:(((in @ X406 @ X404)=>(X405 @ X406))))=>?[X407:$i]:(((in @ X407 @ X404)&~(X405 @ X407)))))=>(![X408:$i > $o]:((?[X409:$i]:(((X408 @ X409)&![X410:$i]:(((X408 @ X410)=>((X409)=(X410))))))=>?[X411:$i]:(((X408 @ X411)&![X412:$i]:(((X408 @ X412)=>((X411)=(X412))))))))=>(![X413:$i > $o]:((?[X414:$i]:((X413 @ X414))=>(![X415:$i, X416:$i]:(((X413 @ X415)=>((X413 @ X416)=>((X415)=(X416)))))=>?[X417:$i]:(((X413 @ X417)&![X418:$i]:(((X413 @ X418)=>((X417)=(X418)))))))))=>(![X419:$i > $o]:((?[X420:$i]:(![X421:$i]:(((X419 @ X421)<=>((X421)=(X420)))))=>?[X422:$i]:(((X419 @ X422)&![X423:$i]:(((X419 @ X423)=>((X422)=(X423))))))))=>(![X424:$i, X425:$i]:((((X424)=(X425))=>![X426:$i, X427:$i]:((((X426)=(X427))=>((in @ X426 @ X424)=>(in @ X427 @ X425))))))=>(![X428:$i, X429:$i]:((((X428)=(X429))=>![X430:$i, X431:$i]:((((X430)=(X431))=>((in @ X430 @ X428)<=>(in @ X431 @ X429))))))=>(![X432:$i > $o]:((?[X433:$i]:(((X432 @ X433)&![X434:$i]:(((X432 @ X434)=>((X433)=(X434))))))=>![X435:$i, X436:$i]:(((X432 @ X435)=>((X432 @ X436)=>((X435)=(X436)))))))=>(![X437:$i > $o, X438:$i > $o]:((![X439:$i, X440:$i]:((((X439)=(X440))=>((X437 @ X439)<=>(X438 @ X440))))=>(?[X441:$i]:(((X437 @ X441)&![X442:$i]:(((X437 @ X442)=>((X441)=(X442))))))<=>?[X443:$i]:(((X438 @ X443)&![X444:$i]:(((X438 @ X444)=>((X443)=(X444)))))))))=>(((emptyset)=(emptyset))=>(![X445:$i, X446:$i]:((((X445)=(X446))=>![X447:$i, X448:$i]:((((X447)=(X448))=>((setadjoin @ X445 @ X447)=(setadjoin @ X446 @ X448))))))=>(![X449:$i, X450:$i]:((((X449)=(X450))=>((powerset @ X449)=(powerset @ X450))))=>(![X451:$i, X452:$i]:((((X451)=(X452))=>((setunion @ X451)=(setunion @ X452))))=>((omega)=(omega)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_84, c_0_85]), prop2setI]), quantDeMorgan4]), notdexE]), notdallE]), c_0_86]), c_0_87]), c_0_88]), inCongP]), in__Cong]), c_0_89]), c_0_90]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), c_0_91]), emptysetE]), prop2setE]), c_0_92]), c_0_93]), emptyinunitempty]), setadjoinIL]), c_0_94]), wellorderingAx]), emptysetimpfalse]), c_0_95]), c_0_96]), noeltsimpempty]), emptyI]), setext]), c_0_97]), notinemptyset]), c_0_98]), c_0_99]), setadjoinOr]), setadjoinE]), setadjoinIR]), c_0_100]), powersetI]), c_0_101]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), c_0_102]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), foundationAx]), notinsingleton]), uniqinunit]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), c_0_103]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])]), c_0_104])).
% 0.22/0.27 thf(c_0_106, negated_conjecture, ![X453:$i, X454:$i, X456:$i, X457:$i, X458:$i, X459:$i, X460:$i, X461:$i, X462:$i, X463:$i, X464:$i, X466:$i, X467:$i, X469:$i, X470:$i, X471:$i, X472:$i, X473:$i, X475:$i, X476:$i > $i > $o, X477:$i, X479:$i, X482:$i, X484:$i, X485:$i, X486:$i, X487:$i, X489:$i, X490:$i, X491:$i > $o, X492:$i, X493:$i, X494:$i > $o, X495:$i, X496:$i, X497:$i > $o, X498:$i, X499:$i > $o, X500:$i, X503:$i, X504:$o, X505:$i, X506:$i, X507:$o, X508:$i, X509:$i, X510:$i > $o, X511:$i, X514:$i, X515:$i, X518:$i, X520:$i, X522:$i, X523:$i > $o, X524:$i, X525:$i, X527:$i, X528:$i > $o, X529:$i, X530:$i, X531:$i, X532:$i, X533:$i, X534:$i, X535:$i, X536:$i, X537:$i, X538:$i, X539:$i, X540:$o, X541:$i, X542:$i, X543:$i, X544:$i, X545:$i, X546:$i, X548:$i, X549:$i, X550:$i, X551:$i, X552:$i, X553:$i, X554:$i, X555:$i, X556:$i, X557:$i, X558:$o, X560:$i, X561:$i, X562:$i > $o, X563:$i, X566:$i, X567:$i, X568:$i, X570:$i, X571:$i, X572:$i, X573:$i, X574:$i, X575:$i, X576:$i, X577:$i, X578:$i, X579:$i, X580:$i, X581:$i, X582:$i, X583:$i, X584:$i, X585:$i, X586:$i > $o, X587:$i, X588:$i > $o, X589:$i, X590:$i, X591:$i > $o, X592:$i, X594:$i, X595:$i > $o, X597:$i, X598:$i, X599:$i > $o, X601:$i, X602:$i, X603:$i > $o, X604:$i, X606:$o, X607:$i, X608:$i > $o, X610:$i, X611:$i, X612:$i > $o, X613:$i, X615:$i > $o, X616:$i, X619:$i, X620:$i > $o, X621:$i, X625:$i, X626:$i > $o, X627:$i, X630:$i, X631:$i, X632:$i, X633:$i, X634:$i, X635:$i, X636:$i, X637:$i, X638:$i, X639:$i > $o, X640:$i, X642:$i, X643:$i, X644:$i > $o, X645:$i > $o, X648:$i, X651:$i, X652:$i, X655:$i, X656:$i, X657:$i, X658:$i, X659:$i, X660:$i, X661:$i, X662:$i, X663:$i]:((((~(in @ (esk1_2 @ X453 @ X454) @ X453)|~(in @ (esk1_2 @ X453 @ X454) @ X454)|((X453)=(X454)))&((in @ (esk1_2 @ X453 @ X454) @ X453)|(in @ (esk1_2 @ X453 @ X454) @ X454)|((X453)=(X454))))&(~(in @ X456 @ emptyset)&(((~(in @ X459 @ (setadjoin @ X457 @ X458))|(((X459)=(X457))|(in @ X459 @ X458)))&((((X459)!=(X457))|(in @ X459 @ (setadjoin @ X457 @ X458)))&(~(in @ X459 @ X458)|(in @ X459 @ (setadjoin @ X457 @ X458)))))&(((~(in @ X461 @ (powerset @ X460))|(~(in @ X462 @ X461)|(in @ X462 @ X460)))&(((in @ (esk2_2 @ X463 @ X464) @ X464)|(in @ X464 @ (powerset @ X463)))&(~(in @ (esk2_2 @ X463 @ X464) @ X463)|(in @ X464 @ (powerset @ X463)))))&(((((in @ X467 @ (esk3_2 @ X466 @ X467))|~(in @ X467 @ (setunion @ X466)))&((in @ (esk3_2 @ X466 @ X467) @ X466)|~(in @ X467 @ (setunion @ X466))))&(~(in @ X470 @ X471)|~(in @ X471 @ X469)|(in @ X470 @ (setunion @ X469))))&((in @ emptyset @ omega)&((~(in @ X472 @ omega)|(in @ (setadjoin @ X472 @ X472) @ omega))&(((((in @ (esk4_1 @ X473) @ omega)|~(in @ emptyset @ X473)|(~(in @ X475 @ omega)|(in @ X475 @ X473)))&((in @ (esk4_1 @ X473) @ X473)|~(in @ emptyset @ X473)|(~(in @ X475 @ omega)|(in @ X475 @ X473))))&(~(in @ (setadjoin @ (esk4_1 @ X473) @ (esk4_1 @ X473)) @ X473)|~(in @ emptyset @ X473)|(~(in @ X475 @ omega)|(in @ X475 @ X473))))&((((((in @ (esk8_3 @ X476 @ X477 @ X482) @ X477)|~(in @ X482 @ (esk7_2 @ X476 @ X477))|(in @ (esk5_2 @ X476 @ X477) @ X477))&((X476 @ (esk8_3 @ X476 @ X477 @ X482) @ X482)|~(in @ X482 @ (esk7_2 @ X476 @ X477))|(in @ (esk5_2 @ X476 @ X477) @ X477)))&(~(in @ X485 @ X477)|~(X476 @ X485 @ X484)|(in @ X484 @ (esk7_2 @ X476 @ X477))|(in @ (esk5_2 @ X476 @ X477) @ X477)))&(((((in @ (esk8_3 @ X476 @ X477 @ X482) @ X477)|~(in @ X482 @ (esk7_2 @ X476 @ X477))|((X476 @ (esk5_2 @ X476 @ X477) @ (esk6_3 @ X476 @ X477 @ X479))|~(X476 @ (esk5_2 @ X476 @ X477) @ X479)))&((X476 @ (esk8_3 @ X476 @ X477 @ X482) @ X482)|~(in @ X482 @ (esk7_2 @ X476 @ X477))|((X476 @ (esk5_2 @ X476 @ X477) @ (esk6_3 @ X476 @ X477 @ X479))|~(X476 @ (esk5_2 @ X476 @ X477) @ X479))))&(~(in @ X485 @ X477)|~(X476 @ X485 @ X484)|(in @ X484 @ (esk7_2 @ X476 @ X477))|((X476 @ (esk5_2 @ X476 @ X477) @ (esk6_3 @ X476 @ X477 @ X479))|~(X476 @ (esk5_2 @ X476 @ X477) @ X479))))&((((in @ (esk8_3 @ X476 @ X477 @ X482) @ X477)|~(in @ X482 @ (esk7_2 @ X476 @ X477))|(((X479)!=(esk6_3 @ X476 @ X477 @ X479))|~(X476 @ (esk5_2 @ X476 @ X477) @ X479)))&((X476 @ (esk8_3 @ X476 @ X477 @ X482) @ X482)|~(in @ X482 @ (esk7_2 @ X476 @ X477))|(((X479)!=(esk6_3 @ X476 @ X477 @ X479))|~(X476 @ (esk5_2 @ X476 @ X477) @ X479))))&(~(in @ X485 @ X477)|~(X476 @ X485 @ X484)|(in @ X484 @ (esk7_2 @ X476 @ X477))|(((X479)!=(esk6_3 @ X476 @ X477 @ X479))|~(X476 @ (esk5_2 @ X476 @ X477) @ X479))))))&((((in @ (esk9_1 @ X486) @ X486)|~(in @ X487 @ X486))&(~(in @ X489 @ (esk9_1 @ X486))|~(in @ X489 @ X486)|~(in @ X487 @ X486)))&((epred1_0)&((descrp)&((~(in @ X492 @ X490)|(~(X491 @ X492)|(in @ X492 @ (dsetconstr @ X490 @ (^[Z0:$i]:((X491 @ Z0)))))))&((~(in @ X495 @ (dsetconstr @ X493 @ (^[Z0:$i]:((X494 @ Z0)))))|(in @ X495 @ X493))&((~(in @ X498 @ (dsetconstr @ X496 @ (^[Z0:$i]:((X497 @ Z0)))))|(X497 @ X498))&(((((X499 @ (esk11_1 @ X499))|((X499 @ (esk10_2 @ X499 @ X500))|~(X499 @ X500)))&(~(X499 @ X503)|((esk11_1 @ X499)=(X503))|((X499 @ (esk10_2 @ X499 @ X500))|~(X499 @ X500))))&(((X499 @ (esk11_1 @ X499))|(((X500)!=(esk10_2 @ X499 @ X500))|~(X499 @ X500)))&(~(X499 @ X503)|((esk11_1 @ X499)=(X503))|(((X500)!=(esk10_2 @ X499 @ X500))|~(X499 @ X500)))))&((~(in @ X505 @ (prop2set @ ((X504))))|(X504))&((~(in @ X506 @ emptyset)|(X507))&(~(in @ X508 @ emptyset)&(~(in @ X509 @ emptyset)&((((X510 @ (esk12_2 @ X510 @ X511))|~(X510 @ X511)|(X510 @ (esk13_1 @ X510)))&(((X511)!=(esk12_2 @ X510 @ X511))|~(X510 @ X511)|(X510 @ (esk13_1 @ X510))))&(((((in @ (esk15_2 @ X514 @ X515) @ X515)|((X514)=(X515))|(in @ (esk14_2 @ X514 @ X515) @ X514))&(~(in @ (esk15_2 @ X514 @ X515) @ X514)|((X514)=(X515))|(in @ (esk14_2 @ X514 @ X515) @ X514)))&(((in @ (esk15_2 @ X514 @ X515) @ X515)|((X514)=(X515))|~(in @ (esk14_2 @ X514 @ X515) @ X515))&(~(in @ (esk15_2 @ X514 @ X515) @ X514)|((X514)=(X515))|~(in @ (esk14_2 @ X514 @ X515) @ X515))))&(((in @ (esk16_1 @ X518) @ X518)|((X518)=(emptyset)))&(((in @ (esk17_1 @ X520) @ X520)|((X520)=(emptyset)))&(((~(in @ X524 @ (dsetconstr @ X522 @ (^[Z0:$i]:((X523 @ Z0)))))|(X523 @ X524)|~(in @ X524 @ X522))&(~(X523 @ X524)|(in @ X524 @ (dsetconstr @ X522 @ (^[Z0:$i]:((X523 @ Z0)))))|~(in @ X524 @ X522)))&((((X525)=(emptyset))|(in @ (esk18_1 @ X525) @ X525))&((~(in @ X529 @ X527)|(~(X528 @ X529)|((dsetconstr @ X527 @ (^[Z0:$i]:((X528 @ Z0))))!=(emptyset))))&((~(in @ X531 @ X530)|((X530)!=(emptyset)))&((in @ X532 @ (setadjoin @ X532 @ X533))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X536 @ X535)|(in @ X536 @ (setadjoin @ X534 @ X535)))&(((((in @ X539 @ X538)|(X540)|((X539)=(X537))|~(in @ X539 @ (setadjoin @ X537 @ X538)))&(~(X540)|(X540)|((X539)=(X537))|~(in @ X539 @ (setadjoin @ X537 @ X538))))&(((in @ X539 @ X538)|(X540)|~(X540)|~(in @ X539 @ (setadjoin @ X537 @ X538)))&(~(X540)|(X540)|~(X540)|~(in @ X539 @ (setadjoin @ X537 @ X538)))))&((~(in @ X543 @ (setadjoin @ X541 @ X542))|(((X543)=(X541))|(in @ X543 @ X542)))&(((dsetconstr @ X544 @ (^[Z0:$i]:(($true))))=(X544))&((((in @ (esk19_2 @ X545 @ X546) @ X546)|(in @ X546 @ (powerset @ X545)))&(~(in @ (esk19_2 @ X545 @ X546) @ X545)|(in @ X546 @ (powerset @ X545))))&((in @ emptyset @ (powerset @ X548))&((in @ emptyset @ (powerset @ X549))&((~(in @ X551 @ (powerset @ X550))|(~(in @ X552 @ X551)|(in @ X552 @ X550)))&((~(in @ X554 @ X555)|(~(in @ X555 @ X553)|(in @ X554 @ (setunion @ X553))))&((((in @ X557 @ (esk20_3 @ X556 @ X557 @ X558))|(X558)|~(in @ X557 @ (setunion @ X556)))&(((in @ (esk20_3 @ X556 @ X557 @ X558) @ X556)|(X558)|~(in @ X557 @ (setunion @ X556)))&(~(X558)|(X558)|~(in @ X557 @ (setunion @ X556)))))&((~(in @ X561 @ X560)|(in @ X561 @ (powerset @ (setunion @ X560))))&((((~(X562 @ X566)|((X566)=(esk22_1 @ X562))|((X562 @ (esk21_2 @ X562 @ X563))|~(X562 @ X563)))&(((X567)!=(esk22_1 @ X562))|(X562 @ X567)|((X562 @ (esk21_2 @ X562 @ X563))|~(X562 @ X563))))&((~(X562 @ X566)|((X566)=(esk22_1 @ X562))|(((X563)!=(esk21_2 @ X562 @ X563))|~(X562 @ X563)))&(((X567)!=(esk22_1 @ X562))|(X562 @ X567)|(((X563)!=(esk21_2 @ X562 @ X563))|~(X562 @ X563)))))&((((X568)=(emptyset))|(in @ (esk23_1 @ X568) @ X568))&((~(in @ X570 @ (setadjoin @ X571 @ emptyset))|((X570)=(X571)))&((((X572)=(X573))|~(in @ X573 @ (setadjoin @ X572 @ emptyset)))&((((X574)!=(X575))|(in @ X574 @ (setadjoin @ X575 @ emptyset)))&((~(in @ X576 @ (setadjoin @ X577 @ emptyset))|(in @ X577 @ (setadjoin @ X576 @ emptyset)))&((~(in @ X580 @ (setadjoin @ X578 @ (setadjoin @ X579 @ emptyset)))|(((X580)=(X578))|((X580)=(X579))))&((in @ X581 @ (setadjoin @ X581 @ (setadjoin @ X582 @ emptyset)))&((in @ X584 @ (setadjoin @ X583 @ (setadjoin @ X584 @ emptyset)))&((~(in @ X587 @ X585)|~(X586 @ X587)|((dsetconstr @ X585 @ (^[Z0:$i]:((X586 @ Z0))))!=(emptyset)))&((~(in @ X589 @ emptyset)|(X588 @ X589))&((((in @ (esk24_2 @ X590 @ X591) @ X590)|(~(in @ X592 @ X590)|(X591 @ X592)))&(~(X591 @ (esk24_2 @ X590 @ X591))|(~(in @ X592 @ X590)|(X591 @ X592))))&((((in @ (esk25_2 @ X594 @ X595) @ X594)|(~(in @ X597 @ X594)|~(X595 @ X597)))&((X595 @ (esk25_2 @ X594 @ X595))|(~(in @ X597 @ X594)|~(X595 @ X597))))&((((in @ (esk26_2 @ X598 @ X599) @ X598)|(~(in @ X601 @ X598)|~(X599 @ X601)))&((X599 @ (esk26_2 @ X598 @ X599))|(~(in @ X601 @ X598)|~(X599 @ X601))))&((((in @ (esk27_2 @ X602 @ X603) @ X602)|(~(in @ X604 @ X602)|(X603 @ X604)))&(~(X603 @ (esk27_2 @ X602 @ X603))|(~(in @ X604 @ X602)|(X603 @ X604))))&((~(X606)|(in @ emptyset @ (prop2set @ ((X606)))))&((prop2set2propI)&((((in @ (esk28_2 @ X607 @ X608) @ X607)|(~(in @ X610 @ X607)|~(X608 @ X610)))&((X608 @ (esk28_2 @ X607 @ X608))|(~(in @ X610 @ X607)|~(X608 @ X610))))&((((in @ (esk29_2 @ X611 @ X612) @ X611)|(~(in @ X613 @ X611)|(X612 @ X613)))&(~(X612 @ (esk29_2 @ X611 @ X612))|(~(in @ X613 @ X611)|(X612 @ X613))))&(((((X615 @ (esk31_1 @ X615))|((X615 @ (esk30_2 @ X615 @ X616))|~(X615 @ X616)))&(~(X615 @ X619)|((esk31_1 @ X615)=(X619))|((X615 @ (esk30_2 @ X615 @ X616))|~(X615 @ X616))))&(((X615 @ (esk31_1 @ X615))|(((X616)!=(esk30_2 @ X615 @ X616))|~(X615 @ X616)))&(~(X615 @ X619)|((esk31_1 @ X615)=(X619))|(((X616)!=(esk30_2 @ X615 @ X616))|~(X615 @ X616)))))&(((((X620 @ (esk34_1 @ X620))|(X620 @ (esk32_1 @ X620))|~(X620 @ X621))&(~(X620 @ X625)|((esk34_1 @ X620)=(X625))|(X620 @ (esk32_1 @ X620))|~(X620 @ X621)))&((((X620 @ (esk34_1 @ X620))|(X620 @ (esk33_1 @ X620))|~(X620 @ X621))&(~(X620 @ X625)|((esk34_1 @ X620)=(X625))|(X620 @ (esk33_1 @ X620))|~(X620 @ X621)))&(((X620 @ (esk34_1 @ X620))|((esk32_1 @ X620)!=(esk33_1 @ X620))|~(X620 @ X621))&(~(X620 @ X625)|((esk34_1 @ X620)=(X625))|((esk32_1 @ X620)!=(esk33_1 @ X620))|~(X620 @ X621)))))&(((((X626 @ (esk36_1 @ X626))|(~(X626 @ (esk35_2 @ X626 @ X627))|((esk35_2 @ X626 @ X627)!=(X627))))&(~(X626 @ X630)|((esk36_1 @ X626)=(X630))|(~(X626 @ (esk35_2 @ X626 @ X627))|((esk35_2 @ X626 @ X627)!=(X627)))))&(((X626 @ (esk36_1 @ X626))|((X626 @ (esk35_2 @ X626 @ X627))|((esk35_2 @ X626 @ X627)=(X627))))&(~(X626 @ X630)|((esk36_1 @ X626)=(X630))|((X626 @ (esk35_2 @ X626 @ X627))|((esk35_2 @ X626 @ X627)=(X627))))))&((((X631)!=(X632))|(((X633)!=(X634))|(~(in @ X633 @ X631)|(in @ X634 @ X632))))&(((~(in @ X637 @ X635)|(in @ X638 @ X636)|((X637)!=(X638))|((X635)!=(X636)))&(~(in @ X638 @ X636)|(in @ X637 @ X635)|((X637)!=(X638))|((X635)!=(X636))))&((((X639 @ (esk37_2 @ X639 @ X640))|~(X639 @ X640)|(~(X639 @ X642)|(~(X639 @ X643)|((X642)=(X643)))))&(((X640)!=(esk37_2 @ X639 @ X640))|~(X639 @ X640)|(~(X639 @ X642)|(~(X639 @ X643)|((X642)=(X643))))))&(((((((X645 @ (esk41_2 @ X644 @ X645))|((X644 @ (esk40_3 @ X644 @ X645 @ X648))|~(X644 @ X648))|((esk38_2 @ X644 @ X645)=(esk39_2 @ X644 @ X645)))&(~(X645 @ X651)|((esk41_2 @ X644 @ X645)=(X651))|((X644 @ (esk40_3 @ X644 @ X645 @ X648))|~(X644 @ X648))|((esk38_2 @ X644 @ X645)=(esk39_2 @ X644 @ X645))))&(((X645 @ (esk41_2 @ X644 @ X645))|(((X648)!=(esk40_3 @ X644 @ X645 @ X648))|~(X644 @ X648))|((esk38_2 @ X644 @ X645)=(esk39_2 @ X644 @ X645)))&(~(X645 @ X651)|((esk41_2 @ X644 @ X645)=(X651))|(((X648)!=(esk40_3 @ X644 @ X645 @ X648))|~(X644 @ X648))|((esk38_2 @ X644 @ X645)=(esk39_2 @ X644 @ X645)))))&((((X644 @ (esk43_2 @ X644 @ X645))|((X645 @ (esk42_3 @ X644 @ X645 @ X652))|~(X645 @ X652))|((esk38_2 @ X644 @ X645)=(esk39_2 @ X644 @ X645)))&(~(X644 @ X655)|((esk43_2 @ X644 @ X645)=(X655))|((X645 @ (esk42_3 @ X644 @ X645 @ X652))|~(X645 @ X652))|((esk38_2 @ X644 @ X645)=(esk39_2 @ X644 @ X645))))&(((X644 @ (esk43_2 @ X644 @ X645))|(((X652)!=(esk42_3 @ X644 @ X645 @ X652))|~(X645 @ X652))|((esk38_2 @ X644 @ X645)=(esk39_2 @ X644 @ X645)))&(~(X644 @ X655)|((esk43_2 @ X644 @ X645)=(X655))|(((X652)!=(esk42_3 @ X644 @ X645 @ X652))|~(X645 @ X652))|((esk38_2 @ X644 @ X645)=(esk39_2 @ X644 @ X645))))))&((((((X645 @ (esk41_2 @ X644 @ X645))|((X644 @ (esk40_3 @ X644 @ X645 @ X648))|~(X644 @ X648))|(~(X644 @ (esk38_2 @ X644 @ X645))|~(X645 @ (esk39_2 @ X644 @ X645))))&(~(X645 @ X651)|((esk41_2 @ X644 @ X645)=(X651))|((X644 @ (esk40_3 @ X644 @ X645 @ X648))|~(X644 @ X648))|(~(X644 @ (esk38_2 @ X644 @ X645))|~(X645 @ (esk39_2 @ X644 @ X645)))))&(((X645 @ (esk41_2 @ X644 @ X645))|(((X648)!=(esk40_3 @ X644 @ X645 @ X648))|~(X644 @ X648))|(~(X644 @ (esk38_2 @ X644 @ X645))|~(X645 @ (esk39_2 @ X644 @ X645))))&(~(X645 @ X651)|((esk41_2 @ X644 @ X645)=(X651))|(((X648)!=(esk40_3 @ X644 @ X645 @ X648))|~(X644 @ X648))|(~(X644 @ (esk38_2 @ X644 @ X645))|~(X645 @ (esk39_2 @ X644 @ X645))))))&((((X644 @ (esk43_2 @ X644 @ X645))|((X645 @ (esk42_3 @ X644 @ X645 @ X652))|~(X645 @ X652))|(~(X644 @ (esk38_2 @ X644 @ X645))|~(X645 @ (esk39_2 @ X644 @ X645))))&(~(X644 @ X655)|((esk43_2 @ X644 @ X645)=(X655))|((X645 @ (esk42_3 @ X644 @ X645 @ X652))|~(X645 @ X652))|(~(X644 @ (esk38_2 @ X644 @ X645))|~(X645 @ (esk39_2 @ X644 @ X645)))))&(((X644 @ (esk43_2 @ X644 @ X645))|(((X652)!=(esk42_3 @ X644 @ X645 @ X652))|~(X645 @ X652))|(~(X644 @ (esk38_2 @ X644 @ X645))|~(X645 @ (esk39_2 @ X644 @ X645))))&(~(X644 @ X655)|((esk43_2 @ X644 @ X645)=(X655))|(((X652)!=(esk42_3 @ X644 @ X645 @ X652))|~(X645 @ X652))|(~(X644 @ (esk38_2 @ X644 @ X645))|~(X645 @ (esk39_2 @ X644 @ X645)))))))&(((((X645 @ (esk41_2 @ X644 @ X645))|((X644 @ (esk40_3 @ X644 @ X645 @ X648))|~(X644 @ X648))|((X644 @ (esk38_2 @ X644 @ X645))|(X645 @ (esk39_2 @ X644 @ X645))))&(~(X645 @ X651)|((esk41_2 @ X644 @ X645)=(X651))|((X644 @ (esk40_3 @ X644 @ X645 @ X648))|~(X644 @ X648))|((X644 @ (esk38_2 @ X644 @ X645))|(X645 @ (esk39_2 @ X644 @ X645)))))&(((X645 @ (esk41_2 @ X644 @ X645))|(((X648)!=(esk40_3 @ X644 @ X645 @ X648))|~(X644 @ X648))|((X644 @ (esk38_2 @ X644 @ X645))|(X645 @ (esk39_2 @ X644 @ X645))))&(~(X645 @ X651)|((esk41_2 @ X644 @ X645)=(X651))|(((X648)!=(esk40_3 @ X644 @ X645 @ X648))|~(X644 @ X648))|((X644 @ (esk38_2 @ X644 @ X645))|(X645 @ (esk39_2 @ X644 @ X645))))))&((((X644 @ (esk43_2 @ X644 @ X645))|((X645 @ (esk42_3 @ X644 @ X645 @ X652))|~(X645 @ X652))|((X644 @ (esk38_2 @ X644 @ X645))|(X645 @ (esk39_2 @ X644 @ X645))))&(~(X644 @ X655)|((esk43_2 @ X644 @ X645)=(X655))|((X645 @ (esk42_3 @ X644 @ X645 @ X652))|~(X645 @ X652))|((X644 @ (esk38_2 @ X644 @ X645))|(X645 @ (esk39_2 @ X644 @ X645)))))&(((X644 @ (esk43_2 @ X644 @ X645))|(((X652)!=(esk42_3 @ X644 @ X645 @ X652))|~(X645 @ X652))|((X644 @ (esk38_2 @ X644 @ X645))|(X645 @ (esk39_2 @ X644 @ X645))))&(~(X644 @ X655)|((esk43_2 @ X644 @ X645)=(X655))|(((X652)!=(esk42_3 @ X644 @ X645 @ X652))|~(X645 @ X652))|((X644 @ (esk38_2 @ X644 @ X645))|(X645 @ (esk39_2 @ X644 @ X645)))))))))&(((emptyset)=(emptyset))&((((X656)!=(X657))|(((X658)!=(X659))|((setadjoin @ X656 @ X658)=(setadjoin @ X657 @ X659))))&((((X660)!=(X661))|((powerset @ X660)=(powerset @ X661)))&((((X662)!=(X663))|((setunion @ X662)=(setunion @ X663)))&((omega)!=(omega)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_105])])])])])])).
% 0.22/0.27 thf(c_0_107, negated_conjecture, ((omega)!=(omega)), inference(split_conjunct,[status(thm)],[c_0_106])).
% 0.22/0.27 thf(c_0_108, negated_conjecture, ($false), inference(cn,[status(thm)],[c_0_107]), ['proof']).
% 0.22/0.27 % SZS output end CNFRefutation
% 0.22/0.27 % Parsed axioms : 157
% 0.22/0.27 % Removed by relevancy pruning/SinE : 85
% 0.22/0.27 % Initial clauses : 162
% 0.22/0.27 % Removed in clause preprocessing : 11
% 0.22/0.27 % Initial clauses in saturation : 151
% 0.22/0.27 % Processed clauses : 1
% 0.22/0.27 % ...of these trivial : 0
% 0.22/0.27 % ...subsumed : 0
% 0.22/0.27 % ...remaining for further processing : 0
% 0.22/0.27 % Other redundant clauses eliminated : 0
% 0.22/0.27 % Clauses deleted for lack of memory : 0
% 0.22/0.27 % Backward-subsumed : 0
% 0.22/0.27 % Backward-rewritten : 0
% 0.22/0.27 % Generated clauses : 0
% 0.22/0.27 % ...of the previous two non-redundant : 0
% 0.22/0.27 % ...aggressively subsumed : 0
% 0.22/0.27 % Contextual simplify-reflections : 0
% 0.22/0.27 % Paramodulations : 0
% 0.22/0.27 % Factorizations : 0
% 0.22/0.27 % NegExts : 0
% 0.22/0.27 % Equation resolutions : 0
% 0.22/0.27 % Disequality decompositions : 0
% 0.22/0.27 % Total rewrite steps : 0
% 0.22/0.27 % ...of those cached : 0
% 0.22/0.27 % Propositional unsat checks : 0
% 0.22/0.27 % Propositional check models : 0
% 0.22/0.27 % Propositional check unsatisfiable : 0
% 0.22/0.27 % Propositional clauses : 0
% 0.22/0.27 % Propositional clauses after purity: 0
% 0.22/0.27 % Propositional unsat core size : 0
% 0.22/0.27 % Propositional preprocessing time : 0.000
% 0.22/0.27 % Propositional encoding time : 0.000
% 0.22/0.27 % Propositional solver time : 0.000
% 0.22/0.27 % Success case prop preproc time : 0.000
% 0.22/0.27 % Success case prop encoding time : 0.000
% 0.22/0.27 % Success case prop solver time : 0.000
% 0.22/0.27 % Current number of processed clauses : 0
% 0.22/0.27 % Positive orientable unit clauses : 0
% 0.22/0.27 % Positive unorientable unit clauses: 0
% 0.22/0.27 % Negative unit clauses : 0
% 0.22/0.27 % Non-unit-clauses : 0
% 0.22/0.27 % Current number of unprocessed clauses: 150
% 0.22/0.27 % ...number of literals in the above : 500
% 0.22/0.27 % Current number of archived formulas : 0
% 0.22/0.27 % Current number of archived clauses : 0
% 0.22/0.27 % Clause-clause subsumption calls (NU) : 0
% 0.22/0.27 % Rec. Clause-clause subsumption calls : 0
% 0.22/0.27 % Non-unit clause-clause subsumptions : 0
% 0.22/0.27 % Unit Clause-clause subsumption calls : 0
% 0.22/0.27 % Rewrite failures with RHS unbound : 0
% 0.22/0.27 % BW rewrite match attempts : 0
% 0.22/0.27 % BW rewrite match successes : 0
% 0.22/0.27 % Condensation attempts : 0
% 0.22/0.27 % Condensation successes : 0
% 0.22/0.27 % Termbank termtop insertions : 16858
% 0.22/0.27 % Search garbage collected termcells : 6508
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.015 s
% 0.22/0.27 % System time : 0.004 s
% 0.22/0.27 % Total time : 0.019 s
% 0.22/0.27 % Maximum resident set size: 5840 pages
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.018 s
% 0.22/0.27 % System time : 0.010 s
% 0.22/0.27 % Total time : 0.028 s
% 0.22/0.27 % Maximum resident set size: 4864 pages
% 0.22/0.27 % E exiting
%------------------------------------------------------------------------------