E---3.5.1.THM-CRf.s

%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : SEU581^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:24:35 AM UTC 2026

% Result   : Theorem 0.22s 0.29s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU581^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05  % Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.18  % Computer : n026.cluster.edu
% 0.11/0.18  % Model    : x86_64 x86_64
% 0.11/0.18  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18  % Memory   : 8046.5625MB
% 0.11/0.18  % OS       : Linux 6.8.0-71-generic
% 0.11/0.18  % CPULimit : 300
% 0.11/0.18  % WCLimit  : 300
% 0.11/0.18  % DateTime : Tue Sep 29 13:54:57 UTC 2026
% 0.11/0.18  % CPUTime  : 
% 0.11/0.18  Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.22  Running higher-order theorem proving
% 0.11/0.25  Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p
% 0.22/0.29  % Version: 3.5.1-ho
% 0.22/0.29  % Preprocessing class: HSMMSLSSLLLCHSA.
% 0.22/0.29  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.29  % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.29  % Starting sh5l with 300s (1) cores
% 0.22/0.29  % Starting new_bool_1 with 300s (1) cores
% 0.22/0.29  % Starting new_bool_2 with 300s (1) cores
% 0.22/0.29  % new_bool_2 with pid 632388 completed with status 0
% 0.22/0.29  % Result found by new_bool_2
% 0.22/0.29  % Preprocessing class: HSMMSLSSLLLCHSA.
% 0.22/0.29  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.29  % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.29  % Starting sh5l with 300s (1) cores
% 0.22/0.29  % Starting new_bool_1 with 300s (1) cores
% 0.22/0.29  % Starting new_bool_2 with 300s (1) cores
% 0.22/0.29  % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.29  % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.29  % Search class: HGHSM-FSLS31-SHSMMSBN
% 0.22/0.29  % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.29  % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.29  % SubtermCWHack with pid 632395 completed with status 0
% 0.22/0.29  % Result found by SubtermCWHack
% 0.22/0.29  % Preprocessing class: HSMMSLSSLLLCHSA.
% 0.22/0.29  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.29  % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.29  % Starting sh5l with 300s (1) cores
% 0.22/0.29  % Starting new_bool_1 with 300s (1) cores
% 0.22/0.29  % Starting new_bool_2 with 300s (1) cores
% 0.22/0.29  % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.29  % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.29  % Search class: HGHSM-FSLS31-SHSMMSBN
% 0.22/0.29  % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.29  % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.29  % Preprocessing time       : 0.004 s
% 0.22/0.29  
% 0.22/0.29  % Proof found!
% 0.22/0.29  % SZS status Theorem
% 0.22/0.29  % SZS output start CNFRefutation
% 0.22/0.29  thf(decl_23, type, in: $i > $i > $o).
% 0.22/0.29  thf(decl_24, type, exu: ($i > $o) > $o).
% 0.22/0.29  thf(decl_25, type, setextAx: $o).
% 0.22/0.29  thf(decl_26, type, emptyset: $i).
% 0.22/0.29  thf(decl_27, type, emptysetAx: $o).
% 0.22/0.29  thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.22/0.29  thf(decl_29, type, setadjoinAx: $o).
% 0.22/0.29  thf(decl_30, type, powerset: $i > $i).
% 0.22/0.29  thf(decl_31, type, powersetAx: $o).
% 0.22/0.29  thf(decl_32, type, setunion: $i > $i).
% 0.22/0.29  thf(decl_33, type, setunionAx: $o).
% 0.22/0.29  thf(decl_34, type, omega: $i).
% 0.22/0.29  thf(decl_35, type, omega0Ax: $o).
% 0.22/0.29  thf(decl_36, type, omegaSAx: $o).
% 0.22/0.29  thf(decl_37, type, omegaIndAx: $o).
% 0.22/0.29  thf(decl_38, type, replAx: $o).
% 0.22/0.29  thf(decl_39, type, foundationAx: $o).
% 0.22/0.29  thf(decl_40, type, wellorderingAx: $o).
% 0.22/0.29  thf(decl_41, type, descr: ($i > $o) > $i).
% 0.22/0.29  thf(decl_42, type, descrp: $o).
% 0.22/0.29  thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.22/0.29  thf(decl_44, type, dsetconstrI: $o).
% 0.22/0.29  thf(decl_45, type, dsetconstrEL: $o).
% 0.22/0.29  thf(decl_46, type, dsetconstrER: $o).
% 0.22/0.29  thf(decl_47, type, exuE1: $o).
% 0.22/0.29  thf(decl_48, type, prop2set: $o > $i).
% 0.22/0.29  thf(decl_49, type, prop2setE: $o).
% 0.22/0.29  thf(decl_50, type, emptysetE: $o).
% 0.22/0.29  thf(decl_51, type, emptysetimpfalse: $o).
% 0.22/0.29  thf(decl_52, type, notinemptyset: $o).
% 0.22/0.29  thf(decl_53, type, exuE3e: $o).
% 0.22/0.29  thf(decl_54, type, setext: $o).
% 0.22/0.29  thf(decl_55, type, emptyI: $o).
% 0.22/0.29  thf(decl_56, type, noeltsimpempty: $o).
% 0.22/0.29  thf(decl_57, type, setbeta: $o).
% 0.22/0.29  thf(decl_58, type, nonempty: $i > $o).
% 0.22/0.29  thf(decl_59, type, nonemptyE1: $o).
% 0.22/0.29  thf(decl_60, type, nonemptyI: $o).
% 0.22/0.29  thf(decl_61, type, nonemptyI1: $o).
% 0.22/0.29  thf(decl_62, type, setadjoinIL: $o).
% 0.22/0.29  thf(decl_63, type, emptyinunitempty: $o).
% 0.22/0.29  thf(decl_64, type, setadjoinIR: $o).
% 0.22/0.29  thf(decl_65, type, setadjoinE: $o).
% 0.22/0.29  thf(decl_66, type, setadjoinOr: $o).
% 0.22/0.29  thf(decl_67, type, setoftrueEq: $o).
% 0.22/0.29  thf(decl_68, type, powersetI: $o).
% 0.22/0.29  thf(decl_69, type, emptyinPowerset: $o).
% 0.22/0.29  thf(decl_70, type, emptyInPowerset: $o).
% 0.22/0.29  thf(decl_71, type, powersetE: $o).
% 0.22/0.29  thf(decl_72, type, setunionI: $o).
% 0.22/0.29  thf(decl_73, type, setunionE: $o).
% 0.22/0.29  thf(decl_74, type, subPowSU: $o).
% 0.22/0.29  thf(decl_75, type, exuE2: $o).
% 0.22/0.29  thf(decl_76, type, nonemptyImpWitness: $o).
% 0.22/0.29  thf(decl_77, type, uniqinunit: $o).
% 0.22/0.29  thf(decl_78, type, notinsingleton: $o).
% 0.22/0.29  thf(decl_79, type, eqinunit: $o).
% 0.22/0.29  thf(decl_80, type, singletonsswitch: $o).
% 0.22/0.29  thf(decl_81, type, upairsetE: $o).
% 0.22/0.29  thf(decl_82, type, upairsetIL: $o).
% 0.22/0.29  thf(decl_83, type, upairsetIR: $o).
% 0.22/0.29  thf(decl_84, type, emptyE1: $o).
% 0.22/0.29  thf(decl_85, type, vacuousDall: $o).
% 0.22/0.29  thf(decl_86, type, quantDeMorgan1: $o).
% 0.22/0.29  thf(decl_87, type, quantDeMorgan2: $o).
% 0.22/0.29  thf(decl_88, type, quantDeMorgan3: $o).
% 0.22/0.29  thf(decl_89, type, quantDeMorgan4: $o).
% 0.22/0.29  thf(decl_90, type, prop2setI: $o).
% 0.22/0.29  thf(decl_92, type, prop2set2propI: $o).
% 0.22/0.29  thf(decl_93, type, notdexE: $o).
% 0.22/0.29  thf(decl_94, type, notdallE: $o).
% 0.22/0.29  thf(decl_95, type, exuI1: $o).
% 0.22/0.29  thf(decl_96, type, exuI3: $o).
% 0.22/0.29  thf(decl_97, type, exuI2: $o).
% 0.22/0.29  thf(decl_98, type, inCongP: $o).
% 0.22/0.29  thf(decl_99, type, in__Cong: $o).
% 0.22/0.29  thf(decl_100, type, exuE3u: $o).
% 0.22/0.29  thf(decl_101, type, exu__Cong: $o).
% 0.22/0.29  thf(decl_102, type, emptyset__Cong: $o).
% 0.22/0.29  thf(decl_103, type, setadjoin__Cong: $o).
% 0.22/0.29  thf(decl_104, type, powerset__Cong: $o).
% 0.22/0.29  thf(decl_105, type, setunion__Cong: $o).
% 0.22/0.29  thf(decl_106, type, omega__Cong: $o).
% 0.22/0.29  thf(decl_107, type, exuEu: $o).
% 0.22/0.29  thf(decl_108, type, descr__Cong: $o).
% 0.22/0.29  thf(decl_109, type, dsetconstr__Cong: $o).
% 0.22/0.29  thf(decl_110, type, subset: $i > $i > $o).
% 0.22/0.29  thf(decl_113, type, subsetI1: $o).
% 0.22/0.29  thf(decl_114, type, eqimpsubset2: $o).
% 0.22/0.29  thf(decl_115, type, eqimpsubset1: $o).
% 0.22/0.29  thf(decl_116, type, subsetI2: $o).
% 0.22/0.29  thf(decl_117, type, emptysetsubset: $o).
% 0.22/0.29  thf(decl_118, type, subsetE: $o).
% 0.22/0.29  thf(decl_119, type, subsetE2: $o).
% 0.22/0.29  thf(decl_120, type, notsubsetI: $o).
% 0.22/0.29  thf(decl_121, type, notequalI1: $o).
% 0.22/0.29  thf(decl_122, type, notequalI2: $o).
% 0.22/0.29  thf(decl_123, type, subsetRefl: $o).
% 0.22/0.29  thf(decl_124, type, subsetTrans: $o).
% 0.22/0.29  thf(decl_125, type, setadjoinSub: $o).
% 0.22/0.29  thf(decl_126, type, setadjoinSub2: $o).
% 0.22/0.29  thf(decl_127, type, subset2powerset: $o).
% 0.22/0.29  thf(decl_128, type, setextsub: $o).
% 0.22/0.29  thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.22/0.29  thf(decl_130, type, powersetI1: $o).
% 0.22/0.29  thf(decl_131, type, powersetE1: $o).
% 0.22/0.29  thf(decl_132, type, inPowerset: $o).
% 0.22/0.29  thf(decl_133, type, powersetsubset: $o).
% 0.22/0.29  thf(decl_134, type, sepInPowerset: $o).
% 0.22/0.29  thf(decl_135, type, epred1_0: $o).
% 0.22/0.29  thf(decl_136, type, esk1_2: $i > $i > $i).
% 0.22/0.29  thf(decl_137, type, esk2_2: $i > $i > $i).
% 0.22/0.29  thf(decl_138, type, esk3_2: $i > $i > $i).
% 0.22/0.29  thf(decl_139, type, esk4_1: $i > $i).
% 0.22/0.29  thf(decl_140, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.22/0.29  thf(decl_141, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.29  thf(decl_142, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.22/0.30  thf(decl_143, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.30  thf(decl_144, type, esk9_1: $i > $i).
% 0.22/0.30  thf(decl_145, type, esk10_2: ($i > $o) > $i > $i).
% 0.22/0.30  thf(decl_146, type, esk11_2: ($i > $o) > $i > $i).
% 0.22/0.30  thf(decl_147, type, esk12_1: ($i > $o) > $i).
% 0.22/0.30  thf(decl_148, type, esk13_2: ($i > $o) > $i > $i).
% 0.22/0.30  thf(decl_149, type, esk14_1: ($i > $o) > $i).
% 0.22/0.30  thf(decl_150, type, esk15_2: $i > $i > $i).
% 0.22/0.30  thf(decl_151, type, esk16_2: $i > $i > $i).
% 0.22/0.30  thf(decl_152, type, esk17_1: $i > $i).
% 0.22/0.30  thf(decl_153, type, esk18_1: $i > $i).
% 0.22/0.30  thf(decl_154, type, esk19_1: $i > $i).
% 0.22/0.30  thf(decl_155, type, esk20_2: $i > $i > $i).
% 0.22/0.30  thf(decl_156, type, esk21_3: $i > $i > $o > $i).
% 0.22/0.30  thf(decl_157, type, esk22_2: ($i > $o) > $i > $i).
% 0.22/0.30  thf(decl_158, type, esk23_1: ($i > $o) > $i).
% 0.22/0.30  thf(decl_159, type, esk24_1: $i > $i).
% 0.22/0.30  thf(decl_160, type, esk25_2: $i > ($i > $o) > $i).
% 0.22/0.30  thf(decl_161, type, esk26_2: $i > ($i > $o) > $i).
% 0.22/0.30  thf(decl_162, type, esk27_2: $i > ($i > $o) > $i).
% 0.22/0.30  thf(decl_163, type, esk28_2: $i > ($i > $o) > $i).
% 0.22/0.30  thf(decl_164, type, esk29_2: $i > ($i > $o) > $i).
% 0.22/0.30  thf(decl_165, type, esk30_2: $i > ($i > $o) > $i).
% 0.22/0.30  thf(decl_166, type, esk31_2: ($i > $o) > $i > $i).
% 0.22/0.30  thf(decl_167, type, esk32_1: ($i > $o) > $i).
% 0.22/0.30  thf(decl_168, type, esk33_1: ($i > $o) > $i).
% 0.22/0.30  thf(decl_169, type, esk34_1: ($i > $o) > $i).
% 0.22/0.30  thf(decl_170, type, esk35_1: ($i > $o) > $i).
% 0.22/0.30  thf(decl_171, type, esk36_2: ($i > $o) > $i > $i).
% 0.22/0.30  thf(decl_172, type, esk37_1: ($i > $o) > $i).
% 0.22/0.30  thf(decl_173, type, esk38_2: ($i > $o) > $i > $i).
% 0.22/0.30  thf(decl_174, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.30  thf(decl_175, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.30  thf(decl_176, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.30  thf(decl_177, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.30  thf(decl_178, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.30  thf(decl_179, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.30  thf(decl_180, type, esk45_2: ($i > $o) > $i > $i).
% 0.22/0.30  thf(decl_181, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.30  thf(decl_182, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.30  thf(decl_183, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.30  thf(decl_184, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.30  thf(decl_185, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.22/0.30  thf(decl_186, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.22/0.30  thf(decl_187, type, esk52_2: $i > $i > $i).
% 0.22/0.30  thf(decl_188, type, esk53_2: $i > $i > $i).
% 0.22/0.30  thf(decl_189, type, esk54_0: $i).
% 0.22/0.30  thf(decl_190, type, epred2_0: $i > $o).
% 0.22/0.30  thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', nonemptyI)).
% 0.22/0.30  thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', nonempty)).
% 0.22/0.30  thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', exuE3e)).
% 0.22/0.30  thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', exu)).
% 0.22/0.30  thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', exuE2)).
% 0.22/0.30  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/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', exuI1)).
% 0.22/0.30  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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', exu__Cong)).
% 0.22/0.30  thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', exuE3u)).
% 0.22/0.30  thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', exuI2)).
% 0.22/0.30  thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', exuI3)).
% 0.22/0.30  thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', descr__Cong)).
% 0.22/0.30  thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', exuEu)).
% 0.22/0.30  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/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', exuE1)).
% 0.22/0.30  thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', descrp)).
% 0.22/0.30  thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', replAx)).
% 0.22/0.30  thf(sepSubset, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', sepSubset)).
% 0.22/0.30  thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', sepInPowerset)).
% 0.22/0.30  thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', nonemptyE1)).
% 0.22/0.30  thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', setbeta)).
% 0.22/0.30  thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', nonemptyI1)).
% 0.22/0.30  thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', setoftrueEq)).
% 0.22/0.30  thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', nonemptyImpWitness)).
% 0.22/0.30  thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', emptyE1)).
% 0.22/0.30  thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', dsetconstr__Cong)).
% 0.22/0.30  thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', dsetconstrER)).
% 0.22/0.30  thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', dsetconstrEL)).
% 0.22/0.30  thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', dsetconstrI)).
% 0.22/0.30  thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', noeltsimpempty)).
% 0.22/0.30  thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', notsubsetI)).
% 0.22/0.30  thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', subsetE2)).
% 0.22/0.30  thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', notequalI1)).
% 0.22/0.30  thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', notequalI2)).
% 0.22/0.30  thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', subsetRefl)).
% 0.22/0.30  thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', subsetTrans)).
% 0.22/0.30  thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', setadjoinSub)).
% 0.22/0.30  thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', setadjoinSub2)).
% 0.22/0.30  thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', subset2powerset)).
% 0.22/0.30  thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', setextsub)).
% 0.22/0.30  thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', subsetemptysetimpeq)).
% 0.22/0.30  thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', powersetI1)).
% 0.22/0.30  thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', powersetE1)).
% 0.22/0.30  thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', inPowerset)).
% 0.22/0.30  thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', powersetsubset)).
% 0.22/0.30  thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', emptysetE)).
% 0.22/0.30  thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', subPowSU)).
% 0.22/0.30  thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', setunionE)).
% 0.22/0.30  thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', emptyI)).
% 0.22/0.30  thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', setext)).
% 0.22/0.30  thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', powersetI)).
% 0.22/0.30  thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', setadjoinOr)).
% 0.22/0.30  thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', setadjoinE)).
% 0.22/0.30  thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', setadjoinIR)).
% 0.22/0.30  thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', emptyinunitempty)).
% 0.22/0.30  thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', emptysetimpfalse)).
% 0.22/0.30  thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', setadjoinIL)).
% 0.22/0.30  thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', emptyinPowerset)).
% 0.22/0.30  thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', setunionI)).
% 0.22/0.30  thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', powersetE)).
% 0.22/0.30  thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', emptyInPowerset)).
% 0.22/0.30  thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', uniqinunit)).
% 0.22/0.30  thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', upairsetIR)).
% 0.22/0.30  thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', upairsetIL)).
% 0.22/0.30  thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', upairsetE)).
% 0.22/0.30  thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', singletonsswitch)).
% 0.22/0.30  thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', eqinunit)).
% 0.22/0.30  thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', notinsingleton)).
% 0.22/0.30  thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', vacuousDall)).
% 0.22/0.30  thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', notinemptyset)).
% 0.22/0.30  thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', notdallE)).
% 0.22/0.30  thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', notdexE)).
% 0.22/0.30  thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', prop2setI)).
% 0.22/0.30  thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', quantDeMorgan4)).
% 0.22/0.30  thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', quantDeMorgan3)).
% 0.22/0.30  thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', quantDeMorgan2)).
% 0.22/0.30  thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', quantDeMorgan1)).
% 0.22/0.30  thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', emptyset__Cong)).
% 0.22/0.30  thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', in__Cong)).
% 0.22/0.30  thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', inCongP)).
% 0.22/0.30  thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', setadjoin__Cong)).
% 0.22/0.30  thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', subsetI1)).
% 0.22/0.30  thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', omega__Cong)).
% 0.22/0.30  thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', setunion__Cong)).
% 0.22/0.30  thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', eqimpsubset1)).
% 0.22/0.30  thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', subsetI2)).
% 0.22/0.30  thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', emptysetsubset)).
% 0.22/0.30  thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', subsetE)).
% 0.22/0.30  thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', powerset__Cong)).
% 0.22/0.30  thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', eqimpsubset2)).
% 0.22/0.30  thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', prop2setE)).
% 0.22/0.30  thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', wellorderingAx)).
% 0.22/0.30  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/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', foundationAx)).
% 0.22/0.30  thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', omegaIndAx)).
% 0.22/0.30  thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', omegaSAx)).
% 0.22/0.30  thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', omega0Ax)).
% 0.22/0.30  thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', setunionAx)).
% 0.22/0.30  thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', powersetAx)).
% 0.22/0.30  thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', setadjoinAx)).
% 0.22/0.30  thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', emptysetAx)).
% 0.22/0.30  thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.WHolM7Nvim/E---3.1_632337.p', setextAx)).
% 0.22/0.30  thf(c_0_99, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.22/0.30  thf(c_0_100, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.22/0.30  thf(c_0_101, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.22/0.30  thf(c_0_102, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.22/0.30  thf(c_0_103, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.22/0.30  thf(c_0_104, 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])).
% 0.22/0.30  thf(c_0_105, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.22/0.30  thf(c_0_106, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.22/0.30  thf(c_0_107, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.22/0.30  thf(c_0_108, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.22/0.30  thf(c_0_109, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.22/0.30  thf(c_0_110, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.22/0.30  thf(c_0_111, 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])).
% 0.22/0.30  thf(c_0_112, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.22/0.30  thf(c_0_113, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.22/0.30  thf(c_0_114, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[sepSubset])).
% 0.22/0.30  thf(c_0_115, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.22/0.30  thf(c_0_116, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_99, c_0_100])).
% 0.22/0.30  thf(c_0_117, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_100])).
% 0.22/0.30  thf(c_0_118, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.22/0.30  thf(c_0_119, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X286:$i]:(((((X1 @ X286)))&(![X287:$i]:(((((X1 @ X287)))=>(((X286)=(X287))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_101, c_0_102])).
% 0.22/0.30  thf(c_0_120, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_100])).
% 0.22/0.30  thf(c_0_121, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.22/0.30  thf(c_0_122, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_100])).
% 0.22/0.30  thf(c_0_123, plain, ((exuE2)=(![X1:$i > $o]:((((?[X288:$i]:(((((X1 @ X288)))&(![X289:$i]:(((((X1 @ X289)))=>(((X288)=(X289))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_103, c_0_102])).
% 0.22/0.30  thf(c_0_124, plain, ((emptyE1)<=>![X4:$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])).
% 0.22/0.30  thf(c_0_125, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X290:$i]:(((((X1 @ X290)))&(![X291:$i]:(((((X1 @ X291)))=>(((X290)=(X291)))))))))))))), inference(apply_def,[status(thm)],[c_0_104, c_0_102])).
% 0.22/0.30  thf(c_0_126, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X298:$i]:(((((X1 @ X298)))&(![X299:$i]:(((((X1 @ X299)))=>(((X298)=(X299))))))))))<=>((?[X300:$i]:(((((X17 @ X300)))&(![X301:$i]:(((((X17 @ X301)))=>(((X300)=(X301)))))))))))))))), inference(apply_def,[status(thm)],[c_0_105, c_0_102])).
% 0.22/0.30  thf(c_0_127, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X296:$i]:(((((X1 @ X296)))&(![X297:$i]:(((((X1 @ X297)))=>(((X296)=(X297))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_106, c_0_102])).
% 0.22/0.30  thf(c_0_128, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X294:$i]:(((((X1 @ X294)))&(![X295:$i]:(((((X1 @ X295)))=>(((X294)=(X295)))))))))))))), inference(apply_def,[status(thm)],[c_0_107, c_0_102])).
% 0.22/0.30  thf(c_0_129, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X292:$i]:(((((X1 @ X292)))&(![X293:$i]:(((((X1 @ X293)))=>(((X292)=(X293)))))))))))))))), inference(apply_def,[status(thm)],[c_0_108, c_0_102])).
% 0.22/0.30  thf(c_0_130, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.22/0.30  thf(c_0_131, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X304:$i]:(((((X1 @ X304)))&(![X305:$i]:(((((X1 @ X305)))=>(((X304)=(X305))))))))))=>((((?[X306:$i]:(((((X17 @ X306)))&(![X307:$i]:(((((X17 @ X307)))=>(((X306)=(X307))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_109, c_0_102])).
% 0.22/0.30  thf(c_0_132, plain, ((exuEu)=(![X1:$i > $o]:((((?[X302:$i]:(((((X1 @ X302)))&(![X303:$i]:(((((X1 @ X303)))=>(((X302)=(X303))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_110, c_0_102])).
% 0.22/0.30  thf(c_0_133, plain, ((exuE1)=(![X1:$i > $o]:((((?[X284:$i]:(((((X1 @ X284)))&(![X285:$i]:(((((X1 @ X285)))=>(((X284)=(X285))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_111, c_0_102])).
% 0.22/0.30  thf(c_0_134, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.22/0.30  thf(c_0_135, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.22/0.30  thf(c_0_136, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.22/0.30  thf(c_0_137, plain, ((descrp)=(![X1:$i > $o]:((((?[X282:$i]:(((((X1 @ X282)))&(![X283:$i]:(((((X1 @ X283)))=>(((X282)=(X283))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_112, c_0_102])).
% 0.22/0.30  thf(c_0_138, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X280:$i]:(((((X6 @ X2 @ X280)))&(![X281:$i]:(((((X6 @ X2 @ X281)))=>(((X280)=(X281)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_113, c_0_102])).
% 0.22/0.30  thf(c_0_139, plain, ((epred1_0)<=>![X337:$i]:(?[X338:$i]:((((![X339:$i]:(((in @ X339 @ X338)=>![X340:$i]:(((in @ X340 @ X339)=>(in @ X340 @ X337)))))&![X341:$i, X342:$i]:((((in @ X341 @ X337)&(in @ X342 @ X337))=>(![X343:$i]:(((in @ X343 @ X338)=>((in @ X341 @ X343)<=>(in @ X342 @ X343))))=>((X341)=(X342))))))&![X344:$i, X345:$i]:((((in @ X344 @ X338)&(in @ X345 @ X338))=>(![X346:$i]:(((in @ X346 @ X344)=>(in @ X346 @ X345)))|![X347:$i]:(((in @ X347 @ X345)=>(in @ X347 @ X344)))))))&![X348:$i]:(((![X349:$i]:(((in @ X349 @ X348)=>(in @ X349 @ X337)))&?[X350:$i]:((in @ X350 @ X348)))=>?[X351:$i, X352:$i]:(((((in @ X351 @ X338)&(in @ X352 @ X348))&~(?[X353:$i]:(((in @ X353 @ X351)&(in @ X353 @ X348)))))&![X354:$i]:(((in @ X354 @ X338)=>(![X355:$i]:(((in @ X355 @ X354)=>(in @ X355 @ X351)))|(in @ X352 @ X354)))))))))))), introduced(definition)).
% 0.22/0.30  thf(c_0_140, negated_conjecture, ~((![X308:$i, X309:$i]:((![X310:$i]:(((in @ X310 @ X308)<=>(in @ X310 @ X309)))=>((X308)=(X309))))=>(![X311:$i]:(~(in @ X311 @ emptyset))=>(![X312:$i, X313:$i, X314:$i]:(((in @ X314 @ (setadjoin @ X312 @ X313))<=>(((X314)=(X312))|(in @ X314 @ X313))))=>(![X315:$i, X316:$i]:(((in @ X316 @ (powerset @ X315))<=>![X317:$i]:(((in @ X317 @ X316)=>(in @ X317 @ X315)))))=>(![X318:$i, X319:$i]:(((in @ X319 @ (setunion @ X318))<=>?[X320:$i]:(((in @ X319 @ X320)&(in @ X320 @ X318)))))=>((in @ emptyset @ omega)=>(![X321:$i]:(((in @ X321 @ omega)=>(in @ (setadjoin @ X321 @ X321) @ omega)))=>(![X322:$i]:((((in @ emptyset @ X322)&![X323:$i]:((((in @ X323 @ omega)&(in @ X323 @ X322))=>(in @ (setadjoin @ X323 @ X323) @ X322))))=>![X324:$i]:(((in @ X324 @ omega)=>(in @ X324 @ X322)))))=>(![X325:$i > $i > $o, X326:$i]:((![X327:$i]:(((in @ X327 @ X326)=>?[X328:$i]:(((X325 @ X327 @ X328)&![X329:$i]:(((X325 @ X327 @ X329)=>((X328)=(X329))))))))=>?[X330:$i]:(![X331:$i]:(((in @ X331 @ X330)<=>?[X332:$i]:(((in @ X332 @ X326)&(X325 @ X332 @ X331))))))))=>(![X333:$i]:((?[X334:$i]:((in @ X334 @ X333))=>?[X335:$i]:(((in @ X335 @ X333)&~(?[X336:$i]:(((in @ X336 @ X335)&(in @ X336 @ X333))))))))=>((epred1_0)=>(![X356:$i > $o]:((?[X357:$i]:(((X356 @ X357)&![X358:$i]:(((X356 @ X358)=>((X357)=(X358))))))=>(X356 @ (descr @ (^[Z0:$i]:((X356 @ Z0)))))))=>(![X359:$i, X360:$i > $o, X361:$i]:(((in @ X361 @ X359)=>((X360 @ X361)=>(in @ X361 @ (dsetconstr @ X359 @ (^[Z0:$i]:((X360 @ Z0))))))))=>(![X362:$i, X363:$i > $o, X364:$i]:(((in @ X364 @ (dsetconstr @ X362 @ (^[Z0:$i]:((X363 @ Z0)))))=>(in @ X364 @ X362)))=>(![X365:$i, X366:$i > $o, X367:$i]:(((in @ X367 @ (dsetconstr @ X365 @ (^[Z0:$i]:((X366 @ Z0)))))=>(X366 @ X367)))=>(![X368:$i > $o]:((?[X369:$i]:(((X368 @ X369)&![X370:$i]:(((X368 @ X370)=>((X369)=(X370))))))=>?[X371:$i]:(((X368 @ X371)&![X372:$i]:(((X368 @ X372)=>((X371)=(X372))))))))=>(![X373:$o, X374:$i]:(((in @ X374 @ (prop2set @ ((X373))))=>(X373)))=>(![X375:$i]:(((in @ X375 @ emptyset)=>![X376:$o]:((X376))))=>(![X377:$i]:(~(in @ X377 @ emptyset))=>(![X378:$i]:(~(in @ X378 @ emptyset))=>(![X379:$i > $o]:((?[X380:$i]:(((X379 @ X380)&![X381:$i]:(((X379 @ X381)=>((X380)=(X381))))))=>?[X382:$i]:((X379 @ X382))))=>(![X383:$i, X384:$i]:((![X385:$i]:(((in @ X385 @ X383)=>(in @ X385 @ X384)))=>(![X386:$i]:(((in @ X386 @ X384)=>(in @ X386 @ X383)))=>((X383)=(X384)))))=>(![X387:$i]:((![X388:$i]:(~(in @ X388 @ X387))=>((X387)=(emptyset))))=>(![X389:$i]:((![X390:$i]:(~(in @ X390 @ X389))=>((X389)=(emptyset))))=>(![X391:$i, X392:$i > $o, X393:$i]:(((in @ X393 @ X391)=>((in @ X393 @ (dsetconstr @ X391 @ (^[Z0:$i]:((X392 @ Z0)))))<=>(X392 @ X393))))=>(![X394:$i]:((((X394)!=(emptyset))=>?[X395:$i]:((in @ X395 @ X394))))=>(![X396:$i, X397:$i > $o, X398:$i]:(((in @ X398 @ X396)=>((X397 @ X398)=>((dsetconstr @ X396 @ (^[Z0:$i]:((X397 @ Z0))))!=(emptyset)))))=>(![X399:$i]:((?[X400:$i]:((in @ X400 @ X399))=>((X399)!=(emptyset))))=>(![X401:$i, X402:$i]:((in @ X401 @ (setadjoin @ X401 @ X402)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X403:$i, X404:$i, X405:$i]:(((in @ X405 @ X404)=>(in @ X405 @ (setadjoin @ X403 @ X404))))=>(![X406:$i, X407:$i, X408:$i]:(((in @ X408 @ (setadjoin @ X406 @ X407))=>![X409:$o]:(((((X408)=(X406))=>(X409))=>(((in @ X408 @ X407)=>(X409))=>(X409))))))=>(![X410:$i, X411:$i, X412:$i]:(((in @ X412 @ (setadjoin @ X410 @ X411))=>(((X412)=(X410))|(in @ X412 @ X411))))=>(![X413:$i]:(((dsetconstr @ X413 @ (^[Z0:$i]:(($true))))=(X413)))=>(![X414:$i, X415:$i]:((![X416:$i]:(((in @ X416 @ X415)=>(in @ X416 @ X414)))=>(in @ X415 @ (powerset @ X414))))=>(![X417:$i]:((in @ emptyset @ (powerset @ X417)))=>(![X418:$i]:((in @ emptyset @ (powerset @ X418)))=>(![X419:$i, X420:$i, X421:$i]:(((in @ X420 @ (powerset @ X419))=>((in @ X421 @ X420)=>(in @ X421 @ X419))))=>(![X422:$i, X423:$i, X424:$i]:(((in @ X423 @ X424)=>((in @ X424 @ X422)=>(in @ X423 @ (setunion @ X422)))))=>(![X425:$i, X426:$i]:(((in @ X426 @ (setunion @ X425))=>![X427:$o]:((![X428:$i]:(((in @ X426 @ X428)=>((in @ X428 @ X425)=>(X427))))=>(X427)))))=>(![X429:$i, X430:$i]:(((in @ X430 @ X429)=>(in @ X430 @ (powerset @ (setunion @ X429)))))=>(![X431:$i > $o]:((?[X432:$i]:(((X431 @ X432)&![X433:$i]:(((X431 @ X433)=>((X432)=(X433))))))=>?[X434:$i]:(![X435:$i]:(((X431 @ X435)<=>((X435)=(X434)))))))=>(![X436:$i]:((((X436)!=(emptyset))=>?[X437:$i]:((in @ X437 @ X436))))=>(![X438:$i, X439:$i]:(((in @ X438 @ (setadjoin @ X439 @ emptyset))=>((X438)=(X439))))=>(![X440:$i, X441:$i]:((((X440)!=(X441))=>~(in @ X441 @ (setadjoin @ X440 @ emptyset))))=>(![X442:$i, X443:$i]:((((X442)=(X443))=>(in @ X442 @ (setadjoin @ X443 @ emptyset))))=>(![X444:$i, X445:$i]:(((in @ X444 @ (setadjoin @ X445 @ emptyset))=>(in @ X445 @ (setadjoin @ X444 @ emptyset))))=>(![X446:$i, X447:$i, X448:$i]:(((in @ X448 @ (setadjoin @ X446 @ (setadjoin @ X447 @ emptyset)))=>(((X448)=(X446))|((X448)=(X447)))))=>(![X449:$i, X450:$i]:((in @ X449 @ (setadjoin @ X449 @ (setadjoin @ X450 @ emptyset))))=>(![X451:$i, X452:$i]:((in @ X452 @ (setadjoin @ X451 @ (setadjoin @ X452 @ emptyset))))=>(![X453:$i, X454:$i > $o]:((?[X455:$i]:(((in @ X455 @ X453)&(X454 @ X455)))=>((dsetconstr @ X453 @ (^[Z0:$i]:((X454 @ Z0))))!=(emptyset))))=>(![X456:$i > $o, X457:$i]:(((in @ X457 @ emptyset)=>(X456 @ X457)))=>(![X458:$i, X459:$i > $o]:((~(![X460:$i]:(((in @ X460 @ X458)=>(X459 @ X460))))=>?[X461:$i]:(((in @ X461 @ X458)&~(X459 @ X461)))))=>(![X462:$i, X463:$i > $o]:((![X464:$i]:(((in @ X464 @ X462)=>~(X463 @ X464)))=>~(?[X465:$i]:(((in @ X465 @ X462)&(X463 @ X465))))))=>(![X466:$i, X467:$i > $o]:((~(?[X468:$i]:(((in @ X468 @ X466)&(X467 @ X468))))=>![X469:$i]:(((in @ X469 @ X466)=>~(X467 @ X469)))))=>(![X470:$i, X471:$i > $o]:((?[X472:$i]:(((in @ X472 @ X470)&~(X471 @ X472)))=>~(![X473:$i]:(((in @ X473 @ X470)=>(X471 @ X473))))))=>(![X474:$o]:(((X474)=>(in @ emptyset @ (prop2set @ ((X474))))))=>((prop2set2propI)=>(![X475:$i, X476:$i > $o]:((~(?[X477:$i]:(((in @ X477 @ X475)&(X476 @ X477))))=>![X478:$i]:(((in @ X478 @ X475)=>~(X476 @ X478)))))=>(![X479:$i, X480:$i > $o]:((~(![X481:$i]:(((in @ X481 @ X479)=>(X480 @ X481))))=>?[X482:$i]:(((in @ X482 @ X479)&~(X480 @ X482)))))=>(![X483:$i > $o]:((?[X484:$i]:(((X483 @ X484)&![X485:$i]:(((X483 @ X485)=>((X484)=(X485))))))=>?[X486:$i]:(((X483 @ X486)&![X487:$i]:(((X483 @ X487)=>((X486)=(X487))))))))=>(![X488:$i > $o]:((?[X489:$i]:((X488 @ X489))=>(![X490:$i, X491:$i]:(((X488 @ X490)=>((X488 @ X491)=>((X490)=(X491)))))=>?[X492:$i]:(((X488 @ X492)&![X493:$i]:(((X488 @ X493)=>((X492)=(X493)))))))))=>(![X494:$i > $o]:((?[X495:$i]:(![X496:$i]:(((X494 @ X496)<=>((X496)=(X495)))))=>?[X497:$i]:(((X494 @ X497)&![X498:$i]:(((X494 @ X498)=>((X497)=(X498))))))))=>(![X499:$i, X500:$i]:((((X499)=(X500))=>![X501:$i, X502:$i]:((((X501)=(X502))=>((in @ X501 @ X499)=>(in @ X502 @ X500))))))=>(![X503:$i, X504:$i]:((((X503)=(X504))=>![X505:$i, X506:$i]:((((X505)=(X506))=>((in @ X505 @ X503)<=>(in @ X506 @ X504))))))=>(![X507:$i > $o]:((?[X508:$i]:(((X507 @ X508)&![X509:$i]:(((X507 @ X509)=>((X508)=(X509))))))=>![X510:$i, X511:$i]:(((X507 @ X510)=>((X507 @ X511)=>((X510)=(X511)))))))=>(![X512:$i > $o, X513:$i > $o]:((![X514:$i, X515:$i]:((((X514)=(X515))=>((X512 @ X514)<=>(X513 @ X515))))=>(?[X516:$i]:(((X512 @ X516)&![X517:$i]:(((X512 @ X517)=>((X516)=(X517))))))<=>?[X518:$i]:(((X513 @ X518)&![X519:$i]:(((X513 @ X519)=>((X518)=(X519)))))))))=>(((emptyset)=(emptyset))=>(![X520:$i, X521:$i]:((((X520)=(X521))=>![X522:$i, X523:$i]:((((X522)=(X523))=>((setadjoin @ X520 @ X522)=(setadjoin @ X521 @ X523))))))=>(![X524:$i, X525:$i]:((((X524)=(X525))=>((powerset @ X524)=(powerset @ X525))))=>(![X526:$i, X527:$i]:((((X526)=(X527))=>((setunion @ X526)=(setunion @ X527))))=>(((omega)=(omega))=>(![X528:$i > $o]:((?[X529:$i]:(((X528 @ X529)&![X530:$i]:(((X528 @ X530)=>((X529)=(X530))))))=>![X531:$i, X532:$i]:(((X528 @ X531)=>((X528 @ X532)=>((X531)=(X532)))))))=>(![X533:$i > $o, X534:$i > $o]:((![X535:$i, X536:$i]:((((X535)=(X536))=>((X533 @ X535)<=>(X534 @ X536))))=>(?[X537:$i]:(((X533 @ X537)&![X538:$i]:(((X533 @ X538)=>((X537)=(X538))))))=>(?[X539:$i]:(((X534 @ X539)&![X540:$i]:(((X534 @ X540)=>((X539)=(X540))))))=>((descr @ (^[Z0:$i]:((X533 @ Z0))))=(descr @ (^[Z0:$i]:((X534 @ Z0)))))))))=>(![X541:$i, X542:$i]:((((X541)=(X542))=>![X543:$i > $o, X544:$i > $o]:((![X545:$i]:(((in @ X545 @ X541)=>![X546:$i]:(((in @ X546 @ X542)=>(((X545)=(X546))=>((X543 @ X545)<=>(X544 @ X546)))))))=>((dsetconstr @ X541 @ (^[Z0:$i]:((X543 @ Z0))))=(dsetconstr @ X542 @ (^[Z0:$i]:((X544 @ Z0)))))))))=>(![X547:$i, X548:$i]:((![X549:$i]:(((in @ X549 @ X547)=>(in @ X549 @ X548)))=>(subset @ X547 @ X548)))=>(![X550:$i, X551:$i]:((((X550)=(X551))=>(subset @ X551 @ X550)))=>(![X552:$i, X553:$i]:((((X552)=(X553))=>(subset @ X552 @ X553)))=>(![X554:$i, X555:$i]:((![X556:$i]:(((in @ X556 @ X554)=>(in @ X556 @ X555)))=>(subset @ X554 @ X555)))=>(![X557:$i]:((subset @ emptyset @ X557))=>(![X558:$i, X559:$i, X560:$i]:(((subset @ X558 @ X559)=>((in @ X560 @ X558)=>(in @ X560 @ X559))))=>(![X561:$i, X562:$i, X563:$i]:(((subset @ X561 @ X562)=>(~(in @ X563 @ X562)=>~(in @ X563 @ X561))))=>(![X564:$i, X565:$i, X566:$i]:(((in @ X566 @ X564)=>(~(in @ X566 @ X565)=>~(subset @ X564 @ X565))))=>(![X567:$i, X568:$i]:((~(subset @ X567 @ X568)=>((X567)!=(X568))))=>(![X569:$i, X570:$i, X571:$i]:(((in @ X571 @ X569)=>(~(in @ X571 @ X570)=>((X569)!=(X570)))))=>(![X572:$i]:((subset @ X572 @ X572))=>(![X573:$i, X574:$i, X575:$i]:(((subset @ X573 @ X574)=>((subset @ X574 @ X575)=>(subset @ X573 @ X575))))=>(![X576:$i, X577:$i]:((subset @ X577 @ (setadjoin @ X576 @ X577)))=>(![X578:$i, X579:$i, X580:$i]:(((subset @ X578 @ X580)=>(subset @ X578 @ (setadjoin @ X579 @ X580))))=>(![X581:$i, X582:$i]:(((subset @ X581 @ X582)=>(in @ X581 @ (powerset @ X582))))=>(![X583:$i, X584:$i]:(((subset @ X583 @ X584)=>((subset @ X584 @ X583)=>((X583)=(X584)))))=>(![X585:$i]:(((subset @ X585 @ emptyset)=>((X585)=(emptyset))))=>(![X586:$i, X587:$i]:(((subset @ X587 @ X586)=>(in @ X587 @ (powerset @ X586))))=>(![X588:$i, X589:$i]:(((in @ X589 @ (powerset @ X588))=>(subset @ X589 @ X588)))=>(![X590:$i]:((in @ X590 @ (powerset @ X590)))=>(![X591:$i, X592:$i]:(((subset @ X591 @ X592)=>(subset @ (powerset @ X591) @ (powerset @ X592))))=>(![X593:$i, X594:$i > $o]:((in @ (dsetconstr @ X593 @ (^[Z0:$i]:((X594 @ Z0)))) @ (powerset @ X593)))=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[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(fof_simplification,[status(thm)],[c_0_114]), noeltsimpempty]), notsubsetI]), subsetE2]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), emptysetE]), c_0_115]), c_0_116]), c_0_117]), c_0_118]), subPowSU]), setunionE]), emptyI]), setext]), c_0_119]), c_0_120]), powersetI]), c_0_121]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), emptysetimpfalse]), setadjoinIL]), emptyinPowerset]), c_0_122]), c_0_123]), setunionI]), powersetE]), emptyInPowerset]), uniqinunit]), c_0_124]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), vacuousDall]), notinemptyset]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), c_0_125]), emptyset__Cong]), c_0_126]), c_0_127]), in__Cong]), inCongP]), c_0_128]), c_0_129]), setadjoin__Cong]), subsetI1]), c_0_130]), c_0_131]), c_0_132]), omega__Cong]), setunion__Cong]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), powerset__Cong]), eqimpsubset2]), prop2setE]), c_0_133]), c_0_134]), c_0_135]), c_0_136]), c_0_137]), wellorderingAx]), foundationAx]), c_0_138]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])]), c_0_139])).
% 0.22/0.30  thf(c_0_141, negated_conjecture, ![X595:$i, X596:$i, X598:$i, X599:$i, X600:$i, X601:$i, X602:$i, X603:$i, X604:$i, X605:$i, X606:$i, X608:$i, X609:$i, X611:$i, X612:$i, X613:$i, X614:$i, X615:$i, X617:$i, X618:$i > $i > $o, X619:$i, X621:$i, X624:$i, X626:$i, X627:$i, X628:$i, X629:$i, X631:$i, X632:$i > $o, X633:$i, X635:$i, X636:$i > $o, X637:$i, X638:$i, X639:$i > $o, X640:$i, X641:$i, X642:$i > $o, X643:$i, X644:$i > $o, X645:$i, X648:$i, X649:$o, X650:$i, X651:$i, X652:$o, X653:$i, X654:$i, X655:$i > $o, X656:$i, X659:$i, X660:$i, X663:$i, X665:$i, X667:$i, X668:$i > $o, X669:$i, X670:$i, X672:$i, X673:$i > $o, X674:$i, X675:$i, X676:$i, X677:$i, X678:$i, X679:$i, X680:$i, X681:$i, X682:$i, X683:$i, X684:$i, X685:$o, X686:$i, X687:$i, X688:$i, X689:$i, X690:$i, X691:$i, X693:$i, X694:$i, X695:$i, X696:$i, X697:$i, X698:$i, X699:$i, X700:$i, X701:$i, X702:$i, X703:$o, X705:$i, X706:$i, X707:$i > $o, X708:$i, X711:$i, X712:$i, X713:$i, X715:$i, X716:$i, X717:$i, X718:$i, X719:$i, X720:$i, X721:$i, X722:$i, X723:$i, X724:$i, X725:$i, X726:$i, X727:$i, X728:$i, X729:$i, X730:$i, X731:$i > $o, X732:$i, X733:$i > $o, X734:$i, X735:$i, X736:$i > $o, X737:$i, X739:$i, X740:$i > $o, X742:$i, X743:$i, X744:$i > $o, X746:$i, X747:$i, X748:$i > $o, X749:$i, X751:$o, X752:$i, X753:$i > $o, X755:$i, X756:$i, X757:$i > $o, X758:$i, X760:$i > $o, X761:$i, X764:$i, X765:$i > $o, X766:$i, X770:$i, X771:$i > $o, X772:$i, X775:$i, X776:$i, X777:$i, X778:$i, X779:$i, X780:$i, X781:$i, X782:$i, X783:$i, X784:$i > $o, X785:$i, X787:$i, X788:$i, X789:$i > $o, X790:$i > $o, X793:$i, X796:$i, X797:$i, X800:$i, X801:$i, X802:$i, X803:$i, X804:$i, X805:$i, X806:$i, X807:$i, X808:$i, X809:$i > $o, X810:$i, X812:$i, X813:$i, X814:$i > $o, X815:$i > $o, X818:$i, X820:$i, X822:$i, X823:$i, X824:$i > $o, X825:$i > $o, X828:$i, X829:$i, X831:$i, X832:$i, X833:$i, X834:$i, X835:$i, X836:$i, X838:$i, X839:$i, X840:$i, X841:$i, X842:$i, X843:$i, X844:$i, X845:$i, X846:$i, X847:$i, X848:$i, X849:$i, X850:$i, X851:$i, X852:$i, X853:$i, X854:$i, X855:$i, X856:$i, X857:$i, X858:$i, X859:$i, X860:$i, X861:$i, X862:$i, X863:$i, X864:$i, X865:$i, X866:$i, X867:$i, X868:$i, X869:$i, X870:$i, X871:$i, X872:$i, X873:$i, X874:$i, X875:$i > $o]:((((~(in @ (esk1_2 @ X595 @ X596) @ X595)|~(in @ (esk1_2 @ X595 @ X596) @ X596)|((X595)=(X596)))&((in @ (esk1_2 @ X595 @ X596) @ X595)|(in @ (esk1_2 @ X595 @ X596) @ X596)|((X595)=(X596))))&(~(in @ X598 @ emptyset)&(((~(in @ X601 @ (setadjoin @ X599 @ X600))|(((X601)=(X599))|(in @ X601 @ X600)))&((((X601)!=(X599))|(in @ X601 @ (setadjoin @ X599 @ X600)))&(~(in @ X601 @ X600)|(in @ X601 @ (setadjoin @ X599 @ X600)))))&(((~(in @ X603 @ (powerset @ X602))|(~(in @ X604 @ X603)|(in @ X604 @ X602)))&(((in @ (esk2_2 @ X605 @ X606) @ X606)|(in @ X606 @ (powerset @ X605)))&(~(in @ (esk2_2 @ X605 @ X606) @ X605)|(in @ X606 @ (powerset @ X605)))))&(((((in @ X609 @ (esk3_2 @ X608 @ X609))|~(in @ X609 @ (setunion @ X608)))&((in @ (esk3_2 @ X608 @ X609) @ X608)|~(in @ X609 @ (setunion @ X608))))&(~(in @ X612 @ X613)|~(in @ X613 @ X611)|(in @ X612 @ (setunion @ X611))))&((in @ emptyset @ omega)&((~(in @ X614 @ omega)|(in @ (setadjoin @ X614 @ X614) @ omega))&(((((in @ (esk4_1 @ X615) @ omega)|~(in @ emptyset @ X615)|(~(in @ X617 @ omega)|(in @ X617 @ X615)))&((in @ (esk4_1 @ X615) @ X615)|~(in @ emptyset @ X615)|(~(in @ X617 @ omega)|(in @ X617 @ X615))))&(~(in @ (setadjoin @ (esk4_1 @ X615) @ (esk4_1 @ X615)) @ X615)|~(in @ emptyset @ X615)|(~(in @ X617 @ omega)|(in @ X617 @ X615))))&((((((in @ (esk8_3 @ X618 @ X619 @ X624) @ X619)|~(in @ X624 @ (esk7_2 @ X618 @ X619))|(in @ (esk5_2 @ X618 @ X619) @ X619))&((X618 @ (esk8_3 @ X618 @ X619 @ X624) @ X624)|~(in @ X624 @ (esk7_2 @ X618 @ X619))|(in @ (esk5_2 @ X618 @ X619) @ X619)))&(~(in @ X627 @ X619)|~(X618 @ X627 @ X626)|(in @ X626 @ (esk7_2 @ X618 @ X619))|(in @ (esk5_2 @ X618 @ X619) @ X619)))&(((((in @ (esk8_3 @ X618 @ X619 @ X624) @ X619)|~(in @ X624 @ (esk7_2 @ X618 @ X619))|((X618 @ (esk5_2 @ X618 @ X619) @ (esk6_3 @ X618 @ X619 @ X621))|~(X618 @ (esk5_2 @ X618 @ X619) @ X621)))&((X618 @ (esk8_3 @ X618 @ X619 @ X624) @ X624)|~(in @ X624 @ (esk7_2 @ X618 @ X619))|((X618 @ (esk5_2 @ X618 @ X619) @ (esk6_3 @ X618 @ X619 @ X621))|~(X618 @ (esk5_2 @ X618 @ X619) @ X621))))&(~(in @ X627 @ X619)|~(X618 @ X627 @ X626)|(in @ X626 @ (esk7_2 @ X618 @ X619))|((X618 @ (esk5_2 @ X618 @ X619) @ (esk6_3 @ X618 @ X619 @ X621))|~(X618 @ (esk5_2 @ X618 @ X619) @ X621))))&((((in @ (esk8_3 @ X618 @ X619 @ X624) @ X619)|~(in @ X624 @ (esk7_2 @ X618 @ X619))|(((X621)!=(esk6_3 @ X618 @ X619 @ X621))|~(X618 @ (esk5_2 @ X618 @ X619) @ X621)))&((X618 @ (esk8_3 @ X618 @ X619 @ X624) @ X624)|~(in @ X624 @ (esk7_2 @ X618 @ X619))|(((X621)!=(esk6_3 @ X618 @ X619 @ X621))|~(X618 @ (esk5_2 @ X618 @ X619) @ X621))))&(~(in @ X627 @ X619)|~(X618 @ X627 @ X626)|(in @ X626 @ (esk7_2 @ X618 @ X619))|(((X621)!=(esk6_3 @ X618 @ X619 @ X621))|~(X618 @ (esk5_2 @ X618 @ X619) @ X621))))))&((((in @ (esk9_1 @ X628) @ X628)|~(in @ X629 @ X628))&(~(in @ X631 @ (esk9_1 @ X628))|~(in @ X631 @ X628)|~(in @ X629 @ X628)))&((epred1_0)&((((X632 @ (esk10_2 @ X632 @ X633))|~(X632 @ X633)|(X632 @ (descr @ (^[Z0:$i]:((X632 @ Z0))))))&(((X633)!=(esk10_2 @ X632 @ X633))|~(X632 @ X633)|(X632 @ (descr @ (^[Z0:$i]:((X632 @ Z0)))))))&((~(in @ X637 @ X635)|(~(X636 @ X637)|(in @ X637 @ (dsetconstr @ X635 @ (^[Z0:$i]:((X636 @ Z0)))))))&((~(in @ X640 @ (dsetconstr @ X638 @ (^[Z0:$i]:((X639 @ Z0)))))|(in @ X640 @ X638))&((~(in @ X643 @ (dsetconstr @ X641 @ (^[Z0:$i]:((X642 @ Z0)))))|(X642 @ X643))&(((((X644 @ (esk12_1 @ X644))|((X644 @ (esk11_2 @ X644 @ X645))|~(X644 @ X645)))&(~(X644 @ X648)|((esk12_1 @ X644)=(X648))|((X644 @ (esk11_2 @ X644 @ X645))|~(X644 @ X645))))&(((X644 @ (esk12_1 @ X644))|(((X645)!=(esk11_2 @ X644 @ X645))|~(X644 @ X645)))&(~(X644 @ X648)|((esk12_1 @ X644)=(X648))|(((X645)!=(esk11_2 @ X644 @ X645))|~(X644 @ X645)))))&((~(in @ X650 @ (prop2set @ ((X649))))|(X649))&((~(in @ X651 @ emptyset)|(X652))&(~(in @ X653 @ emptyset)&(~(in @ X654 @ emptyset)&((((X655 @ (esk13_2 @ X655 @ X656))|~(X655 @ X656)|(X655 @ (esk14_1 @ X655)))&(((X656)!=(esk13_2 @ X655 @ X656))|~(X655 @ X656)|(X655 @ (esk14_1 @ X655))))&(((((in @ (esk16_2 @ X659 @ X660) @ X660)|((X659)=(X660))|(in @ (esk15_2 @ X659 @ X660) @ X659))&(~(in @ (esk16_2 @ X659 @ X660) @ X659)|((X659)=(X660))|(in @ (esk15_2 @ X659 @ X660) @ X659)))&(((in @ (esk16_2 @ X659 @ X660) @ X660)|((X659)=(X660))|~(in @ (esk15_2 @ X659 @ X660) @ X660))&(~(in @ (esk16_2 @ X659 @ X660) @ X659)|((X659)=(X660))|~(in @ (esk15_2 @ X659 @ X660) @ X660))))&(((in @ (esk17_1 @ X663) @ X663)|((X663)=(emptyset)))&(((in @ (esk18_1 @ X665) @ X665)|((X665)=(emptyset)))&(((~(in @ X669 @ (dsetconstr @ X667 @ (^[Z0:$i]:((X668 @ Z0)))))|(X668 @ X669)|~(in @ X669 @ X667))&(~(X668 @ X669)|(in @ X669 @ (dsetconstr @ X667 @ (^[Z0:$i]:((X668 @ Z0)))))|~(in @ X669 @ X667)))&((((X670)=(emptyset))|(in @ (esk19_1 @ X670) @ X670))&((~(in @ X674 @ X672)|(~(X673 @ X674)|((dsetconstr @ X672 @ (^[Z0:$i]:((X673 @ Z0))))!=(emptyset))))&((~(in @ X676 @ X675)|((X675)!=(emptyset)))&((in @ X677 @ (setadjoin @ X677 @ X678))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X681 @ X680)|(in @ X681 @ (setadjoin @ X679 @ X680)))&(((((in @ X684 @ X683)|(X685)|((X684)=(X682))|~(in @ X684 @ (setadjoin @ X682 @ X683)))&(~(X685)|(X685)|((X684)=(X682))|~(in @ X684 @ (setadjoin @ X682 @ X683))))&(((in @ X684 @ X683)|(X685)|~(X685)|~(in @ X684 @ (setadjoin @ X682 @ X683)))&(~(X685)|(X685)|~(X685)|~(in @ X684 @ (setadjoin @ X682 @ X683)))))&((~(in @ X688 @ (setadjoin @ X686 @ X687))|(((X688)=(X686))|(in @ X688 @ X687)))&(((dsetconstr @ X689 @ (^[Z0:$i]:(($true))))=(X689))&((((in @ (esk20_2 @ X690 @ X691) @ X691)|(in @ X691 @ (powerset @ X690)))&(~(in @ (esk20_2 @ X690 @ X691) @ X690)|(in @ X691 @ (powerset @ X690))))&((in @ emptyset @ (powerset @ X693))&((in @ emptyset @ (powerset @ X694))&((~(in @ X696 @ (powerset @ X695))|(~(in @ X697 @ X696)|(in @ X697 @ X695)))&((~(in @ X699 @ X700)|(~(in @ X700 @ X698)|(in @ X699 @ (setunion @ X698))))&((((in @ X702 @ (esk21_3 @ X701 @ X702 @ X703))|(X703)|~(in @ X702 @ (setunion @ X701)))&(((in @ (esk21_3 @ X701 @ X702 @ X703) @ X701)|(X703)|~(in @ X702 @ (setunion @ X701)))&(~(X703)|(X703)|~(in @ X702 @ (setunion @ X701)))))&((~(in @ X706 @ X705)|(in @ X706 @ (powerset @ (setunion @ X705))))&((((~(X707 @ X711)|((X711)=(esk23_1 @ X707))|((X707 @ (esk22_2 @ X707 @ X708))|~(X707 @ X708)))&(((X712)!=(esk23_1 @ X707))|(X707 @ X712)|((X707 @ (esk22_2 @ X707 @ X708))|~(X707 @ X708))))&((~(X707 @ X711)|((X711)=(esk23_1 @ X707))|(((X708)!=(esk22_2 @ X707 @ X708))|~(X707 @ X708)))&(((X712)!=(esk23_1 @ X707))|(X707 @ X712)|(((X708)!=(esk22_2 @ X707 @ X708))|~(X707 @ X708)))))&((((X713)=(emptyset))|(in @ (esk24_1 @ X713) @ X713))&((~(in @ X715 @ (setadjoin @ X716 @ emptyset))|((X715)=(X716)))&((((X717)=(X718))|~(in @ X718 @ (setadjoin @ X717 @ emptyset)))&((((X719)!=(X720))|(in @ X719 @ (setadjoin @ X720 @ emptyset)))&((~(in @ X721 @ (setadjoin @ X722 @ emptyset))|(in @ X722 @ (setadjoin @ X721 @ emptyset)))&((~(in @ X725 @ (setadjoin @ X723 @ (setadjoin @ X724 @ emptyset)))|(((X725)=(X723))|((X725)=(X724))))&((in @ X726 @ (setadjoin @ X726 @ (setadjoin @ X727 @ emptyset)))&((in @ X729 @ (setadjoin @ X728 @ (setadjoin @ X729 @ emptyset)))&((~(in @ X732 @ X730)|~(X731 @ X732)|((dsetconstr @ X730 @ (^[Z0:$i]:((X731 @ Z0))))!=(emptyset)))&((~(in @ X734 @ emptyset)|(X733 @ X734))&((((in @ (esk25_2 @ X735 @ X736) @ X735)|(~(in @ X737 @ X735)|(X736 @ X737)))&(~(X736 @ (esk25_2 @ X735 @ X736))|(~(in @ X737 @ X735)|(X736 @ X737))))&((((in @ (esk26_2 @ X739 @ X740) @ X739)|(~(in @ X742 @ X739)|~(X740 @ X742)))&((X740 @ (esk26_2 @ X739 @ X740))|(~(in @ X742 @ X739)|~(X740 @ X742))))&((((in @ (esk27_2 @ X743 @ X744) @ X743)|(~(in @ X746 @ X743)|~(X744 @ X746)))&((X744 @ (esk27_2 @ X743 @ X744))|(~(in @ X746 @ X743)|~(X744 @ X746))))&((((in @ (esk28_2 @ X747 @ X748) @ X747)|(~(in @ X749 @ X747)|(X748 @ X749)))&(~(X748 @ (esk28_2 @ X747 @ X748))|(~(in @ X749 @ X747)|(X748 @ X749))))&((~(X751)|(in @ emptyset @ (prop2set @ ((X751)))))&((prop2set2propI)&((((in @ (esk29_2 @ X752 @ X753) @ X752)|(~(in @ X755 @ X752)|~(X753 @ X755)))&((X753 @ (esk29_2 @ X752 @ X753))|(~(in @ X755 @ X752)|~(X753 @ X755))))&((((in @ (esk30_2 @ X756 @ X757) @ X756)|(~(in @ X758 @ X756)|(X757 @ X758)))&(~(X757 @ (esk30_2 @ X756 @ X757))|(~(in @ X758 @ X756)|(X757 @ X758))))&(((((X760 @ (esk32_1 @ X760))|((X760 @ (esk31_2 @ X760 @ X761))|~(X760 @ X761)))&(~(X760 @ X764)|((esk32_1 @ X760)=(X764))|((X760 @ (esk31_2 @ X760 @ X761))|~(X760 @ X761))))&(((X760 @ (esk32_1 @ X760))|(((X761)!=(esk31_2 @ X760 @ X761))|~(X760 @ X761)))&(~(X760 @ X764)|((esk32_1 @ X760)=(X764))|(((X761)!=(esk31_2 @ X760 @ X761))|~(X760 @ X761)))))&(((((X765 @ (esk35_1 @ X765))|(X765 @ (esk33_1 @ X765))|~(X765 @ X766))&(~(X765 @ X770)|((esk35_1 @ X765)=(X770))|(X765 @ (esk33_1 @ X765))|~(X765 @ X766)))&((((X765 @ (esk35_1 @ X765))|(X765 @ (esk34_1 @ X765))|~(X765 @ X766))&(~(X765 @ X770)|((esk35_1 @ X765)=(X770))|(X765 @ (esk34_1 @ X765))|~(X765 @ X766)))&(((X765 @ (esk35_1 @ X765))|((esk33_1 @ X765)!=(esk34_1 @ X765))|~(X765 @ X766))&(~(X765 @ X770)|((esk35_1 @ X765)=(X770))|((esk33_1 @ X765)!=(esk34_1 @ X765))|~(X765 @ X766)))))&(((((X771 @ (esk37_1 @ X771))|(~(X771 @ (esk36_2 @ X771 @ X772))|((esk36_2 @ X771 @ X772)!=(X772))))&(~(X771 @ X775)|((esk37_1 @ X771)=(X775))|(~(X771 @ (esk36_2 @ X771 @ X772))|((esk36_2 @ X771 @ X772)!=(X772)))))&(((X771 @ (esk37_1 @ X771))|((X771 @ (esk36_2 @ X771 @ X772))|((esk36_2 @ X771 @ X772)=(X772))))&(~(X771 @ X775)|((esk37_1 @ X771)=(X775))|((X771 @ (esk36_2 @ X771 @ X772))|((esk36_2 @ X771 @ X772)=(X772))))))&((((X776)!=(X777))|(((X778)!=(X779))|(~(in @ X778 @ X776)|(in @ X779 @ X777))))&(((~(in @ X782 @ X780)|(in @ X783 @ X781)|((X782)!=(X783))|((X780)!=(X781)))&(~(in @ X783 @ X781)|(in @ X782 @ X780)|((X782)!=(X783))|((X780)!=(X781))))&((((X784 @ (esk38_2 @ X784 @ X785))|~(X784 @ X785)|(~(X784 @ X787)|(~(X784 @ X788)|((X787)=(X788)))))&(((X785)!=(esk38_2 @ X784 @ X785))|~(X784 @ X785)|(~(X784 @ X787)|(~(X784 @ X788)|((X787)=(X788))))))&(((((((X790 @ (esk42_2 @ X789 @ X790))|((X789 @ (esk41_3 @ X789 @ X790 @ X793))|~(X789 @ X793))|((esk39_2 @ X789 @ X790)=(esk40_2 @ X789 @ X790)))&(~(X790 @ X796)|((esk42_2 @ X789 @ X790)=(X796))|((X789 @ (esk41_3 @ X789 @ X790 @ X793))|~(X789 @ X793))|((esk39_2 @ X789 @ X790)=(esk40_2 @ X789 @ X790))))&(((X790 @ (esk42_2 @ X789 @ X790))|(((X793)!=(esk41_3 @ X789 @ X790 @ X793))|~(X789 @ X793))|((esk39_2 @ X789 @ X790)=(esk40_2 @ X789 @ X790)))&(~(X790 @ X796)|((esk42_2 @ X789 @ X790)=(X796))|(((X793)!=(esk41_3 @ X789 @ X790 @ X793))|~(X789 @ X793))|((esk39_2 @ X789 @ X790)=(esk40_2 @ X789 @ X790)))))&((((X789 @ (esk44_2 @ X789 @ X790))|((X790 @ (esk43_3 @ X789 @ X790 @ X797))|~(X790 @ X797))|((esk39_2 @ X789 @ X790)=(esk40_2 @ X789 @ X790)))&(~(X789 @ X800)|((esk44_2 @ X789 @ X790)=(X800))|((X790 @ (esk43_3 @ X789 @ X790 @ X797))|~(X790 @ X797))|((esk39_2 @ X789 @ X790)=(esk40_2 @ X789 @ X790))))&(((X789 @ (esk44_2 @ X789 @ X790))|(((X797)!=(esk43_3 @ X789 @ X790 @ X797))|~(X790 @ X797))|((esk39_2 @ X789 @ X790)=(esk40_2 @ X789 @ X790)))&(~(X789 @ X800)|((esk44_2 @ X789 @ X790)=(X800))|(((X797)!=(esk43_3 @ X789 @ X790 @ X797))|~(X790 @ X797))|((esk39_2 @ X789 @ X790)=(esk40_2 @ X789 @ X790))))))&((((((X790 @ (esk42_2 @ X789 @ X790))|((X789 @ (esk41_3 @ X789 @ X790 @ X793))|~(X789 @ X793))|(~(X789 @ (esk39_2 @ X789 @ X790))|~(X790 @ (esk40_2 @ X789 @ X790))))&(~(X790 @ X796)|((esk42_2 @ X789 @ X790)=(X796))|((X789 @ (esk41_3 @ X789 @ X790 @ X793))|~(X789 @ X793))|(~(X789 @ (esk39_2 @ X789 @ X790))|~(X790 @ (esk40_2 @ X789 @ X790)))))&(((X790 @ (esk42_2 @ X789 @ X790))|(((X793)!=(esk41_3 @ X789 @ X790 @ X793))|~(X789 @ X793))|(~(X789 @ (esk39_2 @ X789 @ X790))|~(X790 @ (esk40_2 @ X789 @ X790))))&(~(X790 @ X796)|((esk42_2 @ X789 @ X790)=(X796))|(((X793)!=(esk41_3 @ X789 @ X790 @ X793))|~(X789 @ X793))|(~(X789 @ (esk39_2 @ X789 @ X790))|~(X790 @ (esk40_2 @ X789 @ X790))))))&((((X789 @ (esk44_2 @ X789 @ X790))|((X790 @ (esk43_3 @ X789 @ X790 @ X797))|~(X790 @ X797))|(~(X789 @ (esk39_2 @ X789 @ X790))|~(X790 @ (esk40_2 @ X789 @ X790))))&(~(X789 @ X800)|((esk44_2 @ X789 @ X790)=(X800))|((X790 @ (esk43_3 @ X789 @ X790 @ X797))|~(X790 @ X797))|(~(X789 @ (esk39_2 @ X789 @ X790))|~(X790 @ (esk40_2 @ X789 @ X790)))))&(((X789 @ (esk44_2 @ X789 @ X790))|(((X797)!=(esk43_3 @ X789 @ X790 @ X797))|~(X790 @ X797))|(~(X789 @ (esk39_2 @ X789 @ X790))|~(X790 @ (esk40_2 @ X789 @ X790))))&(~(X789 @ X800)|((esk44_2 @ X789 @ X790)=(X800))|(((X797)!=(esk43_3 @ X789 @ X790 @ X797))|~(X790 @ X797))|(~(X789 @ (esk39_2 @ X789 @ X790))|~(X790 @ (esk40_2 @ X789 @ X790)))))))&(((((X790 @ (esk42_2 @ X789 @ X790))|((X789 @ (esk41_3 @ X789 @ X790 @ X793))|~(X789 @ X793))|((X789 @ (esk39_2 @ X789 @ X790))|(X790 @ (esk40_2 @ X789 @ X790))))&(~(X790 @ X796)|((esk42_2 @ X789 @ X790)=(X796))|((X789 @ (esk41_3 @ X789 @ X790 @ X793))|~(X789 @ X793))|((X789 @ (esk39_2 @ X789 @ X790))|(X790 @ (esk40_2 @ X789 @ X790)))))&(((X790 @ (esk42_2 @ X789 @ X790))|(((X793)!=(esk41_3 @ X789 @ X790 @ X793))|~(X789 @ X793))|((X789 @ (esk39_2 @ X789 @ X790))|(X790 @ (esk40_2 @ X789 @ X790))))&(~(X790 @ X796)|((esk42_2 @ X789 @ X790)=(X796))|(((X793)!=(esk41_3 @ X789 @ X790 @ X793))|~(X789 @ X793))|((X789 @ (esk39_2 @ X789 @ X790))|(X790 @ (esk40_2 @ X789 @ X790))))))&((((X789 @ (esk44_2 @ X789 @ X790))|((X790 @ (esk43_3 @ X789 @ X790 @ X797))|~(X790 @ X797))|((X789 @ (esk39_2 @ X789 @ X790))|(X790 @ (esk40_2 @ X789 @ X790))))&(~(X789 @ X800)|((esk44_2 @ X789 @ X790)=(X800))|((X790 @ (esk43_3 @ X789 @ X790 @ X797))|~(X790 @ X797))|((X789 @ (esk39_2 @ X789 @ X790))|(X790 @ (esk40_2 @ X789 @ X790)))))&(((X789 @ (esk44_2 @ X789 @ X790))|(((X797)!=(esk43_3 @ X789 @ X790 @ X797))|~(X790 @ X797))|((X789 @ (esk39_2 @ X789 @ X790))|(X790 @ (esk40_2 @ X789 @ X790))))&(~(X789 @ X800)|((esk44_2 @ X789 @ X790)=(X800))|(((X797)!=(esk43_3 @ X789 @ X790 @ X797))|~(X790 @ X797))|((X789 @ (esk39_2 @ X789 @ X790))|(X790 @ (esk40_2 @ X789 @ X790)))))))))&(((emptyset)=(emptyset))&((((X801)!=(X802))|(((X803)!=(X804))|((setadjoin @ X801 @ X803)=(setadjoin @ X802 @ X804))))&((((X805)!=(X806))|((powerset @ X805)=(powerset @ X806)))&((((X807)!=(X808))|((setunion @ X807)=(setunion @ X808)))&(((omega)=(omega))&((((X809 @ (esk45_2 @ X809 @ X810))|~(X809 @ X810)|(~(X809 @ X812)|(~(X809 @ X813)|((X812)=(X813)))))&(((X810)!=(esk45_2 @ X809 @ X810))|~(X809 @ X810)|(~(X809 @ X812)|(~(X809 @ X813)|((X812)=(X813))))))&((((((X815 @ (esk49_3 @ X814 @ X815 @ X820))|~(X815 @ X820)|((descr @ (^[Z0:$i]:((X814 @ Z0))))=(descr @ (^[Z0:$i]:((X815 @ Z0)))))|((X814 @ (esk48_3 @ X814 @ X815 @ X818))|~(X814 @ X818))|((esk46_2 @ X814 @ X815)=(esk47_2 @ X814 @ X815)))&(((X820)!=(esk49_3 @ X814 @ X815 @ X820))|~(X815 @ X820)|((descr @ (^[Z0:$i]:((X814 @ Z0))))=(descr @ (^[Z0:$i]:((X815 @ Z0)))))|((X814 @ (esk48_3 @ X814 @ X815 @ X818))|~(X814 @ X818))|((esk46_2 @ X814 @ X815)=(esk47_2 @ X814 @ X815))))&(((X815 @ (esk49_3 @ X814 @ X815 @ X820))|~(X815 @ X820)|((descr @ (^[Z0:$i]:((X814 @ Z0))))=(descr @ (^[Z0:$i]:((X815 @ Z0)))))|(((X818)!=(esk48_3 @ X814 @ X815 @ X818))|~(X814 @ X818))|((esk46_2 @ X814 @ X815)=(esk47_2 @ X814 @ X815)))&(((X820)!=(esk49_3 @ X814 @ X815 @ X820))|~(X815 @ X820)|((descr @ (^[Z0:$i]:((X814 @ Z0))))=(descr @ (^[Z0:$i]:((X815 @ Z0)))))|(((X818)!=(esk48_3 @ X814 @ X815 @ X818))|~(X814 @ X818))|((esk46_2 @ X814 @ X815)=(esk47_2 @ X814 @ X815)))))&(((((X815 @ (esk49_3 @ X814 @ X815 @ X820))|~(X815 @ X820)|((descr @ (^[Z0:$i]:((X814 @ Z0))))=(descr @ (^[Z0:$i]:((X815 @ Z0)))))|((X814 @ (esk48_3 @ X814 @ X815 @ X818))|~(X814 @ X818))|(~(X814 @ (esk46_2 @ X814 @ X815))|~(X815 @ (esk47_2 @ X814 @ X815))))&(((X820)!=(esk49_3 @ X814 @ X815 @ X820))|~(X815 @ X820)|((descr @ (^[Z0:$i]:((X814 @ Z0))))=(descr @ (^[Z0:$i]:((X815 @ Z0)))))|((X814 @ (esk48_3 @ X814 @ X815 @ X818))|~(X814 @ X818))|(~(X814 @ (esk46_2 @ X814 @ X815))|~(X815 @ (esk47_2 @ X814 @ X815)))))&(((X815 @ (esk49_3 @ X814 @ X815 @ X820))|~(X815 @ X820)|((descr @ (^[Z0:$i]:((X814 @ Z0))))=(descr @ (^[Z0:$i]:((X815 @ Z0)))))|(((X818)!=(esk48_3 @ X814 @ X815 @ X818))|~(X814 @ X818))|(~(X814 @ (esk46_2 @ X814 @ X815))|~(X815 @ (esk47_2 @ X814 @ X815))))&(((X820)!=(esk49_3 @ X814 @ X815 @ X820))|~(X815 @ X820)|((descr @ (^[Z0:$i]:((X814 @ Z0))))=(descr @ (^[Z0:$i]:((X815 @ Z0)))))|(((X818)!=(esk48_3 @ X814 @ X815 @ X818))|~(X814 @ X818))|(~(X814 @ (esk46_2 @ X814 @ X815))|~(X815 @ (esk47_2 @ X814 @ X815))))))&((((X815 @ (esk49_3 @ X814 @ X815 @ X820))|~(X815 @ X820)|((descr @ (^[Z0:$i]:((X814 @ Z0))))=(descr @ (^[Z0:$i]:((X815 @ Z0)))))|((X814 @ (esk48_3 @ X814 @ X815 @ X818))|~(X814 @ X818))|((X814 @ (esk46_2 @ X814 @ X815))|(X815 @ (esk47_2 @ X814 @ X815))))&(((X820)!=(esk49_3 @ X814 @ X815 @ X820))|~(X815 @ X820)|((descr @ (^[Z0:$i]:((X814 @ Z0))))=(descr @ (^[Z0:$i]:((X815 @ Z0)))))|((X814 @ (esk48_3 @ X814 @ X815 @ X818))|~(X814 @ X818))|((X814 @ (esk46_2 @ X814 @ X815))|(X815 @ (esk47_2 @ X814 @ X815)))))&(((X815 @ (esk49_3 @ X814 @ X815 @ X820))|~(X815 @ X820)|((descr @ (^[Z0:$i]:((X814 @ Z0))))=(descr @ (^[Z0:$i]:((X815 @ Z0)))))|(((X818)!=(esk48_3 @ X814 @ X815 @ X818))|~(X814 @ X818))|((X814 @ (esk46_2 @ X814 @ X815))|(X815 @ (esk47_2 @ X814 @ X815))))&(((X820)!=(esk49_3 @ X814 @ X815 @ X820))|~(X815 @ X820)|((descr @ (^[Z0:$i]:((X814 @ Z0))))=(descr @ (^[Z0:$i]:((X815 @ Z0)))))|(((X818)!=(esk48_3 @ X814 @ X815 @ X818))|~(X814 @ X818))|((X814 @ (esk46_2 @ X814 @ X815))|(X815 @ (esk47_2 @ X814 @ X815))))))))&((((in @ (esk50_4 @ X822 @ X823 @ X824 @ X825) @ X822)|((dsetconstr @ X822 @ (^[Z0:$i]:((X824 @ Z0))))=(dsetconstr @ X823 @ (^[Z0:$i]:((X825 @ Z0)))))|((X822)!=(X823)))&(((in @ (esk51_4 @ X822 @ X823 @ X824 @ X825) @ X823)|((dsetconstr @ X822 @ (^[Z0:$i]:((X824 @ Z0))))=(dsetconstr @ X823 @ (^[Z0:$i]:((X825 @ Z0)))))|((X822)!=(X823)))&((((esk50_4 @ X822 @ X823 @ X824 @ X825)=(esk51_4 @ X822 @ X823 @ X824 @ X825))|((dsetconstr @ X822 @ (^[Z0:$i]:((X824 @ Z0))))=(dsetconstr @ X823 @ (^[Z0:$i]:((X825 @ Z0)))))|((X822)!=(X823)))&((~(X824 @ (esk50_4 @ X822 @ X823 @ X824 @ X825))|~(X825 @ (esk51_4 @ X822 @ X823 @ X824 @ X825))|((dsetconstr @ X822 @ (^[Z0:$i]:((X824 @ Z0))))=(dsetconstr @ X823 @ (^[Z0:$i]:((X825 @ Z0)))))|((X822)!=(X823)))&((X824 @ (esk50_4 @ X822 @ X823 @ X824 @ X825))|(X825 @ (esk51_4 @ X822 @ X823 @ X824 @ X825))|((dsetconstr @ X822 @ (^[Z0:$i]:((X824 @ Z0))))=(dsetconstr @ X823 @ (^[Z0:$i]:((X825 @ Z0)))))|((X822)!=(X823)))))))&((((in @ (esk52_2 @ X828 @ X829) @ X828)|(subset @ X828 @ X829))&(~(in @ (esk52_2 @ X828 @ X829) @ X829)|(subset @ X828 @ X829)))&((((X831)!=(X832))|(subset @ X832 @ X831))&((((X833)!=(X834))|(subset @ X833 @ X834))&((((in @ (esk53_2 @ X835 @ X836) @ X835)|(subset @ X835 @ X836))&(~(in @ (esk53_2 @ X835 @ X836) @ X836)|(subset @ X835 @ X836)))&((subset @ emptyset @ X838)&((~(subset @ X839 @ X840)|(~(in @ X841 @ X839)|(in @ X841 @ X840)))&((~(subset @ X842 @ X843)|((in @ X844 @ X843)|~(in @ X844 @ X842)))&((~(in @ X847 @ X845)|((in @ X847 @ X846)|~(subset @ X845 @ X846)))&(((subset @ X848 @ X849)|((X848)!=(X849)))&((~(in @ X852 @ X850)|((in @ X852 @ X851)|((X850)!=(X851))))&((subset @ X853 @ X853)&((~(subset @ X854 @ X855)|(~(subset @ X855 @ X856)|(subset @ X854 @ X856)))&((subset @ X858 @ (setadjoin @ X857 @ X858))&((~(subset @ X859 @ X861)|(subset @ X859 @ (setadjoin @ X860 @ X861)))&((~(subset @ X862 @ X863)|(in @ X862 @ (powerset @ X863)))&((~(subset @ X864 @ X865)|(~(subset @ X865 @ X864)|((X864)=(X865))))&((~(subset @ X866 @ emptyset)|((X866)=(emptyset)))&((~(subset @ X868 @ X867)|(in @ X868 @ (powerset @ X867)))&((~(in @ X870 @ (powerset @ X869))|(subset @ X870 @ X869))&((in @ X871 @ (powerset @ X871))&((~(subset @ X872 @ X873)|(subset @ (powerset @ X872) @ (powerset @ X873)))&((in @ (dsetconstr @ X874 @ (^[Z0:$i]:((X875 @ Z0)))) @ (powerset @ X874))&~(subset @ (dsetconstr @ esk54_0 @ (^[Z0:$i]:((epred2_0 @ Z0)))) @ esk54_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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_140])])])])])])).
% 0.22/0.30  thf(c_0_142, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ X2 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_141])).
% 0.22/0.30  thf(c_0_143, negated_conjecture, ![X1:$i > $o, X2:$i]:((in @ (dsetconstr @ X2 @ X1) @ (powerset @ X2))), inference(split_conjunct,[status(thm)],[c_0_141])).
% 0.22/0.30  thf(c_0_144, negated_conjecture, ~((subset @ (dsetconstr @ esk54_0 @ epred2_0) @ esk54_0)), inference(split_conjunct,[status(thm)],[c_0_141])).
% 0.22/0.30  thf(c_0_145, negated_conjecture, ![X1:$i > $o, X2:$i]:((subset @ (dsetconstr @ X2 @ X1) @ X2)), inference(spm,[status(thm)],[c_0_142, c_0_143])).
% 0.22/0.30  thf(c_0_146, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_144, c_0_145])]), ['proof']).
% 0.22/0.30  % SZS output end CNFRefutation
% 0.22/0.30  % Parsed axioms                        : 212
% 0.22/0.30  % Removed by relevancy pruning/SinE    : 113
% 0.22/0.30  % Initial clauses                      : 207
% 0.22/0.30  % Removed in clause preprocessing      : 13
% 0.22/0.30  % Initial clauses in saturation        : 194
% 0.22/0.30  % Processed clauses                    : 45
% 0.22/0.30  % ...of these trivial                  : 3
% 0.22/0.30  % ...subsumed                          : 7
% 0.22/0.30  % ...remaining for further processing  : 35
% 0.22/0.30  % Other redundant clauses eliminated   : 5
% 0.22/0.30  % Clauses deleted for lack of memory   : 0
% 0.22/0.30  % Backward-subsumed                    : 0
% 0.22/0.30  % Backward-rewritten                   : 3
% 0.22/0.30  % Generated clauses                    : 33
% 0.22/0.30  % ...of the previous two non-redundant : 21
% 0.22/0.30  % ...aggressively subsumed             : 0
% 0.22/0.30  % Contextual simplify-reflections      : 0
% 0.22/0.30  % Paramodulations                      : 28
% 0.22/0.30  % Factorizations                       : 0
% 0.22/0.30  % NegExts                              : 0
% 0.22/0.30  % Equation resolutions                 : 5
% 0.22/0.30  % Disequality decompositions           : 0
% 0.22/0.30  % Total rewrite steps                  : 16
% 0.22/0.30  % ...of those cached                   : 5
% 0.22/0.30  % Propositional unsat checks           : 0
% 0.22/0.30  %    Propositional check models        : 0
% 0.22/0.30  %    Propositional check unsatisfiable : 0
% 0.22/0.30  %    Propositional clauses             : 0
% 0.22/0.30  %    Propositional clauses after purity: 0
% 0.22/0.30  %    Propositional unsat core size     : 0
% 0.22/0.30  %    Propositional preprocessing time  : 0.000
% 0.22/0.30  %    Propositional encoding time       : 0.000
% 0.22/0.30  %    Propositional solver time         : 0.000
% 0.22/0.30  %    Success case prop preproc time    : 0.000
% 0.22/0.30  %    Success case prop encoding time   : 0.000
% 0.22/0.30  %    Success case prop solver time     : 0.000
% 0.22/0.30  % Current number of processed clauses  : 27
% 0.22/0.30  %    Positive orientable unit clauses  : 18
% 0.22/0.30  %    Positive unorientable unit clauses: 0
% 0.22/0.30  %    Negative unit clauses             : 1
% 0.22/0.30  %    Non-unit-clauses                  : 8
% 0.22/0.30  % Current number of unprocessed clauses: 170
% 0.22/0.30  % ...number of literals in the above   : 629
% 0.22/0.30  % Current number of archived formulas  : 0
% 0.22/0.30  % Current number of archived clauses   : 3
% 0.22/0.30  % Clause-clause subsumption calls (NU) : 6
% 0.22/0.30  % Rec. Clause-clause subsumption calls : 6
% 0.22/0.30  % Non-unit clause-clause subsumptions  : 1
% 0.22/0.30  % Unit Clause-clause subsumption calls : 8
% 0.22/0.30  % Rewrite failures with RHS unbound    : 0
% 0.22/0.30  % BW rewrite match attempts            : 5
% 0.22/0.30  % BW rewrite match successes           : 3
% 0.22/0.30  % Condensation attempts                : 0
% 0.22/0.30  % Condensation successes               : 0
% 0.22/0.30  % Termbank termtop insertions          : 22945
% 0.22/0.30  % Search garbage collected termcells   : 8810
% 0.22/0.30  
% 0.22/0.30  % -------------------------------------------------
% 0.22/0.30  % User time                : 0.015 s
% 0.22/0.30  % System time              : 0.010 s
% 0.22/0.30  % Total time               : 0.024 s
% 0.22/0.30  % Maximum resident set size: 6400 pages
% 0.22/0.30  
% 0.22/0.30  % -------------------------------------------------
% 0.22/0.30  % User time                : 0.021 s
% 0.22/0.30  % System time              : 0.014 s
% 0.22/0.30  % Total time               : 0.035 s
% 0.22/0.30  % Maximum resident set size: 5120 pages
% 0.22/0.30  % E exiting
%------------------------------------------------------------------------------