E---3.5.1.THM-CRf.s

%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : SEU582^1 : 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 : n013.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 08:24:36 AM UTC 2026

% Result   : Theorem 0.22s 0.32s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU582^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05  % Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17  % Computer : n013.cluster.edu
% 0.10/0.17  % Model    : x86_64 x86_64
% 0.10/0.17  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17  % Memory   : 8046.5625MB
% 0.10/0.17  % OS       : Linux 6.8.0-71-generic
% 0.10/0.17  % CPULimit : 300
% 0.10/0.17  % WCLimit  : 300
% 0.10/0.17  % DateTime : Tue Sep 29 13:51:36 UTC 2026
% 0.10/0.17  % CPUTime  : 
% 0.10/0.17  Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22  Running higher-order theorem proving
% 0.10/0.23  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.mTpIoqINTO/E---3.1_2150659.p
% 0.22/0.32  % Version: 3.5.1-ho
% 0.22/0.32  % Preprocessing class: HSMMSLSSLLLCHFA.
% 0.22/0.32  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.32  % Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.22/0.32  % Starting ehoh_best3_rw with 300s (1) cores
% 0.22/0.32  % Starting almost_fo_3 with 300s (1) cores
% 0.22/0.32  % Starting new_ho_13 with 300s (1) cores
% 0.22/0.32  % ehoh_best3_rw with pid 2150673 completed with status 0
% 0.22/0.32  % Result found by ehoh_best3_rw
% 0.22/0.32  % Preprocessing class: HSMMSLSSLLLCHFA.
% 0.22/0.32  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.32  % Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.22/0.32  % Starting ehoh_best3_rw with 300s (1) cores
% 0.22/0.32  % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf120_gu_RUU_F100_L01000)
% 0.22/0.32  % SinE strategy is gf120_gu_RUU_F100_L01000
% 0.22/0.32  % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.22/0.32  % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.32  % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.32  % SubtermCWHack with pid 2150677 completed with status 0
% 0.22/0.32  % Result found by SubtermCWHack
% 0.22/0.32  % Preprocessing class: HSMMSLSSLLLCHFA.
% 0.22/0.32  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.32  % Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.22/0.32  % Starting ehoh_best3_rw with 300s (1) cores
% 0.22/0.32  % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf120_gu_RUU_F100_L01000)
% 0.22/0.32  % SinE strategy is gf120_gu_RUU_F100_L01000
% 0.22/0.32  % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.22/0.32  % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.32  % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.32  % Preprocessing time       : 0.004 s
% 0.22/0.32  
% 0.22/0.32  % Proof found!
% 0.22/0.32  % SZS status Theorem
% 0.22/0.32  % SZS output start CNFRefutation
% 0.22/0.32  thf(decl_23, type, in: $i > $i > $o).
% 0.22/0.32  thf(decl_24, type, exu: ($i > $o) > $o).
% 0.22/0.32  thf(decl_25, type, setextAx: $o).
% 0.22/0.32  thf(decl_26, type, emptyset: $i).
% 0.22/0.32  thf(decl_27, type, emptysetAx: $o).
% 0.22/0.32  thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.22/0.32  thf(decl_29, type, setadjoinAx: $o).
% 0.22/0.32  thf(decl_30, type, powerset: $i > $i).
% 0.22/0.32  thf(decl_31, type, powersetAx: $o).
% 0.22/0.32  thf(decl_32, type, setunion: $i > $i).
% 0.22/0.32  thf(decl_33, type, setunionAx: $o).
% 0.22/0.32  thf(decl_34, type, omega: $i).
% 0.22/0.32  thf(decl_35, type, omega0Ax: $o).
% 0.22/0.32  thf(decl_36, type, omegaSAx: $o).
% 0.22/0.32  thf(decl_37, type, omegaIndAx: $o).
% 0.22/0.32  thf(decl_38, type, replAx: $o).
% 0.22/0.32  thf(decl_39, type, foundationAx: $o).
% 0.22/0.32  thf(decl_40, type, wellorderingAx: $o).
% 0.22/0.32  thf(decl_41, type, descr: ($i > $o) > $i).
% 0.22/0.32  thf(decl_42, type, descrp: $o).
% 0.22/0.32  thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.22/0.32  thf(decl_44, type, dsetconstrI: $o).
% 0.22/0.32  thf(decl_45, type, dsetconstrEL: $o).
% 0.22/0.32  thf(decl_46, type, dsetconstrER: $o).
% 0.22/0.32  thf(decl_47, type, exuE1: $o).
% 0.22/0.32  thf(decl_48, type, prop2set: $o > $i).
% 0.22/0.32  thf(decl_49, type, prop2setE: $o).
% 0.22/0.32  thf(decl_50, type, emptysetE: $o).
% 0.22/0.32  thf(decl_51, type, emptysetimpfalse: $o).
% 0.22/0.32  thf(decl_52, type, notinemptyset: $o).
% 0.22/0.32  thf(decl_53, type, exuE3e: $o).
% 0.22/0.32  thf(decl_54, type, setext: $o).
% 0.22/0.32  thf(decl_55, type, emptyI: $o).
% 0.22/0.32  thf(decl_56, type, noeltsimpempty: $o).
% 0.22/0.32  thf(decl_57, type, setbeta: $o).
% 0.22/0.32  thf(decl_58, type, nonempty: $i > $o).
% 0.22/0.32  thf(decl_59, type, nonemptyE1: $o).
% 0.22/0.32  thf(decl_60, type, nonemptyI: $o).
% 0.22/0.32  thf(decl_61, type, nonemptyI1: $o).
% 0.22/0.32  thf(decl_62, type, setadjoinIL: $o).
% 0.22/0.32  thf(decl_63, type, emptyinunitempty: $o).
% 0.22/0.32  thf(decl_64, type, setadjoinIR: $o).
% 0.22/0.32  thf(decl_65, type, setadjoinE: $o).
% 0.22/0.32  thf(decl_66, type, setadjoinOr: $o).
% 0.22/0.32  thf(decl_67, type, setoftrueEq: $o).
% 0.22/0.32  thf(decl_68, type, powersetI: $o).
% 0.22/0.32  thf(decl_69, type, emptyinPowerset: $o).
% 0.22/0.32  thf(decl_70, type, emptyInPowerset: $o).
% 0.22/0.32  thf(decl_71, type, powersetE: $o).
% 0.22/0.32  thf(decl_72, type, setunionI: $o).
% 0.22/0.32  thf(decl_73, type, setunionE: $o).
% 0.22/0.32  thf(decl_74, type, subPowSU: $o).
% 0.22/0.32  thf(decl_75, type, exuE2: $o).
% 0.22/0.32  thf(decl_76, type, nonemptyImpWitness: $o).
% 0.22/0.32  thf(decl_77, type, uniqinunit: $o).
% 0.22/0.32  thf(decl_78, type, notinsingleton: $o).
% 0.22/0.32  thf(decl_79, type, eqinunit: $o).
% 0.22/0.32  thf(decl_80, type, singletonsswitch: $o).
% 0.22/0.32  thf(decl_81, type, upairsetE: $o).
% 0.22/0.32  thf(decl_82, type, upairsetIL: $o).
% 0.22/0.32  thf(decl_83, type, upairsetIR: $o).
% 0.22/0.32  thf(decl_84, type, emptyE1: $o).
% 0.22/0.32  thf(decl_85, type, vacuousDall: $o).
% 0.22/0.32  thf(decl_86, type, quantDeMorgan1: $o).
% 0.22/0.32  thf(decl_87, type, quantDeMorgan2: $o).
% 0.22/0.32  thf(decl_88, type, quantDeMorgan3: $o).
% 0.22/0.32  thf(decl_89, type, quantDeMorgan4: $o).
% 0.22/0.32  thf(decl_90, type, prop2setI: $o).
% 0.22/0.32  thf(decl_92, type, prop2set2propI: $o).
% 0.22/0.32  thf(decl_93, type, notdexE: $o).
% 0.22/0.32  thf(decl_94, type, notdallE: $o).
% 0.22/0.32  thf(decl_95, type, exuI1: $o).
% 0.22/0.32  thf(decl_96, type, exuI3: $o).
% 0.22/0.32  thf(decl_97, type, exuI2: $o).
% 0.22/0.32  thf(decl_98, type, inCongP: $o).
% 0.22/0.32  thf(decl_99, type, in__Cong: $o).
% 0.22/0.32  thf(decl_100, type, exuE3u: $o).
% 0.22/0.32  thf(decl_101, type, exu__Cong: $o).
% 0.22/0.32  thf(decl_102, type, emptyset__Cong: $o).
% 0.22/0.32  thf(decl_103, type, setadjoin__Cong: $o).
% 0.22/0.32  thf(decl_104, type, powerset__Cong: $o).
% 0.22/0.32  thf(decl_105, type, setunion__Cong: $o).
% 0.22/0.32  thf(decl_106, type, omega__Cong: $o).
% 0.22/0.32  thf(decl_107, type, exuEu: $o).
% 0.22/0.32  thf(decl_108, type, descr__Cong: $o).
% 0.22/0.32  thf(decl_109, type, dsetconstr__Cong: $o).
% 0.22/0.32  thf(decl_110, type, subset: $i > $i > $o).
% 0.22/0.32  thf(decl_113, type, subsetI1: $o).
% 0.22/0.32  thf(decl_114, type, eqimpsubset2: $o).
% 0.22/0.32  thf(decl_115, type, eqimpsubset1: $o).
% 0.22/0.32  thf(decl_116, type, subsetI2: $o).
% 0.22/0.32  thf(decl_117, type, emptysetsubset: $o).
% 0.22/0.32  thf(decl_118, type, subsetE: $o).
% 0.22/0.32  thf(decl_119, type, subsetE2: $o).
% 0.22/0.32  thf(decl_120, type, notsubsetI: $o).
% 0.22/0.32  thf(decl_121, type, notequalI1: $o).
% 0.22/0.32  thf(decl_122, type, notequalI2: $o).
% 0.22/0.32  thf(decl_123, type, subsetRefl: $o).
% 0.22/0.32  thf(decl_124, type, subsetTrans: $o).
% 0.22/0.32  thf(decl_125, type, setadjoinSub: $o).
% 0.22/0.32  thf(decl_126, type, setadjoinSub2: $o).
% 0.22/0.32  thf(decl_127, type, subset2powerset: $o).
% 0.22/0.32  thf(decl_128, type, setextsub: $o).
% 0.22/0.32  thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.22/0.32  thf(decl_130, type, powersetI1: $o).
% 0.22/0.32  thf(decl_131, type, powersetE1: $o).
% 0.22/0.32  thf(decl_132, type, inPowerset: $o).
% 0.22/0.32  thf(decl_133, type, powersetsubset: $o).
% 0.22/0.32  thf(decl_134, type, sepInPowerset: $o).
% 0.22/0.32  thf(decl_135, type, sepSubset: $o).
% 0.22/0.32  thf(decl_136, type, binunion: $i > $i > $i).
% 0.22/0.32  thf(decl_137, type, epred1_0: $o).
% 0.22/0.32  thf(decl_138, type, esk1_2: $i > $i > $i).
% 0.22/0.32  thf(decl_139, type, esk2_2: $i > $i > $i).
% 0.22/0.32  thf(decl_140, type, esk3_2: $i > $i > $i).
% 0.22/0.32  thf(decl_141, type, esk4_1: $i > $i).
% 0.22/0.32  thf(decl_142, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.22/0.32  thf(decl_143, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.32  thf(decl_144, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.22/0.32  thf(decl_145, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.32  thf(decl_146, type, esk9_1: $i > $i).
% 0.22/0.32  thf(decl_147, type, esk10_2: ($i > $o) > $i > $i).
% 0.22/0.32  thf(decl_148, type, esk11_2: ($i > $o) > $i > $i).
% 0.22/0.32  thf(decl_149, type, esk12_1: ($i > $o) > $i).
% 0.22/0.32  thf(decl_150, type, esk13_2: ($i > $o) > $i > $i).
% 0.22/0.32  thf(decl_151, type, esk14_1: ($i > $o) > $i).
% 0.22/0.32  thf(decl_152, type, esk15_2: $i > $i > $i).
% 0.22/0.32  thf(decl_153, type, esk16_2: $i > $i > $i).
% 0.22/0.32  thf(decl_154, type, esk17_1: $i > $i).
% 0.22/0.32  thf(decl_155, type, esk18_1: $i > $i).
% 0.22/0.32  thf(decl_156, type, esk19_1: $i > $i).
% 0.22/0.32  thf(decl_157, type, esk20_2: $i > $i > $i).
% 0.22/0.32  thf(decl_158, type, esk21_3: $i > $i > $o > $i).
% 0.22/0.32  thf(decl_159, type, esk22_2: ($i > $o) > $i > $i).
% 0.22/0.32  thf(decl_160, type, esk23_1: ($i > $o) > $i).
% 0.22/0.32  thf(decl_161, type, esk24_1: $i > $i).
% 0.22/0.32  thf(decl_162, type, esk25_2: $i > ($i > $o) > $i).
% 0.22/0.32  thf(decl_163, type, esk26_2: $i > ($i > $o) > $i).
% 0.22/0.32  thf(decl_164, type, esk27_2: $i > ($i > $o) > $i).
% 0.22/0.32  thf(decl_165, type, esk28_2: $i > ($i > $o) > $i).
% 0.22/0.32  thf(decl_166, type, esk29_2: $i > ($i > $o) > $i).
% 0.22/0.32  thf(decl_167, type, esk30_2: $i > ($i > $o) > $i).
% 0.22/0.32  thf(decl_168, type, esk31_2: ($i > $o) > $i > $i).
% 0.22/0.32  thf(decl_169, type, esk32_1: ($i > $o) > $i).
% 0.22/0.32  thf(decl_170, type, esk33_1: ($i > $o) > $i).
% 0.22/0.32  thf(decl_171, type, esk34_1: ($i > $o) > $i).
% 0.22/0.32  thf(decl_172, type, esk35_1: ($i > $o) > $i).
% 0.22/0.32  thf(decl_173, type, esk36_2: ($i > $o) > $i > $i).
% 0.22/0.32  thf(decl_174, type, esk37_1: ($i > $o) > $i).
% 0.22/0.32  thf(decl_175, type, esk38_2: ($i > $o) > $i > $i).
% 0.22/0.32  thf(decl_176, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.32  thf(decl_177, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.32  thf(decl_178, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.32  thf(decl_179, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.32  thf(decl_180, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.32  thf(decl_181, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.32  thf(decl_182, type, esk45_2: ($i > $o) > $i > $i).
% 0.22/0.32  thf(decl_183, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.32  thf(decl_184, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.32  thf(decl_185, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.32  thf(decl_186, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.32  thf(decl_187, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.22/0.32  thf(decl_188, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.22/0.32  thf(decl_189, type, esk52_2: $i > $i > $i).
% 0.22/0.32  thf(decl_190, type, esk53_2: $i > $i > $i).
% 0.22/0.32  thf(decl_191, type, esk54_0: $i).
% 0.22/0.32  thf(decl_192, type, esk55_0: $i).
% 0.22/0.32  thf(decl_193, type, esk56_0: $i).
% 0.22/0.32  thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', nonempty)).
% 0.22/0.32  thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', nonemptyI)).
% 0.22/0.32  thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', exuE3e)).
% 0.22/0.32  thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', exu)).
% 0.22/0.32  thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', exuE2)).
% 0.22/0.32  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.mTpIoqINTO/E---3.1_2150659.p', exuI2)).
% 0.22/0.32  thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', exuI3)).
% 0.22/0.32  thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', exuI1)).
% 0.22/0.32  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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', exu__Cong)).
% 0.22/0.32  thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', exuE3u)).
% 0.22/0.32  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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', descr__Cong)).
% 0.22/0.32  thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', exuEu)).
% 0.22/0.32  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.mTpIoqINTO/E---3.1_2150659.p', exuE1)).
% 0.22/0.32  thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', descrp)).
% 0.22/0.32  thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', replAx)).
% 0.22/0.32  thf(binunionIL, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', binunionIL)).
% 0.22/0.32  thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', sepInPowerset)).
% 0.22/0.32  thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', sepSubset)).
% 0.22/0.32  thf(binunion, axiom, ((binunion)=(^[X2:$i, X3:$i]:(setunion @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', binunion)).
% 0.22/0.32  thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', nonemptyI1)).
% 0.22/0.32  thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', nonemptyE1)).
% 0.22/0.32  thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', setbeta)).
% 0.22/0.32  thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', setoftrueEq)).
% 0.22/0.32  thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', nonemptyImpWitness)).
% 0.22/0.32  thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.mTpIoqINTO/E---3.1_2150659.p', emptyE1)).
% 0.22/0.32  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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', dsetconstr__Cong)).
% 0.22/0.32  thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', dsetconstrER)).
% 0.22/0.32  thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', dsetconstrEL)).
% 0.22/0.32  thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', dsetconstrI)).
% 0.22/0.32  thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', setadjoinIL)).
% 0.22/0.32  thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', notequalI2)).
% 0.22/0.32  thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', subsetE)).
% 0.22/0.32  thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', subsetE2)).
% 0.22/0.32  thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', notsubsetI)).
% 0.22/0.32  thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', subsetRefl)).
% 0.22/0.32  thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', subsetTrans)).
% 0.22/0.32  thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', setext)).
% 0.22/0.32  thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', setadjoinSub)).
% 0.22/0.32  thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', emptyI)).
% 0.22/0.32  thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', setadjoinSub2)).
% 0.22/0.32  thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', subset2powerset)).
% 0.22/0.32  thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', setextsub)).
% 0.22/0.32  thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', subsetemptysetimpeq)).
% 0.22/0.32  thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', powersetI1)).
% 0.22/0.32  thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', powersetE1)).
% 0.22/0.32  thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', inPowerset)).
% 0.22/0.32  thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', powersetsubset)).
% 0.22/0.32  thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', emptyinunitempty)).
% 0.22/0.32  thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', eqinunit)).
% 0.22/0.32  thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', notinsingleton)).
% 0.22/0.32  thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', noeltsimpempty)).
% 0.22/0.32  thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', setadjoinIR)).
% 0.22/0.32  thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', powersetE)).
% 0.22/0.32  thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', emptyInPowerset)).
% 0.22/0.32  thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', emptyinPowerset)).
% 0.22/0.32  thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', powersetI)).
% 0.22/0.32  thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', setadjoinOr)).
% 0.22/0.32  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.mTpIoqINTO/E---3.1_2150659.p', setadjoinE)).
% 0.22/0.32  thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', setunionI)).
% 0.22/0.32  thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', uniqinunit)).
% 0.22/0.32  thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', subPowSU)).
% 0.22/0.32  thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', setunionE)).
% 0.22/0.32  thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', singletonsswitch)).
% 0.22/0.32  thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', quantDeMorgan2)).
% 0.22/0.32  thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', quantDeMorgan1)).
% 0.22/0.32  thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', vacuousDall)).
% 0.22/0.32  thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', upairsetIR)).
% 0.22/0.32  thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', upairsetIL)).
% 0.22/0.32  thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', upairsetE)).
% 0.22/0.32  thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', quantDeMorgan3)).
% 0.22/0.32  thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', notdallE)).
% 0.22/0.32  thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', notdexE)).
% 0.22/0.32  thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', prop2setI)).
% 0.22/0.32  thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', quantDeMorgan4)).
% 0.22/0.32  thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', inCongP)).
% 0.22/0.32  thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', setunion__Cong)).
% 0.22/0.32  thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', powerset__Cong)).
% 0.22/0.32  thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', setadjoin__Cong)).
% 0.22/0.32  thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', emptyset__Cong)).
% 0.22/0.32  thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', in__Cong)).
% 0.22/0.32  thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', omega__Cong)).
% 0.22/0.32  thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', subsetI2)).
% 0.22/0.32  thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', eqimpsubset1)).
% 0.22/0.32  thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', eqimpsubset2)).
% 0.22/0.32  thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', subsetI1)).
% 0.22/0.32  thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', notequalI1)).
% 0.22/0.32  thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', emptysetsubset)).
% 0.22/0.32  thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', notinemptyset)).
% 0.22/0.32  thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', emptysetimpfalse)).
% 0.22/0.32  thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', emptysetE)).
% 0.22/0.32  thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', prop2setE)).
% 0.22/0.32  thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.mTpIoqINTO/E---3.1_2150659.p', wellorderingAx)).
% 0.22/0.32  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.mTpIoqINTO/E---3.1_2150659.p', foundationAx)).
% 0.22/0.32  thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', omegaIndAx)).
% 0.22/0.32  thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', omegaSAx)).
% 0.22/0.32  thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', omega0Ax)).
% 0.22/0.32  thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', setunionAx)).
% 0.22/0.32  thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', powersetAx)).
% 0.22/0.32  thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', setadjoinAx)).
% 0.22/0.32  thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', emptysetAx)).
% 0.22/0.32  thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.mTpIoqINTO/E---3.1_2150659.p', setextAx)).
% 0.22/0.32  thf(c_0_101, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.22/0.32  thf(c_0_102, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.22/0.32  thf(c_0_103, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.22/0.32  thf(c_0_104, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.22/0.32  thf(c_0_105, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.22/0.32  thf(c_0_106, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.22/0.32  thf(c_0_107, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.22/0.32  thf(c_0_108, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.22/0.32  thf(c_0_109, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.22/0.32  thf(c_0_110, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.22/0.32  thf(c_0_111, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.22/0.32  thf(c_0_112, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.22/0.32  thf(c_0_113, 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])).
% 0.22/0.32  thf(c_0_114, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.22/0.32  thf(c_0_115, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.22/0.32  thf(c_0_116, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[binunionIL])).
% 0.22/0.32  thf(c_0_117, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.22/0.32  thf(c_0_118, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.22/0.32  thf(c_0_119, plain, ((binunion)=(^[Z0:$i, Z1:$i]:(setunion @ (setadjoin @ Z0 @ (setadjoin @ Z1 @ emptyset))))), inference(fof_simplification,[status(thm)],[binunion])).
% 0.22/0.32  thf(c_0_120, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_101])).
% 0.22/0.32  thf(c_0_121, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_102, c_0_101])).
% 0.22/0.32  thf(c_0_122, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_101])).
% 0.22/0.32  thf(c_0_123, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.22/0.32  thf(c_0_124, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X289:$i]:(((((X1 @ X289)))&(![X290:$i]:(((((X1 @ X290)))=>(((X289)=(X290))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_103, c_0_104])).
% 0.22/0.32  thf(c_0_125, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.22/0.32  thf(c_0_126, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_101])).
% 0.22/0.32  thf(c_0_127, plain, ((exuE2)=(![X1:$i > $o]:((((?[X291:$i]:(((((X1 @ X291)))&(![X292:$i]:(((((X1 @ X292)))=>(((X291)=(X292))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_105, c_0_104])).
% 0.22/0.32  thf(c_0_128, plain, ((emptyE1)<=>![X4:$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])).
% 0.22/0.32  thf(c_0_129, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X297:$i]:(((((X1 @ X297)))&(![X298:$i]:(((((X1 @ X298)))=>(((X297)=(X298)))))))))))))), inference(apply_def,[status(thm)],[c_0_106, c_0_104])).
% 0.22/0.32  thf(c_0_130, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X295:$i]:(((((X1 @ X295)))&(![X296:$i]:(((((X1 @ X296)))=>(((X295)=(X296)))))))))))))))), inference(apply_def,[status(thm)],[c_0_107, c_0_104])).
% 0.22/0.32  thf(c_0_131, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X293:$i]:(((((X1 @ X293)))&(![X294:$i]:(((((X1 @ X294)))=>(((X293)=(X294)))))))))))))), inference(apply_def,[status(thm)],[c_0_108, c_0_104])).
% 0.22/0.32  thf(c_0_132, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X301:$i]:(((((X1 @ X301)))&(![X302:$i]:(((((X1 @ X302)))=>(((X301)=(X302))))))))))<=>((?[X303:$i]:(((((X17 @ X303)))&(![X304:$i]:(((((X17 @ X304)))=>(((X303)=(X304)))))))))))))))), inference(apply_def,[status(thm)],[c_0_109, c_0_104])).
% 0.22/0.32  thf(c_0_133, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X299:$i]:(((((X1 @ X299)))&(![X300:$i]:(((((X1 @ X300)))=>(((X299)=(X300))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_110, c_0_104])).
% 0.22/0.32  thf(c_0_134, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.22/0.32  thf(c_0_135, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X307:$i]:(((((X1 @ X307)))&(![X308:$i]:(((((X1 @ X308)))=>(((X307)=(X308))))))))))=>((((?[X309:$i]:(((((X17 @ X309)))&(![X310:$i]:(((((X17 @ X310)))=>(((X309)=(X310))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_111, c_0_104])).
% 0.22/0.32  thf(c_0_136, plain, ((exuEu)=(![X1:$i > $o]:((((?[X305:$i]:(((((X1 @ X305)))&(![X306:$i]:(((((X1 @ X306)))=>(((X305)=(X306))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_112, c_0_104])).
% 0.22/0.32  thf(c_0_137, plain, ((exuE1)=(![X1:$i > $o]:((((?[X287:$i]:(((((X1 @ X287)))&(![X288:$i]:(((((X1 @ X288)))=>(((X287)=(X288))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_113, c_0_104])).
% 0.22/0.32  thf(c_0_138, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.22/0.32  thf(c_0_139, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.22/0.32  thf(c_0_140, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.22/0.32  thf(c_0_141, plain, ((descrp)=(![X1:$i > $o]:((((?[X285:$i]:(((((X1 @ X285)))&(![X286:$i]:(((((X1 @ X286)))=>(((X285)=(X286))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_114, c_0_104])).
% 0.22/0.32  thf(c_0_142, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X283:$i]:(((((X6 @ X2 @ X283)))&(![X284:$i]:(((((X6 @ X2 @ X284)))=>(((X283)=(X284)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_115, c_0_104])).
% 0.22/0.32  thf(c_0_143, plain, ((epred1_0)<=>![X340:$i]:(?[X341:$i]:((((![X342:$i]:(((in @ X342 @ X341)=>![X343:$i]:(((in @ X343 @ X342)=>(in @ X343 @ X340)))))&![X344:$i, X345:$i]:((((in @ X344 @ X340)&(in @ X345 @ X340))=>(![X346:$i]:(((in @ X346 @ X341)=>((in @ X344 @ X346)<=>(in @ X345 @ X346))))=>((X344)=(X345))))))&![X347:$i, X348:$i]:((((in @ X347 @ X341)&(in @ X348 @ X341))=>(![X349:$i]:(((in @ X349 @ X347)=>(in @ X349 @ X348)))|![X350:$i]:(((in @ X350 @ X348)=>(in @ X350 @ X347)))))))&![X351:$i]:(((![X352:$i]:(((in @ X352 @ X351)=>(in @ X352 @ X340)))&?[X353:$i]:((in @ X353 @ X351)))=>?[X354:$i, X355:$i]:(((((in @ X354 @ X341)&(in @ X355 @ X351))&~(?[X356:$i]:(((in @ X356 @ X354)&(in @ X356 @ X351)))))&![X357:$i]:(((in @ X357 @ X341)=>(![X358:$i]:(((in @ X358 @ X357)=>(in @ X358 @ X354)))|(in @ X355 @ X357)))))))))))), introduced(definition)).
% 0.22/0.32  thf(c_0_144, negated_conjecture, ~((![X311:$i, X312:$i]:((![X313:$i]:(((in @ X313 @ X311)<=>(in @ X313 @ X312)))=>((X311)=(X312))))=>(![X314:$i]:(~(in @ X314 @ emptyset))=>(![X315:$i, X316:$i, X317:$i]:(((in @ X317 @ (setadjoin @ X315 @ X316))<=>(((X317)=(X315))|(in @ X317 @ X316))))=>(![X318:$i, X319:$i]:(((in @ X319 @ (powerset @ X318))<=>![X320:$i]:(((in @ X320 @ X319)=>(in @ X320 @ X318)))))=>(![X321:$i, X322:$i]:(((in @ X322 @ (setunion @ X321))<=>?[X323:$i]:(((in @ X322 @ X323)&(in @ X323 @ X321)))))=>((in @ emptyset @ omega)=>(![X324:$i]:(((in @ X324 @ omega)=>(in @ (setadjoin @ X324 @ X324) @ omega)))=>(![X325:$i]:((((in @ emptyset @ X325)&![X326:$i]:((((in @ X326 @ omega)&(in @ X326 @ X325))=>(in @ (setadjoin @ X326 @ X326) @ X325))))=>![X327:$i]:(((in @ X327 @ omega)=>(in @ X327 @ X325)))))=>(![X328:$i > $i > $o, X329:$i]:((![X330:$i]:(((in @ X330 @ X329)=>?[X331:$i]:(((X328 @ X330 @ X331)&![X332:$i]:(((X328 @ X330 @ X332)=>((X331)=(X332))))))))=>?[X333:$i]:(![X334:$i]:(((in @ X334 @ X333)<=>?[X335:$i]:(((in @ X335 @ X329)&(X328 @ X335 @ X334))))))))=>(![X336:$i]:((?[X337:$i]:((in @ X337 @ X336))=>?[X338:$i]:(((in @ X338 @ X336)&~(?[X339:$i]:(((in @ X339 @ X338)&(in @ X339 @ X336))))))))=>((epred1_0)=>(![X359:$i > $o]:((?[X360:$i]:(((X359 @ X360)&![X361:$i]:(((X359 @ X361)=>((X360)=(X361))))))=>(X359 @ (descr @ (^[Z0:$i]:(X359 @ Z0))))))=>(![X362:$i, X363:$i > $o, X364:$i]:(((in @ X364 @ X362)=>((X363 @ X364)=>(in @ X364 @ (dsetconstr @ X362 @ X363)))))=>(![X365:$i, X366:$i > $o, X367:$i]:(((in @ X367 @ (dsetconstr @ X365 @ X366))=>(in @ X367 @ X365)))=>(![X368:$i, X369:$i > $o, X370:$i]:(((in @ X370 @ (dsetconstr @ X368 @ X369))=>(X369 @ X370)))=>(![X371:$i > $o]:((?[X372:$i]:(((X371 @ X372)&![X373:$i]:(((X371 @ X373)=>((X372)=(X373))))))=>?[X374:$i]:(((X371 @ X374)&![X375:$i]:(((X371 @ X375)=>((X374)=(X375))))))))=>(![X376:$o, X377:$i]:(((in @ X377 @ (prop2set @ ((X376))))=>(X376)))=>(![X378:$i]:(((in @ X378 @ emptyset)=>![X379:$o]:((X379))))=>(![X380:$i]:(((in @ X380 @ emptyset)=>~($true)))=>(![X381:$i]:(~(in @ X381 @ emptyset))=>(![X382:$i > $o]:((?[X383:$i]:(((X382 @ X383)&![X384:$i]:(((X382 @ X384)=>((X383)=(X384))))))=>?[X385:$i]:((X382 @ X385))))=>(![X386:$i, X387:$i]:((![X388:$i]:(((in @ X388 @ X386)=>(in @ X388 @ X387)))=>(![X389:$i]:(((in @ X389 @ X387)=>(in @ X389 @ X386)))=>((X386)=(X387)))))=>(![X390:$i]:((![X391:$i]:(~(in @ X391 @ X390))=>((X390)=(emptyset))))=>(![X392:$i]:((![X393:$i]:(~(in @ X393 @ X392))=>((X392)=(emptyset))))=>(![X394:$i, X395:$i > $o, X396:$i]:(((in @ X396 @ X394)=>((in @ X396 @ (dsetconstr @ X394 @ X395))<=>(X395 @ X396))))=>(![X397:$i]:((((X397)!=(emptyset))=>?[X398:$i]:((in @ X398 @ X397))))=>(![X399:$i, X400:$i > $o, X401:$i]:(((in @ X401 @ X399)=>((X400 @ X401)=>((dsetconstr @ X399 @ X400)!=(emptyset)))))=>(![X402:$i]:((?[X403:$i]:((in @ X403 @ X402))=>((X402)!=(emptyset))))=>(![X404:$i, X405:$i]:((in @ X404 @ (setadjoin @ X404 @ X405)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X406:$i, X407:$i, X408:$i]:(((in @ X408 @ X407)=>(in @ X408 @ (setadjoin @ X406 @ X407))))=>(![X409:$i, X410:$i, X411:$i]:(((in @ X411 @ (setadjoin @ X409 @ X410))=>![X412:$o]:(((((X411)=(X409))=>(X412))=>(((in @ X411 @ X410)=>(X412))=>(X412))))))=>(![X413:$i, X414:$i, X415:$i]:(((in @ X415 @ (setadjoin @ X413 @ X414))=>(((X415)=(X413))|(in @ X415 @ X414))))=>(![X416:$i]:(((dsetconstr @ X416 @ (^[Z0:$i]:($true)))=(X416)))=>(![X417:$i, X418:$i]:((![X419:$i]:(((in @ X419 @ X418)=>(in @ X419 @ X417)))=>(in @ X418 @ (powerset @ X417))))=>(![X420:$i]:((in @ emptyset @ (powerset @ X420)))=>(![X421:$i]:((in @ emptyset @ (powerset @ X421)))=>(![X422:$i, X423:$i, X424:$i]:(((in @ X423 @ (powerset @ X422))=>((in @ X424 @ X423)=>(in @ X424 @ X422))))=>(![X425:$i, X426:$i, X427:$i]:(((in @ X426 @ X427)=>((in @ X427 @ X425)=>(in @ X426 @ (setunion @ X425)))))=>(![X428:$i, X429:$i]:(((in @ X429 @ (setunion @ X428))=>![X430:$o]:((![X431:$i]:(((in @ X429 @ X431)=>((in @ X431 @ X428)=>(X430))))=>(X430)))))=>(![X432:$i, X433:$i]:(((in @ X433 @ X432)=>(in @ X433 @ (powerset @ (setunion @ X432)))))=>(![X434:$i > $o]:((?[X435:$i]:(((X434 @ X435)&![X436:$i]:(((X434 @ X436)=>((X435)=(X436))))))=>?[X437:$i]:(![X438:$i]:(((X434 @ X438)<=>((X438)=(X437)))))))=>(![X439:$i]:((((X439)!=(emptyset))=>?[X440:$i]:(((in @ X440 @ X439)&$true))))=>(![X441:$i, X442:$i]:(((in @ X441 @ (setadjoin @ X442 @ emptyset))=>((X441)=(X442))))=>(![X443:$i, X444:$i]:((((X443)!=(X444))=>~(in @ X444 @ (setadjoin @ X443 @ emptyset))))=>(![X445:$i, X446:$i]:((((X445)=(X446))=>(in @ X445 @ (setadjoin @ X446 @ emptyset))))=>(![X447:$i, X448:$i]:(((in @ X447 @ (setadjoin @ X448 @ emptyset))=>(in @ X448 @ (setadjoin @ X447 @ emptyset))))=>(![X449:$i, X450:$i, X451:$i]:(((in @ X451 @ (setadjoin @ X449 @ (setadjoin @ X450 @ emptyset)))=>(((X451)=(X449))|((X451)=(X450)))))=>(![X452:$i, X453:$i]:((in @ X452 @ (setadjoin @ X452 @ (setadjoin @ X453 @ emptyset))))=>(![X454:$i, X455:$i]:((in @ X455 @ (setadjoin @ X454 @ (setadjoin @ X455 @ emptyset))))=>(![X456:$i, X457:$i > $o]:((?[X458:$i]:(((in @ X458 @ X456)&(X457 @ X458)))=>(((dsetconstr @ X456 @ X457)=(emptyset))=>~($true))))=>(![X459:$i > $o, X460:$i]:(((in @ X460 @ emptyset)=>(X459 @ X460)))=>(![X461:$i, X462:$i > $o]:((~(![X463:$i]:(((in @ X463 @ X461)=>(X462 @ X463))))=>?[X464:$i]:(((in @ X464 @ X461)&~((X462 @ X464))))))=>(![X465:$i, X466:$i > $o]:((![X467:$i]:(((in @ X467 @ X465)=>~((X466 @ X467))))=>~(?[X468:$i]:(((in @ X468 @ X465)&(X466 @ X468))))))=>(![X469:$i, X470:$i > $o]:((~(?[X471:$i]:(((in @ X471 @ X469)&(X470 @ X471))))=>![X472:$i]:(((in @ X472 @ X469)=>~((X470 @ X472))))))=>(![X473:$i, X474:$i > $o]:((?[X475:$i]:(((in @ X475 @ X473)&~((X474 @ X475))))=>~(![X476:$i]:(((in @ X476 @ X473)=>(X474 @ X476))))))=>(![X477:$o]:(((X477)=>(in @ emptyset @ (prop2set @ ((X477))))))=>((prop2set2propI)=>(![X478:$i, X479:$i > $o]:((~(?[X480:$i]:(((in @ X480 @ X478)&(X479 @ X480))))=>![X481:$i]:(((in @ X481 @ X478)=>~((X479 @ X481))))))=>(![X482:$i, X483:$i > $o]:((~(![X484:$i]:(((in @ X484 @ X482)=>(X483 @ X484))))=>?[X485:$i]:(((in @ X485 @ X482)&~((X483 @ X485))))))=>(![X486:$i > $o]:((?[X487:$i]:(((X486 @ X487)&![X488:$i]:(((X486 @ X488)=>((X487)=(X488))))))=>?[X489:$i]:(((X486 @ X489)&![X490:$i]:(((X486 @ X490)=>((X489)=(X490))))))))=>(![X491:$i > $o]:((?[X492:$i]:((X491 @ X492))=>(![X493:$i, X494:$i]:(((X491 @ X493)=>((X491 @ X494)=>((X493)=(X494)))))=>?[X495:$i]:(((X491 @ X495)&![X496:$i]:(((X491 @ X496)=>((X495)=(X496)))))))))=>(![X497:$i > $o]:((?[X498:$i]:(![X499:$i]:(((X497 @ X499)<=>((X499)=(X498)))))=>?[X500:$i]:(((X497 @ X500)&![X501:$i]:(((X497 @ X501)=>((X500)=(X501))))))))=>(![X502:$i, X503:$i]:((((X502)=(X503))=>![X504:$i, X505:$i]:((((X504)=(X505))=>((in @ X504 @ X502)=>(in @ X505 @ X503))))))=>(![X506:$i, X507:$i]:((((X506)=(X507))=>![X508:$i, X509:$i]:((((X508)=(X509))=>((in @ X508 @ X506)<=>(in @ X509 @ X507))))))=>(![X510:$i > $o]:((?[X511:$i]:(((X510 @ X511)&![X512:$i]:(((X510 @ X512)=>((X511)=(X512))))))=>![X513:$i, X514:$i]:(((X510 @ X513)=>((X510 @ X514)=>((X513)=(X514)))))))=>(![X515:$i > $o, X516:$i > $o]:((![X517:$i, X518:$i]:((((X517)=(X518))=>((X515 @ X517)<=>(X516 @ X518))))=>(?[X519:$i]:(((X515 @ X519)&![X520:$i]:(((X515 @ X520)=>((X519)=(X520))))))<=>?[X521:$i]:(((X516 @ X521)&![X522:$i]:(((X516 @ X522)=>((X521)=(X522)))))))))=>(((emptyset)=(emptyset))=>(![X523:$i, X524:$i]:((((X523)=(X524))=>![X525:$i, X526:$i]:((((X525)=(X526))=>((setadjoin @ X523 @ X525)=(setadjoin @ X524 @ X526))))))=>(![X527:$i, X528:$i]:((((X527)=(X528))=>((powerset @ X527)=(powerset @ X528))))=>(![X529:$i, X530:$i]:((((X529)=(X530))=>((setunion @ X529)=(setunion @ X530))))=>(((omega)=(omega))=>(![X531:$i > $o]:((?[X532:$i]:(((X531 @ X532)&![X533:$i]:(((X531 @ X533)=>((X532)=(X533))))))=>![X534:$i, X535:$i]:(((X531 @ X534)=>((X531 @ X535)=>((X534)=(X535)))))))=>(![X536:$i > $o, X537:$i > $o]:((![X538:$i, X539:$i]:((((X538)=(X539))=>((X536 @ X538)<=>(X537 @ X539))))=>(?[X540:$i]:(((X536 @ X540)&![X541:$i]:(((X536 @ X541)=>((X540)=(X541))))))=>(?[X542:$i]:(((X537 @ X542)&![X543:$i]:(((X537 @ X543)=>((X542)=(X543))))))=>((descr @ X536)=(descr @ X537))))))=>(![X544:$i, X545:$i]:((((X544)=(X545))=>![X546:$i > $o, X547:$i > $o]:((![X548:$i]:(((in @ X548 @ X544)=>![X549:$i]:(((in @ X549 @ X545)=>(((X548)=(X549))=>((X546 @ X548)<=>(X547 @ X549)))))))=>((dsetconstr @ X544 @ X546)=(dsetconstr @ X545 @ X547))))))=>(![X550:$i, X551:$i]:((![X552:$i]:(((in @ X552 @ X550)=>(in @ X552 @ X551)))=>(subset @ X550 @ X551)))=>(![X553:$i, X554:$i]:((((X553)=(X554))=>(subset @ X554 @ X553)))=>(![X555:$i, X556:$i]:((((X555)=(X556))=>(subset @ X555 @ X556)))=>(![X557:$i, X558:$i]:((![X559:$i]:(((in @ X559 @ X557)=>(in @ X559 @ X558)))=>(subset @ X557 @ X558)))=>(![X560:$i]:((subset @ emptyset @ X560))=>(![X561:$i, X562:$i, X563:$i]:(((subset @ X561 @ X562)=>((in @ X563 @ X561)=>(in @ X563 @ X562))))=>(![X564:$i, X565:$i, X566:$i]:(((subset @ X564 @ X565)=>(~(in @ X566 @ X565)=>~(in @ X566 @ X564))))=>(![X567:$i, X568:$i, X569:$i]:(((in @ X569 @ X567)=>(~(in @ X569 @ X568)=>~(subset @ X567 @ X568))))=>(![X570:$i, X571:$i]:((~(subset @ X570 @ X571)=>((X570)!=(X571))))=>(![X572:$i, X573:$i, X574:$i]:(((in @ X574 @ X572)=>(~(in @ X574 @ X573)=>((X572)!=(X573)))))=>(![X575:$i]:((subset @ X575 @ X575))=>(![X576:$i, X577:$i, X578:$i]:(((subset @ X576 @ X577)=>((subset @ X577 @ X578)=>(subset @ X576 @ X578))))=>(![X579:$i, X580:$i]:((subset @ X580 @ (setadjoin @ X579 @ X580)))=>(![X581:$i, X582:$i, X583:$i]:(((subset @ X581 @ X583)=>(subset @ X581 @ (setadjoin @ X582 @ X583))))=>(![X584:$i, X585:$i]:(((subset @ X584 @ X585)=>(in @ X584 @ (powerset @ X585))))=>(![X586:$i, X587:$i]:(((subset @ X586 @ X587)=>((subset @ X587 @ X586)=>((X586)=(X587)))))=>(![X588:$i]:(((subset @ X588 @ emptyset)=>((X588)=(emptyset))))=>(![X589:$i, X590:$i]:(((subset @ X590 @ X589)=>(in @ X590 @ (powerset @ X589))))=>(![X591:$i, X592:$i]:(((in @ X592 @ (powerset @ X591))=>(subset @ X592 @ X591)))=>(![X593:$i]:((in @ X593 @ (powerset @ X593)))=>(![X594:$i, X595:$i]:(((subset @ X594 @ X595)=>(subset @ (powerset @ X594) @ (powerset @ X595))))=>(![X596:$i, X597:$i > $o]:((in @ (dsetconstr @ X596 @ X597) @ (powerset @ X596)))=>(![X598:$i, X599:$i > $o]:((subset @ (dsetconstr @ X598 @ X599) @ X598))=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (setunion @ (setadjoin @ X4 @ (setadjoin @ X5 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_116, setadjoinIL]), notequalI2]), subsetE]), subsetE2]), notsubsetI]), subsetRefl]), subsetTrans]), setext]), setadjoinSub]), emptyI]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_117]), c_0_118]), c_0_119]), emptyinunitempty]), eqinunit]), notinsingleton]), c_0_120]), c_0_121]), c_0_122]), c_0_123]), noeltsimpempty]), setadjoinIR]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_124]), c_0_125]), setadjoinOr]), setadjoinE]), setunionI]), uniqinunit]), c_0_126]), c_0_127]), subPowSU]), setunionE]), singletonsswitch]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_128]), upairsetIR]), upairsetIL]), upairsetE]), quantDeMorgan3]), c_0_129]), c_0_130]), c_0_131]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), inCongP]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_132]), c_0_133]), in__Cong]), omega__Cong]), subsetI2]), eqimpsubset1]), eqimpsubset2]), subsetI1]), c_0_134]), c_0_135]), c_0_136]), notequalI1]), emptysetsubset]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_137]), c_0_138]), c_0_139]), c_0_140]), c_0_141]), wellorderingAx]), foundationAx]), c_0_142]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_143])).
% 0.22/0.32  thf(c_0_145, negated_conjecture, ![X600:$i, X601:$i, X603:$i, X604:$i, X605:$i, X606:$i, X607:$i, X608:$i, X609:$i, X610:$i, X611:$i, X613:$i, X614:$i, X616:$i, X617:$i, X618:$i, X619:$i, X620:$i, X622:$i, X623:$i > $i > $o, X624:$i, X626:$i, X629:$i, X631:$i, X632:$i, X633:$i, X634:$i, X636:$i, X637:$i > $o, X638:$i, X640:$i, X641:$i > $o, X642:$i, X643:$i, X644:$i > $o, X645:$i, X646:$i, X647:$i > $o, X648:$i, X649:$i > $o, X650:$i, X653:$i, X654:$o, X655:$i, X656:$i, X657:$o, X658:$i, X659:$i, X660:$i > $o, X661:$i, X664:$i, X665:$i, X668:$i, X670:$i, X672:$i, X673:$i > $o, X674:$i, X675:$i, X677:$i, X678:$i > $o, X679:$i, X680:$i, X681:$i, X682:$i, X683:$i, X684:$i, X685:$i, X686:$i, X687:$i, X688:$i, X689:$i, X690:$o, X691:$i, X692:$i, X693:$i, X694:$i, X695:$i, X696:$i, X698:$i, X699:$i, X700:$i, X701:$i, X702:$i, X703:$i, X704:$i, X705:$i, X706:$i, X707:$i, X708:$o, X710:$i, X711:$i, X712:$i > $o, X713:$i, X716:$i, X717:$i, X718:$i, X720:$i, X721:$i, X722:$i, X723:$i, X724:$i, X725:$i, X726:$i, X727:$i, X728:$i, X729:$i, X730:$i, X731:$i, X732:$i, X733:$i, X734:$i, X735:$i, X736:$i > $o, X737:$i, X738:$i > $o, X739:$i, X740:$i, X741:$i > $o, X742:$i, X744:$i, X745:$i > $o, X747:$i, X748:$i, X749:$i > $o, X751:$i, X752:$i, X753:$i > $o, X754:$i, X756:$o, X757:$i, X758:$i > $o, X760:$i, X761:$i, X762:$i > $o, X763:$i, X765:$i > $o, X766:$i, X769:$i, X770:$i > $o, X771:$i, X775:$i, X776:$i > $o, X777:$i, X780:$i, X781:$i, X782:$i, X783:$i, X784:$i, X785:$i, X786:$i, X787:$i, X788:$i, X789:$i > $o, X790:$i, X792:$i, X793:$i, X794:$i > $o, X795:$i > $o, X798:$i, X801:$i, X802:$i, X805:$i, X806:$i, X807:$i, X808:$i, X809:$i, X810:$i, X811:$i, X812:$i, X813:$i, X814:$i > $o, X815:$i, X817:$i, X818:$i, X819:$i > $o, X820:$i > $o, X823:$i, X825:$i, X827:$i, X828:$i, X829:$i > $o, X830:$i > $o, X833:$i, X834:$i, X836:$i, X837:$i, X838:$i, X839:$i, X840:$i, X841:$i, X843:$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, X876:$i, X877:$i, X878:$i, X879:$i, X880:$i > $o, X881:$i, X882:$i > $o]:((((~(in @ (esk1_2 @ X600 @ X601) @ X600)|~(in @ (esk1_2 @ X600 @ X601) @ X601)|((X600)=(X601)))&((in @ (esk1_2 @ X600 @ X601) @ X600)|(in @ (esk1_2 @ X600 @ X601) @ X601)|((X600)=(X601))))&(~(in @ X603 @ emptyset)&(((~(in @ X606 @ (setadjoin @ X604 @ X605))|(((X606)=(X604))|(in @ X606 @ X605)))&((((X606)!=(X604))|(in @ X606 @ (setadjoin @ X604 @ X605)))&(~(in @ X606 @ X605)|(in @ X606 @ (setadjoin @ X604 @ X605)))))&(((~(in @ X608 @ (powerset @ X607))|(~(in @ X609 @ X608)|(in @ X609 @ X607)))&(((in @ (esk2_2 @ X610 @ X611) @ X611)|(in @ X611 @ (powerset @ X610)))&(~(in @ (esk2_2 @ X610 @ X611) @ X610)|(in @ X611 @ (powerset @ X610)))))&(((((in @ X614 @ (esk3_2 @ X613 @ X614))|~(in @ X614 @ (setunion @ X613)))&((in @ (esk3_2 @ X613 @ X614) @ X613)|~(in @ X614 @ (setunion @ X613))))&(~(in @ X617 @ X618)|~(in @ X618 @ X616)|(in @ X617 @ (setunion @ X616))))&((in @ emptyset @ omega)&((~(in @ X619 @ omega)|(in @ (setadjoin @ X619 @ X619) @ omega))&(((((in @ (esk4_1 @ X620) @ omega)|~(in @ emptyset @ X620)|(~(in @ X622 @ omega)|(in @ X622 @ X620)))&((in @ (esk4_1 @ X620) @ X620)|~(in @ emptyset @ X620)|(~(in @ X622 @ omega)|(in @ X622 @ X620))))&(~(in @ (setadjoin @ (esk4_1 @ X620) @ (esk4_1 @ X620)) @ X620)|~(in @ emptyset @ X620)|(~(in @ X622 @ omega)|(in @ X622 @ X620))))&((((((in @ (esk8_3 @ X623 @ X624 @ X629) @ X624)|~(in @ X629 @ (esk7_2 @ X623 @ X624))|(in @ (esk5_2 @ X623 @ X624) @ X624))&((X623 @ (esk8_3 @ X623 @ X624 @ X629) @ X629)|~(in @ X629 @ (esk7_2 @ X623 @ X624))|(in @ (esk5_2 @ X623 @ X624) @ X624)))&(~(in @ X632 @ X624)|~(X623 @ X632 @ X631)|(in @ X631 @ (esk7_2 @ X623 @ X624))|(in @ (esk5_2 @ X623 @ X624) @ X624)))&(((((in @ (esk8_3 @ X623 @ X624 @ X629) @ X624)|~(in @ X629 @ (esk7_2 @ X623 @ X624))|((X623 @ (esk5_2 @ X623 @ X624) @ (esk6_3 @ X623 @ X624 @ X626))|~(X623 @ (esk5_2 @ X623 @ X624) @ X626)))&((X623 @ (esk8_3 @ X623 @ X624 @ X629) @ X629)|~(in @ X629 @ (esk7_2 @ X623 @ X624))|((X623 @ (esk5_2 @ X623 @ X624) @ (esk6_3 @ X623 @ X624 @ X626))|~(X623 @ (esk5_2 @ X623 @ X624) @ X626))))&(~(in @ X632 @ X624)|~(X623 @ X632 @ X631)|(in @ X631 @ (esk7_2 @ X623 @ X624))|((X623 @ (esk5_2 @ X623 @ X624) @ (esk6_3 @ X623 @ X624 @ X626))|~(X623 @ (esk5_2 @ X623 @ X624) @ X626))))&((((in @ (esk8_3 @ X623 @ X624 @ X629) @ X624)|~(in @ X629 @ (esk7_2 @ X623 @ X624))|(((X626)!=(esk6_3 @ X623 @ X624 @ X626))|~(X623 @ (esk5_2 @ X623 @ X624) @ X626)))&((X623 @ (esk8_3 @ X623 @ X624 @ X629) @ X629)|~(in @ X629 @ (esk7_2 @ X623 @ X624))|(((X626)!=(esk6_3 @ X623 @ X624 @ X626))|~(X623 @ (esk5_2 @ X623 @ X624) @ X626))))&(~(in @ X632 @ X624)|~(X623 @ X632 @ X631)|(in @ X631 @ (esk7_2 @ X623 @ X624))|(((X626)!=(esk6_3 @ X623 @ X624 @ X626))|~(X623 @ (esk5_2 @ X623 @ X624) @ X626))))))&((((in @ (esk9_1 @ X633) @ X633)|~(in @ X634 @ X633))&(~(in @ X636 @ (esk9_1 @ X633))|~(in @ X636 @ X633)|~(in @ X634 @ X633)))&((epred1_0)&((((X637 @ (esk10_2 @ X637 @ X638))|~(X637 @ X638)|(X637 @ (descr @ X637)))&(((X638)!=(esk10_2 @ X637 @ X638))|~(X637 @ X638)|(X637 @ (descr @ X637))))&((~(in @ X642 @ X640)|(~(X641 @ X642)|(in @ X642 @ (dsetconstr @ X640 @ X641))))&((~(in @ X645 @ (dsetconstr @ X643 @ X644))|(in @ X645 @ X643))&((~(in @ X648 @ (dsetconstr @ X646 @ X647))|(X647 @ X648))&(((((X649 @ (esk12_1 @ X649))|((X649 @ (esk11_2 @ X649 @ X650))|~(X649 @ X650)))&(~(X649 @ X653)|((esk12_1 @ X649)=(X653))|((X649 @ (esk11_2 @ X649 @ X650))|~(X649 @ X650))))&(((X649 @ (esk12_1 @ X649))|(((X650)!=(esk11_2 @ X649 @ X650))|~(X649 @ X650)))&(~(X649 @ X653)|((esk12_1 @ X649)=(X653))|(((X650)!=(esk11_2 @ X649 @ X650))|~(X649 @ X650)))))&((~(in @ X655 @ (prop2set @ ((X654))))|(X654))&((~(in @ X656 @ emptyset)|(X657))&((~(in @ X658 @ emptyset)|~($true))&(~(in @ X659 @ emptyset)&((((X660 @ (esk13_2 @ X660 @ X661))|~(X660 @ X661)|(X660 @ (esk14_1 @ X660)))&(((X661)!=(esk13_2 @ X660 @ X661))|~(X660 @ X661)|(X660 @ (esk14_1 @ X660))))&(((((in @ (esk16_2 @ X664 @ X665) @ X665)|((X664)=(X665))|(in @ (esk15_2 @ X664 @ X665) @ X664))&(~(in @ (esk16_2 @ X664 @ X665) @ X664)|((X664)=(X665))|(in @ (esk15_2 @ X664 @ X665) @ X664)))&(((in @ (esk16_2 @ X664 @ X665) @ X665)|((X664)=(X665))|~(in @ (esk15_2 @ X664 @ X665) @ X665))&(~(in @ (esk16_2 @ X664 @ X665) @ X664)|((X664)=(X665))|~(in @ (esk15_2 @ X664 @ X665) @ X665))))&(((in @ (esk17_1 @ X668) @ X668)|((X668)=(emptyset)))&(((in @ (esk18_1 @ X670) @ X670)|((X670)=(emptyset)))&(((~(in @ X674 @ (dsetconstr @ X672 @ X673))|(X673 @ X674)|~(in @ X674 @ X672))&(~(X673 @ X674)|(in @ X674 @ (dsetconstr @ X672 @ X673))|~(in @ X674 @ X672)))&((((X675)=(emptyset))|(in @ (esk19_1 @ X675) @ X675))&((~(in @ X679 @ X677)|(~(X678 @ X679)|((dsetconstr @ X677 @ X678)!=(emptyset))))&((~(in @ X681 @ X680)|((X680)!=(emptyset)))&((in @ X682 @ (setadjoin @ X682 @ X683))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X686 @ X685)|(in @ X686 @ (setadjoin @ X684 @ X685)))&(((((in @ X689 @ X688)|(X690)|((X689)=(X687))|~(in @ X689 @ (setadjoin @ X687 @ X688)))&(~(X690)|(X690)|((X689)=(X687))|~(in @ X689 @ (setadjoin @ X687 @ X688))))&(((in @ X689 @ X688)|(X690)|~(X690)|~(in @ X689 @ (setadjoin @ X687 @ X688)))&(~(X690)|(X690)|~(X690)|~(in @ X689 @ (setadjoin @ X687 @ X688)))))&((~(in @ X693 @ (setadjoin @ X691 @ X692))|(((X693)=(X691))|(in @ X693 @ X692)))&(((dsetconstr @ X694 @ (^[Z0:$i]:($true)))=(X694))&((((in @ (esk20_2 @ X695 @ X696) @ X696)|(in @ X696 @ (powerset @ X695)))&(~(in @ (esk20_2 @ X695 @ X696) @ X695)|(in @ X696 @ (powerset @ X695))))&((in @ emptyset @ (powerset @ X698))&((in @ emptyset @ (powerset @ X699))&((~(in @ X701 @ (powerset @ X700))|(~(in @ X702 @ X701)|(in @ X702 @ X700)))&((~(in @ X704 @ X705)|(~(in @ X705 @ X703)|(in @ X704 @ (setunion @ X703))))&((((in @ X707 @ (esk21_3 @ X706 @ X707 @ X708))|(X708)|~(in @ X707 @ (setunion @ X706)))&(((in @ (esk21_3 @ X706 @ X707 @ X708) @ X706)|(X708)|~(in @ X707 @ (setunion @ X706)))&(~(X708)|(X708)|~(in @ X707 @ (setunion @ X706)))))&((~(in @ X711 @ X710)|(in @ X711 @ (powerset @ (setunion @ X710))))&((((~(X712 @ X716)|((X716)=(esk23_1 @ X712))|((X712 @ (esk22_2 @ X712 @ X713))|~(X712 @ X713)))&(((X717)!=(esk23_1 @ X712))|(X712 @ X717)|((X712 @ (esk22_2 @ X712 @ X713))|~(X712 @ X713))))&((~(X712 @ X716)|((X716)=(esk23_1 @ X712))|(((X713)!=(esk22_2 @ X712 @ X713))|~(X712 @ X713)))&(((X717)!=(esk23_1 @ X712))|(X712 @ X717)|(((X713)!=(esk22_2 @ X712 @ X713))|~(X712 @ X713)))))&((((in @ (esk24_1 @ X718) @ X718)|((X718)=(emptyset)))&(($true)|((X718)=(emptyset))))&((~(in @ X720 @ (setadjoin @ X721 @ emptyset))|((X720)=(X721)))&((((X722)=(X723))|~(in @ X723 @ (setadjoin @ X722 @ emptyset)))&((((X724)!=(X725))|(in @ X724 @ (setadjoin @ X725 @ emptyset)))&((~(in @ X726 @ (setadjoin @ X727 @ emptyset))|(in @ X727 @ (setadjoin @ X726 @ emptyset)))&((~(in @ X730 @ (setadjoin @ X728 @ (setadjoin @ X729 @ emptyset)))|(((X730)=(X728))|((X730)=(X729))))&((in @ X731 @ (setadjoin @ X731 @ (setadjoin @ X732 @ emptyset)))&((in @ X734 @ (setadjoin @ X733 @ (setadjoin @ X734 @ emptyset)))&((~(in @ X737 @ X735)|~(X736 @ X737)|(((dsetconstr @ X735 @ X736)!=(emptyset))|~($true)))&((~(in @ X739 @ emptyset)|(X738 @ X739))&((((in @ (esk25_2 @ X740 @ X741) @ X740)|(~(in @ X742 @ X740)|(X741 @ X742)))&(~(X741 @ (esk25_2 @ X740 @ X741))|(~(in @ X742 @ X740)|(X741 @ X742))))&((((in @ (esk26_2 @ X744 @ X745) @ X744)|(~(in @ X747 @ X744)|~(X745 @ X747)))&((X745 @ (esk26_2 @ X744 @ X745))|(~(in @ X747 @ X744)|~(X745 @ X747))))&((((in @ (esk27_2 @ X748 @ X749) @ X748)|(~(in @ X751 @ X748)|~(X749 @ X751)))&((X749 @ (esk27_2 @ X748 @ X749))|(~(in @ X751 @ X748)|~(X749 @ X751))))&((((in @ (esk28_2 @ X752 @ X753) @ X752)|(~(in @ X754 @ X752)|(X753 @ X754)))&(~(X753 @ (esk28_2 @ X752 @ X753))|(~(in @ X754 @ X752)|(X753 @ X754))))&((~(X756)|(in @ emptyset @ (prop2set @ ((X756)))))&((prop2set2propI)&((((in @ (esk29_2 @ X757 @ X758) @ X757)|(~(in @ X760 @ X757)|~(X758 @ X760)))&((X758 @ (esk29_2 @ X757 @ X758))|(~(in @ X760 @ X757)|~(X758 @ X760))))&((((in @ (esk30_2 @ X761 @ X762) @ X761)|(~(in @ X763 @ X761)|(X762 @ X763)))&(~(X762 @ (esk30_2 @ X761 @ X762))|(~(in @ X763 @ X761)|(X762 @ X763))))&(((((X765 @ (esk32_1 @ X765))|((X765 @ (esk31_2 @ X765 @ X766))|~(X765 @ X766)))&(~(X765 @ X769)|((esk32_1 @ X765)=(X769))|((X765 @ (esk31_2 @ X765 @ X766))|~(X765 @ X766))))&(((X765 @ (esk32_1 @ X765))|(((X766)!=(esk31_2 @ X765 @ X766))|~(X765 @ X766)))&(~(X765 @ X769)|((esk32_1 @ X765)=(X769))|(((X766)!=(esk31_2 @ X765 @ X766))|~(X765 @ X766)))))&(((((X770 @ (esk35_1 @ X770))|(X770 @ (esk33_1 @ X770))|~(X770 @ X771))&(~(X770 @ X775)|((esk35_1 @ X770)=(X775))|(X770 @ (esk33_1 @ X770))|~(X770 @ X771)))&((((X770 @ (esk35_1 @ X770))|(X770 @ (esk34_1 @ X770))|~(X770 @ X771))&(~(X770 @ X775)|((esk35_1 @ X770)=(X775))|(X770 @ (esk34_1 @ X770))|~(X770 @ X771)))&(((X770 @ (esk35_1 @ X770))|((esk33_1 @ X770)!=(esk34_1 @ X770))|~(X770 @ X771))&(~(X770 @ X775)|((esk35_1 @ X770)=(X775))|((esk33_1 @ X770)!=(esk34_1 @ X770))|~(X770 @ X771)))))&(((((X776 @ (esk37_1 @ X776))|(~(X776 @ (esk36_2 @ X776 @ X777))|((esk36_2 @ X776 @ X777)!=(X777))))&(~(X776 @ X780)|((esk37_1 @ X776)=(X780))|(~(X776 @ (esk36_2 @ X776 @ X777))|((esk36_2 @ X776 @ X777)!=(X777)))))&(((X776 @ (esk37_1 @ X776))|((X776 @ (esk36_2 @ X776 @ X777))|((esk36_2 @ X776 @ X777)=(X777))))&(~(X776 @ X780)|((esk37_1 @ X776)=(X780))|((X776 @ (esk36_2 @ X776 @ X777))|((esk36_2 @ X776 @ X777)=(X777))))))&((((X781)!=(X782))|(((X783)!=(X784))|(~(in @ X783 @ X781)|(in @ X784 @ X782))))&(((~(in @ X787 @ X785)|(in @ X788 @ X786)|((X787)!=(X788))|((X785)!=(X786)))&(~(in @ X788 @ X786)|(in @ X787 @ X785)|((X787)!=(X788))|((X785)!=(X786))))&((((X789 @ (esk38_2 @ X789 @ X790))|~(X789 @ X790)|(~(X789 @ X792)|(~(X789 @ X793)|((X792)=(X793)))))&(((X790)!=(esk38_2 @ X789 @ X790))|~(X789 @ X790)|(~(X789 @ X792)|(~(X789 @ X793)|((X792)=(X793))))))&(((((((X795 @ (esk42_2 @ X794 @ X795))|((X794 @ (esk41_3 @ X794 @ X795 @ X798))|~(X794 @ X798))|((esk39_2 @ X794 @ X795)=(esk40_2 @ X794 @ X795)))&(~(X795 @ X801)|((esk42_2 @ X794 @ X795)=(X801))|((X794 @ (esk41_3 @ X794 @ X795 @ X798))|~(X794 @ X798))|((esk39_2 @ X794 @ X795)=(esk40_2 @ X794 @ X795))))&(((X795 @ (esk42_2 @ X794 @ X795))|(((X798)!=(esk41_3 @ X794 @ X795 @ X798))|~(X794 @ X798))|((esk39_2 @ X794 @ X795)=(esk40_2 @ X794 @ X795)))&(~(X795 @ X801)|((esk42_2 @ X794 @ X795)=(X801))|(((X798)!=(esk41_3 @ X794 @ X795 @ X798))|~(X794 @ X798))|((esk39_2 @ X794 @ X795)=(esk40_2 @ X794 @ X795)))))&((((X794 @ (esk44_2 @ X794 @ X795))|((X795 @ (esk43_3 @ X794 @ X795 @ X802))|~(X795 @ X802))|((esk39_2 @ X794 @ X795)=(esk40_2 @ X794 @ X795)))&(~(X794 @ X805)|((esk44_2 @ X794 @ X795)=(X805))|((X795 @ (esk43_3 @ X794 @ X795 @ X802))|~(X795 @ X802))|((esk39_2 @ X794 @ X795)=(esk40_2 @ X794 @ X795))))&(((X794 @ (esk44_2 @ X794 @ X795))|(((X802)!=(esk43_3 @ X794 @ X795 @ X802))|~(X795 @ X802))|((esk39_2 @ X794 @ X795)=(esk40_2 @ X794 @ X795)))&(~(X794 @ X805)|((esk44_2 @ X794 @ X795)=(X805))|(((X802)!=(esk43_3 @ X794 @ X795 @ X802))|~(X795 @ X802))|((esk39_2 @ X794 @ X795)=(esk40_2 @ X794 @ X795))))))&((((((X795 @ (esk42_2 @ X794 @ X795))|((X794 @ (esk41_3 @ X794 @ X795 @ X798))|~(X794 @ X798))|(~(X794 @ (esk39_2 @ X794 @ X795))|~(X795 @ (esk40_2 @ X794 @ X795))))&(~(X795 @ X801)|((esk42_2 @ X794 @ X795)=(X801))|((X794 @ (esk41_3 @ X794 @ X795 @ X798))|~(X794 @ X798))|(~(X794 @ (esk39_2 @ X794 @ X795))|~(X795 @ (esk40_2 @ X794 @ X795)))))&(((X795 @ (esk42_2 @ X794 @ X795))|(((X798)!=(esk41_3 @ X794 @ X795 @ X798))|~(X794 @ X798))|(~(X794 @ (esk39_2 @ X794 @ X795))|~(X795 @ (esk40_2 @ X794 @ X795))))&(~(X795 @ X801)|((esk42_2 @ X794 @ X795)=(X801))|(((X798)!=(esk41_3 @ X794 @ X795 @ X798))|~(X794 @ X798))|(~(X794 @ (esk39_2 @ X794 @ X795))|~(X795 @ (esk40_2 @ X794 @ X795))))))&((((X794 @ (esk44_2 @ X794 @ X795))|((X795 @ (esk43_3 @ X794 @ X795 @ X802))|~(X795 @ X802))|(~(X794 @ (esk39_2 @ X794 @ X795))|~(X795 @ (esk40_2 @ X794 @ X795))))&(~(X794 @ X805)|((esk44_2 @ X794 @ X795)=(X805))|((X795 @ (esk43_3 @ X794 @ X795 @ X802))|~(X795 @ X802))|(~(X794 @ (esk39_2 @ X794 @ X795))|~(X795 @ (esk40_2 @ X794 @ X795)))))&(((X794 @ (esk44_2 @ X794 @ X795))|(((X802)!=(esk43_3 @ X794 @ X795 @ X802))|~(X795 @ X802))|(~(X794 @ (esk39_2 @ X794 @ X795))|~(X795 @ (esk40_2 @ X794 @ X795))))&(~(X794 @ X805)|((esk44_2 @ X794 @ X795)=(X805))|(((X802)!=(esk43_3 @ X794 @ X795 @ X802))|~(X795 @ X802))|(~(X794 @ (esk39_2 @ X794 @ X795))|~(X795 @ (esk40_2 @ X794 @ X795)))))))&(((((X795 @ (esk42_2 @ X794 @ X795))|((X794 @ (esk41_3 @ X794 @ X795 @ X798))|~(X794 @ X798))|((X794 @ (esk39_2 @ X794 @ X795))|(X795 @ (esk40_2 @ X794 @ X795))))&(~(X795 @ X801)|((esk42_2 @ X794 @ X795)=(X801))|((X794 @ (esk41_3 @ X794 @ X795 @ X798))|~(X794 @ X798))|((X794 @ (esk39_2 @ X794 @ X795))|(X795 @ (esk40_2 @ X794 @ X795)))))&(((X795 @ (esk42_2 @ X794 @ X795))|(((X798)!=(esk41_3 @ X794 @ X795 @ X798))|~(X794 @ X798))|((X794 @ (esk39_2 @ X794 @ X795))|(X795 @ (esk40_2 @ X794 @ X795))))&(~(X795 @ X801)|((esk42_2 @ X794 @ X795)=(X801))|(((X798)!=(esk41_3 @ X794 @ X795 @ X798))|~(X794 @ X798))|((X794 @ (esk39_2 @ X794 @ X795))|(X795 @ (esk40_2 @ X794 @ X795))))))&((((X794 @ (esk44_2 @ X794 @ X795))|((X795 @ (esk43_3 @ X794 @ X795 @ X802))|~(X795 @ X802))|((X794 @ (esk39_2 @ X794 @ X795))|(X795 @ (esk40_2 @ X794 @ X795))))&(~(X794 @ X805)|((esk44_2 @ X794 @ X795)=(X805))|((X795 @ (esk43_3 @ X794 @ X795 @ X802))|~(X795 @ X802))|((X794 @ (esk39_2 @ X794 @ X795))|(X795 @ (esk40_2 @ X794 @ X795)))))&(((X794 @ (esk44_2 @ X794 @ X795))|(((X802)!=(esk43_3 @ X794 @ X795 @ X802))|~(X795 @ X802))|((X794 @ (esk39_2 @ X794 @ X795))|(X795 @ (esk40_2 @ X794 @ X795))))&(~(X794 @ X805)|((esk44_2 @ X794 @ X795)=(X805))|(((X802)!=(esk43_3 @ X794 @ X795 @ X802))|~(X795 @ X802))|((X794 @ (esk39_2 @ X794 @ X795))|(X795 @ (esk40_2 @ X794 @ X795)))))))))&(((emptyset)=(emptyset))&((((X806)!=(X807))|(((X808)!=(X809))|((setadjoin @ X806 @ X808)=(setadjoin @ X807 @ X809))))&((((X810)!=(X811))|((powerset @ X810)=(powerset @ X811)))&((((X812)!=(X813))|((setunion @ X812)=(setunion @ X813)))&(((omega)=(omega))&((((X814 @ (esk45_2 @ X814 @ X815))|~(X814 @ X815)|(~(X814 @ X817)|(~(X814 @ X818)|((X817)=(X818)))))&(((X815)!=(esk45_2 @ X814 @ X815))|~(X814 @ X815)|(~(X814 @ X817)|(~(X814 @ X818)|((X817)=(X818))))))&((((((X820 @ (esk49_3 @ X819 @ X820 @ X825))|~(X820 @ X825)|((descr @ X819)=(descr @ X820))|((X819 @ (esk48_3 @ X819 @ X820 @ X823))|~(X819 @ X823))|((esk46_2 @ X819 @ X820)=(esk47_2 @ X819 @ X820)))&(((X825)!=(esk49_3 @ X819 @ X820 @ X825))|~(X820 @ X825)|((descr @ X819)=(descr @ X820))|((X819 @ (esk48_3 @ X819 @ X820 @ X823))|~(X819 @ X823))|((esk46_2 @ X819 @ X820)=(esk47_2 @ X819 @ X820))))&(((X820 @ (esk49_3 @ X819 @ X820 @ X825))|~(X820 @ X825)|((descr @ X819)=(descr @ X820))|(((X823)!=(esk48_3 @ X819 @ X820 @ X823))|~(X819 @ X823))|((esk46_2 @ X819 @ X820)=(esk47_2 @ X819 @ X820)))&(((X825)!=(esk49_3 @ X819 @ X820 @ X825))|~(X820 @ X825)|((descr @ X819)=(descr @ X820))|(((X823)!=(esk48_3 @ X819 @ X820 @ X823))|~(X819 @ X823))|((esk46_2 @ X819 @ X820)=(esk47_2 @ X819 @ X820)))))&(((((X820 @ (esk49_3 @ X819 @ X820 @ X825))|~(X820 @ X825)|((descr @ X819)=(descr @ X820))|((X819 @ (esk48_3 @ X819 @ X820 @ X823))|~(X819 @ X823))|(~(X819 @ (esk46_2 @ X819 @ X820))|~(X820 @ (esk47_2 @ X819 @ X820))))&(((X825)!=(esk49_3 @ X819 @ X820 @ X825))|~(X820 @ X825)|((descr @ X819)=(descr @ X820))|((X819 @ (esk48_3 @ X819 @ X820 @ X823))|~(X819 @ X823))|(~(X819 @ (esk46_2 @ X819 @ X820))|~(X820 @ (esk47_2 @ X819 @ X820)))))&(((X820 @ (esk49_3 @ X819 @ X820 @ X825))|~(X820 @ X825)|((descr @ X819)=(descr @ X820))|(((X823)!=(esk48_3 @ X819 @ X820 @ X823))|~(X819 @ X823))|(~(X819 @ (esk46_2 @ X819 @ X820))|~(X820 @ (esk47_2 @ X819 @ X820))))&(((X825)!=(esk49_3 @ X819 @ X820 @ X825))|~(X820 @ X825)|((descr @ X819)=(descr @ X820))|(((X823)!=(esk48_3 @ X819 @ X820 @ X823))|~(X819 @ X823))|(~(X819 @ (esk46_2 @ X819 @ X820))|~(X820 @ (esk47_2 @ X819 @ X820))))))&((((X820 @ (esk49_3 @ X819 @ X820 @ X825))|~(X820 @ X825)|((descr @ X819)=(descr @ X820))|((X819 @ (esk48_3 @ X819 @ X820 @ X823))|~(X819 @ X823))|((X819 @ (esk46_2 @ X819 @ X820))|(X820 @ (esk47_2 @ X819 @ X820))))&(((X825)!=(esk49_3 @ X819 @ X820 @ X825))|~(X820 @ X825)|((descr @ X819)=(descr @ X820))|((X819 @ (esk48_3 @ X819 @ X820 @ X823))|~(X819 @ X823))|((X819 @ (esk46_2 @ X819 @ X820))|(X820 @ (esk47_2 @ X819 @ X820)))))&(((X820 @ (esk49_3 @ X819 @ X820 @ X825))|~(X820 @ X825)|((descr @ X819)=(descr @ X820))|(((X823)!=(esk48_3 @ X819 @ X820 @ X823))|~(X819 @ X823))|((X819 @ (esk46_2 @ X819 @ X820))|(X820 @ (esk47_2 @ X819 @ X820))))&(((X825)!=(esk49_3 @ X819 @ X820 @ X825))|~(X820 @ X825)|((descr @ X819)=(descr @ X820))|(((X823)!=(esk48_3 @ X819 @ X820 @ X823))|~(X819 @ X823))|((X819 @ (esk46_2 @ X819 @ X820))|(X820 @ (esk47_2 @ X819 @ X820))))))))&((((in @ (esk50_4 @ X827 @ X828 @ X829 @ X830) @ X827)|((dsetconstr @ X827 @ X829)=(dsetconstr @ X828 @ X830))|((X827)!=(X828)))&(((in @ (esk51_4 @ X827 @ X828 @ X829 @ X830) @ X828)|((dsetconstr @ X827 @ X829)=(dsetconstr @ X828 @ X830))|((X827)!=(X828)))&((((esk50_4 @ X827 @ X828 @ X829 @ X830)=(esk51_4 @ X827 @ X828 @ X829 @ X830))|((dsetconstr @ X827 @ X829)=(dsetconstr @ X828 @ X830))|((X827)!=(X828)))&((~(X829 @ (esk50_4 @ X827 @ X828 @ X829 @ X830))|~(X830 @ (esk51_4 @ X827 @ X828 @ X829 @ X830))|((dsetconstr @ X827 @ X829)=(dsetconstr @ X828 @ X830))|((X827)!=(X828)))&((X829 @ (esk50_4 @ X827 @ X828 @ X829 @ X830))|(X830 @ (esk51_4 @ X827 @ X828 @ X829 @ X830))|((dsetconstr @ X827 @ X829)=(dsetconstr @ X828 @ X830))|((X827)!=(X828)))))))&((((in @ (esk52_2 @ X833 @ X834) @ X833)|(subset @ X833 @ X834))&(~(in @ (esk52_2 @ X833 @ X834) @ X834)|(subset @ X833 @ X834)))&((((X836)!=(X837))|(subset @ X837 @ X836))&((((X838)!=(X839))|(subset @ X838 @ X839))&((((in @ (esk53_2 @ X840 @ X841) @ X840)|(subset @ X840 @ X841))&(~(in @ (esk53_2 @ X840 @ X841) @ X841)|(subset @ X840 @ X841)))&((subset @ emptyset @ X843)&((~(subset @ X844 @ X845)|(~(in @ X846 @ X844)|(in @ X846 @ X845)))&((~(subset @ X847 @ X848)|((in @ X849 @ X848)|~(in @ X849 @ X847)))&((~(in @ X852 @ X850)|((in @ X852 @ X851)|~(subset @ X850 @ X851)))&(((subset @ X853 @ X854)|((X853)!=(X854)))&((~(in @ X857 @ X855)|((in @ X857 @ X856)|((X855)!=(X856))))&((subset @ X858 @ X858)&((~(subset @ X859 @ X860)|(~(subset @ X860 @ X861)|(subset @ X859 @ X861)))&((subset @ X863 @ (setadjoin @ X862 @ X863))&((~(subset @ X864 @ X866)|(subset @ X864 @ (setadjoin @ X865 @ X866)))&((~(subset @ X867 @ X868)|(in @ X867 @ (powerset @ X868)))&((~(subset @ X869 @ X870)|(~(subset @ X870 @ X869)|((X869)=(X870))))&((~(subset @ X871 @ emptyset)|((X871)=(emptyset)))&((~(subset @ X873 @ X872)|(in @ X873 @ (powerset @ X872)))&((~(in @ X875 @ (powerset @ X874))|(subset @ X875 @ X874))&((in @ X876 @ (powerset @ X876))&((~(subset @ X877 @ X878)|(subset @ (powerset @ X877) @ (powerset @ X878)))&((in @ (dsetconstr @ X879 @ X880) @ (powerset @ X879))&((subset @ (dsetconstr @ X881 @ X882) @ X881)&((in @ esk56_0 @ esk54_0)&~(in @ esk56_0 @ (setunion @ (setadjoin @ esk54_0 @ (setadjoin @ esk55_0 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[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_144])])])])])])])).
% 0.22/0.32  thf(c_0_146, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ (setunion @ X4))|~((in @ X2 @ X3))|~((in @ X3 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 0.22/0.32  thf(c_0_147, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 0.22/0.32  thf(c_0_148, negated_conjecture, ~((in @ esk56_0 @ (setunion @ (setadjoin @ esk54_0 @ (setadjoin @ esk55_0 @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 0.22/0.32  thf(c_0_149, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setunion @ (setadjoin @ X3 @ X4)))|~((in @ X2 @ X3)))), inference(spm,[status(thm)],[c_0_146, c_0_147])).
% 0.22/0.32  thf(c_0_150, negated_conjecture, (in @ esk56_0 @ esk54_0), inference(split_conjunct,[status(thm)],[c_0_145])).
% 0.22/0.32  thf(c_0_151, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148, c_0_149]), c_0_150])]), ['proof']).
% 0.22/0.32  % SZS output end CNFRefutation
% 0.22/0.32  % Parsed axioms                        : 216
% 0.22/0.32  % Removed by relevancy pruning/SinE    : 115
% 0.22/0.32  % Initial clauses                      : 210
% 0.22/0.32  % Removed in clause preprocessing      : 14
% 0.22/0.32  % Initial clauses in saturation        : 196
% 0.22/0.32  % Processed clauses                    : 248
% 0.22/0.32  % ...of these trivial                  : 6
% 0.22/0.32  % ...subsumed                          : 94
% 0.22/0.32  % ...remaining for further processing  : 148
% 0.22/0.32  % Other redundant clauses eliminated   : 8
% 0.22/0.32  % Clauses deleted for lack of memory   : 0
% 0.22/0.32  % Backward-subsumed                    : 0
% 0.22/0.32  % Backward-rewritten                   : 4
% 0.22/0.32  % Generated clauses                    : 1082
% 0.22/0.32  % ...of the previous two non-redundant : 930
% 0.22/0.32  % ...aggressively subsumed             : 0
% 0.22/0.32  % Contextual simplify-reflections      : 0
% 0.22/0.32  % Paramodulations                      : 1074
% 0.22/0.32  % Factorizations                       : 0
% 0.22/0.32  % NegExts                              : 0
% 0.22/0.32  % Equation resolutions                 : 8
% 0.22/0.32  % Disequality decompositions           : 0
% 0.22/0.32  % Total rewrite steps                  : 225
% 0.22/0.32  % ...of those cached                   : 187
% 0.22/0.32  % Propositional unsat checks           : 0
% 0.22/0.32  %    Propositional check models        : 0
% 0.22/0.32  %    Propositional check unsatisfiable : 0
% 0.22/0.32  %    Propositional clauses             : 0
% 0.22/0.32  %    Propositional clauses after purity: 0
% 0.22/0.32  %    Propositional unsat core size     : 0
% 0.22/0.32  %    Propositional preprocessing time  : 0.000
% 0.22/0.32  %    Propositional encoding time       : 0.000
% 0.22/0.32  %    Propositional solver time         : 0.000
% 0.22/0.32  %    Success case prop preproc time    : 0.000
% 0.22/0.32  %    Success case prop encoding time   : 0.000
% 0.22/0.32  %    Success case prop solver time     : 0.000
% 0.22/0.32  % Current number of processed clauses  : 137
% 0.22/0.32  %    Positive orientable unit clauses  : 38
% 0.22/0.32  %    Positive unorientable unit clauses: 0
% 0.22/0.32  %    Negative unit clauses             : 2
% 0.22/0.32  %    Non-unit-clauses                  : 97
% 0.22/0.32  % Current number of unprocessed clauses: 863
% 0.22/0.32  % ...number of literals in the above   : 2454
% 0.22/0.32  % Current number of archived formulas  : 0
% 0.22/0.32  % Current number of archived clauses   : 4
% 0.22/0.32  % Clause-clause subsumption calls (NU) : 1192
% 0.22/0.32  % Rec. Clause-clause subsumption calls : 974
% 0.22/0.32  % Non-unit clause-clause subsumptions  : 74
% 0.22/0.32  % Unit Clause-clause subsumption calls : 32
% 0.22/0.32  % Rewrite failures with RHS unbound    : 0
% 0.22/0.32  % BW rewrite match attempts            : 32
% 0.22/0.32  % BW rewrite match successes           : 3
% 0.22/0.32  % Condensation attempts                : 0
% 0.22/0.32  % Condensation successes               : 0
% 0.22/0.32  % Termbank termtop insertions          : 39782
% 0.22/0.32  % Search garbage collected termcells   : 10552
% 0.22/0.32  
% 0.22/0.32  % -------------------------------------------------
% 0.22/0.32  % User time                : 0.053 s
% 0.22/0.32  % System time              : 0.011 s
% 0.22/0.32  % Total time               : 0.064 s
% 0.22/0.32  % Maximum resident set size: 6148 pages
% 0.22/0.32  
% 0.22/0.32  % -------------------------------------------------
% 0.22/0.32  % User time                : 0.059 s
% 0.22/0.32  % System time              : 0.017 s
% 0.22/0.32  % Total time               : 0.077 s
% 0.22/0.32  % Maximum resident set size: 5120 pages
% 0.22/0.32  % E exiting
%------------------------------------------------------------------------------