E-SAT---3.5.1.THM-CRf.s

%------------------------------------------------------------------------------
% File     : E-SAT---3.5.1
% Problem  : SEU629^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:26:59 AM UTC 2026

% Result   : Theorem 0.25s 0.68s
% Output   : CNFRefutation 0.25s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU629^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05  % Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20  % Computer : n026.cluster.edu
% 0.08/0.20  % Model    : x86_64 x86_64
% 0.08/0.20  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20  % Memory   : 8046.5625MB
% 0.08/0.20  % OS       : Linux 6.8.0-71-generic
% 0.08/0.20  % CPULimit : 300
% 0.08/0.20  % WCLimit  : 300
% 0.08/0.20  % DateTime : Tue Sep 29 14:02:12 UTC 2026
% 0.08/0.20  % CPUTime  : 
% 0.08/0.20  Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25  Running higher-order theorem proving
% 0.21/0.29  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.xl164fgHXZ/E---3.1_646864.p
% 0.25/0.68  % Version: 3.5.1-ho
% 0.25/0.68  % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.25/0.68  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.68  % Starting ehoh_best5 with 300s (1) cores
% 0.25/0.68  % Starting almost_fo_3_lam with 300s (1) cores
% 0.25/0.68  % Starting new_bool_5 with 300s (1) cores
% 0.25/0.68  % Starting pre_casc_3 with 300s (1) cores
% 0.25/0.68  % Starting ho_unfolding_8 with 300s (1) cores
% 0.25/0.68  % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.25/0.68  % Starting new_bool_3 with 300s (1) cores
% 0.25/0.68  % Starting new_ho_5 with 300s (1) cores
% 0.25/0.68  % new_bool_5 with pid 646879 completed with status 0
% 0.25/0.68  % Result found by new_bool_5
% 0.25/0.68  % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.25/0.68  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.68  % Starting ehoh_best5 with 300s (1) cores
% 0.25/0.68  % Starting almost_fo_3_lam with 300s (1) cores
% 0.25/0.68  % Starting new_bool_5 with 300s (1) cores
% 0.25/0.68  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.25/0.68  % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.25/0.68  % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.25/0.68  % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.68  % Starting SubtermCWHack with 28s (1) cores
% 0.25/0.68  % SubtermCWHack with pid 646889 completed with status 0
% 0.25/0.68  % Result found by SubtermCWHack
% 0.25/0.68  % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.25/0.68  % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.68  % Starting ehoh_best5 with 300s (1) cores
% 0.25/0.68  % Starting almost_fo_3_lam with 300s (1) cores
% 0.25/0.68  % Starting new_bool_5 with 300s (1) cores
% 0.25/0.68  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.25/0.68  % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.25/0.68  % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.25/0.68  % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.68  % Starting SubtermCWHack with 28s (1) cores
% 0.25/0.68  % Preprocessing time       : 0.004 s
% 0.25/0.68  
% 0.25/0.68  % Proof found!
% 0.25/0.68  % SZS status Theorem
% 0.25/0.68  % SZS output start CNFRefutation
% 0.25/0.68  thf(decl_23, type, in: $i > $i > $o).
% 0.25/0.68  thf(decl_24, type, exu: ($i > $o) > $o).
% 0.25/0.68  thf(decl_25, type, setextAx: $o).
% 0.25/0.68  thf(decl_26, type, emptyset: $i).
% 0.25/0.68  thf(decl_27, type, emptysetAx: $o).
% 0.25/0.68  thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.25/0.68  thf(decl_29, type, setadjoinAx: $o).
% 0.25/0.68  thf(decl_30, type, powerset: $i > $i).
% 0.25/0.68  thf(decl_31, type, powersetAx: $o).
% 0.25/0.68  thf(decl_32, type, setunion: $i > $i).
% 0.25/0.68  thf(decl_33, type, setunionAx: $o).
% 0.25/0.68  thf(decl_34, type, omega: $i).
% 0.25/0.68  thf(decl_35, type, omega0Ax: $o).
% 0.25/0.68  thf(decl_36, type, omegaSAx: $o).
% 0.25/0.68  thf(decl_37, type, omegaIndAx: $o).
% 0.25/0.68  thf(decl_38, type, replAx: $o).
% 0.25/0.68  thf(decl_39, type, foundationAx: $o).
% 0.25/0.68  thf(decl_40, type, wellorderingAx: $o).
% 0.25/0.68  thf(decl_41, type, descr: ($i > $o) > $i).
% 0.25/0.68  thf(decl_42, type, descrp: $o).
% 0.25/0.68  thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.25/0.68  thf(decl_44, type, dsetconstrI: $o).
% 0.25/0.68  thf(decl_45, type, dsetconstrEL: $o).
% 0.25/0.68  thf(decl_46, type, dsetconstrER: $o).
% 0.25/0.68  thf(decl_47, type, exuE1: $o).
% 0.25/0.68  thf(decl_48, type, prop2set: $o > $i).
% 0.25/0.68  thf(decl_49, type, prop2setE: $o).
% 0.25/0.68  thf(decl_50, type, emptysetE: $o).
% 0.25/0.68  thf(decl_51, type, emptysetimpfalse: $o).
% 0.25/0.68  thf(decl_52, type, notinemptyset: $o).
% 0.25/0.68  thf(decl_53, type, exuE3e: $o).
% 0.25/0.68  thf(decl_54, type, setext: $o).
% 0.25/0.68  thf(decl_55, type, emptyI: $o).
% 0.25/0.68  thf(decl_56, type, noeltsimpempty: $o).
% 0.25/0.68  thf(decl_57, type, setbeta: $o).
% 0.25/0.68  thf(decl_58, type, nonempty: $i > $o).
% 0.25/0.68  thf(decl_59, type, nonemptyE1: $o).
% 0.25/0.68  thf(decl_60, type, nonemptyI: $o).
% 0.25/0.68  thf(decl_61, type, nonemptyI1: $o).
% 0.25/0.68  thf(decl_62, type, setadjoinIL: $o).
% 0.25/0.68  thf(decl_63, type, emptyinunitempty: $o).
% 0.25/0.68  thf(decl_64, type, setadjoinIR: $o).
% 0.25/0.68  thf(decl_65, type, setadjoinE: $o).
% 0.25/0.68  thf(decl_66, type, setadjoinOr: $o).
% 0.25/0.68  thf(decl_67, type, setoftrueEq: $o).
% 0.25/0.68  thf(decl_68, type, powersetI: $o).
% 0.25/0.68  thf(decl_69, type, emptyinPowerset: $o).
% 0.25/0.68  thf(decl_70, type, emptyInPowerset: $o).
% 0.25/0.68  thf(decl_71, type, powersetE: $o).
% 0.25/0.68  thf(decl_72, type, setunionI: $o).
% 0.25/0.68  thf(decl_73, type, setunionE: $o).
% 0.25/0.68  thf(decl_74, type, subPowSU: $o).
% 0.25/0.68  thf(decl_75, type, exuE2: $o).
% 0.25/0.68  thf(decl_76, type, nonemptyImpWitness: $o).
% 0.25/0.68  thf(decl_77, type, uniqinunit: $o).
% 0.25/0.68  thf(decl_78, type, notinsingleton: $o).
% 0.25/0.68  thf(decl_79, type, eqinunit: $o).
% 0.25/0.68  thf(decl_80, type, singletonsswitch: $o).
% 0.25/0.68  thf(decl_81, type, upairsetE: $o).
% 0.25/0.68  thf(decl_82, type, upairsetIL: $o).
% 0.25/0.68  thf(decl_83, type, upairsetIR: $o).
% 0.25/0.68  thf(decl_84, type, emptyE1: $o).
% 0.25/0.68  thf(decl_85, type, vacuousDall: $o).
% 0.25/0.68  thf(decl_86, type, quantDeMorgan1: $o).
% 0.25/0.68  thf(decl_87, type, quantDeMorgan2: $o).
% 0.25/0.68  thf(decl_88, type, quantDeMorgan3: $o).
% 0.25/0.68  thf(decl_89, type, quantDeMorgan4: $o).
% 0.25/0.68  thf(decl_90, type, prop2setI: $o).
% 0.25/0.68  thf(decl_92, type, prop2set2propI: $o).
% 0.25/0.68  thf(decl_93, type, notdexE: $o).
% 0.25/0.68  thf(decl_94, type, notdallE: $o).
% 0.25/0.68  thf(decl_95, type, exuI1: $o).
% 0.25/0.68  thf(decl_96, type, exuI3: $o).
% 0.25/0.68  thf(decl_97, type, exuI2: $o).
% 0.25/0.68  thf(decl_98, type, inCongP: $o).
% 0.25/0.68  thf(decl_99, type, in__Cong: $o).
% 0.25/0.68  thf(decl_100, type, exuE3u: $o).
% 0.25/0.68  thf(decl_101, type, exu__Cong: $o).
% 0.25/0.68  thf(decl_102, type, emptyset__Cong: $o).
% 0.25/0.68  thf(decl_103, type, setadjoin__Cong: $o).
% 0.25/0.68  thf(decl_104, type, powerset__Cong: $o).
% 0.25/0.68  thf(decl_105, type, setunion__Cong: $o).
% 0.25/0.68  thf(decl_106, type, omega__Cong: $o).
% 0.25/0.68  thf(decl_107, type, exuEu: $o).
% 0.25/0.68  thf(decl_108, type, descr__Cong: $o).
% 0.25/0.68  thf(decl_109, type, dsetconstr__Cong: $o).
% 0.25/0.68  thf(decl_110, type, subset: $i > $i > $o).
% 0.25/0.68  thf(decl_113, type, subsetI1: $o).
% 0.25/0.68  thf(decl_114, type, eqimpsubset2: $o).
% 0.25/0.68  thf(decl_115, type, eqimpsubset1: $o).
% 0.25/0.68  thf(decl_116, type, subsetI2: $o).
% 0.25/0.68  thf(decl_117, type, emptysetsubset: $o).
% 0.25/0.68  thf(decl_118, type, subsetE: $o).
% 0.25/0.68  thf(decl_119, type, subsetE2: $o).
% 0.25/0.68  thf(decl_120, type, notsubsetI: $o).
% 0.25/0.68  thf(decl_121, type, notequalI1: $o).
% 0.25/0.68  thf(decl_122, type, notequalI2: $o).
% 0.25/0.68  thf(decl_123, type, subsetRefl: $o).
% 0.25/0.68  thf(decl_124, type, subsetTrans: $o).
% 0.25/0.68  thf(decl_125, type, setadjoinSub: $o).
% 0.25/0.68  thf(decl_126, type, setadjoinSub2: $o).
% 0.25/0.68  thf(decl_127, type, subset2powerset: $o).
% 0.25/0.68  thf(decl_128, type, setextsub: $o).
% 0.25/0.68  thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.25/0.68  thf(decl_130, type, powersetI1: $o).
% 0.25/0.68  thf(decl_131, type, powersetE1: $o).
% 0.25/0.68  thf(decl_132, type, inPowerset: $o).
% 0.25/0.68  thf(decl_133, type, powersetsubset: $o).
% 0.25/0.68  thf(decl_134, type, sepInPowerset: $o).
% 0.25/0.68  thf(decl_135, type, sepSubset: $o).
% 0.25/0.68  thf(decl_136, type, binunion: $i > $i > $i).
% 0.25/0.68  thf(decl_137, type, binunionIL: $o).
% 0.25/0.68  thf(decl_138, type, upairset2IR: $o).
% 0.25/0.68  thf(decl_139, type, binunionIR: $o).
% 0.25/0.68  thf(decl_140, type, binunionEcases: $o).
% 0.25/0.68  thf(decl_141, type, binunionE: $o).
% 0.25/0.68  thf(decl_142, type, binunionLsub: $o).
% 0.25/0.68  thf(decl_143, type, binunionRsub: $o).
% 0.25/0.68  thf(decl_144, type, binintersect: $i > $i > $i).
% 0.25/0.68  thf(decl_145, type, binintersectI: $o).
% 0.25/0.68  thf(decl_146, type, binintersectSubset5: $o).
% 0.25/0.68  thf(decl_147, type, binintersectEL: $o).
% 0.25/0.68  thf(decl_148, type, binintersectLsub: $o).
% 0.25/0.68  thf(decl_149, type, binintersectSubset2: $o).
% 0.25/0.68  thf(decl_150, type, binintersectSubset3: $o).
% 0.25/0.68  thf(decl_151, type, binintersectER: $o).
% 0.25/0.68  thf(decl_152, type, disjointsetsI1: $o).
% 0.25/0.68  thf(decl_153, type, binintersectRsub: $o).
% 0.25/0.68  thf(decl_154, type, binintersectSubset4: $o).
% 0.25/0.68  thf(decl_155, type, binintersectSubset1: $o).
% 0.25/0.68  thf(decl_156, type, bs114d: $o).
% 0.25/0.68  thf(decl_158, type, setminus: $i > $i > $i).
% 0.25/0.68  thf(decl_159, type, setminusI: $o).
% 0.25/0.68  thf(decl_160, type, setminusEL: $o).
% 0.25/0.68  thf(decl_161, type, setminusER: $o).
% 0.25/0.68  thf(decl_162, type, setminusSubset2: $o).
% 0.25/0.68  thf(decl_163, type, setminusERneg: $o).
% 0.25/0.68  thf(decl_164, type, setminusELneg: $o).
% 0.25/0.68  thf(decl_165, type, setminusILneg: $o).
% 0.25/0.68  thf(decl_166, type, setminusIRneg: $o).
% 0.25/0.69  thf(decl_167, type, setminusLsub: $o).
% 0.25/0.69  thf(decl_168, type, setminusSubset1: $o).
% 0.25/0.69  thf(decl_169, type, symdiff: $i > $i > $i).
% 0.25/0.69  thf(decl_170, type, symdiffE: $o).
% 0.25/0.69  thf(decl_171, type, symdiffI1: $o).
% 0.25/0.69  thf(decl_172, type, symdiffI2: $o).
% 0.25/0.69  thf(decl_173, type, symdiffIneg1: $o).
% 0.25/0.69  thf(decl_174, type, symdiffIneg2: $o).
% 0.25/0.69  thf(decl_175, type, iskpair: $i > $o).
% 0.25/0.69  thf(decl_176, type, secondinupair: $o).
% 0.25/0.69  thf(decl_177, type, setukpairIL: $o).
% 0.25/0.69  thf(decl_178, type, setukpairIR: $o).
% 0.25/0.69  thf(decl_179, type, kpairiskpair: $o).
% 0.25/0.69  thf(decl_180, type, kpair: $i > $i > $i).
% 0.25/0.69  thf(decl_181, type, kpairp: $o).
% 0.25/0.69  thf(decl_183, type, singletonsubset: $o).
% 0.25/0.69  thf(decl_184, type, singletoninpowerset: $o).
% 0.25/0.69  thf(decl_185, type, singletoninpowunion: $o).
% 0.25/0.69  thf(decl_186, type, upairset2E: $o).
% 0.25/0.69  thf(decl_187, type, upairsubunion: $o).
% 0.25/0.69  thf(decl_188, type, upairinpowunion: $o).
% 0.25/0.69  thf(decl_189, type, ubforcartprodlem1: $o).
% 0.25/0.69  thf(decl_190, type, ubforcartprodlem2: $o).
% 0.25/0.69  thf(decl_191, type, epred1_0: $o).
% 0.25/0.69  thf(decl_192, type, esk1_2: $i > $i > $i).
% 0.25/0.69  thf(decl_193, type, esk2_2: $i > $i > $i).
% 0.25/0.69  thf(decl_194, type, esk3_2: $i > $i > $i).
% 0.25/0.69  thf(decl_195, type, esk4_1: $i > $i).
% 0.25/0.69  thf(decl_196, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.25/0.69  thf(decl_197, type, esk6_2: ($i > $i > $o) > $i > $i).
% 0.25/0.69  thf(decl_198, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 0.25/0.69  thf(decl_199, type, esk8_1: $i > $i).
% 0.25/0.69  thf(decl_200, type, esk9_1: ($i > $o) > $i).
% 0.25/0.69  thf(decl_201, type, esk10_1: ($i > $o) > $i).
% 0.25/0.69  thf(decl_202, type, esk11_2: $i > $i > $i).
% 0.25/0.69  thf(decl_203, type, esk12_2: $i > $i > $i).
% 0.25/0.69  thf(decl_204, type, esk13_1: $i > $i).
% 0.25/0.69  thf(decl_205, type, esk14_1: $i > $i).
% 0.25/0.69  thf(decl_206, type, esk15_1: $i > $i).
% 0.25/0.69  thf(decl_207, type, esk16_2: $i > $i > $i).
% 0.25/0.69  thf(decl_208, type, esk17_3: $i > $i > $o > $i).
% 0.25/0.69  thf(decl_209, type, esk18_1: ($i > $o) > $i).
% 0.25/0.69  thf(decl_210, type, esk19_1: $i > $i).
% 0.25/0.69  thf(decl_211, type, esk20_2: $i > ($i > $o) > $i).
% 0.25/0.69  thf(decl_212, type, esk21_2: $i > ($i > $o) > $i).
% 0.25/0.69  thf(decl_213, type, esk22_2: $i > ($i > $o) > $i).
% 0.25/0.69  thf(decl_214, type, esk23_2: $i > ($i > $o) > $i).
% 0.25/0.69  thf(decl_215, type, esk24_2: $i > ($i > $o) > $i).
% 0.25/0.69  thf(decl_216, type, esk25_2: $i > ($i > $o) > $i).
% 0.25/0.69  thf(decl_217, type, esk26_2: ($i > $o) > $i > $i).
% 0.25/0.69  thf(decl_218, type, esk27_1: ($i > $o) > $i).
% 0.25/0.69  thf(decl_219, type, esk28_1: ($i > $o) > $i).
% 0.25/0.69  thf(decl_220, type, esk29_2: ($i > $o) > $i > $i).
% 0.25/0.69  thf(decl_221, type, esk30_2: ($i > $o) > ($i > $o) > $i).
% 0.25/0.69  thf(decl_222, type, esk31_2: ($i > $o) > ($i > $o) > $i).
% 0.25/0.69  thf(decl_223, type, esk32_2: ($i > $o) > ($i > $o) > $i).
% 0.25/0.69  thf(decl_224, type, esk33_2: ($i > $o) > ($i > $o) > $i).
% 0.25/0.69  thf(decl_225, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.25/0.69  thf(decl_226, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.25/0.69  thf(decl_227, type, esk36_2: $i > $i > $i).
% 0.25/0.69  thf(decl_228, type, esk37_2: $i > $i > $i).
% 0.25/0.69  thf(decl_229, type, esk38_2: $i > $i > $i).
% 0.25/0.69  thf(decl_230, type, esk39_0: $i).
% 0.25/0.69  thf(decl_231, type, esk40_0: $i).
% 0.25/0.69  thf(decl_232, type, esk41_0: $i).
% 0.25/0.69  thf(decl_233, type, esk42_0: $i).
% 0.25/0.69  thf(ubforcartprodlem3, 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)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', ubforcartprodlem3)).
% 0.25/0.69  thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', nonemptyI)).
% 0.25/0.69  thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setbeta)).
% 0.25/0.69  thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setoftrueEq)).
% 0.25/0.69  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.xl164fgHXZ/E---3.1_646864.p', exuE2)).
% 0.25/0.69  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.xl164fgHXZ/E---3.1_646864.p', emptyE1)).
% 0.25/0.69  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.xl164fgHXZ/E---3.1_646864.p', exuI2)).
% 0.25/0.69  thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', exuI3)).
% 0.25/0.69  thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', exuI1)).
% 0.25/0.69  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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', exu__Cong)).
% 0.25/0.69  thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', exuE3u)).
% 0.25/0.69  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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', dsetconstr__Cong)).
% 0.25/0.69  thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', descr__Cong)).
% 0.25/0.69  thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', exuEu)).
% 0.25/0.69  thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', sepSubset)).
% 0.25/0.69  thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', sepInPowerset)).
% 0.25/0.69  thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', exuE3e)).
% 0.25/0.69  thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', exuE1)).
% 0.25/0.69  thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', dsetconstrER)).
% 0.25/0.69  thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', dsetconstrEL)).
% 0.25/0.69  thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', dsetconstrI)).
% 0.25/0.69  thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', descrp)).
% 0.25/0.69  thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', replAx)).
% 0.25/0.69  thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setminusI)).
% 0.25/0.69  thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', bs114d)).
% 0.25/0.69  thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setminusEL)).
% 0.25/0.69  thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setminusER)).
% 0.25/0.69  thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setminusSubset2)).
% 0.25/0.69  thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setminusERneg)).
% 0.25/0.69  thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setminusELneg)).
% 0.25/0.69  thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setminusILneg)).
% 0.25/0.69  thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', emptyinunitempty)).
% 0.25/0.69  thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setminusIRneg)).
% 0.25/0.69  thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setadjoinIL)).
% 0.25/0.69  thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setminusLsub)).
% 0.25/0.69  thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', nonemptyI1)).
% 0.25/0.69  thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setminusSubset1)).
% 0.25/0.69  thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', symdiffE)).
% 0.25/0.69  thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', nonemptyE1)).
% 0.25/0.69  thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', symdiffI1)).
% 0.25/0.69  thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', symdiffI2)).
% 0.25/0.69  thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', noeltsimpempty)).
% 0.25/0.69  thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', symdiffIneg1)).
% 0.25/0.69  thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setadjoinIR)).
% 0.25/0.69  thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', symdiffIneg2)).
% 0.25/0.69  thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', secondinupair)).
% 0.25/0.69  thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setukpairIL)).
% 0.25/0.69  thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setukpairIR)).
% 0.25/0.69  thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', kpairiskpair)).
% 0.25/0.69  thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', kpairp)).
% 0.25/0.69  thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', singletonsubset)).
% 0.25/0.69  thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', singletoninpowerset)).
% 0.25/0.69  thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', singletoninpowunion)).
% 0.25/0.69  thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', upairset2E)).
% 0.25/0.69  thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', upairsubunion)).
% 0.25/0.69  thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', upairinpowunion)).
% 0.25/0.69  thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', ubforcartprodlem1)).
% 0.25/0.69  thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', ubforcartprodlem2)).
% 0.25/0.69  thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', powersetE)).
% 0.25/0.69  thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', emptyInPowerset)).
% 0.25/0.69  thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', emptyinPowerset)).
% 0.25/0.69  thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', powersetI)).
% 0.25/0.69  thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setadjoinOr)).
% 0.25/0.69  thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setadjoinE)).
% 0.25/0.69  thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setunionI)).
% 0.25/0.69  thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', eqinunit)).
% 0.25/0.69  thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', notinsingleton)).
% 0.25/0.69  thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', uniqinunit)).
% 0.25/0.69  thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', nonemptyImpWitness)).
% 0.25/0.69  thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', subPowSU)).
% 0.25/0.69  thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setunionE)).
% 0.25/0.69  thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', singletonsswitch)).
% 0.25/0.69  thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', subsetTrans)).
% 0.25/0.69  thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', subsetRefl)).
% 0.25/0.69  thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', notequalI2)).
% 0.25/0.69  thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', notequalI1)).
% 0.25/0.69  thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', notsubsetI)).
% 0.25/0.69  thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', quantDeMorgan2)).
% 0.25/0.69  thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', quantDeMorgan1)).
% 0.25/0.69  thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', vacuousDall)).
% 0.25/0.69  thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', upairsetIR)).
% 0.25/0.69  thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', upairsetIL)).
% 0.25/0.69  thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', upairsetE)).
% 0.25/0.69  thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', quantDeMorgan3)).
% 0.25/0.69  thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', notdallE)).
% 0.25/0.69  thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', notdexE)).
% 0.25/0.69  thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', prop2setI)).
% 0.25/0.69  thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', quantDeMorgan4)).
% 0.25/0.69  thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', inCongP)).
% 0.25/0.69  thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setunion__Cong)).
% 0.25/0.69  thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', powerset__Cong)).
% 0.25/0.69  thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setadjoin__Cong)).
% 0.25/0.69  thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', emptyset__Cong)).
% 0.25/0.69  thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', in__Cong)).
% 0.25/0.69  thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', omega__Cong)).
% 0.25/0.69  thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', subsetI2)).
% 0.25/0.69  thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', eqimpsubset1)).
% 0.25/0.69  thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', eqimpsubset2)).
% 0.25/0.69  thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', subsetI1)).
% 0.25/0.69  thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', emptysetsubset)).
% 0.25/0.69  thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', subsetE2)).
% 0.25/0.69  thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', subsetE)).
% 0.25/0.69  thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setadjoinSub)).
% 0.25/0.69  thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', inPowerset)).
% 0.25/0.69  thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', powersetE1)).
% 0.25/0.69  thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', powersetI1)).
% 0.25/0.69  thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', subsetemptysetimpeq)).
% 0.25/0.69  thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setextsub)).
% 0.25/0.69  thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', subset2powerset)).
% 0.25/0.69  thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setadjoinSub2)).
% 0.25/0.69  thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', powersetsubset)).
% 0.25/0.69  thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', binunionE)).
% 0.25/0.69  thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', binunionEcases)).
% 0.25/0.69  thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', binunionIR)).
% 0.25/0.69  thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', upairset2IR)).
% 0.25/0.69  thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', binunionIL)).
% 0.25/0.69  thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', binunionLsub)).
% 0.25/0.69  thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', binintersectSubset3)).
% 0.25/0.69  thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', binintersectSubset2)).
% 0.25/0.69  thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', binintersectLsub)).
% 0.25/0.69  thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', binintersectEL)).
% 0.25/0.69  thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', binintersectSubset5)).
% 0.25/0.69  thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', binintersectI)).
% 0.25/0.69  thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', binunionRsub)).
% 0.25/0.69  thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', disjointsetsI1)).
% 0.25/0.69  thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', binintersectRsub)).
% 0.25/0.69  thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', binintersectSubset4)).
% 0.25/0.69  thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', binintersectSubset1)).
% 0.25/0.69  thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', binintersectER)).
% 0.25/0.69  thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', emptyI)).
% 0.25/0.69  thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setext)).
% 0.25/0.69  thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', notinemptyset)).
% 0.25/0.69  thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', emptysetimpfalse)).
% 0.25/0.69  thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', emptysetE)).
% 0.25/0.69  thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', prop2setE)).
% 0.25/0.69  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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', wellorderingAx)).
% 0.25/0.69  thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', foundationAx)).
% 0.25/0.69  thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.xl164fgHXZ/E---3.1_646864.p', omegaIndAx)).
% 0.25/0.69  thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', omegaSAx)).
% 0.25/0.69  thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', omega0Ax)).
% 0.25/0.69  thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setunionAx)).
% 0.25/0.69  thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', powersetAx)).
% 0.25/0.69  thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setadjoinAx)).
% 0.25/0.69  thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', emptysetAx)).
% 0.25/0.69  thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', setextAx)).
% 0.25/0.69  thf(kpair, axiom, ((kpair)=(^[X2:$i, X3:$i]:(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.xl164fgHXZ/E---3.1_646864.p', kpair)).
% 0.25/0.69  thf(c_0_146, 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)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[ubforcartprodlem3])).
% 0.25/0.69  thf(c_0_147, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.25/0.69  thf(c_0_148, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.25/0.69  thf(c_0_149, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.25/0.69  thf(c_0_150, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.25/0.69  thf(c_0_151, 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])).
% 0.25/0.69  thf(c_0_152, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.25/0.69  thf(c_0_153, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.25/0.69  thf(c_0_154, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.25/0.69  thf(c_0_155, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.25/0.69  thf(c_0_156, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.25/0.69  thf(c_0_157, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.25/0.69  thf(c_0_158, plain, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.25/0.69  thf(c_0_159, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.25/0.69  thf(c_0_160, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.25/0.69  thf(c_0_161, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.25/0.69  thf(c_0_162, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.25/0.69  thf(c_0_163, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.25/0.69  thf(c_0_164, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.25/0.69  thf(c_0_165, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.25/0.69  thf(c_0_166, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.25/0.69  thf(c_0_167, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.25/0.69  thf(c_0_168, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.25/0.69  thf(c_0_169, plain, ((epred1_0)<=>![X441:$i]:(?[X442:$i]:((((![X443:$i]:(((in @ X443 @ X442)=>![X444:$i]:(((in @ X444 @ X443)=>(in @ X444 @ X441)))))&![X445:$i, X446:$i]:((((in @ X445 @ X441)&(in @ X446 @ X441))=>(![X447:$i]:(((in @ X447 @ X442)=>((in @ X445 @ X447)<=>(in @ X446 @ X447))))=>((X445)=(X446))))))&![X448:$i, X449:$i]:((((in @ X448 @ X442)&(in @ X449 @ X442))=>(![X450:$i]:(((in @ X450 @ X448)=>(in @ X450 @ X449)))|![X451:$i]:(((in @ X451 @ X449)=>(in @ X451 @ X448)))))))&![X452:$i]:(((![X453:$i]:(((in @ X453 @ X452)=>(in @ X453 @ X441)))&?[X454:$i]:((in @ X454 @ X452)))=>?[X455:$i, X456:$i]:(((((in @ X455 @ X442)&(in @ X456 @ X452))&~(?[X457:$i]:(((in @ X457 @ X455)&(in @ X457 @ X452)))))&![X458:$i]:(((in @ X458 @ X442)=>(![X459:$i]:(((in @ X459 @ X458)=>(in @ X459 @ X455)))|(in @ X456 @ X458)))))))))))), introduced(definition)).
% 0.25/0.69  thf(c_0_170, negated_conjecture, ~((![X414:$i, X415:$i]:((![X416:$i]:(((in @ X416 @ X414)<=>(in @ X416 @ X415)))=>((X414)=(X415))))=>(![X417:$i]:(~(in @ X417 @ emptyset))=>(![X418:$i, X419:$i, X420:$i]:(((in @ X420 @ (setadjoin @ X418 @ X419))<=>(((X420)=(X418))|(in @ X420 @ X419))))=>(![X421:$i, X422:$i]:(((in @ X422 @ (powerset @ X421))<=>![X423:$i]:(((in @ X423 @ X422)=>(in @ X423 @ X421)))))=>(![X424:$i, X425:$i]:(((in @ X425 @ (setunion @ X424))<=>?[X426:$i]:(((in @ X425 @ X426)&(in @ X426 @ X424)))))=>((in @ emptyset @ omega)=>(![X427:$i]:(((in @ X427 @ omega)=>(in @ (setadjoin @ X427 @ X427) @ omega)))=>(![X428:$i]:((((in @ emptyset @ X428)&![X429:$i]:((((in @ X429 @ omega)&(in @ X429 @ X428))=>(in @ (setadjoin @ X429 @ X429) @ X428))))=>![X430:$i]:(((in @ X430 @ omega)=>(in @ X430 @ X428)))))=>(![X431:$i > $i > $o, X432:$i]:((![X433:$i]:(((in @ X433 @ X432)=>(exu @ (X431 @ X433))))=>?[X434:$i]:(![X435:$i]:(((in @ X435 @ X434)<=>?[X436:$i]:(((in @ X436 @ X432)&(X431 @ X436 @ X435))))))))=>(![X437:$i]:((?[X438:$i]:((in @ X438 @ X437))=>?[X439:$i]:(((in @ X439 @ X437)&~(?[X440:$i]:(((in @ X440 @ X439)&(in @ X440 @ X437))))))))=>((epred1_0)=>(![X460:$i > $o]:(((exu @ X460)=>(X460 @ (descr @ (^[Z0:$i]:(X460 @ Z0))))))=>(![X461:$i, X462:$i > $o, X463:$i]:(((in @ X463 @ X461)=>((X462 @ X463)=>(in @ X463 @ (dsetconstr @ X461 @ X462)))))=>(![X464:$i, X465:$i > $o, X466:$i]:(((in @ X466 @ (dsetconstr @ X464 @ X465))=>(in @ X466 @ X464)))=>(![X467:$i, X468:$i > $o, X469:$i]:(((in @ X469 @ (dsetconstr @ X467 @ X468))=>(X468 @ X469)))=>(![X470:$i > $o]:(((exu @ X470)=>?[X471:$i]:(((X470 @ X471)&![X472:$i]:(((X470 @ X472)=>((X471)=(X472))))))))=>(![X473:$o, X474:$i]:(((in @ X474 @ (prop2set @ ((X473))))=>(X473)))=>(![X475:$i]:(((in @ X475 @ emptyset)=>![X476:$o]:((X476))))=>(![X477:$i]:(((in @ X477 @ emptyset)=>~($true)))=>(![X478:$i]:(~(in @ X478 @ emptyset))=>(![X479:$i > $o]:(((exu @ X479)=>?[X480:$i]:((X479 @ X480))))=>(![X481:$i, X482:$i]:((![X483:$i]:(((in @ X483 @ X481)=>(in @ X483 @ X482)))=>(![X484:$i]:(((in @ X484 @ X482)=>(in @ X484 @ X481)))=>((X481)=(X482)))))=>(![X485:$i]:((![X486:$i]:(~(in @ X486 @ X485))=>((X485)=(emptyset))))=>(![X487:$i]:((![X488:$i]:(~(in @ X488 @ X487))=>((X487)=(emptyset))))=>(![X489:$i, X490:$i > $o, X491:$i]:(((in @ X491 @ X489)=>((in @ X491 @ (dsetconstr @ X489 @ X490))<=>(X490 @ X491))))=>(![X492:$i]:(((nonempty @ X492)=>?[X493:$i]:((in @ X493 @ X492))))=>(![X494:$i, X495:$i > $o, X496:$i]:(((in @ X496 @ X494)=>((X495 @ X496)=>(nonempty @ (dsetconstr @ X494 @ X495)))))=>(![X497:$i]:((?[X498:$i]:((in @ X498 @ X497))=>(nonempty @ X497)))=>(![X499:$i, X500:$i]:((in @ X499 @ (setadjoin @ X499 @ X500)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X501:$i, X502:$i, X503:$i]:(((in @ X503 @ X502)=>(in @ X503 @ (setadjoin @ X501 @ X502))))=>(![X504:$i, X505:$i, X506:$i]:(((in @ X506 @ (setadjoin @ X504 @ X505))=>![X507:$o]:(((((X506)=(X504))=>(X507))=>(((in @ X506 @ X505)=>(X507))=>(X507))))))=>(![X508:$i, X509:$i, X510:$i]:(((in @ X510 @ (setadjoin @ X508 @ X509))=>(((X510)=(X508))|(in @ X510 @ X509))))=>(![X511:$i]:(((dsetconstr @ X511 @ (^[Z0:$i]:($true)))=(X511)))=>(![X512:$i, X513:$i]:((![X514:$i]:(((in @ X514 @ X513)=>(in @ X514 @ X512)))=>(in @ X513 @ (powerset @ X512))))=>(![X515:$i]:((in @ emptyset @ (powerset @ X515)))=>(![X516:$i]:((in @ emptyset @ (powerset @ X516)))=>(![X517:$i, X518:$i, X519:$i]:(((in @ X518 @ (powerset @ X517))=>((in @ X519 @ X518)=>(in @ X519 @ X517))))=>(![X520:$i, X521:$i, X522:$i]:(((in @ X521 @ X522)=>((in @ X522 @ X520)=>(in @ X521 @ (setunion @ X520)))))=>(![X523:$i, X524:$i]:(((in @ X524 @ (setunion @ X523))=>![X525:$o]:((![X526:$i]:(((in @ X524 @ X526)=>((in @ X526 @ X523)=>(X525))))=>(X525)))))=>(![X527:$i, X528:$i]:(((in @ X528 @ X527)=>(in @ X528 @ (powerset @ (setunion @ X527)))))=>(![X529:$i > $o]:(((exu @ X529)=>?[X530:$i]:(![X531:$i]:(((X529 @ X531)<=>((X531)=(X530)))))))=>(![X532:$i]:(((nonempty @ X532)=>?[X533:$i]:(((in @ X533 @ X532)&$true))))=>(![X534:$i, X535:$i]:(((in @ X534 @ (setadjoin @ X535 @ emptyset))=>((X534)=(X535))))=>(![X536:$i, X537:$i]:((((X536)!=(X537))=>~(in @ X537 @ (setadjoin @ X536 @ emptyset))))=>(![X538:$i, X539:$i]:((((X538)=(X539))=>(in @ X538 @ (setadjoin @ X539 @ emptyset))))=>(![X540:$i, X541:$i]:(((in @ X540 @ (setadjoin @ X541 @ emptyset))=>(in @ X541 @ (setadjoin @ X540 @ emptyset))))=>(![X542:$i, X543:$i, X544:$i]:(((in @ X544 @ (setadjoin @ X542 @ (setadjoin @ X543 @ emptyset)))=>(((X544)=(X542))|((X544)=(X543)))))=>(![X545:$i, X546:$i]:((in @ X545 @ (setadjoin @ X545 @ (setadjoin @ X546 @ emptyset))))=>(![X547:$i, X548:$i]:((in @ X548 @ (setadjoin @ X547 @ (setadjoin @ X548 @ emptyset))))=>(![X549:$i, X550:$i > $o]:((?[X551:$i]:(((in @ X551 @ X549)&(X550 @ X551)))=>(((dsetconstr @ X549 @ X550)=(emptyset))=>~($true))))=>(![X552:$i > $o, X553:$i]:(((in @ X553 @ emptyset)=>(X552 @ X553)))=>(![X554:$i, X555:$i > $o]:((~(![X556:$i]:(((in @ X556 @ X554)=>(X555 @ X556))))=>?[X557:$i]:(((in @ X557 @ X554)&~((X555 @ X557))))))=>(![X558:$i, X559:$i > $o]:((![X560:$i]:(((in @ X560 @ X558)=>~((X559 @ X560))))=>~(?[X561:$i]:(((in @ X561 @ X558)&(X559 @ X561))))))=>(![X562:$i, X563:$i > $o]:((~(?[X564:$i]:(((in @ X564 @ X562)&(X563 @ X564))))=>![X565:$i]:(((in @ X565 @ X562)=>~((X563 @ X565))))))=>(![X566:$i, X567:$i > $o]:((?[X568:$i]:(((in @ X568 @ X566)&~((X567 @ X568))))=>~(![X569:$i]:(((in @ X569 @ X566)=>(X567 @ X569))))))=>(![X570:$o]:(((X570)=>(in @ emptyset @ (prop2set @ ((X570))))))=>((prop2set2propI)=>(![X571:$i, X572:$i > $o]:((~(?[X573:$i]:(((in @ X573 @ X571)&(X572 @ X573))))=>![X574:$i]:(((in @ X574 @ X571)=>~((X572 @ X574))))))=>(![X575:$i, X576:$i > $o]:((~(![X577:$i]:(((in @ X577 @ X575)=>(X576 @ X577))))=>?[X578:$i]:(((in @ X578 @ X575)&~((X576 @ X578))))))=>(![X579:$i > $o]:((?[X580:$i]:(((X579 @ X580)&![X581:$i]:(((X579 @ X581)=>((X580)=(X581))))))=>(exu @ X579)))=>(![X582:$i > $o]:((?[X583:$i]:((X582 @ X583))=>(![X584:$i, X585:$i]:(((X582 @ X584)=>((X582 @ X585)=>((X584)=(X585)))))=>(exu @ X582))))=>(![X586:$i > $o]:((?[X587:$i]:(![X588:$i]:(((X586 @ X588)<=>((X588)=(X587)))))=>(exu @ X586)))=>(![X589:$i, X590:$i]:((((X589)=(X590))=>![X591:$i, X592:$i]:((((X591)=(X592))=>((in @ X591 @ X589)=>(in @ X592 @ X590))))))=>(![X593:$i, X594:$i]:((((X593)=(X594))=>![X595:$i, X596:$i]:((((X595)=(X596))=>((in @ X595 @ X593)<=>(in @ X596 @ X594))))))=>(![X597:$i > $o]:(((exu @ X597)=>![X598:$i, X599:$i]:(((X597 @ X598)=>((X597 @ X599)=>((X598)=(X599)))))))=>(![X600:$i > $o, X601:$i > $o]:((![X602:$i, X603:$i]:((((X602)=(X603))=>((X600 @ X602)<=>(X601 @ X603))))=>((exu @ X600)<=>(exu @ X601))))=>(((emptyset)=(emptyset))=>(![X604:$i, X605:$i]:((((X604)=(X605))=>![X606:$i, X607:$i]:((((X606)=(X607))=>((setadjoin @ X604 @ X606)=(setadjoin @ X605 @ X607))))))=>(![X608:$i, X609:$i]:((((X608)=(X609))=>((powerset @ X608)=(powerset @ X609))))=>(![X610:$i, X611:$i]:((((X610)=(X611))=>((setunion @ X610)=(setunion @ X611))))=>(((omega)=(omega))=>(![X612:$i > $o]:(((exu @ X612)=>![X613:$i, X614:$i]:(((X612 @ X613)=>((X612 @ X614)=>((X613)=(X614)))))))=>(![X615:$i > $o, X616:$i > $o]:((![X617:$i, X618:$i]:((((X617)=(X618))=>((X615 @ X617)<=>(X616 @ X618))))=>((exu @ X615)=>((exu @ X616)=>((descr @ X615)=(descr @ X616))))))=>(![X619:$i, X620:$i]:((((X619)=(X620))=>![X621:$i > $o, X622:$i > $o]:((![X623:$i]:(((in @ X623 @ X619)=>![X624:$i]:(((in @ X624 @ X620)=>(((X623)=(X624))=>((X621 @ X623)<=>(X622 @ X624)))))))=>((dsetconstr @ X619 @ X621)=(dsetconstr @ X620 @ X622))))))=>(![X625:$i, X626:$i]:((![X627:$i]:(((in @ X627 @ X625)=>(in @ X627 @ X626)))=>(subset @ X625 @ X626)))=>(![X628:$i, X629:$i]:((((X628)=(X629))=>(subset @ X629 @ X628)))=>(![X630:$i, X631:$i]:((((X630)=(X631))=>(subset @ X630 @ X631)))=>(![X632:$i, X633:$i]:((![X634:$i]:(((in @ X634 @ X632)=>(in @ X634 @ X633)))=>(subset @ X632 @ X633)))=>(![X635:$i]:((subset @ emptyset @ X635))=>(![X636:$i, X637:$i, X638:$i]:(((subset @ X636 @ X637)=>((in @ X638 @ X636)=>(in @ X638 @ X637))))=>(![X639:$i, X640:$i, X641:$i]:(((subset @ X639 @ X640)=>(~(in @ X641 @ X640)=>~(in @ X641 @ X639))))=>(![X642:$i, X643:$i, X644:$i]:(((in @ X644 @ X642)=>(~(in @ X644 @ X643)=>~(subset @ X642 @ X643))))=>(![X645:$i, X646:$i]:((~(subset @ X645 @ X646)=>((X645)!=(X646))))=>(![X647:$i, X648:$i, X649:$i]:(((in @ X649 @ X647)=>(~(in @ X649 @ X648)=>((X647)!=(X648)))))=>(![X650:$i]:((subset @ X650 @ X650))=>(![X651:$i, X652:$i, X653:$i]:(((subset @ X651 @ X652)=>((subset @ X652 @ X653)=>(subset @ X651 @ X653))))=>(![X654:$i, X655:$i]:((subset @ X655 @ (setadjoin @ X654 @ X655)))=>(![X656:$i, X657:$i, X658:$i]:(((subset @ X656 @ X658)=>(subset @ X656 @ (setadjoin @ X657 @ X658))))=>(![X659:$i, X660:$i]:(((subset @ X659 @ X660)=>(in @ X659 @ (powerset @ X660))))=>(![X661:$i, X662:$i]:(((subset @ X661 @ X662)=>((subset @ X662 @ X661)=>((X661)=(X662)))))=>(![X663:$i]:(((subset @ X663 @ emptyset)=>((X663)=(emptyset))))=>(![X664:$i, X665:$i]:(((subset @ X665 @ X664)=>(in @ X665 @ (powerset @ X664))))=>(![X666:$i, X667:$i]:(((in @ X667 @ (powerset @ X666))=>(subset @ X667 @ X666)))=>(![X668:$i]:((in @ X668 @ (powerset @ X668)))=>(![X669:$i, X670:$i]:(((subset @ X669 @ X670)=>(subset @ (powerset @ X669) @ (powerset @ X670))))=>(![X671:$i, X672:$i > $o]:((in @ (dsetconstr @ X671 @ X672) @ (powerset @ X671)))=>(![X673:$i, X674:$i > $o]:((subset @ (dsetconstr @ X673 @ X674) @ X673))=>(![X675:$i, X676:$i, X677:$i]:(((in @ X677 @ X675)=>(in @ X677 @ (binunion @ X675 @ X676))))=>(![X678:$i, X679:$i]:((in @ X679 @ (setadjoin @ X678 @ (setadjoin @ X679 @ emptyset))))=>(![X680:$i, X681:$i, X682:$i]:(((in @ X682 @ X681)=>(in @ X682 @ (binunion @ X680 @ X681))))=>(![X683:$i, X684:$i, X685:$i, X686:$o]:(((in @ X685 @ (binunion @ X683 @ X684))=>(((in @ X685 @ X683)=>(X686))=>(((in @ X685 @ X684)=>(X686))=>(X686)))))=>(![X687:$i, X688:$i, X689:$i]:(((in @ X689 @ (binunion @ X687 @ X688))=>((in @ X689 @ X687)|(in @ X689 @ X688))))=>(![X690:$i, X691:$i]:((subset @ X690 @ (binunion @ X690 @ X691)))=>(![X692:$i, X693:$i]:((subset @ X693 @ (binunion @ X692 @ X693)))=>(![X694:$i, X695:$i, X696:$i]:(((in @ X696 @ X694)=>((in @ X696 @ X695)=>(in @ X696 @ (binintersect @ X694 @ X695)))))=>(![X697:$i, X698:$i, X699:$i]:(((subset @ X699 @ X697)=>((subset @ X699 @ X698)=>(subset @ X699 @ (binintersect @ X697 @ X698)))))=>(![X700:$i, X701:$i, X702:$i]:(((in @ X702 @ (binintersect @ X700 @ X701))=>(in @ X702 @ X700)))=>(![X703:$i, X704:$i]:((subset @ (binintersect @ X703 @ X704) @ X703))=>(![X705:$i, X706:$i]:(((subset @ X705 @ X706)=>((binintersect @ X705 @ X706)=(X705))))=>(![X707:$i, X708:$i]:((((binintersect @ X707 @ X708)=(X708))=>(subset @ X708 @ X707)))=>(![X709:$i, X710:$i, X711:$i]:(((in @ X711 @ (binintersect @ X709 @ X710))=>(in @ X711 @ X710)))=>(![X712:$i, X713:$i]:((~(?[X714:$i]:(((in @ X714 @ X712)&(in @ X714 @ X713))))=>((binintersect @ X712 @ X713)=(emptyset))))=>(![X715:$i, X716:$i]:((subset @ (binintersect @ X715 @ X716) @ X716))=>(![X717:$i, X718:$i]:(((subset @ X718 @ X717)=>((binintersect @ X717 @ X718)=(X718))))=>(![X719:$i, X720:$i]:((((binintersect @ X719 @ X720)=(X719))=>(subset @ X719 @ X720)))=>(![X721:$i, X722:$i, X723:$i]:(((binintersect @ X721 @ (binunion @ X722 @ X723))=(binunion @ (binintersect @ X721 @ X722) @ (binintersect @ X721 @ X723))))=>(![X724:$i, X725:$i, X726:$i]:(((in @ X726 @ X724)=>(~(in @ X726 @ X725)=>(in @ X726 @ (setminus @ X724 @ X725)))))=>(![X727:$i, X728:$i, X729:$i]:(((in @ X729 @ (setminus @ X727 @ X728))=>(in @ X729 @ X727)))=>(![X730:$i, X731:$i, X732:$i]:(((in @ X732 @ (setminus @ X730 @ X731))=>~(in @ X732 @ X731)))=>(![X733:$i, X734:$i]:(((subset @ X733 @ X734)=>((setminus @ X733 @ X734)=(emptyset))))=>(![X735:$i, X736:$i, X737:$i]:((~(in @ X737 @ (setminus @ X735 @ X736))=>((in @ X737 @ X735)=>(in @ X737 @ X736))))=>(![X738:$i, X739:$i, X740:$i]:((~(in @ X740 @ (setminus @ X738 @ X739))=>(~(in @ X740 @ X739)=>~(in @ X740 @ X738))))=>(![X741:$i, X742:$i, X743:$i]:((~(in @ X743 @ X741)=>~(in @ X743 @ (setminus @ X741 @ X742))))=>(![X744:$i, X745:$i, X746:$i]:(((in @ X746 @ X745)=>~(in @ X746 @ (setminus @ X744 @ X745))))=>(![X747:$i, X748:$i]:((subset @ (setminus @ X747 @ X748) @ X747))=>(![X749:$i, X750:$i]:((((setminus @ X749 @ X750)=(emptyset))=>(subset @ X749 @ X750)))=>(![X751:$i, X752:$i, X753:$i]:(((in @ X753 @ (symdiff @ X751 @ X752))=>![X754:$o]:((((in @ X753 @ X751)=>(~(in @ X753 @ X752)=>(X754)))=>((~(in @ X753 @ X751)=>((in @ X753 @ X752)=>(X754)))=>(X754))))))=>(![X755:$i, X756:$i, X757:$i]:(((in @ X757 @ X755)=>(~(in @ X757 @ X756)=>(in @ X757 @ (symdiff @ X755 @ X756)))))=>(![X758:$i, X759:$i, X760:$i]:((~(in @ X760 @ X758)=>((in @ X760 @ X759)=>(in @ X760 @ (symdiff @ X758 @ X759)))))=>(![X761:$i, X762:$i, X763:$i]:(((in @ X763 @ X761)=>((in @ X763 @ X762)=>~(in @ X763 @ (symdiff @ X761 @ X762)))))=>(![X764:$i, X765:$i, X766:$i]:((~(in @ X766 @ X764)=>(~(in @ X766 @ X765)=>~(in @ X766 @ (symdiff @ X764 @ X765)))))=>(![X767:$i, X768:$i]:((in @ X768 @ (setadjoin @ X767 @ (setadjoin @ X768 @ emptyset))))=>(![X769:$i, X770:$i]:((in @ X769 @ (setunion @ (setadjoin @ (setadjoin @ X769 @ emptyset) @ (setadjoin @ (setadjoin @ X769 @ (setadjoin @ X770 @ emptyset)) @ emptyset)))))=>(![X771:$i, X772:$i]:((in @ X772 @ (setunion @ (setadjoin @ (setadjoin @ X771 @ emptyset) @ (setadjoin @ (setadjoin @ X771 @ (setadjoin @ X772 @ emptyset)) @ emptyset)))))=>(![X773:$i, X774:$i]:((iskpair @ (setadjoin @ (setadjoin @ X773 @ emptyset) @ (setadjoin @ (setadjoin @ X773 @ (setadjoin @ X774 @ emptyset)) @ emptyset))))=>(![X775:$i, X776:$i]:((iskpair @ (kpair @ X775 @ X776)))=>(![X777:$i, X778:$i]:(((in @ X778 @ X777)=>(subset @ (setadjoin @ X778 @ emptyset) @ X777)))=>(![X779:$i, X780:$i]:(((in @ X780 @ X779)=>(in @ (setadjoin @ X780 @ emptyset) @ (powerset @ X779))))=>(![X781:$i, X782:$i, X783:$i]:(((in @ X783 @ X781)=>(in @ (setadjoin @ X783 @ emptyset) @ (powerset @ (binunion @ X781 @ X782)))))=>(![X784:$i, X785:$i, X786:$i]:(((in @ X786 @ (setadjoin @ X784 @ (setadjoin @ X785 @ emptyset)))=>(((X786)=(X784))|((X786)=(X785)))))=>(![X787:$i, X788:$i, X789:$i]:(((in @ X789 @ X787)=>![X790:$i]:(((in @ X790 @ X788)=>(subset @ (setadjoin @ X789 @ (setadjoin @ X790 @ emptyset)) @ (binunion @ X787 @ X788))))))=>(![X791:$i, X792:$i, X793:$i]:(((in @ X793 @ X791)=>![X794:$i]:(((in @ X794 @ X792)=>(in @ (setadjoin @ X793 @ (setadjoin @ X794 @ emptyset)) @ (powerset @ (binunion @ X791 @ X792)))))))=>(![X795:$i, X796:$i, X797:$i]:(((in @ X797 @ X795)=>![X798:$i]:(((in @ X798 @ X796)=>(subset @ (setadjoin @ (setadjoin @ X797 @ emptyset) @ (setadjoin @ (setadjoin @ X797 @ (setadjoin @ X798 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X795 @ X796)))))))=>(![X799:$i, X800:$i, X801:$i]:(((in @ X801 @ X799)=>![X802:$i]:(((in @ X802 @ X800)=>(in @ (setadjoin @ (setadjoin @ X801 @ emptyset) @ (setadjoin @ (setadjoin @ X801 @ (setadjoin @ X802 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X799 @ X800))))))))=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[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_146, setminusI]), bs114d]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), emptyinunitempty]), setminusIRneg]), setadjoinIL]), setminusLsub]), nonemptyI1]), setminusSubset1]), c_0_147]), symdiffE]), nonemptyE1]), symdiffI1]), c_0_148]), symdiffI2]), noeltsimpempty]), symdiffIneg1]), setadjoinIR]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_149]), setadjoinOr]), setadjoinE]), setunionI]), eqinunit]), notinsingleton]), uniqinunit]), nonemptyImpWitness]), c_0_150]), subPowSU]), setunionE]), singletonsswitch]), subsetTrans]), subsetRefl]), notequalI2]), notequalI1]), notsubsetI]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_151]), upairsetIR]), upairsetIL]), upairsetE]), quantDeMorgan3]), c_0_152]), c_0_153]), c_0_154]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), inCongP]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_155]), c_0_156]), in__Cong]), omega__Cong]), subsetI2]), eqimpsubset1]), eqimpsubset2]), subsetI1]), c_0_157]), c_0_158]), c_0_159]), emptysetsubset]), subsetE2]), subsetE]), setadjoinSub]), inPowerset]), powersetE1]), powersetI1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), setadjoinSub2]), powersetsubset]), binunionE]), binunionEcases]), binunionIR]), upairset2IR]), binunionIL]), c_0_160]), c_0_161]), binunionLsub]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectI]), binunionRsub]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), binintersectER]), emptyI]), setext]), c_0_162]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_163]), c_0_164]), c_0_165]), c_0_166]), c_0_167]), wellorderingAx]), foundationAx]), c_0_168]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_169])).
% 0.25/0.69  thf(c_0_171, plain, ![X803:$i, X804:$i]:(((kpair @ X803 @ X804)=(setadjoin @ (setadjoin @ X803 @ emptyset) @ (setadjoin @ (setadjoin @ X803 @ (setadjoin @ X804 @ emptyset)) @ emptyset)))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])])).
% 0.25/0.69  thf(c_0_172, negated_conjecture, ![X805:$i, X806:$i, X808:$i, X809:$i, X810:$i, X811:$i, X812:$i, X813:$i, X814:$i, X815:$i, X816:$i, X818:$i, X819:$i, X821:$i, X822:$i, X823:$i, X824:$i, X825:$i, X827:$i, X828:$i > $i > $o, X829:$i, X832:$i, X834:$i, X835:$i, X836:$i, X837:$i, X839:$i, X840:$i > $o, X841:$i, X842:$i > $o, X843:$i, X844:$i, X845:$i > $o, X846:$i, X847:$i, X848:$i > $o, X849:$i, X850:$i > $o, X852:$i, X853:$o, X854:$i, X855:$i, X856:$o, X857:$i, X858:$i, X859:$i > $o, X861:$i, X862:$i, X865:$i, X867:$i, X869:$i, X870:$i > $o, X871:$i, X872:$i, X874:$i, X875:$i > $o, X876:$i, X877:$i, X878:$i, X879:$i, X880:$i, X881:$i, X882:$i, X883:$i, X884:$i, X885:$i, X886:$i, X887:$o, X888:$i, X889:$i, X890:$i, X891:$i, X892:$i, X893:$i, X895:$i, X896:$i, X897:$i, X898:$i, X899:$i, X900:$i, X901:$i, X902:$i, X903:$i, X904:$i, X905:$o, X907:$i, X908:$i, X909:$i > $o, X911:$i, X912:$i, X913:$i, X915:$i, X916:$i, X917:$i, X918:$i, X919:$i, X920:$i, X921:$i, X922:$i, X923:$i, X924:$i, X925:$i, X926:$i, X927:$i, X928:$i, X929:$i, X930:$i, X931:$i > $o, X932:$i, X933:$i > $o, X934:$i, X935:$i, X936:$i > $o, X937:$i, X939:$i, X940:$i > $o, X942:$i, X943:$i, X944:$i > $o, X946:$i, X947:$i, X948:$i > $o, X949:$i, X951:$o, X952:$i, X953:$i > $o, X955:$i, X956:$i, X957:$i > $o, X958:$i, X960:$i > $o, X961:$i, X963:$i > $o, X964:$i, X967:$i > $o, X968:$i, X970:$i, X971:$i, X972:$i, X973:$i, X974:$i, X975:$i, X976:$i, X977:$i, X978:$i > $o, X979:$i, X980:$i, X981:$i > $o, X982:$i > $o, X985:$i, X986:$i, X987:$i, X988:$i, X989:$i, X990:$i, X991:$i, X992:$i, X993:$i > $o, X994:$i, X995:$i, X996:$i > $o, X997:$i > $o, X1000:$i, X1001:$i, X1002:$i > $o, X1003:$i > $o, X1006:$i, X1007:$i, X1009:$i, X1010:$i, X1011:$i, X1012:$i, X1013:$i, X1014:$i, X1016:$i, X1017:$i, X1018:$i, X1019:$i, X1020:$i, X1021:$i, X1022:$i, X1023:$i, X1024:$i, X1025:$i, X1026:$i, X1027:$i, X1028:$i, X1029:$i, X1030:$i, X1031:$i, X1032:$i, X1033:$i, X1034:$i, X1035:$i, X1036:$i, X1037:$i, X1038:$i, X1039:$i, X1040:$i, X1041:$i, X1042:$i, X1043:$i, X1044:$i, X1045:$i, X1046:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$i, X1053:$i > $o, X1054:$i, X1055:$i > $o, X1056:$i, X1057:$i, X1058:$i, X1059:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i, X1064:$i, X1065:$i, X1066:$i, X1067:$o, X1068:$i, X1069:$i, X1070:$i, X1071:$i, X1072:$i, X1073:$i, X1074:$i, X1075:$i, X1076:$i, X1077:$i, X1078:$i, X1079:$i, X1080:$i, X1081:$i, X1082:$i, X1083:$i, X1084:$i, X1085:$i, X1086:$i, X1087:$i, X1088:$i, X1089:$i, X1090:$i, X1091:$i, X1092:$i, X1093:$i, X1094:$i, X1096:$i, X1097:$i, X1098:$i, X1099:$i, X1100:$i, X1101:$i, X1102:$i, X1103:$i, X1104:$i, X1105:$i, X1106:$i, X1107:$i, X1108:$i, X1109:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1114:$i, X1115:$i, X1116:$i, X1117:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i, X1126:$i, X1127:$i, X1128:$i, X1129:$i, X1130:$i, X1131:$i, X1132:$i, X1133:$i, X1134:$i, X1135:$o, X1136:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1147:$i, X1148:$i, X1149:$i, X1150:$i, X1151:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$i, X1162:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$i, X1171:$i, X1172:$i, X1173:$i, X1174:$i, X1175:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i]:((((~(in @ (esk1_2 @ X805 @ X806) @ X805)|~(in @ (esk1_2 @ X805 @ X806) @ X806)|((X805)=(X806)))&((in @ (esk1_2 @ X805 @ X806) @ X805)|(in @ (esk1_2 @ X805 @ X806) @ X806)|((X805)=(X806))))&(~(in @ X808 @ emptyset)&(((~(in @ X811 @ (setadjoin @ X809 @ X810))|(((X811)=(X809))|(in @ X811 @ X810)))&((((X811)!=(X809))|(in @ X811 @ (setadjoin @ X809 @ X810)))&(~(in @ X811 @ X810)|(in @ X811 @ (setadjoin @ X809 @ X810)))))&(((~(in @ X813 @ (powerset @ X812))|(~(in @ X814 @ X813)|(in @ X814 @ X812)))&(((in @ (esk2_2 @ X815 @ X816) @ X816)|(in @ X816 @ (powerset @ X815)))&(~(in @ (esk2_2 @ X815 @ X816) @ X815)|(in @ X816 @ (powerset @ X815)))))&(((((in @ X819 @ (esk3_2 @ X818 @ X819))|~(in @ X819 @ (setunion @ X818)))&((in @ (esk3_2 @ X818 @ X819) @ X818)|~(in @ X819 @ (setunion @ X818))))&(~(in @ X822 @ X823)|~(in @ X823 @ X821)|(in @ X822 @ (setunion @ X821))))&((in @ emptyset @ omega)&((~(in @ X824 @ omega)|(in @ (setadjoin @ X824 @ X824) @ omega))&(((((in @ (esk4_1 @ X825) @ omega)|~(in @ emptyset @ X825)|(~(in @ X827 @ omega)|(in @ X827 @ X825)))&((in @ (esk4_1 @ X825) @ X825)|~(in @ emptyset @ X825)|(~(in @ X827 @ omega)|(in @ X827 @ X825))))&(~(in @ (setadjoin @ (esk4_1 @ X825) @ (esk4_1 @ X825)) @ X825)|~(in @ emptyset @ X825)|(~(in @ X827 @ omega)|(in @ X827 @ X825))))&((((((in @ (esk7_3 @ X828 @ X829 @ X832) @ X829)|~(in @ X832 @ (esk6_2 @ X828 @ X829))|(in @ (esk5_2 @ X828 @ X829) @ X829))&((X828 @ (esk7_3 @ X828 @ X829 @ X832) @ X832)|~(in @ X832 @ (esk6_2 @ X828 @ X829))|(in @ (esk5_2 @ X828 @ X829) @ X829)))&(~(in @ X835 @ X829)|~(X828 @ X835 @ X834)|(in @ X834 @ (esk6_2 @ X828 @ X829))|(in @ (esk5_2 @ X828 @ X829) @ X829)))&((((in @ (esk7_3 @ X828 @ X829 @ X832) @ X829)|~(in @ X832 @ (esk6_2 @ X828 @ X829))|~(exu @ (X828 @ (esk5_2 @ X828 @ X829))))&((X828 @ (esk7_3 @ X828 @ X829 @ X832) @ X832)|~(in @ X832 @ (esk6_2 @ X828 @ X829))|~(exu @ (X828 @ (esk5_2 @ X828 @ X829)))))&(~(in @ X835 @ X829)|~(X828 @ X835 @ X834)|(in @ X834 @ (esk6_2 @ X828 @ X829))|~(exu @ (X828 @ (esk5_2 @ X828 @ X829))))))&((((in @ (esk8_1 @ X836) @ X836)|~(in @ X837 @ X836))&(~(in @ X839 @ (esk8_1 @ X836))|~(in @ X839 @ X836)|~(in @ X837 @ X836)))&((epred1_0)&((~(exu @ X840)|(X840 @ (descr @ X840)))&((~(in @ X843 @ X841)|(~(X842 @ X843)|(in @ X843 @ (dsetconstr @ X841 @ X842))))&((~(in @ X846 @ (dsetconstr @ X844 @ X845))|(in @ X846 @ X844))&((~(in @ X849 @ (dsetconstr @ X847 @ X848))|(X848 @ X849))&((((X850 @ (esk9_1 @ X850))|~(exu @ X850))&(~(X850 @ X852)|((esk9_1 @ X850)=(X852))|~(exu @ X850)))&((~(in @ X854 @ (prop2set @ ((X853))))|(X853))&((~(in @ X855 @ emptyset)|(X856))&((~(in @ X857 @ emptyset)|~($true))&(~(in @ X858 @ emptyset)&((~(exu @ X859)|(X859 @ (esk10_1 @ X859)))&(((((in @ (esk12_2 @ X861 @ X862) @ X862)|((X861)=(X862))|(in @ (esk11_2 @ X861 @ X862) @ X861))&(~(in @ (esk12_2 @ X861 @ X862) @ X861)|((X861)=(X862))|(in @ (esk11_2 @ X861 @ X862) @ X861)))&(((in @ (esk12_2 @ X861 @ X862) @ X862)|((X861)=(X862))|~(in @ (esk11_2 @ X861 @ X862) @ X862))&(~(in @ (esk12_2 @ X861 @ X862) @ X861)|((X861)=(X862))|~(in @ (esk11_2 @ X861 @ X862) @ X862))))&(((in @ (esk13_1 @ X865) @ X865)|((X865)=(emptyset)))&(((in @ (esk14_1 @ X867) @ X867)|((X867)=(emptyset)))&(((~(in @ X871 @ (dsetconstr @ X869 @ X870))|(X870 @ X871)|~(in @ X871 @ X869))&(~(X870 @ X871)|(in @ X871 @ (dsetconstr @ X869 @ X870))|~(in @ X871 @ X869)))&((~(nonempty @ X872)|(in @ (esk15_1 @ X872) @ X872))&((~(in @ X876 @ X874)|(~(X875 @ X876)|(nonempty @ (dsetconstr @ X874 @ X875))))&((~(in @ X878 @ X877)|(nonempty @ X877))&((in @ X879 @ (setadjoin @ X879 @ X880))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X883 @ X882)|(in @ X883 @ (setadjoin @ X881 @ X882)))&(((((in @ X886 @ X885)|(X887)|((X886)=(X884))|~(in @ X886 @ (setadjoin @ X884 @ X885)))&(~(X887)|(X887)|((X886)=(X884))|~(in @ X886 @ (setadjoin @ X884 @ X885))))&(((in @ X886 @ X885)|(X887)|~(X887)|~(in @ X886 @ (setadjoin @ X884 @ X885)))&(~(X887)|(X887)|~(X887)|~(in @ X886 @ (setadjoin @ X884 @ X885)))))&((~(in @ X890 @ (setadjoin @ X888 @ X889))|(((X890)=(X888))|(in @ X890 @ X889)))&(((dsetconstr @ X891 @ (^[Z0:$i]:($true)))=(X891))&((((in @ (esk16_2 @ X892 @ X893) @ X893)|(in @ X893 @ (powerset @ X892)))&(~(in @ (esk16_2 @ X892 @ X893) @ X892)|(in @ X893 @ (powerset @ X892))))&((in @ emptyset @ (powerset @ X895))&((in @ emptyset @ (powerset @ X896))&((~(in @ X898 @ (powerset @ X897))|(~(in @ X899 @ X898)|(in @ X899 @ X897)))&((~(in @ X901 @ X902)|(~(in @ X902 @ X900)|(in @ X901 @ (setunion @ X900))))&((((in @ X904 @ (esk17_3 @ X903 @ X904 @ X905))|(X905)|~(in @ X904 @ (setunion @ X903)))&(((in @ (esk17_3 @ X903 @ X904 @ X905) @ X903)|(X905)|~(in @ X904 @ (setunion @ X903)))&(~(X905)|(X905)|~(in @ X904 @ (setunion @ X903)))))&((~(in @ X908 @ X907)|(in @ X908 @ (powerset @ (setunion @ X907))))&(((~(X909 @ X911)|((X911)=(esk18_1 @ X909))|~(exu @ X909))&(((X912)!=(esk18_1 @ X909))|(X909 @ X912)|~(exu @ X909)))&((((in @ (esk19_1 @ X913) @ X913)|~(nonempty @ X913))&(($true)|~(nonempty @ X913)))&((~(in @ X915 @ (setadjoin @ X916 @ emptyset))|((X915)=(X916)))&((((X917)=(X918))|~(in @ X918 @ (setadjoin @ X917 @ emptyset)))&((((X919)!=(X920))|(in @ X919 @ (setadjoin @ X920 @ emptyset)))&((~(in @ X921 @ (setadjoin @ X922 @ emptyset))|(in @ X922 @ (setadjoin @ X921 @ emptyset)))&((~(in @ X925 @ (setadjoin @ X923 @ (setadjoin @ X924 @ emptyset)))|(((X925)=(X923))|((X925)=(X924))))&((in @ X926 @ (setadjoin @ X926 @ (setadjoin @ X927 @ emptyset)))&((in @ X929 @ (setadjoin @ X928 @ (setadjoin @ X929 @ emptyset)))&((~(in @ X932 @ X930)|~(X931 @ X932)|(((dsetconstr @ X930 @ X931)!=(emptyset))|~($true)))&((~(in @ X934 @ emptyset)|(X933 @ X934))&((((in @ (esk20_2 @ X935 @ X936) @ X935)|(~(in @ X937 @ X935)|(X936 @ X937)))&(~(X936 @ (esk20_2 @ X935 @ X936))|(~(in @ X937 @ X935)|(X936 @ X937))))&((((in @ (esk21_2 @ X939 @ X940) @ X939)|(~(in @ X942 @ X939)|~(X940 @ X942)))&((X940 @ (esk21_2 @ X939 @ X940))|(~(in @ X942 @ X939)|~(X940 @ X942))))&((((in @ (esk22_2 @ X943 @ X944) @ X943)|(~(in @ X946 @ X943)|~(X944 @ X946)))&((X944 @ (esk22_2 @ X943 @ X944))|(~(in @ X946 @ X943)|~(X944 @ X946))))&((((in @ (esk23_2 @ X947 @ X948) @ X947)|(~(in @ X949 @ X947)|(X948 @ X949)))&(~(X948 @ (esk23_2 @ X947 @ X948))|(~(in @ X949 @ X947)|(X948 @ X949))))&((~(X951)|(in @ emptyset @ (prop2set @ ((X951)))))&((prop2set2propI)&((((in @ (esk24_2 @ X952 @ X953) @ X952)|(~(in @ X955 @ X952)|~(X953 @ X955)))&((X953 @ (esk24_2 @ X952 @ X953))|(~(in @ X955 @ X952)|~(X953 @ X955))))&((((in @ (esk25_2 @ X956 @ X957) @ X956)|(~(in @ X958 @ X956)|(X957 @ X958)))&(~(X957 @ (esk25_2 @ X956 @ X957))|(~(in @ X958 @ X956)|(X957 @ X958))))&((((X960 @ (esk26_2 @ X960 @ X961))|~(X960 @ X961)|(exu @ X960))&(((X961)!=(esk26_2 @ X960 @ X961))|~(X960 @ X961)|(exu @ X960)))&((((X963 @ (esk27_1 @ X963))|(exu @ X963)|~(X963 @ X964))&(((X963 @ (esk28_1 @ X963))|(exu @ X963)|~(X963 @ X964))&(((esk27_1 @ X963)!=(esk28_1 @ X963))|(exu @ X963)|~(X963 @ X964))))&(((~(X967 @ (esk29_2 @ X967 @ X968))|((esk29_2 @ X967 @ X968)!=(X968))|(exu @ X967))&((X967 @ (esk29_2 @ X967 @ X968))|((esk29_2 @ X967 @ X968)=(X968))|(exu @ X967)))&((((X970)!=(X971))|(((X972)!=(X973))|(~(in @ X972 @ X970)|(in @ X973 @ X971))))&(((~(in @ X976 @ X974)|(in @ X977 @ X975)|((X976)!=(X977))|((X974)!=(X975)))&(~(in @ X977 @ X975)|(in @ X976 @ X974)|((X976)!=(X977))|((X974)!=(X975))))&((~(exu @ X978)|(~(X978 @ X979)|(~(X978 @ X980)|((X979)=(X980)))))&((((~(exu @ X981)|(exu @ X982)|((esk30_2 @ X981 @ X982)=(esk31_2 @ X981 @ X982)))&(~(exu @ X982)|(exu @ X981)|((esk30_2 @ X981 @ X982)=(esk31_2 @ X981 @ X982))))&(((~(exu @ X981)|(exu @ X982)|(~(X981 @ (esk30_2 @ X981 @ X982))|~(X982 @ (esk31_2 @ X981 @ X982))))&(~(exu @ X982)|(exu @ X981)|(~(X981 @ (esk30_2 @ X981 @ X982))|~(X982 @ (esk31_2 @ X981 @ X982)))))&((~(exu @ X981)|(exu @ X982)|((X981 @ (esk30_2 @ X981 @ X982))|(X982 @ (esk31_2 @ X981 @ X982))))&(~(exu @ X982)|(exu @ X981)|((X981 @ (esk30_2 @ X981 @ X982))|(X982 @ (esk31_2 @ X981 @ X982)))))))&(((emptyset)=(emptyset))&((((X985)!=(X986))|(((X987)!=(X988))|((setadjoin @ X985 @ X987)=(setadjoin @ X986 @ X988))))&((((X989)!=(X990))|((powerset @ X989)=(powerset @ X990)))&((((X991)!=(X992))|((setunion @ X991)=(setunion @ X992)))&(((omega)=(omega))&((~(exu @ X993)|(~(X993 @ X994)|(~(X993 @ X995)|((X994)=(X995)))))&(((((esk32_2 @ X996 @ X997)=(esk33_2 @ X996 @ X997))|(~(exu @ X996)|(~(exu @ X997)|((descr @ X996)=(descr @ X997)))))&((~(X996 @ (esk32_2 @ X996 @ X997))|~(X997 @ (esk33_2 @ X996 @ X997))|(~(exu @ X996)|(~(exu @ X997)|((descr @ X996)=(descr @ X997)))))&((X996 @ (esk32_2 @ X996 @ X997))|(X997 @ (esk33_2 @ X996 @ X997))|(~(exu @ X996)|(~(exu @ X997)|((descr @ X996)=(descr @ X997)))))))&((((in @ (esk34_4 @ X1000 @ X1001 @ X1002 @ X1003) @ X1000)|((dsetconstr @ X1000 @ X1002)=(dsetconstr @ X1001 @ X1003))|((X1000)!=(X1001)))&(((in @ (esk35_4 @ X1000 @ X1001 @ X1002 @ X1003) @ X1001)|((dsetconstr @ X1000 @ X1002)=(dsetconstr @ X1001 @ X1003))|((X1000)!=(X1001)))&((((esk34_4 @ X1000 @ X1001 @ X1002 @ X1003)=(esk35_4 @ X1000 @ X1001 @ X1002 @ X1003))|((dsetconstr @ X1000 @ X1002)=(dsetconstr @ X1001 @ X1003))|((X1000)!=(X1001)))&((~(X1002 @ (esk34_4 @ X1000 @ X1001 @ X1002 @ X1003))|~(X1003 @ (esk35_4 @ X1000 @ X1001 @ X1002 @ X1003))|((dsetconstr @ X1000 @ X1002)=(dsetconstr @ X1001 @ X1003))|((X1000)!=(X1001)))&((X1002 @ (esk34_4 @ X1000 @ X1001 @ X1002 @ X1003))|(X1003 @ (esk35_4 @ X1000 @ X1001 @ X1002 @ X1003))|((dsetconstr @ X1000 @ X1002)=(dsetconstr @ X1001 @ X1003))|((X1000)!=(X1001)))))))&((((in @ (esk36_2 @ X1006 @ X1007) @ X1006)|(subset @ X1006 @ X1007))&(~(in @ (esk36_2 @ X1006 @ X1007) @ X1007)|(subset @ X1006 @ X1007)))&((((X1009)!=(X1010))|(subset @ X1010 @ X1009))&((((X1011)!=(X1012))|(subset @ X1011 @ X1012))&((((in @ (esk37_2 @ X1013 @ X1014) @ X1013)|(subset @ X1013 @ X1014))&(~(in @ (esk37_2 @ X1013 @ X1014) @ X1014)|(subset @ X1013 @ X1014)))&((subset @ emptyset @ X1016)&((~(subset @ X1017 @ X1018)|(~(in @ X1019 @ X1017)|(in @ X1019 @ X1018)))&((~(subset @ X1020 @ X1021)|((in @ X1022 @ X1021)|~(in @ X1022 @ X1020)))&((~(in @ X1025 @ X1023)|((in @ X1025 @ X1024)|~(subset @ X1023 @ X1024)))&(((subset @ X1026 @ X1027)|((X1026)!=(X1027)))&((~(in @ X1030 @ X1028)|((in @ X1030 @ X1029)|((X1028)!=(X1029))))&((subset @ X1031 @ X1031)&((~(subset @ X1032 @ X1033)|(~(subset @ X1033 @ X1034)|(subset @ X1032 @ X1034)))&((subset @ X1036 @ (setadjoin @ X1035 @ X1036))&((~(subset @ X1037 @ X1039)|(subset @ X1037 @ (setadjoin @ X1038 @ X1039)))&((~(subset @ X1040 @ X1041)|(in @ X1040 @ (powerset @ X1041)))&((~(subset @ X1042 @ X1043)|(~(subset @ X1043 @ X1042)|((X1042)=(X1043))))&((~(subset @ X1044 @ emptyset)|((X1044)=(emptyset)))&((~(subset @ X1046 @ X1045)|(in @ X1046 @ (powerset @ X1045)))&((~(in @ X1048 @ (powerset @ X1047))|(subset @ X1048 @ X1047))&((in @ X1049 @ (powerset @ X1049))&((~(subset @ X1050 @ X1051)|(subset @ (powerset @ X1050) @ (powerset @ X1051)))&((in @ (dsetconstr @ X1052 @ X1053) @ (powerset @ X1052))&((subset @ (dsetconstr @ X1054 @ X1055) @ X1054)&((~(in @ X1058 @ X1056)|(in @ X1058 @ (binunion @ X1056 @ X1057)))&((in @ X1060 @ (setadjoin @ X1059 @ (setadjoin @ X1060 @ emptyset)))&((~(in @ X1063 @ X1062)|(in @ X1063 @ (binunion @ X1061 @ X1062)))&(((((in @ X1066 @ X1065)|(X1067)|(in @ X1066 @ X1064)|~(in @ X1066 @ (binunion @ X1064 @ X1065)))&(~(X1067)|(X1067)|(in @ X1066 @ X1064)|~(in @ X1066 @ (binunion @ X1064 @ X1065))))&(((in @ X1066 @ X1065)|(X1067)|~(X1067)|~(in @ X1066 @ (binunion @ X1064 @ X1065)))&(~(X1067)|(X1067)|~(X1067)|~(in @ X1066 @ (binunion @ X1064 @ X1065)))))&((~(in @ X1070 @ (binunion @ X1068 @ X1069))|((in @ X1070 @ X1068)|(in @ X1070 @ X1069)))&((subset @ X1071 @ (binunion @ X1071 @ X1072))&((subset @ X1074 @ (binunion @ X1073 @ X1074))&((~(in @ X1077 @ X1075)|(~(in @ X1077 @ X1076)|(in @ X1077 @ (binintersect @ X1075 @ X1076))))&((~(subset @ X1080 @ X1078)|(~(subset @ X1080 @ X1079)|(subset @ X1080 @ (binintersect @ X1078 @ X1079))))&((~(in @ X1083 @ (binintersect @ X1081 @ X1082))|(in @ X1083 @ X1081))&((subset @ (binintersect @ X1084 @ X1085) @ X1084)&((~(subset @ X1086 @ X1087)|((binintersect @ X1086 @ X1087)=(X1086)))&((((binintersect @ X1088 @ X1089)!=(X1089))|(subset @ X1089 @ X1088))&((~(in @ X1092 @ (binintersect @ X1090 @ X1091))|(in @ X1092 @ X1091))&((((in @ (esk38_2 @ X1093 @ X1094) @ X1093)|((binintersect @ X1093 @ X1094)=(emptyset)))&((in @ (esk38_2 @ X1093 @ X1094) @ X1094)|((binintersect @ X1093 @ X1094)=(emptyset))))&((subset @ (binintersect @ X1096 @ X1097) @ X1097)&((~(subset @ X1099 @ X1098)|((binintersect @ X1098 @ X1099)=(X1099)))&((((binintersect @ X1100 @ X1101)!=(X1100))|(subset @ X1100 @ X1101))&(((binintersect @ X1102 @ (binunion @ X1103 @ X1104))=(binunion @ (binintersect @ X1102 @ X1103) @ (binintersect @ X1102 @ X1104)))&((~(in @ X1107 @ X1105)|((in @ X1107 @ X1106)|(in @ X1107 @ (setminus @ X1105 @ X1106))))&((~(in @ X1110 @ (setminus @ X1108 @ X1109))|(in @ X1110 @ X1108))&((~(in @ X1113 @ (setminus @ X1111 @ X1112))|~(in @ X1113 @ X1112))&((~(subset @ X1114 @ X1115)|((setminus @ X1114 @ X1115)=(emptyset)))&(((in @ X1118 @ (setminus @ X1116 @ X1117))|(~(in @ X1118 @ X1116)|(in @ X1118 @ X1117)))&(((in @ X1121 @ (setminus @ X1119 @ X1120))|((in @ X1121 @ X1120)|~(in @ X1121 @ X1119)))&(((in @ X1124 @ X1122)|~(in @ X1124 @ (setminus @ X1122 @ X1123)))&((~(in @ X1127 @ X1126)|~(in @ X1127 @ (setminus @ X1125 @ X1126)))&((subset @ (setminus @ X1128 @ X1129) @ X1128)&((((setminus @ X1130 @ X1131)!=(emptyset))|(subset @ X1130 @ X1131))&((((~(in @ X1134 @ X1132)|(X1135)|(in @ X1134 @ X1132)|~(in @ X1134 @ (symdiff @ X1132 @ X1133)))&(((in @ X1134 @ X1133)|(X1135)|(in @ X1134 @ X1132)|~(in @ X1134 @ (symdiff @ X1132 @ X1133)))&(~(X1135)|(X1135)|(in @ X1134 @ X1132)|~(in @ X1134 @ (symdiff @ X1132 @ X1133)))))&(((~(in @ X1134 @ X1132)|(X1135)|~(in @ X1134 @ X1133)|~(in @ X1134 @ (symdiff @ X1132 @ X1133)))&(((in @ X1134 @ X1133)|(X1135)|~(in @ X1134 @ X1133)|~(in @ X1134 @ (symdiff @ X1132 @ X1133)))&(~(X1135)|(X1135)|~(in @ X1134 @ X1133)|~(in @ X1134 @ (symdiff @ X1132 @ X1133)))))&((~(in @ X1134 @ X1132)|(X1135)|~(X1135)|~(in @ X1134 @ (symdiff @ X1132 @ X1133)))&(((in @ X1134 @ X1133)|(X1135)|~(X1135)|~(in @ X1134 @ (symdiff @ X1132 @ X1133)))&(~(X1135)|(X1135)|~(X1135)|~(in @ X1134 @ (symdiff @ X1132 @ X1133)))))))&((~(in @ X1138 @ X1136)|((in @ X1138 @ X1137)|(in @ X1138 @ (symdiff @ X1136 @ X1137))))&(((in @ X1141 @ X1139)|(~(in @ X1141 @ X1140)|(in @ X1141 @ (symdiff @ X1139 @ X1140))))&((~(in @ X1144 @ X1142)|(~(in @ X1144 @ X1143)|~(in @ X1144 @ (symdiff @ X1142 @ X1143))))&(((in @ X1147 @ X1145)|((in @ X1147 @ X1146)|~(in @ X1147 @ (symdiff @ X1145 @ X1146))))&((in @ X1149 @ (setadjoin @ X1148 @ (setadjoin @ X1149 @ emptyset)))&((in @ X1150 @ (setunion @ (setadjoin @ (setadjoin @ X1150 @ emptyset) @ (setadjoin @ (setadjoin @ X1150 @ (setadjoin @ X1151 @ emptyset)) @ emptyset))))&((in @ X1153 @ (setunion @ (setadjoin @ (setadjoin @ X1152 @ emptyset) @ (setadjoin @ (setadjoin @ X1152 @ (setadjoin @ X1153 @ emptyset)) @ emptyset))))&((iskpair @ (setadjoin @ (setadjoin @ X1154 @ emptyset) @ (setadjoin @ (setadjoin @ X1154 @ (setadjoin @ X1155 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X1156 @ X1157))&((~(in @ X1159 @ X1158)|(subset @ (setadjoin @ X1159 @ emptyset) @ X1158))&((~(in @ X1161 @ X1160)|(in @ (setadjoin @ X1161 @ emptyset) @ (powerset @ X1160)))&((~(in @ X1164 @ X1162)|(in @ (setadjoin @ X1164 @ emptyset) @ (powerset @ (binunion @ X1162 @ X1163))))&((~(in @ X1167 @ (setadjoin @ X1165 @ (setadjoin @ X1166 @ emptyset)))|(((X1167)=(X1165))|((X1167)=(X1166))))&((~(in @ X1170 @ X1168)|(~(in @ X1171 @ X1169)|(subset @ (setadjoin @ X1170 @ (setadjoin @ X1171 @ emptyset)) @ (binunion @ X1168 @ X1169))))&((~(in @ X1174 @ X1172)|(~(in @ X1175 @ X1173)|(in @ (setadjoin @ X1174 @ (setadjoin @ X1175 @ emptyset)) @ (powerset @ (binunion @ X1172 @ X1173)))))&((~(in @ X1178 @ X1176)|(~(in @ X1179 @ X1177)|(subset @ (setadjoin @ (setadjoin @ X1178 @ emptyset) @ (setadjoin @ (setadjoin @ X1178 @ (setadjoin @ X1179 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1176 @ X1177)))))&((~(in @ X1182 @ X1180)|(~(in @ X1183 @ X1181)|(in @ (setadjoin @ (setadjoin @ X1182 @ emptyset) @ (setadjoin @ (setadjoin @ X1182 @ (setadjoin @ X1183 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1180 @ X1181))))))&((in @ esk41_0 @ esk39_0)&((in @ esk42_0 @ esk40_0)&~(in @ (kpair @ esk41_0 @ esk42_0) @ (powerset @ (powerset @ (binunion @ esk39_0 @ esk40_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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_170])])])])])])])).
% 0.25/0.69  thf(c_0_173, plain, ![X1188:$i, X1189:$i]:(((kpair @ X1188 @ X1189)=(setadjoin @ (setadjoin @ X1188 @ emptyset) @ (setadjoin @ (setadjoin @ X1188 @ (setadjoin @ X1189 @ emptyset)) @ emptyset)))), inference(variable_rename,[status(thm)],[c_0_171])).
% 0.25/0.69  thf(c_0_174, negated_conjecture, ![X2:$i, X3:$i, X4:$i, X5:$i]:(((in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X3 @ X5))))|~((in @ X2 @ X3))|~((in @ X4 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_172])).
% 0.25/0.69  thf(c_0_175, plain, ![X2:$i, X3:$i]:(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_173])).
% 0.25/0.69  thf(c_0_176, negated_conjecture, ~((in @ (kpair @ esk41_0 @ esk42_0) @ (powerset @ (powerset @ (binunion @ esk39_0 @ esk40_0))))), inference(split_conjunct,[status(thm)],[c_0_172])).
% 0.25/0.69  thf(c_0_177, negated_conjecture, ![X3:$i, X2:$i, X5:$i, X4:$i]:(((in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))|~((in @ X3 @ X5))|~((in @ X2 @ X4)))), inference(rw,[status(thm)],[c_0_174, c_0_175])).
% 0.25/0.69  thf(c_0_178, negated_conjecture, (in @ esk42_0 @ esk40_0), inference(split_conjunct,[status(thm)],[c_0_172])).
% 0.25/0.69  thf(c_0_179, negated_conjecture, (in @ esk41_0 @ esk39_0), inference(split_conjunct,[status(thm)],[c_0_172])).
% 0.25/0.69  thf(c_0_180, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176, c_0_177]), c_0_178]), c_0_179])]), ['proof']).
% 0.25/0.69  % SZS output end CNFRefutation
% 0.25/0.69  % Parsed axioms                        : 319
% 0.25/0.69  % Removed by relevancy pruning/SinE    : 173
% 0.25/0.69  % Initial clauses                      : 228
% 0.25/0.69  % Removed in clause preprocessing      : 25
% 0.25/0.69  % Initial clauses in saturation        : 203
% 0.25/0.69  % Processed clauses                    : 1573
% 0.25/0.69  % ...of these trivial                  : 30
% 0.25/0.69  % ...subsumed                          : 969
% 0.25/0.69  % ...remaining for further processing  : 574
% 0.25/0.69  % Other redundant clauses eliminated   : 44
% 0.25/0.69  % Clauses deleted for lack of memory   : 0
% 0.25/0.69  % Backward-subsumed                    : 72
% 0.25/0.69  % Backward-rewritten                   : 11
% 0.25/0.69  % Generated clauses                    : 10225
% 0.25/0.69  % ...of the previous two non-redundant : 8760
% 0.25/0.69  % ...aggressively subsumed             : 0
% 0.25/0.69  % Contextual simplify-reflections      : 0
% 0.25/0.69  % Paramodulations                      : 10177
% 0.25/0.69  % Factorizations                       : 4
% 0.25/0.69  % NegExts                              : 0
% 0.25/0.69  % Equation resolutions                 : 44
% 0.25/0.69  % Disequality decompositions           : 0
% 0.25/0.69  % Total rewrite steps                  : 1718
% 0.25/0.69  % ...of those cached                   : 1563
% 0.25/0.69  % Propositional unsat checks           : 0
% 0.25/0.69  %    Propositional check models        : 0
% 0.25/0.69  %    Propositional check unsatisfiable : 0
% 0.25/0.69  %    Propositional clauses             : 0
% 0.25/0.69  %    Propositional clauses after purity: 0
% 0.25/0.69  %    Propositional unsat core size     : 0
% 0.25/0.69  %    Propositional preprocessing time  : 0.000
% 0.25/0.69  %    Propositional encoding time       : 0.000
% 0.25/0.69  %    Propositional solver time         : 0.000
% 0.25/0.69  %    Success case prop preproc time    : 0.000
% 0.25/0.69  %    Success case prop encoding time   : 0.000
% 0.25/0.69  %    Success case prop solver time     : 0.000
% 0.25/0.69  % Current number of processed clauses  : 482
% 0.25/0.69  %    Positive orientable unit clauses  : 119
% 0.25/0.69  %    Positive unorientable unit clauses: 0
% 0.25/0.69  %    Negative unit clauses             : 3
% 0.25/0.69  %    Non-unit-clauses                  : 360
% 0.25/0.69  % Current number of unprocessed clauses: 7201
% 0.25/0.69  % ...number of literals in the above   : 21705
% 0.25/0.69  % Current number of archived formulas  : 0
% 0.25/0.69  % Current number of archived clauses   : 83
% 0.25/0.69  % Clause-clause subsumption calls (NU) : 15114
% 0.25/0.69  % Rec. Clause-clause subsumption calls : 12585
% 0.25/0.69  % Non-unit clause-clause subsumptions  : 1003
% 0.25/0.69  % Unit Clause-clause subsumption calls : 317
% 0.25/0.69  % Rewrite failures with RHS unbound    : 0
% 0.25/0.69  % BW rewrite match attempts            : 119
% 0.25/0.69  % BW rewrite match successes           : 6
% 0.25/0.69  % Condensation attempts                : 0
% 0.25/0.69  % Condensation successes               : 0
% 0.25/0.69  % Termbank termtop insertions          : 141349
% 0.25/0.69  % Search garbage collected termcells   : 12615
% 0.25/0.69  
% 0.25/0.69  % -------------------------------------------------
% 0.25/0.69  % User time                : 0.274 s
% 0.25/0.69  % System time              : 0.023 s
% 0.25/0.69  % Total time               : 0.297 s
% 0.25/0.69  % Maximum resident set size: 6712 pages
% 0.25/0.69  
% 0.25/0.69  % -------------------------------------------------
% 0.25/0.69  % User time                : 0.283 s
% 0.25/0.69  % System time              : 0.030 s
% 0.25/0.69  % Total time               : 0.312 s
% 0.25/0.69  % Maximum resident set size: 5120 pages
% 0.25/0.69  % E exiting
%------------------------------------------------------------------------------