%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU623^1 : 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 : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:46 AM UTC 2026
% Result : Theorem 0.22s 0.34s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU623^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n016.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:03:49 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.25 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p
% 0.22/0.34 % Version: 3.5.1-ho
% 0.22/0.34 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.22/0.34 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.34 % Starting ehoh_best5 with 300s (1) cores
% 0.22/0.34 % Starting almost_fo_3_lam with 300s (1) cores
% 0.22/0.34 % Starting new_bool_5 with 300s (1) cores
% 0.22/0.34 % Starting pre_casc_3 with 300s (1) cores
% 0.22/0.34 % Starting ho_unfolding_8 with 300s (1) cores
% 0.22/0.34 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.22/0.34 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.34 % Starting new_ho_5 with 300s (1) cores
% 0.22/0.34 % ehoh_best5 with pid 404151 completed with status 0
% 0.22/0.34 % Result found by ehoh_best5
% 0.22/0.34 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.22/0.34 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.34 % Starting ehoh_best5 with 300s (1) cores
% 0.22/0.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.34 % No SInE strategy applied
% 0.22/0.34 % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.22/0.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.34 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.34 % SubtermCWHack with pid 404162 completed with status 0
% 0.22/0.34 % Result found by SubtermCWHack
% 0.22/0.34 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.22/0.34 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.34 % Starting ehoh_best5 with 300s (1) cores
% 0.22/0.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.34 % No SInE strategy applied
% 0.22/0.34 % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.22/0.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.34 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.34 % Preprocessing time : 0.005 s
% 0.22/0.34
% 0.22/0.34 % Proof found!
% 0.22/0.34 % SZS status Theorem
% 0.22/0.34 % SZS output start CNFRefutation
% 0.22/0.34 thf(decl_23, type, in: $i > $i > $o).
% 0.22/0.34 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.22/0.34 thf(decl_25, type, setextAx: $o).
% 0.22/0.34 thf(decl_26, type, emptyset: $i).
% 0.22/0.34 thf(decl_27, type, emptysetAx: $o).
% 0.22/0.34 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.22/0.34 thf(decl_29, type, setadjoinAx: $o).
% 0.22/0.34 thf(decl_30, type, powerset: $i > $i).
% 0.22/0.34 thf(decl_31, type, powersetAx: $o).
% 0.22/0.34 thf(decl_32, type, setunion: $i > $i).
% 0.22/0.34 thf(decl_33, type, setunionAx: $o).
% 0.22/0.34 thf(decl_34, type, omega: $i).
% 0.22/0.34 thf(decl_35, type, omega0Ax: $o).
% 0.22/0.34 thf(decl_36, type, omegaSAx: $o).
% 0.22/0.34 thf(decl_37, type, omegaIndAx: $o).
% 0.22/0.34 thf(decl_38, type, replAx: $o).
% 0.22/0.34 thf(decl_39, type, foundationAx: $o).
% 0.22/0.34 thf(decl_40, type, wellorderingAx: $o).
% 0.22/0.34 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.22/0.34 thf(decl_42, type, descrp: $o).
% 0.22/0.34 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.22/0.34 thf(decl_44, type, dsetconstrI: $o).
% 0.22/0.34 thf(decl_45, type, dsetconstrEL: $o).
% 0.22/0.34 thf(decl_46, type, dsetconstrER: $o).
% 0.22/0.34 thf(decl_47, type, exuE1: $o).
% 0.22/0.34 thf(decl_48, type, prop2set: $o > $i).
% 0.22/0.34 thf(decl_49, type, prop2setE: $o).
% 0.22/0.34 thf(decl_50, type, emptysetE: $o).
% 0.22/0.34 thf(decl_51, type, emptysetimpfalse: $o).
% 0.22/0.34 thf(decl_52, type, notinemptyset: $o).
% 0.22/0.34 thf(decl_53, type, exuE3e: $o).
% 0.22/0.34 thf(decl_54, type, setext: $o).
% 0.22/0.34 thf(decl_55, type, emptyI: $o).
% 0.22/0.34 thf(decl_56, type, noeltsimpempty: $o).
% 0.22/0.34 thf(decl_57, type, setbeta: $o).
% 0.22/0.34 thf(decl_58, type, nonempty: $i > $o).
% 0.22/0.34 thf(decl_59, type, nonemptyE1: $o).
% 0.22/0.34 thf(decl_60, type, nonemptyI: $o).
% 0.22/0.34 thf(decl_61, type, nonemptyI1: $o).
% 0.22/0.34 thf(decl_62, type, setadjoinIL: $o).
% 0.22/0.34 thf(decl_63, type, emptyinunitempty: $o).
% 0.22/0.34 thf(decl_64, type, setadjoinIR: $o).
% 0.22/0.34 thf(decl_65, type, setadjoinE: $o).
% 0.22/0.34 thf(decl_66, type, setadjoinOr: $o).
% 0.22/0.34 thf(decl_67, type, setoftrueEq: $o).
% 0.22/0.34 thf(decl_68, type, powersetI: $o).
% 0.22/0.34 thf(decl_69, type, emptyinPowerset: $o).
% 0.22/0.34 thf(decl_70, type, emptyInPowerset: $o).
% 0.22/0.34 thf(decl_71, type, powersetE: $o).
% 0.22/0.34 thf(decl_72, type, setunionI: $o).
% 0.22/0.34 thf(decl_73, type, setunionE: $o).
% 0.22/0.34 thf(decl_74, type, subPowSU: $o).
% 0.22/0.34 thf(decl_75, type, exuE2: $o).
% 0.22/0.34 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.22/0.34 thf(decl_77, type, uniqinunit: $o).
% 0.22/0.34 thf(decl_78, type, notinsingleton: $o).
% 0.22/0.34 thf(decl_79, type, eqinunit: $o).
% 0.22/0.34 thf(decl_80, type, singletonsswitch: $o).
% 0.22/0.34 thf(decl_81, type, upairsetE: $o).
% 0.22/0.34 thf(decl_82, type, upairsetIL: $o).
% 0.22/0.34 thf(decl_83, type, upairsetIR: $o).
% 0.22/0.34 thf(decl_84, type, emptyE1: $o).
% 0.22/0.34 thf(decl_85, type, vacuousDall: $o).
% 0.22/0.34 thf(decl_86, type, quantDeMorgan1: $o).
% 0.22/0.34 thf(decl_87, type, quantDeMorgan2: $o).
% 0.22/0.34 thf(decl_88, type, quantDeMorgan3: $o).
% 0.22/0.34 thf(decl_89, type, quantDeMorgan4: $o).
% 0.22/0.34 thf(decl_90, type, prop2setI: $o).
% 0.22/0.34 thf(decl_91, type, set2prop: $i > $o).
% 0.22/0.35 thf(decl_92, type, prop2set2propI: $o).
% 0.22/0.35 thf(decl_93, type, notdexE: $o).
% 0.22/0.35 thf(decl_94, type, notdallE: $o).
% 0.22/0.35 thf(decl_95, type, exuI1: $o).
% 0.22/0.35 thf(decl_96, type, exuI3: $o).
% 0.22/0.35 thf(decl_97, type, exuI2: $o).
% 0.22/0.35 thf(decl_98, type, inCongP: $o).
% 0.22/0.35 thf(decl_99, type, in__Cong: $o).
% 0.22/0.35 thf(decl_100, type, exuE3u: $o).
% 0.22/0.35 thf(decl_101, type, exu__Cong: $o).
% 0.22/0.35 thf(decl_102, type, emptyset__Cong: $o).
% 0.22/0.35 thf(decl_103, type, setadjoin__Cong: $o).
% 0.22/0.35 thf(decl_104, type, powerset__Cong: $o).
% 0.22/0.35 thf(decl_105, type, setunion__Cong: $o).
% 0.22/0.35 thf(decl_106, type, omega__Cong: $o).
% 0.22/0.35 thf(decl_107, type, exuEu: $o).
% 0.22/0.35 thf(decl_108, type, descr__Cong: $o).
% 0.22/0.35 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.22/0.35 thf(decl_110, type, subset: $i > $i > $o).
% 0.22/0.35 thf(decl_113, type, subsetI1: $o).
% 0.22/0.35 thf(decl_114, type, eqimpsubset2: $o).
% 0.22/0.35 thf(decl_115, type, eqimpsubset1: $o).
% 0.22/0.35 thf(decl_116, type, subsetI2: $o).
% 0.22/0.35 thf(decl_117, type, emptysetsubset: $o).
% 0.22/0.35 thf(decl_118, type, subsetE: $o).
% 0.22/0.35 thf(decl_119, type, subsetE2: $o).
% 0.22/0.35 thf(decl_120, type, notsubsetI: $o).
% 0.22/0.35 thf(decl_121, type, notequalI1: $o).
% 0.22/0.35 thf(decl_122, type, notequalI2: $o).
% 0.22/0.35 thf(decl_123, type, subsetRefl: $o).
% 0.22/0.35 thf(decl_124, type, subsetTrans: $o).
% 0.22/0.35 thf(decl_125, type, setadjoinSub: $o).
% 0.22/0.35 thf(decl_126, type, setadjoinSub2: $o).
% 0.22/0.35 thf(decl_127, type, subset2powerset: $o).
% 0.22/0.35 thf(decl_128, type, setextsub: $o).
% 0.22/0.35 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.22/0.35 thf(decl_130, type, powersetI1: $o).
% 0.22/0.35 thf(decl_131, type, powersetE1: $o).
% 0.22/0.35 thf(decl_132, type, inPowerset: $o).
% 0.22/0.35 thf(decl_133, type, powersetsubset: $o).
% 0.22/0.35 thf(decl_134, type, sepInPowerset: $o).
% 0.22/0.35 thf(decl_135, type, sepSubset: $o).
% 0.22/0.35 thf(decl_136, type, binunion: $i > $i > $i).
% 0.22/0.35 thf(decl_137, type, binunionIL: $o).
% 0.22/0.35 thf(decl_138, type, upairset2IR: $o).
% 0.22/0.35 thf(decl_139, type, binunionIR: $o).
% 0.22/0.35 thf(decl_140, type, binunionEcases: $o).
% 0.22/0.35 thf(decl_141, type, binunionE: $o).
% 0.22/0.35 thf(decl_142, type, binunionLsub: $o).
% 0.22/0.35 thf(decl_143, type, binunionRsub: $o).
% 0.22/0.35 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.22/0.35 thf(decl_145, type, binintersectI: $o).
% 0.22/0.35 thf(decl_146, type, binintersectSubset5: $o).
% 0.22/0.35 thf(decl_147, type, binintersectEL: $o).
% 0.22/0.35 thf(decl_148, type, binintersectLsub: $o).
% 0.22/0.35 thf(decl_149, type, binintersectSubset2: $o).
% 0.22/0.35 thf(decl_150, type, binintersectSubset3: $o).
% 0.22/0.35 thf(decl_151, type, binintersectER: $o).
% 0.22/0.35 thf(decl_152, type, disjointsetsI1: $o).
% 0.22/0.35 thf(decl_153, type, binintersectRsub: $o).
% 0.22/0.35 thf(decl_154, type, binintersectSubset4: $o).
% 0.22/0.35 thf(decl_155, type, binintersectSubset1: $o).
% 0.22/0.35 thf(decl_156, type, bs114d: $o).
% 0.22/0.35 thf(decl_158, type, setminus: $i > $i > $i).
% 0.22/0.35 thf(decl_159, type, setminusI: $o).
% 0.22/0.35 thf(decl_160, type, setminusEL: $o).
% 0.22/0.35 thf(decl_161, type, setminusER: $o).
% 0.22/0.35 thf(decl_162, type, setminusSubset2: $o).
% 0.22/0.35 thf(decl_163, type, setminusERneg: $o).
% 0.22/0.35 thf(decl_164, type, setminusELneg: $o).
% 0.22/0.35 thf(decl_165, type, setminusILneg: $o).
% 0.22/0.35 thf(decl_166, type, setminusIRneg: $o).
% 0.22/0.35 thf(decl_167, type, setminusLsub: $o).
% 0.22/0.35 thf(decl_168, type, setminusSubset1: $o).
% 0.22/0.35 thf(decl_169, type, symdiff: $i > $i > $i).
% 0.22/0.35 thf(decl_170, type, symdiffE: $o).
% 0.22/0.35 thf(decl_171, type, symdiffI1: $o).
% 0.22/0.35 thf(decl_172, type, symdiffI2: $o).
% 0.22/0.35 thf(decl_173, type, symdiffIneg1: $o).
% 0.22/0.35 thf(decl_174, type, symdiffIneg2: $o).
% 0.22/0.35 thf(decl_175, type, iskpair: $i > $o).
% 0.22/0.35 thf(decl_176, type, secondinupair: $o).
% 0.22/0.35 thf(decl_177, type, setukpairIL: $o).
% 0.22/0.35 thf(decl_178, type, setukpairIR: $o).
% 0.22/0.35 thf(decl_179, type, kpairiskpair: $o).
% 0.22/0.35 thf(decl_180, type, kpair: $i > $i > $i).
% 0.22/0.35 thf(decl_181, type, kpairp: $o).
% 0.22/0.35 thf(decl_183, type, singletonsubset: $o).
% 0.22/0.35 thf(decl_184, type, singletoninpowerset: $o).
% 0.22/0.35 thf(decl_185, type, epred1_0: $o).
% 0.22/0.35 thf(decl_186, type, esk1_2: $i > $i > $i).
% 0.22/0.35 thf(decl_187, type, esk2_2: $i > $i > $i).
% 0.22/0.35 thf(decl_188, type, esk3_2: $i > $i > $i).
% 0.22/0.35 thf(decl_189, type, esk4_1: $i > $i).
% 0.22/0.35 thf(decl_190, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.22/0.35 thf(decl_191, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.35 thf(decl_192, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.22/0.35 thf(decl_193, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.35 thf(decl_194, type, esk9_1: $i > $i).
% 0.22/0.35 thf(decl_195, type, esk10_2: ($i > $o) > $i > $i).
% 0.22/0.35 thf(decl_196, type, esk11_2: ($i > $o) > $i > $i).
% 0.22/0.35 thf(decl_197, type, esk12_1: ($i > $o) > $i).
% 0.22/0.35 thf(decl_198, type, esk13_2: ($i > $o) > $i > $i).
% 0.22/0.35 thf(decl_199, type, esk14_1: ($i > $o) > $i).
% 0.22/0.35 thf(decl_200, type, esk15_2: $i > $i > $i).
% 0.22/0.35 thf(decl_201, type, esk16_2: $i > $i > $i).
% 0.22/0.35 thf(decl_202, type, esk17_1: $i > $i).
% 0.22/0.35 thf(decl_203, type, esk18_1: $i > $i).
% 0.22/0.35 thf(decl_204, type, esk19_1: $i > $i).
% 0.22/0.35 thf(decl_205, type, esk20_2: $i > $i > $i).
% 0.22/0.35 thf(decl_206, type, esk21_3: $i > $i > $o > $i).
% 0.22/0.35 thf(decl_207, type, esk22_2: ($i > $o) > $i > $i).
% 0.22/0.35 thf(decl_208, type, esk23_1: ($i > $o) > $i).
% 0.22/0.35 thf(decl_209, type, esk24_1: $i > $i).
% 0.22/0.35 thf(decl_210, type, esk25_2: $i > ($i > $o) > $i).
% 0.22/0.35 thf(decl_211, type, esk26_2: $i > ($i > $o) > $i).
% 0.22/0.35 thf(decl_212, type, esk27_2: $i > ($i > $o) > $i).
% 0.22/0.35 thf(decl_213, type, esk28_2: $i > ($i > $o) > $i).
% 0.22/0.35 thf(decl_214, type, esk29_2: $i > ($i > $o) > $i).
% 0.22/0.35 thf(decl_215, type, esk30_2: $i > ($i > $o) > $i).
% 0.22/0.35 thf(decl_216, type, esk31_2: ($i > $o) > $i > $i).
% 0.22/0.35 thf(decl_217, type, esk32_1: ($i > $o) > $i).
% 0.22/0.35 thf(decl_218, type, esk33_1: ($i > $o) > $i).
% 0.22/0.35 thf(decl_219, type, esk34_1: ($i > $o) > $i).
% 0.22/0.35 thf(decl_220, type, esk35_1: ($i > $o) > $i).
% 0.22/0.35 thf(decl_221, type, esk36_2: ($i > $o) > $i > $i).
% 0.22/0.35 thf(decl_222, type, esk37_1: ($i > $o) > $i).
% 0.22/0.35 thf(decl_223, type, esk38_2: ($i > $o) > $i > $i).
% 0.22/0.35 thf(decl_224, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.35 thf(decl_225, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.35 thf(decl_226, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.35 thf(decl_227, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.35 thf(decl_228, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.35 thf(decl_229, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.35 thf(decl_230, type, esk45_2: ($i > $o) > $i > $i).
% 0.22/0.35 thf(decl_231, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.35 thf(decl_232, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.35 thf(decl_233, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.35 thf(decl_234, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.35 thf(decl_235, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.22/0.35 thf(decl_236, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.22/0.35 thf(decl_237, type, esk52_2: $i > $i > $i).
% 0.22/0.35 thf(decl_238, type, esk53_2: $i > $i > $i).
% 0.22/0.35 thf(decl_239, type, esk54_2: $i > $i > $i).
% 0.22/0.35 thf(decl_240, type, esk55_2: $i > $i > $i).
% 0.22/0.35 thf(decl_241, type, esk56_2: $i > $i > $i).
% 0.22/0.35 thf(decl_242, type, esk57_2: $i > $i > $i).
% 0.22/0.35 thf(decl_243, type, esk58_2: $i > $i > $i).
% 0.22/0.35 thf(decl_244, type, esk59_0: $i).
% 0.22/0.35 thf(decl_245, type, esk60_0: $i).
% 0.22/0.35 thf(decl_246, type, esk61_0: $i).
% 0.22/0.35 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', replAx)).
% 0.22/0.35 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', exu)).
% 0.22/0.35 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', descrp)).
% 0.22/0.35 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', exuE1)).
% 0.22/0.35 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', exuE3e)).
% 0.22/0.35 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', nonempty)).
% 0.22/0.35 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', nonemptyI)).
% 0.22/0.35 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', exuE2)).
% 0.22/0.35 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.863Q0otAWj/E---3.1_404138.p', exuI1)).
% 0.22/0.35 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', exuI3)).
% 0.22/0.35 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', exuI2)).
% 0.22/0.35 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.863Q0otAWj/E---3.1_404138.p', exuE3u)).
% 0.22/0.35 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', exu__Cong)).
% 0.22/0.35 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', exuEu)).
% 0.22/0.35 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', descr__Cong)).
% 0.22/0.35 thf(iskpair, axiom, ((iskpair)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ (setunion @ X4)))&(?[X3:$i]:((((in @ X3 @ (setunion @ X4)))&(((X4)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', iskpair)).
% 0.22/0.35 thf(singletoninpowunion, 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)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', singletoninpowunion)).
% 0.22/0.35 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', dsetconstrI)).
% 0.22/0.35 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', dsetconstrEL)).
% 0.22/0.35 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', dsetconstrER)).
% 0.22/0.35 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setbeta)).
% 0.22/0.35 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', nonemptyE1)).
% 0.22/0.35 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', nonemptyI1)).
% 0.22/0.35 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setoftrueEq)).
% 0.22/0.35 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', nonemptyImpWitness)).
% 0.22/0.35 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.863Q0otAWj/E---3.1_404138.p', emptyE1)).
% 0.22/0.35 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', dsetconstr__Cong)).
% 0.22/0.35 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', sepInPowerset)).
% 0.22/0.35 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', sepSubset)).
% 0.22/0.35 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.863Q0otAWj/E---3.1_404138.p', kpairiskpair)).
% 0.22/0.35 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', kpairp)).
% 0.22/0.35 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setextAx)).
% 0.22/0.35 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', emptysetAx)).
% 0.22/0.35 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setadjoinAx)).
% 0.22/0.35 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', powersetAx)).
% 0.22/0.35 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setunionAx)).
% 0.22/0.35 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', omega0Ax)).
% 0.22/0.35 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', omegaSAx)).
% 0.22/0.35 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', omegaIndAx)).
% 0.22/0.35 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', foundationAx)).
% 0.22/0.35 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.863Q0otAWj/E---3.1_404138.p', wellorderingAx)).
% 0.22/0.35 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', prop2setE)).
% 0.22/0.35 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', emptysetE)).
% 0.22/0.35 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', emptysetimpfalse)).
% 0.22/0.35 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', notinemptyset)).
% 0.22/0.35 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setext)).
% 0.22/0.35 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', emptyI)).
% 0.22/0.35 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', noeltsimpempty)).
% 0.22/0.35 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setadjoinIL)).
% 0.22/0.35 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', emptyinunitempty)).
% 0.22/0.35 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setadjoinIR)).
% 0.22/0.35 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.863Q0otAWj/E---3.1_404138.p', setadjoinE)).
% 0.22/0.35 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setadjoinOr)).
% 0.22/0.35 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', powersetI)).
% 0.22/0.35 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', emptyinPowerset)).
% 0.22/0.35 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', emptyInPowerset)).
% 0.22/0.35 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', powersetE)).
% 0.22/0.35 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setunionI)).
% 0.22/0.35 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.863Q0otAWj/E---3.1_404138.p', setunionE)).
% 0.22/0.35 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', subPowSU)).
% 0.22/0.35 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', uniqinunit)).
% 0.22/0.35 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', notinsingleton)).
% 0.22/0.35 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', eqinunit)).
% 0.22/0.35 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', singletonsswitch)).
% 0.22/0.35 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', upairsetE)).
% 0.22/0.35 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', upairsetIL)).
% 0.22/0.35 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', upairsetIR)).
% 0.22/0.35 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', vacuousDall)).
% 0.22/0.35 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', quantDeMorgan1)).
% 0.22/0.35 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', quantDeMorgan2)).
% 0.22/0.35 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', quantDeMorgan3)).
% 0.22/0.35 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', quantDeMorgan4)).
% 0.22/0.35 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', prop2setI)).
% 0.22/0.35 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', prop2set2propI)).
% 0.22/0.35 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', notdexE)).
% 0.22/0.35 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', notdallE)).
% 0.22/0.35 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', inCongP)).
% 0.22/0.35 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', in__Cong)).
% 0.22/0.35 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', emptyset__Cong)).
% 0.22/0.35 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setadjoin__Cong)).
% 0.22/0.35 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', powerset__Cong)).
% 0.22/0.35 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setunion__Cong)).
% 0.22/0.35 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', omega__Cong)).
% 0.22/0.35 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', subsetI1)).
% 0.22/0.35 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', eqimpsubset2)).
% 0.22/0.35 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', eqimpsubset1)).
% 0.22/0.35 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', subsetI2)).
% 0.22/0.35 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', emptysetsubset)).
% 0.22/0.35 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', subsetE)).
% 0.22/0.35 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', subsetE2)).
% 0.22/0.35 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', notsubsetI)).
% 0.22/0.35 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', notequalI1)).
% 0.22/0.35 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', notequalI2)).
% 0.22/0.35 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', subsetRefl)).
% 0.22/0.35 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', subsetTrans)).
% 0.22/0.35 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setadjoinSub)).
% 0.22/0.35 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setadjoinSub2)).
% 0.22/0.35 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', subset2powerset)).
% 0.22/0.35 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setextsub)).
% 0.22/0.35 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', subsetemptysetimpeq)).
% 0.22/0.35 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', powersetI1)).
% 0.22/0.35 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', powersetE1)).
% 0.22/0.35 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', inPowerset)).
% 0.22/0.35 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', powersetsubset)).
% 0.22/0.35 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', binunionIL)).
% 0.22/0.35 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', upairset2IR)).
% 0.22/0.35 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', binunionIR)).
% 0.22/0.35 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', binunionEcases)).
% 0.22/0.35 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', binunionE)).
% 0.22/0.35 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', binunionLsub)).
% 0.22/0.35 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', binunionRsub)).
% 0.22/0.35 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', binintersectI)).
% 0.22/0.35 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', binintersectSubset5)).
% 0.22/0.35 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', binintersectEL)).
% 0.22/0.35 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', binintersectLsub)).
% 0.22/0.35 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', binintersectSubset2)).
% 0.22/0.35 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', binintersectSubset3)).
% 0.22/0.35 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', binintersectER)).
% 0.22/0.35 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', disjointsetsI1)).
% 0.22/0.35 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', binintersectRsub)).
% 0.22/0.35 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', binintersectSubset4)).
% 0.22/0.35 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', binintersectSubset1)).
% 0.22/0.35 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', bs114d)).
% 0.22/0.35 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setminusI)).
% 0.22/0.35 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setminusEL)).
% 0.22/0.35 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setminusER)).
% 0.22/0.35 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setminusSubset2)).
% 0.22/0.35 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setminusERneg)).
% 0.22/0.35 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setminusELneg)).
% 0.22/0.35 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setminusILneg)).
% 0.22/0.35 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setminusIRneg)).
% 0.22/0.35 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setminusLsub)).
% 0.22/0.35 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setminusSubset1)).
% 0.22/0.35 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', symdiffE)).
% 0.22/0.35 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', symdiffI1)).
% 0.22/0.35 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', symdiffI2)).
% 0.22/0.35 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', symdiffIneg1)).
% 0.22/0.35 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', symdiffIneg2)).
% 0.22/0.35 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', secondinupair)).
% 0.22/0.35 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setukpairIL)).
% 0.22/0.35 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', setukpairIR)).
% 0.22/0.35 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', singletonsubset)).
% 0.22/0.35 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.863Q0otAWj/E---3.1_404138.p', singletoninpowerset)).
% 0.22/0.35 thf(c_0_143, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.22/0.35 thf(c_0_144, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.22/0.35 thf(c_0_145, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.22/0.35 thf(c_0_146, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.22/0.35 thf(c_0_147, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.22/0.35 thf(c_0_148, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.22/0.35 thf(c_0_149, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.22/0.35 thf(c_0_150, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.22/0.35 thf(c_0_151, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.22/0.35 thf(c_0_152, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.22/0.35 thf(c_0_153, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.22/0.35 thf(c_0_154, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.22/0.35 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.22/0.35 thf(c_0_156, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.22/0.35 thf(c_0_157, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.22/0.35 thf(c_0_158, plain, ((iskpair)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ (setunion @ Z0)))&(?[X3:$i]:((((in @ X3 @ (setunion @ Z0)))&(((Z0)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))))), inference(fof_simplification,[status(thm)],[iskpair])).
% 0.22/0.35 thf(c_0_159, 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)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[singletoninpowunion])).
% 0.22/0.35 thf(c_0_160, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X392:$i]:(((((X6 @ X2 @ X392)))&(![X393:$i]:(((((X6 @ X2 @ X393)))=>(((X392)=(X393)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_143, c_0_144])).
% 0.22/0.35 thf(c_0_161, plain, ((descrp)=(![X1:$i > $o]:((((?[X394:$i]:(((((X1 @ X394)))&(![X395:$i]:(((((X1 @ X395)))=>(((X394)=(X395))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_145, c_0_144])).
% 0.22/0.35 thf(c_0_162, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.22/0.35 thf(c_0_163, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.22/0.35 thf(c_0_164, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.22/0.35 thf(c_0_165, plain, ((exuE1)=(![X1:$i > $o]:((((?[X396:$i]:(((((X1 @ X396)))&(![X397:$i]:(((((X1 @ X397)))=>(((X396)=(X397))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_146, c_0_144])).
% 0.22/0.35 thf(c_0_166, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X398:$i]:(((((X1 @ X398)))&(![X399:$i]:(((((X1 @ X399)))=>(((X398)=(X399))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_147, c_0_144])).
% 0.22/0.35 thf(c_0_167, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.22/0.35 thf(c_0_168, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_148])).
% 0.22/0.35 thf(c_0_169, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_149, c_0_148])).
% 0.22/0.35 thf(c_0_170, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_148])).
% 0.22/0.35 thf(c_0_171, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.22/0.35 thf(c_0_172, plain, ((exuE2)=(![X1:$i > $o]:((((?[X400:$i]:(((((X1 @ X400)))&(![X401:$i]:(((((X1 @ X401)))=>(((X400)=(X401))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_150, c_0_144])).
% 0.22/0.35 thf(c_0_173, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_148])).
% 0.22/0.35 thf(c_0_174, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 0.22/0.35 thf(c_0_175, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X402:$i]:(((((X1 @ X402)))&(![X403:$i]:(((((X1 @ X403)))=>(((X402)=(X403)))))))))))))), inference(apply_def,[status(thm)],[c_0_151, c_0_144])).
% 0.22/0.35 thf(c_0_176, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X404:$i]:(((((X1 @ X404)))&(![X405:$i]:(((((X1 @ X405)))=>(((X404)=(X405)))))))))))))))), inference(apply_def,[status(thm)],[c_0_152, c_0_144])).
% 0.22/0.35 thf(c_0_177, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X406:$i]:(((((X1 @ X406)))&(![X407:$i]:(((((X1 @ X407)))=>(((X406)=(X407)))))))))))))), inference(apply_def,[status(thm)],[c_0_153, c_0_144])).
% 0.22/0.35 thf(c_0_178, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X408:$i]:(((((X1 @ X408)))&(![X409:$i]:(((((X1 @ X409)))=>(((X408)=(X409))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_154, c_0_144])).
% 0.22/0.35 thf(c_0_179, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X410:$i]:(((((X1 @ X410)))&(![X411:$i]:(((((X1 @ X411)))=>(((X410)=(X411))))))))))<=>((?[X412:$i]:(((((X17 @ X412)))&(![X413:$i]:(((((X17 @ X413)))=>(((X412)=(X413)))))))))))))))), inference(apply_def,[status(thm)],[c_0_155, c_0_144])).
% 0.22/0.35 thf(c_0_180, plain, ((exuEu)=(![X1:$i > $o]:((((?[X414:$i]:(((((X1 @ X414)))&(![X415:$i]:(((((X1 @ X415)))=>(((X414)=(X415))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_156, c_0_144])).
% 0.22/0.35 thf(c_0_181, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X416:$i]:(((((X1 @ X416)))&(![X417:$i]:(((((X1 @ X417)))=>(((X416)=(X417))))))))))=>((((?[X418:$i]:(((((X17 @ X418)))&(![X419:$i]:(((((X17 @ X419)))=>(((X418)=(X419))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_157, c_0_144])).
% 0.22/0.35 thf(c_0_182, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.22/0.35 thf(c_0_183, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.22/0.35 thf(c_0_184, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.22/0.35 thf(c_0_185, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X420:$i]:((((in @ X420 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))&(?[X421:$i]:((((in @ X421 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))&(((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X420 @ emptyset) @ (setadjoin @ (setadjoin @ X420 @ (setadjoin @ X421 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_158])).
% 0.22/0.35 thf(c_0_186, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X422:$i]:((((in @ X422 @ (setunion @ (kpair @ X2 @ X3))))&(?[X423:$i]:((((in @ X423 @ (setunion @ (kpair @ X2 @ X3))))&(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X422 @ emptyset) @ (setadjoin @ (setadjoin @ X422 @ (setadjoin @ X423 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairp, c_0_158])).
% 0.22/0.35 thf(c_0_187, plain, ((epred1_0)<=>![X453:$i]:(?[X454:$i]:((((![X455:$i]:(((in @ X455 @ X454)=>![X456:$i]:(((in @ X456 @ X455)=>(in @ X456 @ X453)))))&![X457:$i, X458:$i]:((((in @ X457 @ X453)&(in @ X458 @ X453))=>(![X459:$i]:(((in @ X459 @ X454)=>((in @ X457 @ X459)<=>(in @ X458 @ X459))))=>((X457)=(X458))))))&![X460:$i, X461:$i]:((((in @ X460 @ X454)&(in @ X461 @ X454))=>(![X462:$i]:(((in @ X462 @ X460)=>(in @ X462 @ X461)))|![X463:$i]:(((in @ X463 @ X461)=>(in @ X463 @ X460)))))))&![X464:$i]:(((![X465:$i]:(((in @ X465 @ X464)=>(in @ X465 @ X453)))&?[X466:$i]:((in @ X466 @ X464)))=>?[X467:$i, X468:$i]:(((((in @ X467 @ X454)&(in @ X468 @ X464))&~(?[X469:$i]:(((in @ X469 @ X467)&(in @ X469 @ X464)))))&![X470:$i]:(((in @ X470 @ X454)=>(![X471:$i]:(((in @ X471 @ X470)=>(in @ X471 @ X467)))|(in @ X468 @ X470)))))))))))), introduced(definition)).
% 0.22/0.35 thf(c_0_188, negated_conjecture, ~((![X424:$i, X425:$i]:((![X426:$i]:(((in @ X426 @ X424)<=>(in @ X426 @ X425)))=>((X424)=(X425))))=>(![X427:$i]:(~(in @ X427 @ emptyset))=>(![X428:$i, X429:$i, X430:$i]:(((in @ X430 @ (setadjoin @ X428 @ X429))<=>(((X430)=(X428))|(in @ X430 @ X429))))=>(![X431:$i, X432:$i]:(((in @ X432 @ (powerset @ X431))<=>![X433:$i]:(((in @ X433 @ X432)=>(in @ X433 @ X431)))))=>(![X434:$i, X435:$i]:(((in @ X435 @ (setunion @ X434))<=>?[X436:$i]:(((in @ X435 @ X436)&(in @ X436 @ X434)))))=>((in @ emptyset @ omega)=>(![X437:$i]:(((in @ X437 @ omega)=>(in @ (setadjoin @ X437 @ X437) @ omega)))=>(![X438:$i]:((((in @ emptyset @ X438)&![X439:$i]:((((in @ X439 @ omega)&(in @ X439 @ X438))=>(in @ (setadjoin @ X439 @ X439) @ X438))))=>![X440:$i]:(((in @ X440 @ omega)=>(in @ X440 @ X438)))))=>(![X441:$i > $i > $o, X442:$i]:((![X443:$i]:(((in @ X443 @ X442)=>?[X444:$i]:(((X441 @ X443 @ X444)&![X445:$i]:(((X441 @ X443 @ X445)=>((X444)=(X445))))))))=>?[X446:$i]:(![X447:$i]:(((in @ X447 @ X446)<=>?[X448:$i]:(((in @ X448 @ X442)&(X441 @ X448 @ X447))))))))=>(![X449:$i]:((?[X450:$i]:((in @ X450 @ X449))=>?[X451:$i]:(((in @ X451 @ X449)&~(?[X452:$i]:(((in @ X452 @ X451)&(in @ X452 @ X449))))))))=>((epred1_0)=>(![X472:$i > $o]:((?[X473:$i]:(((X472 @ X473)&![X474:$i]:(((X472 @ X474)=>((X473)=(X474))))))=>(X472 @ (descr @ (^[Z0:$i]:(X472 @ Z0))))))=>(![X475:$i, X476:$i > $o, X477:$i]:(((in @ X477 @ X475)=>((X476 @ X477)=>(in @ X477 @ (dsetconstr @ X475 @ X476)))))=>(![X478:$i, X479:$i > $o, X480:$i]:(((in @ X480 @ (dsetconstr @ X478 @ X479))=>(in @ X480 @ X478)))=>(![X481:$i, X482:$i > $o, X483:$i]:(((in @ X483 @ (dsetconstr @ X481 @ X482))=>(X482 @ X483)))=>(![X484:$i > $o]:((?[X485:$i]:(((X484 @ X485)&![X486:$i]:(((X484 @ X486)=>((X485)=(X486))))))=>?[X487:$i]:(((X484 @ X487)&![X488:$i]:(((X484 @ X488)=>((X487)=(X488))))))))=>(![X489:$o, X490:$i]:(((in @ X490 @ (prop2set @ ((X489))))=>(X489)))=>(![X491:$i]:(((in @ X491 @ emptyset)=>![X492:$o]:((X492))))=>(![X493:$i]:(((in @ X493 @ emptyset)=>~($true)))=>(![X494:$i]:(~(in @ X494 @ emptyset))=>(![X495:$i > $o]:((?[X496:$i]:(((X495 @ X496)&![X497:$i]:(((X495 @ X497)=>((X496)=(X497))))))=>?[X498:$i]:((X495 @ X498))))=>(![X499:$i, X500:$i]:((![X501:$i]:(((in @ X501 @ X499)=>(in @ X501 @ X500)))=>(![X502:$i]:(((in @ X502 @ X500)=>(in @ X502 @ X499)))=>((X499)=(X500)))))=>(![X503:$i]:((![X504:$i]:(~(in @ X504 @ X503))=>((X503)=(emptyset))))=>(![X505:$i]:((![X506:$i]:(~(in @ X506 @ X505))=>((X505)=(emptyset))))=>(![X507:$i, X508:$i > $o, X509:$i]:(((in @ X509 @ X507)=>((in @ X509 @ (dsetconstr @ X507 @ X508))<=>(X508 @ X509))))=>(![X510:$i]:((((X510)!=(emptyset))=>?[X511:$i]:((in @ X511 @ X510))))=>(![X512:$i, X513:$i > $o, X514:$i]:(((in @ X514 @ X512)=>((X513 @ X514)=>((dsetconstr @ X512 @ X513)!=(emptyset)))))=>(![X515:$i]:((?[X516:$i]:((in @ X516 @ X515))=>((X515)!=(emptyset))))=>(![X517:$i, X518:$i]:((in @ X517 @ (setadjoin @ X517 @ X518)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X519:$i, X520:$i, X521:$i]:(((in @ X521 @ X520)=>(in @ X521 @ (setadjoin @ X519 @ X520))))=>(![X522:$i, X523:$i, X524:$i]:(((in @ X524 @ (setadjoin @ X522 @ X523))=>![X525:$o]:(((((X524)=(X522))=>(X525))=>(((in @ X524 @ X523)=>(X525))=>(X525))))))=>(![X526:$i, X527:$i, X528:$i]:(((in @ X528 @ (setadjoin @ X526 @ X527))=>(((X528)=(X526))|(in @ X528 @ X527))))=>(![X529:$i]:(((dsetconstr @ X529 @ (^[Z0:$i]:($true)))=(X529)))=>(![X530:$i, X531:$i]:((![X532:$i]:(((in @ X532 @ X531)=>(in @ X532 @ X530)))=>(in @ X531 @ (powerset @ X530))))=>(![X533:$i]:((in @ emptyset @ (powerset @ X533)))=>(![X534:$i]:((in @ emptyset @ (powerset @ X534)))=>(![X535:$i, X536:$i, X537:$i]:(((in @ X536 @ (powerset @ X535))=>((in @ X537 @ X536)=>(in @ X537 @ X535))))=>(![X538:$i, X539:$i, X540:$i]:(((in @ X539 @ X540)=>((in @ X540 @ X538)=>(in @ X539 @ (setunion @ X538)))))=>(![X541:$i, X542:$i]:(((in @ X542 @ (setunion @ X541))=>![X543:$o]:((![X544:$i]:(((in @ X542 @ X544)=>((in @ X544 @ X541)=>(X543))))=>(X543)))))=>(![X545:$i, X546:$i]:(((in @ X546 @ X545)=>(in @ X546 @ (powerset @ (setunion @ X545)))))=>(![X547:$i > $o]:((?[X548:$i]:(((X547 @ X548)&![X549:$i]:(((X547 @ X549)=>((X548)=(X549))))))=>?[X550:$i]:(![X551:$i]:(((X547 @ X551)<=>((X551)=(X550)))))))=>(![X552:$i]:((((X552)!=(emptyset))=>?[X553:$i]:(((in @ X553 @ X552)&$true))))=>(![X554:$i, X555:$i]:(((in @ X554 @ (setadjoin @ X555 @ emptyset))=>((X554)=(X555))))=>(![X556:$i, X557:$i]:((((X556)!=(X557))=>~(in @ X557 @ (setadjoin @ X556 @ emptyset))))=>(![X558:$i, X559:$i]:((((X558)=(X559))=>(in @ X558 @ (setadjoin @ X559 @ emptyset))))=>(![X560:$i, X561:$i]:(((in @ X560 @ (setadjoin @ X561 @ emptyset))=>(in @ X561 @ (setadjoin @ X560 @ emptyset))))=>(![X562:$i, X563:$i, X564:$i]:(((in @ X564 @ (setadjoin @ X562 @ (setadjoin @ X563 @ emptyset)))=>(((X564)=(X562))|((X564)=(X563)))))=>(![X565:$i, X566:$i]:((in @ X565 @ (setadjoin @ X565 @ (setadjoin @ X566 @ emptyset))))=>(![X567:$i, X568:$i]:((in @ X568 @ (setadjoin @ X567 @ (setadjoin @ X568 @ emptyset))))=>(![X569:$i, X570:$i > $o]:((?[X571:$i]:(((in @ X571 @ X569)&(X570 @ X571)))=>(((dsetconstr @ X569 @ X570)=(emptyset))=>~($true))))=>(![X572:$i > $o, X573:$i]:(((in @ X573 @ emptyset)=>(X572 @ X573)))=>(![X574:$i, X575:$i > $o]:((~(![X576:$i]:(((in @ X576 @ X574)=>(X575 @ X576))))=>?[X577:$i]:(((in @ X577 @ X574)&~((X575 @ X577))))))=>(![X578:$i, X579:$i > $o]:((![X580:$i]:(((in @ X580 @ X578)=>~((X579 @ X580))))=>~(?[X581:$i]:(((in @ X581 @ X578)&(X579 @ X581))))))=>(![X582:$i, X583:$i > $o]:((~(?[X584:$i]:(((in @ X584 @ X582)&(X583 @ X584))))=>![X585:$i]:(((in @ X585 @ X582)=>~((X583 @ X585))))))=>(![X586:$i, X587:$i > $o]:((?[X588:$i]:(((in @ X588 @ X586)&~((X587 @ X588))))=>~(![X589:$i]:(((in @ X589 @ X586)=>(X587 @ X589))))))=>(![X590:$o]:(((X590)=>(in @ emptyset @ (prop2set @ ((X590))))))=>(![X591:$o]:(((X591)=>(set2prop @ (prop2set @ ((X591))))))=>(![X592:$i, X593:$i > $o]:((~(?[X594:$i]:(((in @ X594 @ X592)&(X593 @ X594))))=>![X595:$i]:(((in @ X595 @ X592)=>~((X593 @ X595))))))=>(![X596:$i, X597:$i > $o]:((~(![X598:$i]:(((in @ X598 @ X596)=>(X597 @ X598))))=>?[X599:$i]:(((in @ X599 @ X596)&~((X597 @ X599))))))=>(![X600:$i > $o]:((?[X601:$i]:(((X600 @ X601)&![X602:$i]:(((X600 @ X602)=>((X601)=(X602))))))=>?[X603:$i]:(((X600 @ X603)&![X604:$i]:(((X600 @ X604)=>((X603)=(X604))))))))=>(![X605:$i > $o]:((?[X606:$i]:((X605 @ X606))=>(![X607:$i, X608:$i]:(((X605 @ X607)=>((X605 @ X608)=>((X607)=(X608)))))=>?[X609:$i]:(((X605 @ X609)&![X610:$i]:(((X605 @ X610)=>((X609)=(X610)))))))))=>(![X611:$i > $o]:((?[X612:$i]:(![X613:$i]:(((X611 @ X613)<=>((X613)=(X612)))))=>?[X614:$i]:(((X611 @ X614)&![X615:$i]:(((X611 @ X615)=>((X614)=(X615))))))))=>(![X616:$i, X617:$i]:((((X616)=(X617))=>![X618:$i, X619:$i]:((((X618)=(X619))=>((in @ X618 @ X616)=>(in @ X619 @ X617))))))=>(![X620:$i, X621:$i]:((((X620)=(X621))=>![X622:$i, X623:$i]:((((X622)=(X623))=>((in @ X622 @ X620)<=>(in @ X623 @ X621))))))=>(![X624:$i > $o]:((?[X625:$i]:(((X624 @ X625)&![X626:$i]:(((X624 @ X626)=>((X625)=(X626))))))=>![X627:$i, X628:$i]:(((X624 @ X627)=>((X624 @ X628)=>((X627)=(X628)))))))=>(![X629:$i > $o, X630:$i > $o]:((![X631:$i, X632:$i]:((((X631)=(X632))=>((X629 @ X631)<=>(X630 @ X632))))=>(?[X633:$i]:(((X629 @ X633)&![X634:$i]:(((X629 @ X634)=>((X633)=(X634))))))<=>?[X635:$i]:(((X630 @ X635)&![X636:$i]:(((X630 @ X636)=>((X635)=(X636)))))))))=>(((emptyset)=(emptyset))=>(![X637:$i, X638:$i]:((((X637)=(X638))=>![X639:$i, X640:$i]:((((X639)=(X640))=>((setadjoin @ X637 @ X639)=(setadjoin @ X638 @ X640))))))=>(![X641:$i, X642:$i]:((((X641)=(X642))=>((powerset @ X641)=(powerset @ X642))))=>(![X643:$i, X644:$i]:((((X643)=(X644))=>((setunion @ X643)=(setunion @ X644))))=>(((omega)=(omega))=>(![X645:$i > $o]:((?[X646:$i]:(((X645 @ X646)&![X647:$i]:(((X645 @ X647)=>((X646)=(X647))))))=>![X648:$i, X649:$i]:(((X645 @ X648)=>((X645 @ X649)=>((X648)=(X649)))))))=>(![X650:$i > $o, X651:$i > $o]:((![X652:$i, X653:$i]:((((X652)=(X653))=>((X650 @ X652)<=>(X651 @ X653))))=>(?[X654:$i]:(((X650 @ X654)&![X655:$i]:(((X650 @ X655)=>((X654)=(X655))))))=>(?[X656:$i]:(((X651 @ X656)&![X657:$i]:(((X651 @ X657)=>((X656)=(X657))))))=>((descr @ X650)=(descr @ X651))))))=>(![X658:$i, X659:$i]:((((X658)=(X659))=>![X660:$i > $o, X661:$i > $o]:((![X662:$i]:(((in @ X662 @ X658)=>![X663:$i]:(((in @ X663 @ X659)=>(((X662)=(X663))=>((X660 @ X662)<=>(X661 @ X663)))))))=>((dsetconstr @ X658 @ X660)=(dsetconstr @ X659 @ X661))))))=>(![X664:$i, X665:$i]:((![X666:$i]:(((in @ X666 @ X664)=>(in @ X666 @ X665)))=>(subset @ X664 @ X665)))=>(![X667:$i, X668:$i]:((((X667)=(X668))=>(subset @ X668 @ X667)))=>(![X669:$i, X670:$i]:((((X669)=(X670))=>(subset @ X669 @ X670)))=>(![X671:$i, X672:$i]:((![X673:$i]:(((in @ X673 @ X671)=>(in @ X673 @ X672)))=>(subset @ X671 @ X672)))=>(![X674:$i]:((subset @ emptyset @ X674))=>(![X675:$i, X676:$i, X677:$i]:(((subset @ X675 @ X676)=>((in @ X677 @ X675)=>(in @ X677 @ X676))))=>(![X678:$i, X679:$i, X680:$i]:(((subset @ X678 @ X679)=>(~(in @ X680 @ X679)=>~(in @ X680 @ X678))))=>(![X681:$i, X682:$i, X683:$i]:(((in @ X683 @ X681)=>(~(in @ X683 @ X682)=>~(subset @ X681 @ X682))))=>(![X684:$i, X685:$i]:((~(subset @ X684 @ X685)=>((X684)!=(X685))))=>(![X686:$i, X687:$i, X688:$i]:(((in @ X688 @ X686)=>(~(in @ X688 @ X687)=>((X686)!=(X687)))))=>(![X689:$i]:((subset @ X689 @ X689))=>(![X690:$i, X691:$i, X692:$i]:(((subset @ X690 @ X691)=>((subset @ X691 @ X692)=>(subset @ X690 @ X692))))=>(![X693:$i, X694:$i]:((subset @ X694 @ (setadjoin @ X693 @ X694)))=>(![X695:$i, X696:$i, X697:$i]:(((subset @ X695 @ X697)=>(subset @ X695 @ (setadjoin @ X696 @ X697))))=>(![X698:$i, X699:$i]:(((subset @ X698 @ X699)=>(in @ X698 @ (powerset @ X699))))=>(![X700:$i, X701:$i]:(((subset @ X700 @ X701)=>((subset @ X701 @ X700)=>((X700)=(X701)))))=>(![X702:$i]:(((subset @ X702 @ emptyset)=>((X702)=(emptyset))))=>(![X703:$i, X704:$i]:(((subset @ X704 @ X703)=>(in @ X704 @ (powerset @ X703))))=>(![X705:$i, X706:$i]:(((in @ X706 @ (powerset @ X705))=>(subset @ X706 @ X705)))=>(![X707:$i]:((in @ X707 @ (powerset @ X707)))=>(![X708:$i, X709:$i]:(((subset @ X708 @ X709)=>(subset @ (powerset @ X708) @ (powerset @ X709))))=>(![X710:$i, X711:$i > $o]:((in @ (dsetconstr @ X710 @ X711) @ (powerset @ X710)))=>(![X712:$i, X713:$i > $o]:((subset @ (dsetconstr @ X712 @ X713) @ X712))=>(![X714:$i, X715:$i, X716:$i]:(((in @ X716 @ X714)=>(in @ X716 @ (binunion @ X714 @ X715))))=>(![X717:$i, X718:$i]:((in @ X718 @ (setadjoin @ X717 @ (setadjoin @ X718 @ emptyset))))=>(![X719:$i, X720:$i, X721:$i]:(((in @ X721 @ X720)=>(in @ X721 @ (binunion @ X719 @ X720))))=>(![X722:$i, X723:$i, X724:$i, X725:$o]:(((in @ X724 @ (binunion @ X722 @ X723))=>(((in @ X724 @ X722)=>(X725))=>(((in @ X724 @ X723)=>(X725))=>(X725)))))=>(![X726:$i, X727:$i, X728:$i]:(((in @ X728 @ (binunion @ X726 @ X727))=>((in @ X728 @ X726)|(in @ X728 @ X727))))=>(![X729:$i, X730:$i]:((subset @ X729 @ (binunion @ X729 @ X730)))=>(![X731:$i, X732:$i]:((subset @ X732 @ (binunion @ X731 @ X732)))=>(![X733:$i, X734:$i, X735:$i]:(((in @ X735 @ X733)=>((in @ X735 @ X734)=>(in @ X735 @ (binintersect @ X733 @ X734)))))=>(![X736:$i, X737:$i, X738:$i]:(((subset @ X738 @ X736)=>((subset @ X738 @ X737)=>(subset @ X738 @ (binintersect @ X736 @ X737)))))=>(![X739:$i, X740:$i, X741:$i]:(((in @ X741 @ (binintersect @ X739 @ X740))=>(in @ X741 @ X739)))=>(![X742:$i, X743:$i]:((subset @ (binintersect @ X742 @ X743) @ X742))=>(![X744:$i, X745:$i]:(((subset @ X744 @ X745)=>((binintersect @ X744 @ X745)=(X744))))=>(![X746:$i, X747:$i]:((((binintersect @ X746 @ X747)=(X747))=>(subset @ X747 @ X746)))=>(![X748:$i, X749:$i, X750:$i]:(((in @ X750 @ (binintersect @ X748 @ X749))=>(in @ X750 @ X749)))=>(![X751:$i, X752:$i]:((~(?[X753:$i]:(((in @ X753 @ X751)&(in @ X753 @ X752))))=>((binintersect @ X751 @ X752)=(emptyset))))=>(![X754:$i, X755:$i]:((subset @ (binintersect @ X754 @ X755) @ X755))=>(![X756:$i, X757:$i]:(((subset @ X757 @ X756)=>((binintersect @ X756 @ X757)=(X757))))=>(![X758:$i, X759:$i]:((((binintersect @ X758 @ X759)=(X758))=>(subset @ X758 @ X759)))=>(![X760:$i, X761:$i, X762:$i]:(((binintersect @ X760 @ (binunion @ X761 @ X762))=(binunion @ (binintersect @ X760 @ X761) @ (binintersect @ X760 @ X762))))=>(![X763:$i, X764:$i, X765:$i]:(((in @ X765 @ X763)=>(~(in @ X765 @ X764)=>(in @ X765 @ (setminus @ X763 @ X764)))))=>(![X766:$i, X767:$i, X768:$i]:(((in @ X768 @ (setminus @ X766 @ X767))=>(in @ X768 @ X766)))=>(![X769:$i, X770:$i, X771:$i]:(((in @ X771 @ (setminus @ X769 @ X770))=>~(in @ X771 @ X770)))=>(![X772:$i, X773:$i]:(((subset @ X772 @ X773)=>((setminus @ X772 @ X773)=(emptyset))))=>(![X774:$i, X775:$i, X776:$i]:((~(in @ X776 @ (setminus @ X774 @ X775))=>((in @ X776 @ X774)=>(in @ X776 @ X775))))=>(![X777:$i, X778:$i, X779:$i]:((~(in @ X779 @ (setminus @ X777 @ X778))=>(~(in @ X779 @ X778)=>~(in @ X779 @ X777))))=>(![X780:$i, X781:$i, X782:$i]:((~(in @ X782 @ X780)=>~(in @ X782 @ (setminus @ X780 @ X781))))=>(![X783:$i, X784:$i, X785:$i]:(((in @ X785 @ X784)=>~(in @ X785 @ (setminus @ X783 @ X784))))=>(![X786:$i, X787:$i]:((subset @ (setminus @ X786 @ X787) @ X786))=>(![X788:$i, X789:$i]:((((setminus @ X788 @ X789)=(emptyset))=>(subset @ X788 @ X789)))=>(![X790:$i, X791:$i, X792:$i]:(((in @ X792 @ (symdiff @ X790 @ X791))=>![X793:$o]:((((in @ X792 @ X790)=>(~(in @ X792 @ X791)=>(X793)))=>((~(in @ X792 @ X790)=>((in @ X792 @ X791)=>(X793)))=>(X793))))))=>(![X794:$i, X795:$i, X796:$i]:(((in @ X796 @ X794)=>(~(in @ X796 @ X795)=>(in @ X796 @ (symdiff @ X794 @ X795)))))=>(![X797:$i, X798:$i, X799:$i]:((~(in @ X799 @ X797)=>((in @ X799 @ X798)=>(in @ X799 @ (symdiff @ X797 @ X798)))))=>(![X800:$i, X801:$i, X802:$i]:(((in @ X802 @ X800)=>((in @ X802 @ X801)=>~(in @ X802 @ (symdiff @ X800 @ X801)))))=>(![X803:$i, X804:$i, X805:$i]:((~(in @ X805 @ X803)=>(~(in @ X805 @ X804)=>~(in @ X805 @ (symdiff @ X803 @ X804)))))=>(![X806:$i, X807:$i]:((in @ X807 @ (setadjoin @ X806 @ (setadjoin @ X807 @ emptyset))))=>(![X808:$i, X809:$i]:((in @ X808 @ (setunion @ (setadjoin @ (setadjoin @ X808 @ emptyset) @ (setadjoin @ (setadjoin @ X808 @ (setadjoin @ X809 @ emptyset)) @ emptyset)))))=>(![X810:$i, X811:$i]:((in @ X811 @ (setunion @ (setadjoin @ (setadjoin @ X810 @ emptyset) @ (setadjoin @ (setadjoin @ X810 @ (setadjoin @ X811 @ emptyset)) @ emptyset)))))=>(![X812:$i, X813:$i]:(?[X814:$i]:(((in @ X814 @ (setunion @ (setadjoin @ (setadjoin @ X812 @ emptyset) @ (setadjoin @ (setadjoin @ X812 @ (setadjoin @ X813 @ emptyset)) @ emptyset))))&?[X815:$i]:(((in @ X815 @ (setunion @ (setadjoin @ (setadjoin @ X812 @ emptyset) @ (setadjoin @ (setadjoin @ X812 @ (setadjoin @ X813 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X812 @ emptyset) @ (setadjoin @ (setadjoin @ X812 @ (setadjoin @ X813 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X814 @ emptyset) @ (setadjoin @ (setadjoin @ X814 @ (setadjoin @ X815 @ emptyset)) @ emptyset))))))))=>(![X816:$i, X817:$i]:(?[X818:$i]:(((in @ X818 @ (setunion @ (kpair @ X816 @ X817)))&?[X819:$i]:(((in @ X819 @ (setunion @ (kpair @ X816 @ X817)))&((kpair @ X816 @ X817)=(setadjoin @ (setadjoin @ X818 @ emptyset) @ (setadjoin @ (setadjoin @ X818 @ (setadjoin @ X819 @ emptyset)) @ emptyset))))))))=>(![X820:$i, X821:$i]:(((in @ X821 @ X820)=>(subset @ (setadjoin @ X821 @ emptyset) @ X820)))=>(![X822:$i, X823:$i]:(((in @ X823 @ X822)=>(in @ (setadjoin @ X823 @ emptyset) @ (powerset @ X822))))=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (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)],[c_0_159, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_160]), foundationAx]), wellorderingAx]), c_0_161]), c_0_162]), c_0_163]), c_0_164]), c_0_165]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_166]), setext]), emptyI]), noeltsimpempty]), c_0_167]), c_0_168]), c_0_169]), c_0_170]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_171]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_172]), c_0_173]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_174]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_175]), c_0_176]), c_0_177]), inCongP]), in__Cong]), c_0_178]), c_0_179]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_180]), c_0_181]), c_0_182]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_183]), c_0_184]), 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]), c_0_185]), c_0_186]), singletonsubset]), singletoninpowerset])])]), c_0_187])).
% 0.22/0.35 thf(c_0_189, negated_conjecture, ![X832:$i, X833:$i, X835:$i, X836:$i, X837:$i, X838:$i, X839:$i, X840:$i, X841:$i, X842:$i, X843:$i, X845:$i, X846:$i, X848:$i, X849:$i, X850:$i, X851:$i, X852:$i, X854:$i, X855:$i > $i > $o, X856:$i, X858:$i, X861:$i, X863:$i, X864:$i, X865:$i, X866:$i, X868:$i, X869:$i > $o, X870:$i, X872:$i, X873:$i > $o, X874:$i, X875:$i, X876:$i > $o, X877:$i, X878:$i, X879:$i > $o, X880:$i, X881:$i > $o, X882:$i, X885:$i, X886:$o, X887:$i, X888:$i, X889:$o, X890:$i, X891:$i, X892:$i > $o, X893:$i, X896:$i, X897:$i, X900:$i, X902:$i, X904:$i, X905:$i > $o, X906:$i, X907:$i, X909:$i, X910:$i > $o, X911:$i, X912:$i, X913:$i, X914:$i, X915:$i, X916:$i, X917:$i, X918:$i, X919:$i, X920:$i, X921:$i, X922:$o, X923:$i, X924:$i, X925:$i, X926:$i, X927:$i, X928:$i, X930:$i, X931:$i, X932:$i, X933:$i, X934:$i, X935:$i, X936:$i, X937:$i, X938:$i, X939:$i, X940:$o, X942:$i, X943:$i, X944:$i > $o, X945:$i, X948:$i, X949:$i, X950:$i, X952:$i, X953:$i, X954:$i, X955:$i, X956:$i, X957:$i, X958:$i, X959:$i, X960:$i, X961:$i, X962:$i, X963:$i, X964:$i, X965:$i, X966:$i, X967:$i, X968:$i > $o, X969:$i, X970:$i > $o, X971:$i, X972:$i, X973:$i > $o, X974:$i, X976:$i, X977:$i > $o, X979:$i, X980:$i, X981:$i > $o, X983:$i, X984:$i, X985:$i > $o, X986:$i, X988:$o, X989:$o, X990:$i, X991:$i > $o, X993:$i, X994:$i, X995:$i > $o, X996:$i, X998:$i > $o, X999:$i, X1002:$i, X1003:$i > $o, X1004:$i, X1008:$i, X1009:$i > $o, X1010:$i, X1013:$i, X1014:$i, X1015:$i, X1016:$i, X1017:$i, X1018:$i, X1019:$i, X1020:$i, X1021:$i, X1022:$i > $o, X1023:$i, X1025:$i, X1026:$i, X1027:$i > $o, X1028:$i > $o, X1031:$i, X1034:$i, X1035:$i, X1038:$i, X1039:$i, X1040:$i, X1041:$i, X1042:$i, X1043:$i, X1044:$i, X1045:$i, X1046:$i, X1047:$i > $o, X1048:$i, X1050:$i, X1051:$i, X1052:$i > $o, X1053:$i > $o, X1056:$i, X1058:$i, X1060:$i, X1061:$i, X1062:$i > $o, X1063:$i > $o, X1066:$i, X1067:$i, X1069:$i, X1070:$i, X1071:$i, X1072:$i, X1073:$i, X1074:$i, X1076:$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, X1095:$i, X1096:$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 > $o, X1114:$i, X1115:$i > $o, X1116:$i, X1117:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i, X1126:$i, X1127:$o, X1128:$i, X1129:$i, X1130:$i, X1131:$i, X1132:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$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, 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, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$o, X1196:$i, X1197:$i, X1198:$i, X1199:$i, X1200:$i, X1201:$i, X1202:$i, X1203:$i, X1204:$i, X1205:$i, X1206:$i, X1207:$i, X1208:$i, X1209:$i, X1210:$i, X1211:$i, X1212:$i, X1213:$i, X1214:$i, X1215:$i, X1218:$i, X1219:$i, X1222:$i, X1223:$i, X1224:$i, X1225:$i]:((((~(in @ (esk1_2 @ X832 @ X833) @ X832)|~(in @ (esk1_2 @ X832 @ X833) @ X833)|((X832)=(X833)))&((in @ (esk1_2 @ X832 @ X833) @ X832)|(in @ (esk1_2 @ X832 @ X833) @ X833)|((X832)=(X833))))&(~(in @ X835 @ emptyset)&(((~(in @ X838 @ (setadjoin @ X836 @ X837))|(((X838)=(X836))|(in @ X838 @ X837)))&((((X838)!=(X836))|(in @ X838 @ (setadjoin @ X836 @ X837)))&(~(in @ X838 @ X837)|(in @ X838 @ (setadjoin @ X836 @ X837)))))&(((~(in @ X840 @ (powerset @ X839))|(~(in @ X841 @ X840)|(in @ X841 @ X839)))&(((in @ (esk2_2 @ X842 @ X843) @ X843)|(in @ X843 @ (powerset @ X842)))&(~(in @ (esk2_2 @ X842 @ X843) @ X842)|(in @ X843 @ (powerset @ X842)))))&(((((in @ X846 @ (esk3_2 @ X845 @ X846))|~(in @ X846 @ (setunion @ X845)))&((in @ (esk3_2 @ X845 @ X846) @ X845)|~(in @ X846 @ (setunion @ X845))))&(~(in @ X849 @ X850)|~(in @ X850 @ X848)|(in @ X849 @ (setunion @ X848))))&((in @ emptyset @ omega)&((~(in @ X851 @ omega)|(in @ (setadjoin @ X851 @ X851) @ omega))&(((((in @ (esk4_1 @ X852) @ omega)|~(in @ emptyset @ X852)|(~(in @ X854 @ omega)|(in @ X854 @ X852)))&((in @ (esk4_1 @ X852) @ X852)|~(in @ emptyset @ X852)|(~(in @ X854 @ omega)|(in @ X854 @ X852))))&(~(in @ (setadjoin @ (esk4_1 @ X852) @ (esk4_1 @ X852)) @ X852)|~(in @ emptyset @ X852)|(~(in @ X854 @ omega)|(in @ X854 @ X852))))&((((((in @ (esk8_3 @ X855 @ X856 @ X861) @ X856)|~(in @ X861 @ (esk7_2 @ X855 @ X856))|(in @ (esk5_2 @ X855 @ X856) @ X856))&((X855 @ (esk8_3 @ X855 @ X856 @ X861) @ X861)|~(in @ X861 @ (esk7_2 @ X855 @ X856))|(in @ (esk5_2 @ X855 @ X856) @ X856)))&(~(in @ X864 @ X856)|~(X855 @ X864 @ X863)|(in @ X863 @ (esk7_2 @ X855 @ X856))|(in @ (esk5_2 @ X855 @ X856) @ X856)))&(((((in @ (esk8_3 @ X855 @ X856 @ X861) @ X856)|~(in @ X861 @ (esk7_2 @ X855 @ X856))|((X855 @ (esk5_2 @ X855 @ X856) @ (esk6_3 @ X855 @ X856 @ X858))|~(X855 @ (esk5_2 @ X855 @ X856) @ X858)))&((X855 @ (esk8_3 @ X855 @ X856 @ X861) @ X861)|~(in @ X861 @ (esk7_2 @ X855 @ X856))|((X855 @ (esk5_2 @ X855 @ X856) @ (esk6_3 @ X855 @ X856 @ X858))|~(X855 @ (esk5_2 @ X855 @ X856) @ X858))))&(~(in @ X864 @ X856)|~(X855 @ X864 @ X863)|(in @ X863 @ (esk7_2 @ X855 @ X856))|((X855 @ (esk5_2 @ X855 @ X856) @ (esk6_3 @ X855 @ X856 @ X858))|~(X855 @ (esk5_2 @ X855 @ X856) @ X858))))&((((in @ (esk8_3 @ X855 @ X856 @ X861) @ X856)|~(in @ X861 @ (esk7_2 @ X855 @ X856))|(((X858)!=(esk6_3 @ X855 @ X856 @ X858))|~(X855 @ (esk5_2 @ X855 @ X856) @ X858)))&((X855 @ (esk8_3 @ X855 @ X856 @ X861) @ X861)|~(in @ X861 @ (esk7_2 @ X855 @ X856))|(((X858)!=(esk6_3 @ X855 @ X856 @ X858))|~(X855 @ (esk5_2 @ X855 @ 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(esk52_2 @ X1066 @ X1067) @ X1066)|(subset @ X1066 @ X1067))&(~(in @ (esk52_2 @ X1066 @ X1067) @ X1067)|(subset @ X1066 @ X1067)))&((((X1069)!=(X1070))|(subset @ X1070 @ X1069))&((((X1071)!=(X1072))|(subset @ X1071 @ X1072))&((((in @ (esk53_2 @ X1073 @ X1074) @ X1073)|(subset @ X1073 @ X1074))&(~(in @ (esk53_2 @ X1073 @ X1074) @ X1074)|(subset @ X1073 @ X1074)))&((subset @ emptyset @ X1076)&((~(subset @ X1077 @ X1078)|(~(in @ X1079 @ X1077)|(in @ X1079 @ X1078)))&((~(subset @ X1080 @ X1081)|((in @ X1082 @ X1081)|~(in @ X1082 @ X1080)))&((~(in @ X1085 @ X1083)|((in @ X1085 @ X1084)|~(subset @ X1083 @ X1084)))&(((subset @ X1086 @ X1087)|((X1086)!=(X1087)))&((~(in @ X1090 @ X1088)|((in @ X1090 @ X1089)|((X1088)!=(X1089))))&((subset @ X1091 @ X1091)&((~(subset @ X1092 @ X1093)|(~(subset @ X1093 @ X1094)|(subset @ X1092 @ X1094)))&((subset @ X1096 @ (setadjoin @ X1095 @ X1096))&((~(subset @ X1097 @ X1099)|(subset @ X1097 @ (setadjoin @ X1098 @ X1099)))&((~(subset @ X1100 @ X1101)|(in @ X1100 @ (powerset @ X1101)))&((~(subset @ X1102 @ X1103)|(~(subset @ X1103 @ X1102)|((X1102)=(X1103))))&((~(subset @ X1104 @ emptyset)|((X1104)=(emptyset)))&((~(subset @ X1106 @ X1105)|(in @ X1106 @ (powerset @ X1105)))&((~(in @ X1108 @ (powerset @ X1107))|(subset @ X1108 @ X1107))&((in @ X1109 @ (powerset @ X1109))&((~(subset @ X1110 @ X1111)|(subset @ (powerset @ X1110) @ (powerset @ X1111)))&((in @ (dsetconstr @ X1112 @ X1113) @ (powerset @ X1112))&((subset @ (dsetconstr @ X1114 @ X1115) @ X1114)&((~(in @ X1118 @ X1116)|(in @ X1118 @ (binunion @ X1116 @ X1117)))&((in @ X1120 @ (setadjoin @ X1119 @ (setadjoin @ X1120 @ emptyset)))&((~(in @ X1123 @ X1122)|(in @ X1123 @ (binunion @ X1121 @ X1122)))&(((((in @ X1126 @ X1125)|(X1127)|(in @ X1126 @ X1124)|~(in @ X1126 @ (binunion @ X1124 @ X1125)))&(~(X1127)|(X1127)|(in @ X1126 @ X1124)|~(in @ X1126 @ (binunion @ X1124 @ X1125))))&(((in @ X1126 @ X1125)|(X1127)|~(X1127)|~(in @ X1126 @ (binunion @ X1124 @ X1125)))&(~(X1127)|(X1127)|~(X1127)|~(in @ X1126 @ (binunion @ X1124 @ X1125)))))&((~(in @ X1130 @ (binunion @ X1128 @ X1129))|((in @ X1130 @ X1128)|(in @ X1130 @ X1129)))&((subset @ X1131 @ (binunion @ X1131 @ X1132))&((subset @ X1134 @ (binunion @ X1133 @ X1134))&((~(in @ X1137 @ X1135)|(~(in @ X1137 @ X1136)|(in @ X1137 @ (binintersect @ X1135 @ X1136))))&((~(subset @ X1140 @ X1138)|(~(subset @ X1140 @ X1139)|(subset @ X1140 @ (binintersect @ X1138 @ X1139))))&((~(in @ X1143 @ (binintersect @ X1141 @ X1142))|(in @ X1143 @ X1141))&((subset @ (binintersect @ X1144 @ X1145) @ X1144)&((~(subset @ X1146 @ X1147)|((binintersect @ X1146 @ X1147)=(X1146)))&((((binintersect @ X1148 @ X1149)!=(X1149))|(subset @ X1149 @ X1148))&((~(in @ X1152 @ (binintersect @ X1150 @ X1151))|(in @ X1152 @ X1151))&((((in @ (esk54_2 @ X1153 @ X1154) @ X1153)|((binintersect @ X1153 @ X1154)=(emptyset)))&((in @ (esk54_2 @ X1153 @ X1154) @ X1154)|((binintersect @ X1153 @ X1154)=(emptyset))))&((subset @ (binintersect @ X1156 @ X1157) @ X1157)&((~(subset @ X1159 @ X1158)|((binintersect @ X1158 @ X1159)=(X1159)))&((((binintersect @ X1160 @ X1161)!=(X1160))|(subset @ X1160 @ X1161))&(((binintersect @ X1162 @ (binunion @ X1163 @ X1164))=(binunion @ (binintersect @ X1162 @ X1163) @ (binintersect @ X1162 @ X1164)))&((~(in @ X1167 @ X1165)|((in @ X1167 @ X1166)|(in @ X1167 @ (setminus @ X1165 @ X1166))))&((~(in @ X1170 @ (setminus @ X1168 @ X1169))|(in @ X1170 @ X1168))&((~(in @ X1173 @ (setminus @ X1171 @ X1172))|~(in @ X1173 @ X1172))&((~(subset @ X1174 @ X1175)|((setminus @ X1174 @ X1175)=(emptyset)))&(((in @ X1178 @ (setminus @ X1176 @ X1177))|(~(in @ X1178 @ X1176)|(in @ X1178 @ X1177)))&(((in @ X1181 @ (setminus @ X1179 @ X1180))|((in @ X1181 @ X1180)|~(in @ X1181 @ X1179)))&(((in @ X1184 @ X1182)|~(in @ X1184 @ (setminus @ X1182 @ X1183)))&((~(in @ X1187 @ X1186)|~(in @ X1187 @ (setminus @ X1185 @ X1186)))&((subset @ (setminus @ X1188 @ X1189) @ X1188)&((((setminus @ X1190 @ X1191)!=(emptyset))|(subset @ X1190 @ X1191))&((((~(in @ X1194 @ X1192)|(X1195)|(in @ X1194 @ X1192)|~(in @ X1194 @ (symdiff @ X1192 @ X1193)))&(((in @ X1194 @ X1193)|(X1195)|(in @ X1194 @ X1192)|~(in @ X1194 @ (symdiff @ X1192 @ X1193)))&(~(X1195)|(X1195)|(in @ X1194 @ X1192)|~(in @ X1194 @ (symdiff @ X1192 @ X1193)))))&(((~(in @ X1194 @ X1192)|(X1195)|~(in @ X1194 @ X1193)|~(in @ X1194 @ (symdiff @ X1192 @ X1193)))&(((in @ X1194 @ X1193)|(X1195)|~(in @ X1194 @ X1193)|~(in @ X1194 @ (symdiff @ X1192 @ X1193)))&(~(X1195)|(X1195)|~(in @ X1194 @ X1193)|~(in @ X1194 @ (symdiff @ X1192 @ X1193)))))&((~(in @ X1194 @ X1192)|(X1195)|~(X1195)|~(in @ X1194 @ (symdiff @ X1192 @ X1193)))&(((in @ X1194 @ X1193)|(X1195)|~(X1195)|~(in @ X1194 @ (symdiff @ X1192 @ X1193)))&(~(X1195)|(X1195)|~(X1195)|~(in @ X1194 @ (symdiff @ X1192 @ X1193)))))))&((~(in @ X1198 @ X1196)|((in @ X1198 @ X1197)|(in @ X1198 @ (symdiff @ X1196 @ X1197))))&(((in @ X1201 @ X1199)|(~(in @ X1201 @ X1200)|(in @ X1201 @ (symdiff @ X1199 @ X1200))))&((~(in @ X1204 @ X1202)|(~(in @ X1204 @ X1203)|~(in @ X1204 @ (symdiff @ X1202 @ X1203))))&(((in @ X1207 @ X1205)|((in @ X1207 @ X1206)|~(in @ X1207 @ (symdiff @ X1205 @ X1206))))&((in @ X1209 @ (setadjoin @ X1208 @ (setadjoin @ X1209 @ emptyset)))&((in @ X1210 @ (setunion @ (setadjoin @ (setadjoin @ X1210 @ emptyset) @ (setadjoin @ (setadjoin @ X1210 @ (setadjoin @ X1211 @ emptyset)) @ emptyset))))&((in @ X1213 @ (setunion @ (setadjoin @ (setadjoin @ X1212 @ emptyset) @ (setadjoin @ (setadjoin @ X1212 @ (setadjoin @ X1213 @ emptyset)) @ emptyset))))&(((in @ (esk55_2 @ X1214 @ X1215) @ (setunion @ (setadjoin @ (setadjoin @ X1214 @ emptyset) @ (setadjoin @ (setadjoin @ X1214 @ (setadjoin @ X1215 @ emptyset)) @ emptyset))))&((in @ (esk56_2 @ X1214 @ X1215) @ (setunion @ (setadjoin @ (setadjoin @ X1214 @ emptyset) @ (setadjoin @ (setadjoin @ X1214 @ (setadjoin @ X1215 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1214 @ emptyset) @ (setadjoin @ (setadjoin @ X1214 @ (setadjoin @ X1215 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk55_2 @ X1214 @ X1215) @ emptyset) @ (setadjoin @ (setadjoin @ (esk55_2 @ X1214 @ X1215) @ (setadjoin @ (esk56_2 @ X1214 @ X1215) @ emptyset)) @ emptyset)))))&(((in @ (esk57_2 @ X1218 @ X1219) @ (setunion @ (kpair @ X1218 @ X1219)))&((in @ (esk58_2 @ X1218 @ X1219) @ (setunion @ (kpair @ X1218 @ X1219)))&((kpair @ X1218 @ X1219)=(setadjoin @ (setadjoin @ (esk57_2 @ X1218 @ X1219) @ emptyset) @ (setadjoin @ (setadjoin @ (esk57_2 @ X1218 @ X1219) @ (setadjoin @ (esk58_2 @ X1218 @ X1219) @ emptyset)) @ emptyset)))))&((~(in @ X1223 @ X1222)|(subset @ (setadjoin @ X1223 @ emptyset) @ X1222))&((~(in @ X1225 @ X1224)|(in @ (setadjoin @ X1225 @ emptyset) @ (powerset @ X1224)))&((in @ esk61_0 @ esk59_0)&~(in @ (setadjoin @ esk61_0 @ emptyset) @ (powerset @ (binunion @ esk59_0 @ esk60_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_188])])])])])])])).
% 0.22/0.35 thf(c_0_190, negated_conjecture, ~((in @ (setadjoin @ esk61_0 @ emptyset) @ (powerset @ (binunion @ esk59_0 @ esk60_0)))), inference(split_conjunct,[status(thm)],[c_0_189])).
% 0.22/0.35 thf(c_0_191, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ X3))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_189])).
% 0.22/0.35 thf(c_0_192, negated_conjecture, ~((subset @ (setadjoin @ esk61_0 @ emptyset) @ (binunion @ esk59_0 @ esk60_0))), inference(spm,[status(thm)],[c_0_190, c_0_191])).
% 0.22/0.35 thf(c_0_193, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ (setadjoin @ X2 @ emptyset) @ X3)|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_189])).
% 0.22/0.35 thf(c_0_194, negated_conjecture, ~((in @ esk61_0 @ (binunion @ esk59_0 @ esk60_0))), inference(spm,[status(thm)],[c_0_192, c_0_193])).
% 0.22/0.35 thf(c_0_195, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X3 @ X4))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_189])).
% 0.22/0.35 thf(c_0_196, negated_conjecture, (in @ esk61_0 @ esk59_0), inference(split_conjunct,[status(thm)],[c_0_189])).
% 0.22/0.35 thf(c_0_197, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194, c_0_195]), c_0_196])]), ['proof']).
% 0.22/0.35 % SZS output end CNFRefutation
% 0.22/0.35 % Parsed axioms : 307
% 0.22/0.35 % Removed by relevancy pruning/SinE : 0
% 0.22/0.35 % Initial clauses : 437
% 0.22/0.35 % Removed in clause preprocessing : 187
% 0.22/0.35 % Initial clauses in saturation : 250
% 0.22/0.35 % Processed clauses : 125
% 0.22/0.35 % ...of these trivial : 6
% 0.22/0.35 % ...subsumed : 29
% 0.22/0.35 % ...remaining for further processing : 90
% 0.22/0.35 % Other redundant clauses eliminated : 10
% 0.22/0.35 % Clauses deleted for lack of memory : 0
% 0.22/0.35 % Backward-subsumed : 0
% 0.22/0.35 % Backward-rewritten : 2
% 0.22/0.35 % Generated clauses : 314
% 0.22/0.35 % ...of the previous two non-redundant : 245
% 0.22/0.35 % ...aggressively subsumed : 0
% 0.22/0.35 % Contextual simplify-reflections : 0
% 0.22/0.35 % Paramodulations : 304
% 0.22/0.35 % Factorizations : 0
% 0.22/0.35 % NegExts : 0
% 0.22/0.35 % Equation resolutions : 10
% 0.22/0.35 % Disequality decompositions : 0
% 0.22/0.35 % Total rewrite steps : 66
% 0.22/0.35 % ...of those cached : 36
% 0.22/0.35 % Propositional unsat checks : 0
% 0.22/0.35 % Propositional check models : 0
% 0.22/0.35 % Propositional check unsatisfiable : 0
% 0.22/0.35 % Propositional clauses : 0
% 0.22/0.35 % Propositional clauses after purity: 0
% 0.22/0.35 % Propositional unsat core size : 0
% 0.22/0.35 % Propositional preprocessing time : 0.000
% 0.22/0.35 % Propositional encoding time : 0.000
% 0.22/0.35 % Propositional solver time : 0.000
% 0.22/0.35 % Success case prop preproc time : 0.000
% 0.22/0.35 % Success case prop encoding time : 0.000
% 0.22/0.35 % Success case prop solver time : 0.000
% 0.22/0.35 % Current number of processed clauses : 82
% 0.22/0.35 % Positive orientable unit clauses : 34
% 0.22/0.35 % Positive unorientable unit clauses: 0
% 0.22/0.35 % Negative unit clauses : 4
% 0.22/0.35 % Non-unit-clauses : 44
% 0.22/0.35 % Current number of unprocessed clauses: 370
% 0.22/0.35 % ...number of literals in the above : 1083
% 0.22/0.35 % Current number of archived formulas : 0
% 0.22/0.35 % Current number of archived clauses : 2
% 0.22/0.35 % Clause-clause subsumption calls (NU) : 145
% 0.22/0.35 % Rec. Clause-clause subsumption calls : 132
% 0.22/0.35 % Non-unit clause-clause subsumptions : 18
% 0.22/0.35 % Unit Clause-clause subsumption calls : 4
% 0.22/0.35 % Rewrite failures with RHS unbound : 0
% 0.22/0.35 % BW rewrite match attempts : 6
% 0.22/0.35 % BW rewrite match successes : 2
% 0.22/0.35 % Condensation attempts : 0
% 0.22/0.35 % Condensation successes : 0
% 0.22/0.35 % Termbank termtop insertions : 39433
% 0.22/0.35 % Search garbage collected termcells : 13709
% 0.22/0.35
% 0.22/0.35 % -------------------------------------------------
% 0.22/0.35 % User time : 0.051 s
% 0.22/0.35 % System time : 0.013 s
% 0.22/0.35 % Total time : 0.063 s
% 0.22/0.35 % Maximum resident set size: 6752 pages
% 0.22/0.35
% 0.22/0.35 % -------------------------------------------------
% 0.22/0.35 % User time : 0.059 s
% 0.22/0.35 % System time : 0.019 s
% 0.22/0.35 % Total time : 0.078 s
% 0.22/0.35 % Maximum resident set size: 5120 pages
% 0.22/0.35 % E exiting
%------------------------------------------------------------------------------