%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU635^1 : 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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:27:00 AM UTC 2026
% Result : Theorem 0.57s 0.43s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU635^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 % Computer : n015.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 14:04:03 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.22 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.28 Running higher-order theorem proving
% 0.25/0.32 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.33slpoNXPQ/E---3.1_3572842.p
% 0.57/0.43 % Version: 3.5.1-ho
% 0.57/0.43 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.57/0.43 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.43 % Starting ehoh_best5 with 300s (1) cores
% 0.57/0.43 % Starting almost_fo_3_lam with 300s (1) cores
% 0.57/0.43 % Starting new_bool_5 with 300s (1) cores
% 0.57/0.43 % Starting pre_casc_3 with 300s (1) cores
% 0.57/0.43 % Starting ho_unfolding_8 with 300s (1) cores
% 0.57/0.43 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.57/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.57/0.43 % Starting new_ho_5 with 300s (1) cores
% 0.57/0.43 % almost_fo_3_lam with pid 3572858 completed with status 0
% 0.57/0.43 % Result found by almost_fo_3_lam
% 0.57/0.43 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.57/0.43 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.43 % Starting ehoh_best5 with 300s (1) cores
% 0.57/0.43 % Starting almost_fo_3_lam with 300s (1) cores
% 0.57/0.43 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.57/0.43 % No SInE strategy applied
% 0.57/0.43 % Search class: HGHSM-FSLS31-MHFMMSBN
% 0.57/0.43 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.57/0.43 % Starting SubtermCWHack with 28s (1) cores
% 0.57/0.43 % SubtermCWHack with pid 3572867 completed with status 0
% 0.57/0.43 % Result found by SubtermCWHack
% 0.57/0.43 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.57/0.43 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.43 % Starting ehoh_best5 with 300s (1) cores
% 0.57/0.43 % Starting almost_fo_3_lam with 300s (1) cores
% 0.57/0.43 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.57/0.43 % No SInE strategy applied
% 0.57/0.43 % Search class: HGHSM-FSLS31-MHFMMSBN
% 0.57/0.43 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.57/0.43 % Starting SubtermCWHack with 28s (1) cores
% 0.57/0.43 % Preprocessing time : 0.005 s
% 0.57/0.43
% 0.57/0.43 % Proof found!
% 0.57/0.43 % SZS status Theorem
% 0.57/0.43 % SZS output start CNFRefutation
% 0.57/0.43 thf(decl_23, type, in: $i > $i > $o).
% 0.57/0.43 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.57/0.43 thf(decl_25, type, setextAx: $o).
% 0.57/0.43 thf(decl_26, type, emptyset: $i).
% 0.57/0.43 thf(decl_27, type, emptysetAx: $o).
% 0.57/0.43 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.57/0.43 thf(decl_29, type, setadjoinAx: $o).
% 0.57/0.43 thf(decl_30, type, powerset: $i > $i).
% 0.57/0.43 thf(decl_31, type, powersetAx: $o).
% 0.57/0.43 thf(decl_32, type, setunion: $i > $i).
% 0.57/0.43 thf(decl_33, type, setunionAx: $o).
% 0.57/0.43 thf(decl_34, type, omega: $i).
% 0.57/0.43 thf(decl_35, type, omega0Ax: $o).
% 0.57/0.43 thf(decl_36, type, omegaSAx: $o).
% 0.57/0.43 thf(decl_37, type, omegaIndAx: $o).
% 0.57/0.43 thf(decl_38, type, replAx: $o).
% 0.57/0.43 thf(decl_39, type, foundationAx: $o).
% 0.57/0.43 thf(decl_40, type, wellorderingAx: $o).
% 0.57/0.43 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.57/0.43 thf(decl_42, type, descrp: $o).
% 0.57/0.43 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.57/0.43 thf(decl_44, type, dsetconstrI: $o).
% 0.57/0.43 thf(decl_45, type, dsetconstrEL: $o).
% 0.57/0.43 thf(decl_46, type, dsetconstrER: $o).
% 0.57/0.43 thf(decl_47, type, exuE1: $o).
% 0.57/0.43 thf(decl_48, type, prop2set: $o > $i).
% 0.57/0.43 thf(decl_49, type, prop2setE: $o).
% 0.57/0.43 thf(decl_50, type, emptysetE: $o).
% 0.57/0.43 thf(decl_51, type, emptysetimpfalse: $o).
% 0.57/0.43 thf(decl_52, type, notinemptyset: $o).
% 0.57/0.43 thf(decl_53, type, exuE3e: $o).
% 0.57/0.43 thf(decl_54, type, setext: $o).
% 0.57/0.43 thf(decl_55, type, emptyI: $o).
% 0.57/0.43 thf(decl_56, type, noeltsimpempty: $o).
% 0.57/0.43 thf(decl_57, type, setbeta: $o).
% 0.57/0.43 thf(decl_58, type, nonempty: $i > $o).
% 0.57/0.43 thf(decl_59, type, nonemptyE1: $o).
% 0.57/0.43 thf(decl_60, type, nonemptyI: $o).
% 0.57/0.43 thf(decl_61, type, nonemptyI1: $o).
% 0.57/0.43 thf(decl_62, type, setadjoinIL: $o).
% 0.57/0.43 thf(decl_63, type, emptyinunitempty: $o).
% 0.57/0.43 thf(decl_64, type, setadjoinIR: $o).
% 0.57/0.43 thf(decl_65, type, setadjoinE: $o).
% 0.57/0.43 thf(decl_66, type, setadjoinOr: $o).
% 0.57/0.43 thf(decl_67, type, setoftrueEq: $o).
% 0.57/0.43 thf(decl_68, type, powersetI: $o).
% 0.57/0.43 thf(decl_69, type, emptyinPowerset: $o).
% 0.57/0.43 thf(decl_70, type, emptyInPowerset: $o).
% 0.57/0.43 thf(decl_71, type, powersetE: $o).
% 0.57/0.43 thf(decl_72, type, setunionI: $o).
% 0.57/0.43 thf(decl_73, type, setunionE: $o).
% 0.57/0.43 thf(decl_74, type, subPowSU: $o).
% 0.57/0.43 thf(decl_75, type, exuE2: $o).
% 0.57/0.43 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.57/0.43 thf(decl_77, type, uniqinunit: $o).
% 0.57/0.43 thf(decl_78, type, notinsingleton: $o).
% 0.57/0.43 thf(decl_79, type, eqinunit: $o).
% 0.57/0.43 thf(decl_80, type, singletonsswitch: $o).
% 0.57/0.43 thf(decl_81, type, upairsetE: $o).
% 0.57/0.43 thf(decl_82, type, upairsetIL: $o).
% 0.57/0.43 thf(decl_83, type, upairsetIR: $o).
% 0.57/0.43 thf(decl_84, type, emptyE1: $o).
% 0.57/0.43 thf(decl_85, type, vacuousDall: $o).
% 0.57/0.43 thf(decl_86, type, quantDeMorgan1: $o).
% 0.57/0.43 thf(decl_87, type, quantDeMorgan2: $o).
% 0.57/0.43 thf(decl_88, type, quantDeMorgan3: $o).
% 0.57/0.43 thf(decl_89, type, quantDeMorgan4: $o).
% 0.57/0.43 thf(decl_90, type, prop2setI: $o).
% 0.57/0.43 thf(decl_91, type, set2prop: $i > $o).
% 0.57/0.43 thf(decl_92, type, prop2set2propI: $o).
% 0.57/0.43 thf(decl_93, type, notdexE: $o).
% 0.57/0.43 thf(decl_94, type, notdallE: $o).
% 0.57/0.43 thf(decl_95, type, exuI1: $o).
% 0.57/0.43 thf(decl_96, type, exuI3: $o).
% 0.57/0.43 thf(decl_97, type, exuI2: $o).
% 0.57/0.43 thf(decl_98, type, inCongP: $o).
% 0.57/0.43 thf(decl_99, type, in__Cong: $o).
% 0.57/0.43 thf(decl_100, type, exuE3u: $o).
% 0.57/0.43 thf(decl_101, type, exu__Cong: $o).
% 0.57/0.43 thf(decl_102, type, emptyset__Cong: $o).
% 0.57/0.43 thf(decl_103, type, setadjoin__Cong: $o).
% 0.57/0.43 thf(decl_104, type, powerset__Cong: $o).
% 0.57/0.43 thf(decl_105, type, setunion__Cong: $o).
% 0.57/0.43 thf(decl_106, type, omega__Cong: $o).
% 0.57/0.43 thf(decl_107, type, exuEu: $o).
% 0.57/0.43 thf(decl_108, type, descr__Cong: $o).
% 0.57/0.43 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.57/0.43 thf(decl_110, type, subset: $i > $i > $o).
% 0.57/0.43 thf(decl_113, type, subsetI1: $o).
% 0.57/0.43 thf(decl_114, type, eqimpsubset2: $o).
% 0.57/0.43 thf(decl_115, type, eqimpsubset1: $o).
% 0.57/0.43 thf(decl_116, type, subsetI2: $o).
% 0.57/0.43 thf(decl_117, type, emptysetsubset: $o).
% 0.57/0.43 thf(decl_118, type, subsetE: $o).
% 0.57/0.43 thf(decl_119, type, subsetE2: $o).
% 0.57/0.43 thf(decl_120, type, notsubsetI: $o).
% 0.57/0.43 thf(decl_121, type, notequalI1: $o).
% 0.57/0.43 thf(decl_122, type, notequalI2: $o).
% 0.57/0.43 thf(decl_123, type, subsetRefl: $o).
% 0.57/0.43 thf(decl_124, type, subsetTrans: $o).
% 0.57/0.43 thf(decl_125, type, setadjoinSub: $o).
% 0.57/0.43 thf(decl_126, type, setadjoinSub2: $o).
% 0.57/0.43 thf(decl_127, type, subset2powerset: $o).
% 0.57/0.43 thf(decl_128, type, setextsub: $o).
% 0.57/0.43 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.57/0.43 thf(decl_130, type, powersetI1: $o).
% 0.57/0.43 thf(decl_131, type, powersetE1: $o).
% 0.57/0.43 thf(decl_132, type, inPowerset: $o).
% 0.57/0.43 thf(decl_133, type, powersetsubset: $o).
% 0.57/0.43 thf(decl_134, type, sepInPowerset: $o).
% 0.57/0.43 thf(decl_135, type, sepSubset: $o).
% 0.57/0.43 thf(decl_136, type, binunion: $i > $i > $i).
% 0.57/0.43 thf(decl_137, type, binunionIL: $o).
% 0.57/0.43 thf(decl_138, type, upairset2IR: $o).
% 0.57/0.43 thf(decl_139, type, binunionIR: $o).
% 0.57/0.43 thf(decl_140, type, binunionEcases: $o).
% 0.57/0.43 thf(decl_141, type, binunionE: $o).
% 0.57/0.43 thf(decl_142, type, binunionLsub: $o).
% 0.57/0.43 thf(decl_143, type, binunionRsub: $o).
% 0.57/0.43 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.57/0.43 thf(decl_145, type, binintersectI: $o).
% 0.57/0.43 thf(decl_146, type, binintersectSubset5: $o).
% 0.57/0.43 thf(decl_147, type, binintersectEL: $o).
% 0.57/0.43 thf(decl_148, type, binintersectLsub: $o).
% 0.57/0.43 thf(decl_149, type, binintersectSubset2: $o).
% 0.57/0.43 thf(decl_150, type, binintersectSubset3: $o).
% 0.57/0.43 thf(decl_151, type, binintersectER: $o).
% 0.57/0.43 thf(decl_152, type, disjointsetsI1: $o).
% 0.57/0.43 thf(decl_153, type, binintersectRsub: $o).
% 0.57/0.43 thf(decl_154, type, binintersectSubset4: $o).
% 0.57/0.43 thf(decl_155, type, binintersectSubset1: $o).
% 0.57/0.43 thf(decl_156, type, bs114d: $o).
% 0.57/0.43 thf(decl_158, type, setminus: $i > $i > $i).
% 0.57/0.43 thf(decl_159, type, setminusI: $o).
% 0.57/0.43 thf(decl_160, type, setminusEL: $o).
% 0.57/0.43 thf(decl_161, type, setminusER: $o).
% 0.57/0.43 thf(decl_162, type, setminusSubset2: $o).
% 0.57/0.43 thf(decl_163, type, setminusERneg: $o).
% 0.57/0.43 thf(decl_164, type, setminusELneg: $o).
% 0.57/0.43 thf(decl_165, type, setminusILneg: $o).
% 0.57/0.43 thf(decl_166, type, setminusIRneg: $o).
% 0.57/0.43 thf(decl_167, type, setminusLsub: $o).
% 0.57/0.43 thf(decl_168, type, setminusSubset1: $o).
% 0.57/0.43 thf(decl_169, type, symdiff: $i > $i > $i).
% 0.57/0.43 thf(decl_170, type, symdiffE: $o).
% 0.57/0.43 thf(decl_171, type, symdiffI1: $o).
% 0.57/0.43 thf(decl_172, type, symdiffI2: $o).
% 0.57/0.43 thf(decl_173, type, symdiffIneg1: $o).
% 0.57/0.43 thf(decl_174, type, symdiffIneg2: $o).
% 0.57/0.43 thf(decl_175, type, iskpair: $i > $o).
% 0.57/0.43 thf(decl_176, type, secondinupair: $o).
% 0.57/0.43 thf(decl_177, type, setukpairIL: $o).
% 0.57/0.43 thf(decl_178, type, setukpairIR: $o).
% 0.57/0.43 thf(decl_179, type, kpairiskpair: $o).
% 0.57/0.43 thf(decl_180, type, kpair: $i > $i > $i).
% 0.57/0.43 thf(decl_181, type, kpairp: $o).
% 0.57/0.43 thf(decl_182, type, cartprod: $i > $i > $i).
% 0.57/0.43 thf(decl_183, type, singletonsubset: $o).
% 0.57/0.43 thf(decl_184, type, singletoninpowerset: $o).
% 0.57/0.43 thf(decl_185, type, singletoninpowunion: $o).
% 0.57/0.43 thf(decl_186, type, upairset2E: $o).
% 0.57/0.43 thf(decl_187, type, upairsubunion: $o).
% 0.57/0.43 thf(decl_188, type, upairinpowunion: $o).
% 0.57/0.43 thf(decl_189, type, ubforcartprodlem1: $o).
% 0.57/0.43 thf(decl_190, type, ubforcartprodlem2: $o).
% 0.57/0.43 thf(decl_191, type, ubforcartprodlem3: $o).
% 0.57/0.43 thf(decl_192, type, cartprodpairin: $o).
% 0.57/0.43 thf(decl_193, type, cartprodmempair1: $o).
% 0.57/0.43 thf(decl_194, type, cartprodmempair: $o).
% 0.57/0.43 thf(decl_195, type, setunionE2: $o).
% 0.57/0.43 thf(decl_196, type, setunionsingleton1: $o).
% 0.57/0.43 thf(decl_197, type, epred1_0: $o).
% 0.57/0.43 thf(decl_198, type, esk1_2: $i > $i > $i).
% 0.57/0.43 thf(decl_199, type, esk2_2: $i > $i > $i).
% 0.57/0.43 thf(decl_200, type, esk3_2: $i > $i > $i).
% 0.57/0.43 thf(decl_201, type, esk4_1: $i > $i).
% 0.57/0.43 thf(decl_202, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.57/0.43 thf(decl_203, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.57/0.43 thf(decl_204, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.57/0.43 thf(decl_205, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.57/0.43 thf(decl_206, type, esk9_1: $i > $i).
% 0.57/0.43 thf(decl_207, type, esk10_2: ($i > $o) > $i > $i).
% 0.57/0.43 thf(decl_208, type, esk11_2: ($i > $o) > $i > $i).
% 0.57/0.43 thf(decl_209, type, esk12_1: ($i > $o) > $i).
% 0.57/0.43 thf(decl_210, type, esk13_2: ($i > $o) > $i > $i).
% 0.57/0.43 thf(decl_211, type, esk14_1: ($i > $o) > $i).
% 0.57/0.43 thf(decl_212, type, esk15_2: $i > $i > $i).
% 0.57/0.43 thf(decl_213, type, esk16_2: $i > $i > $i).
% 0.57/0.43 thf(decl_214, type, esk17_1: $i > $i).
% 0.57/0.43 thf(decl_215, type, esk18_1: $i > $i).
% 0.57/0.43 thf(decl_216, type, esk19_1: $i > $i).
% 0.57/0.43 thf(decl_217, type, esk20_2: $i > $i > $i).
% 0.57/0.43 thf(decl_218, type, esk21_3: $i > $i > $o > $i).
% 0.57/0.43 thf(decl_219, type, esk22_2: ($i > $o) > $i > $i).
% 0.57/0.43 thf(decl_220, type, esk23_1: ($i > $o) > $i).
% 0.57/0.43 thf(decl_221, type, esk24_1: $i > $i).
% 0.57/0.43 thf(decl_222, type, esk25_2: $i > ($i > $o) > $i).
% 0.57/0.43 thf(decl_223, type, esk26_2: $i > ($i > $o) > $i).
% 0.57/0.43 thf(decl_224, type, esk27_2: $i > ($i > $o) > $i).
% 0.57/0.43 thf(decl_225, type, esk28_2: $i > ($i > $o) > $i).
% 0.57/0.43 thf(decl_226, type, esk29_2: $i > ($i > $o) > $i).
% 0.57/0.43 thf(decl_227, type, esk30_2: $i > ($i > $o) > $i).
% 0.57/0.43 thf(decl_228, type, esk31_2: ($i > $o) > $i > $i).
% 0.57/0.43 thf(decl_229, type, esk32_1: ($i > $o) > $i).
% 0.57/0.43 thf(decl_230, type, esk33_1: ($i > $o) > $i).
% 0.57/0.43 thf(decl_231, type, esk34_1: ($i > $o) > $i).
% 0.57/0.43 thf(decl_232, type, esk35_1: ($i > $o) > $i).
% 0.57/0.43 thf(decl_233, type, esk36_2: ($i > $o) > $i > $i).
% 0.57/0.43 thf(decl_234, type, esk37_1: ($i > $o) > $i).
% 0.57/0.43 thf(decl_235, type, esk38_2: ($i > $o) > $i > $i).
% 0.57/0.43 thf(decl_236, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.57/0.43 thf(decl_237, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.57/0.43 thf(decl_238, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.57/0.43 thf(decl_239, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.57/0.43 thf(decl_240, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.57/0.43 thf(decl_241, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.57/0.43 thf(decl_242, type, esk45_2: ($i > $o) > $i > $i).
% 0.57/0.43 thf(decl_243, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.57/0.43 thf(decl_244, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.57/0.43 thf(decl_245, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.57/0.43 thf(decl_246, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.57/0.43 thf(decl_247, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.57/0.43 thf(decl_248, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.57/0.43 thf(decl_249, type, esk52_2: $i > $i > $i).
% 0.57/0.43 thf(decl_250, type, esk53_2: $i > $i > $i).
% 0.57/0.43 thf(decl_251, type, esk54_2: $i > $i > $i).
% 0.57/0.43 thf(decl_252, type, esk55_2: $i > $i > $i).
% 0.57/0.43 thf(decl_253, type, esk56_2: $i > $i > $i).
% 0.57/0.43 thf(decl_254, type, esk57_2: $i > $i > $i).
% 0.57/0.43 thf(decl_255, type, esk58_2: $i > $i > $i).
% 0.57/0.43 thf(decl_256, type, esk59_3: $i > $i > $i > $i).
% 0.57/0.43 thf(decl_257, type, esk60_3: $i > $i > $i > $i).
% 0.57/0.43 thf(decl_258, type, esk61_3: $i > $i > $i > $i).
% 0.57/0.43 thf(decl_259, type, esk62_3: $i > $i > $i > $i).
% 0.57/0.43 thf(decl_260, type, esk63_2: $i > $i > $i).
% 0.57/0.43 thf(decl_261, type, esk64_0: $i).
% 0.57/0.43 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', replAx)).
% 0.57/0.43 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', exu)).
% 0.57/0.43 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', descrp)).
% 0.57/0.43 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', exuE1)).
% 0.57/0.43 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', exuE3e)).
% 0.57/0.43 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', nonempty)).
% 0.57/0.43 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', nonemptyI)).
% 0.57/0.43 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', exuE2)).
% 0.57/0.43 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.33slpoNXPQ/E---3.1_3572842.p', exuI1)).
% 0.57/0.43 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', exuI3)).
% 0.57/0.43 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', exuI2)).
% 0.57/0.43 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.33slpoNXPQ/E---3.1_3572842.p', exuE3u)).
% 0.57/0.43 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', exu__Cong)).
% 0.57/0.43 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', exuEu)).
% 0.57/0.43 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', descr__Cong)).
% 0.57/0.43 thf(iskpair, axiom, ((iskpair)=(^[X4:$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.33slpoNXPQ/E---3.1_3572842.p', iskpair)).
% 0.57/0.43 thf(setunionsingleton2, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setunionsingleton2)).
% 0.57/0.43 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', dsetconstrI)).
% 0.57/0.43 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', dsetconstrEL)).
% 0.57/0.43 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', dsetconstrER)).
% 0.57/0.43 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setbeta)).
% 0.57/0.43 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', nonemptyE1)).
% 0.57/0.43 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', nonemptyI1)).
% 0.57/0.43 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setoftrueEq)).
% 0.57/0.43 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', nonemptyImpWitness)).
% 0.57/0.43 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.33slpoNXPQ/E---3.1_3572842.p', emptyE1)).
% 0.57/0.43 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', dsetconstr__Cong)).
% 0.57/0.43 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', sepInPowerset)).
% 0.57/0.43 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', sepSubset)).
% 0.57/0.43 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.33slpoNXPQ/E---3.1_3572842.p', kpairiskpair)).
% 0.57/0.43 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', kpairp)).
% 0.57/0.43 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', cartprodmempair)).
% 0.57/0.43 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setextAx)).
% 0.57/0.43 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', emptysetAx)).
% 0.57/0.43 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setadjoinAx)).
% 0.57/0.43 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', powersetAx)).
% 0.57/0.43 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setunionAx)).
% 0.57/0.43 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', omega0Ax)).
% 0.57/0.43 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', omegaSAx)).
% 0.57/0.43 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.33slpoNXPQ/E---3.1_3572842.p', omegaIndAx)).
% 0.57/0.43 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.33slpoNXPQ/E---3.1_3572842.p', foundationAx)).
% 0.57/0.43 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', wellorderingAx)).
% 0.57/0.43 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', prop2setE)).
% 0.57/0.43 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', emptysetE)).
% 0.57/0.43 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', emptysetimpfalse)).
% 0.57/0.43 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', notinemptyset)).
% 0.57/0.43 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.33slpoNXPQ/E---3.1_3572842.p', setext)).
% 0.57/0.43 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', emptyI)).
% 0.57/0.43 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', noeltsimpempty)).
% 0.57/0.43 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setadjoinIL)).
% 0.57/0.43 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', emptyinunitempty)).
% 0.57/0.43 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setadjoinIR)).
% 0.57/0.43 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setadjoinE)).
% 0.57/0.43 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setadjoinOr)).
% 0.57/0.43 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', powersetI)).
% 0.57/0.43 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', emptyinPowerset)).
% 0.57/0.43 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', emptyInPowerset)).
% 0.57/0.43 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', powersetE)).
% 0.57/0.43 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setunionI)).
% 0.57/0.43 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setunionE)).
% 0.57/0.43 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', subPowSU)).
% 0.57/0.43 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', uniqinunit)).
% 0.57/0.43 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', notinsingleton)).
% 0.57/0.43 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', eqinunit)).
% 0.57/0.43 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', singletonsswitch)).
% 0.57/0.43 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', upairsetE)).
% 0.57/0.43 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', upairsetIL)).
% 0.57/0.43 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', upairsetIR)).
% 0.57/0.43 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', vacuousDall)).
% 0.57/0.43 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', quantDeMorgan1)).
% 0.57/0.43 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', quantDeMorgan2)).
% 0.57/0.43 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', quantDeMorgan3)).
% 0.57/0.43 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', quantDeMorgan4)).
% 0.57/0.43 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', prop2setI)).
% 0.57/0.43 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', prop2set2propI)).
% 0.57/0.43 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', notdexE)).
% 0.57/0.43 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', notdallE)).
% 0.57/0.43 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', inCongP)).
% 0.57/0.43 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', in__Cong)).
% 0.57/0.43 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', emptyset__Cong)).
% 0.57/0.43 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setadjoin__Cong)).
% 0.57/0.43 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', powerset__Cong)).
% 0.57/0.43 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setunion__Cong)).
% 0.57/0.43 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', omega__Cong)).
% 0.57/0.43 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', subsetI1)).
% 0.57/0.43 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', eqimpsubset2)).
% 0.57/0.43 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', eqimpsubset1)).
% 0.57/0.43 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', subsetI2)).
% 0.57/0.43 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', emptysetsubset)).
% 0.57/0.43 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', subsetE)).
% 0.57/0.43 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', subsetE2)).
% 0.57/0.43 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', notsubsetI)).
% 0.57/0.43 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', notequalI1)).
% 0.57/0.43 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', notequalI2)).
% 0.57/0.43 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', subsetRefl)).
% 0.57/0.43 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', subsetTrans)).
% 0.57/0.43 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setadjoinSub)).
% 0.57/0.43 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setadjoinSub2)).
% 0.57/0.43 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', subset2powerset)).
% 0.57/0.43 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setextsub)).
% 0.57/0.43 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', subsetemptysetimpeq)).
% 0.57/0.43 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', powersetI1)).
% 0.57/0.43 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', powersetE1)).
% 0.57/0.43 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', inPowerset)).
% 0.57/0.43 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', powersetsubset)).
% 0.57/0.43 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', binunionIL)).
% 0.57/0.43 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', upairset2IR)).
% 0.57/0.43 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', binunionIR)).
% 0.57/0.43 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', binunionEcases)).
% 0.57/0.43 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', binunionE)).
% 0.57/0.43 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', binunionLsub)).
% 0.57/0.43 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', binunionRsub)).
% 0.57/0.43 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', binintersectI)).
% 0.57/0.43 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', binintersectSubset5)).
% 0.57/0.43 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', binintersectEL)).
% 0.57/0.43 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', binintersectLsub)).
% 0.57/0.43 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', binintersectSubset2)).
% 0.57/0.43 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', binintersectSubset3)).
% 0.57/0.43 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', binintersectER)).
% 0.57/0.43 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', disjointsetsI1)).
% 0.57/0.43 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', binintersectRsub)).
% 0.57/0.43 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', binintersectSubset4)).
% 0.57/0.43 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', binintersectSubset1)).
% 0.57/0.43 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', bs114d)).
% 0.57/0.43 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setminusI)).
% 0.57/0.43 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setminusEL)).
% 0.57/0.43 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setminusER)).
% 0.57/0.43 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setminusSubset2)).
% 0.57/0.43 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setminusERneg)).
% 0.57/0.43 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setminusELneg)).
% 0.57/0.43 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setminusILneg)).
% 0.57/0.43 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setminusIRneg)).
% 0.57/0.43 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setminusLsub)).
% 0.57/0.43 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setminusSubset1)).
% 0.57/0.43 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', symdiffE)).
% 0.57/0.43 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', symdiffI1)).
% 0.57/0.43 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', symdiffI2)).
% 0.57/0.43 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', symdiffIneg1)).
% 0.57/0.43 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', symdiffIneg2)).
% 0.57/0.43 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', secondinupair)).
% 0.57/0.43 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setukpairIL)).
% 0.57/0.43 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setukpairIR)).
% 0.57/0.43 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', singletonsubset)).
% 0.57/0.43 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', singletoninpowerset)).
% 0.57/0.43 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', singletoninpowunion)).
% 0.57/0.43 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', upairset2E)).
% 0.57/0.43 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', upairsubunion)).
% 0.57/0.43 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', upairinpowunion)).
% 0.57/0.43 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', ubforcartprodlem1)).
% 0.57/0.43 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', ubforcartprodlem2)).
% 0.57/0.43 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', ubforcartprodlem3)).
% 0.57/0.43 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', cartprodpairin)).
% 0.57/0.43 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', cartprodmempair1)).
% 0.57/0.43 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setunionE2)).
% 0.57/0.43 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.33slpoNXPQ/E---3.1_3572842.p', setunionsingleton1)).
% 0.57/0.43 thf(c_0_155, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.57/0.43 thf(c_0_156, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.57/0.43 thf(c_0_157, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.57/0.43 thf(c_0_158, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.57/0.43 thf(c_0_159, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.57/0.43 thf(c_0_160, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.57/0.43 thf(c_0_161, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.57/0.43 thf(c_0_162, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.57/0.43 thf(c_0_163, 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])).
% 0.57/0.43 thf(c_0_164, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.57/0.43 thf(c_0_165, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.57/0.43 thf(c_0_166, 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])).
% 0.57/0.43 thf(c_0_167, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.57/0.43 thf(c_0_168, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.57/0.43 thf(c_0_169, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.57/0.43 thf(c_0_170, plain, ((iskpair)=(^[Z0:$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])).
% 0.57/0.43 thf(c_0_171, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setunionsingleton2])).
% 0.57/0.43 thf(c_0_172, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X433:$i]:(((((X6 @ X2 @ X433)))&(![X434:$i]:(((((X6 @ X2 @ X434)))=>(((X433)=(X434)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_155, c_0_156])).
% 0.57/0.43 thf(c_0_173, plain, ((descrp)=(![X1:$i > $o]:((((?[X435:$i]:(((((X1 @ X435)))&(![X436:$i]:(((((X1 @ X436)))=>(((X435)=(X436))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_157, c_0_156])).
% 0.57/0.43 thf(c_0_174, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.57/0.43 thf(c_0_175, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.57/0.43 thf(c_0_176, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.57/0.43 thf(c_0_177, plain, ((exuE1)=(![X1:$i > $o]:((((?[X437:$i]:(((((X1 @ X437)))&(![X438:$i]:(((((X1 @ X438)))=>(((X437)=(X438))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_158, c_0_156])).
% 0.57/0.43 thf(c_0_178, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X439:$i]:(((((X1 @ X439)))&(![X440:$i]:(((((X1 @ X440)))=>(((X439)=(X440))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_159, c_0_156])).
% 0.57/0.43 thf(c_0_179, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.57/0.43 thf(c_0_180, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_160])).
% 0.57/0.43 thf(c_0_181, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_161, c_0_160])).
% 0.57/0.43 thf(c_0_182, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_160])).
% 0.57/0.43 thf(c_0_183, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.57/0.43 thf(c_0_184, plain, ((exuE2)=(![X1:$i > $o]:((((?[X441:$i]:(((((X1 @ X441)))&(![X442:$i]:(((((X1 @ X442)))=>(((X441)=(X442))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_162, c_0_156])).
% 0.57/0.43 thf(c_0_185, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_160])).
% 0.57/0.43 thf(c_0_186, 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])).
% 0.57/0.43 thf(c_0_187, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X443:$i]:(((((X1 @ X443)))&(![X444:$i]:(((((X1 @ X444)))=>(((X443)=(X444)))))))))))))), inference(apply_def,[status(thm)],[c_0_163, c_0_156])).
% 0.57/0.43 thf(c_0_188, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X445:$i]:(((((X1 @ X445)))&(![X446:$i]:(((((X1 @ X446)))=>(((X445)=(X446)))))))))))))))), inference(apply_def,[status(thm)],[c_0_164, c_0_156])).
% 0.57/0.43 thf(c_0_189, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X447:$i]:(((((X1 @ X447)))&(![X448:$i]:(((((X1 @ X448)))=>(((X447)=(X448)))))))))))))), inference(apply_def,[status(thm)],[c_0_165, c_0_156])).
% 0.57/0.43 thf(c_0_190, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X449:$i]:(((((X1 @ X449)))&(![X450:$i]:(((((X1 @ X450)))=>(((X449)=(X450))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_166, c_0_156])).
% 0.57/0.43 thf(c_0_191, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X451:$i]:(((((X1 @ X451)))&(![X452:$i]:(((((X1 @ X452)))=>(((X451)=(X452))))))))))<=>((?[X453:$i]:(((((X17 @ X453)))&(![X454:$i]:(((((X17 @ X454)))=>(((X453)=(X454)))))))))))))))), inference(apply_def,[status(thm)],[c_0_167, c_0_156])).
% 0.57/0.43 thf(c_0_192, plain, ((exuEu)=(![X1:$i > $o]:((((?[X455:$i]:(((((X1 @ X455)))&(![X456:$i]:(((((X1 @ X456)))=>(((X455)=(X456))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_168, c_0_156])).
% 0.57/0.43 thf(c_0_193, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X457:$i]:(((((X1 @ X457)))&(![X458:$i]:(((((X1 @ X458)))=>(((X457)=(X458))))))))))=>((((?[X459:$i]:(((((X17 @ X459)))&(![X460:$i]:(((((X17 @ X460)))=>(((X459)=(X460))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_169, c_0_156])).
% 0.57/0.43 thf(c_0_194, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.57/0.43 thf(c_0_195, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.57/0.43 thf(c_0_196, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.57/0.43 thf(c_0_197, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X461:$i]:((((in @ X461 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))&(?[X462:$i]:((((in @ X462 @ (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 @ X461 @ emptyset) @ (setadjoin @ (setadjoin @ X461 @ (setadjoin @ X462 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_170])).
% 0.57/0.43 thf(c_0_198, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X463:$i]:((((in @ X463 @ (setunion @ (kpair @ X2 @ X3))))&(?[X464:$i]:((((in @ X464 @ (setunion @ (kpair @ X2 @ X3))))&(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X463 @ emptyset) @ (setadjoin @ (setadjoin @ X463 @ (setadjoin @ X464 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairp, c_0_170])).
% 0.57/0.43 thf(c_0_199, axiom, ((cartprodmempair)=(![X4:$i, X5:$i, X18:$i]:((((in @ X18 @ (cartprod @ X4 @ X5)))=>((?[X465:$i]:((((in @ X465 @ (setunion @ X18)))&(?[X466:$i]:((((in @ X466 @ (setunion @ X18)))&(((X18)=(setadjoin @ (setadjoin @ X465 @ emptyset) @ (setadjoin @ (setadjoin @ X465 @ (setadjoin @ X466 @ emptyset)) @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[cartprodmempair, c_0_170])).
% 0.57/0.43 thf(c_0_200, plain, ((epred1_0)<=>![X496:$i]:(?[X497:$i]:((((![X498:$i]:(((in @ X498 @ X497)=>![X499:$i]:(((in @ X499 @ X498)=>(in @ X499 @ X496)))))&![X500:$i, X501:$i]:((((in @ X500 @ X496)&(in @ X501 @ X496))=>(![X502:$i]:(((in @ X502 @ X497)=>((in @ X500 @ X502)<=>(in @ X501 @ X502))))=>((X500)=(X501))))))&![X503:$i, X504:$i]:((((in @ X503 @ X497)&(in @ X504 @ X497))=>(![X505:$i]:(((in @ X505 @ X503)=>(in @ X505 @ X504)))|![X506:$i]:(((in @ X506 @ X504)=>(in @ X506 @ X503)))))))&![X507:$i]:(((![X508:$i]:(((in @ X508 @ X507)=>(in @ X508 @ X496)))&?[X509:$i]:((in @ X509 @ X507)))=>?[X510:$i, X511:$i]:(((((in @ X510 @ X497)&(in @ X511 @ X507))&~(?[X512:$i]:(((in @ X512 @ X510)&(in @ X512 @ X507)))))&![X513:$i]:(((in @ X513 @ X497)=>(![X514:$i]:(((in @ X514 @ X513)=>(in @ X514 @ X510)))|(in @ X511 @ X513)))))))))))), introduced(definition)).
% 0.57/0.43 thf(c_0_201, negated_conjecture, ~((![X467:$i, X468:$i]:((![X469:$i]:(((in @ X469 @ X467)<=>(in @ X469 @ X468)))=>((X467)=(X468))))=>(![X470:$i]:(~(in @ X470 @ emptyset))=>(![X471:$i, X472:$i, X473:$i]:(((in @ X473 @ (setadjoin @ X471 @ X472))<=>(((X473)=(X471))|(in @ X473 @ X472))))=>(![X474:$i, X475:$i]:(((in @ X475 @ (powerset @ X474))<=>![X476:$i]:(((in @ X476 @ X475)=>(in @ X476 @ X474)))))=>(![X477:$i, X478:$i]:(((in @ X478 @ (setunion @ X477))<=>?[X479:$i]:(((in @ X478 @ X479)&(in @ X479 @ X477)))))=>((in @ emptyset @ omega)=>(![X480:$i]:(((in @ X480 @ omega)=>(in @ (setadjoin @ X480 @ X480) @ omega)))=>(![X481:$i]:((((in @ emptyset @ X481)&![X482:$i]:((((in @ X482 @ omega)&(in @ X482 @ X481))=>(in @ (setadjoin @ X482 @ X482) @ X481))))=>![X483:$i]:(((in @ X483 @ omega)=>(in @ X483 @ X481)))))=>(![X484:$i > $i > $o, X485:$i]:((![X486:$i]:(((in @ X486 @ X485)=>?[X487:$i]:(((X484 @ X486 @ X487)&![X488:$i]:(((X484 @ X486 @ X488)=>((X487)=(X488))))))))=>?[X489:$i]:(![X490:$i]:(((in @ X490 @ X489)<=>?[X491:$i]:(((in @ X491 @ X485)&(X484 @ X491 @ X490))))))))=>(![X492:$i]:((?[X493:$i]:((in @ X493 @ X492))=>?[X494:$i]:(((in @ X494 @ X492)&~(?[X495:$i]:(((in @ X495 @ X494)&(in @ X495 @ X492))))))))=>((epred1_0)=>(![X515:$i > $o]:((?[X516:$i]:(((X515 @ X516)&![X517:$i]:(((X515 @ X517)=>((X516)=(X517))))))=>(X515 @ (descr @ (^[Z0:$i]:(X515 @ Z0))))))=>(![X518:$i, X519:$i > $o, X520:$i]:(((in @ X520 @ X518)=>((X519 @ X520)=>(in @ X520 @ (dsetconstr @ X518 @ X519)))))=>(![X521:$i, X522:$i > $o, X523:$i]:(((in @ X523 @ (dsetconstr @ X521 @ X522))=>(in @ X523 @ X521)))=>(![X524:$i, X525:$i > $o, X526:$i]:(((in @ X526 @ (dsetconstr @ X524 @ X525))=>(X525 @ X526)))=>(![X527:$i > $o]:((?[X528:$i]:(((X527 @ X528)&![X529:$i]:(((X527 @ X529)=>((X528)=(X529))))))=>?[X530:$i]:(((X527 @ X530)&![X531:$i]:(((X527 @ X531)=>((X530)=(X531))))))))=>(![X532:$o, X533:$i]:(((in @ X533 @ (prop2set @ ((X532))))=>(X532)))=>(![X534:$i]:(((in @ X534 @ emptyset)=>![X535:$o]:((X535))))=>(![X536:$i]:(((in @ X536 @ emptyset)=>~($true)))=>(![X537:$i]:(~(in @ X537 @ emptyset))=>(![X538:$i > $o]:((?[X539:$i]:(((X538 @ X539)&![X540:$i]:(((X538 @ X540)=>((X539)=(X540))))))=>?[X541:$i]:((X538 @ X541))))=>(![X542:$i, X543:$i]:((![X544:$i]:(((in @ X544 @ X542)=>(in @ X544 @ X543)))=>(![X545:$i]:(((in @ X545 @ X543)=>(in @ X545 @ X542)))=>((X542)=(X543)))))=>(![X546:$i]:((![X547:$i]:(~(in @ X547 @ X546))=>((X546)=(emptyset))))=>(![X548:$i]:((![X549:$i]:(~(in @ X549 @ X548))=>((X548)=(emptyset))))=>(![X550:$i, X551:$i > $o, X552:$i]:(((in @ X552 @ X550)=>((in @ X552 @ (dsetconstr @ X550 @ X551))<=>(X551 @ X552))))=>(![X553:$i]:((((X553)!=(emptyset))=>?[X554:$i]:((in @ X554 @ X553))))=>(![X555:$i, X556:$i > $o, X557:$i]:(((in @ X557 @ X555)=>((X556 @ X557)=>((dsetconstr @ X555 @ X556)!=(emptyset)))))=>(![X558:$i]:((?[X559:$i]:((in @ X559 @ X558))=>((X558)!=(emptyset))))=>(![X560:$i, X561:$i]:((in @ X560 @ (setadjoin @ X560 @ X561)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X562:$i, X563:$i, X564:$i]:(((in @ X564 @ X563)=>(in @ X564 @ (setadjoin @ X562 @ X563))))=>(![X565:$i, X566:$i, X567:$i]:(((in @ X567 @ (setadjoin @ X565 @ X566))=>![X568:$o]:(((((X567)=(X565))=>(X568))=>(((in @ X567 @ X566)=>(X568))=>(X568))))))=>(![X569:$i, X570:$i, X571:$i]:(((in @ X571 @ (setadjoin @ X569 @ X570))=>(((X571)=(X569))|(in @ X571 @ X570))))=>(![X572:$i]:(((dsetconstr @ X572 @ (^[Z0:$i]:($true)))=(X572)))=>(![X573:$i, X574:$i]:((![X575:$i]:(((in @ X575 @ X574)=>(in @ X575 @ X573)))=>(in @ X574 @ (powerset @ X573))))=>(![X576:$i]:((in @ emptyset @ (powerset @ X576)))=>(![X577:$i]:((in @ emptyset @ (powerset @ X577)))=>(![X578:$i, X579:$i, X580:$i]:(((in @ X579 @ (powerset @ X578))=>((in @ X580 @ X579)=>(in @ X580 @ X578))))=>(![X581:$i, X582:$i, X583:$i]:(((in @ X582 @ X583)=>((in @ X583 @ X581)=>(in @ X582 @ (setunion @ X581)))))=>(![X584:$i, X585:$i]:(((in @ X585 @ (setunion @ X584))=>![X586:$o]:((![X587:$i]:(((in @ X585 @ X587)=>((in @ X587 @ X584)=>(X586))))=>(X586)))))=>(![X588:$i, X589:$i]:(((in @ X589 @ X588)=>(in @ X589 @ (powerset @ (setunion @ X588)))))=>(![X590:$i > $o]:((?[X591:$i]:(((X590 @ X591)&![X592:$i]:(((X590 @ X592)=>((X591)=(X592))))))=>?[X593:$i]:(![X594:$i]:(((X590 @ X594)<=>((X594)=(X593)))))))=>(![X595:$i]:((((X595)!=(emptyset))=>?[X596:$i]:(((in @ X596 @ X595)&$true))))=>(![X597:$i, X598:$i]:(((in @ X597 @ (setadjoin @ X598 @ emptyset))=>((X597)=(X598))))=>(![X599:$i, X600:$i]:((((X599)!=(X600))=>~(in @ X600 @ (setadjoin @ X599 @ emptyset))))=>(![X601:$i, X602:$i]:((((X601)=(X602))=>(in @ X601 @ (setadjoin @ X602 @ emptyset))))=>(![X603:$i, X604:$i]:(((in @ X603 @ (setadjoin @ X604 @ emptyset))=>(in @ X604 @ (setadjoin @ X603 @ emptyset))))=>(![X605:$i, X606:$i, X607:$i]:(((in @ X607 @ (setadjoin @ X605 @ (setadjoin @ X606 @ emptyset)))=>(((X607)=(X605))|((X607)=(X606)))))=>(![X608:$i, X609:$i]:((in @ X608 @ (setadjoin @ X608 @ (setadjoin @ X609 @ emptyset))))=>(![X610:$i, X611:$i]:((in @ X611 @ (setadjoin @ X610 @ (setadjoin @ X611 @ emptyset))))=>(![X612:$i, X613:$i > $o]:((?[X614:$i]:(((in @ X614 @ X612)&(X613 @ X614)))=>(((dsetconstr @ X612 @ X613)=(emptyset))=>~($true))))=>(![X615:$i > $o, X616:$i]:(((in @ X616 @ emptyset)=>(X615 @ X616)))=>(![X617:$i, X618:$i > $o]:((~(![X619:$i]:(((in @ X619 @ X617)=>(X618 @ X619))))=>?[X620:$i]:(((in @ X620 @ X617)&~((X618 @ X620))))))=>(![X621:$i, X622:$i > $o]:((![X623:$i]:(((in @ X623 @ X621)=>~((X622 @ X623))))=>~(?[X624:$i]:(((in @ X624 @ X621)&(X622 @ X624))))))=>(![X625:$i, X626:$i > $o]:((~(?[X627:$i]:(((in @ X627 @ X625)&(X626 @ X627))))=>![X628:$i]:(((in @ X628 @ X625)=>~((X626 @ X628))))))=>(![X629:$i, X630:$i > $o]:((?[X631:$i]:(((in @ X631 @ X629)&~((X630 @ X631))))=>~(![X632:$i]:(((in @ X632 @ X629)=>(X630 @ X632))))))=>(![X633:$o]:(((X633)=>(in @ emptyset @ (prop2set @ ((X633))))))=>(![X634:$o]:(((X634)=>(set2prop @ (prop2set @ ((X634))))))=>(![X635:$i, X636:$i > $o]:((~(?[X637:$i]:(((in @ X637 @ X635)&(X636 @ X637))))=>![X638:$i]:(((in @ X638 @ X635)=>~((X636 @ X638))))))=>(![X639:$i, X640:$i > $o]:((~(![X641:$i]:(((in @ X641 @ X639)=>(X640 @ X641))))=>?[X642:$i]:(((in @ X642 @ X639)&~((X640 @ X642))))))=>(![X643:$i > $o]:((?[X644:$i]:(((X643 @ X644)&![X645:$i]:(((X643 @ X645)=>((X644)=(X645))))))=>?[X646:$i]:(((X643 @ X646)&![X647:$i]:(((X643 @ X647)=>((X646)=(X647))))))))=>(![X648:$i > $o]:((?[X649:$i]:((X648 @ X649))=>(![X650:$i, X651:$i]:(((X648 @ X650)=>((X648 @ X651)=>((X650)=(X651)))))=>?[X652:$i]:(((X648 @ X652)&![X653:$i]:(((X648 @ X653)=>((X652)=(X653)))))))))=>(![X654:$i > $o]:((?[X655:$i]:(![X656:$i]:(((X654 @ X656)<=>((X656)=(X655)))))=>?[X657:$i]:(((X654 @ X657)&![X658:$i]:(((X654 @ X658)=>((X657)=(X658))))))))=>(![X659:$i, X660:$i]:((((X659)=(X660))=>![X661:$i, X662:$i]:((((X661)=(X662))=>((in @ X661 @ X659)=>(in @ X662 @ X660))))))=>(![X663:$i, X664:$i]:((((X663)=(X664))=>![X665:$i, X666:$i]:((((X665)=(X666))=>((in @ X665 @ X663)<=>(in @ X666 @ X664))))))=>(![X667:$i > $o]:((?[X668:$i]:(((X667 @ X668)&![X669:$i]:(((X667 @ X669)=>((X668)=(X669))))))=>![X670:$i, X671:$i]:(((X667 @ X670)=>((X667 @ X671)=>((X670)=(X671)))))))=>(![X672:$i > $o, X673:$i > $o]:((![X674:$i, X675:$i]:((((X674)=(X675))=>((X672 @ X674)<=>(X673 @ X675))))=>(?[X676:$i]:(((X672 @ X676)&![X677:$i]:(((X672 @ X677)=>((X676)=(X677))))))<=>?[X678:$i]:(((X673 @ X678)&![X679:$i]:(((X673 @ X679)=>((X678)=(X679)))))))))=>(((emptyset)=(emptyset))=>(![X680:$i, X681:$i]:((((X680)=(X681))=>![X682:$i, X683:$i]:((((X682)=(X683))=>((setadjoin @ X680 @ X682)=(setadjoin @ X681 @ X683))))))=>(![X684:$i, X685:$i]:((((X684)=(X685))=>((powerset @ X684)=(powerset @ X685))))=>(![X686:$i, X687:$i]:((((X686)=(X687))=>((setunion @ X686)=(setunion @ X687))))=>(((omega)=(omega))=>(![X688:$i > $o]:((?[X689:$i]:(((X688 @ X689)&![X690:$i]:(((X688 @ X690)=>((X689)=(X690))))))=>![X691:$i, X692:$i]:(((X688 @ X691)=>((X688 @ X692)=>((X691)=(X692)))))))=>(![X693:$i > $o, X694:$i > $o]:((![X695:$i, X696:$i]:((((X695)=(X696))=>((X693 @ X695)<=>(X694 @ X696))))=>(?[X697:$i]:(((X693 @ X697)&![X698:$i]:(((X693 @ X698)=>((X697)=(X698))))))=>(?[X699:$i]:(((X694 @ X699)&![X700:$i]:(((X694 @ X700)=>((X699)=(X700))))))=>((descr @ X693)=(descr @ X694))))))=>(![X701:$i, X702:$i]:((((X701)=(X702))=>![X703:$i > $o, X704:$i > $o]:((![X705:$i]:(((in @ X705 @ X701)=>![X706:$i]:(((in @ X706 @ X702)=>(((X705)=(X706))=>((X703 @ X705)<=>(X704 @ X706)))))))=>((dsetconstr @ X701 @ X703)=(dsetconstr @ X702 @ X704))))))=>(![X707:$i, X708:$i]:((![X709:$i]:(((in @ X709 @ X707)=>(in @ X709 @ X708)))=>(subset @ X707 @ X708)))=>(![X710:$i, X711:$i]:((((X710)=(X711))=>(subset @ X711 @ X710)))=>(![X712:$i, X713:$i]:((((X712)=(X713))=>(subset @ X712 @ X713)))=>(![X714:$i, X715:$i]:((![X716:$i]:(((in @ X716 @ X714)=>(in @ X716 @ X715)))=>(subset @ X714 @ X715)))=>(![X717:$i]:((subset @ emptyset @ X717))=>(![X718:$i, X719:$i, X720:$i]:(((subset @ X718 @ X719)=>((in @ X720 @ X718)=>(in @ X720 @ X719))))=>(![X721:$i, X722:$i, X723:$i]:(((subset @ X721 @ X722)=>(~(in @ X723 @ X722)=>~(in @ X723 @ X721))))=>(![X724:$i, X725:$i, X726:$i]:(((in @ X726 @ X724)=>(~(in @ X726 @ X725)=>~(subset @ X724 @ X725))))=>(![X727:$i, X728:$i]:((~(subset @ X727 @ X728)=>((X727)!=(X728))))=>(![X729:$i, X730:$i, X731:$i]:(((in @ X731 @ X729)=>(~(in @ X731 @ X730)=>((X729)!=(X730)))))=>(![X732:$i]:((subset @ X732 @ X732))=>(![X733:$i, X734:$i, X735:$i]:(((subset @ X733 @ X734)=>((subset @ X734 @ X735)=>(subset @ X733 @ X735))))=>(![X736:$i, X737:$i]:((subset @ X737 @ (setadjoin @ X736 @ X737)))=>(![X738:$i, X739:$i, X740:$i]:(((subset @ X738 @ X740)=>(subset @ X738 @ (setadjoin @ X739 @ X740))))=>(![X741:$i, X742:$i]:(((subset @ X741 @ X742)=>(in @ X741 @ (powerset @ X742))))=>(![X743:$i, X744:$i]:(((subset @ X743 @ X744)=>((subset @ X744 @ X743)=>((X743)=(X744)))))=>(![X745:$i]:(((subset @ X745 @ emptyset)=>((X745)=(emptyset))))=>(![X746:$i, X747:$i]:(((subset @ X747 @ X746)=>(in @ X747 @ (powerset @ X746))))=>(![X748:$i, X749:$i]:(((in @ X749 @ (powerset @ X748))=>(subset @ X749 @ X748)))=>(![X750:$i]:((in @ X750 @ (powerset @ X750)))=>(![X751:$i, X752:$i]:(((subset @ X751 @ X752)=>(subset @ (powerset @ X751) @ (powerset @ X752))))=>(![X753:$i, X754:$i > $o]:((in @ (dsetconstr @ X753 @ X754) @ (powerset @ X753)))=>(![X755:$i, X756:$i > $o]:((subset @ (dsetconstr @ X755 @ X756) @ X755))=>(![X757:$i, X758:$i, X759:$i]:(((in @ X759 @ X757)=>(in @ X759 @ (binunion @ X757 @ X758))))=>(![X760:$i, X761:$i]:((in @ X761 @ (setadjoin @ X760 @ (setadjoin @ X761 @ emptyset))))=>(![X762:$i, X763:$i, X764:$i]:(((in @ X764 @ X763)=>(in @ X764 @ (binunion @ X762 @ X763))))=>(![X765:$i, X766:$i, X767:$i, X768:$o]:(((in @ X767 @ (binunion @ X765 @ X766))=>(((in @ X767 @ X765)=>(X768))=>(((in @ X767 @ X766)=>(X768))=>(X768)))))=>(![X769:$i, X770:$i, X771:$i]:(((in @ X771 @ (binunion @ X769 @ X770))=>((in @ X771 @ X769)|(in @ X771 @ X770))))=>(![X772:$i, X773:$i]:((subset @ X772 @ (binunion @ X772 @ X773)))=>(![X774:$i, X775:$i]:((subset @ X775 @ (binunion @ X774 @ X775)))=>(![X776:$i, X777:$i, X778:$i]:(((in @ X778 @ X776)=>((in @ X778 @ X777)=>(in @ X778 @ (binintersect @ X776 @ X777)))))=>(![X779:$i, X780:$i, X781:$i]:(((subset @ X781 @ X779)=>((subset @ X781 @ X780)=>(subset @ X781 @ (binintersect @ X779 @ X780)))))=>(![X782:$i, X783:$i, X784:$i]:(((in @ X784 @ (binintersect @ X782 @ X783))=>(in @ X784 @ X782)))=>(![X785:$i, X786:$i]:((subset @ (binintersect @ X785 @ X786) @ X785))=>(![X787:$i, X788:$i]:(((subset @ X787 @ X788)=>((binintersect @ X787 @ X788)=(X787))))=>(![X789:$i, X790:$i]:((((binintersect @ X789 @ X790)=(X790))=>(subset @ X790 @ X789)))=>(![X791:$i, X792:$i, X793:$i]:(((in @ X793 @ (binintersect @ X791 @ X792))=>(in @ X793 @ X792)))=>(![X794:$i, X795:$i]:((~(?[X796:$i]:(((in @ X796 @ X794)&(in @ X796 @ X795))))=>((binintersect @ X794 @ X795)=(emptyset))))=>(![X797:$i, X798:$i]:((subset @ (binintersect @ X797 @ X798) @ X798))=>(![X799:$i, X800:$i]:(((subset @ X800 @ X799)=>((binintersect @ X799 @ X800)=(X800))))=>(![X801:$i, X802:$i]:((((binintersect @ X801 @ X802)=(X801))=>(subset @ X801 @ X802)))=>(![X803:$i, X804:$i, X805:$i]:(((binintersect @ X803 @ (binunion @ X804 @ X805))=(binunion @ (binintersect @ X803 @ X804) @ (binintersect @ X803 @ X805))))=>(![X806:$i, X807:$i, X808:$i]:(((in @ X808 @ X806)=>(~(in @ X808 @ X807)=>(in @ X808 @ (setminus @ X806 @ X807)))))=>(![X809:$i, X810:$i, X811:$i]:(((in @ X811 @ (setminus @ X809 @ X810))=>(in @ X811 @ X809)))=>(![X812:$i, X813:$i, X814:$i]:(((in @ X814 @ (setminus @ X812 @ X813))=>~(in @ X814 @ X813)))=>(![X815:$i, X816:$i]:(((subset @ X815 @ X816)=>((setminus @ X815 @ X816)=(emptyset))))=>(![X817:$i, X818:$i, X819:$i]:((~(in @ X819 @ (setminus @ X817 @ X818))=>((in @ X819 @ X817)=>(in @ X819 @ X818))))=>(![X820:$i, X821:$i, X822:$i]:((~(in @ X822 @ (setminus @ X820 @ X821))=>(~(in @ X822 @ X821)=>~(in @ X822 @ X820))))=>(![X823:$i, X824:$i, X825:$i]:((~(in @ X825 @ X823)=>~(in @ X825 @ (setminus @ X823 @ X824))))=>(![X826:$i, X827:$i, X828:$i]:(((in @ X828 @ X827)=>~(in @ X828 @ (setminus @ X826 @ X827))))=>(![X829:$i, X830:$i]:((subset @ (setminus @ X829 @ X830) @ X829))=>(![X831:$i, X832:$i]:((((setminus @ X831 @ X832)=(emptyset))=>(subset @ X831 @ X832)))=>(![X833:$i, X834:$i, X835:$i]:(((in @ X835 @ (symdiff @ X833 @ X834))=>![X836:$o]:((((in @ X835 @ X833)=>(~(in @ X835 @ X834)=>(X836)))=>((~(in @ X835 @ X833)=>((in @ X835 @ X834)=>(X836)))=>(X836))))))=>(![X837:$i, X838:$i, X839:$i]:(((in @ X839 @ X837)=>(~(in @ X839 @ X838)=>(in @ X839 @ (symdiff @ X837 @ X838)))))=>(![X840:$i, X841:$i, X842:$i]:((~(in @ X842 @ X840)=>((in @ X842 @ X841)=>(in @ X842 @ (symdiff @ X840 @ X841)))))=>(![X843:$i, X844:$i, X845:$i]:(((in @ X845 @ X843)=>((in @ X845 @ X844)=>~(in @ X845 @ (symdiff @ X843 @ X844)))))=>(![X846:$i, X847:$i, X848:$i]:((~(in @ X848 @ X846)=>(~(in @ X848 @ X847)=>~(in @ X848 @ (symdiff @ X846 @ X847)))))=>(![X849:$i, X850:$i]:((in @ X850 @ (setadjoin @ X849 @ (setadjoin @ X850 @ emptyset))))=>(![X851:$i, X852:$i]:((in @ X851 @ (setunion @ (setadjoin @ (setadjoin @ X851 @ emptyset) @ (setadjoin @ (setadjoin @ X851 @ (setadjoin @ X852 @ emptyset)) @ emptyset)))))=>(![X853:$i, X854:$i]:((in @ X854 @ (setunion @ (setadjoin @ (setadjoin @ X853 @ emptyset) @ (setadjoin @ (setadjoin @ X853 @ (setadjoin @ X854 @ emptyset)) @ emptyset)))))=>(![X855:$i, X856:$i]:(?[X857:$i]:(((in @ X857 @ (setunion @ (setadjoin @ (setadjoin @ X855 @ emptyset) @ (setadjoin @ (setadjoin @ X855 @ (setadjoin @ X856 @ emptyset)) @ emptyset))))&?[X858:$i]:(((in @ X858 @ (setunion @ (setadjoin @ (setadjoin @ X855 @ emptyset) @ (setadjoin @ (setadjoin @ X855 @ (setadjoin @ X856 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X855 @ emptyset) @ (setadjoin @ (setadjoin @ X855 @ (setadjoin @ X856 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X857 @ emptyset) @ (setadjoin @ (setadjoin @ X857 @ (setadjoin @ X858 @ emptyset)) @ emptyset))))))))=>(![X859:$i, X860:$i]:(?[X861:$i]:(((in @ X861 @ (setunion @ (kpair @ X859 @ X860)))&?[X862:$i]:(((in @ X862 @ (setunion @ (kpair @ X859 @ X860)))&((kpair @ X859 @ X860)=(setadjoin @ (setadjoin @ X861 @ emptyset) @ (setadjoin @ (setadjoin @ X861 @ (setadjoin @ X862 @ emptyset)) @ emptyset))))))))=>(![X863:$i, X864:$i]:(((in @ X864 @ X863)=>(subset @ (setadjoin @ X864 @ emptyset) @ X863)))=>(![X865:$i, X866:$i]:(((in @ X866 @ X865)=>(in @ (setadjoin @ X866 @ emptyset) @ (powerset @ X865))))=>(![X867:$i, X868:$i, X869:$i]:(((in @ X869 @ X867)=>(in @ (setadjoin @ X869 @ emptyset) @ (powerset @ (binunion @ X867 @ X868)))))=>(![X870:$i, X871:$i, X872:$i]:(((in @ X872 @ (setadjoin @ X870 @ (setadjoin @ X871 @ emptyset)))=>(((X872)=(X870))|((X872)=(X871)))))=>(![X873:$i, X874:$i, X875:$i]:(((in @ X875 @ X873)=>![X876:$i]:(((in @ X876 @ X874)=>(subset @ (setadjoin @ X875 @ (setadjoin @ X876 @ emptyset)) @ (binunion @ X873 @ X874))))))=>(![X877:$i, X878:$i, X879:$i]:(((in @ X879 @ X877)=>![X880:$i]:(((in @ X880 @ X878)=>(in @ (setadjoin @ X879 @ (setadjoin @ X880 @ emptyset)) @ (powerset @ (binunion @ X877 @ X878)))))))=>(![X881:$i, X882:$i, X883:$i]:(((in @ X883 @ X881)=>![X884:$i]:(((in @ X884 @ X882)=>(subset @ (setadjoin @ (setadjoin @ X883 @ emptyset) @ (setadjoin @ (setadjoin @ X883 @ (setadjoin @ X884 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X881 @ X882)))))))=>(![X885:$i, X886:$i, X887:$i]:(((in @ X887 @ X885)=>![X888:$i]:(((in @ X888 @ X886)=>(in @ (setadjoin @ (setadjoin @ X887 @ emptyset) @ (setadjoin @ (setadjoin @ X887 @ (setadjoin @ X888 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X885 @ X886))))))))=>(![X889:$i, X890:$i, X891:$i]:(((in @ X891 @ X889)=>![X892:$i]:(((in @ X892 @ X890)=>(in @ (kpair @ X891 @ X892) @ (powerset @ (powerset @ (binunion @ X889 @ X890))))))))=>(![X893:$i, X894:$i, X895:$i]:(((in @ X895 @ X893)=>![X896:$i]:(((in @ X896 @ X894)=>(in @ (kpair @ X895 @ X896) @ (cartprod @ X893 @ X894))))))=>(![X897:$i, X898:$i, X899:$i]:(((in @ X899 @ (cartprod @ X897 @ X898))=>?[X900:$i]:(((in @ X900 @ X897)&?[X901:$i]:(((in @ X901 @ X898)&((X899)=(kpair @ X900 @ X901))))))))=>(![X902:$i, X903:$i, X904:$i]:(((in @ X904 @ (cartprod @ X902 @ X903))=>?[X905:$i]:(((in @ X905 @ (setunion @ X904))&?[X906:$i]:(((in @ X906 @ (setunion @ X904))&((X904)=(setadjoin @ (setadjoin @ X905 @ emptyset) @ (setadjoin @ (setadjoin @ X905 @ (setadjoin @ X906 @ emptyset)) @ emptyset)))))))))=>(![X907:$i, X908:$i]:(((in @ X908 @ (setunion @ X907))=>?[X909:$i]:(((in @ X909 @ X907)&(in @ X908 @ X909)))))=>(![X910:$i]:((subset @ (setunion @ (setadjoin @ X910 @ emptyset)) @ X910))=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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_171, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_172]), foundationAx]), wellorderingAx]), c_0_173]), c_0_174]), c_0_175]), c_0_176]), c_0_177]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_178]), setext]), emptyI]), noeltsimpempty]), c_0_179]), c_0_180]), c_0_181]), c_0_182]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_183]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_184]), c_0_185]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_186]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_187]), c_0_188]), c_0_189]), inCongP]), in__Cong]), c_0_190]), c_0_191]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_192]), c_0_193]), c_0_194]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_195]), c_0_196]), 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_197]), c_0_198]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), c_0_199]), setunionE2]), setunionsingleton1])])]), c_0_200])).
% 0.57/0.43 thf(c_0_202, negated_conjecture, ![X915:$i, X916:$i, X918:$i, X919:$i, X920:$i, X921:$i, X922:$i, X923:$i, X924:$i, X925:$i, X926:$i, X928:$i, X929:$i, X931:$i, X932:$i, X933:$i, X934:$i, X935:$i, X937:$i, X938:$i > $i > $o, X939:$i, X941:$i, X944:$i, X946:$i, X947:$i, X948:$i, X949:$i, X951:$i, X952:$i > $o, X953:$i, X955:$i, X956:$i > $o, X957:$i, X958:$i, X959:$i > $o, X960:$i, X961:$i, X962:$i > $o, X963:$i, X964:$i > $o, X965:$i, X968:$i, X969:$o, X970:$i, X971:$i, X972:$o, X973:$i, X974:$i, X975:$i > $o, X976:$i, X979:$i, X980:$i, X983:$i, X985:$i, X987:$i, X988:$i > $o, X989:$i, X990:$i, X992:$i, X993:$i > $o, X994:$i, X995:$i, X996:$i, X997:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i, X1003:$i, X1004:$i, X1005:$o, X1006:$i, X1007:$i, X1008:$i, X1009:$i, X1010:$i, X1011:$i, X1013:$i, X1014:$i, X1015:$i, X1016:$i, X1017:$i, X1018:$i, X1019:$i, X1020:$i, X1021:$i, X1022:$i, X1023:$o, X1025:$i, X1026:$i, X1027:$i > $o, X1028:$i, X1031:$i, X1032:$i, X1033:$i, X1035:$i, X1036:$i, X1037:$i, X1038:$i, X1039:$i, X1040:$i, X1041:$i, X1042:$i, X1043:$i, X1044:$i, X1045:$i, X1046:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i > $o, X1052:$i, X1053:$i > $o, X1054:$i, X1055:$i, X1056:$i > $o, X1057:$i, X1059:$i, X1060:$i > $o, X1062:$i, X1063:$i, X1064:$i > $o, X1066:$i, X1067:$i, X1068:$i > $o, X1069:$i, X1071:$o, X1072:$o, X1073:$i, X1074:$i > $o, X1076:$i, X1077:$i, X1078:$i > $o, X1079:$i, X1081:$i > $o, X1082:$i, X1085:$i, X1086:$i > $o, X1087:$i, X1091:$i, X1092:$i > $o, X1093:$i, X1096:$i, X1097:$i, X1098:$i, X1099:$i, X1100:$i, X1101:$i, X1102:$i, X1103:$i, X1104:$i, X1105:$i > $o, X1106:$i, X1108:$i, X1109:$i, X1110:$i > $o, X1111:$i > $o, X1114:$i, X1117:$i, X1118:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i, X1126:$i, X1127:$i, X1128:$i, X1129:$i, X1130:$i > $o, X1131:$i, X1133:$i, X1134:$i, X1135:$i > $o, X1136:$i > $o, X1139:$i, X1141:$i, X1143:$i, X1144:$i, X1145:$i > $o, X1146:$i > $o, X1149:$i, X1150:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1159:$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:$i, X1195:$i, X1196:$i > $o, X1197:$i, X1198:$i > $o, X1199:$i, X1200:$i, X1201:$i, X1202:$i, X1203:$i, X1204:$i, X1205:$i, X1206:$i, X1207:$i, X1208:$i, X1209:$i, X1210:$o, X1211:$i, X1212:$i, X1213:$i, X1214:$i, X1215:$i, X1216:$i, X1217:$i, X1218:$i, X1219:$i, X1220:$i, X1221:$i, X1222:$i, X1223:$i, X1224:$i, X1225:$i, X1226:$i, X1227:$i, X1228:$i, X1229:$i, X1230:$i, X1231:$i, X1232:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1239:$i, X1240:$i, X1241:$i, X1242:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i, X1251:$i, X1252:$i, X1253:$i, X1254:$i, X1255:$i, X1256:$i, X1257:$i, X1258:$i, X1259:$i, X1260:$i, X1261:$i, X1262:$i, X1263:$i, X1264:$i, X1265:$i, X1266:$i, X1267:$i, X1268:$i, X1269:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$i, X1278:$o, X1279:$i, X1280:$i, X1281:$i, X1282:$i, X1283:$i, X1284:$i, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$i, X1290:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1296:$i, X1297:$i, X1298:$i, X1301:$i, X1302:$i, X1305:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1326:$i, X1327:$i, X1328:$i, X1329:$i, X1330:$i, X1331:$i, X1332:$i, X1333:$i, X1334:$i, X1335:$i, X1336:$i, X1337:$i, X1338:$i, X1339:$i, X1340:$i, X1341:$i, X1344:$i, X1345:$i, X1346:$i, X1349:$i, X1350:$i, X1352:$i]:((((~(in @ (esk1_2 @ X915 @ X916) @ X915)|~(in @ (esk1_2 @ X915 @ X916) @ X916)|((X915)=(X916)))&((in @ (esk1_2 @ X915 @ X916) @ X915)|(in @ (esk1_2 @ X915 @ X916) @ X916)|((X915)=(X916))))&(~(in @ X918 @ emptyset)&(((~(in @ X921 @ (setadjoin @ X919 @ X920))|(((X921)=(X919))|(in @ X921 @ X920)))&((((X921)!=(X919))|(in @ X921 @ (setadjoin @ X919 @ X920)))&(~(in @ X921 @ X920)|(in @ X921 @ (setadjoin @ X919 @ X920)))))&(((~(in @ X923 @ (powerset @ X922))|(~(in @ X924 @ X923)|(in @ X924 @ X922)))&(((in @ (esk2_2 @ X925 @ X926) @ X926)|(in @ X926 @ (powerset @ X925)))&(~(in @ (esk2_2 @ X925 @ X926) @ X925)|(in @ X926 @ (powerset @ X925)))))&(((((in @ X929 @ (esk3_2 @ X928 @ X929))|~(in @ X929 @ (setunion @ X928)))&((in @ (esk3_2 @ X928 @ X929) @ X928)|~(in @ X929 @ (setunion @ X928))))&(~(in @ X932 @ X933)|~(in @ X933 @ X931)|(in @ X932 @ (setunion @ X931))))&((in @ emptyset @ omega)&((~(in @ X934 @ omega)|(in @ (setadjoin @ X934 @ X934) @ omega))&(((((in @ (esk4_1 @ X935) @ omega)|~(in @ emptyset @ X935)|(~(in @ X937 @ omega)|(in @ X937 @ X935)))&((in @ (esk4_1 @ X935) @ X935)|~(in @ emptyset @ X935)|(~(in @ X937 @ omega)|(in @ X937 @ X935))))&(~(in @ (setadjoin @ (esk4_1 @ X935) @ (esk4_1 @ X935)) @ X935)|~(in @ emptyset @ X935)|(~(in @ X937 @ omega)|(in @ X937 @ X935))))&((((((in @ (esk8_3 @ X938 @ X939 @ X944) @ X939)|~(in @ X944 @ (esk7_2 @ X938 @ X939))|(in @ (esk5_2 @ X938 @ X939) @ X939))&((X938 @ (esk8_3 @ X938 @ X939 @ X944) @ X944)|~(in @ X944 @ (esk7_2 @ X938 @ X939))|(in @ (esk5_2 @ X938 @ X939) @ X939)))&(~(in @ X947 @ X939)|~(X938 @ X947 @ X946)|(in @ X946 @ (esk7_2 @ X938 @ X939))|(in @ (esk5_2 @ X938 @ X939) @ X939)))&(((((in @ (esk8_3 @ X938 @ X939 @ X944) @ X939)|~(in @ X944 @ (esk7_2 @ X938 @ X939))|((X938 @ (esk5_2 @ X938 @ X939) @ (esk6_3 @ X938 @ X939 @ X941))|~(X938 @ (esk5_2 @ X938 @ X939) @ X941)))&((X938 @ (esk8_3 @ X938 @ X939 @ X944) @ X944)|~(in @ X944 @ (esk7_2 @ X938 @ X939))|((X938 @ (esk5_2 @ X938 @ X939) @ (esk6_3 @ X938 @ X939 @ X941))|~(X938 @ (esk5_2 @ X938 @ X939) @ X941))))&(~(in @ X947 @ X939)|~(X938 @ X947 @ X946)|(in @ X946 @ (esk7_2 @ X938 @ X939))|((X938 @ (esk5_2 @ X938 @ X939) @ (esk6_3 @ X938 @ X939 @ X941))|~(X938 @ (esk5_2 @ X938 @ X939) @ X941))))&((((in @ (esk8_3 @ X938 @ X939 @ X944) @ X939)|~(in @ X944 @ (esk7_2 @ X938 @ X939))|(((X941)!=(esk6_3 @ X938 @ X939 @ X941))|~(X938 @ (esk5_2 @ X938 @ X939) @ X941)))&((X938 @ (esk8_3 @ X938 @ X939 @ X944) @ X944)|~(in @ X944 @ (esk7_2 @ X938 @ X939))|(((X941)!=(esk6_3 @ X938 @ X939 @ X941))|~(X938 @ (esk5_2 @ X938 @ X939) @ X941))))&(~(in @ X947 @ X939)|~(X938 @ X947 @ X946)|(in @ X946 @ (esk7_2 @ X938 @ X939))|(((X941)!=(esk6_3 @ X938 @ X939 @ X941))|~(X938 @ (esk5_2 @ X938 @ X939) @ X941))))))&((((in @ (esk9_1 @ X948) @ X948)|~(in @ X949 @ X948))&(~(in @ X951 @ (esk9_1 @ X948))|~(in @ X951 @ X948)|~(in @ X949 @ X948)))&((epred1_0)&((((X952 @ (esk10_2 @ X952 @ X953))|~(X952 @ X953)|(X952 @ (descr @ X952)))&(((X953)!=(esk10_2 @ X952 @ X953))|~(X952 @ X953)|(X952 @ (descr @ X952))))&((~(in @ X957 @ X955)|(~(X956 @ X957)|(in @ X957 @ (dsetconstr @ X955 @ X956))))&((~(in @ X960 @ (dsetconstr @ X958 @ X959))|(in @ X960 @ X958))&((~(in @ X963 @ (dsetconstr @ X961 @ X962))|(X962 @ X963))&(((((X964 @ (esk12_1 @ X964))|((X964 @ (esk11_2 @ X964 @ X965))|~(X964 @ X965)))&(~(X964 @ X968)|((esk12_1 @ X964)=(X968))|((X964 @ (esk11_2 @ X964 @ X965))|~(X964 @ X965))))&(((X964 @ (esk12_1 @ X964))|(((X965)!=(esk11_2 @ X964 @ X965))|~(X964 @ X965)))&(~(X964 @ X968)|((esk12_1 @ X964)=(X968))|(((X965)!=(esk11_2 @ X964 @ X965))|~(X964 @ X965)))))&((~(in @ X970 @ (prop2set @ ((X969))))|(X969))&((~(in @ X971 @ emptyset)|(X972))&((~(in @ X973 @ emptyset)|~($true))&(~(in @ X974 @ emptyset)&((((X975 @ (esk13_2 @ X975 @ X976))|~(X975 @ X976)|(X975 @ (esk14_1 @ X975)))&(((X976)!=(esk13_2 @ X975 @ X976))|~(X975 @ X976)|(X975 @ (esk14_1 @ X975))))&(((((in @ (esk16_2 @ X979 @ X980) @ X980)|((X979)=(X980))|(in @ (esk15_2 @ X979 @ X980) @ X979))&(~(in @ (esk16_2 @ X979 @ X980) @ X979)|((X979)=(X980))|(in @ (esk15_2 @ X979 @ X980) @ X979)))&(((in @ (esk16_2 @ X979 @ X980) @ X980)|((X979)=(X980))|~(in @ (esk15_2 @ X979 @ X980) @ X980))&(~(in @ (esk16_2 @ X979 @ X980) @ X979)|((X979)=(X980))|~(in @ (esk15_2 @ X979 @ X980) @ X980))))&(((in @ (esk17_1 @ X983) @ X983)|((X983)=(emptyset)))&(((in @ (esk18_1 @ X985) @ X985)|((X985)=(emptyset)))&(((~(in @ X989 @ (dsetconstr @ X987 @ X988))|(X988 @ X989)|~(in @ X989 @ X987))&(~(X988 @ X989)|(in @ X989 @ (dsetconstr @ X987 @ X988))|~(in @ X989 @ X987)))&((((X990)=(emptyset))|(in @ (esk19_1 @ X990) @ X990))&((~(in @ X994 @ X992)|(~(X993 @ X994)|((dsetconstr @ X992 @ X993)!=(emptyset))))&((~(in @ X996 @ X995)|((X995)!=(emptyset)))&((in @ X997 @ (setadjoin @ X997 @ X998))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1001 @ X1000)|(in @ X1001 @ (setadjoin @ X999 @ X1000)))&(((((in @ X1004 @ X1003)|(X1005)|((X1004)=(X1002))|~(in @ X1004 @ (setadjoin @ X1002 @ X1003)))&(~(X1005)|(X1005)|((X1004)=(X1002))|~(in @ X1004 @ (setadjoin @ X1002 @ X1003))))&(((in @ X1004 @ X1003)|(X1005)|~(X1005)|~(in @ X1004 @ (setadjoin @ X1002 @ X1003)))&(~(X1005)|(X1005)|~(X1005)|~(in @ X1004 @ (setadjoin @ X1002 @ X1003)))))&((~(in @ X1008 @ (setadjoin @ X1006 @ X1007))|(((X1008)=(X1006))|(in @ X1008 @ X1007)))&(((dsetconstr @ X1009 @ (^[Z0:$i]:($true)))=(X1009))&((((in @ (esk20_2 @ X1010 @ X1011) @ X1011)|(in @ X1011 @ (powerset @ X1010)))&(~(in @ (esk20_2 @ X1010 @ X1011) @ X1010)|(in @ X1011 @ (powerset @ X1010))))&((in @ emptyset @ (powerset @ X1013))&((in @ emptyset @ (powerset @ X1014))&((~(in @ X1016 @ (powerset @ X1015))|(~(in @ X1017 @ X1016)|(in @ X1017 @ X1015)))&((~(in @ X1019 @ X1020)|(~(in @ X1020 @ X1018)|(in @ X1019 @ (setunion @ X1018))))&((((in @ X1022 @ (esk21_3 @ X1021 @ X1022 @ X1023))|(X1023)|~(in @ X1022 @ (setunion @ X1021)))&(((in @ (esk21_3 @ X1021 @ X1022 @ X1023) @ X1021)|(X1023)|~(in @ X1022 @ (setunion @ X1021)))&(~(X1023)|(X1023)|~(in @ X1022 @ (setunion @ X1021)))))&((~(in @ X1026 @ X1025)|(in @ X1026 @ (powerset @ (setunion @ X1025))))&((((~(X1027 @ X1031)|((X1031)=(esk23_1 @ X1027))|((X1027 @ (esk22_2 @ X1027 @ X1028))|~(X1027 @ X1028)))&(((X1032)!=(esk23_1 @ X1027))|(X1027 @ X1032)|((X1027 @ (esk22_2 @ X1027 @ X1028))|~(X1027 @ X1028))))&((~(X1027 @ X1031)|((X1031)=(esk23_1 @ X1027))|(((X1028)!=(esk22_2 @ X1027 @ X1028))|~(X1027 @ X1028)))&(((X1032)!=(esk23_1 @ X1027))|(X1027 @ X1032)|(((X1028)!=(esk22_2 @ X1027 @ X1028))|~(X1027 @ X1028)))))&((((in @ (esk24_1 @ X1033) @ X1033)|((X1033)=(emptyset)))&(($true)|((X1033)=(emptyset))))&((~(in @ X1035 @ (setadjoin @ X1036 @ emptyset))|((X1035)=(X1036)))&((((X1037)=(X1038))|~(in @ X1038 @ (setadjoin @ X1037 @ emptyset)))&((((X1039)!=(X1040))|(in @ X1039 @ (setadjoin @ X1040 @ emptyset)))&((~(in @ X1041 @ (setadjoin @ X1042 @ emptyset))|(in @ X1042 @ (setadjoin @ X1041 @ emptyset)))&((~(in @ X1045 @ (setadjoin @ X1043 @ (setadjoin @ X1044 @ emptyset)))|(((X1045)=(X1043))|((X1045)=(X1044))))&((in @ X1046 @ (setadjoin @ X1046 @ (setadjoin @ X1047 @ emptyset)))&((in @ X1049 @ (setadjoin @ X1048 @ (setadjoin @ X1049 @ emptyset)))&((~(in @ X1052 @ X1050)|~(X1051 @ X1052)|(((dsetconstr @ X1050 @ X1051)!=(emptyset))|~($true)))&((~(in @ X1054 @ emptyset)|(X1053 @ X1054))&((((in @ (esk25_2 @ X1055 @ X1056) @ X1055)|(~(in @ X1057 @ X1055)|(X1056 @ X1057)))&(~(X1056 @ (esk25_2 @ X1055 @ X1056))|(~(in @ X1057 @ X1055)|(X1056 @ X1057))))&((((in @ (esk26_2 @ X1059 @ X1060) @ X1059)|(~(in @ X1062 @ X1059)|~(X1060 @ X1062)))&((X1060 @ (esk26_2 @ X1059 @ X1060))|(~(in @ X1062 @ X1059)|~(X1060 @ X1062))))&((((in @ (esk27_2 @ X1063 @ X1064) @ X1063)|(~(in @ X1066 @ X1063)|~(X1064 @ X1066)))&((X1064 @ (esk27_2 @ X1063 @ X1064))|(~(in @ X1066 @ X1063)|~(X1064 @ X1066))))&((((in @ (esk28_2 @ X1067 @ X1068) @ X1067)|(~(in @ X1069 @ X1067)|(X1068 @ X1069)))&(~(X1068 @ (esk28_2 @ X1067 @ X1068))|(~(in @ X1069 @ X1067)|(X1068 @ X1069))))&((~(X1071)|(in @ emptyset @ (prop2set @ ((X1071)))))&((~(X1072)|(set2prop @ (prop2set @ ((X1072)))))&((((in @ (esk29_2 @ X1073 @ X1074) @ X1073)|(~(in @ X1076 @ X1073)|~(X1074 @ X1076)))&((X1074 @ (esk29_2 @ X1073 @ X1074))|(~(in @ X1076 @ X1073)|~(X1074 @ X1076))))&((((in @ (esk30_2 @ X1077 @ X1078) @ X1077)|(~(in @ X1079 @ X1077)|(X1078 @ X1079)))&(~(X1078 @ (esk30_2 @ X1077 @ X1078))|(~(in @ X1079 @ X1077)|(X1078 @ X1079))))&(((((X1081 @ (esk32_1 @ X1081))|((X1081 @ (esk31_2 @ X1081 @ X1082))|~(X1081 @ X1082)))&(~(X1081 @ X1085)|((esk32_1 @ X1081)=(X1085))|((X1081 @ (esk31_2 @ X1081 @ X1082))|~(X1081 @ X1082))))&(((X1081 @ (esk32_1 @ X1081))|(((X1082)!=(esk31_2 @ X1081 @ X1082))|~(X1081 @ X1082)))&(~(X1081 @ X1085)|((esk32_1 @ X1081)=(X1085))|(((X1082)!=(esk31_2 @ X1081 @ X1082))|~(X1081 @ X1082)))))&(((((X1086 @ (esk35_1 @ X1086))|(X1086 @ (esk33_1 @ X1086))|~(X1086 @ X1087))&(~(X1086 @ X1091)|((esk35_1 @ X1086)=(X1091))|(X1086 @ (esk33_1 @ X1086))|~(X1086 @ X1087)))&((((X1086 @ (esk35_1 @ X1086))|(X1086 @ (esk34_1 @ X1086))|~(X1086 @ X1087))&(~(X1086 @ X1091)|((esk35_1 @ X1086)=(X1091))|(X1086 @ (esk34_1 @ 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(symdiff @ X1275 @ X1276)))&(((in @ X1277 @ X1276)|(X1278)|~(in @ X1277 @ X1276)|~(in @ X1277 @ (symdiff @ X1275 @ X1276)))&(~(X1278)|(X1278)|~(in @ X1277 @ X1276)|~(in @ X1277 @ (symdiff @ X1275 @ X1276)))))&((~(in @ X1277 @ X1275)|(X1278)|~(X1278)|~(in @ X1277 @ (symdiff @ X1275 @ X1276)))&(((in @ X1277 @ X1276)|(X1278)|~(X1278)|~(in @ X1277 @ (symdiff @ X1275 @ X1276)))&(~(X1278)|(X1278)|~(X1278)|~(in @ X1277 @ (symdiff @ X1275 @ X1276)))))))&((~(in @ X1281 @ X1279)|((in @ X1281 @ X1280)|(in @ X1281 @ (symdiff @ X1279 @ X1280))))&(((in @ X1284 @ X1282)|(~(in @ X1284 @ X1283)|(in @ X1284 @ (symdiff @ X1282 @ X1283))))&((~(in @ X1287 @ X1285)|(~(in @ X1287 @ X1286)|~(in @ X1287 @ (symdiff @ X1285 @ X1286))))&(((in @ X1290 @ X1288)|((in @ X1290 @ X1289)|~(in @ X1290 @ (symdiff @ X1288 @ X1289))))&((in @ X1292 @ (setadjoin @ X1291 @ (setadjoin @ X1292 @ emptyset)))&((in @ X1293 @ (setunion @ (setadjoin @ (setadjoin @ X1293 @ emptyset) @ (setadjoin @ (setadjoin @ X1293 @ (setadjoin @ X1294 @ emptyset)) @ emptyset))))&((in @ X1296 @ (setunion @ (setadjoin @ (setadjoin @ X1295 @ emptyset) @ (setadjoin @ (setadjoin @ X1295 @ (setadjoin @ X1296 @ emptyset)) @ emptyset))))&(((in @ (esk55_2 @ X1297 @ X1298) @ (setunion @ (setadjoin @ (setadjoin @ X1297 @ emptyset) @ (setadjoin @ (setadjoin @ X1297 @ (setadjoin @ X1298 @ emptyset)) @ emptyset))))&((in @ (esk56_2 @ X1297 @ X1298) @ (setunion @ (setadjoin @ (setadjoin @ X1297 @ emptyset) @ (setadjoin @ (setadjoin @ X1297 @ (setadjoin @ X1298 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1297 @ emptyset) @ (setadjoin @ (setadjoin @ X1297 @ (setadjoin @ X1298 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk55_2 @ X1297 @ X1298) @ emptyset) @ (setadjoin @ (setadjoin @ (esk55_2 @ X1297 @ X1298) @ (setadjoin @ (esk56_2 @ X1297 @ X1298) @ emptyset)) @ emptyset)))))&(((in @ (esk57_2 @ X1301 @ X1302) @ (setunion @ (kpair @ X1301 @ X1302)))&((in @ (esk58_2 @ X1301 @ X1302) @ (setunion @ (kpair @ X1301 @ X1302)))&((kpair @ X1301 @ X1302)=(setadjoin @ (setadjoin @ (esk57_2 @ X1301 @ X1302) @ emptyset) @ (setadjoin @ (setadjoin @ (esk57_2 @ X1301 @ X1302) @ (setadjoin @ (esk58_2 @ X1301 @ X1302) @ emptyset)) @ emptyset)))))&((~(in @ X1306 @ X1305)|(subset @ (setadjoin @ X1306 @ emptyset) @ X1305))&((~(in @ X1308 @ X1307)|(in @ (setadjoin @ X1308 @ emptyset) @ (powerset @ X1307)))&((~(in @ X1311 @ X1309)|(in @ (setadjoin @ X1311 @ emptyset) @ (powerset @ (binunion @ X1309 @ X1310))))&((~(in @ X1314 @ (setadjoin @ X1312 @ (setadjoin @ X1313 @ emptyset)))|(((X1314)=(X1312))|((X1314)=(X1313))))&((~(in @ X1317 @ X1315)|(~(in @ X1318 @ X1316)|(subset @ (setadjoin @ X1317 @ (setadjoin @ X1318 @ emptyset)) @ (binunion @ X1315 @ X1316))))&((~(in @ X1321 @ X1319)|(~(in @ X1322 @ X1320)|(in @ (setadjoin @ X1321 @ (setadjoin @ X1322 @ emptyset)) @ (powerset @ (binunion @ X1319 @ X1320)))))&((~(in @ X1325 @ X1323)|(~(in @ X1326 @ X1324)|(subset @ (setadjoin @ (setadjoin @ X1325 @ emptyset) @ (setadjoin @ (setadjoin @ X1325 @ (setadjoin @ X1326 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1323 @ X1324)))))&((~(in @ X1329 @ X1327)|(~(in @ X1330 @ X1328)|(in @ (setadjoin @ (setadjoin @ X1329 @ emptyset) @ (setadjoin @ (setadjoin @ X1329 @ (setadjoin @ X1330 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1327 @ X1328))))))&((~(in @ X1333 @ X1331)|(~(in @ X1334 @ X1332)|(in @ (kpair @ X1333 @ X1334) @ (powerset @ (powerset @ (binunion @ X1331 @ X1332))))))&((~(in @ X1337 @ X1335)|(~(in @ X1338 @ X1336)|(in @ (kpair @ X1337 @ X1338) @ (cartprod @ X1335 @ X1336))))&((((in @ (esk59_3 @ X1339 @ X1340 @ X1341) @ X1339)|~(in @ X1341 @ (cartprod @ X1339 @ X1340)))&(((in @ (esk60_3 @ X1339 @ X1340 @ X1341) @ X1340)|~(in @ X1341 @ (cartprod @ X1339 @ X1340)))&(((X1341)=(kpair @ (esk59_3 @ X1339 @ X1340 @ X1341) @ (esk60_3 @ X1339 @ X1340 @ X1341)))|~(in @ X1341 @ (cartprod @ X1339 @ X1340)))))&((((in @ (esk61_3 @ X1344 @ X1345 @ X1346) @ (setunion @ X1346))|~(in @ X1346 @ (cartprod @ X1344 @ X1345)))&(((in @ (esk62_3 @ X1344 @ X1345 @ X1346) @ (setunion @ X1346))|~(in @ X1346 @ (cartprod @ X1344 @ X1345)))&(((X1346)=(setadjoin @ (setadjoin @ (esk61_3 @ X1344 @ X1345 @ X1346) @ emptyset) @ (setadjoin @ (setadjoin @ (esk61_3 @ X1344 @ X1345 @ X1346) @ (setadjoin @ (esk62_3 @ X1344 @ X1345 @ X1346) @ emptyset)) @ emptyset)))|~(in @ X1346 @ (cartprod @ X1344 @ X1345)))))&((((in @ (esk63_2 @ X1349 @ X1350) @ X1349)|~(in @ X1350 @ (setunion @ X1349)))&((in @ X1350 @ (esk63_2 @ X1349 @ X1350))|~(in @ X1350 @ (setunion @ X1349))))&((subset @ (setunion @ (setadjoin @ X1352 @ emptyset)) @ X1352)&~(subset @ esk64_0 @ (setunion @ (setadjoin @ esk64_0 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_201])])])])])])])).
% 0.57/0.43 thf(c_0_203, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ X2 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_202])).
% 0.57/0.43 thf(c_0_204, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ (setunion @ X3)))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_202])).
% 0.57/0.43 thf(c_0_205, negated_conjecture, ~((subset @ esk64_0 @ (setunion @ (setadjoin @ esk64_0 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_202])).
% 0.57/0.43 thf(c_0_206, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ (setunion @ X3))|~((in @ X2 @ X3)))), inference(spm,[status(thm)],[c_0_203, c_0_204])).
% 0.57/0.43 thf(c_0_207, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_202])).
% 0.57/0.43 thf(c_0_208, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205, c_0_206]), c_0_207])]), ['proof']).
% 0.57/0.43 % SZS output end CNFRefutation
% 0.57/0.43 % Parsed axioms : 330
% 0.57/0.43 % Removed by relevancy pruning/SinE : 0
% 0.57/0.43 % Initial clauses : 458
% 0.57/0.43 % Removed in clause preprocessing : 198
% 0.57/0.43 % Initial clauses in saturation : 260
% 0.57/0.43 % Processed clauses : 85
% 0.57/0.43 % ...of these trivial : 6
% 0.57/0.43 % ...subsumed : 16
% 0.57/0.43 % ...remaining for further processing : 63
% 0.57/0.43 % Other redundant clauses eliminated : 10
% 0.57/0.43 % Clauses deleted for lack of memory : 0
% 0.57/0.43 % Backward-subsumed : 0
% 0.57/0.43 % Backward-rewritten : 2
% 0.57/0.43 % Generated clauses : 98
% 0.57/0.43 % ...of the previous two non-redundant : 46
% 0.57/0.43 % ...aggressively subsumed : 0
% 0.57/0.43 % Contextual simplify-reflections : 0
% 0.57/0.43 % Paramodulations : 88
% 0.57/0.43 % Factorizations : 0
% 0.57/0.43 % NegExts : 0
% 0.57/0.43 % Equation resolutions : 10
% 0.57/0.43 % Disequality decompositions : 0
% 0.57/0.43 % Total rewrite steps : 52
% 0.57/0.43 % ...of those cached : 32
% 0.57/0.43 % Propositional unsat checks : 0
% 0.57/0.43 % Propositional check models : 0
% 0.57/0.43 % Propositional check unsatisfiable : 0
% 0.57/0.43 % Propositional clauses : 0
% 0.57/0.43 % Propositional clauses after purity: 0
% 0.57/0.43 % Propositional unsat core size : 0
% 0.57/0.43 % Propositional preprocessing time : 0.000
% 0.57/0.43 % Propositional encoding time : 0.000
% 0.57/0.43 % Propositional solver time : 0.000
% 0.57/0.43 % Success case prop preproc time : 0.000
% 0.57/0.43 % Success case prop encoding time : 0.000
% 0.57/0.43 % Success case prop solver time : 0.000
% 0.57/0.43 % Current number of processed clauses : 55
% 0.57/0.43 % Positive orientable unit clauses : 31
% 0.57/0.43 % Positive unorientable unit clauses: 0
% 0.57/0.43 % Negative unit clauses : 2
% 0.57/0.43 % Non-unit-clauses : 22
% 0.57/0.43 % Current number of unprocessed clauses: 221
% 0.57/0.43 % ...number of literals in the above : 744
% 0.57/0.43 % Current number of archived formulas : 0
% 0.57/0.43 % Current number of archived clauses : 2
% 0.57/0.43 % Clause-clause subsumption calls (NU) : 50
% 0.57/0.43 % Rec. Clause-clause subsumption calls : 44
% 0.57/0.43 % Non-unit clause-clause subsumptions : 9
% 0.57/0.43 % Unit Clause-clause subsumption calls : 3
% 0.57/0.43 % Rewrite failures with RHS unbound : 0
% 0.57/0.43 % BW rewrite match attempts : 6
% 0.57/0.43 % BW rewrite match successes : 2
% 0.57/0.43 % Condensation attempts : 0
% 0.57/0.43 % Condensation successes : 0
% 0.57/0.43 % Termbank termtop insertions : 39253
% 0.57/0.43 % Search garbage collected termcells : 14591
% 0.57/0.43
% 0.57/0.43 % -------------------------------------------------
% 0.57/0.43 % User time : 0.054 s
% 0.57/0.43 % System time : 0.006 s
% 0.57/0.43 % Total time : 0.060 s
% 0.57/0.43 % Maximum resident set size: 7292 pages
% 0.57/0.43
% 0.57/0.43 % -------------------------------------------------
% 0.57/0.43 % User time : 0.063 s
% 0.57/0.43 % System time : 0.013 s
% 0.57/0.43 % Total time : 0.075 s
% 0.57/0.43 % Maximum resident set size: 5120 pages
% 0.57/0.43 % E exiting
%------------------------------------------------------------------------------