%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU621^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:26:57 AM UTC 2026
% Result : Theorem 1.51s 0.49s
% Output : CNFRefutation 1.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU621^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n013.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 13:58:06 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.24 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.DvZ3lTpEUC/E---3.1_2162190.p
% 1.51/0.49 % Version: 3.5.1-ho
% 1.51/0.49 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.51/0.49 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.51/0.49 % Starting ehoh_best5 with 300s (1) cores
% 1.51/0.49 % Starting almost_fo_3_lam with 300s (1) cores
% 1.51/0.49 % Starting new_bool_5 with 300s (1) cores
% 1.51/0.49 % Starting pre_casc_3 with 300s (1) cores
% 1.51/0.49 % Starting ho_unfolding_8 with 300s (1) cores
% 1.51/0.49 % Starting new_ho_10_cnf2 with 300s (1) cores
% 1.51/0.49 % Starting new_bool_3 with 300s (1) cores
% 1.51/0.49 % Starting new_ho_5 with 300s (1) cores
% 1.51/0.49 % new_ho_5 with pid 2162210 completed with status 9
% 1.51/0.49 % new_bool_3 with pid 2162209 completed with status 0
% 1.51/0.49 % Result found by new_bool_3
% 1.51/0.49 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.51/0.49 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.51/0.49 % Starting ehoh_best5 with 300s (1) cores
% 1.51/0.49 % Starting almost_fo_3_lam with 300s (1) cores
% 1.51/0.49 % Starting new_bool_5 with 300s (1) cores
% 1.51/0.49 % Starting pre_casc_3 with 300s (1) cores
% 1.51/0.49 % Starting ho_unfolding_8 with 300s (1) cores
% 1.51/0.49 % Starting new_ho_10_cnf2 with 300s (1) cores
% 1.51/0.49 % Starting new_bool_3 with 300s (1) cores
% 1.51/0.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.51/0.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.51/0.49 % Search class: HGHSM-FSLM31-MHFMMSBN
% 1.51/0.49 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.51/0.49 % Starting SubtermCWHack with 28s (1) cores
% 1.51/0.49 % SubtermCWHack with pid 2162214 completed with status 0
% 1.51/0.49 % Result found by SubtermCWHack
% 1.51/0.49 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.51/0.49 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.51/0.49 % Starting ehoh_best5 with 300s (1) cores
% 1.51/0.49 % Starting almost_fo_3_lam with 300s (1) cores
% 1.51/0.49 % Starting new_bool_5 with 300s (1) cores
% 1.51/0.49 % Starting pre_casc_3 with 300s (1) cores
% 1.51/0.49 % Starting ho_unfolding_8 with 300s (1) cores
% 1.51/0.49 % Starting new_ho_10_cnf2 with 300s (1) cores
% 1.51/0.49 % Starting new_bool_3 with 300s (1) cores
% 1.51/0.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.51/0.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.51/0.49 % Search class: HGHSM-FSLM31-MHFMMSBN
% 1.51/0.49 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.51/0.49 % Starting SubtermCWHack with 28s (1) cores
% 1.51/0.49 % Preprocessing time : 0.003 s
% 1.51/0.49
% 1.51/0.49 % Proof found!
% 1.51/0.49 % SZS status Theorem
% 1.51/0.49 % SZS output start CNFRefutation
% 1.51/0.49 thf(decl_23, type, in: $i > $i > $o).
% 1.51/0.49 thf(decl_24, type, exu: ($i > $o) > $o).
% 1.51/0.49 thf(decl_25, type, setextAx: $o).
% 1.51/0.49 thf(decl_26, type, emptyset: $i).
% 1.51/0.49 thf(decl_27, type, emptysetAx: $o).
% 1.51/0.49 thf(decl_28, type, setadjoin: $i > $i > $i).
% 1.51/0.49 thf(decl_29, type, setadjoinAx: $o).
% 1.51/0.49 thf(decl_30, type, powerset: $i > $i).
% 1.51/0.49 thf(decl_31, type, powersetAx: $o).
% 1.51/0.49 thf(decl_32, type, setunion: $i > $i).
% 1.51/0.49 thf(decl_33, type, setunionAx: $o).
% 1.51/0.49 thf(decl_34, type, omega: $i).
% 1.51/0.49 thf(decl_35, type, omega0Ax: $o).
% 1.51/0.49 thf(decl_36, type, omegaSAx: $o).
% 1.51/0.49 thf(decl_37, type, omegaIndAx: $o).
% 1.51/0.49 thf(decl_38, type, replAx: $o).
% 1.51/0.49 thf(decl_39, type, foundationAx: $o).
% 1.51/0.49 thf(decl_40, type, wellorderingAx: $o).
% 1.51/0.49 thf(decl_41, type, descr: ($i > $o) > $i).
% 1.51/0.49 thf(decl_42, type, descrp: $o).
% 1.51/0.49 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 1.51/0.49 thf(decl_44, type, dsetconstrI: $o).
% 1.51/0.49 thf(decl_45, type, dsetconstrEL: $o).
% 1.51/0.49 thf(decl_46, type, dsetconstrER: $o).
% 1.51/0.49 thf(decl_47, type, exuE1: $o).
% 1.51/0.49 thf(decl_48, type, prop2set: $o > $i).
% 1.51/0.49 thf(decl_49, type, prop2setE: $o).
% 1.51/0.49 thf(decl_50, type, emptysetE: $o).
% 1.51/0.49 thf(decl_51, type, emptysetimpfalse: $o).
% 1.51/0.49 thf(decl_52, type, notinemptyset: $o).
% 1.51/0.49 thf(decl_53, type, exuE3e: $o).
% 1.51/0.49 thf(decl_54, type, setext: $o).
% 1.51/0.49 thf(decl_55, type, emptyI: $o).
% 1.51/0.49 thf(decl_56, type, noeltsimpempty: $o).
% 1.51/0.49 thf(decl_57, type, setbeta: $o).
% 1.51/0.49 thf(decl_58, type, nonempty: $i > $o).
% 1.51/0.49 thf(decl_59, type, nonemptyE1: $o).
% 1.51/0.49 thf(decl_60, type, nonemptyI: $o).
% 1.51/0.49 thf(decl_61, type, nonemptyI1: $o).
% 1.51/0.49 thf(decl_62, type, setadjoinIL: $o).
% 1.51/0.49 thf(decl_63, type, emptyinunitempty: $o).
% 1.51/0.49 thf(decl_64, type, setadjoinIR: $o).
% 1.51/0.49 thf(decl_65, type, setadjoinE: $o).
% 1.51/0.49 thf(decl_66, type, setadjoinOr: $o).
% 1.51/0.49 thf(decl_67, type, setoftrueEq: $o).
% 1.51/0.49 thf(decl_68, type, powersetI: $o).
% 1.51/0.49 thf(decl_69, type, emptyinPowerset: $o).
% 1.51/0.49 thf(decl_70, type, emptyInPowerset: $o).
% 1.51/0.49 thf(decl_71, type, powersetE: $o).
% 1.51/0.49 thf(decl_72, type, setunionI: $o).
% 1.51/0.49 thf(decl_73, type, setunionE: $o).
% 1.51/0.49 thf(decl_74, type, subPowSU: $o).
% 1.51/0.49 thf(decl_75, type, exuE2: $o).
% 1.51/0.49 thf(decl_76, type, nonemptyImpWitness: $o).
% 1.51/0.49 thf(decl_77, type, uniqinunit: $o).
% 1.51/0.49 thf(decl_78, type, notinsingleton: $o).
% 1.51/0.49 thf(decl_79, type, eqinunit: $o).
% 1.51/0.49 thf(decl_80, type, singletonsswitch: $o).
% 1.51/0.49 thf(decl_81, type, upairsetE: $o).
% 1.51/0.49 thf(decl_82, type, upairsetIL: $o).
% 1.51/0.49 thf(decl_83, type, upairsetIR: $o).
% 1.51/0.49 thf(decl_84, type, emptyE1: $o).
% 1.51/0.49 thf(decl_85, type, vacuousDall: $o).
% 1.51/0.49 thf(decl_86, type, quantDeMorgan1: $o).
% 1.51/0.49 thf(decl_87, type, quantDeMorgan2: $o).
% 1.51/0.49 thf(decl_88, type, quantDeMorgan3: $o).
% 1.51/0.49 thf(decl_89, type, quantDeMorgan4: $o).
% 1.51/0.49 thf(decl_90, type, prop2setI: $o).
% 1.51/0.49 thf(decl_92, type, prop2set2propI: $o).
% 1.51/0.49 thf(decl_93, type, notdexE: $o).
% 1.51/0.49 thf(decl_94, type, notdallE: $o).
% 1.51/0.49 thf(decl_95, type, exuI1: $o).
% 1.51/0.49 thf(decl_96, type, exuI3: $o).
% 1.51/0.49 thf(decl_97, type, exuI2: $o).
% 1.51/0.49 thf(decl_98, type, inCongP: $o).
% 1.51/0.49 thf(decl_99, type, in__Cong: $o).
% 1.51/0.49 thf(decl_100, type, exuE3u: $o).
% 1.51/0.49 thf(decl_101, type, exu__Cong: $o).
% 1.51/0.49 thf(decl_102, type, emptyset__Cong: $o).
% 1.51/0.49 thf(decl_103, type, setadjoin__Cong: $o).
% 1.51/0.49 thf(decl_104, type, powerset__Cong: $o).
% 1.51/0.49 thf(decl_105, type, setunion__Cong: $o).
% 1.51/0.49 thf(decl_106, type, omega__Cong: $o).
% 1.51/0.49 thf(decl_107, type, exuEu: $o).
% 1.51/0.49 thf(decl_108, type, descr__Cong: $o).
% 1.51/0.49 thf(decl_109, type, dsetconstr__Cong: $o).
% 1.51/0.49 thf(decl_110, type, subset: $i > $i > $o).
% 1.51/0.49 thf(decl_113, type, subsetI1: $o).
% 1.51/0.49 thf(decl_114, type, eqimpsubset2: $o).
% 1.51/0.49 thf(decl_115, type, eqimpsubset1: $o).
% 1.51/0.49 thf(decl_116, type, subsetI2: $o).
% 1.51/0.49 thf(decl_117, type, emptysetsubset: $o).
% 1.51/0.49 thf(decl_118, type, subsetE: $o).
% 1.51/0.49 thf(decl_119, type, subsetE2: $o).
% 1.51/0.49 thf(decl_120, type, notsubsetI: $o).
% 1.51/0.49 thf(decl_121, type, notequalI1: $o).
% 1.51/0.49 thf(decl_122, type, notequalI2: $o).
% 1.51/0.49 thf(decl_123, type, subsetRefl: $o).
% 1.51/0.49 thf(decl_124, type, subsetTrans: $o).
% 1.51/0.49 thf(decl_125, type, setadjoinSub: $o).
% 1.51/0.49 thf(decl_126, type, setadjoinSub2: $o).
% 1.51/0.49 thf(decl_127, type, subset2powerset: $o).
% 1.51/0.49 thf(decl_128, type, setextsub: $o).
% 1.51/0.49 thf(decl_129, type, subsetemptysetimpeq: $o).
% 1.51/0.49 thf(decl_130, type, powersetI1: $o).
% 1.51/0.49 thf(decl_131, type, powersetE1: $o).
% 1.51/0.49 thf(decl_132, type, inPowerset: $o).
% 1.51/0.49 thf(decl_133, type, powersetsubset: $o).
% 1.51/0.49 thf(decl_134, type, sepInPowerset: $o).
% 1.51/0.49 thf(decl_135, type, sepSubset: $o).
% 1.51/0.49 thf(decl_136, type, binunion: $i > $i > $i).
% 1.51/0.49 thf(decl_137, type, binunionIL: $o).
% 1.51/0.49 thf(decl_138, type, upairset2IR: $o).
% 1.51/0.49 thf(decl_139, type, binunionIR: $o).
% 1.51/0.49 thf(decl_140, type, binunionEcases: $o).
% 1.51/0.49 thf(decl_141, type, binunionE: $o).
% 1.51/0.49 thf(decl_142, type, binunionLsub: $o).
% 1.51/0.49 thf(decl_143, type, binunionRsub: $o).
% 1.51/0.49 thf(decl_144, type, binintersect: $i > $i > $i).
% 1.51/0.49 thf(decl_145, type, binintersectI: $o).
% 1.51/0.49 thf(decl_146, type, binintersectSubset5: $o).
% 1.51/0.49 thf(decl_147, type, binintersectEL: $o).
% 1.51/0.49 thf(decl_148, type, binintersectLsub: $o).
% 1.51/0.49 thf(decl_149, type, binintersectSubset2: $o).
% 1.51/0.49 thf(decl_150, type, binintersectSubset3: $o).
% 1.51/0.49 thf(decl_151, type, binintersectER: $o).
% 1.51/0.49 thf(decl_152, type, disjointsetsI1: $o).
% 1.51/0.49 thf(decl_153, type, binintersectRsub: $o).
% 1.51/0.49 thf(decl_154, type, binintersectSubset4: $o).
% 1.51/0.49 thf(decl_155, type, binintersectSubset1: $o).
% 1.51/0.49 thf(decl_156, type, bs114d: $o).
% 1.51/0.49 thf(decl_158, type, setminus: $i > $i > $i).
% 1.51/0.49 thf(decl_159, type, setminusI: $o).
% 1.51/0.49 thf(decl_160, type, setminusEL: $o).
% 1.51/0.49 thf(decl_161, type, setminusER: $o).
% 1.51/0.49 thf(decl_162, type, setminusSubset2: $o).
% 1.51/0.49 thf(decl_163, type, setminusERneg: $o).
% 1.51/0.49 thf(decl_164, type, setminusELneg: $o).
% 1.51/0.49 thf(decl_165, type, setminusILneg: $o).
% 1.51/0.49 thf(decl_166, type, setminusIRneg: $o).
% 1.51/0.49 thf(decl_167, type, setminusLsub: $o).
% 1.51/0.49 thf(decl_168, type, setminusSubset1: $o).
% 1.51/0.49 thf(decl_169, type, symdiff: $i > $i > $i).
% 1.51/0.49 thf(decl_170, type, symdiffE: $o).
% 1.51/0.49 thf(decl_171, type, symdiffI1: $o).
% 1.51/0.49 thf(decl_172, type, symdiffI2: $o).
% 1.51/0.49 thf(decl_173, type, symdiffIneg1: $o).
% 1.51/0.49 thf(decl_174, type, symdiffIneg2: $o).
% 1.51/0.49 thf(decl_175, type, iskpair: $i > $o).
% 1.51/0.49 thf(decl_176, type, secondinupair: $o).
% 1.51/0.49 thf(decl_177, type, setukpairIL: $o).
% 1.51/0.49 thf(decl_178, type, setukpairIR: $o).
% 1.51/0.49 thf(decl_179, type, kpairiskpair: $o).
% 1.51/0.49 thf(decl_180, type, kpair: $i > $i > $i).
% 1.51/0.49 thf(decl_181, type, kpairp: $o).
% 1.51/0.49 thf(decl_183, type, epred1_0: $o).
% 1.51/0.49 thf(decl_184, type, esk1_2: $i > $i > $i).
% 1.51/0.49 thf(decl_185, type, esk2_2: $i > $i > $i).
% 1.51/0.49 thf(decl_186, type, esk3_2: $i > $i > $i).
% 1.51/0.49 thf(decl_187, type, esk4_1: $i > $i).
% 1.51/0.49 thf(decl_188, type, esk5_2: ($i > $i > $o) > $i > $i).
% 1.51/0.49 thf(decl_189, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 1.51/0.49 thf(decl_190, type, esk7_2: ($i > $i > $o) > $i > $i).
% 1.51/0.49 thf(decl_191, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 1.51/0.49 thf(decl_192, type, esk9_1: $i > $i).
% 1.51/0.49 thf(decl_193, type, esk10_2: ($i > $o) > $i > $i).
% 1.51/0.49 thf(decl_194, type, esk11_2: ($i > $o) > $i > $i).
% 1.51/0.49 thf(decl_195, type, esk12_1: ($i > $o) > $i).
% 1.51/0.49 thf(decl_196, type, esk13_2: ($i > $o) > $i > $i).
% 1.51/0.49 thf(decl_197, type, esk14_1: ($i > $o) > $i).
% 1.51/0.49 thf(decl_198, type, esk15_2: $i > $i > $i).
% 1.51/0.49 thf(decl_199, type, esk16_2: $i > $i > $i).
% 1.51/0.49 thf(decl_200, type, esk17_1: $i > $i).
% 1.51/0.49 thf(decl_201, type, esk18_1: $i > $i).
% 1.51/0.49 thf(decl_202, type, esk19_1: $i > $i).
% 1.51/0.49 thf(decl_203, type, esk20_2: $i > $i > $i).
% 1.51/0.49 thf(decl_204, type, esk21_3: $i > $i > $o > $i).
% 1.51/0.49 thf(decl_205, type, esk22_2: ($i > $o) > $i > $i).
% 1.51/0.49 thf(decl_206, type, esk23_1: ($i > $o) > $i).
% 1.51/0.49 thf(decl_207, type, esk24_1: $i > $i).
% 1.51/0.49 thf(decl_208, type, esk25_2: $i > ($i > $o) > $i).
% 1.51/0.49 thf(decl_209, type, esk26_2: $i > ($i > $o) > $i).
% 1.51/0.49 thf(decl_210, type, esk27_2: $i > ($i > $o) > $i).
% 1.51/0.49 thf(decl_211, type, esk28_2: $i > ($i > $o) > $i).
% 1.51/0.49 thf(decl_212, type, esk29_2: $i > ($i > $o) > $i).
% 1.51/0.49 thf(decl_213, type, esk30_2: $i > ($i > $o) > $i).
% 1.51/0.49 thf(decl_214, type, esk31_2: ($i > $o) > $i > $i).
% 1.51/0.49 thf(decl_215, type, esk32_1: ($i > $o) > $i).
% 1.51/0.49 thf(decl_216, type, esk33_1: ($i > $o) > $i).
% 1.51/0.49 thf(decl_217, type, esk34_1: ($i > $o) > $i).
% 1.51/0.49 thf(decl_218, type, esk35_1: ($i > $o) > $i).
% 1.51/0.49 thf(decl_219, type, esk36_2: ($i > $o) > $i > $i).
% 1.51/0.49 thf(decl_220, type, esk37_1: ($i > $o) > $i).
% 1.51/0.49 thf(decl_221, type, esk38_2: ($i > $o) > $i > $i).
% 1.51/0.49 thf(decl_222, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 1.51/0.49 thf(decl_223, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 1.51/0.49 thf(decl_224, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.51/0.49 thf(decl_225, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 1.51/0.49 thf(decl_226, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.51/0.49 thf(decl_227, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 1.51/0.49 thf(decl_228, type, esk45_2: ($i > $o) > $i > $i).
% 1.51/0.49 thf(decl_229, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 1.51/0.49 thf(decl_230, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 1.51/0.49 thf(decl_231, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.51/0.49 thf(decl_232, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.51/0.49 thf(decl_233, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.51/0.49 thf(decl_234, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.51/0.49 thf(decl_235, type, esk52_2: $i > $i > $i).
% 1.51/0.49 thf(decl_236, type, esk53_2: $i > $i > $i).
% 1.51/0.49 thf(decl_237, type, esk54_2: $i > $i > $i).
% 1.51/0.49 thf(decl_238, type, esk55_2: $i > $i > $i).
% 1.51/0.49 thf(decl_239, type, esk56_2: $i > $i > $i).
% 1.51/0.49 thf(decl_240, type, esk57_2: $i > $i > $i).
% 1.51/0.49 thf(decl_241, type, esk58_2: $i > $i > $i).
% 1.51/0.49 thf(decl_242, type, esk59_0: $i).
% 1.51/0.49 thf(decl_243, type, esk60_0: $i).
% 1.51/0.49 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', nonempty)).
% 1.51/0.49 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', nonemptyI)).
% 1.51/0.49 thf(iskpair, axiom, ((iskpair)=(^[X4:$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.DvZ3lTpEUC/E---3.1_2162190.p', iskpair)).
% 1.51/0.49 thf(kpair, axiom, ((kpair)=(^[X2:$i, X3:$i]:(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', kpair)).
% 1.51/0.49 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.DvZ3lTpEUC/E---3.1_2162190.p', exuE2)).
% 1.51/0.49 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', exu)).
% 1.51/0.49 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', exuI3)).
% 1.51/0.49 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', exuI1)).
% 1.51/0.49 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.DvZ3lTpEUC/E---3.1_2162190.p', exuI2)).
% 1.51/0.49 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', exu__Cong)).
% 1.51/0.49 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', exuE3u)).
% 1.51/0.49 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', descr__Cong)).
% 1.51/0.49 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', exuEu)).
% 1.51/0.49 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', exuE3e)).
% 1.51/0.49 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', exuE1)).
% 1.51/0.49 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', descrp)).
% 1.51/0.49 thf(replAx, axiom, ((replAx)<=>![X6:$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.DvZ3lTpEUC/E---3.1_2162190.p', replAx)).
% 1.51/0.49 thf(singletonsubset, 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)=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', singletonsubset)).
% 1.51/0.49 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', nonemptyI1)).
% 1.51/0.49 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', nonemptyE1)).
% 1.51/0.49 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', kpairiskpair)).
% 1.51/0.49 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', kpairp)).
% 1.51/0.49 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setoftrueEq)).
% 1.51/0.49 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', nonemptyImpWitness)).
% 1.51/0.49 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.DvZ3lTpEUC/E---3.1_2162190.p', emptyE1)).
% 1.51/0.49 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', dsetconstr__Cong)).
% 1.51/0.49 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', sepSubset)).
% 1.51/0.49 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', sepInPowerset)).
% 1.51/0.49 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setbeta)).
% 1.51/0.49 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', dsetconstrER)).
% 1.51/0.49 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', dsetconstrEL)).
% 1.51/0.49 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', dsetconstrI)).
% 1.51/0.49 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', binintersectSubset1)).
% 1.51/0.49 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', bs114d)).
% 1.51/0.49 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setminusI)).
% 1.51/0.49 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setadjoinIL)).
% 1.51/0.49 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setminusEL)).
% 1.51/0.49 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setminusER)).
% 1.51/0.49 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setminusSubset2)).
% 1.51/0.49 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', emptyinunitempty)).
% 1.51/0.49 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setminusERneg)).
% 1.51/0.49 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setminusELneg)).
% 1.51/0.49 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setminusILneg)).
% 1.51/0.49 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setminusIRneg)).
% 1.51/0.49 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setminusLsub)).
% 1.51/0.49 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setminusSubset1)).
% 1.51/0.49 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', symdiffE)).
% 1.51/0.49 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', symdiffI1)).
% 1.51/0.49 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', symdiffI2)).
% 1.51/0.49 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', symdiffIneg1)).
% 1.51/0.49 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', symdiffIneg2)).
% 1.51/0.49 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', secondinupair)).
% 1.51/0.49 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setukpairIL)).
% 1.51/0.49 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setukpairIR)).
% 1.51/0.49 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', emptyInPowerset)).
% 1.51/0.49 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', emptyinPowerset)).
% 1.51/0.49 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', powersetI)).
% 1.51/0.49 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setadjoinOr)).
% 1.51/0.49 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setadjoinE)).
% 1.51/0.49 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setadjoinIR)).
% 1.51/0.49 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', powersetE)).
% 1.51/0.49 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', notinsingleton)).
% 1.51/0.49 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', uniqinunit)).
% 1.51/0.49 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', subPowSU)).
% 1.51/0.49 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setunionE)).
% 1.51/0.49 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setunionI)).
% 1.51/0.49 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', eqinunit)).
% 1.51/0.49 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', powersetI1)).
% 1.51/0.49 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', subsetemptysetimpeq)).
% 1.51/0.49 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setextsub)).
% 1.51/0.49 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', subset2powerset)).
% 1.51/0.49 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setadjoinSub2)).
% 1.51/0.49 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setadjoinSub)).
% 1.51/0.49 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', quantDeMorgan1)).
% 1.51/0.49 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', vacuousDall)).
% 1.51/0.49 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', upairsetIR)).
% 1.51/0.49 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', upairsetIL)).
% 1.51/0.49 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', upairsetE)).
% 1.51/0.49 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', singletonsswitch)).
% 1.51/0.49 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', quantDeMorgan2)).
% 1.51/0.49 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', notdallE)).
% 1.51/0.49 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', notdexE)).
% 1.51/0.49 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', prop2setI)).
% 1.51/0.49 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', quantDeMorgan4)).
% 1.51/0.49 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', quantDeMorgan3)).
% 1.51/0.49 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', powerset__Cong)).
% 1.51/0.49 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setadjoin__Cong)).
% 1.51/0.49 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', emptyset__Cong)).
% 1.51/0.49 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', in__Cong)).
% 1.51/0.49 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', inCongP)).
% 1.51/0.49 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setunion__Cong)).
% 1.51/0.49 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', eqimpsubset1)).
% 1.51/0.49 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', eqimpsubset2)).
% 1.51/0.49 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', subsetI1)).
% 1.51/0.49 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', omega__Cong)).
% 1.51/0.49 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', subsetI2)).
% 1.51/0.49 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', subsetRefl)).
% 1.51/0.49 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', notequalI2)).
% 1.51/0.49 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', notequalI1)).
% 1.51/0.49 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', notsubsetI)).
% 1.51/0.49 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', subsetE2)).
% 1.51/0.49 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', subsetE)).
% 1.51/0.49 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', emptysetsubset)).
% 1.51/0.49 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', subsetTrans)).
% 1.51/0.49 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', powersetE1)).
% 1.51/0.49 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', inPowerset)).
% 1.51/0.49 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', binunionEcases)).
% 1.51/0.49 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', binunionIR)).
% 1.51/0.49 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', upairset2IR)).
% 1.51/0.49 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', binunionIL)).
% 1.51/0.49 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', powersetsubset)).
% 1.51/0.49 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', binunionE)).
% 1.51/0.49 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', binintersectSubset2)).
% 1.51/0.49 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', binintersectLsub)).
% 1.51/0.49 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', binintersectEL)).
% 1.51/0.49 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', binintersectSubset5)).
% 1.51/0.49 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', binintersectI)).
% 1.51/0.49 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', binunionRsub)).
% 1.51/0.49 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', binunionLsub)).
% 1.51/0.49 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', binintersectSubset3)).
% 1.51/0.49 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', binintersectER)).
% 1.51/0.49 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', disjointsetsI1)).
% 1.51/0.49 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', binintersectRsub)).
% 1.51/0.49 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', binintersectSubset4)).
% 1.51/0.49 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', noeltsimpempty)).
% 1.51/0.49 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', emptyI)).
% 1.51/0.49 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setext)).
% 1.51/0.49 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', notinemptyset)).
% 1.51/0.49 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', emptysetimpfalse)).
% 1.51/0.49 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', emptysetE)).
% 1.51/0.49 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', prop2setE)).
% 1.51/0.49 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', wellorderingAx)).
% 1.51/0.49 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', foundationAx)).
% 1.51/0.49 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.DvZ3lTpEUC/E---3.1_2162190.p', omegaIndAx)).
% 1.51/0.49 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', omegaSAx)).
% 1.51/0.49 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', omega0Ax)).
% 1.51/0.49 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setunionAx)).
% 1.51/0.49 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', powersetAx)).
% 1.51/0.49 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setadjoinAx)).
% 1.51/0.49 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', emptysetAx)).
% 1.51/0.49 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.DvZ3lTpEUC/E---3.1_2162190.p', setextAx)).
% 1.51/0.49 thf(c_0_141, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 1.51/0.49 thf(c_0_142, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 1.51/0.49 thf(c_0_143, plain, ((iskpair)=(^[Z0:$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])).
% 1.51/0.50 thf(c_0_144, plain, ((kpair)=(^[Z0:$i, Z1:$i]:(setadjoin @ (setadjoin @ Z0 @ emptyset) @ (setadjoin @ (setadjoin @ Z0 @ (setadjoin @ Z1 @ emptyset)) @ emptyset)))), inference(fof_simplification,[status(thm)],[kpair])).
% 1.51/0.50 thf(c_0_145, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 1.51/0.50 thf(c_0_146, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 1.51/0.50 thf(c_0_147, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 1.51/0.50 thf(c_0_148, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 1.51/0.50 thf(c_0_149, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 1.51/0.50 thf(c_0_150, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 1.51/0.50 thf(c_0_151, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 1.51/0.50 thf(c_0_152, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 1.51/0.50 thf(c_0_153, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 1.51/0.50 thf(c_0_154, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 1.51/0.50 thf(c_0_155, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 1.51/0.50 thf(c_0_156, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 1.51/0.50 thf(c_0_157, plain, ((replAx)<=>![X6:$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])).
% 1.51/0.50 thf(c_0_158, 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)=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[singletonsubset])).
% 1.51/0.50 thf(c_0_159, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_141])).
% 1.51/0.50 thf(c_0_160, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_142, c_0_141])).
% 1.51/0.50 thf(c_0_161, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_141])).
% 1.51/0.50 thf(c_0_162, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X414:$i]:((((in @ X414 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))&(?[X415:$i]:((((in @ X415 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))&(((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X414 @ emptyset) @ (setadjoin @ (setadjoin @ X414 @ (setadjoin @ X415 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_143])).
% 1.51/0.50 thf(c_0_163, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X416:$i]:((((in @ X416 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))&(?[X417:$i]:((((in @ X417 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))&(((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X416 @ emptyset) @ (setadjoin @ (setadjoin @ X416 @ (setadjoin @ X417 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[kpairp, c_0_143]), c_0_144])).
% 1.51/0.50 thf(c_0_164, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 1.51/0.50 thf(c_0_165, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_141])).
% 1.51/0.50 thf(c_0_166, plain, ((exuE2)=(![X1:$i > $o]:((((?[X394:$i]:(((((X1 @ X394)))&(![X395:$i]:(((((X1 @ X395)))=>(((X394)=(X395))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_145, c_0_146])).
% 1.51/0.50 thf(c_0_167, plain, ((emptyE1)<=>![X4:$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])).
% 1.51/0.50 thf(c_0_168, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X398:$i]:(((((X1 @ X398)))&(![X399:$i]:(((((X1 @ X399)))=>(((X398)=(X399)))))))))))))))), inference(apply_def,[status(thm)],[c_0_147, c_0_146])).
% 1.51/0.50 thf(c_0_169, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X396:$i]:(((((X1 @ X396)))&(![X397:$i]:(((((X1 @ X397)))=>(((X396)=(X397)))))))))))))), inference(apply_def,[status(thm)],[c_0_148, c_0_146])).
% 1.51/0.50 thf(c_0_170, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X400:$i]:(((((X1 @ X400)))&(![X401:$i]:(((((X1 @ X401)))=>(((X400)=(X401)))))))))))))), inference(apply_def,[status(thm)],[c_0_149, c_0_146])).
% 1.51/0.50 thf(c_0_171, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X404:$i]:(((((X1 @ X404)))&(![X405:$i]:(((((X1 @ X405)))=>(((X404)=(X405))))))))))<=>((?[X406:$i]:(((((X17 @ X406)))&(![X407:$i]:(((((X17 @ X407)))=>(((X406)=(X407)))))))))))))))), inference(apply_def,[status(thm)],[c_0_150, c_0_146])).
% 1.51/0.50 thf(c_0_172, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X402:$i]:(((((X1 @ X402)))&(![X403:$i]:(((((X1 @ X403)))=>(((X402)=(X403))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_151, c_0_146])).
% 1.51/0.50 thf(c_0_173, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 1.51/0.50 thf(c_0_174, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X410:$i]:(((((X1 @ X410)))&(![X411:$i]:(((((X1 @ X411)))=>(((X410)=(X411))))))))))=>((((?[X412:$i]:(((((X17 @ X412)))&(![X413:$i]:(((((X17 @ X413)))=>(((X412)=(X413))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_152, c_0_146])).
% 1.51/0.50 thf(c_0_175, plain, ((exuEu)=(![X1:$i > $o]:((((?[X408:$i]:(((((X1 @ X408)))&(![X409:$i]:(((((X1 @ X409)))=>(((X408)=(X409))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_153, c_0_146])).
% 1.51/0.50 thf(c_0_176, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 1.51/0.50 thf(c_0_177, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 1.51/0.50 thf(c_0_178, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 1.51/0.50 thf(c_0_179, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X392:$i]:(((((X1 @ X392)))&(![X393:$i]:(((((X1 @ X393)))=>(((X392)=(X393))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_154, c_0_146])).
% 1.51/0.50 thf(c_0_180, plain, ((exuE1)=(![X1:$i > $o]:((((?[X390:$i]:(((((X1 @ X390)))&(![X391:$i]:(((((X1 @ X391)))=>(((X390)=(X391))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_155, c_0_146])).
% 1.51/0.50 thf(c_0_181, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 1.51/0.50 thf(c_0_182, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 1.51/0.50 thf(c_0_183, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 1.51/0.50 thf(c_0_184, plain, ((descrp)=(![X1:$i > $o]:((((?[X388:$i]:(((((X1 @ X388)))&(![X389:$i]:(((((X1 @ X389)))=>(((X388)=(X389))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_156, c_0_146])).
% 1.51/0.50 thf(c_0_185, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X386:$i]:(((((X6 @ X2 @ X386)))&(![X387:$i]:(((((X6 @ X2 @ X387)))=>(((X386)=(X387)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_157, c_0_146])).
% 1.51/0.50 thf(c_0_186, plain, ((epred1_0)<=>![X447:$i]:(?[X448:$i]:((((![X449:$i]:(((in @ X449 @ X448)=>![X450:$i]:(((in @ X450 @ X449)=>(in @ X450 @ X447)))))&![X451:$i, X452:$i]:((((in @ X451 @ X447)&(in @ X452 @ X447))=>(![X453:$i]:(((in @ X453 @ X448)=>((in @ X451 @ X453)<=>(in @ X452 @ X453))))=>((X451)=(X452))))))&![X454:$i, X455:$i]:((((in @ X454 @ X448)&(in @ X455 @ X448))=>(![X456:$i]:(((in @ X456 @ X454)=>(in @ X456 @ X455)))|![X457:$i]:(((in @ X457 @ X455)=>(in @ X457 @ X454)))))))&![X458:$i]:(((![X459:$i]:(((in @ X459 @ X458)=>(in @ X459 @ X447)))&?[X460:$i]:((in @ X460 @ X458)))=>?[X461:$i, X462:$i]:(((((in @ X461 @ X448)&(in @ X462 @ X458))&~(?[X463:$i]:(((in @ X463 @ X461)&(in @ X463 @ X458)))))&![X464:$i]:(((in @ X464 @ X448)=>(![X465:$i]:(((in @ X465 @ X464)=>(in @ X465 @ X461)))|(in @ X462 @ X464)))))))))))), introduced(definition)).
% 1.51/0.50 thf(c_0_187, negated_conjecture, ~((![X418:$i, X419:$i]:((![X420:$i]:(((in @ X420 @ X418)<=>(in @ X420 @ X419)))=>((X418)=(X419))))=>(![X421:$i]:(~(in @ X421 @ emptyset))=>(![X422:$i, X423:$i, X424:$i]:(((in @ X424 @ (setadjoin @ X422 @ X423))<=>(((X424)=(X422))|(in @ X424 @ X423))))=>(![X425:$i, X426:$i]:(((in @ X426 @ (powerset @ X425))<=>![X427:$i]:(((in @ X427 @ X426)=>(in @ X427 @ X425)))))=>(![X428:$i, X429:$i]:(((in @ X429 @ (setunion @ X428))<=>?[X430:$i]:(((in @ X429 @ X430)&(in @ X430 @ X428)))))=>((in @ emptyset @ omega)=>(![X431:$i]:(((in @ X431 @ omega)=>(in @ (setadjoin @ X431 @ X431) @ omega)))=>(![X432:$i]:((((in @ emptyset @ X432)&![X433:$i]:((((in @ X433 @ omega)&(in @ X433 @ X432))=>(in @ (setadjoin @ X433 @ X433) @ X432))))=>![X434:$i]:(((in @ X434 @ omega)=>(in @ X434 @ X432)))))=>(![X435:$i > $i > $o, X436:$i]:((![X437:$i]:(((in @ X437 @ X436)=>?[X438:$i]:(((X435 @ X437 @ X438)&![X439:$i]:(((X435 @ X437 @ X439)=>((X438)=(X439))))))))=>?[X440:$i]:(![X441:$i]:(((in @ X441 @ X440)<=>?[X442:$i]:(((in @ X442 @ X436)&(X435 @ X442 @ X441))))))))=>(![X443:$i]:((?[X444:$i]:((in @ X444 @ X443))=>?[X445:$i]:(((in @ X445 @ X443)&~(?[X446:$i]:(((in @ X446 @ X445)&(in @ X446 @ X443))))))))=>((epred1_0)=>(![X466:$i > $o]:((?[X467:$i]:(((X466 @ X467)&![X468:$i]:(((X466 @ X468)=>((X467)=(X468))))))=>(X466 @ (descr @ (^[Z0:$i]:(X466 @ Z0))))))=>(![X469:$i, X470:$i > $o, X471:$i]:(((in @ X471 @ X469)=>((X470 @ X471)=>(in @ X471 @ (dsetconstr @ X469 @ X470)))))=>(![X472:$i, X473:$i > $o, X474:$i]:(((in @ X474 @ (dsetconstr @ X472 @ X473))=>(in @ X474 @ X472)))=>(![X475:$i, X476:$i > $o, X477:$i]:(((in @ X477 @ (dsetconstr @ X475 @ X476))=>(X476 @ X477)))=>(![X478:$i > $o]:((?[X479:$i]:(((X478 @ X479)&![X480:$i]:(((X478 @ X480)=>((X479)=(X480))))))=>?[X481:$i]:(((X478 @ X481)&![X482:$i]:(((X478 @ X482)=>((X481)=(X482))))))))=>(![X483:$o, X484:$i]:(((in @ X484 @ (prop2set @ ((X483))))=>(X483)))=>(![X485:$i]:(((in @ X485 @ emptyset)=>![X486:$o]:((X486))))=>(![X487:$i]:(((in @ X487 @ emptyset)=>~($true)))=>(![X488:$i]:(~(in @ X488 @ emptyset))=>(![X489:$i > $o]:((?[X490:$i]:(((X489 @ X490)&![X491:$i]:(((X489 @ X491)=>((X490)=(X491))))))=>?[X492:$i]:((X489 @ X492))))=>(![X493:$i, X494:$i]:((![X495:$i]:(((in @ X495 @ X493)=>(in @ X495 @ X494)))=>(![X496:$i]:(((in @ X496 @ X494)=>(in @ X496 @ X493)))=>((X493)=(X494)))))=>(![X497:$i]:((![X498:$i]:(~(in @ X498 @ X497))=>((X497)=(emptyset))))=>(![X499:$i]:((![X500:$i]:(~(in @ X500 @ X499))=>((X499)=(emptyset))))=>(![X501:$i, X502:$i > $o, X503:$i]:(((in @ X503 @ X501)=>((in @ X503 @ (dsetconstr @ X501 @ X502))<=>(X502 @ X503))))=>(![X504:$i]:((((X504)!=(emptyset))=>?[X505:$i]:((in @ X505 @ X504))))=>(![X506:$i, X507:$i > $o, X508:$i]:(((in @ X508 @ X506)=>((X507 @ X508)=>((dsetconstr @ X506 @ X507)!=(emptyset)))))=>(![X509:$i]:((?[X510:$i]:((in @ X510 @ X509))=>((X509)!=(emptyset))))=>(![X511:$i, X512:$i]:((in @ X511 @ (setadjoin @ X511 @ X512)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X513:$i, X514:$i, X515:$i]:(((in @ X515 @ X514)=>(in @ X515 @ (setadjoin @ X513 @ X514))))=>(![X516:$i, X517:$i, X518:$i]:(((in @ X518 @ (setadjoin @ X516 @ X517))=>![X519:$o]:(((((X518)=(X516))=>(X519))=>(((in @ X518 @ X517)=>(X519))=>(X519))))))=>(![X520:$i, X521:$i, X522:$i]:(((in @ X522 @ (setadjoin @ X520 @ X521))=>(((X522)=(X520))|(in @ X522 @ X521))))=>(![X523:$i]:(((dsetconstr @ X523 @ (^[Z0:$i]:($true)))=(X523)))=>(![X524:$i, X525:$i]:((![X526:$i]:(((in @ X526 @ X525)=>(in @ X526 @ X524)))=>(in @ X525 @ (powerset @ X524))))=>(![X527:$i]:((in @ emptyset @ (powerset @ X527)))=>(![X528:$i]:((in @ emptyset @ (powerset @ X528)))=>(![X529:$i, X530:$i, X531:$i]:(((in @ X530 @ (powerset @ X529))=>((in @ X531 @ X530)=>(in @ X531 @ X529))))=>(![X532:$i, X533:$i, X534:$i]:(((in @ X533 @ X534)=>((in @ X534 @ X532)=>(in @ X533 @ (setunion @ X532)))))=>(![X535:$i, X536:$i]:(((in @ X536 @ (setunion @ X535))=>![X537:$o]:((![X538:$i]:(((in @ X536 @ X538)=>((in @ X538 @ X535)=>(X537))))=>(X537)))))=>(![X539:$i, X540:$i]:(((in @ X540 @ X539)=>(in @ X540 @ (powerset @ (setunion @ X539)))))=>(![X541:$i > $o]:((?[X542:$i]:(((X541 @ X542)&![X543:$i]:(((X541 @ X543)=>((X542)=(X543))))))=>?[X544:$i]:(![X545:$i]:(((X541 @ X545)<=>((X545)=(X544)))))))=>(![X546:$i]:((((X546)!=(emptyset))=>?[X547:$i]:(((in @ X547 @ X546)&$true))))=>(![X548:$i, X549:$i]:(((in @ X548 @ (setadjoin @ X549 @ emptyset))=>((X548)=(X549))))=>(![X550:$i, X551:$i]:((((X550)!=(X551))=>~(in @ X551 @ (setadjoin @ X550 @ emptyset))))=>(![X552:$i, X553:$i]:((((X552)=(X553))=>(in @ X552 @ (setadjoin @ X553 @ emptyset))))=>(![X554:$i, X555:$i]:(((in @ X554 @ (setadjoin @ X555 @ emptyset))=>(in @ X555 @ (setadjoin @ X554 @ emptyset))))=>(![X556:$i, X557:$i, X558:$i]:(((in @ X558 @ (setadjoin @ X556 @ (setadjoin @ X557 @ emptyset)))=>(((X558)=(X556))|((X558)=(X557)))))=>(![X559:$i, X560:$i]:((in @ X559 @ (setadjoin @ X559 @ (setadjoin @ X560 @ emptyset))))=>(![X561:$i, X562:$i]:((in @ X562 @ (setadjoin @ X561 @ (setadjoin @ X562 @ emptyset))))=>(![X563:$i, X564:$i > $o]:((?[X565:$i]:(((in @ X565 @ X563)&(X564 @ X565)))=>(((dsetconstr @ X563 @ X564)=(emptyset))=>~($true))))=>(![X566:$i > $o, X567:$i]:(((in @ X567 @ emptyset)=>(X566 @ X567)))=>(![X568:$i, X569:$i > $o]:((~(![X570:$i]:(((in @ X570 @ X568)=>(X569 @ X570))))=>?[X571:$i]:(((in @ X571 @ X568)&~((X569 @ X571))))))=>(![X572:$i, X573:$i > $o]:((![X574:$i]:(((in @ X574 @ X572)=>~((X573 @ X574))))=>~(?[X575:$i]:(((in @ X575 @ X572)&(X573 @ X575))))))=>(![X576:$i, X577:$i > $o]:((~(?[X578:$i]:(((in @ X578 @ X576)&(X577 @ X578))))=>![X579:$i]:(((in @ X579 @ X576)=>~((X577 @ X579))))))=>(![X580:$i, X581:$i > $o]:((?[X582:$i]:(((in @ X582 @ X580)&~((X581 @ X582))))=>~(![X583:$i]:(((in @ X583 @ X580)=>(X581 @ X583))))))=>(![X584:$o]:(((X584)=>(in @ emptyset @ (prop2set @ ((X584))))))=>((prop2set2propI)=>(![X585:$i, X586:$i > $o]:((~(?[X587:$i]:(((in @ X587 @ X585)&(X586 @ X587))))=>![X588:$i]:(((in @ X588 @ X585)=>~((X586 @ X588))))))=>(![X589:$i, X590:$i > $o]:((~(![X591:$i]:(((in @ X591 @ X589)=>(X590 @ X591))))=>?[X592:$i]:(((in @ X592 @ X589)&~((X590 @ X592))))))=>(![X593:$i > $o]:((?[X594:$i]:(((X593 @ X594)&![X595:$i]:(((X593 @ X595)=>((X594)=(X595))))))=>?[X596:$i]:(((X593 @ X596)&![X597:$i]:(((X593 @ X597)=>((X596)=(X597))))))))=>(![X598:$i > $o]:((?[X599:$i]:((X598 @ X599))=>(![X600:$i, X601:$i]:(((X598 @ X600)=>((X598 @ X601)=>((X600)=(X601)))))=>?[X602:$i]:(((X598 @ X602)&![X603:$i]:(((X598 @ X603)=>((X602)=(X603)))))))))=>(![X604:$i > $o]:((?[X605:$i]:(![X606:$i]:(((X604 @ X606)<=>((X606)=(X605)))))=>?[X607:$i]:(((X604 @ X607)&![X608:$i]:(((X604 @ X608)=>((X607)=(X608))))))))=>(![X609:$i, X610:$i]:((((X609)=(X610))=>![X611:$i, X612:$i]:((((X611)=(X612))=>((in @ X611 @ X609)=>(in @ X612 @ X610))))))=>(![X613:$i, X614:$i]:((((X613)=(X614))=>![X615:$i, X616:$i]:((((X615)=(X616))=>((in @ X615 @ X613)<=>(in @ X616 @ X614))))))=>(![X617:$i > $o]:((?[X618:$i]:(((X617 @ X618)&![X619:$i]:(((X617 @ X619)=>((X618)=(X619))))))=>![X620:$i, X621:$i]:(((X617 @ X620)=>((X617 @ X621)=>((X620)=(X621)))))))=>(![X622:$i > $o, X623:$i > $o]:((![X624:$i, X625:$i]:((((X624)=(X625))=>((X622 @ X624)<=>(X623 @ X625))))=>(?[X626:$i]:(((X622 @ X626)&![X627:$i]:(((X622 @ X627)=>((X626)=(X627))))))<=>?[X628:$i]:(((X623 @ X628)&![X629:$i]:(((X623 @ X629)=>((X628)=(X629)))))))))=>(((emptyset)=(emptyset))=>(![X630:$i, X631:$i]:((((X630)=(X631))=>![X632:$i, X633:$i]:((((X632)=(X633))=>((setadjoin @ X630 @ X632)=(setadjoin @ X631 @ X633))))))=>(![X634:$i, X635:$i]:((((X634)=(X635))=>((powerset @ X634)=(powerset @ X635))))=>(![X636:$i, X637:$i]:((((X636)=(X637))=>((setunion @ X636)=(setunion @ X637))))=>(((omega)=(omega))=>(![X638:$i > $o]:((?[X639:$i]:(((X638 @ X639)&![X640:$i]:(((X638 @ X640)=>((X639)=(X640))))))=>![X641:$i, X642:$i]:(((X638 @ X641)=>((X638 @ X642)=>((X641)=(X642)))))))=>(![X643:$i > $o, X644:$i > $o]:((![X645:$i, X646:$i]:((((X645)=(X646))=>((X643 @ X645)<=>(X644 @ X646))))=>(?[X647:$i]:(((X643 @ X647)&![X648:$i]:(((X643 @ X648)=>((X647)=(X648))))))=>(?[X649:$i]:(((X644 @ X649)&![X650:$i]:(((X644 @ X650)=>((X649)=(X650))))))=>((descr @ X643)=(descr @ X644))))))=>(![X651:$i, X652:$i]:((((X651)=(X652))=>![X653:$i > $o, X654:$i > $o]:((![X655:$i]:(((in @ X655 @ X651)=>![X656:$i]:(((in @ X656 @ X652)=>(((X655)=(X656))=>((X653 @ X655)<=>(X654 @ X656)))))))=>((dsetconstr @ X651 @ X653)=(dsetconstr @ X652 @ X654))))))=>(![X657:$i, X658:$i]:((![X659:$i]:(((in @ X659 @ X657)=>(in @ X659 @ X658)))=>(subset @ X657 @ X658)))=>(![X660:$i, X661:$i]:((((X660)=(X661))=>(subset @ X661 @ X660)))=>(![X662:$i, X663:$i]:((((X662)=(X663))=>(subset @ X662 @ X663)))=>(![X664:$i, X665:$i]:((![X666:$i]:(((in @ X666 @ X664)=>(in @ X666 @ X665)))=>(subset @ X664 @ X665)))=>(![X667:$i]:((subset @ emptyset @ X667))=>(![X668:$i, X669:$i, X670:$i]:(((subset @ X668 @ X669)=>((in @ X670 @ X668)=>(in @ X670 @ X669))))=>(![X671:$i, X672:$i, X673:$i]:(((subset @ X671 @ X672)=>(~(in @ X673 @ X672)=>~(in @ X673 @ X671))))=>(![X674:$i, X675:$i, X676:$i]:(((in @ X676 @ X674)=>(~(in @ X676 @ X675)=>~(subset @ X674 @ X675))))=>(![X677:$i, X678:$i]:((~(subset @ X677 @ X678)=>((X677)!=(X678))))=>(![X679:$i, X680:$i, X681:$i]:(((in @ X681 @ X679)=>(~(in @ X681 @ X680)=>((X679)!=(X680)))))=>(![X682:$i]:((subset @ X682 @ X682))=>(![X683:$i, X684:$i, X685:$i]:(((subset @ X683 @ X684)=>((subset @ X684 @ X685)=>(subset @ X683 @ X685))))=>(![X686:$i, X687:$i]:((subset @ X687 @ (setadjoin @ X686 @ X687)))=>(![X688:$i, X689:$i, X690:$i]:(((subset @ X688 @ X690)=>(subset @ X688 @ (setadjoin @ X689 @ X690))))=>(![X691:$i, X692:$i]:(((subset @ X691 @ X692)=>(in @ X691 @ (powerset @ X692))))=>(![X693:$i, X694:$i]:(((subset @ X693 @ X694)=>((subset @ X694 @ X693)=>((X693)=(X694)))))=>(![X695:$i]:(((subset @ X695 @ emptyset)=>((X695)=(emptyset))))=>(![X696:$i, X697:$i]:(((subset @ X697 @ X696)=>(in @ X697 @ (powerset @ X696))))=>(![X698:$i, X699:$i]:(((in @ X699 @ (powerset @ X698))=>(subset @ X699 @ X698)))=>(![X700:$i]:((in @ X700 @ (powerset @ X700)))=>(![X701:$i, X702:$i]:(((subset @ X701 @ X702)=>(subset @ (powerset @ X701) @ (powerset @ X702))))=>(![X703:$i, X704:$i > $o]:((in @ (dsetconstr @ X703 @ X704) @ (powerset @ X703)))=>(![X705:$i, X706:$i > $o]:((subset @ (dsetconstr @ X705 @ X706) @ X705))=>(![X707:$i, X708:$i, X709:$i]:(((in @ X709 @ X707)=>(in @ X709 @ (binunion @ X707 @ X708))))=>(![X710:$i, X711:$i]:((in @ X711 @ (setadjoin @ X710 @ (setadjoin @ X711 @ emptyset))))=>(![X712:$i, X713:$i, X714:$i]:(((in @ X714 @ X713)=>(in @ X714 @ (binunion @ X712 @ X713))))=>(![X715:$i, X716:$i, X717:$i, X718:$o]:(((in @ X717 @ (binunion @ X715 @ X716))=>(((in @ X717 @ X715)=>(X718))=>(((in @ X717 @ X716)=>(X718))=>(X718)))))=>(![X719:$i, X720:$i, X721:$i]:(((in @ X721 @ (binunion @ X719 @ X720))=>((in @ X721 @ X719)|(in @ X721 @ X720))))=>(![X722:$i, X723:$i]:((subset @ X722 @ (binunion @ X722 @ X723)))=>(![X724:$i, X725:$i]:((subset @ X725 @ (binunion @ X724 @ X725)))=>(![X726:$i, X727:$i, X728:$i]:(((in @ X728 @ X726)=>((in @ X728 @ X727)=>(in @ X728 @ (binintersect @ X726 @ X727)))))=>(![X729:$i, X730:$i, X731:$i]:(((subset @ X731 @ X729)=>((subset @ X731 @ X730)=>(subset @ X731 @ (binintersect @ X729 @ X730)))))=>(![X732:$i, X733:$i, X734:$i]:(((in @ X734 @ (binintersect @ X732 @ X733))=>(in @ X734 @ X732)))=>(![X735:$i, X736:$i]:((subset @ (binintersect @ X735 @ X736) @ X735))=>(![X737:$i, X738:$i]:(((subset @ X737 @ X738)=>((binintersect @ X737 @ X738)=(X737))))=>(![X739:$i, X740:$i]:((((binintersect @ X739 @ X740)=(X740))=>(subset @ X740 @ X739)))=>(![X741:$i, X742:$i, X743:$i]:(((in @ X743 @ (binintersect @ X741 @ X742))=>(in @ X743 @ X742)))=>(![X744:$i, X745:$i]:((~(?[X746:$i]:(((in @ X746 @ X744)&(in @ X746 @ X745))))=>((binintersect @ X744 @ X745)=(emptyset))))=>(![X747:$i, X748:$i]:((subset @ (binintersect @ X747 @ X748) @ X748))=>(![X749:$i, X750:$i]:(((subset @ X750 @ X749)=>((binintersect @ X749 @ X750)=(X750))))=>(![X751:$i, X752:$i]:((((binintersect @ X751 @ X752)=(X751))=>(subset @ X751 @ X752)))=>(![X753:$i, X754:$i, X755:$i]:(((binintersect @ X753 @ (binunion @ X754 @ X755))=(binunion @ (binintersect @ X753 @ X754) @ (binintersect @ X753 @ X755))))=>(![X756:$i, X757:$i, X758:$i]:(((in @ X758 @ X756)=>(~(in @ X758 @ X757)=>(in @ X758 @ (setminus @ X756 @ X757)))))=>(![X759:$i, X760:$i, X761:$i]:(((in @ X761 @ (setminus @ X759 @ X760))=>(in @ X761 @ X759)))=>(![X762:$i, X763:$i, X764:$i]:(((in @ X764 @ (setminus @ X762 @ X763))=>~(in @ X764 @ X763)))=>(![X765:$i, X766:$i]:(((subset @ X765 @ X766)=>((setminus @ X765 @ X766)=(emptyset))))=>(![X767:$i, X768:$i, X769:$i]:((~(in @ X769 @ (setminus @ X767 @ X768))=>((in @ X769 @ X767)=>(in @ X769 @ X768))))=>(![X770:$i, X771:$i, X772:$i]:((~(in @ X772 @ (setminus @ X770 @ X771))=>(~(in @ X772 @ X771)=>~(in @ X772 @ X770))))=>(![X773:$i, X774:$i, X775:$i]:((~(in @ X775 @ X773)=>~(in @ X775 @ (setminus @ X773 @ X774))))=>(![X776:$i, X777:$i, X778:$i]:(((in @ X778 @ X777)=>~(in @ X778 @ (setminus @ X776 @ X777))))=>(![X779:$i, X780:$i]:((subset @ (setminus @ X779 @ X780) @ X779))=>(![X781:$i, X782:$i]:((((setminus @ X781 @ X782)=(emptyset))=>(subset @ X781 @ X782)))=>(![X783:$i, X784:$i, X785:$i]:(((in @ X785 @ (symdiff @ X783 @ X784))=>![X786:$o]:((((in @ X785 @ X783)=>(~(in @ X785 @ X784)=>(X786)))=>((~(in @ X785 @ X783)=>((in @ X785 @ X784)=>(X786)))=>(X786))))))=>(![X787:$i, X788:$i, X789:$i]:(((in @ X789 @ X787)=>(~(in @ X789 @ X788)=>(in @ X789 @ (symdiff @ X787 @ X788)))))=>(![X790:$i, X791:$i, X792:$i]:((~(in @ X792 @ X790)=>((in @ X792 @ X791)=>(in @ X792 @ (symdiff @ X790 @ X791)))))=>(![X793:$i, X794:$i, X795:$i]:(((in @ X795 @ X793)=>((in @ X795 @ X794)=>~(in @ X795 @ (symdiff @ X793 @ X794)))))=>(![X796:$i, X797:$i, X798:$i]:((~(in @ X798 @ X796)=>(~(in @ X798 @ X797)=>~(in @ X798 @ (symdiff @ X796 @ X797)))))=>(![X799:$i, X800:$i]:((in @ X800 @ (setadjoin @ X799 @ (setadjoin @ X800 @ emptyset))))=>(![X801:$i, X802:$i]:((in @ X801 @ (setunion @ (setadjoin @ (setadjoin @ X801 @ emptyset) @ (setadjoin @ (setadjoin @ X801 @ (setadjoin @ X802 @ emptyset)) @ emptyset)))))=>(![X803:$i, X804:$i]:((in @ X804 @ (setunion @ (setadjoin @ (setadjoin @ X803 @ emptyset) @ (setadjoin @ (setadjoin @ X803 @ (setadjoin @ X804 @ emptyset)) @ emptyset)))))=>(![X805:$i, X806:$i]:(?[X807:$i]:(((in @ X807 @ (setunion @ (setadjoin @ (setadjoin @ X805 @ emptyset) @ (setadjoin @ (setadjoin @ X805 @ (setadjoin @ X806 @ emptyset)) @ emptyset))))&?[X808:$i]:(((in @ X808 @ (setunion @ (setadjoin @ (setadjoin @ X805 @ emptyset) @ (setadjoin @ (setadjoin @ X805 @ (setadjoin @ X806 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X805 @ emptyset) @ (setadjoin @ (setadjoin @ X805 @ (setadjoin @ X806 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X807 @ emptyset) @ (setadjoin @ (setadjoin @ X807 @ (setadjoin @ X808 @ emptyset)) @ emptyset))))))))=>(![X809:$i, X810:$i]:(?[X811:$i]:(((in @ X811 @ (setunion @ (setadjoin @ (setadjoin @ X809 @ emptyset) @ (setadjoin @ (setadjoin @ X809 @ (setadjoin @ X810 @ emptyset)) @ emptyset))))&?[X812:$i]:(((in @ X812 @ (setunion @ (setadjoin @ (setadjoin @ X809 @ emptyset) @ (setadjoin @ (setadjoin @ X809 @ (setadjoin @ X810 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X809 @ emptyset) @ (setadjoin @ (setadjoin @ X809 @ (setadjoin @ X810 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X811 @ emptyset) @ (setadjoin @ (setadjoin @ X811 @ (setadjoin @ X812 @ emptyset)) @ emptyset))))))))=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_158, binintersectSubset1]), bs114d]), setminusI]), setadjoinIL]), setminusEL]), c_0_159]), setminusER]), c_0_160]), setminusSubset2]), emptyinunitempty]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), c_0_161]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), emptyInPowerset]), c_0_162]), emptyinPowerset]), c_0_163]), powersetI]), c_0_164]), setadjoinOr]), setadjoinE]), setadjoinIR]), powersetE]), notinsingleton]), uniqinunit]), c_0_165]), c_0_166]), subPowSU]), setunionE]), setunionI]), eqinunit]), powersetI1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), setadjoinSub2]), setadjoinSub]), quantDeMorgan1]), vacuousDall]), c_0_167]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), quantDeMorgan2]), c_0_168]), c_0_169]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), c_0_170]), powerset__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_171]), c_0_172]), in__Cong]), inCongP]), setunion__Cong]), eqimpsubset1]), eqimpsubset2]), subsetI1]), c_0_173]), c_0_174]), c_0_175]), omega__Cong]), subsetI2]), subsetRefl]), notequalI2]), notequalI1]), notsubsetI]), subsetE2]), subsetE]), emptysetsubset]), subsetTrans]), powersetE1]), inPowerset]), binunionEcases]), binunionIR]), upairset2IR]), binunionIL]), c_0_176]), c_0_177]), powersetsubset]), binunionE]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectI]), binunionRsub]), binunionLsub]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), c_0_178]), noeltsimpempty]), emptyI]), setext]), c_0_179]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_180]), c_0_181]), c_0_182]), c_0_183]), c_0_184]), wellorderingAx]), foundationAx]), c_0_185]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_186])).
% 1.51/0.50 thf(c_0_188, negated_conjecture, ![X813:$i, X814:$i, X816:$i, X817:$i, X818:$i, X819:$i, X820:$i, X821:$i, X822:$i, X823:$i, X824:$i, X826:$i, X827:$i, X829:$i, X830:$i, X831:$i, X832:$i, X833:$i, X835:$i, X836:$i > $i > $o, X837:$i, X839:$i, X842:$i, X844:$i, X845:$i, X846:$i, X847:$i, X849:$i, X850:$i > $o, X851:$i, X853:$i, X854:$i > $o, X855:$i, X856:$i, X857:$i > $o, X858:$i, X859:$i, X860:$i > $o, X861:$i, X862:$i > $o, X863:$i, X866:$i, X867:$o, X868:$i, X869:$i, X870:$o, X871:$i, X872:$i, X873:$i > $o, X874:$i, X877:$i, X878:$i, X881:$i, X883:$i, X885:$i, X886:$i > $o, X887:$i, X888:$i, X890:$i, X891:$i > $o, X892:$i, X893:$i, X894:$i, X895:$i, X896:$i, X897:$i, X898:$i, X899:$i, X900:$i, X901:$i, X902:$i, X903:$o, X904:$i, X905:$i, X906:$i, X907:$i, X908:$i, X909:$i, X911:$i, X912:$i, X913:$i, X914:$i, X915:$i, X916:$i, X917:$i, X918:$i, X919:$i, X920:$i, X921:$o, X923:$i, X924:$i, X925:$i > $o, X926:$i, X929:$i, X930:$i, X931:$i, X933:$i, X934:$i, X935:$i, X936:$i, X937:$i, X938:$i, X939:$i, X940:$i, X941:$i, X942:$i, X943:$i, X944:$i, X945:$i, X946:$i, X947:$i, X948:$i, X949:$i > $o, X950:$i, X951:$i > $o, X952:$i, X953:$i, X954:$i > $o, X955:$i, X957:$i, X958:$i > $o, X960:$i, X961:$i, X962:$i > $o, X964:$i, X965:$i, X966:$i > $o, X967:$i, X969:$o, X970:$i, X971:$i > $o, X973:$i, X974:$i, X975:$i > $o, X976:$i, X978:$i > $o, X979:$i, X982:$i, X983:$i > $o, X984:$i, X988:$i, X989:$i > $o, X990:$i, X993:$i, X994:$i, X995:$i, X996:$i, X997:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i > $o, X1003:$i, X1005:$i, X1006:$i, X1007:$i > $o, X1008:$i > $o, X1011:$i, X1014:$i, X1015:$i, X1018:$i, X1019:$i, X1020:$i, X1021:$i, X1022:$i, X1023:$i, X1024:$i, X1025:$i, X1026:$i, X1027:$i > $o, X1028:$i, X1030:$i, X1031:$i, X1032:$i > $o, X1033:$i > $o, X1036:$i, X1038:$i, X1040:$i, X1041:$i, X1042:$i > $o, X1043:$i > $o, X1046:$i, X1047:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$i, X1053:$i, X1054:$i, X1056:$i, X1057:$i, X1058:$i, X1059:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i, X1064:$i, X1065:$i, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1070:$i, X1071:$i, X1072:$i, X1073:$i, X1074:$i, X1075:$i, X1076:$i, X1077:$i, X1078:$i, X1079:$i, X1080:$i, X1081:$i, X1082:$i, X1083:$i, X1084:$i, X1085:$i, X1086:$i, X1087:$i, X1088:$i, X1089:$i, X1090:$i, X1091:$i, X1092:$i, X1093:$i > $o, X1094:$i, X1095:$i > $o, X1096:$i, X1097:$i, X1098:$i, X1099:$i, X1100:$i, X1101:$i, X1102:$i, X1103:$i, X1104:$i, X1105:$i, X1106:$i, X1107:$o, X1108:$i, X1109:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1114:$i, X1115:$i, X1116:$i, X1117:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i, X1126:$i, X1127:$i, X1128:$i, X1129:$i, X1130:$i, X1131:$i, X1132:$i, X1133:$i, X1134:$i, X1136:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1147:$i, X1148:$i, X1149:$i, X1150:$i, X1151:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$i, X1162:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$i, X1171:$i, X1172:$i, X1173:$i, X1174:$i, X1175:$o, 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, X1198:$i, X1199:$i]:((((~(in @ (esk1_2 @ X813 @ X814) @ X813)|~(in @ (esk1_2 @ X813 @ X814) @ X814)|((X813)=(X814)))&((in @ (esk1_2 @ X813 @ X814) @ X813)|(in @ (esk1_2 @ X813 @ X814) @ X814)|((X813)=(X814))))&(~(in @ X816 @ emptyset)&(((~(in @ X819 @ (setadjoin @ X817 @ X818))|(((X819)=(X817))|(in @ X819 @ X818)))&((((X819)!=(X817))|(in @ X819 @ (setadjoin @ X817 @ X818)))&(~(in @ X819 @ X818)|(in @ X819 @ (setadjoin @ X817 @ X818)))))&(((~(in @ X821 @ (powerset @ X820))|(~(in @ X822 @ X821)|(in @ X822 @ X820)))&(((in @ (esk2_2 @ X823 @ X824) @ X824)|(in @ X824 @ (powerset @ X823)))&(~(in @ (esk2_2 @ X823 @ X824) @ X823)|(in @ X824 @ (powerset @ X823)))))&(((((in @ X827 @ (esk3_2 @ X826 @ X827))|~(in @ X827 @ (setunion @ X826)))&((in @ (esk3_2 @ X826 @ X827) @ X826)|~(in @ X827 @ (setunion @ X826))))&(~(in @ X830 @ X831)|~(in @ X831 @ X829)|(in @ X830 @ (setunion @ X829))))&((in @ emptyset @ omega)&((~(in @ X832 @ omega)|(in @ (setadjoin @ X832 @ X832) @ omega))&(((((in @ (esk4_1 @ X833) @ omega)|~(in @ emptyset @ X833)|(~(in @ X835 @ omega)|(in @ X835 @ X833)))&((in @ (esk4_1 @ X833) @ X833)|~(in @ emptyset @ X833)|(~(in @ X835 @ omega)|(in @ X835 @ X833))))&(~(in @ (setadjoin @ (esk4_1 @ X833) @ (esk4_1 @ X833)) @ X833)|~(in @ emptyset @ X833)|(~(in @ X835 @ omega)|(in @ X835 @ X833))))&((((((in @ (esk8_3 @ X836 @ X837 @ X842) @ X837)|~(in @ X842 @ (esk7_2 @ X836 @ X837))|(in @ (esk5_2 @ X836 @ X837) @ X837))&((X836 @ (esk8_3 @ X836 @ X837 @ X842) @ X842)|~(in @ X842 @ (esk7_2 @ X836 @ X837))|(in @ (esk5_2 @ X836 @ X837) @ X837)))&(~(in @ X845 @ X837)|~(X836 @ X845 @ X844)|(in @ X844 @ (esk7_2 @ X836 @ 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X1038))|~(X1033 @ X1038)|((descr @ X1032)=(descr @ X1033))|((X1032 @ (esk48_3 @ X1032 @ X1033 @ X1036))|~(X1032 @ X1036))|(~(X1032 @ (esk46_2 @ X1032 @ X1033))|~(X1033 @ (esk47_2 @ X1032 @ X1033))))&(((X1038)!=(esk49_3 @ X1032 @ X1033 @ X1038))|~(X1033 @ X1038)|((descr @ X1032)=(descr @ X1033))|((X1032 @ (esk48_3 @ X1032 @ X1033 @ X1036))|~(X1032 @ X1036))|(~(X1032 @ (esk46_2 @ X1032 @ X1033))|~(X1033 @ (esk47_2 @ X1032 @ X1033)))))&(((X1033 @ (esk49_3 @ X1032 @ X1033 @ X1038))|~(X1033 @ X1038)|((descr @ X1032)=(descr @ X1033))|(((X1036)!=(esk48_3 @ X1032 @ X1033 @ X1036))|~(X1032 @ X1036))|(~(X1032 @ (esk46_2 @ X1032 @ X1033))|~(X1033 @ (esk47_2 @ X1032 @ X1033))))&(((X1038)!=(esk49_3 @ X1032 @ X1033 @ X1038))|~(X1033 @ X1038)|((descr @ X1032)=(descr @ X1033))|(((X1036)!=(esk48_3 @ X1032 @ X1033 @ X1036))|~(X1032 @ X1036))|(~(X1032 @ (esk46_2 @ X1032 @ X1033))|~(X1033 @ (esk47_2 @ X1032 @ X1033))))))&((((X1033 @ (esk49_3 @ X1032 @ X1033 @ X1038))|~(X1033 @ X1038)|((descr @ X1032)=(descr @ X1033))|((X1032 @ (esk48_3 @ X1032 @ X1033 @ X1036))|~(X1032 @ X1036))|((X1032 @ (esk46_2 @ X1032 @ X1033))|(X1033 @ (esk47_2 @ X1032 @ X1033))))&(((X1038)!=(esk49_3 @ X1032 @ X1033 @ X1038))|~(X1033 @ X1038)|((descr @ X1032)=(descr @ X1033))|((X1032 @ (esk48_3 @ X1032 @ X1033 @ X1036))|~(X1032 @ X1036))|((X1032 @ (esk46_2 @ X1032 @ X1033))|(X1033 @ (esk47_2 @ X1032 @ X1033)))))&(((X1033 @ (esk49_3 @ X1032 @ X1033 @ X1038))|~(X1033 @ X1038)|((descr @ X1032)=(descr @ X1033))|(((X1036)!=(esk48_3 @ X1032 @ X1033 @ X1036))|~(X1032 @ X1036))|((X1032 @ (esk46_2 @ X1032 @ X1033))|(X1033 @ (esk47_2 @ X1032 @ X1033))))&(((X1038)!=(esk49_3 @ X1032 @ X1033 @ X1038))|~(X1033 @ X1038)|((descr @ X1032)=(descr @ X1033))|(((X1036)!=(esk48_3 @ X1032 @ X1033 @ X1036))|~(X1032 @ X1036))|((X1032 @ (esk46_2 @ X1032 @ X1033))|(X1033 @ (esk47_2 @ X1032 @ X1033))))))))&((((in @ (esk50_4 @ X1040 @ X1041 @ X1042 @ X1043) @ X1040)|((dsetconstr @ X1040 @ X1042)=(dsetconstr @ X1041 @ X1043))|((X1040)!=(X1041)))&(((in @ (esk51_4 @ X1040 @ X1041 @ X1042 @ X1043) @ X1041)|((dsetconstr @ X1040 @ X1042)=(dsetconstr @ X1041 @ X1043))|((X1040)!=(X1041)))&((((esk50_4 @ X1040 @ X1041 @ X1042 @ X1043)=(esk51_4 @ X1040 @ X1041 @ X1042 @ X1043))|((dsetconstr @ X1040 @ X1042)=(dsetconstr @ X1041 @ X1043))|((X1040)!=(X1041)))&((~(X1042 @ (esk50_4 @ X1040 @ X1041 @ X1042 @ X1043))|~(X1043 @ (esk51_4 @ X1040 @ X1041 @ X1042 @ X1043))|((dsetconstr @ X1040 @ X1042)=(dsetconstr @ X1041 @ X1043))|((X1040)!=(X1041)))&((X1042 @ (esk50_4 @ X1040 @ X1041 @ X1042 @ X1043))|(X1043 @ (esk51_4 @ X1040 @ X1041 @ X1042 @ X1043))|((dsetconstr @ X1040 @ X1042)=(dsetconstr @ X1041 @ X1043))|((X1040)!=(X1041)))))))&((((in @ (esk52_2 @ X1046 @ X1047) @ X1046)|(subset @ X1046 @ X1047))&(~(in @ (esk52_2 @ X1046 @ X1047) @ X1047)|(subset @ X1046 @ X1047)))&((((X1049)!=(X1050))|(subset @ X1050 @ X1049))&((((X1051)!=(X1052))|(subset @ X1051 @ X1052))&((((in @ (esk53_2 @ X1053 @ X1054) @ X1053)|(subset @ X1053 @ X1054))&(~(in @ (esk53_2 @ X1053 @ X1054) @ X1054)|(subset @ X1053 @ X1054)))&((subset @ emptyset @ X1056)&((~(subset @ X1057 @ X1058)|(~(in @ X1059 @ X1057)|(in @ X1059 @ X1058)))&((~(subset @ X1060 @ X1061)|((in @ X1062 @ X1061)|~(in @ X1062 @ X1060)))&((~(in @ X1065 @ X1063)|((in @ X1065 @ X1064)|~(subset @ X1063 @ X1064)))&(((subset @ X1066 @ X1067)|((X1066)!=(X1067)))&((~(in @ X1070 @ X1068)|((in @ X1070 @ X1069)|((X1068)!=(X1069))))&((subset @ X1071 @ X1071)&((~(subset @ X1072 @ X1073)|(~(subset @ X1073 @ X1074)|(subset @ X1072 @ X1074)))&((subset @ X1076 @ (setadjoin @ X1075 @ X1076))&((~(subset @ X1077 @ X1079)|(subset @ X1077 @ (setadjoin @ X1078 @ X1079)))&((~(subset @ X1080 @ X1081)|(in @ X1080 @ (powerset @ X1081)))&((~(subset @ X1082 @ X1083)|(~(subset @ X1083 @ X1082)|((X1082)=(X1083))))&((~(subset @ X1084 @ emptyset)|((X1084)=(emptyset)))&((~(subset @ X1086 @ X1085)|(in @ X1086 @ (powerset @ X1085)))&((~(in @ X1088 @ (powerset @ X1087))|(subset @ X1088 @ X1087))&((in @ X1089 @ (powerset @ X1089))&((~(subset @ X1090 @ X1091)|(subset @ (powerset @ X1090) @ (powerset @ X1091)))&((in @ (dsetconstr @ X1092 @ X1093) @ (powerset @ X1092))&((subset @ (dsetconstr @ X1094 @ X1095) @ X1094)&((~(in @ X1098 @ X1096)|(in @ X1098 @ (binunion @ X1096 @ X1097)))&((in @ X1100 @ (setadjoin @ X1099 @ (setadjoin @ X1100 @ emptyset)))&((~(in @ X1103 @ X1102)|(in @ X1103 @ (binunion @ X1101 @ X1102)))&(((((in @ X1106 @ X1105)|(X1107)|(in @ X1106 @ X1104)|~(in @ X1106 @ (binunion @ X1104 @ X1105)))&(~(X1107)|(X1107)|(in @ X1106 @ X1104)|~(in @ X1106 @ (binunion @ X1104 @ X1105))))&(((in @ X1106 @ X1105)|(X1107)|~(X1107)|~(in @ X1106 @ (binunion @ X1104 @ X1105)))&(~(X1107)|(X1107)|~(X1107)|~(in @ X1106 @ (binunion @ X1104 @ X1105)))))&((~(in @ X1110 @ (binunion @ X1108 @ X1109))|((in @ X1110 @ X1108)|(in @ X1110 @ X1109)))&((subset @ X1111 @ (binunion @ X1111 @ X1112))&((subset @ X1114 @ (binunion @ X1113 @ X1114))&((~(in @ X1117 @ X1115)|(~(in @ X1117 @ X1116)|(in @ X1117 @ (binintersect @ X1115 @ X1116))))&((~(subset @ X1120 @ X1118)|(~(subset @ X1120 @ X1119)|(subset @ X1120 @ (binintersect @ X1118 @ X1119))))&((~(in @ X1123 @ (binintersect @ X1121 @ X1122))|(in @ X1123 @ X1121))&((subset @ (binintersect @ X1124 @ X1125) @ X1124)&((~(subset @ X1126 @ X1127)|((binintersect @ X1126 @ X1127)=(X1126)))&((((binintersect @ X1128 @ X1129)!=(X1129))|(subset @ X1129 @ X1128))&((~(in @ X1132 @ (binintersect @ X1130 @ X1131))|(in @ X1132 @ X1131))&((((in @ (esk54_2 @ X1133 @ X1134) @ X1133)|((binintersect @ X1133 @ X1134)=(emptyset)))&((in @ (esk54_2 @ X1133 @ X1134) @ X1134)|((binintersect @ X1133 @ X1134)=(emptyset))))&((subset @ (binintersect @ X1136 @ X1137) @ X1137)&((~(subset @ X1139 @ X1138)|((binintersect @ X1138 @ X1139)=(X1139)))&((((binintersect @ X1140 @ X1141)!=(X1140))|(subset @ X1140 @ X1141))&(((binintersect @ X1142 @ (binunion @ X1143 @ X1144))=(binunion @ (binintersect @ X1142 @ X1143) @ (binintersect @ X1142 @ X1144)))&((~(in @ X1147 @ X1145)|((in @ X1147 @ X1146)|(in @ X1147 @ (setminus @ X1145 @ X1146))))&((~(in @ X1150 @ (setminus @ X1148 @ X1149))|(in @ X1150 @ X1148))&((~(in @ X1153 @ (setminus @ X1151 @ X1152))|~(in @ X1153 @ X1152))&((~(subset @ X1154 @ X1155)|((setminus @ X1154 @ X1155)=(emptyset)))&(((in @ X1158 @ (setminus @ X1156 @ X1157))|(~(in @ X1158 @ X1156)|(in @ X1158 @ X1157)))&(((in @ X1161 @ (setminus @ X1159 @ X1160))|((in @ X1161 @ X1160)|~(in @ X1161 @ X1159)))&(((in @ X1164 @ X1162)|~(in @ X1164 @ (setminus @ X1162 @ X1163)))&((~(in @ X1167 @ X1166)|~(in @ X1167 @ (setminus @ X1165 @ X1166)))&((subset @ (setminus @ X1168 @ X1169) @ X1168)&((((setminus @ X1170 @ X1171)!=(emptyset))|(subset @ X1170 @ X1171))&((((~(in @ X1174 @ X1172)|(X1175)|(in @ X1174 @ X1172)|~(in @ X1174 @ (symdiff @ X1172 @ X1173)))&(((in @ X1174 @ X1173)|(X1175)|(in @ X1174 @ X1172)|~(in @ X1174 @ (symdiff @ X1172 @ X1173)))&(~(X1175)|(X1175)|(in @ X1174 @ X1172)|~(in @ X1174 @ (symdiff @ X1172 @ X1173)))))&(((~(in @ X1174 @ X1172)|(X1175)|~(in @ X1174 @ X1173)|~(in @ X1174 @ (symdiff @ X1172 @ X1173)))&(((in @ X1174 @ X1173)|(X1175)|~(in @ X1174 @ X1173)|~(in @ X1174 @ (symdiff @ X1172 @ X1173)))&(~(X1175)|(X1175)|~(in @ X1174 @ X1173)|~(in @ X1174 @ (symdiff @ X1172 @ X1173)))))&((~(in @ X1174 @ X1172)|(X1175)|~(X1175)|~(in @ X1174 @ (symdiff @ X1172 @ X1173)))&(((in @ X1174 @ X1173)|(X1175)|~(X1175)|~(in @ X1174 @ (symdiff @ X1172 @ X1173)))&(~(X1175)|(X1175)|~(X1175)|~(in @ X1174 @ (symdiff @ X1172 @ X1173)))))))&((~(in @ X1178 @ X1176)|((in @ X1178 @ X1177)|(in @ X1178 @ (symdiff @ X1176 @ X1177))))&(((in @ X1181 @ X1179)|(~(in @ X1181 @ X1180)|(in @ X1181 @ (symdiff @ X1179 @ X1180))))&((~(in @ X1184 @ X1182)|(~(in @ X1184 @ X1183)|~(in @ X1184 @ (symdiff @ X1182 @ X1183))))&(((in @ X1187 @ X1185)|((in @ X1187 @ X1186)|~(in @ X1187 @ (symdiff @ X1185 @ X1186))))&((in @ X1189 @ (setadjoin @ X1188 @ (setadjoin @ X1189 @ emptyset)))&((in @ X1190 @ (setunion @ (setadjoin @ (setadjoin @ X1190 @ emptyset) @ (setadjoin @ (setadjoin @ X1190 @ (setadjoin @ X1191 @ emptyset)) @ emptyset))))&((in @ X1193 @ (setunion @ (setadjoin @ (setadjoin @ X1192 @ emptyset) @ (setadjoin @ (setadjoin @ X1192 @ (setadjoin @ X1193 @ emptyset)) @ emptyset))))&(((in @ (esk55_2 @ X1194 @ X1195) @ (setunion @ (setadjoin @ (setadjoin @ X1194 @ emptyset) @ (setadjoin @ (setadjoin @ X1194 @ (setadjoin @ X1195 @ emptyset)) @ emptyset))))&((in @ (esk56_2 @ X1194 @ X1195) @ (setunion @ (setadjoin @ (setadjoin @ X1194 @ emptyset) @ (setadjoin @ (setadjoin @ X1194 @ (setadjoin @ X1195 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1194 @ emptyset) @ (setadjoin @ (setadjoin @ X1194 @ (setadjoin @ X1195 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk55_2 @ X1194 @ X1195) @ emptyset) @ (setadjoin @ (setadjoin @ (esk55_2 @ X1194 @ X1195) @ (setadjoin @ (esk56_2 @ X1194 @ X1195) @ emptyset)) @ emptyset)))))&(((in @ (esk57_2 @ X1198 @ X1199) @ (setunion @ (setadjoin @ (setadjoin @ X1198 @ emptyset) @ (setadjoin @ (setadjoin @ X1198 @ (setadjoin @ X1199 @ emptyset)) @ emptyset))))&((in @ (esk58_2 @ X1198 @ X1199) @ (setunion @ (setadjoin @ (setadjoin @ X1198 @ emptyset) @ (setadjoin @ (setadjoin @ X1198 @ (setadjoin @ X1199 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1198 @ emptyset) @ (setadjoin @ (setadjoin @ X1198 @ (setadjoin @ X1199 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk57_2 @ X1198 @ X1199) @ emptyset) @ (setadjoin @ (setadjoin @ (esk57_2 @ X1198 @ X1199) @ (setadjoin @ (esk58_2 @ X1198 @ X1199) @ emptyset)) @ emptyset)))))&((in @ esk60_0 @ esk59_0)&~(subset @ (setadjoin @ esk60_0 @ emptyset) @ esk59_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_187])])])])])])])).
% 1.51/0.50 thf(c_0_189, negated_conjecture, ![X3:$i, X2:$i]:((((X2)=(X3))|~((in @ X3 @ (setadjoin @ X2 @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_188])).
% 1.51/0.50 thf(c_0_190, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk53_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_188])).
% 1.51/0.50 thf(c_0_191, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk53_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_188])).
% 1.51/0.50 thf(c_0_192, negated_conjecture, ![X2:$i, X3:$i]:((((esk53_2 @ (setadjoin @ X2 @ emptyset) @ X3)=(X2))|(subset @ (setadjoin @ X2 @ emptyset) @ X3))), inference(spm,[status(thm)],[c_0_189, c_0_190])).
% 1.51/0.50 thf(c_0_193, negated_conjecture, ~((subset @ (setadjoin @ esk60_0 @ emptyset) @ esk59_0)), inference(split_conjunct,[status(thm)],[c_0_188])).
% 1.51/0.50 thf(c_0_194, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ (setadjoin @ X2 @ emptyset) @ X3)|~((in @ X2 @ X3)))), inference(spm,[status(thm)],[c_0_191, c_0_192])).
% 1.51/0.50 thf(c_0_195, negated_conjecture, (in @ esk60_0 @ esk59_0), inference(split_conjunct,[status(thm)],[c_0_188])).
% 1.51/0.50 thf(c_0_196, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193, c_0_194]), c_0_195])]), ['proof']).
% 1.51/0.50 % SZS output end CNFRefutation
% 1.51/0.50 % Parsed axioms : 303
% 1.51/0.50 % Removed by relevancy pruning/SinE : 162
% 1.51/0.50 % Initial clauses : 265
% 1.51/0.50 % Removed in clause preprocessing : 24
% 1.51/0.50 % Initial clauses in saturation : 241
% 1.51/0.50 % Processed clauses : 1831
% 1.51/0.50 % ...of these trivial : 11
% 1.51/0.50 % ...subsumed : 1250
% 1.51/0.50 % ...remaining for further processing : 570
% 1.51/0.50 % Other redundant clauses eliminated : 26
% 1.51/0.50 % Clauses deleted for lack of memory : 0
% 1.51/0.50 % Backward-subsumed : 2
% 1.51/0.50 % Backward-rewritten : 6
% 1.51/0.50 % Generated clauses : 18261
% 1.51/0.50 % ...of the previous two non-redundant : 15908
% 1.51/0.50 % ...aggressively subsumed : 0
% 1.51/0.50 % Contextual simplify-reflections : 1
% 1.51/0.50 % Paramodulations : 18233
% 1.51/0.50 % Factorizations : 2
% 1.51/0.50 % NegExts : 0
% 1.51/0.50 % Equation resolutions : 26
% 1.51/0.50 % Disequality decompositions : 0
% 1.51/0.50 % Total rewrite steps : 6632
% 1.51/0.50 % ...of those cached : 6447
% 1.51/0.50 % Propositional unsat checks : 0
% 1.51/0.50 % Propositional check models : 0
% 1.51/0.50 % Propositional check unsatisfiable : 0
% 1.51/0.50 % Propositional clauses : 0
% 1.51/0.50 % Propositional clauses after purity: 0
% 1.51/0.50 % Propositional unsat core size : 0
% 1.51/0.50 % Propositional preprocessing time : 0.000
% 1.51/0.50 % Propositional encoding time : 0.000
% 1.51/0.50 % Propositional solver time : 0.000
% 1.51/0.50 % Success case prop preproc time : 0.000
% 1.51/0.50 % Success case prop encoding time : 0.000
% 1.51/0.50 % Success case prop solver time : 0.000
% 1.51/0.50 % Current number of processed clauses : 549
% 1.51/0.50 % Positive orientable unit clauses : 195
% 1.51/0.50 % Positive unorientable unit clauses: 0
% 1.51/0.50 % Negative unit clauses : 2
% 1.51/0.50 % Non-unit-clauses : 352
% 1.51/0.50 % Current number of unprocessed clauses: 14227
% 1.51/0.50 % ...number of literals in the above : 50137
% 1.51/0.50 % Current number of archived formulas : 0
% 1.51/0.50 % Current number of archived clauses : 8
% 1.51/0.50 % Clause-clause subsumption calls (NU) : 18553
% 1.51/0.50 % Rec. Clause-clause subsumption calls : 10293
% 1.51/0.50 % Non-unit clause-clause subsumptions : 715
% 1.51/0.50 % Unit Clause-clause subsumption calls : 259
% 1.51/0.50 % Rewrite failures with RHS unbound : 0
% 1.51/0.50 % BW rewrite match attempts : 945
% 1.51/0.50 % BW rewrite match successes : 4
% 1.51/0.50 % Condensation attempts : 0
% 1.51/0.50 % Condensation successes : 0
% 1.51/0.50 % Termbank termtop insertions : 369502
% 1.51/0.50 % Search garbage collected termcells : 13384
% 1.51/0.50
% 1.51/0.50 % -------------------------------------------------
% 1.51/0.50 % User time : 0.203 s
% 1.51/0.50 % System time : 0.016 s
% 1.51/0.50 % Total time : 0.218 s
% 1.51/0.50 % Maximum resident set size: 6952 pages
% 1.51/0.50
% 1.51/0.50 % -------------------------------------------------
% 1.51/0.50 % User time : 0.275 s
% 1.51/0.50 % System time : 0.058 s
% 1.51/0.50 % Total time : 0.333 s
% 1.51/0.50 % Maximum resident set size: 5120 pages
% 1.51/0.50 % E exiting
%------------------------------------------------------------------------------