%------------------------------------------------------------------------------
% File : E---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 : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:45 AM UTC 2026
% Result : Theorem 1.81s 0.55s
% Output : CNFRefutation 1.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU621^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n010.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 13:59:03 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.20/0.26 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.9ji6MKpz7n/E---3.1_2901106.p
% 1.81/0.55 % Version: 3.5.1-ho
% 1.81/0.55 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.81/0.55 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.81/0.55 % Starting ehoh_best5 with 300s (1) cores
% 1.81/0.55 % Starting almost_fo_3_lam with 300s (1) cores
% 1.81/0.55 % Starting new_bool_5 with 300s (1) cores
% 1.81/0.55 % Starting pre_casc_3 with 300s (1) cores
% 1.81/0.55 % Starting ho_unfolding_8 with 300s (1) cores
% 1.81/0.55 % Starting new_ho_10_cnf2 with 300s (1) cores
% 1.81/0.55 % Starting new_bool_3 with 300s (1) cores
% 1.81/0.55 % Starting new_ho_5 with 300s (1) cores
% 1.81/0.55 % new_ho_5 with pid 2901149 completed with status 9
% 1.81/0.55 % ehoh_best5 with pid 2901141 completed with status 0
% 1.81/0.55 % Result found by ehoh_best5
% 1.81/0.55 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.81/0.55 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.81/0.55 % Starting ehoh_best5 with 300s (1) cores
% 1.81/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.81/0.55 % No SInE strategy applied
% 1.81/0.55 % Search class: HGHSM-FSLM31-MHFMMSBN
% 1.81/0.55 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.81/0.55 % Starting SubtermCWHack with 28s (1) cores
% 1.81/0.55 % SubtermCWHack with pid 2901162 completed with status 0
% 1.81/0.55 % Result found by SubtermCWHack
% 1.81/0.55 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.81/0.55 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.81/0.55 % Starting ehoh_best5 with 300s (1) cores
% 1.81/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.81/0.55 % No SInE strategy applied
% 1.81/0.55 % Search class: HGHSM-FSLM31-MHFMMSBN
% 1.81/0.55 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.81/0.55 % Starting SubtermCWHack with 28s (1) cores
% 1.81/0.55 % Preprocessing time : 0.003 s
% 1.81/0.55
% 1.81/0.55 % Proof found!
% 1.81/0.55 % SZS status Theorem
% 1.81/0.55 % SZS output start CNFRefutation
% 1.81/0.55 thf(decl_23, type, in: $i > $i > $o).
% 1.81/0.55 thf(decl_24, type, exu: ($i > $o) > $o).
% 1.81/0.55 thf(decl_25, type, setextAx: $o).
% 1.81/0.55 thf(decl_26, type, emptyset: $i).
% 1.81/0.55 thf(decl_27, type, emptysetAx: $o).
% 1.81/0.55 thf(decl_28, type, setadjoin: $i > $i > $i).
% 1.81/0.55 thf(decl_29, type, setadjoinAx: $o).
% 1.81/0.55 thf(decl_30, type, powerset: $i > $i).
% 1.81/0.55 thf(decl_31, type, powersetAx: $o).
% 1.81/0.55 thf(decl_32, type, setunion: $i > $i).
% 1.81/0.55 thf(decl_33, type, setunionAx: $o).
% 1.81/0.55 thf(decl_34, type, omega: $i).
% 1.81/0.55 thf(decl_35, type, omega0Ax: $o).
% 1.81/0.55 thf(decl_36, type, omegaSAx: $o).
% 1.81/0.55 thf(decl_37, type, omegaIndAx: $o).
% 1.81/0.55 thf(decl_38, type, replAx: $o).
% 1.81/0.55 thf(decl_39, type, foundationAx: $o).
% 1.81/0.55 thf(decl_40, type, wellorderingAx: $o).
% 1.81/0.55 thf(decl_41, type, descr: ($i > $o) > $i).
% 1.81/0.55 thf(decl_42, type, descrp: $o).
% 1.81/0.55 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 1.81/0.55 thf(decl_44, type, dsetconstrI: $o).
% 1.81/0.55 thf(decl_45, type, dsetconstrEL: $o).
% 1.81/0.55 thf(decl_46, type, dsetconstrER: $o).
% 1.81/0.55 thf(decl_47, type, exuE1: $o).
% 1.81/0.55 thf(decl_48, type, prop2set: $o > $i).
% 1.81/0.55 thf(decl_49, type, prop2setE: $o).
% 1.81/0.55 thf(decl_50, type, emptysetE: $o).
% 1.81/0.55 thf(decl_51, type, emptysetimpfalse: $o).
% 1.81/0.55 thf(decl_52, type, notinemptyset: $o).
% 1.81/0.55 thf(decl_53, type, exuE3e: $o).
% 1.81/0.55 thf(decl_54, type, setext: $o).
% 1.81/0.55 thf(decl_55, type, emptyI: $o).
% 1.81/0.55 thf(decl_56, type, noeltsimpempty: $o).
% 1.81/0.55 thf(decl_57, type, setbeta: $o).
% 1.81/0.55 thf(decl_58, type, nonempty: $i > $o).
% 1.81/0.55 thf(decl_59, type, nonemptyE1: $o).
% 1.81/0.55 thf(decl_60, type, nonemptyI: $o).
% 1.81/0.55 thf(decl_61, type, nonemptyI1: $o).
% 1.81/0.55 thf(decl_62, type, setadjoinIL: $o).
% 1.81/0.55 thf(decl_63, type, emptyinunitempty: $o).
% 1.81/0.55 thf(decl_64, type, setadjoinIR: $o).
% 1.81/0.55 thf(decl_65, type, setadjoinE: $o).
% 1.81/0.55 thf(decl_66, type, setadjoinOr: $o).
% 1.81/0.55 thf(decl_67, type, setoftrueEq: $o).
% 1.81/0.55 thf(decl_68, type, powersetI: $o).
% 1.81/0.55 thf(decl_69, type, emptyinPowerset: $o).
% 1.81/0.55 thf(decl_70, type, emptyInPowerset: $o).
% 1.81/0.55 thf(decl_71, type, powersetE: $o).
% 1.81/0.55 thf(decl_72, type, setunionI: $o).
% 1.81/0.55 thf(decl_73, type, setunionE: $o).
% 1.81/0.55 thf(decl_74, type, subPowSU: $o).
% 1.81/0.55 thf(decl_75, type, exuE2: $o).
% 1.81/0.55 thf(decl_76, type, nonemptyImpWitness: $o).
% 1.81/0.55 thf(decl_77, type, uniqinunit: $o).
% 1.81/0.55 thf(decl_78, type, notinsingleton: $o).
% 1.81/0.55 thf(decl_79, type, eqinunit: $o).
% 1.81/0.55 thf(decl_80, type, singletonsswitch: $o).
% 1.81/0.55 thf(decl_81, type, upairsetE: $o).
% 1.81/0.55 thf(decl_82, type, upairsetIL: $o).
% 1.81/0.55 thf(decl_83, type, upairsetIR: $o).
% 1.81/0.55 thf(decl_84, type, emptyE1: $o).
% 1.81/0.55 thf(decl_85, type, vacuousDall: $o).
% 1.81/0.55 thf(decl_86, type, quantDeMorgan1: $o).
% 1.81/0.55 thf(decl_87, type, quantDeMorgan2: $o).
% 1.81/0.55 thf(decl_88, type, quantDeMorgan3: $o).
% 1.81/0.55 thf(decl_89, type, quantDeMorgan4: $o).
% 1.81/0.55 thf(decl_90, type, prop2setI: $o).
% 1.81/0.55 thf(decl_91, type, set2prop: $i > $o).
% 1.81/0.55 thf(decl_92, type, prop2set2propI: $o).
% 1.81/0.55 thf(decl_93, type, notdexE: $o).
% 1.81/0.55 thf(decl_94, type, notdallE: $o).
% 1.81/0.55 thf(decl_95, type, exuI1: $o).
% 1.81/0.55 thf(decl_96, type, exuI3: $o).
% 1.81/0.55 thf(decl_97, type, exuI2: $o).
% 1.81/0.55 thf(decl_98, type, inCongP: $o).
% 1.81/0.55 thf(decl_99, type, in__Cong: $o).
% 1.81/0.55 thf(decl_100, type, exuE3u: $o).
% 1.81/0.55 thf(decl_101, type, exu__Cong: $o).
% 1.81/0.55 thf(decl_102, type, emptyset__Cong: $o).
% 1.81/0.55 thf(decl_103, type, setadjoin__Cong: $o).
% 1.81/0.55 thf(decl_104, type, powerset__Cong: $o).
% 1.81/0.55 thf(decl_105, type, setunion__Cong: $o).
% 1.81/0.55 thf(decl_106, type, omega__Cong: $o).
% 1.81/0.55 thf(decl_107, type, exuEu: $o).
% 1.81/0.55 thf(decl_108, type, descr__Cong: $o).
% 1.81/0.55 thf(decl_109, type, dsetconstr__Cong: $o).
% 1.81/0.55 thf(decl_110, type, subset: $i > $i > $o).
% 1.81/0.55 thf(decl_113, type, subsetI1: $o).
% 1.81/0.55 thf(decl_114, type, eqimpsubset2: $o).
% 1.81/0.55 thf(decl_115, type, eqimpsubset1: $o).
% 1.81/0.55 thf(decl_116, type, subsetI2: $o).
% 1.81/0.55 thf(decl_117, type, emptysetsubset: $o).
% 1.81/0.55 thf(decl_118, type, subsetE: $o).
% 1.81/0.55 thf(decl_119, type, subsetE2: $o).
% 1.81/0.55 thf(decl_120, type, notsubsetI: $o).
% 1.81/0.55 thf(decl_121, type, notequalI1: $o).
% 1.81/0.55 thf(decl_122, type, notequalI2: $o).
% 1.81/0.55 thf(decl_123, type, subsetRefl: $o).
% 1.81/0.55 thf(decl_124, type, subsetTrans: $o).
% 1.81/0.55 thf(decl_125, type, setadjoinSub: $o).
% 1.81/0.55 thf(decl_126, type, setadjoinSub2: $o).
% 1.81/0.55 thf(decl_127, type, subset2powerset: $o).
% 1.81/0.55 thf(decl_128, type, setextsub: $o).
% 1.81/0.55 thf(decl_129, type, subsetemptysetimpeq: $o).
% 1.81/0.55 thf(decl_130, type, powersetI1: $o).
% 1.81/0.55 thf(decl_131, type, powersetE1: $o).
% 1.81/0.55 thf(decl_132, type, inPowerset: $o).
% 1.81/0.55 thf(decl_133, type, powersetsubset: $o).
% 1.81/0.55 thf(decl_134, type, sepInPowerset: $o).
% 1.81/0.55 thf(decl_135, type, sepSubset: $o).
% 1.81/0.55 thf(decl_136, type, binunion: $i > $i > $i).
% 1.81/0.55 thf(decl_137, type, binunionIL: $o).
% 1.81/0.55 thf(decl_138, type, upairset2IR: $o).
% 1.81/0.55 thf(decl_139, type, binunionIR: $o).
% 1.81/0.55 thf(decl_140, type, binunionEcases: $o).
% 1.81/0.55 thf(decl_141, type, binunionE: $o).
% 1.81/0.55 thf(decl_142, type, binunionLsub: $o).
% 1.81/0.55 thf(decl_143, type, binunionRsub: $o).
% 1.81/0.55 thf(decl_144, type, binintersect: $i > $i > $i).
% 1.81/0.55 thf(decl_145, type, binintersectI: $o).
% 1.81/0.55 thf(decl_146, type, binintersectSubset5: $o).
% 1.81/0.55 thf(decl_147, type, binintersectEL: $o).
% 1.81/0.55 thf(decl_148, type, binintersectLsub: $o).
% 1.81/0.55 thf(decl_149, type, binintersectSubset2: $o).
% 1.81/0.55 thf(decl_150, type, binintersectSubset3: $o).
% 1.81/0.55 thf(decl_151, type, binintersectER: $o).
% 1.81/0.55 thf(decl_152, type, disjointsetsI1: $o).
% 1.81/0.55 thf(decl_153, type, binintersectRsub: $o).
% 1.81/0.55 thf(decl_154, type, binintersectSubset4: $o).
% 1.81/0.55 thf(decl_155, type, binintersectSubset1: $o).
% 1.81/0.55 thf(decl_156, type, bs114d: $o).
% 1.81/0.55 thf(decl_158, type, setminus: $i > $i > $i).
% 1.81/0.55 thf(decl_159, type, setminusI: $o).
% 1.81/0.55 thf(decl_160, type, setminusEL: $o).
% 1.81/0.55 thf(decl_161, type, setminusER: $o).
% 1.81/0.55 thf(decl_162, type, setminusSubset2: $o).
% 1.81/0.55 thf(decl_163, type, setminusERneg: $o).
% 1.81/0.55 thf(decl_164, type, setminusELneg: $o).
% 1.81/0.55 thf(decl_165, type, setminusILneg: $o).
% 1.81/0.55 thf(decl_166, type, setminusIRneg: $o).
% 1.81/0.55 thf(decl_167, type, setminusLsub: $o).
% 1.81/0.55 thf(decl_168, type, setminusSubset1: $o).
% 1.81/0.55 thf(decl_169, type, symdiff: $i > $i > $i).
% 1.81/0.55 thf(decl_170, type, symdiffE: $o).
% 1.81/0.55 thf(decl_171, type, symdiffI1: $o).
% 1.81/0.55 thf(decl_172, type, symdiffI2: $o).
% 1.81/0.55 thf(decl_173, type, symdiffIneg1: $o).
% 1.81/0.55 thf(decl_174, type, symdiffIneg2: $o).
% 1.81/0.55 thf(decl_175, type, iskpair: $i > $o).
% 1.81/0.55 thf(decl_176, type, secondinupair: $o).
% 1.81/0.55 thf(decl_177, type, setukpairIL: $o).
% 1.81/0.55 thf(decl_178, type, setukpairIR: $o).
% 1.81/0.55 thf(decl_179, type, kpairiskpair: $o).
% 1.81/0.55 thf(decl_180, type, kpair: $i > $i > $i).
% 1.81/0.55 thf(decl_181, type, kpairp: $o).
% 1.81/0.55 thf(decl_183, type, epred1_0: $o).
% 1.81/0.55 thf(decl_184, type, esk1_2: $i > $i > $i).
% 1.81/0.55 thf(decl_185, type, esk2_2: $i > $i > $i).
% 1.81/0.55 thf(decl_186, type, esk3_2: $i > $i > $i).
% 1.81/0.55 thf(decl_187, type, esk4_1: $i > $i).
% 1.81/0.55 thf(decl_188, type, esk5_2: ($i > $i > $o) > $i > $i).
% 1.81/0.55 thf(decl_189, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 1.81/0.55 thf(decl_190, type, esk7_2: ($i > $i > $o) > $i > $i).
% 1.81/0.55 thf(decl_191, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 1.81/0.55 thf(decl_192, type, esk9_1: $i > $i).
% 1.81/0.55 thf(decl_193, type, esk10_2: ($i > $o) > $i > $i).
% 1.81/0.55 thf(decl_194, type, esk11_2: ($i > $o) > $i > $i).
% 1.81/0.55 thf(decl_195, type, esk12_1: ($i > $o) > $i).
% 1.81/0.55 thf(decl_196, type, esk13_2: ($i > $o) > $i > $i).
% 1.81/0.55 thf(decl_197, type, esk14_1: ($i > $o) > $i).
% 1.81/0.55 thf(decl_198, type, esk15_2: $i > $i > $i).
% 1.81/0.55 thf(decl_199, type, esk16_2: $i > $i > $i).
% 1.81/0.55 thf(decl_200, type, esk17_1: $i > $i).
% 1.81/0.55 thf(decl_201, type, esk18_1: $i > $i).
% 1.81/0.55 thf(decl_202, type, esk19_1: $i > $i).
% 1.81/0.55 thf(decl_203, type, esk20_2: $i > $i > $i).
% 1.81/0.55 thf(decl_204, type, esk21_3: $i > $i > $o > $i).
% 1.81/0.55 thf(decl_205, type, esk22_2: ($i > $o) > $i > $i).
% 1.81/0.55 thf(decl_206, type, esk23_1: ($i > $o) > $i).
% 1.81/0.55 thf(decl_207, type, esk24_1: $i > $i).
% 1.81/0.55 thf(decl_208, type, esk25_2: $i > ($i > $o) > $i).
% 1.81/0.55 thf(decl_209, type, esk26_2: $i > ($i > $o) > $i).
% 1.81/0.55 thf(decl_210, type, esk27_2: $i > ($i > $o) > $i).
% 1.81/0.55 thf(decl_211, type, esk28_2: $i > ($i > $o) > $i).
% 1.81/0.55 thf(decl_212, type, esk29_2: $i > ($i > $o) > $i).
% 1.81/0.55 thf(decl_213, type, esk30_2: $i > ($i > $o) > $i).
% 1.81/0.55 thf(decl_214, type, esk31_2: ($i > $o) > $i > $i).
% 1.81/0.55 thf(decl_215, type, esk32_1: ($i > $o) > $i).
% 1.81/0.55 thf(decl_216, type, esk33_1: ($i > $o) > $i).
% 1.81/0.55 thf(decl_217, type, esk34_1: ($i > $o) > $i).
% 1.81/0.55 thf(decl_218, type, esk35_1: ($i > $o) > $i).
% 1.81/0.55 thf(decl_219, type, esk36_2: ($i > $o) > $i > $i).
% 1.81/0.55 thf(decl_220, type, esk37_1: ($i > $o) > $i).
% 1.81/0.55 thf(decl_221, type, esk38_2: ($i > $o) > $i > $i).
% 1.81/0.55 thf(decl_222, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 1.81/0.55 thf(decl_223, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 1.81/0.55 thf(decl_224, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.81/0.55 thf(decl_225, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 1.81/0.55 thf(decl_226, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.81/0.55 thf(decl_227, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 1.81/0.55 thf(decl_228, type, esk45_2: ($i > $o) > $i > $i).
% 1.81/0.55 thf(decl_229, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 1.81/0.55 thf(decl_230, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 1.81/0.55 thf(decl_231, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.81/0.55 thf(decl_232, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.81/0.55 thf(decl_233, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.81/0.55 thf(decl_234, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.81/0.55 thf(decl_235, type, esk52_2: $i > $i > $i).
% 1.81/0.55 thf(decl_236, type, esk53_2: $i > $i > $i).
% 1.81/0.55 thf(decl_237, type, esk54_2: $i > $i > $i).
% 1.81/0.55 thf(decl_238, type, esk55_2: $i > $i > $i).
% 1.81/0.55 thf(decl_239, type, esk56_2: $i > $i > $i).
% 1.81/0.55 thf(decl_240, type, esk57_2: $i > $i > $i).
% 1.81/0.55 thf(decl_241, type, esk58_2: $i > $i > $i).
% 1.81/0.55 thf(decl_242, type, esk59_0: $i).
% 1.81/0.55 thf(decl_243, type, esk60_0: $i).
% 1.81/0.55 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', replAx)).
% 1.81/0.55 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', exu)).
% 1.81/0.55 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', descrp)).
% 1.81/0.55 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', exuE1)).
% 1.81/0.55 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', exuE3e)).
% 1.81/0.55 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', nonempty)).
% 1.81/0.55 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', nonemptyI)).
% 1.81/0.55 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', exuE2)).
% 1.81/0.55 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.9ji6MKpz7n/E---3.1_2901106.p', exuI1)).
% 1.81/0.55 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', exuI3)).
% 1.81/0.55 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', exuI2)).
% 1.81/0.55 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.9ji6MKpz7n/E---3.1_2901106.p', exuE3u)).
% 1.81/0.55 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', exu__Cong)).
% 1.81/0.55 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', exuEu)).
% 1.81/0.55 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', descr__Cong)).
% 1.81/0.55 thf(iskpair, axiom, ((iskpair)=(^[X4:$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.9ji6MKpz7n/E---3.1_2901106.p', iskpair)).
% 1.81/0.55 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.9ji6MKpz7n/E---3.1_2901106.p', singletonsubset)).
% 1.81/0.55 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', dsetconstrI)).
% 1.81/0.55 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', dsetconstrEL)).
% 1.81/0.55 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', dsetconstrER)).
% 1.81/0.55 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setbeta)).
% 1.81/0.55 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', nonemptyE1)).
% 1.81/0.55 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', nonemptyI1)).
% 1.81/0.55 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setoftrueEq)).
% 1.81/0.55 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', nonemptyImpWitness)).
% 1.81/0.55 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.9ji6MKpz7n/E---3.1_2901106.p', emptyE1)).
% 1.81/0.55 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', dsetconstr__Cong)).
% 1.81/0.55 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', sepInPowerset)).
% 1.81/0.55 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', sepSubset)).
% 1.81/0.55 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.9ji6MKpz7n/E---3.1_2901106.p', kpairiskpair)).
% 1.81/0.55 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', kpairp)).
% 1.81/0.55 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setextAx)).
% 1.81/0.55 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', emptysetAx)).
% 1.81/0.55 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setadjoinAx)).
% 1.81/0.55 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', powersetAx)).
% 1.81/0.55 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setunionAx)).
% 1.81/0.55 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', omega0Ax)).
% 1.81/0.55 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', omegaSAx)).
% 1.81/0.55 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', omegaIndAx)).
% 1.81/0.55 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', foundationAx)).
% 1.81/0.55 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.9ji6MKpz7n/E---3.1_2901106.p', wellorderingAx)).
% 1.81/0.55 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', prop2setE)).
% 1.81/0.55 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', emptysetE)).
% 1.81/0.55 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', emptysetimpfalse)).
% 1.81/0.55 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', notinemptyset)).
% 1.81/0.55 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setext)).
% 1.81/0.55 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', emptyI)).
% 1.81/0.55 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', noeltsimpempty)).
% 1.81/0.55 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setadjoinIL)).
% 1.81/0.55 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', emptyinunitempty)).
% 1.81/0.55 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setadjoinIR)).
% 1.81/0.55 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.9ji6MKpz7n/E---3.1_2901106.p', setadjoinE)).
% 1.81/0.55 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setadjoinOr)).
% 1.81/0.55 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', powersetI)).
% 1.81/0.55 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', emptyinPowerset)).
% 1.81/0.55 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', emptyInPowerset)).
% 1.81/0.55 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', powersetE)).
% 1.81/0.55 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setunionI)).
% 1.81/0.55 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.9ji6MKpz7n/E---3.1_2901106.p', setunionE)).
% 1.81/0.55 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', subPowSU)).
% 1.81/0.55 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', uniqinunit)).
% 1.81/0.55 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', notinsingleton)).
% 1.81/0.55 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', eqinunit)).
% 1.81/0.55 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', singletonsswitch)).
% 1.81/0.55 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', upairsetE)).
% 1.81/0.55 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', upairsetIL)).
% 1.81/0.55 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', upairsetIR)).
% 1.81/0.55 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', vacuousDall)).
% 1.81/0.55 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', quantDeMorgan1)).
% 1.81/0.55 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', quantDeMorgan2)).
% 1.81/0.55 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', quantDeMorgan3)).
% 1.81/0.55 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', quantDeMorgan4)).
% 1.81/0.55 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', prop2setI)).
% 1.81/0.55 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', prop2set2propI)).
% 1.81/0.55 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', notdexE)).
% 1.81/0.55 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', notdallE)).
% 1.81/0.55 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', inCongP)).
% 1.81/0.55 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', in__Cong)).
% 1.81/0.55 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', emptyset__Cong)).
% 1.81/0.55 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setadjoin__Cong)).
% 1.81/0.55 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', powerset__Cong)).
% 1.81/0.55 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setunion__Cong)).
% 1.81/0.55 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', omega__Cong)).
% 1.81/0.55 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', subsetI1)).
% 1.81/0.55 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', eqimpsubset2)).
% 1.81/0.55 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', eqimpsubset1)).
% 1.81/0.55 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', subsetI2)).
% 1.81/0.55 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', emptysetsubset)).
% 1.81/0.55 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', subsetE)).
% 1.81/0.55 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', subsetE2)).
% 1.81/0.55 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', notsubsetI)).
% 1.81/0.55 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', notequalI1)).
% 1.81/0.55 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', notequalI2)).
% 1.81/0.55 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', subsetRefl)).
% 1.81/0.55 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', subsetTrans)).
% 1.81/0.55 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setadjoinSub)).
% 1.81/0.55 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setadjoinSub2)).
% 1.81/0.55 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', subset2powerset)).
% 1.81/0.55 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setextsub)).
% 1.81/0.55 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', subsetemptysetimpeq)).
% 1.81/0.55 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', powersetI1)).
% 1.81/0.55 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', powersetE1)).
% 1.81/0.55 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', inPowerset)).
% 1.81/0.55 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', powersetsubset)).
% 1.81/0.55 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', binunionIL)).
% 1.81/0.55 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', upairset2IR)).
% 1.81/0.55 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', binunionIR)).
% 1.81/0.55 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', binunionEcases)).
% 1.81/0.55 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', binunionE)).
% 1.81/0.55 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', binunionLsub)).
% 1.81/0.55 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', binunionRsub)).
% 1.81/0.55 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', binintersectI)).
% 1.81/0.55 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', binintersectSubset5)).
% 1.81/0.55 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', binintersectEL)).
% 1.81/0.55 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', binintersectLsub)).
% 1.81/0.55 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', binintersectSubset2)).
% 1.81/0.55 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', binintersectSubset3)).
% 1.81/0.55 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', binintersectER)).
% 1.81/0.55 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', disjointsetsI1)).
% 1.81/0.55 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', binintersectRsub)).
% 1.81/0.55 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', binintersectSubset4)).
% 1.81/0.55 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', binintersectSubset1)).
% 1.81/0.55 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', bs114d)).
% 1.81/0.55 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setminusI)).
% 1.81/0.55 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setminusEL)).
% 1.81/0.55 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setminusER)).
% 1.81/0.55 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setminusSubset2)).
% 1.81/0.55 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setminusERneg)).
% 1.81/0.55 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setminusELneg)).
% 1.81/0.55 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setminusILneg)).
% 1.81/0.55 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setminusIRneg)).
% 1.81/0.55 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setminusLsub)).
% 1.81/0.55 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setminusSubset1)).
% 1.81/0.55 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', symdiffE)).
% 1.81/0.55 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', symdiffI1)).
% 1.81/0.55 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', symdiffI2)).
% 1.81/0.55 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', symdiffIneg1)).
% 1.81/0.55 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', symdiffIneg2)).
% 1.81/0.55 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', secondinupair)).
% 1.81/0.55 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setukpairIL)).
% 1.81/0.55 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.9ji6MKpz7n/E---3.1_2901106.p', setukpairIR)).
% 1.81/0.55 thf(c_0_141, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 1.81/0.55 thf(c_0_142, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 1.81/0.55 thf(c_0_143, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 1.81/0.55 thf(c_0_144, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 1.81/0.55 thf(c_0_145, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 1.81/0.55 thf(c_0_146, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 1.81/0.55 thf(c_0_147, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 1.81/0.55 thf(c_0_148, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 1.81/0.55 thf(c_0_149, 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])).
% 1.81/0.55 thf(c_0_150, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 1.81/0.55 thf(c_0_151, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 1.81/0.55 thf(c_0_152, 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])).
% 1.81/0.55 thf(c_0_153, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 1.81/0.55 thf(c_0_154, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 1.81/0.55 thf(c_0_155, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 1.81/0.55 thf(c_0_156, plain, ((iskpair)=(^[Z0:$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])).
% 1.81/0.55 thf(c_0_157, 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])).
% 1.81/0.55 thf(c_0_158, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X387:$i]:(((((X6 @ X2 @ X387)))&(![X388:$i]:(((((X6 @ X2 @ X388)))=>(((X387)=(X388)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_141, c_0_142])).
% 1.81/0.55 thf(c_0_159, plain, ((descrp)=(![X1:$i > $o]:((((?[X389:$i]:(((((X1 @ X389)))&(![X390:$i]:(((((X1 @ X390)))=>(((X389)=(X390))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_143, c_0_142])).
% 1.81/0.55 thf(c_0_160, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 1.81/0.55 thf(c_0_161, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 1.81/0.55 thf(c_0_162, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 1.81/0.55 thf(c_0_163, plain, ((exuE1)=(![X1:$i > $o]:((((?[X391:$i]:(((((X1 @ X391)))&(![X392:$i]:(((((X1 @ X392)))=>(((X391)=(X392))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_144, c_0_142])).
% 1.81/0.55 thf(c_0_164, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X393:$i]:(((((X1 @ X393)))&(![X394:$i]:(((((X1 @ X394)))=>(((X393)=(X394))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_145, c_0_142])).
% 1.81/0.55 thf(c_0_165, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 1.81/0.55 thf(c_0_166, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_146])).
% 1.81/0.55 thf(c_0_167, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_147, c_0_146])).
% 1.81/0.55 thf(c_0_168, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_146])).
% 1.81/0.55 thf(c_0_169, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 1.81/0.55 thf(c_0_170, plain, ((exuE2)=(![X1:$i > $o]:((((?[X395:$i]:(((((X1 @ X395)))&(![X396:$i]:(((((X1 @ X396)))=>(((X395)=(X396))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_148, c_0_142])).
% 1.81/0.55 thf(c_0_171, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_146])).
% 1.81/0.55 thf(c_0_172, 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])).
% 1.81/0.55 thf(c_0_173, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X397:$i]:(((((X1 @ X397)))&(![X398:$i]:(((((X1 @ X398)))=>(((X397)=(X398)))))))))))))), inference(apply_def,[status(thm)],[c_0_149, c_0_142])).
% 1.81/0.55 thf(c_0_174, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X399:$i]:(((((X1 @ X399)))&(![X400:$i]:(((((X1 @ X400)))=>(((X399)=(X400)))))))))))))))), inference(apply_def,[status(thm)],[c_0_150, c_0_142])).
% 1.81/0.55 thf(c_0_175, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X401:$i]:(((((X1 @ X401)))&(![X402:$i]:(((((X1 @ X402)))=>(((X401)=(X402)))))))))))))), inference(apply_def,[status(thm)],[c_0_151, c_0_142])).
% 1.81/0.55 thf(c_0_176, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X403:$i]:(((((X1 @ X403)))&(![X404:$i]:(((((X1 @ X404)))=>(((X403)=(X404))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_152, c_0_142])).
% 1.81/0.55 thf(c_0_177, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X405:$i]:(((((X1 @ X405)))&(![X406:$i]:(((((X1 @ X406)))=>(((X405)=(X406))))))))))<=>((?[X407:$i]:(((((X17 @ X407)))&(![X408:$i]:(((((X17 @ X408)))=>(((X407)=(X408)))))))))))))))), inference(apply_def,[status(thm)],[c_0_153, c_0_142])).
% 1.81/0.55 thf(c_0_178, plain, ((exuEu)=(![X1:$i > $o]:((((?[X409:$i]:(((((X1 @ X409)))&(![X410:$i]:(((((X1 @ X410)))=>(((X409)=(X410))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_154, c_0_142])).
% 1.81/0.55 thf(c_0_179, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X411:$i]:(((((X1 @ X411)))&(![X412:$i]:(((((X1 @ X412)))=>(((X411)=(X412))))))))))=>((((?[X413:$i]:(((((X17 @ X413)))&(![X414:$i]:(((((X17 @ X414)))=>(((X413)=(X414))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_155, c_0_142])).
% 1.81/0.55 thf(c_0_180, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 1.81/0.55 thf(c_0_181, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 1.81/0.55 thf(c_0_182, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 1.81/0.55 thf(c_0_183, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X415:$i]:((((in @ X415 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))&(?[X416:$i]:((((in @ X416 @ (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 @ X415 @ emptyset) @ (setadjoin @ (setadjoin @ X415 @ (setadjoin @ X416 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_156])).
% 1.81/0.55 thf(c_0_184, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X417:$i]:((((in @ X417 @ (setunion @ (kpair @ X2 @ X3))))&(?[X418:$i]:((((in @ X418 @ (setunion @ (kpair @ X2 @ X3))))&(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X417 @ emptyset) @ (setadjoin @ (setadjoin @ X417 @ (setadjoin @ X418 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairp, c_0_156])).
% 1.81/0.55 thf(c_0_185, plain, ((epred1_0)<=>![X448:$i]:(?[X449:$i]:((((![X450:$i]:(((in @ X450 @ X449)=>![X451:$i]:(((in @ X451 @ X450)=>(in @ X451 @ X448)))))&![X452:$i, X453:$i]:((((in @ X452 @ X448)&(in @ X453 @ X448))=>(![X454:$i]:(((in @ X454 @ X449)=>((in @ X452 @ X454)<=>(in @ X453 @ X454))))=>((X452)=(X453))))))&![X455:$i, X456:$i]:((((in @ X455 @ X449)&(in @ X456 @ X449))=>(![X457:$i]:(((in @ X457 @ X455)=>(in @ X457 @ X456)))|![X458:$i]:(((in @ X458 @ X456)=>(in @ X458 @ X455)))))))&![X459:$i]:(((![X460:$i]:(((in @ X460 @ X459)=>(in @ X460 @ X448)))&?[X461:$i]:((in @ X461 @ X459)))=>?[X462:$i, X463:$i]:(((((in @ X462 @ X449)&(in @ X463 @ X459))&~(?[X464:$i]:(((in @ X464 @ X462)&(in @ X464 @ X459)))))&![X465:$i]:(((in @ X465 @ X449)=>(![X466:$i]:(((in @ X466 @ X465)=>(in @ X466 @ X462)))|(in @ X463 @ X465)))))))))))), introduced(definition)).
% 1.81/0.55 thf(c_0_186, negated_conjecture, ~((![X419:$i, X420:$i]:((![X421:$i]:(((in @ X421 @ X419)<=>(in @ X421 @ X420)))=>((X419)=(X420))))=>(![X422:$i]:(~(in @ X422 @ emptyset))=>(![X423:$i, X424:$i, X425:$i]:(((in @ X425 @ (setadjoin @ X423 @ X424))<=>(((X425)=(X423))|(in @ X425 @ X424))))=>(![X426:$i, X427:$i]:(((in @ X427 @ (powerset @ X426))<=>![X428:$i]:(((in @ X428 @ X427)=>(in @ X428 @ X426)))))=>(![X429:$i, X430:$i]:(((in @ X430 @ (setunion @ X429))<=>?[X431:$i]:(((in @ X430 @ X431)&(in @ X431 @ X429)))))=>((in @ emptyset @ omega)=>(![X432:$i]:(((in @ X432 @ omega)=>(in @ (setadjoin @ X432 @ X432) @ omega)))=>(![X433:$i]:((((in @ emptyset @ X433)&![X434:$i]:((((in @ X434 @ omega)&(in @ X434 @ X433))=>(in @ (setadjoin @ X434 @ X434) @ X433))))=>![X435:$i]:(((in @ X435 @ omega)=>(in @ X435 @ X433)))))=>(![X436:$i > $i > $o, X437:$i]:((![X438:$i]:(((in @ X438 @ X437)=>?[X439:$i]:(((X436 @ X438 @ X439)&![X440:$i]:(((X436 @ X438 @ X440)=>((X439)=(X440))))))))=>?[X441:$i]:(![X442:$i]:(((in @ X442 @ X441)<=>?[X443:$i]:(((in @ X443 @ X437)&(X436 @ X443 @ X442))))))))=>(![X444:$i]:((?[X445:$i]:((in @ X445 @ X444))=>?[X446:$i]:(((in @ X446 @ X444)&~(?[X447:$i]:(((in @ X447 @ X446)&(in @ X447 @ X444))))))))=>((epred1_0)=>(![X467:$i > $o]:((?[X468:$i]:(((X467 @ X468)&![X469:$i]:(((X467 @ X469)=>((X468)=(X469))))))=>(X467 @ (descr @ (^[Z0:$i]:(X467 @ Z0))))))=>(![X470:$i, X471:$i > $o, X472:$i]:(((in @ X472 @ X470)=>((X471 @ X472)=>(in @ X472 @ (dsetconstr @ X470 @ X471)))))=>(![X473:$i, X474:$i > $o, X475:$i]:(((in @ X475 @ (dsetconstr @ X473 @ X474))=>(in @ X475 @ X473)))=>(![X476:$i, X477:$i > $o, X478:$i]:(((in @ X478 @ (dsetconstr @ X476 @ X477))=>(X477 @ X478)))=>(![X479:$i > $o]:((?[X480:$i]:(((X479 @ X480)&![X481:$i]:(((X479 @ X481)=>((X480)=(X481))))))=>?[X482:$i]:(((X479 @ X482)&![X483:$i]:(((X479 @ X483)=>((X482)=(X483))))))))=>(![X484:$o, X485:$i]:(((in @ X485 @ (prop2set @ ((X484))))=>(X484)))=>(![X486:$i]:(((in @ X486 @ emptyset)=>![X487:$o]:((X487))))=>(![X488:$i]:(((in @ X488 @ emptyset)=>~($true)))=>(![X489:$i]:(~(in @ X489 @ emptyset))=>(![X490:$i > $o]:((?[X491:$i]:(((X490 @ X491)&![X492:$i]:(((X490 @ X492)=>((X491)=(X492))))))=>?[X493:$i]:((X490 @ X493))))=>(![X494:$i, X495:$i]:((![X496:$i]:(((in @ X496 @ X494)=>(in @ X496 @ X495)))=>(![X497:$i]:(((in @ X497 @ X495)=>(in @ X497 @ X494)))=>((X494)=(X495)))))=>(![X498:$i]:((![X499:$i]:(~(in @ X499 @ X498))=>((X498)=(emptyset))))=>(![X500:$i]:((![X501:$i]:(~(in @ X501 @ X500))=>((X500)=(emptyset))))=>(![X502:$i, X503:$i > $o, X504:$i]:(((in @ X504 @ X502)=>((in @ X504 @ (dsetconstr @ X502 @ X503))<=>(X503 @ X504))))=>(![X505:$i]:((((X505)!=(emptyset))=>?[X506:$i]:((in @ X506 @ X505))))=>(![X507:$i, X508:$i > $o, X509:$i]:(((in @ X509 @ X507)=>((X508 @ X509)=>((dsetconstr @ X507 @ X508)!=(emptyset)))))=>(![X510:$i]:((?[X511:$i]:((in @ X511 @ X510))=>((X510)!=(emptyset))))=>(![X512:$i, X513:$i]:((in @ X512 @ (setadjoin @ X512 @ X513)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X514:$i, X515:$i, X516:$i]:(((in @ X516 @ X515)=>(in @ X516 @ (setadjoin @ X514 @ X515))))=>(![X517:$i, X518:$i, X519:$i]:(((in @ X519 @ (setadjoin @ X517 @ X518))=>![X520:$o]:(((((X519)=(X517))=>(X520))=>(((in @ X519 @ X518)=>(X520))=>(X520))))))=>(![X521:$i, X522:$i, X523:$i]:(((in @ X523 @ (setadjoin @ X521 @ X522))=>(((X523)=(X521))|(in @ X523 @ X522))))=>(![X524:$i]:(((dsetconstr @ X524 @ (^[Z0:$i]:($true)))=(X524)))=>(![X525:$i, X526:$i]:((![X527:$i]:(((in @ X527 @ X526)=>(in @ X527 @ X525)))=>(in @ X526 @ (powerset @ X525))))=>(![X528:$i]:((in @ emptyset @ (powerset @ X528)))=>(![X529:$i]:((in @ emptyset @ (powerset @ X529)))=>(![X530:$i, X531:$i, X532:$i]:(((in @ X531 @ (powerset @ X530))=>((in @ X532 @ X531)=>(in @ X532 @ X530))))=>(![X533:$i, X534:$i, X535:$i]:(((in @ X534 @ X535)=>((in @ X535 @ X533)=>(in @ X534 @ (setunion @ X533)))))=>(![X536:$i, X537:$i]:(((in @ X537 @ (setunion @ X536))=>![X538:$o]:((![X539:$i]:(((in @ X537 @ X539)=>((in @ X539 @ X536)=>(X538))))=>(X538)))))=>(![X540:$i, X541:$i]:(((in @ X541 @ X540)=>(in @ X541 @ (powerset @ (setunion @ X540)))))=>(![X542:$i > $o]:((?[X543:$i]:(((X542 @ X543)&![X544:$i]:(((X542 @ X544)=>((X543)=(X544))))))=>?[X545:$i]:(![X546:$i]:(((X542 @ X546)<=>((X546)=(X545)))))))=>(![X547:$i]:((((X547)!=(emptyset))=>?[X548:$i]:(((in @ X548 @ X547)&$true))))=>(![X549:$i, X550:$i]:(((in @ X549 @ (setadjoin @ X550 @ emptyset))=>((X549)=(X550))))=>(![X551:$i, X552:$i]:((((X551)!=(X552))=>~(in @ X552 @ (setadjoin @ X551 @ emptyset))))=>(![X553:$i, X554:$i]:((((X553)=(X554))=>(in @ X553 @ (setadjoin @ X554 @ emptyset))))=>(![X555:$i, X556:$i]:(((in @ X555 @ (setadjoin @ X556 @ emptyset))=>(in @ X556 @ (setadjoin @ X555 @ emptyset))))=>(![X557:$i, X558:$i, X559:$i]:(((in @ X559 @ (setadjoin @ X557 @ (setadjoin @ X558 @ emptyset)))=>(((X559)=(X557))|((X559)=(X558)))))=>(![X560:$i, X561:$i]:((in @ X560 @ (setadjoin @ X560 @ (setadjoin @ X561 @ emptyset))))=>(![X562:$i, X563:$i]:((in @ X563 @ (setadjoin @ X562 @ (setadjoin @ X563 @ emptyset))))=>(![X564:$i, X565:$i > $o]:((?[X566:$i]:(((in @ X566 @ X564)&(X565 @ X566)))=>(((dsetconstr @ X564 @ X565)=(emptyset))=>~($true))))=>(![X567:$i > $o, X568:$i]:(((in @ X568 @ emptyset)=>(X567 @ X568)))=>(![X569:$i, X570:$i > $o]:((~(![X571:$i]:(((in @ X571 @ X569)=>(X570 @ X571))))=>?[X572:$i]:(((in @ X572 @ X569)&~((X570 @ X572))))))=>(![X573:$i, X574:$i > $o]:((![X575:$i]:(((in @ X575 @ X573)=>~((X574 @ X575))))=>~(?[X576:$i]:(((in @ X576 @ X573)&(X574 @ X576))))))=>(![X577:$i, X578:$i > $o]:((~(?[X579:$i]:(((in @ X579 @ X577)&(X578 @ X579))))=>![X580:$i]:(((in @ X580 @ X577)=>~((X578 @ X580))))))=>(![X581:$i, X582:$i > $o]:((?[X583:$i]:(((in @ X583 @ X581)&~((X582 @ X583))))=>~(![X584:$i]:(((in @ X584 @ X581)=>(X582 @ X584))))))=>(![X585:$o]:(((X585)=>(in @ emptyset @ (prop2set @ ((X585))))))=>(![X586:$o]:(((X586)=>(set2prop @ (prop2set @ ((X586))))))=>(![X587:$i, X588:$i > $o]:((~(?[X589:$i]:(((in @ X589 @ X587)&(X588 @ X589))))=>![X590:$i]:(((in @ X590 @ X587)=>~((X588 @ X590))))))=>(![X591:$i, X592:$i > $o]:((~(![X593:$i]:(((in @ X593 @ X591)=>(X592 @ X593))))=>?[X594:$i]:(((in @ X594 @ X591)&~((X592 @ X594))))))=>(![X595:$i > $o]:((?[X596:$i]:(((X595 @ X596)&![X597:$i]:(((X595 @ X597)=>((X596)=(X597))))))=>?[X598:$i]:(((X595 @ X598)&![X599:$i]:(((X595 @ X599)=>((X598)=(X599))))))))=>(![X600:$i > $o]:((?[X601:$i]:((X600 @ X601))=>(![X602:$i, X603:$i]:(((X600 @ X602)=>((X600 @ X603)=>((X602)=(X603)))))=>?[X604:$i]:(((X600 @ X604)&![X605:$i]:(((X600 @ X605)=>((X604)=(X605)))))))))=>(![X606:$i > $o]:((?[X607:$i]:(![X608:$i]:(((X606 @ X608)<=>((X608)=(X607)))))=>?[X609:$i]:(((X606 @ X609)&![X610:$i]:(((X606 @ X610)=>((X609)=(X610))))))))=>(![X611:$i, X612:$i]:((((X611)=(X612))=>![X613:$i, X614:$i]:((((X613)=(X614))=>((in @ X613 @ X611)=>(in @ X614 @ X612))))))=>(![X615:$i, X616:$i]:((((X615)=(X616))=>![X617:$i, X618:$i]:((((X617)=(X618))=>((in @ X617 @ X615)<=>(in @ X618 @ X616))))))=>(![X619:$i > $o]:((?[X620:$i]:(((X619 @ X620)&![X621:$i]:(((X619 @ X621)=>((X620)=(X621))))))=>![X622:$i, X623:$i]:(((X619 @ X622)=>((X619 @ X623)=>((X622)=(X623)))))))=>(![X624:$i > $o, X625:$i > $o]:((![X626:$i, X627:$i]:((((X626)=(X627))=>((X624 @ X626)<=>(X625 @ X627))))=>(?[X628:$i]:(((X624 @ X628)&![X629:$i]:(((X624 @ X629)=>((X628)=(X629))))))<=>?[X630:$i]:(((X625 @ X630)&![X631:$i]:(((X625 @ X631)=>((X630)=(X631)))))))))=>(((emptyset)=(emptyset))=>(![X632:$i, X633:$i]:((((X632)=(X633))=>![X634:$i, X635:$i]:((((X634)=(X635))=>((setadjoin @ X632 @ X634)=(setadjoin @ X633 @ X635))))))=>(![X636:$i, X637:$i]:((((X636)=(X637))=>((powerset @ X636)=(powerset @ X637))))=>(![X638:$i, X639:$i]:((((X638)=(X639))=>((setunion @ X638)=(setunion @ X639))))=>(((omega)=(omega))=>(![X640:$i > $o]:((?[X641:$i]:(((X640 @ X641)&![X642:$i]:(((X640 @ X642)=>((X641)=(X642))))))=>![X643:$i, X644:$i]:(((X640 @ X643)=>((X640 @ X644)=>((X643)=(X644)))))))=>(![X645:$i > $o, X646:$i > $o]:((![X647:$i, X648:$i]:((((X647)=(X648))=>((X645 @ X647)<=>(X646 @ X648))))=>(?[X649:$i]:(((X645 @ X649)&![X650:$i]:(((X645 @ X650)=>((X649)=(X650))))))=>(?[X651:$i]:(((X646 @ X651)&![X652:$i]:(((X646 @ X652)=>((X651)=(X652))))))=>((descr @ X645)=(descr @ X646))))))=>(![X653:$i, X654:$i]:((((X653)=(X654))=>![X655:$i > $o, X656:$i > $o]:((![X657:$i]:(((in @ X657 @ X653)=>![X658:$i]:(((in @ X658 @ X654)=>(((X657)=(X658))=>((X655 @ X657)<=>(X656 @ X658)))))))=>((dsetconstr @ X653 @ X655)=(dsetconstr @ X654 @ X656))))))=>(![X659:$i, X660:$i]:((![X661:$i]:(((in @ X661 @ X659)=>(in @ X661 @ X660)))=>(subset @ X659 @ X660)))=>(![X662:$i, X663:$i]:((((X662)=(X663))=>(subset @ X663 @ X662)))=>(![X664:$i, X665:$i]:((((X664)=(X665))=>(subset @ X664 @ X665)))=>(![X666:$i, X667:$i]:((![X668:$i]:(((in @ X668 @ X666)=>(in @ X668 @ X667)))=>(subset @ X666 @ X667)))=>(![X669:$i]:((subset @ emptyset @ X669))=>(![X670:$i, X671:$i, X672:$i]:(((subset @ X670 @ X671)=>((in @ X672 @ X670)=>(in @ X672 @ X671))))=>(![X673:$i, X674:$i, X675:$i]:(((subset @ X673 @ X674)=>(~(in @ X675 @ X674)=>~(in @ X675 @ X673))))=>(![X676:$i, X677:$i, X678:$i]:(((in @ X678 @ X676)=>(~(in @ X678 @ X677)=>~(subset @ X676 @ X677))))=>(![X679:$i, X680:$i]:((~(subset @ X679 @ X680)=>((X679)!=(X680))))=>(![X681:$i, X682:$i, X683:$i]:(((in @ X683 @ X681)=>(~(in @ X683 @ X682)=>((X681)!=(X682)))))=>(![X684:$i]:((subset @ X684 @ X684))=>(![X685:$i, X686:$i, X687:$i]:(((subset @ X685 @ X686)=>((subset @ X686 @ X687)=>(subset @ X685 @ X687))))=>(![X688:$i, X689:$i]:((subset @ X689 @ (setadjoin @ X688 @ X689)))=>(![X690:$i, X691:$i, X692:$i]:(((subset @ X690 @ X692)=>(subset @ X690 @ (setadjoin @ X691 @ X692))))=>(![X693:$i, X694:$i]:(((subset @ X693 @ X694)=>(in @ X693 @ (powerset @ X694))))=>(![X695:$i, X696:$i]:(((subset @ X695 @ X696)=>((subset @ X696 @ X695)=>((X695)=(X696)))))=>(![X697:$i]:(((subset @ X697 @ emptyset)=>((X697)=(emptyset))))=>(![X698:$i, X699:$i]:(((subset @ X699 @ X698)=>(in @ X699 @ (powerset @ X698))))=>(![X700:$i, X701:$i]:(((in @ X701 @ (powerset @ X700))=>(subset @ X701 @ X700)))=>(![X702:$i]:((in @ X702 @ (powerset @ X702)))=>(![X703:$i, X704:$i]:(((subset @ X703 @ X704)=>(subset @ (powerset @ X703) @ (powerset @ X704))))=>(![X705:$i, X706:$i > $o]:((in @ (dsetconstr @ X705 @ X706) @ (powerset @ X705)))=>(![X707:$i, X708:$i > $o]:((subset @ (dsetconstr @ X707 @ X708) @ X707))=>(![X709:$i, X710:$i, X711:$i]:(((in @ X711 @ X709)=>(in @ X711 @ (binunion @ X709 @ X710))))=>(![X712:$i, X713:$i]:((in @ X713 @ (setadjoin @ X712 @ (setadjoin @ X713 @ emptyset))))=>(![X714:$i, X715:$i, X716:$i]:(((in @ X716 @ X715)=>(in @ X716 @ (binunion @ X714 @ X715))))=>(![X717:$i, X718:$i, X719:$i, X720:$o]:(((in @ X719 @ (binunion @ X717 @ X718))=>(((in @ X719 @ X717)=>(X720))=>(((in @ X719 @ X718)=>(X720))=>(X720)))))=>(![X721:$i, X722:$i, X723:$i]:(((in @ X723 @ (binunion @ X721 @ X722))=>((in @ X723 @ X721)|(in @ X723 @ X722))))=>(![X724:$i, X725:$i]:((subset @ X724 @ (binunion @ X724 @ X725)))=>(![X726:$i, X727:$i]:((subset @ X727 @ (binunion @ X726 @ X727)))=>(![X728:$i, X729:$i, X730:$i]:(((in @ X730 @ X728)=>((in @ X730 @ X729)=>(in @ X730 @ (binintersect @ X728 @ X729)))))=>(![X731:$i, X732:$i, X733:$i]:(((subset @ X733 @ X731)=>((subset @ X733 @ X732)=>(subset @ X733 @ (binintersect @ X731 @ X732)))))=>(![X734:$i, X735:$i, X736:$i]:(((in @ X736 @ (binintersect @ X734 @ X735))=>(in @ X736 @ X734)))=>(![X737:$i, X738:$i]:((subset @ (binintersect @ X737 @ X738) @ X737))=>(![X739:$i, X740:$i]:(((subset @ X739 @ X740)=>((binintersect @ X739 @ X740)=(X739))))=>(![X741:$i, X742:$i]:((((binintersect @ X741 @ X742)=(X742))=>(subset @ X742 @ X741)))=>(![X743:$i, X744:$i, X745:$i]:(((in @ X745 @ (binintersect @ X743 @ X744))=>(in @ X745 @ X744)))=>(![X746:$i, X747:$i]:((~(?[X748:$i]:(((in @ X748 @ X746)&(in @ X748 @ X747))))=>((binintersect @ X746 @ X747)=(emptyset))))=>(![X749:$i, X750:$i]:((subset @ (binintersect @ X749 @ X750) @ X750))=>(![X751:$i, X752:$i]:(((subset @ X752 @ X751)=>((binintersect @ X751 @ X752)=(X752))))=>(![X753:$i, X754:$i]:((((binintersect @ X753 @ X754)=(X753))=>(subset @ X753 @ X754)))=>(![X755:$i, X756:$i, X757:$i]:(((binintersect @ X755 @ (binunion @ X756 @ X757))=(binunion @ (binintersect @ X755 @ X756) @ (binintersect @ X755 @ X757))))=>(![X758:$i, X759:$i, X760:$i]:(((in @ X760 @ X758)=>(~(in @ X760 @ X759)=>(in @ X760 @ (setminus @ X758 @ X759)))))=>(![X761:$i, X762:$i, X763:$i]:(((in @ X763 @ (setminus @ X761 @ X762))=>(in @ X763 @ X761)))=>(![X764:$i, X765:$i, X766:$i]:(((in @ X766 @ (setminus @ X764 @ X765))=>~(in @ X766 @ X765)))=>(![X767:$i, X768:$i]:(((subset @ X767 @ X768)=>((setminus @ X767 @ X768)=(emptyset))))=>(![X769:$i, X770:$i, X771:$i]:((~(in @ X771 @ (setminus @ X769 @ X770))=>((in @ X771 @ X769)=>(in @ X771 @ X770))))=>(![X772:$i, X773:$i, X774:$i]:((~(in @ X774 @ (setminus @ X772 @ X773))=>(~(in @ X774 @ X773)=>~(in @ X774 @ X772))))=>(![X775:$i, X776:$i, X777:$i]:((~(in @ X777 @ X775)=>~(in @ X777 @ (setminus @ X775 @ X776))))=>(![X778:$i, X779:$i, X780:$i]:(((in @ X780 @ X779)=>~(in @ X780 @ (setminus @ X778 @ X779))))=>(![X781:$i, X782:$i]:((subset @ (setminus @ X781 @ X782) @ X781))=>(![X783:$i, X784:$i]:((((setminus @ X783 @ X784)=(emptyset))=>(subset @ X783 @ X784)))=>(![X785:$i, X786:$i, X787:$i]:(((in @ X787 @ (symdiff @ X785 @ X786))=>![X788:$o]:((((in @ X787 @ X785)=>(~(in @ X787 @ X786)=>(X788)))=>((~(in @ X787 @ X785)=>((in @ X787 @ X786)=>(X788)))=>(X788))))))=>(![X789:$i, X790:$i, X791:$i]:(((in @ X791 @ X789)=>(~(in @ X791 @ X790)=>(in @ X791 @ (symdiff @ X789 @ X790)))))=>(![X792:$i, X793:$i, X794:$i]:((~(in @ X794 @ X792)=>((in @ X794 @ X793)=>(in @ X794 @ (symdiff @ X792 @ X793)))))=>(![X795:$i, X796:$i, X797:$i]:(((in @ X797 @ X795)=>((in @ X797 @ X796)=>~(in @ X797 @ (symdiff @ X795 @ X796)))))=>(![X798:$i, X799:$i, X800:$i]:((~(in @ X800 @ X798)=>(~(in @ X800 @ X799)=>~(in @ X800 @ (symdiff @ X798 @ X799)))))=>(![X801:$i, X802:$i]:((in @ X802 @ (setadjoin @ X801 @ (setadjoin @ X802 @ emptyset))))=>(![X803:$i, X804:$i]:((in @ X803 @ (setunion @ (setadjoin @ (setadjoin @ X803 @ emptyset) @ (setadjoin @ (setadjoin @ X803 @ (setadjoin @ X804 @ emptyset)) @ emptyset)))))=>(![X805:$i, X806:$i]:((in @ X806 @ (setunion @ (setadjoin @ (setadjoin @ X805 @ emptyset) @ (setadjoin @ (setadjoin @ X805 @ (setadjoin @ X806 @ emptyset)) @ emptyset)))))=>(![X807:$i, X808:$i]:(?[X809:$i]:(((in @ X809 @ (setunion @ (setadjoin @ (setadjoin @ X807 @ emptyset) @ (setadjoin @ (setadjoin @ X807 @ (setadjoin @ X808 @ emptyset)) @ emptyset))))&?[X810:$i]:(((in @ X810 @ (setunion @ (setadjoin @ (setadjoin @ X807 @ emptyset) @ (setadjoin @ (setadjoin @ X807 @ (setadjoin @ X808 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X807 @ emptyset) @ (setadjoin @ (setadjoin @ X807 @ (setadjoin @ X808 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X809 @ emptyset) @ (setadjoin @ (setadjoin @ X809 @ (setadjoin @ X810 @ emptyset)) @ emptyset))))))))=>(![X811:$i, X812:$i]:(?[X813:$i]:(((in @ X813 @ (setunion @ (kpair @ X811 @ X812)))&?[X814:$i]:(((in @ X814 @ (setunion @ (kpair @ X811 @ X812)))&((kpair @ X811 @ X812)=(setadjoin @ (setadjoin @ X813 @ emptyset) @ (setadjoin @ (setadjoin @ X813 @ (setadjoin @ X814 @ emptyset)) @ emptyset))))))))=>![X4:$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)],[inference(apply_def,[status(thm)],[c_0_157, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_158]), foundationAx]), wellorderingAx]), c_0_159]), c_0_160]), c_0_161]), c_0_162]), c_0_163]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_164]), setext]), emptyI]), noeltsimpempty]), c_0_165]), c_0_166]), c_0_167]), c_0_168]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_169]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_170]), c_0_171]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_172]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_173]), c_0_174]), c_0_175]), inCongP]), in__Cong]), c_0_176]), c_0_177]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_178]), c_0_179]), c_0_180]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_181]), c_0_182]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), c_0_183]), c_0_184])])]), c_0_185])).
% 1.81/0.55 thf(c_0_187, negated_conjecture, ![X823:$i, X824:$i, X826:$i, X827:$i, X828:$i, X829:$i, X830:$i, X831:$i, X832:$i, X833:$i, X834:$i, X836:$i, X837:$i, X839:$i, X840:$i, X841:$i, X842:$i, X843:$i, X845:$i, X846:$i > $i > $o, X847:$i, X849:$i, X852:$i, X854:$i, X855:$i, X856:$i, X857:$i, X859:$i, X860:$i > $o, X861:$i, X863:$i, X864:$i > $o, X865:$i, X866:$i, X867:$i > $o, X868:$i, X869:$i, X870:$i > $o, X871:$i, X872:$i > $o, X873:$i, X876:$i, X877:$o, X878:$i, X879:$i, X880:$o, X881:$i, X882:$i, X883:$i > $o, X884:$i, X887:$i, X888:$i, X891:$i, X893:$i, X895:$i, X896:$i > $o, X897:$i, X898:$i, X900:$i, X901:$i > $o, X902:$i, X903:$i, X904:$i, X905:$i, X906:$i, X907:$i, X908:$i, X909:$i, X910:$i, X911:$i, X912:$i, X913:$o, X914:$i, X915:$i, X916:$i, X917:$i, X918:$i, X919:$i, X921:$i, X922:$i, X923:$i, X924:$i, X925:$i, X926:$i, X927:$i, X928:$i, X929:$i, X930:$i, X931:$o, X933:$i, X934:$i, X935:$i > $o, X936:$i, X939:$i, X940:$i, X941:$i, X943:$i, X944:$i, X945:$i, X946:$i, X947:$i, X948:$i, X949:$i, X950:$i, X951:$i, X952:$i, X953:$i, X954:$i, X955:$i, X956:$i, X957:$i, X958:$i, X959:$i > $o, X960:$i, X961:$i > $o, X962:$i, X963:$i, X964:$i > $o, X965:$i, X967:$i, X968:$i > $o, X970:$i, X971:$i, X972:$i > $o, X974:$i, X975:$i, X976:$i > $o, X977:$i, X979:$o, X980:$o, X981:$i, X982:$i > $o, X984:$i, X985:$i, X986:$i > $o, X987:$i, X989:$i > $o, X990:$i, X993:$i, X994:$i > $o, X995:$i, X999:$i, X1000:$i > $o, X1001:$i, X1004:$i, X1005:$i, X1006:$i, X1007:$i, X1008:$i, X1009:$i, X1010:$i, X1011:$i, X1012:$i, X1013:$i > $o, X1014:$i, X1016:$i, X1017:$i, X1018:$i > $o, X1019:$i > $o, X1022:$i, X1025:$i, X1026:$i, X1029:$i, X1030:$i, X1031:$i, X1032:$i, X1033:$i, X1034:$i, X1035:$i, X1036:$i, X1037:$i, X1038:$i > $o, X1039:$i, X1041:$i, X1042:$i, X1043:$i > $o, X1044:$i > $o, X1047:$i, X1049:$i, X1051:$i, X1052:$i, X1053:$i > $o, X1054:$i > $o, X1057:$i, X1058:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i, X1064:$i, X1065:$i, X1067:$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, X1094:$i, X1095:$i, X1096:$i, X1097:$i, X1098:$i, X1099:$i, X1100:$i, X1101:$i, X1102:$i, X1103:$i, X1104:$i > $o, X1105:$i, X1106:$i > $o, X1107:$i, X1108:$i, X1109:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1114:$i, X1115:$i, X1116:$i, X1117:$i, X1118:$o, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i, X1126:$i, X1127:$i, X1128:$i, X1129:$i, X1130:$i, X1131:$i, X1132:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i, X1147:$i, X1148:$i, X1149:$i, X1150:$i, X1151:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$i, X1162:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$i, X1171:$i, X1172:$i, X1173:$i, X1174:$i, X1175:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1185:$i, X1186:$o, X1187:$i, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i, X1198:$i, X1199:$i, X1200:$i, X1201:$i, X1202:$i, X1203:$i, X1204:$i, X1205:$i, X1206:$i, X1209:$i, X1210:$i]:((((~(in @ (esk1_2 @ X823 @ X824) @ X823)|~(in @ (esk1_2 @ X823 @ X824) @ X824)|((X823)=(X824)))&((in @ (esk1_2 @ X823 @ X824) @ X823)|(in @ (esk1_2 @ X823 @ X824) @ X824)|((X823)=(X824))))&(~(in @ X826 @ emptyset)&(((~(in @ X829 @ (setadjoin @ X827 @ X828))|(((X829)=(X827))|(in @ X829 @ X828)))&((((X829)!=(X827))|(in @ X829 @ (setadjoin @ X827 @ X828)))&(~(in @ X829 @ X828)|(in @ X829 @ (setadjoin @ X827 @ X828)))))&(((~(in @ X831 @ (powerset @ X830))|(~(in @ X832 @ X831)|(in @ X832 @ X830)))&(((in @ (esk2_2 @ X833 @ X834) @ X834)|(in @ X834 @ (powerset @ X833)))&(~(in @ (esk2_2 @ X833 @ X834) @ X833)|(in @ X834 @ (powerset @ X833)))))&(((((in @ X837 @ (esk3_2 @ X836 @ X837))|~(in @ X837 @ (setunion @ X836)))&((in @ (esk3_2 @ X836 @ X837) @ X836)|~(in @ X837 @ (setunion @ X836))))&(~(in @ X840 @ X841)|~(in @ X841 @ X839)|(in @ X840 @ (setunion @ X839))))&((in @ emptyset @ omega)&((~(in @ X842 @ omega)|(in @ (setadjoin @ X842 @ X842) @ omega))&(((((in @ (esk4_1 @ X843) @ omega)|~(in @ emptyset @ X843)|(~(in @ X845 @ omega)|(in @ X845 @ X843)))&((in @ (esk4_1 @ X843) @ X843)|~(in @ emptyset @ X843)|(~(in @ X845 @ omega)|(in @ X845 @ X843))))&(~(in @ (setadjoin @ (esk4_1 @ X843) @ (esk4_1 @ X843)) @ X843)|~(in @ emptyset @ X843)|(~(in @ X845 @ omega)|(in @ X845 @ X843))))&((((((in @ (esk8_3 @ X846 @ X847 @ X852) @ X847)|~(in @ X852 @ (esk7_2 @ X846 @ X847))|(in @ (esk5_2 @ X846 @ X847) @ X847))&((X846 @ (esk8_3 @ X846 @ X847 @ X852) @ X852)|~(in @ X852 @ (esk7_2 @ X846 @ X847))|(in @ (esk5_2 @ X846 @ X847) @ X847)))&(~(in @ X855 @ X847)|~(X846 @ X855 @ X854)|(in @ X854 @ (esk7_2 @ X846 @ X847))|(in @ (esk5_2 @ X846 @ X847) @ X847)))&(((((in @ (esk8_3 @ X846 @ X847 @ X852) @ X847)|~(in @ X852 @ (esk7_2 @ X846 @ X847))|((X846 @ (esk5_2 @ X846 @ X847) @ (esk6_3 @ X846 @ X847 @ X849))|~(X846 @ (esk5_2 @ X846 @ X847) @ X849)))&((X846 @ (esk8_3 @ X846 @ X847 @ X852) @ X852)|~(in @ X852 @ (esk7_2 @ X846 @ X847))|((X846 @ (esk5_2 @ X846 @ X847) @ (esk6_3 @ X846 @ X847 @ X849))|~(X846 @ (esk5_2 @ X846 @ X847) @ X849))))&(~(in @ X855 @ X847)|~(X846 @ X855 @ X854)|(in @ X854 @ (esk7_2 @ X846 @ X847))|((X846 @ (esk5_2 @ X846 @ X847) @ (esk6_3 @ X846 @ X847 @ X849))|~(X846 @ (esk5_2 @ X846 @ X847) @ X849))))&((((in @ (esk8_3 @ X846 @ X847 @ X852) @ X847)|~(in @ X852 @ (esk7_2 @ X846 @ X847))|(((X849)!=(esk6_3 @ X846 @ X847 @ X849))|~(X846 @ (esk5_2 @ X846 @ X847) @ X849)))&((X846 @ (esk8_3 @ X846 @ X847 @ X852) @ X852)|~(in @ X852 @ (esk7_2 @ X846 @ X847))|(((X849)!=(esk6_3 @ X846 @ X847 @ X849))|~(X846 @ (esk5_2 @ X846 @ X847) @ X849))))&(~(in @ X855 @ X847)|~(X846 @ X855 @ X854)|(in @ X854 @ (esk7_2 @ X846 @ X847))|(((X849)!=(esk6_3 @ X846 @ X847 @ X849))|~(X846 @ (esk5_2 @ X846 @ X847) @ X849))))))&((((in @ (esk9_1 @ X856) @ X856)|~(in @ X857 @ X856))&(~(in @ X859 @ (esk9_1 @ X856))|~(in @ X859 @ X856)|~(in @ X857 @ X856)))&((epred1_0)&((((X860 @ (esk10_2 @ X860 @ X861))|~(X860 @ X861)|(X860 @ (descr @ X860)))&(((X861)!=(esk10_2 @ X860 @ X861))|~(X860 @ X861)|(X860 @ (descr @ X860))))&((~(in @ X865 @ X863)|(~(X864 @ X865)|(in @ X865 @ (dsetconstr @ X863 @ X864))))&((~(in @ X868 @ (dsetconstr @ X866 @ X867))|(in @ X868 @ X866))&((~(in @ X871 @ (dsetconstr @ X869 @ X870))|(X870 @ X871))&(((((X872 @ (esk12_1 @ X872))|((X872 @ (esk11_2 @ X872 @ X873))|~(X872 @ X873)))&(~(X872 @ X876)|((esk12_1 @ X872)=(X876))|((X872 @ (esk11_2 @ X872 @ X873))|~(X872 @ X873))))&(((X872 @ (esk12_1 @ X872))|(((X873)!=(esk11_2 @ X872 @ X873))|~(X872 @ X873)))&(~(X872 @ X876)|((esk12_1 @ X872)=(X876))|(((X873)!=(esk11_2 @ X872 @ X873))|~(X872 @ 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X1060))&((((X1062)!=(X1063))|(subset @ X1062 @ X1063))&((((in @ (esk53_2 @ X1064 @ X1065) @ X1064)|(subset @ X1064 @ X1065))&(~(in @ (esk53_2 @ X1064 @ X1065) @ X1065)|(subset @ X1064 @ X1065)))&((subset @ emptyset @ X1067)&((~(subset @ X1068 @ X1069)|(~(in @ X1070 @ X1068)|(in @ X1070 @ X1069)))&((~(subset @ X1071 @ X1072)|((in @ X1073 @ X1072)|~(in @ X1073 @ X1071)))&((~(in @ X1076 @ X1074)|((in @ X1076 @ X1075)|~(subset @ X1074 @ X1075)))&(((subset @ X1077 @ X1078)|((X1077)!=(X1078)))&((~(in @ X1081 @ X1079)|((in @ X1081 @ X1080)|((X1079)!=(X1080))))&((subset @ X1082 @ X1082)&((~(subset @ X1083 @ X1084)|(~(subset @ X1084 @ X1085)|(subset @ X1083 @ X1085)))&((subset @ X1087 @ (setadjoin @ X1086 @ X1087))&((~(subset @ X1088 @ X1090)|(subset @ X1088 @ (setadjoin @ X1089 @ X1090)))&((~(subset @ X1091 @ X1092)|(in @ X1091 @ (powerset @ X1092)))&((~(subset @ X1093 @ X1094)|(~(subset @ X1094 @ X1093)|((X1093)=(X1094))))&((~(subset @ X1095 @ emptyset)|((X1095)=(emptyset)))&((~(subset @ X1097 @ X1096)|(in @ X1097 @ (powerset @ X1096)))&((~(in @ X1099 @ (powerset @ X1098))|(subset @ X1099 @ X1098))&((in @ X1100 @ (powerset @ X1100))&((~(subset @ X1101 @ X1102)|(subset @ (powerset @ X1101) @ (powerset @ X1102)))&((in @ (dsetconstr @ X1103 @ X1104) @ (powerset @ X1103))&((subset @ (dsetconstr @ X1105 @ X1106) @ X1105)&((~(in @ X1109 @ X1107)|(in @ X1109 @ (binunion @ X1107 @ X1108)))&((in @ X1111 @ (setadjoin @ X1110 @ (setadjoin @ X1111 @ emptyset)))&((~(in @ X1114 @ X1113)|(in @ X1114 @ (binunion @ X1112 @ X1113)))&(((((in @ X1117 @ X1116)|(X1118)|(in @ X1117 @ X1115)|~(in @ X1117 @ (binunion @ X1115 @ X1116)))&(~(X1118)|(X1118)|(in @ X1117 @ X1115)|~(in @ X1117 @ (binunion @ X1115 @ X1116))))&(((in @ X1117 @ X1116)|(X1118)|~(X1118)|~(in @ X1117 @ (binunion @ X1115 @ X1116)))&(~(X1118)|(X1118)|~(X1118)|~(in @ X1117 @ (binunion @ X1115 @ X1116)))))&((~(in @ X1121 @ (binunion @ X1119 @ X1120))|((in @ X1121 @ X1119)|(in @ X1121 @ X1120)))&((subset @ X1122 @ (binunion @ X1122 @ X1123))&((subset @ X1125 @ (binunion @ X1124 @ X1125))&((~(in @ X1128 @ X1126)|(~(in @ X1128 @ X1127)|(in @ X1128 @ (binintersect @ X1126 @ X1127))))&((~(subset @ X1131 @ X1129)|(~(subset @ X1131 @ X1130)|(subset @ X1131 @ (binintersect @ X1129 @ X1130))))&((~(in @ X1134 @ (binintersect @ X1132 @ X1133))|(in @ X1134 @ X1132))&((subset @ (binintersect @ X1135 @ X1136) @ X1135)&((~(subset @ X1137 @ X1138)|((binintersect @ X1137 @ X1138)=(X1137)))&((((binintersect @ X1139 @ X1140)!=(X1140))|(subset @ X1140 @ X1139))&((~(in @ X1143 @ (binintersect @ X1141 @ X1142))|(in @ X1143 @ X1142))&((((in @ (esk54_2 @ X1144 @ X1145) @ X1144)|((binintersect @ X1144 @ X1145)=(emptyset)))&((in @ (esk54_2 @ X1144 @ X1145) @ X1145)|((binintersect @ X1144 @ X1145)=(emptyset))))&((subset @ (binintersect @ X1147 @ X1148) @ X1148)&((~(subset @ X1150 @ X1149)|((binintersect @ X1149 @ X1150)=(X1150)))&((((binintersect @ X1151 @ X1152)!=(X1151))|(subset @ X1151 @ X1152))&(((binintersect @ X1153 @ (binunion @ X1154 @ X1155))=(binunion @ (binintersect @ X1153 @ X1154) @ (binintersect @ X1153 @ X1155)))&((~(in @ X1158 @ X1156)|((in @ X1158 @ X1157)|(in @ X1158 @ (setminus @ X1156 @ X1157))))&((~(in @ X1161 @ (setminus @ X1159 @ X1160))|(in @ X1161 @ X1159))&((~(in @ X1164 @ (setminus @ X1162 @ X1163))|~(in @ X1164 @ X1163))&((~(subset @ X1165 @ X1166)|((setminus @ X1165 @ X1166)=(emptyset)))&(((in @ X1169 @ (setminus @ X1167 @ X1168))|(~(in @ X1169 @ X1167)|(in @ X1169 @ X1168)))&(((in @ X1172 @ (setminus @ X1170 @ X1171))|((in @ X1172 @ X1171)|~(in @ X1172 @ X1170)))&(((in @ X1175 @ X1173)|~(in @ X1175 @ (setminus @ X1173 @ X1174)))&((~(in @ X1178 @ X1177)|~(in @ X1178 @ (setminus @ X1176 @ X1177)))&((subset @ (setminus @ X1179 @ X1180) @ X1179)&((((setminus @ X1181 @ X1182)!=(emptyset))|(subset @ X1181 @ X1182))&((((~(in @ X1185 @ X1183)|(X1186)|(in @ X1185 @ X1183)|~(in @ X1185 @ (symdiff @ X1183 @ X1184)))&(((in @ X1185 @ X1184)|(X1186)|(in @ X1185 @ X1183)|~(in @ X1185 @ (symdiff @ X1183 @ X1184)))&(~(X1186)|(X1186)|(in @ X1185 @ X1183)|~(in @ X1185 @ (symdiff @ X1183 @ X1184)))))&(((~(in @ X1185 @ X1183)|(X1186)|~(in @ X1185 @ X1184)|~(in @ X1185 @ (symdiff @ X1183 @ X1184)))&(((in @ X1185 @ X1184)|(X1186)|~(in @ X1185 @ X1184)|~(in @ X1185 @ (symdiff @ X1183 @ X1184)))&(~(X1186)|(X1186)|~(in @ X1185 @ X1184)|~(in @ X1185 @ (symdiff @ X1183 @ X1184)))))&((~(in @ X1185 @ X1183)|(X1186)|~(X1186)|~(in @ X1185 @ (symdiff @ X1183 @ X1184)))&(((in @ X1185 @ X1184)|(X1186)|~(X1186)|~(in @ X1185 @ (symdiff @ X1183 @ X1184)))&(~(X1186)|(X1186)|~(X1186)|~(in @ X1185 @ (symdiff @ X1183 @ X1184)))))))&((~(in @ X1189 @ X1187)|((in @ X1189 @ X1188)|(in @ X1189 @ (symdiff @ X1187 @ X1188))))&(((in @ X1192 @ X1190)|(~(in @ X1192 @ X1191)|(in @ X1192 @ (symdiff @ X1190 @ X1191))))&((~(in @ X1195 @ X1193)|(~(in @ X1195 @ X1194)|~(in @ X1195 @ (symdiff @ X1193 @ X1194))))&(((in @ X1198 @ X1196)|((in @ X1198 @ X1197)|~(in @ X1198 @ (symdiff @ X1196 @ X1197))))&((in @ X1200 @ (setadjoin @ X1199 @ (setadjoin @ X1200 @ emptyset)))&((in @ X1201 @ (setunion @ (setadjoin @ (setadjoin @ X1201 @ emptyset) @ (setadjoin @ (setadjoin @ X1201 @ (setadjoin @ X1202 @ emptyset)) @ emptyset))))&((in @ X1204 @ (setunion @ (setadjoin @ (setadjoin @ X1203 @ emptyset) @ (setadjoin @ (setadjoin @ X1203 @ (setadjoin @ X1204 @ emptyset)) @ emptyset))))&(((in @ (esk55_2 @ X1205 @ X1206) @ (setunion @ (setadjoin @ (setadjoin @ X1205 @ emptyset) @ (setadjoin @ (setadjoin @ X1205 @ (setadjoin @ X1206 @ emptyset)) @ emptyset))))&((in @ (esk56_2 @ X1205 @ X1206) @ (setunion @ (setadjoin @ (setadjoin @ X1205 @ emptyset) @ (setadjoin @ (setadjoin @ X1205 @ (setadjoin @ X1206 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1205 @ emptyset) @ (setadjoin @ (setadjoin @ X1205 @ (setadjoin @ X1206 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk55_2 @ X1205 @ X1206) @ emptyset) @ (setadjoin @ (setadjoin @ (esk55_2 @ X1205 @ X1206) @ (setadjoin @ (esk56_2 @ X1205 @ X1206) @ emptyset)) @ emptyset)))))&(((in @ (esk57_2 @ X1209 @ X1210) @ (setunion @ (kpair @ X1209 @ X1210)))&((in @ (esk58_2 @ X1209 @ X1210) @ (setunion @ (kpair @ X1209 @ X1210)))&((kpair @ X1209 @ X1210)=(setadjoin @ (setadjoin @ (esk57_2 @ X1209 @ X1210) @ emptyset) @ (setadjoin @ (setadjoin @ (esk57_2 @ X1209 @ X1210) @ (setadjoin @ (esk58_2 @ X1209 @ X1210) @ 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_186])])])])])])])).
% 1.81/0.55 thf(c_0_188, negated_conjecture, ![X3:$i, X2:$i]:((((X2)=(X3))|~((in @ X3 @ (setadjoin @ X2 @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_187])).
% 1.81/0.55 thf(c_0_189, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk53_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_187])).
% 1.81/0.55 thf(c_0_190, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk53_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_187])).
% 1.81/0.55 thf(c_0_191, negated_conjecture, ![X2:$i, X3:$i]:((((esk53_2 @ (setadjoin @ X2 @ emptyset) @ X3)=(X2))|(subset @ (setadjoin @ X2 @ emptyset) @ X3))), inference(spm,[status(thm)],[c_0_188, c_0_189])).
% 1.81/0.55 thf(c_0_192, negated_conjecture, ~((subset @ (setadjoin @ esk60_0 @ emptyset) @ esk59_0)), inference(split_conjunct,[status(thm)],[c_0_187])).
% 1.81/0.55 thf(c_0_193, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ (setadjoin @ X2 @ emptyset) @ X3)|~((in @ X2 @ X3)))), inference(spm,[status(thm)],[c_0_190, c_0_191])).
% 1.81/0.55 thf(c_0_194, negated_conjecture, (in @ esk60_0 @ esk59_0), inference(split_conjunct,[status(thm)],[c_0_187])).
% 1.81/0.55 thf(c_0_195, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192, c_0_193]), c_0_194])]), ['proof']).
% 1.81/0.55 % SZS output end CNFRefutation
% 1.81/0.55 % Parsed axioms : 303
% 1.81/0.55 % Removed by relevancy pruning/SinE : 0
% 1.81/0.55 % Initial clauses : 433
% 1.81/0.55 % Removed in clause preprocessing : 185
% 1.81/0.55 % Initial clauses in saturation : 248
% 1.81/0.55 % Processed clauses : 2020
% 1.81/0.55 % ...of these trivial : 21
% 1.81/0.55 % ...subsumed : 1391
% 1.81/0.55 % ...remaining for further processing : 608
% 1.81/0.55 % Other redundant clauses eliminated : 27
% 1.81/0.55 % Clauses deleted for lack of memory : 0
% 1.81/0.55 % Backward-subsumed : 2
% 1.81/0.55 % Backward-rewritten : 6
% 1.81/0.55 % Generated clauses : 19701
% 1.81/0.55 % ...of the previous two non-redundant : 17102
% 1.81/0.55 % ...aggressively subsumed : 0
% 1.81/0.55 % Contextual simplify-reflections : 1
% 1.81/0.55 % Paramodulations : 19672
% 1.81/0.55 % Factorizations : 2
% 1.81/0.55 % NegExts : 0
% 1.81/0.55 % Equation resolutions : 27
% 1.81/0.55 % Disequality decompositions : 0
% 1.81/0.55 % Total rewrite steps : 7085
% 1.81/0.55 % ...of those cached : 6856
% 1.81/0.55 % Propositional unsat checks : 0
% 1.81/0.55 % Propositional check models : 0
% 1.81/0.55 % Propositional check unsatisfiable : 0
% 1.81/0.55 % Propositional clauses : 0
% 1.81/0.55 % Propositional clauses after purity: 0
% 1.81/0.55 % Propositional unsat core size : 0
% 1.81/0.55 % Propositional preprocessing time : 0.000
% 1.81/0.55 % Propositional encoding time : 0.000
% 1.81/0.55 % Propositional solver time : 0.000
% 1.81/0.55 % Success case prop preproc time : 0.000
% 1.81/0.55 % Success case prop encoding time : 0.000
% 1.81/0.55 % Success case prop solver time : 0.000
% 1.81/0.55 % Current number of processed clauses : 586
% 1.81/0.55 % Positive orientable unit clauses : 206
% 1.81/0.55 % Positive unorientable unit clauses: 0
% 1.81/0.55 % Negative unit clauses : 4
% 1.81/0.55 % Non-unit-clauses : 376
% 1.81/0.55 % Current number of unprocessed clauses: 15234
% 1.81/0.55 % ...number of literals in the above : 52965
% 1.81/0.55 % Current number of archived formulas : 0
% 1.81/0.55 % Current number of archived clauses : 8
% 1.81/0.55 % Clause-clause subsumption calls (NU) : 19683
% 1.81/0.55 % Rec. Clause-clause subsumption calls : 11033
% 1.81/0.55 % Non-unit clause-clause subsumptions : 775
% 1.81/0.55 % Unit Clause-clause subsumption calls : 883
% 1.81/0.55 % Rewrite failures with RHS unbound : 0
% 1.81/0.55 % BW rewrite match attempts : 947
% 1.81/0.55 % BW rewrite match successes : 4
% 1.81/0.55 % Condensation attempts : 0
% 1.81/0.55 % Condensation successes : 0
% 1.81/0.55 % Termbank termtop insertions : 385215
% 1.81/0.55 % Search garbage collected termcells : 13588
% 1.81/0.55
% 1.81/0.55 % -------------------------------------------------
% 1.81/0.55 % User time : 0.227 s
% 1.81/0.55 % System time : 0.024 s
% 1.81/0.55 % Total time : 0.251 s
% 1.81/0.55 % Maximum resident set size: 6236 pages
% 1.81/0.55
% 1.81/0.55 % -------------------------------------------------
% 1.81/0.55 % User time : 0.314 s
% 1.81/0.55 % System time : 0.072 s
% 1.81/0.55 % Total time : 0.385 s
% 1.81/0.55 % Maximum resident set size: 5120 pages
% 1.81/0.55 % E exiting
%------------------------------------------------------------------------------