%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU622^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:26:57 AM UTC 2026
% Result : Theorem 0.33s 0.47s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU622^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 % Computer : n002.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Tue Sep 29 14:01:37 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.32 Running higher-order theorem proving
% 0.33/0.37 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p
% 0.33/0.47 % Version: 3.5.1-ho
% 0.33/0.47 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.33/0.47 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.47 % Starting ehoh_best5 with 300s (1) cores
% 0.33/0.47 % Starting almost_fo_3_lam with 300s (1) cores
% 0.33/0.47 % Starting new_bool_5 with 300s (1) cores
% 0.33/0.47 % Starting pre_casc_3 with 300s (1) cores
% 0.33/0.47 % Starting ho_unfolding_8 with 300s (1) cores
% 0.33/0.47 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.33/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.33/0.47 % Starting new_ho_5 with 300s (1) cores
% 0.33/0.47 % ho_unfolding_8 with pid 1332344 completed with status 0
% 0.33/0.47 % Result found by ho_unfolding_8
% 0.33/0.47 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.33/0.47 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.47 % Starting ehoh_best5 with 300s (1) cores
% 0.33/0.47 % Starting almost_fo_3_lam with 300s (1) cores
% 0.33/0.47 % Starting new_bool_5 with 300s (1) cores
% 0.33/0.47 % Starting pre_casc_3 with 300s (1) cores
% 0.33/0.47 % Starting ho_unfolding_8 with 300s (1) cores
% 0.33/0.47 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.33/0.47 % No SInE strategy applied
% 0.33/0.47 % Search class: HGHSM-FSLM31-DHFMMSBN
% 0.33/0.47 % partial match(1): HGHSM-FSLM31-MHFMMSBN
% 0.33/0.47 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.33/0.47 % Starting SubtermCWHack with 28s (1) cores
% 0.33/0.47 % SubtermCWHack with pid 1332352 completed with status 0
% 0.33/0.47 % Result found by SubtermCWHack
% 0.33/0.47 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.33/0.47 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.47 % Starting ehoh_best5 with 300s (1) cores
% 0.33/0.47 % Starting almost_fo_3_lam with 300s (1) cores
% 0.33/0.47 % Starting new_bool_5 with 300s (1) cores
% 0.33/0.47 % Starting pre_casc_3 with 300s (1) cores
% 0.33/0.47 % Starting ho_unfolding_8 with 300s (1) cores
% 0.33/0.47 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.33/0.47 % No SInE strategy applied
% 0.33/0.47 % Search class: HGHSM-FSLM31-DHFMMSBN
% 0.33/0.47 % partial match(1): HGHSM-FSLM31-MHFMMSBN
% 0.33/0.47 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.33/0.47 % Starting SubtermCWHack with 28s (1) cores
% 0.33/0.47 % Preprocessing time : 0.005 s
% 0.33/0.47
% 0.33/0.47 % Proof found!
% 0.33/0.47 % SZS status Theorem
% 0.33/0.47 % SZS output start CNFRefutation
% 0.33/0.47 thf(decl_23, type, in: $i > $i > $o).
% 0.33/0.47 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.33/0.47 thf(decl_25, type, setextAx: $o).
% 0.33/0.47 thf(decl_26, type, emptyset: $i).
% 0.33/0.47 thf(decl_27, type, emptysetAx: $o).
% 0.33/0.47 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.33/0.47 thf(decl_29, type, setadjoinAx: $o).
% 0.33/0.47 thf(decl_30, type, powerset: $i > $i).
% 0.33/0.47 thf(decl_31, type, powersetAx: $o).
% 0.33/0.47 thf(decl_32, type, setunion: $i > $i).
% 0.33/0.47 thf(decl_33, type, setunionAx: $o).
% 0.33/0.47 thf(decl_34, type, omega: $i).
% 0.33/0.47 thf(decl_35, type, omega0Ax: $o).
% 0.33/0.47 thf(decl_36, type, omegaSAx: $o).
% 0.33/0.47 thf(decl_37, type, omegaIndAx: $o).
% 0.33/0.47 thf(decl_38, type, replAx: $o).
% 0.33/0.47 thf(decl_39, type, foundationAx: $o).
% 0.33/0.47 thf(decl_40, type, wellorderingAx: $o).
% 0.33/0.47 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.33/0.47 thf(decl_42, type, descrp: $o).
% 0.33/0.47 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.33/0.47 thf(decl_44, type, dsetconstrI: $o).
% 0.33/0.47 thf(decl_45, type, dsetconstrEL: $o).
% 0.33/0.47 thf(decl_46, type, dsetconstrER: $o).
% 0.33/0.47 thf(decl_47, type, exuE1: $o).
% 0.33/0.47 thf(decl_48, type, prop2set: $o > $i).
% 0.33/0.47 thf(decl_49, type, prop2setE: $o).
% 0.33/0.47 thf(decl_50, type, emptysetE: $o).
% 0.33/0.47 thf(decl_51, type, emptysetimpfalse: $o).
% 0.33/0.47 thf(decl_52, type, notinemptyset: $o).
% 0.33/0.47 thf(decl_53, type, exuE3e: $o).
% 0.33/0.47 thf(decl_54, type, setext: $o).
% 0.33/0.47 thf(decl_55, type, emptyI: $o).
% 0.33/0.47 thf(decl_56, type, noeltsimpempty: $o).
% 0.33/0.47 thf(decl_57, type, setbeta: $o).
% 0.33/0.47 thf(decl_58, type, nonempty: $i > $o).
% 0.33/0.47 thf(decl_59, type, nonemptyE1: $o).
% 0.33/0.47 thf(decl_60, type, nonemptyI: $o).
% 0.33/0.47 thf(decl_61, type, nonemptyI1: $o).
% 0.33/0.47 thf(decl_62, type, setadjoinIL: $o).
% 0.33/0.47 thf(decl_63, type, emptyinunitempty: $o).
% 0.33/0.47 thf(decl_64, type, setadjoinIR: $o).
% 0.33/0.47 thf(decl_65, type, setadjoinE: $o).
% 0.33/0.47 thf(decl_66, type, setadjoinOr: $o).
% 0.33/0.47 thf(decl_67, type, setoftrueEq: $o).
% 0.33/0.47 thf(decl_68, type, powersetI: $o).
% 0.33/0.47 thf(decl_69, type, emptyinPowerset: $o).
% 0.33/0.47 thf(decl_70, type, emptyInPowerset: $o).
% 0.33/0.47 thf(decl_71, type, powersetE: $o).
% 0.33/0.47 thf(decl_72, type, setunionI: $o).
% 0.33/0.47 thf(decl_73, type, setunionE: $o).
% 0.33/0.47 thf(decl_74, type, subPowSU: $o).
% 0.33/0.47 thf(decl_75, type, exuE2: $o).
% 0.33/0.47 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.33/0.47 thf(decl_77, type, uniqinunit: $o).
% 0.33/0.47 thf(decl_78, type, notinsingleton: $o).
% 0.33/0.47 thf(decl_79, type, eqinunit: $o).
% 0.33/0.47 thf(decl_80, type, singletonsswitch: $o).
% 0.33/0.47 thf(decl_81, type, upairsetE: $o).
% 0.33/0.47 thf(decl_82, type, upairsetIL: $o).
% 0.33/0.47 thf(decl_83, type, upairsetIR: $o).
% 0.33/0.47 thf(decl_84, type, emptyE1: $o).
% 0.33/0.47 thf(decl_85, type, vacuousDall: $o).
% 0.33/0.47 thf(decl_86, type, quantDeMorgan1: $o).
% 0.33/0.47 thf(decl_87, type, quantDeMorgan2: $o).
% 0.33/0.47 thf(decl_88, type, quantDeMorgan3: $o).
% 0.33/0.47 thf(decl_89, type, quantDeMorgan4: $o).
% 0.33/0.47 thf(decl_90, type, prop2setI: $o).
% 0.33/0.47 thf(decl_91, type, set2prop: $i > $o).
% 0.33/0.47 thf(decl_92, type, prop2set2propI: $o).
% 0.33/0.47 thf(decl_93, type, notdexE: $o).
% 0.33/0.47 thf(decl_94, type, notdallE: $o).
% 0.33/0.47 thf(decl_95, type, exuI1: $o).
% 0.33/0.47 thf(decl_96, type, exuI3: $o).
% 0.33/0.47 thf(decl_97, type, exuI2: $o).
% 0.33/0.47 thf(decl_98, type, inCongP: $o).
% 0.33/0.47 thf(decl_99, type, in__Cong: $o).
% 0.33/0.47 thf(decl_100, type, exuE3u: $o).
% 0.33/0.47 thf(decl_101, type, exu__Cong: $o).
% 0.33/0.47 thf(decl_102, type, emptyset__Cong: $o).
% 0.33/0.47 thf(decl_103, type, setadjoin__Cong: $o).
% 0.33/0.47 thf(decl_104, type, powerset__Cong: $o).
% 0.33/0.47 thf(decl_105, type, setunion__Cong: $o).
% 0.33/0.47 thf(decl_106, type, omega__Cong: $o).
% 0.33/0.47 thf(decl_107, type, exuEu: $o).
% 0.33/0.47 thf(decl_108, type, descr__Cong: $o).
% 0.33/0.47 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.33/0.47 thf(decl_110, type, subset: $i > $i > $o).
% 0.33/0.47 thf(decl_113, type, subsetI1: $o).
% 0.33/0.47 thf(decl_114, type, eqimpsubset2: $o).
% 0.33/0.47 thf(decl_115, type, eqimpsubset1: $o).
% 0.33/0.47 thf(decl_116, type, subsetI2: $o).
% 0.33/0.47 thf(decl_117, type, emptysetsubset: $o).
% 0.33/0.47 thf(decl_118, type, subsetE: $o).
% 0.33/0.47 thf(decl_119, type, subsetE2: $o).
% 0.33/0.47 thf(decl_120, type, notsubsetI: $o).
% 0.33/0.47 thf(decl_121, type, notequalI1: $o).
% 0.33/0.47 thf(decl_122, type, notequalI2: $o).
% 0.33/0.47 thf(decl_123, type, subsetRefl: $o).
% 0.33/0.47 thf(decl_124, type, subsetTrans: $o).
% 0.33/0.47 thf(decl_125, type, setadjoinSub: $o).
% 0.33/0.47 thf(decl_126, type, setadjoinSub2: $o).
% 0.33/0.47 thf(decl_127, type, subset2powerset: $o).
% 0.33/0.47 thf(decl_128, type, setextsub: $o).
% 0.33/0.47 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.33/0.47 thf(decl_130, type, powersetI1: $o).
% 0.33/0.47 thf(decl_131, type, powersetE1: $o).
% 0.33/0.47 thf(decl_132, type, inPowerset: $o).
% 0.33/0.47 thf(decl_133, type, powersetsubset: $o).
% 0.33/0.47 thf(decl_134, type, sepInPowerset: $o).
% 0.33/0.47 thf(decl_135, type, sepSubset: $o).
% 0.33/0.47 thf(decl_136, type, binunion: $i > $i > $i).
% 0.33/0.47 thf(decl_137, type, binunionIL: $o).
% 0.33/0.47 thf(decl_138, type, upairset2IR: $o).
% 0.33/0.47 thf(decl_139, type, binunionIR: $o).
% 0.33/0.47 thf(decl_140, type, binunionEcases: $o).
% 0.33/0.47 thf(decl_141, type, binunionE: $o).
% 0.33/0.47 thf(decl_142, type, binunionLsub: $o).
% 0.33/0.47 thf(decl_143, type, binunionRsub: $o).
% 0.33/0.47 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.33/0.47 thf(decl_145, type, binintersectI: $o).
% 0.33/0.47 thf(decl_146, type, binintersectSubset5: $o).
% 0.33/0.47 thf(decl_147, type, binintersectEL: $o).
% 0.33/0.47 thf(decl_148, type, binintersectLsub: $o).
% 0.33/0.47 thf(decl_149, type, binintersectSubset2: $o).
% 0.33/0.47 thf(decl_150, type, binintersectSubset3: $o).
% 0.33/0.47 thf(decl_151, type, binintersectER: $o).
% 0.33/0.47 thf(decl_152, type, disjointsetsI1: $o).
% 0.33/0.47 thf(decl_153, type, binintersectRsub: $o).
% 0.33/0.47 thf(decl_154, type, binintersectSubset4: $o).
% 0.33/0.47 thf(decl_155, type, binintersectSubset1: $o).
% 0.33/0.47 thf(decl_156, type, bs114d: $o).
% 0.33/0.47 thf(decl_158, type, setminus: $i > $i > $i).
% 0.33/0.47 thf(decl_159, type, setminusI: $o).
% 0.33/0.47 thf(decl_160, type, setminusEL: $o).
% 0.33/0.47 thf(decl_161, type, setminusER: $o).
% 0.33/0.47 thf(decl_162, type, setminusSubset2: $o).
% 0.33/0.47 thf(decl_163, type, setminusERneg: $o).
% 0.33/0.47 thf(decl_164, type, setminusELneg: $o).
% 0.33/0.47 thf(decl_165, type, setminusILneg: $o).
% 0.33/0.47 thf(decl_166, type, setminusIRneg: $o).
% 0.33/0.47 thf(decl_167, type, setminusLsub: $o).
% 0.33/0.47 thf(decl_168, type, setminusSubset1: $o).
% 0.33/0.47 thf(decl_169, type, symdiff: $i > $i > $i).
% 0.33/0.47 thf(decl_170, type, symdiffE: $o).
% 0.33/0.47 thf(decl_171, type, symdiffI1: $o).
% 0.33/0.47 thf(decl_172, type, symdiffI2: $o).
% 0.33/0.47 thf(decl_173, type, symdiffIneg1: $o).
% 0.33/0.47 thf(decl_174, type, symdiffIneg2: $o).
% 0.33/0.47 thf(decl_175, type, iskpair: $i > $o).
% 0.33/0.47 thf(decl_176, type, secondinupair: $o).
% 0.33/0.47 thf(decl_177, type, setukpairIL: $o).
% 0.33/0.47 thf(decl_178, type, setukpairIR: $o).
% 0.33/0.47 thf(decl_179, type, kpairiskpair: $o).
% 0.33/0.47 thf(decl_180, type, kpair: $i > $i > $i).
% 0.33/0.47 thf(decl_181, type, kpairp: $o).
% 0.33/0.47 thf(decl_183, type, singletonsubset: $o).
% 0.33/0.47 thf(decl_184, type, epred1_0: $o).
% 0.33/0.47 thf(decl_185, type, esk1_2: $i > $i > $i).
% 0.33/0.47 thf(decl_186, type, esk2_2: $i > $i > $i).
% 0.33/0.47 thf(decl_187, type, esk3_2: $i > $i > $i).
% 0.33/0.47 thf(decl_188, type, esk4_1: $i > $i).
% 0.33/0.47 thf(decl_189, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.33/0.47 thf(decl_190, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.33/0.47 thf(decl_191, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.33/0.47 thf(decl_192, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.33/0.47 thf(decl_193, type, esk9_1: $i > $i).
% 0.33/0.47 thf(decl_194, type, esk10_2: ($i > $o) > $i > $i).
% 0.33/0.47 thf(decl_195, type, esk11_2: ($i > $o) > $i > $i).
% 0.33/0.47 thf(decl_196, type, esk12_1: ($i > $o) > $i).
% 0.33/0.47 thf(decl_197, type, esk13_2: ($i > $o) > $i > $i).
% 0.33/0.47 thf(decl_198, type, esk14_1: ($i > $o) > $i).
% 0.33/0.47 thf(decl_199, type, esk15_2: $i > $i > $i).
% 0.33/0.47 thf(decl_200, type, esk16_2: $i > $i > $i).
% 0.33/0.47 thf(decl_201, type, esk17_1: $i > $i).
% 0.33/0.47 thf(decl_202, type, esk18_1: $i > $i).
% 0.33/0.47 thf(decl_203, type, esk19_1: $i > $i).
% 0.33/0.47 thf(decl_204, type, esk20_2: $i > $i > $i).
% 0.33/0.47 thf(decl_205, type, esk21_3: $i > $i > $o > $i).
% 0.33/0.47 thf(decl_206, type, esk22_2: ($i > $o) > $i > $i).
% 0.33/0.47 thf(decl_207, type, esk23_1: ($i > $o) > $i).
% 0.33/0.47 thf(decl_208, type, esk24_1: $i > $i).
% 0.33/0.47 thf(decl_209, type, esk25_2: $i > ($i > $o) > $i).
% 0.33/0.47 thf(decl_210, type, esk26_2: $i > ($i > $o) > $i).
% 0.33/0.47 thf(decl_211, type, esk27_2: $i > ($i > $o) > $i).
% 0.33/0.47 thf(decl_212, type, esk28_2: $i > ($i > $o) > $i).
% 0.33/0.47 thf(decl_213, type, esk29_2: $i > ($i > $o) > $i).
% 0.33/0.47 thf(decl_214, type, esk30_2: $i > ($i > $o) > $i).
% 0.33/0.47 thf(decl_215, type, esk31_2: ($i > $o) > $i > $i).
% 0.33/0.47 thf(decl_216, type, esk32_1: ($i > $o) > $i).
% 0.33/0.47 thf(decl_217, type, esk33_1: ($i > $o) > $i).
% 0.33/0.47 thf(decl_218, type, esk34_1: ($i > $o) > $i).
% 0.33/0.47 thf(decl_219, type, esk35_1: ($i > $o) > $i).
% 0.33/0.47 thf(decl_220, type, esk36_2: ($i > $o) > $i > $i).
% 0.33/0.47 thf(decl_221, type, esk37_1: ($i > $o) > $i).
% 0.33/0.47 thf(decl_222, type, esk38_2: ($i > $o) > $i > $i).
% 0.33/0.47 thf(decl_223, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.33/0.47 thf(decl_224, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.33/0.47 thf(decl_225, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.33/0.47 thf(decl_226, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.33/0.47 thf(decl_227, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.33/0.47 thf(decl_228, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.33/0.47 thf(decl_229, type, esk45_2: ($i > $o) > $i > $i).
% 0.33/0.47 thf(decl_230, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.33/0.47 thf(decl_231, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.33/0.47 thf(decl_232, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.33/0.47 thf(decl_233, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.33/0.47 thf(decl_234, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.33/0.47 thf(decl_235, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.33/0.47 thf(decl_236, type, esk52_2: $i > $i > $i).
% 0.33/0.47 thf(decl_237, type, esk53_2: $i > $i > $i).
% 0.33/0.47 thf(decl_238, type, esk54_2: $i > $i > $i).
% 0.33/0.47 thf(decl_239, type, esk55_2: $i > $i > $i).
% 0.33/0.47 thf(decl_240, type, esk56_2: $i > $i > $i).
% 0.33/0.47 thf(decl_241, type, esk57_2: $i > $i > $i).
% 0.33/0.47 thf(decl_242, type, esk58_2: $i > $i > $i).
% 0.33/0.47 thf(decl_243, type, esk59_0: $i).
% 0.33/0.47 thf(decl_244, type, esk60_0: $i).
% 0.33/0.47 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', replAx)).
% 0.33/0.47 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', exu)).
% 0.33/0.47 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', descrp)).
% 0.33/0.47 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', exuE1)).
% 0.33/0.47 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', exuE3e)).
% 0.33/0.47 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', nonempty)).
% 0.33/0.47 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', nonemptyI)).
% 0.33/0.47 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', exuE2)).
% 0.33/0.47 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/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', exuI1)).
% 0.33/0.47 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', exuI3)).
% 0.33/0.47 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', exuI2)).
% 0.33/0.47 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/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', exuE3u)).
% 0.33/0.47 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', exu__Cong)).
% 0.33/0.47 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', exuEu)).
% 0.33/0.47 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', descr__Cong)).
% 0.33/0.47 thf(iskpair, axiom, ((iskpair)=(^[X4:$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/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', iskpair)).
% 0.33/0.47 thf(singletoninpowerset, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', singletoninpowerset)).
% 0.33/0.47 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', dsetconstrI)).
% 0.33/0.47 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', dsetconstrEL)).
% 0.33/0.47 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', dsetconstrER)).
% 0.33/0.47 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setbeta)).
% 0.33/0.47 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', nonemptyE1)).
% 0.33/0.47 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', nonemptyI1)).
% 0.33/0.47 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setoftrueEq)).
% 0.33/0.47 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', nonemptyImpWitness)).
% 0.33/0.47 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', emptyE1)).
% 0.33/0.47 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', dsetconstr__Cong)).
% 0.33/0.47 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', sepInPowerset)).
% 0.33/0.47 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', sepSubset)).
% 0.33/0.47 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', kpairiskpair)).
% 0.33/0.47 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', kpairp)).
% 0.33/0.47 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setextAx)).
% 0.33/0.47 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', emptysetAx)).
% 0.33/0.47 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setadjoinAx)).
% 0.33/0.47 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', powersetAx)).
% 0.33/0.47 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setunionAx)).
% 0.33/0.47 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', omega0Ax)).
% 0.33/0.47 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', omegaSAx)).
% 0.33/0.47 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', omegaIndAx)).
% 0.33/0.47 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', foundationAx)).
% 0.33/0.47 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', wellorderingAx)).
% 0.33/0.47 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', prop2setE)).
% 0.33/0.47 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', emptysetE)).
% 0.33/0.47 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', emptysetimpfalse)).
% 0.33/0.47 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', notinemptyset)).
% 0.33/0.47 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setext)).
% 0.33/0.47 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', emptyI)).
% 0.33/0.47 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', noeltsimpempty)).
% 0.33/0.47 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setadjoinIL)).
% 0.33/0.47 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', emptyinunitempty)).
% 0.33/0.47 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setadjoinIR)).
% 0.33/0.47 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/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setadjoinE)).
% 0.33/0.47 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setadjoinOr)).
% 0.33/0.47 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', powersetI)).
% 0.33/0.47 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', emptyinPowerset)).
% 0.33/0.47 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', emptyInPowerset)).
% 0.33/0.47 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', powersetE)).
% 0.33/0.47 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setunionI)).
% 0.33/0.47 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/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setunionE)).
% 0.33/0.47 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', subPowSU)).
% 0.33/0.47 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', uniqinunit)).
% 0.33/0.47 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', notinsingleton)).
% 0.33/0.47 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', eqinunit)).
% 0.33/0.47 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', singletonsswitch)).
% 0.33/0.47 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', upairsetE)).
% 0.33/0.47 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', upairsetIL)).
% 0.33/0.47 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', upairsetIR)).
% 0.33/0.47 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', vacuousDall)).
% 0.33/0.47 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', quantDeMorgan1)).
% 0.33/0.47 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', quantDeMorgan2)).
% 0.33/0.47 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', quantDeMorgan3)).
% 0.33/0.47 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', quantDeMorgan4)).
% 0.33/0.47 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', prop2setI)).
% 0.33/0.47 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', prop2set2propI)).
% 0.33/0.47 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', notdexE)).
% 0.33/0.47 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', notdallE)).
% 0.33/0.47 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', inCongP)).
% 0.33/0.47 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', in__Cong)).
% 0.33/0.47 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', emptyset__Cong)).
% 0.33/0.47 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setadjoin__Cong)).
% 0.33/0.47 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', powerset__Cong)).
% 0.33/0.47 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setunion__Cong)).
% 0.33/0.47 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', omega__Cong)).
% 0.33/0.47 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', subsetI1)).
% 0.33/0.47 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', eqimpsubset2)).
% 0.33/0.47 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', eqimpsubset1)).
% 0.33/0.47 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', subsetI2)).
% 0.33/0.47 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', emptysetsubset)).
% 0.33/0.47 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', subsetE)).
% 0.33/0.47 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', subsetE2)).
% 0.33/0.47 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', notsubsetI)).
% 0.33/0.47 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', notequalI1)).
% 0.33/0.47 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', notequalI2)).
% 0.33/0.47 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', subsetRefl)).
% 0.33/0.47 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', subsetTrans)).
% 0.33/0.47 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setadjoinSub)).
% 0.33/0.47 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setadjoinSub2)).
% 0.33/0.47 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', subset2powerset)).
% 0.33/0.47 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setextsub)).
% 0.33/0.47 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', subsetemptysetimpeq)).
% 0.33/0.47 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', powersetI1)).
% 0.33/0.47 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', powersetE1)).
% 0.33/0.47 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', inPowerset)).
% 0.33/0.47 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', powersetsubset)).
% 0.33/0.47 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', binunionIL)).
% 0.33/0.47 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', upairset2IR)).
% 0.33/0.47 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', binunionIR)).
% 0.33/0.47 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', binunionEcases)).
% 0.33/0.47 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', binunionE)).
% 0.33/0.47 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', binunionLsub)).
% 0.33/0.47 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', binunionRsub)).
% 0.33/0.47 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', binintersectI)).
% 0.33/0.47 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', binintersectSubset5)).
% 0.33/0.47 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', binintersectEL)).
% 0.33/0.47 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', binintersectLsub)).
% 0.33/0.47 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', binintersectSubset2)).
% 0.33/0.47 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', binintersectSubset3)).
% 0.33/0.47 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', binintersectER)).
% 0.33/0.47 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', disjointsetsI1)).
% 0.33/0.47 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', binintersectRsub)).
% 0.33/0.47 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', binintersectSubset4)).
% 0.33/0.47 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', binintersectSubset1)).
% 0.33/0.47 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', bs114d)).
% 0.33/0.47 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setminusI)).
% 0.33/0.47 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setminusEL)).
% 0.33/0.47 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setminusER)).
% 0.33/0.47 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setminusSubset2)).
% 0.33/0.47 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setminusERneg)).
% 0.33/0.47 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setminusELneg)).
% 0.33/0.47 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setminusILneg)).
% 0.33/0.47 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setminusIRneg)).
% 0.33/0.47 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setminusLsub)).
% 0.33/0.47 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setminusSubset1)).
% 0.33/0.47 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', symdiffE)).
% 0.33/0.47 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', symdiffI1)).
% 0.33/0.47 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', symdiffI2)).
% 0.33/0.47 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', symdiffIneg1)).
% 0.33/0.47 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', symdiffIneg2)).
% 0.33/0.47 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', secondinupair)).
% 0.33/0.47 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setukpairIL)).
% 0.33/0.47 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', setukpairIR)).
% 0.33/0.47 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4tuDbep7PU/E---3.1_1332325.p', singletonsubset)).
% 0.33/0.47 thf(c_0_142, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.33/0.47 thf(c_0_143, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.33/0.47 thf(c_0_144, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.33/0.47 thf(c_0_145, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.33/0.47 thf(c_0_146, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.33/0.47 thf(c_0_147, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.33/0.47 thf(c_0_148, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.33/0.47 thf(c_0_149, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.33/0.47 thf(c_0_150, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.33/0.47 thf(c_0_151, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.33/0.47 thf(c_0_152, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.33/0.47 thf(c_0_153, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.33/0.47 thf(c_0_154, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.33/0.47 thf(c_0_155, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.33/0.47 thf(c_0_156, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.33/0.47 thf(c_0_157, plain, ((iskpair)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ (setunion @ Z0)))&(?[X3:$i]:((((in @ X3 @ (setunion @ Z0)))&(((Z0)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))))), inference(fof_simplification,[status(thm)],[iskpair])).
% 0.33/0.47 thf(c_0_158, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[singletoninpowerset])).
% 0.33/0.47 thf(c_0_159, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X389:$i]:(((((X6 @ X2 @ X389)))&(![X390:$i]:(((((X6 @ X2 @ X390)))=>(((X389)=(X390)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_142, c_0_143])).
% 0.33/0.47 thf(c_0_160, plain, ((descrp)=(![X1:$i > $o]:((((?[X391:$i]:(((((X1 @ X391)))&(![X392:$i]:(((((X1 @ X392)))=>(((X391)=(X392))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_144, c_0_143])).
% 0.33/0.47 thf(c_0_161, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.33/0.47 thf(c_0_162, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.33/0.47 thf(c_0_163, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.33/0.47 thf(c_0_164, plain, ((exuE1)=(![X1:$i > $o]:((((?[X393:$i]:(((((X1 @ X393)))&(![X394:$i]:(((((X1 @ X394)))=>(((X393)=(X394))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_145, c_0_143])).
% 0.33/0.47 thf(c_0_165, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X395:$i]:(((((X1 @ X395)))&(![X396:$i]:(((((X1 @ X396)))=>(((X395)=(X396))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_146, c_0_143])).
% 0.33/0.47 thf(c_0_166, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.33/0.47 thf(c_0_167, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_147])).
% 0.33/0.47 thf(c_0_168, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_148, c_0_147])).
% 0.33/0.47 thf(c_0_169, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_147])).
% 0.33/0.47 thf(c_0_170, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.33/0.47 thf(c_0_171, plain, ((exuE2)=(![X1:$i > $o]:((((?[X397:$i]:(((((X1 @ X397)))&(![X398:$i]:(((((X1 @ X398)))=>(((X397)=(X398))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_149, c_0_143])).
% 0.33/0.47 thf(c_0_172, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_147])).
% 0.33/0.47 thf(c_0_173, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 0.33/0.47 thf(c_0_174, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X399:$i]:(((((X1 @ X399)))&(![X400:$i]:(((((X1 @ X400)))=>(((X399)=(X400)))))))))))))), inference(apply_def,[status(thm)],[c_0_150, c_0_143])).
% 0.33/0.47 thf(c_0_175, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X401:$i]:(((((X1 @ X401)))&(![X402:$i]:(((((X1 @ X402)))=>(((X401)=(X402)))))))))))))))), inference(apply_def,[status(thm)],[c_0_151, c_0_143])).
% 0.33/0.47 thf(c_0_176, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X403:$i]:(((((X1 @ X403)))&(![X404:$i]:(((((X1 @ X404)))=>(((X403)=(X404)))))))))))))), inference(apply_def,[status(thm)],[c_0_152, c_0_143])).
% 0.33/0.47 thf(c_0_177, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X405:$i]:(((((X1 @ X405)))&(![X406:$i]:(((((X1 @ X406)))=>(((X405)=(X406))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_153, c_0_143])).
% 0.33/0.47 thf(c_0_178, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X407:$i]:(((((X1 @ X407)))&(![X408:$i]:(((((X1 @ X408)))=>(((X407)=(X408))))))))))<=>((?[X409:$i]:(((((X17 @ X409)))&(![X410:$i]:(((((X17 @ X410)))=>(((X409)=(X410)))))))))))))))), inference(apply_def,[status(thm)],[c_0_154, c_0_143])).
% 0.33/0.47 thf(c_0_179, plain, ((exuEu)=(![X1:$i > $o]:((((?[X411:$i]:(((((X1 @ X411)))&(![X412:$i]:(((((X1 @ X412)))=>(((X411)=(X412))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_155, c_0_143])).
% 0.33/0.47 thf(c_0_180, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X413:$i]:(((((X1 @ X413)))&(![X414:$i]:(((((X1 @ X414)))=>(((X413)=(X414))))))))))=>((((?[X415:$i]:(((((X17 @ X415)))&(![X416:$i]:(((((X17 @ X416)))=>(((X415)=(X416))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_156, c_0_143])).
% 0.33/0.47 thf(c_0_181, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.33/0.47 thf(c_0_182, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.33/0.47 thf(c_0_183, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.33/0.47 thf(c_0_184, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X417:$i]:((((in @ X417 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))&(?[X418:$i]:((((in @ X418 @ (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 @ X417 @ emptyset) @ (setadjoin @ (setadjoin @ X417 @ (setadjoin @ X418 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_157])).
% 0.33/0.47 thf(c_0_185, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X419:$i]:((((in @ X419 @ (setunion @ (kpair @ X2 @ X3))))&(?[X420:$i]:((((in @ X420 @ (setunion @ (kpair @ X2 @ X3))))&(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X419 @ emptyset) @ (setadjoin @ (setadjoin @ X419 @ (setadjoin @ X420 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairp, c_0_157])).
% 0.33/0.47 thf(c_0_186, plain, ((epred1_0)<=>![X450:$i]:(?[X451:$i]:((((![X452:$i]:(((in @ X452 @ X451)=>![X453:$i]:(((in @ X453 @ X452)=>(in @ X453 @ X450)))))&![X454:$i, X455:$i]:((((in @ X454 @ X450)&(in @ X455 @ X450))=>(![X456:$i]:(((in @ X456 @ X451)=>((in @ X454 @ X456)<=>(in @ X455 @ X456))))=>((X454)=(X455))))))&![X457:$i, X458:$i]:((((in @ X457 @ X451)&(in @ X458 @ X451))=>(![X459:$i]:(((in @ X459 @ X457)=>(in @ X459 @ X458)))|![X460:$i]:(((in @ X460 @ X458)=>(in @ X460 @ X457)))))))&![X461:$i]:(((![X462:$i]:(((in @ X462 @ X461)=>(in @ X462 @ X450)))&?[X463:$i]:((in @ X463 @ X461)))=>?[X464:$i, X465:$i]:(((((in @ X464 @ X451)&(in @ X465 @ X461))&~(?[X466:$i]:(((in @ X466 @ X464)&(in @ X466 @ X461)))))&![X467:$i]:(((in @ X467 @ X451)=>(![X468:$i]:(((in @ X468 @ X467)=>(in @ X468 @ X464)))|(in @ X465 @ X467)))))))))))), introduced(definition)).
% 0.33/0.47 thf(c_0_187, negated_conjecture, ~((![X421:$i, X422:$i]:((![X423:$i]:(((in @ X423 @ X421)<=>(in @ X423 @ X422)))=>((X421)=(X422))))=>(![X424:$i]:(~(in @ X424 @ emptyset))=>(![X425:$i, X426:$i, X427:$i]:(((in @ X427 @ (setadjoin @ X425 @ X426))<=>(((X427)=(X425))|(in @ X427 @ X426))))=>(![X428:$i, X429:$i]:(((in @ X429 @ (powerset @ X428))<=>![X430:$i]:(((in @ X430 @ X429)=>(in @ X430 @ X428)))))=>(![X431:$i, X432:$i]:(((in @ X432 @ (setunion @ X431))<=>?[X433:$i]:(((in @ X432 @ X433)&(in @ X433 @ X431)))))=>((in @ emptyset @ omega)=>(![X434:$i]:(((in @ X434 @ omega)=>(in @ (setadjoin @ X434 @ X434) @ omega)))=>(![X435:$i]:((((in @ emptyset @ X435)&![X436:$i]:((((in @ X436 @ omega)&(in @ X436 @ X435))=>(in @ (setadjoin @ X436 @ X436) @ X435))))=>![X437:$i]:(((in @ X437 @ omega)=>(in @ X437 @ X435)))))=>(![X438:$i > $i > $o, X439:$i]:((![X440:$i]:(((in @ X440 @ X439)=>?[X441:$i]:(((X438 @ X440 @ X441)&![X442:$i]:(((X438 @ X440 @ X442)=>((X441)=(X442))))))))=>?[X443:$i]:(![X444:$i]:(((in @ X444 @ X443)<=>?[X445:$i]:(((in @ X445 @ X439)&(X438 @ X445 @ X444))))))))=>(![X446:$i]:((?[X447:$i]:((in @ X447 @ X446))=>?[X448:$i]:(((in @ X448 @ X446)&~(?[X449:$i]:(((in @ X449 @ X448)&(in @ X449 @ X446))))))))=>((epred1_0)=>(![X469:$i > $o]:((?[X470:$i]:(((X469 @ X470)&![X471:$i]:(((X469 @ X471)=>((X470)=(X471))))))=>(X469 @ (descr @ (^[Z0:$i]:(X469 @ Z0))))))=>(![X472:$i, X473:$i > $o, X474:$i]:(((in @ X474 @ X472)=>((X473 @ X474)=>(in @ X474 @ (dsetconstr @ X472 @ X473)))))=>(![X475:$i, X476:$i > $o, X477:$i]:(((in @ X477 @ (dsetconstr @ X475 @ X476))=>(in @ X477 @ X475)))=>(![X478:$i, X479:$i > $o, X480:$i]:(((in @ X480 @ (dsetconstr @ X478 @ X479))=>(X479 @ X480)))=>(![X481:$i > $o]:((?[X482:$i]:(((X481 @ X482)&![X483:$i]:(((X481 @ X483)=>((X482)=(X483))))))=>?[X484:$i]:(((X481 @ X484)&![X485:$i]:(((X481 @ X485)=>((X484)=(X485))))))))=>(![X486:$o, X487:$i]:(((in @ X487 @ (prop2set @ ((X486))))=>(X486)))=>(![X488:$i]:(((in @ X488 @ emptyset)=>![X489:$o]:((X489))))=>(![X490:$i]:(((in @ X490 @ emptyset)=>~($true)))=>(![X491:$i]:(~(in @ X491 @ emptyset))=>(![X492:$i > $o]:((?[X493:$i]:(((X492 @ X493)&![X494:$i]:(((X492 @ X494)=>((X493)=(X494))))))=>?[X495:$i]:((X492 @ X495))))=>(![X496:$i, X497:$i]:((![X498:$i]:(((in @ X498 @ X496)=>(in @ X498 @ X497)))=>(![X499:$i]:(((in @ X499 @ X497)=>(in @ X499 @ X496)))=>((X496)=(X497)))))=>(![X500:$i]:((![X501:$i]:(~(in @ X501 @ X500))=>((X500)=(emptyset))))=>(![X502:$i]:((![X503:$i]:(~(in @ X503 @ X502))=>((X502)=(emptyset))))=>(![X504:$i, X505:$i > $o, X506:$i]:(((in @ X506 @ X504)=>((in @ X506 @ (dsetconstr @ X504 @ X505))<=>(X505 @ X506))))=>(![X507:$i]:((((X507)!=(emptyset))=>?[X508:$i]:((in @ X508 @ X507))))=>(![X509:$i, X510:$i > $o, X511:$i]:(((in @ X511 @ X509)=>((X510 @ X511)=>((dsetconstr @ X509 @ X510)!=(emptyset)))))=>(![X512:$i]:((?[X513:$i]:((in @ X513 @ X512))=>((X512)!=(emptyset))))=>(![X514:$i, X515:$i]:((in @ X514 @ (setadjoin @ X514 @ X515)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X516:$i, X517:$i, X518:$i]:(((in @ X518 @ X517)=>(in @ X518 @ (setadjoin @ X516 @ X517))))=>(![X519:$i, X520:$i, X521:$i]:(((in @ X521 @ (setadjoin @ X519 @ X520))=>![X522:$o]:(((((X521)=(X519))=>(X522))=>(((in @ X521 @ X520)=>(X522))=>(X522))))))=>(![X523:$i, X524:$i, X525:$i]:(((in @ X525 @ (setadjoin @ X523 @ X524))=>(((X525)=(X523))|(in @ X525 @ X524))))=>(![X526:$i]:(((dsetconstr @ X526 @ (^[Z0:$i]:($true)))=(X526)))=>(![X527:$i, X528:$i]:((![X529:$i]:(((in @ X529 @ X528)=>(in @ X529 @ X527)))=>(in @ X528 @ (powerset @ X527))))=>(![X530:$i]:((in @ emptyset @ (powerset @ X530)))=>(![X531:$i]:((in @ emptyset @ (powerset @ X531)))=>(![X532:$i, X533:$i, X534:$i]:(((in @ X533 @ (powerset @ X532))=>((in @ X534 @ X533)=>(in @ X534 @ X532))))=>(![X535:$i, X536:$i, X537:$i]:(((in @ X536 @ X537)=>((in @ X537 @ X535)=>(in @ X536 @ (setunion @ X535)))))=>(![X538:$i, X539:$i]:(((in @ X539 @ (setunion @ X538))=>![X540:$o]:((![X541:$i]:(((in @ X539 @ X541)=>((in @ X541 @ X538)=>(X540))))=>(X540)))))=>(![X542:$i, X543:$i]:(((in @ X543 @ X542)=>(in @ X543 @ (powerset @ (setunion @ X542)))))=>(![X544:$i > $o]:((?[X545:$i]:(((X544 @ X545)&![X546:$i]:(((X544 @ X546)=>((X545)=(X546))))))=>?[X547:$i]:(![X548:$i]:(((X544 @ X548)<=>((X548)=(X547)))))))=>(![X549:$i]:((((X549)!=(emptyset))=>?[X550:$i]:(((in @ X550 @ X549)&$true))))=>(![X551:$i, X552:$i]:(((in @ X551 @ (setadjoin @ X552 @ emptyset))=>((X551)=(X552))))=>(![X553:$i, X554:$i]:((((X553)!=(X554))=>~(in @ X554 @ (setadjoin @ X553 @ emptyset))))=>(![X555:$i, X556:$i]:((((X555)=(X556))=>(in @ X555 @ (setadjoin @ X556 @ emptyset))))=>(![X557:$i, X558:$i]:(((in @ X557 @ (setadjoin @ X558 @ emptyset))=>(in @ X558 @ (setadjoin @ X557 @ emptyset))))=>(![X559:$i, X560:$i, X561:$i]:(((in @ X561 @ (setadjoin @ X559 @ (setadjoin @ X560 @ emptyset)))=>(((X561)=(X559))|((X561)=(X560)))))=>(![X562:$i, X563:$i]:((in @ X562 @ (setadjoin @ X562 @ (setadjoin @ X563 @ emptyset))))=>(![X564:$i, X565:$i]:((in @ X565 @ (setadjoin @ X564 @ (setadjoin @ X565 @ emptyset))))=>(![X566:$i, X567:$i > $o]:((?[X568:$i]:(((in @ X568 @ X566)&(X567 @ X568)))=>(((dsetconstr @ X566 @ X567)=(emptyset))=>~($true))))=>(![X569:$i > $o, X570:$i]:(((in @ X570 @ emptyset)=>(X569 @ X570)))=>(![X571:$i, X572:$i > $o]:((~(![X573:$i]:(((in @ X573 @ X571)=>(X572 @ X573))))=>?[X574:$i]:(((in @ X574 @ X571)&~((X572 @ X574))))))=>(![X575:$i, X576:$i > $o]:((![X577:$i]:(((in @ X577 @ X575)=>~((X576 @ X577))))=>~(?[X578:$i]:(((in @ X578 @ X575)&(X576 @ X578))))))=>(![X579:$i, X580:$i > $o]:((~(?[X581:$i]:(((in @ X581 @ X579)&(X580 @ X581))))=>![X582:$i]:(((in @ X582 @ X579)=>~((X580 @ X582))))))=>(![X583:$i, X584:$i > $o]:((?[X585:$i]:(((in @ X585 @ X583)&~((X584 @ X585))))=>~(![X586:$i]:(((in @ X586 @ X583)=>(X584 @ X586))))))=>(![X587:$o]:(((X587)=>(in @ emptyset @ (prop2set @ ((X587))))))=>(![X588:$o]:(((X588)=>(set2prop @ (prop2set @ ((X588))))))=>(![X589:$i, X590:$i > $o]:((~(?[X591:$i]:(((in @ X591 @ X589)&(X590 @ X591))))=>![X592:$i]:(((in @ X592 @ X589)=>~((X590 @ X592))))))=>(![X593:$i, X594:$i > $o]:((~(![X595:$i]:(((in @ X595 @ X593)=>(X594 @ X595))))=>?[X596:$i]:(((in @ X596 @ X593)&~((X594 @ X596))))))=>(![X597:$i > $o]:((?[X598:$i]:(((X597 @ X598)&![X599:$i]:(((X597 @ X599)=>((X598)=(X599))))))=>?[X600:$i]:(((X597 @ X600)&![X601:$i]:(((X597 @ X601)=>((X600)=(X601))))))))=>(![X602:$i > $o]:((?[X603:$i]:((X602 @ X603))=>(![X604:$i, X605:$i]:(((X602 @ X604)=>((X602 @ X605)=>((X604)=(X605)))))=>?[X606:$i]:(((X602 @ X606)&![X607:$i]:(((X602 @ X607)=>((X606)=(X607)))))))))=>(![X608:$i > $o]:((?[X609:$i]:(![X610:$i]:(((X608 @ X610)<=>((X610)=(X609)))))=>?[X611:$i]:(((X608 @ X611)&![X612:$i]:(((X608 @ X612)=>((X611)=(X612))))))))=>(![X613:$i, X614:$i]:((((X613)=(X614))=>![X615:$i, X616:$i]:((((X615)=(X616))=>((in @ X615 @ X613)=>(in @ X616 @ X614))))))=>(![X617:$i, X618:$i]:((((X617)=(X618))=>![X619:$i, X620:$i]:((((X619)=(X620))=>((in @ X619 @ X617)<=>(in @ X620 @ X618))))))=>(![X621:$i > $o]:((?[X622:$i]:(((X621 @ X622)&![X623:$i]:(((X621 @ X623)=>((X622)=(X623))))))=>![X624:$i, X625:$i]:(((X621 @ X624)=>((X621 @ X625)=>((X624)=(X625)))))))=>(![X626:$i > $o, X627:$i > $o]:((![X628:$i, X629:$i]:((((X628)=(X629))=>((X626 @ X628)<=>(X627 @ X629))))=>(?[X630:$i]:(((X626 @ X630)&![X631:$i]:(((X626 @ X631)=>((X630)=(X631))))))<=>?[X632:$i]:(((X627 @ X632)&![X633:$i]:(((X627 @ X633)=>((X632)=(X633)))))))))=>(((emptyset)=(emptyset))=>(![X634:$i, X635:$i]:((((X634)=(X635))=>![X636:$i, X637:$i]:((((X636)=(X637))=>((setadjoin @ X634 @ X636)=(setadjoin @ X635 @ X637))))))=>(![X638:$i, X639:$i]:((((X638)=(X639))=>((powerset @ X638)=(powerset @ X639))))=>(![X640:$i, X641:$i]:((((X640)=(X641))=>((setunion @ X640)=(setunion @ X641))))=>(((omega)=(omega))=>(![X642:$i > $o]:((?[X643:$i]:(((X642 @ X643)&![X644:$i]:(((X642 @ X644)=>((X643)=(X644))))))=>![X645:$i, X646:$i]:(((X642 @ X645)=>((X642 @ X646)=>((X645)=(X646)))))))=>(![X647:$i > $o, X648:$i > $o]:((![X649:$i, X650:$i]:((((X649)=(X650))=>((X647 @ X649)<=>(X648 @ X650))))=>(?[X651:$i]:(((X647 @ X651)&![X652:$i]:(((X647 @ X652)=>((X651)=(X652))))))=>(?[X653:$i]:(((X648 @ X653)&![X654:$i]:(((X648 @ X654)=>((X653)=(X654))))))=>((descr @ X647)=(descr @ X648))))))=>(![X655:$i, X656:$i]:((((X655)=(X656))=>![X657:$i > $o, X658:$i > $o]:((![X659:$i]:(((in @ X659 @ X655)=>![X660:$i]:(((in @ X660 @ X656)=>(((X659)=(X660))=>((X657 @ X659)<=>(X658 @ X660)))))))=>((dsetconstr @ X655 @ X657)=(dsetconstr @ X656 @ X658))))))=>(![X661:$i, X662:$i]:((![X663:$i]:(((in @ X663 @ X661)=>(in @ X663 @ X662)))=>(subset @ X661 @ X662)))=>(![X664:$i, X665:$i]:((((X664)=(X665))=>(subset @ X665 @ X664)))=>(![X666:$i, X667:$i]:((((X666)=(X667))=>(subset @ X666 @ X667)))=>(![X668:$i, X669:$i]:((![X670:$i]:(((in @ X670 @ X668)=>(in @ X670 @ X669)))=>(subset @ X668 @ X669)))=>(![X671:$i]:((subset @ emptyset @ X671))=>(![X672:$i, X673:$i, X674:$i]:(((subset @ X672 @ X673)=>((in @ X674 @ X672)=>(in @ X674 @ X673))))=>(![X675:$i, X676:$i, X677:$i]:(((subset @ X675 @ X676)=>(~(in @ X677 @ X676)=>~(in @ X677 @ X675))))=>(![X678:$i, X679:$i, X680:$i]:(((in @ X680 @ X678)=>(~(in @ X680 @ X679)=>~(subset @ X678 @ X679))))=>(![X681:$i, X682:$i]:((~(subset @ X681 @ X682)=>((X681)!=(X682))))=>(![X683:$i, X684:$i, X685:$i]:(((in @ X685 @ X683)=>(~(in @ X685 @ X684)=>((X683)!=(X684)))))=>(![X686:$i]:((subset @ X686 @ X686))=>(![X687:$i, X688:$i, X689:$i]:(((subset @ X687 @ X688)=>((subset @ X688 @ X689)=>(subset @ X687 @ X689))))=>(![X690:$i, X691:$i]:((subset @ X691 @ (setadjoin @ X690 @ X691)))=>(![X692:$i, X693:$i, X694:$i]:(((subset @ X692 @ X694)=>(subset @ X692 @ (setadjoin @ X693 @ X694))))=>(![X695:$i, X696:$i]:(((subset @ X695 @ X696)=>(in @ X695 @ (powerset @ X696))))=>(![X697:$i, X698:$i]:(((subset @ X697 @ X698)=>((subset @ X698 @ X697)=>((X697)=(X698)))))=>(![X699:$i]:(((subset @ X699 @ emptyset)=>((X699)=(emptyset))))=>(![X700:$i, X701:$i]:(((subset @ X701 @ X700)=>(in @ X701 @ (powerset @ X700))))=>(![X702:$i, X703:$i]:(((in @ X703 @ (powerset @ X702))=>(subset @ X703 @ X702)))=>(![X704:$i]:((in @ X704 @ (powerset @ X704)))=>(![X705:$i, X706:$i]:(((subset @ X705 @ X706)=>(subset @ (powerset @ X705) @ (powerset @ X706))))=>(![X707:$i, X708:$i > $o]:((in @ (dsetconstr @ X707 @ X708) @ (powerset @ X707)))=>(![X709:$i, X710:$i > $o]:((subset @ (dsetconstr @ X709 @ X710) @ X709))=>(![X711:$i, X712:$i, X713:$i]:(((in @ X713 @ X711)=>(in @ X713 @ (binunion @ X711 @ X712))))=>(![X714:$i, X715:$i]:((in @ X715 @ (setadjoin @ X714 @ (setadjoin @ X715 @ emptyset))))=>(![X716:$i, X717:$i, X718:$i]:(((in @ X718 @ X717)=>(in @ X718 @ (binunion @ X716 @ X717))))=>(![X719:$i, X720:$i, X721:$i, X722:$o]:(((in @ X721 @ (binunion @ X719 @ X720))=>(((in @ X721 @ X719)=>(X722))=>(((in @ X721 @ X720)=>(X722))=>(X722)))))=>(![X723:$i, X724:$i, X725:$i]:(((in @ X725 @ (binunion @ X723 @ X724))=>((in @ X725 @ X723)|(in @ X725 @ X724))))=>(![X726:$i, X727:$i]:((subset @ X726 @ (binunion @ X726 @ X727)))=>(![X728:$i, X729:$i]:((subset @ X729 @ (binunion @ X728 @ X729)))=>(![X730:$i, X731:$i, X732:$i]:(((in @ X732 @ X730)=>((in @ X732 @ X731)=>(in @ X732 @ (binintersect @ X730 @ X731)))))=>(![X733:$i, X734:$i, X735:$i]:(((subset @ X735 @ X733)=>((subset @ X735 @ X734)=>(subset @ X735 @ (binintersect @ X733 @ X734)))))=>(![X736:$i, X737:$i, X738:$i]:(((in @ X738 @ (binintersect @ X736 @ X737))=>(in @ X738 @ X736)))=>(![X739:$i, X740:$i]:((subset @ (binintersect @ X739 @ X740) @ X739))=>(![X741:$i, X742:$i]:(((subset @ X741 @ X742)=>((binintersect @ X741 @ X742)=(X741))))=>(![X743:$i, X744:$i]:((((binintersect @ X743 @ X744)=(X744))=>(subset @ X744 @ X743)))=>(![X745:$i, X746:$i, X747:$i]:(((in @ X747 @ (binintersect @ X745 @ X746))=>(in @ X747 @ X746)))=>(![X748:$i, X749:$i]:((~(?[X750:$i]:(((in @ X750 @ X748)&(in @ X750 @ X749))))=>((binintersect @ X748 @ X749)=(emptyset))))=>(![X751:$i, X752:$i]:((subset @ (binintersect @ X751 @ X752) @ X752))=>(![X753:$i, X754:$i]:(((subset @ X754 @ X753)=>((binintersect @ X753 @ X754)=(X754))))=>(![X755:$i, X756:$i]:((((binintersect @ X755 @ X756)=(X755))=>(subset @ X755 @ X756)))=>(![X757:$i, X758:$i, X759:$i]:(((binintersect @ X757 @ (binunion @ X758 @ X759))=(binunion @ (binintersect @ X757 @ X758) @ (binintersect @ X757 @ X759))))=>(![X760:$i, X761:$i, X762:$i]:(((in @ X762 @ X760)=>(~(in @ X762 @ X761)=>(in @ X762 @ (setminus @ X760 @ X761)))))=>(![X763:$i, X764:$i, X765:$i]:(((in @ X765 @ (setminus @ X763 @ X764))=>(in @ X765 @ X763)))=>(![X766:$i, X767:$i, X768:$i]:(((in @ X768 @ (setminus @ X766 @ X767))=>~(in @ X768 @ X767)))=>(![X769:$i, X770:$i]:(((subset @ X769 @ X770)=>((setminus @ X769 @ X770)=(emptyset))))=>(![X771:$i, X772:$i, X773:$i]:((~(in @ X773 @ (setminus @ X771 @ X772))=>((in @ X773 @ X771)=>(in @ X773 @ X772))))=>(![X774:$i, X775:$i, X776:$i]:((~(in @ X776 @ (setminus @ X774 @ X775))=>(~(in @ X776 @ X775)=>~(in @ X776 @ X774))))=>(![X777:$i, X778:$i, X779:$i]:((~(in @ X779 @ X777)=>~(in @ X779 @ (setminus @ X777 @ X778))))=>(![X780:$i, X781:$i, X782:$i]:(((in @ X782 @ X781)=>~(in @ X782 @ (setminus @ X780 @ X781))))=>(![X783:$i, X784:$i]:((subset @ (setminus @ X783 @ X784) @ X783))=>(![X785:$i, X786:$i]:((((setminus @ X785 @ X786)=(emptyset))=>(subset @ X785 @ X786)))=>(![X787:$i, X788:$i, X789:$i]:(((in @ X789 @ (symdiff @ X787 @ X788))=>![X790:$o]:((((in @ X789 @ X787)=>(~(in @ X789 @ X788)=>(X790)))=>((~(in @ X789 @ X787)=>((in @ X789 @ X788)=>(X790)))=>(X790))))))=>(![X791:$i, X792:$i, X793:$i]:(((in @ X793 @ X791)=>(~(in @ X793 @ X792)=>(in @ X793 @ (symdiff @ X791 @ X792)))))=>(![X794:$i, X795:$i, X796:$i]:((~(in @ X796 @ X794)=>((in @ X796 @ X795)=>(in @ X796 @ (symdiff @ X794 @ X795)))))=>(![X797:$i, X798:$i, X799:$i]:(((in @ X799 @ X797)=>((in @ X799 @ X798)=>~(in @ X799 @ (symdiff @ X797 @ X798)))))=>(![X800:$i, X801:$i, X802:$i]:((~(in @ X802 @ X800)=>(~(in @ X802 @ X801)=>~(in @ X802 @ (symdiff @ X800 @ X801)))))=>(![X803:$i, X804:$i]:((in @ X804 @ (setadjoin @ X803 @ (setadjoin @ X804 @ emptyset))))=>(![X805:$i, X806:$i]:((in @ X805 @ (setunion @ (setadjoin @ (setadjoin @ X805 @ emptyset) @ (setadjoin @ (setadjoin @ X805 @ (setadjoin @ X806 @ emptyset)) @ emptyset)))))=>(![X807:$i, X808:$i]:((in @ X808 @ (setunion @ (setadjoin @ (setadjoin @ X807 @ emptyset) @ (setadjoin @ (setadjoin @ X807 @ (setadjoin @ X808 @ emptyset)) @ emptyset)))))=>(![X809:$i, X810:$i]:(?[X811:$i]:(((in @ X811 @ (setunion @ (setadjoin @ (setadjoin @ X809 @ emptyset) @ (setadjoin @ (setadjoin @ X809 @ (setadjoin @ X810 @ emptyset)) @ emptyset))))&?[X812:$i]:(((in @ X812 @ (setunion @ (setadjoin @ (setadjoin @ X809 @ emptyset) @ (setadjoin @ (setadjoin @ X809 @ (setadjoin @ X810 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X809 @ emptyset) @ (setadjoin @ (setadjoin @ X809 @ (setadjoin @ X810 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X811 @ emptyset) @ (setadjoin @ (setadjoin @ X811 @ (setadjoin @ X812 @ emptyset)) @ emptyset))))))))=>(![X813:$i, X814:$i]:(?[X815:$i]:(((in @ X815 @ (setunion @ (kpair @ X813 @ X814)))&?[X816:$i]:(((in @ X816 @ (setunion @ (kpair @ X813 @ X814)))&((kpair @ X813 @ X814)=(setadjoin @ (setadjoin @ X815 @ emptyset) @ (setadjoin @ (setadjoin @ X815 @ (setadjoin @ X816 @ emptyset)) @ emptyset))))))))=>(![X817:$i, X818:$i]:(((in @ X818 @ X817)=>(subset @ (setadjoin @ X818 @ emptyset) @ X817)))=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ 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)],[inference(apply_def,[status(thm)],[c_0_158, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_159]), foundationAx]), wellorderingAx]), c_0_160]), c_0_161]), c_0_162]), c_0_163]), c_0_164]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_165]), setext]), emptyI]), noeltsimpempty]), c_0_166]), c_0_167]), c_0_168]), c_0_169]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_170]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_171]), c_0_172]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_173]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_174]), c_0_175]), c_0_176]), inCongP]), in__Cong]), c_0_177]), c_0_178]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_179]), c_0_180]), c_0_181]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_182]), c_0_183]), 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_184]), c_0_185]), singletonsubset])])]), c_0_186])).
% 0.33/0.47 thf(c_0_188, negated_conjecture, ![X827:$i, X828:$i, X830:$i, X831:$i, X832:$i, X833:$i, X834:$i, X835:$i, X836:$i, X837:$i, X838:$i, X840:$i, X841:$i, X843:$i, X844:$i, X845:$i, X846:$i, X847:$i, X849:$i, X850:$i > $i > $o, X851:$i, X853:$i, X856:$i, X858:$i, X859:$i, X860:$i, X861:$i, X863:$i, X864:$i > $o, X865:$i, X867:$i, X868:$i > $o, X869:$i, X870:$i, X871:$i > $o, X872:$i, X873:$i, X874:$i > $o, X875:$i, X876:$i > $o, X877:$i, X880:$i, X881:$o, X882:$i, X883:$i, X884:$o, X885:$i, X886:$i, X887:$i > $o, X888:$i, X891:$i, X892:$i, X895:$i, X897:$i, X899:$i, X900:$i > $o, X901:$i, X902:$i, X904:$i, X905:$i > $o, X906:$i, X907:$i, X908:$i, X909:$i, X910:$i, X911:$i, X912:$i, X913:$i, X914:$i, X915:$i, X916:$i, X917:$o, X918:$i, X919:$i, X920:$i, X921:$i, X922:$i, X923:$i, X925:$i, X926:$i, X927:$i, X928:$i, X929:$i, X930:$i, X931:$i, X932:$i, X933:$i, X934:$i, X935:$o, X937:$i, X938:$i, X939:$i > $o, X940:$i, X943:$i, X944:$i, X945:$i, X947:$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, X960:$i, X961:$i, X962:$i, X963:$i > $o, X964:$i, X965:$i > $o, X966:$i, X967:$i, X968:$i > $o, X969:$i, X971:$i, X972:$i > $o, X974:$i, X975:$i, X976:$i > $o, X978:$i, X979:$i, X980:$i > $o, X981:$i, X983:$o, X984:$o, X985:$i, X986:$i > $o, X988:$i, X989:$i, X990:$i > $o, X991:$i, X993:$i > $o, X994:$i, X997:$i, X998:$i > $o, X999:$i, X1003:$i, X1004:$i > $o, X1005:$i, X1008:$i, X1009:$i, X1010:$i, X1011:$i, X1012:$i, X1013:$i, X1014:$i, X1015:$i, X1016:$i, X1017:$i > $o, X1018:$i, X1020:$i, X1021:$i, X1022:$i > $o, X1023:$i > $o, X1026:$i, X1029:$i, X1030:$i, X1033:$i, X1034:$i, X1035:$i, X1036:$i, X1037:$i, X1038:$i, X1039:$i, X1040:$i, X1041:$i, X1042:$i > $o, X1043:$i, X1045:$i, X1046:$i, X1047:$i > $o, X1048:$i > $o, X1051:$i, X1053:$i, X1055:$i, X1056:$i, X1057:$i > $o, X1058:$i > $o, X1061:$i, X1062:$i, X1064:$i, X1065:$i, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1071:$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:$i, X1105:$i, X1106:$i, X1107:$i, X1108:$i > $o, X1109:$i, X1110:$i > $o, X1111:$i, X1112:$i, X1113:$i, X1114:$i, X1115:$i, X1116:$i, X1117:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$o, X1123:$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, X1146:$i, X1147:$i, X1148:$i, X1149:$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:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$i, X1190:$o, 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, X1207:$i, X1208:$i, X1209:$i, X1210:$i, X1213:$i, X1214:$i, X1217:$i, X1218:$i]:((((~(in @ (esk1_2 @ X827 @ X828) @ X827)|~(in @ (esk1_2 @ X827 @ X828) @ X828)|((X827)=(X828)))&((in @ (esk1_2 @ X827 @ X828) @ X827)|(in @ (esk1_2 @ X827 @ X828) @ X828)|((X827)=(X828))))&(~(in @ X830 @ emptyset)&(((~(in @ X833 @ (setadjoin @ X831 @ X832))|(((X833)=(X831))|(in @ X833 @ X832)))&((((X833)!=(X831))|(in @ X833 @ (setadjoin @ X831 @ X832)))&(~(in @ X833 @ X832)|(in @ X833 @ (setadjoin @ X831 @ X832)))))&(((~(in @ X835 @ (powerset @ X834))|(~(in @ X836 @ X835)|(in @ X836 @ X834)))&(((in @ (esk2_2 @ X837 @ X838) @ X838)|(in @ X838 @ (powerset @ X837)))&(~(in @ (esk2_2 @ X837 @ X838) @ X837)|(in @ X838 @ (powerset @ X837)))))&(((((in @ X841 @ (esk3_2 @ X840 @ X841))|~(in @ X841 @ (setunion @ X840)))&((in @ (esk3_2 @ X840 @ X841) @ X840)|~(in @ X841 @ (setunion @ X840))))&(~(in @ X844 @ X845)|~(in @ X845 @ X843)|(in @ X844 @ (setunion @ X843))))&((in @ emptyset @ omega)&((~(in @ X846 @ omega)|(in @ (setadjoin @ X846 @ X846) @ omega))&(((((in @ (esk4_1 @ X847) @ omega)|~(in @ emptyset @ X847)|(~(in @ X849 @ omega)|(in @ X849 @ X847)))&((in @ (esk4_1 @ X847) @ X847)|~(in @ emptyset @ X847)|(~(in @ X849 @ omega)|(in @ X849 @ X847))))&(~(in @ (setadjoin @ (esk4_1 @ X847) @ (esk4_1 @ X847)) @ X847)|~(in @ emptyset @ X847)|(~(in @ X849 @ omega)|(in @ X849 @ X847))))&((((((in @ (esk8_3 @ X850 @ X851 @ X856) @ X851)|~(in @ X856 @ (esk7_2 @ X850 @ X851))|(in @ (esk5_2 @ X850 @ X851) @ X851))&((X850 @ (esk8_3 @ X850 @ X851 @ X856) @ X856)|~(in @ X856 @ (esk7_2 @ X850 @ X851))|(in @ (esk5_2 @ X850 @ X851) @ X851)))&(~(in @ X859 @ X851)|~(X850 @ X859 @ X858)|(in @ X858 @ (esk7_2 @ X850 @ X851))|(in @ (esk5_2 @ X850 @ X851) @ X851)))&(((((in @ (esk8_3 @ X850 @ X851 @ X856) @ X851)|~(in @ X856 @ (esk7_2 @ X850 @ X851))|((X850 @ (esk5_2 @ X850 @ X851) @ (esk6_3 @ X850 @ X851 @ X853))|~(X850 @ (esk5_2 @ X850 @ X851) @ X853)))&((X850 @ (esk8_3 @ X850 @ X851 @ X856) @ X856)|~(in @ X856 @ (esk7_2 @ X850 @ X851))|((X850 @ (esk5_2 @ X850 @ X851) @ (esk6_3 @ X850 @ X851 @ X853))|~(X850 @ (esk5_2 @ X850 @ X851) @ X853))))&(~(in @ X859 @ X851)|~(X850 @ X859 @ X858)|(in @ X858 @ (esk7_2 @ X850 @ X851))|((X850 @ (esk5_2 @ X850 @ X851) @ (esk6_3 @ X850 @ X851 @ X853))|~(X850 @ (esk5_2 @ X850 @ X851) @ X853))))&((((in @ (esk8_3 @ X850 @ X851 @ X856) @ X851)|~(in @ X856 @ (esk7_2 @ X850 @ X851))|(((X853)!=(esk6_3 @ X850 @ X851 @ X853))|~(X850 @ (esk5_2 @ X850 @ X851) @ X853)))&((X850 @ (esk8_3 @ X850 @ X851 @ X856) @ X856)|~(in @ X856 @ (esk7_2 @ X850 @ X851))|(((X853)!=(esk6_3 @ X850 @ X851 @ X853))|~(X850 @ (esk5_2 @ X850 @ X851) @ X853))))&(~(in @ 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X1064))&((((X1066)!=(X1067))|(subset @ X1066 @ X1067))&((((in @ (esk53_2 @ X1068 @ X1069) @ X1068)|(subset @ X1068 @ X1069))&(~(in @ (esk53_2 @ X1068 @ X1069) @ X1069)|(subset @ X1068 @ X1069)))&((subset @ emptyset @ X1071)&((~(subset @ X1072 @ X1073)|(~(in @ X1074 @ X1072)|(in @ X1074 @ X1073)))&((~(subset @ X1075 @ X1076)|((in @ X1077 @ X1076)|~(in @ X1077 @ X1075)))&((~(in @ X1080 @ X1078)|((in @ X1080 @ X1079)|~(subset @ X1078 @ X1079)))&(((subset @ X1081 @ X1082)|((X1081)!=(X1082)))&((~(in @ X1085 @ X1083)|((in @ X1085 @ X1084)|((X1083)!=(X1084))))&((subset @ X1086 @ X1086)&((~(subset @ X1087 @ X1088)|(~(subset @ X1088 @ X1089)|(subset @ X1087 @ X1089)))&((subset @ X1091 @ (setadjoin @ X1090 @ X1091))&((~(subset @ X1092 @ X1094)|(subset @ X1092 @ (setadjoin @ X1093 @ X1094)))&((~(subset @ X1095 @ X1096)|(in @ X1095 @ (powerset @ X1096)))&((~(subset @ X1097 @ X1098)|(~(subset @ X1098 @ X1097)|((X1097)=(X1098))))&((~(subset @ X1099 @ emptyset)|((X1099)=(emptyset)))&((~(subset @ X1101 @ X1100)|(in @ X1101 @ (powerset @ X1100)))&((~(in @ X1103 @ (powerset @ X1102))|(subset @ X1103 @ X1102))&((in @ X1104 @ (powerset @ X1104))&((~(subset @ X1105 @ X1106)|(subset @ (powerset @ X1105) @ (powerset @ X1106)))&((in @ (dsetconstr @ X1107 @ X1108) @ (powerset @ X1107))&((subset @ (dsetconstr @ X1109 @ X1110) @ X1109)&((~(in @ X1113 @ X1111)|(in @ X1113 @ (binunion @ X1111 @ X1112)))&((in @ X1115 @ (setadjoin @ X1114 @ (setadjoin @ X1115 @ emptyset)))&((~(in @ X1118 @ X1117)|(in @ X1118 @ (binunion @ X1116 @ X1117)))&(((((in @ X1121 @ X1120)|(X1122)|(in @ X1121 @ X1119)|~(in @ X1121 @ (binunion @ X1119 @ X1120)))&(~(X1122)|(X1122)|(in @ X1121 @ X1119)|~(in @ X1121 @ (binunion @ X1119 @ X1120))))&(((in @ X1121 @ X1120)|(X1122)|~(X1122)|~(in @ X1121 @ (binunion @ X1119 @ X1120)))&(~(X1122)|(X1122)|~(X1122)|~(in @ X1121 @ (binunion @ X1119 @ X1120)))))&((~(in @ X1125 @ (binunion @ X1123 @ X1124))|((in @ X1125 @ X1123)|(in @ X1125 @ X1124)))&((subset @ X1126 @ (binunion @ X1126 @ X1127))&((subset @ X1129 @ (binunion @ X1128 @ X1129))&((~(in @ X1132 @ X1130)|(~(in @ X1132 @ X1131)|(in @ X1132 @ (binintersect @ X1130 @ X1131))))&((~(subset @ X1135 @ X1133)|(~(subset @ X1135 @ X1134)|(subset @ X1135 @ (binintersect @ X1133 @ X1134))))&((~(in @ X1138 @ (binintersect @ X1136 @ X1137))|(in @ X1138 @ X1136))&((subset @ (binintersect @ X1139 @ X1140) @ X1139)&((~(subset @ X1141 @ X1142)|((binintersect @ X1141 @ X1142)=(X1141)))&((((binintersect @ X1143 @ X1144)!=(X1144))|(subset @ X1144 @ X1143))&((~(in @ X1147 @ (binintersect @ X1145 @ X1146))|(in @ X1147 @ X1146))&((((in @ (esk54_2 @ X1148 @ X1149) @ X1148)|((binintersect @ X1148 @ X1149)=(emptyset)))&((in @ (esk54_2 @ X1148 @ X1149) @ X1149)|((binintersect @ X1148 @ X1149)=(emptyset))))&((subset @ (binintersect @ X1151 @ X1152) @ X1152)&((~(subset @ X1154 @ X1153)|((binintersect @ X1153 @ X1154)=(X1154)))&((((binintersect @ X1155 @ X1156)!=(X1155))|(subset @ X1155 @ X1156))&(((binintersect @ X1157 @ (binunion @ X1158 @ X1159))=(binunion @ (binintersect @ X1157 @ X1158) @ (binintersect @ X1157 @ X1159)))&((~(in @ X1162 @ X1160)|((in @ X1162 @ X1161)|(in @ X1162 @ (setminus @ X1160 @ X1161))))&((~(in @ X1165 @ (setminus @ X1163 @ X1164))|(in @ X1165 @ X1163))&((~(in @ X1168 @ (setminus @ X1166 @ X1167))|~(in @ X1168 @ X1167))&((~(subset @ X1169 @ X1170)|((setminus @ X1169 @ X1170)=(emptyset)))&(((in @ X1173 @ (setminus @ X1171 @ X1172))|(~(in @ X1173 @ X1171)|(in @ X1173 @ X1172)))&(((in @ X1176 @ (setminus @ X1174 @ X1175))|((in @ X1176 @ X1175)|~(in @ X1176 @ X1174)))&(((in @ X1179 @ X1177)|~(in @ X1179 @ (setminus @ X1177 @ X1178)))&((~(in @ X1182 @ X1181)|~(in @ X1182 @ (setminus @ X1180 @ X1181)))&((subset @ (setminus @ X1183 @ X1184) @ X1183)&((((setminus @ X1185 @ X1186)!=(emptyset))|(subset @ X1185 @ X1186))&((((~(in @ X1189 @ X1187)|(X1190)|(in @ X1189 @ X1187)|~(in @ X1189 @ (symdiff @ X1187 @ X1188)))&(((in @ X1189 @ X1188)|(X1190)|(in @ X1189 @ X1187)|~(in @ X1189 @ (symdiff @ X1187 @ X1188)))&(~(X1190)|(X1190)|(in @ X1189 @ X1187)|~(in @ X1189 @ (symdiff @ X1187 @ X1188)))))&(((~(in @ X1189 @ X1187)|(X1190)|~(in @ X1189 @ X1188)|~(in @ X1189 @ (symdiff @ X1187 @ X1188)))&(((in @ X1189 @ X1188)|(X1190)|~(in @ X1189 @ X1188)|~(in @ X1189 @ (symdiff @ X1187 @ X1188)))&(~(X1190)|(X1190)|~(in @ X1189 @ X1188)|~(in @ X1189 @ (symdiff @ X1187 @ X1188)))))&((~(in @ X1189 @ X1187)|(X1190)|~(X1190)|~(in @ X1189 @ (symdiff @ X1187 @ X1188)))&(((in @ X1189 @ X1188)|(X1190)|~(X1190)|~(in @ X1189 @ (symdiff @ X1187 @ X1188)))&(~(X1190)|(X1190)|~(X1190)|~(in @ X1189 @ (symdiff @ X1187 @ X1188)))))))&((~(in @ X1193 @ X1191)|((in @ X1193 @ X1192)|(in @ X1193 @ (symdiff @ X1191 @ X1192))))&(((in @ X1196 @ X1194)|(~(in @ X1196 @ X1195)|(in @ X1196 @ (symdiff @ X1194 @ X1195))))&((~(in @ X1199 @ X1197)|(~(in @ X1199 @ X1198)|~(in @ X1199 @ (symdiff @ X1197 @ X1198))))&(((in @ X1202 @ X1200)|((in @ X1202 @ X1201)|~(in @ X1202 @ (symdiff @ X1200 @ X1201))))&((in @ X1204 @ (setadjoin @ X1203 @ (setadjoin @ X1204 @ emptyset)))&((in @ X1205 @ (setunion @ (setadjoin @ (setadjoin @ X1205 @ emptyset) @ (setadjoin @ (setadjoin @ X1205 @ (setadjoin @ X1206 @ emptyset)) @ emptyset))))&((in @ X1208 @ (setunion @ (setadjoin @ (setadjoin @ X1207 @ emptyset) @ (setadjoin @ (setadjoin @ X1207 @ (setadjoin @ X1208 @ emptyset)) @ emptyset))))&(((in @ (esk55_2 @ X1209 @ X1210) @ (setunion @ (setadjoin @ (setadjoin @ X1209 @ emptyset) @ (setadjoin @ (setadjoin @ X1209 @ (setadjoin @ X1210 @ emptyset)) @ emptyset))))&((in @ (esk56_2 @ X1209 @ X1210) @ (setunion @ (setadjoin @ (setadjoin @ X1209 @ emptyset) @ (setadjoin @ (setadjoin @ X1209 @ (setadjoin @ X1210 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1209 @ emptyset) @ (setadjoin @ (setadjoin @ X1209 @ (setadjoin @ X1210 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk55_2 @ X1209 @ X1210) @ emptyset) @ (setadjoin @ (setadjoin @ (esk55_2 @ X1209 @ X1210) @ (setadjoin @ (esk56_2 @ X1209 @ X1210) @ emptyset)) @ emptyset)))))&(((in @ (esk57_2 @ X1213 @ X1214) @ (setunion @ (kpair @ X1213 @ X1214)))&((in @ (esk58_2 @ X1213 @ X1214) @ (setunion @ (kpair @ X1213 @ X1214)))&((kpair @ X1213 @ X1214)=(setadjoin @ (setadjoin @ (esk57_2 @ X1213 @ X1214) @ emptyset) @ (setadjoin @ (setadjoin @ (esk57_2 @ X1213 @ X1214) @ (setadjoin @ (esk58_2 @ X1213 @ X1214) @ emptyset)) @ emptyset)))))&((~(in @ X1218 @ X1217)|(subset @ (setadjoin @ X1218 @ emptyset) @ X1217))&((in @ esk60_0 @ esk59_0)&~(in @ (setadjoin @ esk60_0 @ emptyset) @ (powerset @ esk59_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_187])])])])])])])).
% 0.33/0.47 thf(c_0_189, negated_conjecture, ~((in @ (setadjoin @ esk60_0 @ emptyset) @ (powerset @ esk59_0))), inference(split_conjunct,[status(thm)],[c_0_188])).
% 0.33/0.47 thf(c_0_190, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ X3))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_188])).
% 0.33/0.47 thf(c_0_191, negated_conjecture, ~((subset @ (setadjoin @ esk60_0 @ emptyset) @ esk59_0)), inference(spm,[status(thm)],[c_0_189, c_0_190])).
% 0.33/0.47 thf(c_0_192, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ (setadjoin @ X2 @ emptyset) @ X3)|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_188])).
% 0.33/0.47 thf(c_0_193, negated_conjecture, (in @ esk60_0 @ esk59_0), inference(split_conjunct,[status(thm)],[c_0_188])).
% 0.33/0.47 thf(c_0_194, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191, c_0_192]), c_0_193])]), ['proof']).
% 0.33/0.47 % SZS output end CNFRefutation
% 0.33/0.47 % Parsed axioms : 305
% 0.33/0.47 % Removed by relevancy pruning/SinE : 0
% 0.33/0.47 % Initial clauses : 429
% 0.33/0.47 % Removed in clause preprocessing : 186
% 0.33/0.47 % Initial clauses in saturation : 243
% 0.33/0.47 % Processed clauses : 90
% 0.33/0.47 % ...of these trivial : 6
% 0.33/0.47 % ...subsumed : 17
% 0.33/0.47 % ...remaining for further processing : 67
% 0.33/0.47 % Other redundant clauses eliminated : 10
% 0.33/0.47 % Clauses deleted for lack of memory : 0
% 0.33/0.47 % Backward-subsumed : 0
% 0.33/0.47 % Backward-rewritten : 2
% 0.33/0.47 % Generated clauses : 112
% 0.33/0.47 % ...of the previous two non-redundant : 60
% 0.33/0.47 % ...aggressively subsumed : 0
% 0.33/0.47 % Contextual simplify-reflections : 0
% 0.33/0.47 % Paramodulations : 102
% 0.33/0.47 % Factorizations : 0
% 0.33/0.47 % NegExts : 0
% 0.33/0.47 % Equation resolutions : 10
% 0.33/0.47 % Disequality decompositions : 0
% 0.33/0.47 % Total rewrite steps : 53
% 0.33/0.47 % ...of those cached : 32
% 0.33/0.47 % Propositional unsat checks : 0
% 0.33/0.47 % Propositional check models : 0
% 0.33/0.47 % Propositional check unsatisfiable : 0
% 0.33/0.47 % Propositional clauses : 0
% 0.33/0.47 % Propositional clauses after purity: 0
% 0.33/0.47 % Propositional unsat core size : 0
% 0.33/0.47 % Propositional preprocessing time : 0.000
% 0.33/0.47 % Propositional encoding time : 0.000
% 0.33/0.47 % Propositional solver time : 0.000
% 0.33/0.47 % Success case prop preproc time : 0.000
% 0.33/0.47 % Success case prop encoding time : 0.000
% 0.33/0.47 % Success case prop solver time : 0.000
% 0.33/0.47 % Current number of processed clauses : 59
% 0.33/0.47 % Positive orientable unit clauses : 31
% 0.33/0.47 % Positive unorientable unit clauses: 0
% 0.33/0.47 % Negative unit clauses : 3
% 0.33/0.47 % Non-unit-clauses : 25
% 0.33/0.47 % Current number of unprocessed clauses: 211
% 0.33/0.47 % ...number of literals in the above : 719
% 0.33/0.47 % Current number of archived formulas : 0
% 0.33/0.47 % Current number of archived clauses : 3
% 0.33/0.47 % Clause-clause subsumption calls (NU) : 88
% 0.33/0.47 % Rec. Clause-clause subsumption calls : 81
% 0.33/0.47 % Non-unit clause-clause subsumptions : 10
% 0.33/0.47 % Unit Clause-clause subsumption calls : 1
% 0.33/0.47 % Rewrite failures with RHS unbound : 0
% 0.33/0.47 % BW rewrite match attempts : 6
% 0.33/0.47 % BW rewrite match successes : 2
% 0.33/0.47 % Condensation attempts : 0
% 0.33/0.47 % Condensation successes : 0
% 0.33/0.47 % Termbank termtop insertions : 36476
% 0.33/0.47 % Search garbage collected termcells : 13491
% 0.33/0.47
% 0.33/0.47 % -------------------------------------------------
% 0.33/0.47 % User time : 0.047 s
% 0.33/0.47 % System time : 0.008 s
% 0.33/0.47 % Total time : 0.054 s
% 0.33/0.47 % Maximum resident set size: 7008 pages
% 0.33/0.47
% 0.33/0.47 % -------------------------------------------------
% 0.33/0.47 % User time : 0.057 s
% 0.33/0.47 % System time : 0.012 s
% 0.33/0.47 % Total time : 0.070 s
% 0.33/0.47 % Maximum resident set size: 4864 pages
% 0.33/0.47 % E exiting
%------------------------------------------------------------------------------