%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU604^1 : 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 : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:41 AM UTC 2026
% Result : Theorem 32.11s 5.00s
% Output : CNFRefutation 32.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU604^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n019.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:57:17 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.26 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.xRYPDGpK5X/E---3.1_808293.p
% 32.11/5.00 % Version: 3.5.1-ho
% 32.11/5.00 % Preprocessing class: HSLMSLSSLLLCHFA.
% 32.11/5.00 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 32.11/5.00 % Starting ehoh_best5 with 300s (1) cores
% 32.11/5.00 % Starting almost_fo_3_lam with 300s (1) cores
% 32.11/5.00 % Starting new_bool_5 with 300s (1) cores
% 32.11/5.00 % Starting pre_casc_3 with 300s (1) cores
% 32.11/5.00 % Starting ho_unfolding_8 with 300s (1) cores
% 32.11/5.00 % Starting new_ho_10_cnf2 with 300s (1) cores
% 32.11/5.00 % Starting new_bool_3 with 300s (1) cores
% 32.11/5.00 % Starting new_ho_5 with 300s (1) cores
% 32.11/5.00 % new_bool_5 with pid 808308 completed with status 0
% 32.11/5.00 % Result found by new_bool_5
% 32.11/5.00 % Preprocessing class: HSLMSLSSLLLCHFA.
% 32.11/5.00 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 32.11/5.00 % Starting ehoh_best5 with 300s (1) cores
% 32.11/5.00 % Starting almost_fo_3_lam with 300s (1) cores
% 32.11/5.00 % Starting new_bool_5 with 300s (1) cores
% 32.11/5.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 32.11/5.00 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 32.11/5.00 % Search class: HGHSM-FSLM31-SHFMMSBN
% 32.11/5.00 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 32.11/5.00 % Starting SubtermCWHack with 28s (1) cores
% 32.11/5.00 % SubtermCWHack with pid 808316 completed with status 0
% 32.11/5.00 % Result found by SubtermCWHack
% 32.11/5.00 % Preprocessing class: HSLMSLSSLLLCHFA.
% 32.11/5.00 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 32.11/5.00 % Starting ehoh_best5 with 300s (1) cores
% 32.11/5.00 % Starting almost_fo_3_lam with 300s (1) cores
% 32.11/5.00 % Starting new_bool_5 with 300s (1) cores
% 32.11/5.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 32.11/5.00 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 32.11/5.00 % Search class: HGHSM-FSLM31-SHFMMSBN
% 32.11/5.00 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 32.11/5.00 % Starting SubtermCWHack with 28s (1) cores
% 32.11/5.00 % Preprocessing time : 0.002 s
% 32.11/5.00
% 32.11/5.00 % Proof found!
% 32.11/5.00 % SZS status Theorem
% 32.11/5.00 % SZS output start CNFRefutation
% 32.11/5.00 thf(decl_23, type, in: $i > $i > $o).
% 32.11/5.00 thf(decl_24, type, exu: ($i > $o) > $o).
% 32.11/5.00 thf(decl_25, type, setextAx: $o).
% 32.11/5.00 thf(decl_26, type, emptyset: $i).
% 32.11/5.00 thf(decl_27, type, emptysetAx: $o).
% 32.11/5.00 thf(decl_28, type, setadjoin: $i > $i > $i).
% 32.11/5.00 thf(decl_29, type, setadjoinAx: $o).
% 32.11/5.00 thf(decl_30, type, powerset: $i > $i).
% 32.11/5.00 thf(decl_31, type, powersetAx: $o).
% 32.11/5.00 thf(decl_32, type, setunion: $i > $i).
% 32.11/5.00 thf(decl_33, type, setunionAx: $o).
% 32.11/5.00 thf(decl_34, type, omega: $i).
% 32.11/5.00 thf(decl_35, type, omega0Ax: $o).
% 32.11/5.00 thf(decl_36, type, omegaSAx: $o).
% 32.11/5.00 thf(decl_37, type, omegaIndAx: $o).
% 32.11/5.00 thf(decl_38, type, replAx: $o).
% 32.11/5.00 thf(decl_39, type, foundationAx: $o).
% 32.11/5.00 thf(decl_40, type, wellorderingAx: $o).
% 32.11/5.00 thf(decl_41, type, descr: ($i > $o) > $i).
% 32.11/5.00 thf(decl_42, type, descrp: $o).
% 32.11/5.00 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 32.11/5.00 thf(decl_44, type, dsetconstrI: $o).
% 32.11/5.00 thf(decl_45, type, dsetconstrEL: $o).
% 32.11/5.00 thf(decl_46, type, dsetconstrER: $o).
% 32.11/5.00 thf(decl_47, type, exuE1: $o).
% 32.11/5.00 thf(decl_48, type, prop2set: $o > $i).
% 32.11/5.00 thf(decl_49, type, prop2setE: $o).
% 32.11/5.00 thf(decl_50, type, emptysetE: $o).
% 32.11/5.00 thf(decl_51, type, emptysetimpfalse: $o).
% 32.11/5.00 thf(decl_52, type, notinemptyset: $o).
% 32.11/5.00 thf(decl_53, type, exuE3e: $o).
% 32.11/5.00 thf(decl_54, type, setext: $o).
% 32.11/5.00 thf(decl_55, type, emptyI: $o).
% 32.11/5.00 thf(decl_56, type, noeltsimpempty: $o).
% 32.11/5.00 thf(decl_57, type, setbeta: $o).
% 32.11/5.00 thf(decl_58, type, nonempty: $i > $o).
% 32.11/5.00 thf(decl_59, type, nonemptyE1: $o).
% 32.11/5.00 thf(decl_60, type, nonemptyI: $o).
% 32.11/5.00 thf(decl_61, type, nonemptyI1: $o).
% 32.11/5.00 thf(decl_62, type, setadjoinIL: $o).
% 32.11/5.00 thf(decl_63, type, emptyinunitempty: $o).
% 32.11/5.00 thf(decl_64, type, setadjoinIR: $o).
% 32.11/5.00 thf(decl_65, type, setadjoinE: $o).
% 32.11/5.00 thf(decl_66, type, setadjoinOr: $o).
% 32.11/5.00 thf(decl_67, type, setoftrueEq: $o).
% 32.11/5.00 thf(decl_68, type, powersetI: $o).
% 32.11/5.00 thf(decl_69, type, emptyinPowerset: $o).
% 32.11/5.00 thf(decl_70, type, emptyInPowerset: $o).
% 32.11/5.00 thf(decl_71, type, powersetE: $o).
% 32.11/5.00 thf(decl_72, type, setunionI: $o).
% 32.11/5.00 thf(decl_73, type, setunionE: $o).
% 32.11/5.00 thf(decl_74, type, subPowSU: $o).
% 32.11/5.00 thf(decl_75, type, exuE2: $o).
% 32.11/5.00 thf(decl_76, type, nonemptyImpWitness: $o).
% 32.11/5.00 thf(decl_77, type, uniqinunit: $o).
% 32.11/5.00 thf(decl_78, type, notinsingleton: $o).
% 32.11/5.00 thf(decl_79, type, eqinunit: $o).
% 32.11/5.00 thf(decl_80, type, singletonsswitch: $o).
% 32.11/5.00 thf(decl_81, type, upairsetE: $o).
% 32.11/5.00 thf(decl_82, type, upairsetIL: $o).
% 32.11/5.00 thf(decl_83, type, upairsetIR: $o).
% 32.11/5.00 thf(decl_84, type, emptyE1: $o).
% 32.11/5.00 thf(decl_85, type, vacuousDall: $o).
% 32.11/5.00 thf(decl_86, type, quantDeMorgan1: $o).
% 32.11/5.00 thf(decl_87, type, quantDeMorgan2: $o).
% 32.11/5.00 thf(decl_88, type, quantDeMorgan3: $o).
% 32.11/5.00 thf(decl_89, type, quantDeMorgan4: $o).
% 32.11/5.00 thf(decl_90, type, prop2setI: $o).
% 32.11/5.00 thf(decl_92, type, prop2set2propI: $o).
% 32.11/5.00 thf(decl_93, type, notdexE: $o).
% 32.11/5.00 thf(decl_94, type, notdallE: $o).
% 32.11/5.00 thf(decl_95, type, exuI1: $o).
% 32.11/5.00 thf(decl_96, type, exuI3: $o).
% 32.11/5.00 thf(decl_97, type, exuI2: $o).
% 32.11/5.00 thf(decl_98, type, inCongP: $o).
% 32.11/5.00 thf(decl_99, type, in__Cong: $o).
% 32.11/5.00 thf(decl_100, type, exuE3u: $o).
% 32.11/5.00 thf(decl_101, type, exu__Cong: $o).
% 32.11/5.00 thf(decl_102, type, emptyset__Cong: $o).
% 32.11/5.00 thf(decl_103, type, setadjoin__Cong: $o).
% 32.11/5.00 thf(decl_104, type, powerset__Cong: $o).
% 32.11/5.00 thf(decl_105, type, setunion__Cong: $o).
% 32.11/5.00 thf(decl_106, type, omega__Cong: $o).
% 32.11/5.00 thf(decl_107, type, exuEu: $o).
% 32.11/5.00 thf(decl_108, type, descr__Cong: $o).
% 32.11/5.00 thf(decl_109, type, dsetconstr__Cong: $o).
% 32.11/5.00 thf(decl_110, type, subset: $i > $i > $o).
% 32.11/5.00 thf(decl_113, type, subsetI1: $o).
% 32.11/5.00 thf(decl_114, type, eqimpsubset2: $o).
% 32.11/5.00 thf(decl_115, type, eqimpsubset1: $o).
% 32.11/5.00 thf(decl_116, type, subsetI2: $o).
% 32.11/5.00 thf(decl_117, type, emptysetsubset: $o).
% 32.11/5.00 thf(decl_118, type, subsetE: $o).
% 32.11/5.00 thf(decl_119, type, subsetE2: $o).
% 32.11/5.00 thf(decl_120, type, notsubsetI: $o).
% 32.11/5.00 thf(decl_121, type, notequalI1: $o).
% 32.11/5.00 thf(decl_122, type, notequalI2: $o).
% 32.11/5.00 thf(decl_123, type, subsetRefl: $o).
% 32.11/5.00 thf(decl_124, type, subsetTrans: $o).
% 32.11/5.00 thf(decl_125, type, setadjoinSub: $o).
% 32.11/5.00 thf(decl_126, type, setadjoinSub2: $o).
% 32.11/5.00 thf(decl_127, type, subset2powerset: $o).
% 32.11/5.00 thf(decl_128, type, setextsub: $o).
% 32.11/5.00 thf(decl_129, type, subsetemptysetimpeq: $o).
% 32.11/5.00 thf(decl_130, type, powersetI1: $o).
% 32.11/5.00 thf(decl_131, type, powersetE1: $o).
% 32.11/5.00 thf(decl_132, type, inPowerset: $o).
% 32.11/5.00 thf(decl_133, type, powersetsubset: $o).
% 32.11/5.00 thf(decl_134, type, sepInPowerset: $o).
% 32.11/5.00 thf(decl_135, type, sepSubset: $o).
% 32.11/5.00 thf(decl_136, type, binunion: $i > $i > $i).
% 32.11/5.00 thf(decl_137, type, binunionIL: $o).
% 32.11/5.00 thf(decl_138, type, upairset2IR: $o).
% 32.11/5.00 thf(decl_139, type, binunionIR: $o).
% 32.11/5.00 thf(decl_140, type, binunionEcases: $o).
% 32.11/5.00 thf(decl_141, type, binunionE: $o).
% 32.11/5.00 thf(decl_142, type, binunionLsub: $o).
% 32.11/5.00 thf(decl_143, type, binunionRsub: $o).
% 32.11/5.00 thf(decl_144, type, binintersect: $i > $i > $i).
% 32.11/5.00 thf(decl_145, type, binintersectI: $o).
% 32.11/5.00 thf(decl_146, type, binintersectSubset5: $o).
% 32.11/5.00 thf(decl_147, type, binintersectEL: $o).
% 32.11/5.00 thf(decl_148, type, binintersectLsub: $o).
% 32.11/5.00 thf(decl_149, type, binintersectSubset2: $o).
% 32.11/5.00 thf(decl_150, type, binintersectSubset3: $o).
% 32.11/5.00 thf(decl_151, type, binintersectER: $o).
% 32.11/5.00 thf(decl_152, type, disjointsetsI1: $o).
% 32.11/5.00 thf(decl_153, type, binintersectRsub: $o).
% 32.11/5.00 thf(decl_154, type, binintersectSubset4: $o).
% 32.11/5.00 thf(decl_155, type, binintersectSubset1: $o).
% 32.11/5.00 thf(decl_156, type, bs114d: $o).
% 32.11/5.00 thf(decl_158, type, setminus: $i > $i > $i).
% 32.11/5.00 thf(decl_159, type, setminusI: $o).
% 32.11/5.00 thf(decl_160, type, setminusEL: $o).
% 32.11/5.00 thf(decl_161, type, setminusER: $o).
% 32.11/5.00 thf(decl_162, type, epred1_0: $o).
% 32.11/5.00 thf(decl_163, type, esk1_2: $i > $i > $i).
% 32.11/5.00 thf(decl_164, type, esk2_2: $i > $i > $i).
% 32.11/5.00 thf(decl_165, type, esk3_2: $i > $i > $i).
% 32.11/5.00 thf(decl_166, type, esk4_1: $i > $i).
% 32.11/5.00 thf(decl_167, type, esk5_2: ($i > $i > $o) > $i > $i).
% 32.11/5.00 thf(decl_168, type, esk6_2: ($i > $i > $o) > $i > $i).
% 32.11/5.00 thf(decl_169, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 32.11/5.00 thf(decl_170, type, esk8_1: $i > $i).
% 32.11/5.00 thf(decl_171, type, esk9_1: ($i > $o) > $i).
% 32.11/5.00 thf(decl_172, type, esk10_1: ($i > $o) > $i).
% 32.11/5.00 thf(decl_173, type, esk11_2: $i > $i > $i).
% 32.11/5.00 thf(decl_174, type, esk12_2: $i > $i > $i).
% 32.11/5.00 thf(decl_175, type, esk13_1: $i > $i).
% 32.11/5.00 thf(decl_176, type, esk14_1: $i > $i).
% 32.11/5.00 thf(decl_177, type, esk15_1: $i > $i).
% 32.11/5.00 thf(decl_178, type, esk16_2: $i > $i > $i).
% 32.11/5.00 thf(decl_179, type, esk17_3: $i > $i > $o > $i).
% 32.11/5.00 thf(decl_180, type, esk18_1: ($i > $o) > $i).
% 32.11/5.00 thf(decl_181, type, esk19_1: $i > $i).
% 32.11/5.00 thf(decl_182, type, esk20_2: $i > ($i > $o) > $i).
% 32.11/5.00 thf(decl_183, type, esk21_2: $i > ($i > $o) > $i).
% 32.11/5.00 thf(decl_184, type, esk22_2: $i > ($i > $o) > $i).
% 32.11/5.00 thf(decl_185, type, esk23_2: $i > ($i > $o) > $i).
% 32.11/5.00 thf(decl_186, type, esk24_2: $i > ($i > $o) > $i).
% 32.11/5.00 thf(decl_187, type, esk25_2: $i > ($i > $o) > $i).
% 32.11/5.00 thf(decl_188, type, esk26_2: ($i > $o) > $i > $i).
% 32.11/5.00 thf(decl_189, type, esk27_1: ($i > $o) > $i).
% 32.11/5.00 thf(decl_190, type, esk28_1: ($i > $o) > $i).
% 32.11/5.00 thf(decl_191, type, esk29_2: ($i > $o) > $i > $i).
% 32.11/5.00 thf(decl_192, type, esk30_2: ($i > $o) > ($i > $o) > $i).
% 32.11/5.00 thf(decl_193, type, esk31_2: ($i > $o) > ($i > $o) > $i).
% 32.11/5.00 thf(decl_194, type, esk32_2: ($i > $o) > ($i > $o) > $i).
% 32.11/5.00 thf(decl_195, type, esk33_2: ($i > $o) > ($i > $o) > $i).
% 32.11/5.00 thf(decl_196, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 32.11/5.00 thf(decl_197, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 32.11/5.00 thf(decl_198, type, esk36_2: $i > $i > $i).
% 32.11/5.00 thf(decl_199, type, esk37_2: $i > $i > $i).
% 32.11/5.00 thf(decl_200, type, esk38_2: $i > $i > $i).
% 32.11/5.00 thf(decl_201, type, esk39_0: $i).
% 32.11/5.00 thf(decl_202, type, esk40_0: $i).
% 32.11/5.00 thf(setminusSubset2, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setminusSubset2)).
% 32.11/5.00 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', sepSubset)).
% 32.11/5.00 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', sepInPowerset)).
% 32.11/5.00 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setbeta)).
% 32.11/5.00 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', exuE3e)).
% 32.11/5.00 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', nonemptyI)).
% 32.11/5.00 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setoftrueEq)).
% 32.11/5.00 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.xRYPDGpK5X/E---3.1_808293.p', exuE2)).
% 32.11/5.00 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.xRYPDGpK5X/E---3.1_808293.p', emptyE1)).
% 32.11/5.00 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.xRYPDGpK5X/E---3.1_808293.p', exuE3u)).
% 32.11/5.00 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.xRYPDGpK5X/E---3.1_808293.p', exuI2)).
% 32.11/5.00 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', exuI3)).
% 32.11/5.00 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', exuI1)).
% 32.11/5.00 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', exu__Cong)).
% 32.11/5.00 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', descr__Cong)).
% 32.11/5.00 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', exuEu)).
% 32.11/5.00 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', dsetconstr__Cong)).
% 32.11/5.00 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', exuE1)).
% 32.11/5.00 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', dsetconstrER)).
% 32.11/5.00 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', dsetconstrEL)).
% 32.11/5.00 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', dsetconstrI)).
% 32.11/5.00 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', descrp)).
% 32.11/5.00 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', replAx)).
% 32.11/5.00 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', powersetsubset)).
% 32.11/5.00 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', binunionIL)).
% 32.11/5.00 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', upairset2IR)).
% 32.11/5.00 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', binunionIR)).
% 32.11/5.00 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', binunionEcases)).
% 32.11/5.00 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', binunionE)).
% 32.11/5.00 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', noeltsimpempty)).
% 32.11/5.00 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', binunionLsub)).
% 32.11/5.00 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', emptyI)).
% 32.11/5.00 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', binunionRsub)).
% 32.11/5.00 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.xRYPDGpK5X/E---3.1_808293.p', setext)).
% 32.11/5.00 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', binintersectI)).
% 32.11/5.00 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', binintersectSubset5)).
% 32.11/5.00 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', notinemptyset)).
% 32.11/5.00 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', binintersectEL)).
% 32.11/5.00 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', emptysetimpfalse)).
% 32.11/5.00 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', binintersectLsub)).
% 32.11/5.00 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', nonemptyE1)).
% 32.11/5.00 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', binintersectSubset2)).
% 32.11/5.00 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', binintersectSubset3)).
% 32.11/5.00 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', binintersectER)).
% 32.11/5.00 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', disjointsetsI1)).
% 32.11/5.00 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', binintersectRsub)).
% 32.11/5.00 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', binintersectSubset4)).
% 32.11/5.00 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', binintersectSubset1)).
% 32.11/5.00 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', bs114d)).
% 32.11/5.00 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setminusI)).
% 32.11/5.00 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setminusEL)).
% 32.11/5.00 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setminusER)).
% 32.11/5.00 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setadjoinOr)).
% 32.11/5.00 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setadjoinE)).
% 32.11/5.00 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setadjoinIR)).
% 32.11/5.00 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', emptyinunitempty)).
% 32.11/5.00 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setadjoinIL)).
% 32.11/5.00 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', nonemptyI1)).
% 32.11/5.00 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', subPowSU)).
% 32.11/5.00 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.xRYPDGpK5X/E---3.1_808293.p', setunionE)).
% 32.11/5.00 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setunionI)).
% 32.11/5.00 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', powersetE)).
% 32.11/5.00 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', emptyInPowerset)).
% 32.11/5.00 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', emptyinPowerset)).
% 32.11/5.00 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', powersetI)).
% 32.11/5.00 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setextsub)).
% 32.11/5.00 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', upairsetIL)).
% 32.11/5.00 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', upairsetE)).
% 32.11/5.00 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', singletonsswitch)).
% 32.11/5.00 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', eqinunit)).
% 32.11/5.00 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', notinsingleton)).
% 32.11/5.00 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', uniqinunit)).
% 32.11/5.00 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', nonemptyImpWitness)).
% 32.11/5.00 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', upairsetIR)).
% 32.11/5.00 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', prop2setI)).
% 32.11/5.00 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', quantDeMorgan4)).
% 32.11/5.00 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', quantDeMorgan3)).
% 32.11/5.00 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', quantDeMorgan2)).
% 32.11/5.00 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', quantDeMorgan1)).
% 32.11/5.00 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', vacuousDall)).
% 32.11/5.00 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', notdexE)).
% 32.11/5.00 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', in__Cong)).
% 32.11/5.00 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', inCongP)).
% 32.11/5.00 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', notdallE)).
% 32.11/5.00 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', omega__Cong)).
% 32.11/5.00 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setunion__Cong)).
% 32.11/5.00 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', powerset__Cong)).
% 32.11/5.00 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setadjoin__Cong)).
% 32.11/5.00 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', emptyset__Cong)).
% 32.11/5.00 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', subsetE2)).
% 32.11/5.00 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', subsetE)).
% 32.11/5.00 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', emptysetsubset)).
% 32.11/5.00 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', subsetI2)).
% 32.11/5.00 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', eqimpsubset1)).
% 32.11/5.00 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', eqimpsubset2)).
% 32.11/5.00 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', subsetI1)).
% 32.11/5.00 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', notsubsetI)).
% 32.11/5.00 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', subset2powerset)).
% 32.11/5.00 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setadjoinSub2)).
% 32.11/5.00 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setadjoinSub)).
% 32.11/5.00 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', subsetTrans)).
% 32.11/5.00 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', subsetRefl)).
% 32.11/5.00 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', notequalI2)).
% 32.11/5.00 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', notequalI1)).
% 32.11/5.00 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', subsetemptysetimpeq)).
% 32.11/5.00 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', powersetI1)).
% 32.11/5.00 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', powersetE1)).
% 32.11/5.00 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', inPowerset)).
% 32.11/5.00 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', emptysetE)).
% 32.11/5.00 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', prop2setE)).
% 32.11/5.00 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.xRYPDGpK5X/E---3.1_808293.p', wellorderingAx)).
% 32.11/5.00 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.xRYPDGpK5X/E---3.1_808293.p', foundationAx)).
% 32.11/5.00 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', omegaIndAx)).
% 32.11/5.00 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', omegaSAx)).
% 32.11/5.00 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', omega0Ax)).
% 32.11/5.00 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setunionAx)).
% 32.11/5.00 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', powersetAx)).
% 32.11/5.00 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setadjoinAx)).
% 32.11/5.00 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', emptysetAx)).
% 32.11/5.00 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.xRYPDGpK5X/E---3.1_808293.p', setextAx)).
% 32.11/5.00 thf(c_0_120, 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)=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setminusSubset2])).
% 32.11/5.00 thf(c_0_121, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 32.11/5.00 thf(c_0_122, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 32.11/5.00 thf(c_0_123, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 32.11/5.00 thf(c_0_124, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 32.11/5.00 thf(c_0_125, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 32.11/5.00 thf(c_0_126, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 32.11/5.00 thf(c_0_127, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 32.11/5.00 thf(c_0_128, 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])).
% 32.11/5.00 thf(c_0_129, 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])).
% 32.11/5.00 thf(c_0_130, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 32.11/5.00 thf(c_0_131, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 32.11/5.00 thf(c_0_132, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 32.11/5.00 thf(c_0_133, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 32.11/5.00 thf(c_0_134, plain, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 32.11/5.00 thf(c_0_135, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 32.11/5.00 thf(c_0_136, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 32.11/5.00 thf(c_0_137, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 32.11/5.00 thf(c_0_138, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 32.11/5.00 thf(c_0_139, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 32.11/5.00 thf(c_0_140, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 32.11/5.00 thf(c_0_141, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 32.11/5.00 thf(c_0_142, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 32.11/5.00 thf(c_0_143, plain, ((epred1_0)<=>![X368:$i]:(?[X369:$i]:((((![X370:$i]:(((in @ X370 @ X369)=>![X371:$i]:(((in @ X371 @ X370)=>(in @ X371 @ X368)))))&![X372:$i, X373:$i]:((((in @ X372 @ X368)&(in @ X373 @ X368))=>(![X374:$i]:(((in @ X374 @ X369)=>((in @ X372 @ X374)<=>(in @ X373 @ X374))))=>((X372)=(X373))))))&![X375:$i, X376:$i]:((((in @ X375 @ X369)&(in @ X376 @ X369))=>(![X377:$i]:(((in @ X377 @ X375)=>(in @ X377 @ X376)))|![X378:$i]:(((in @ X378 @ X376)=>(in @ X378 @ X375)))))))&![X379:$i]:(((![X380:$i]:(((in @ X380 @ X379)=>(in @ X380 @ X368)))&?[X381:$i]:((in @ X381 @ X379)))=>?[X382:$i, X383:$i]:(((((in @ X382 @ X369)&(in @ X383 @ X379))&~(?[X384:$i]:(((in @ X384 @ X382)&(in @ X384 @ X379)))))&![X385:$i]:(((in @ X385 @ X369)=>(![X386:$i]:(((in @ X386 @ X385)=>(in @ X386 @ X382)))|(in @ X383 @ X385)))))))))))), introduced(definition)).
% 32.11/5.00 thf(c_0_144, negated_conjecture, ~((![X341:$i, X342:$i]:((![X343:$i]:(((in @ X343 @ X341)<=>(in @ X343 @ X342)))=>((X341)=(X342))))=>(![X344:$i]:(~(in @ X344 @ emptyset))=>(![X345:$i, X346:$i, X347:$i]:(((in @ X347 @ (setadjoin @ X345 @ X346))<=>(((X347)=(X345))|(in @ X347 @ X346))))=>(![X348:$i, X349:$i]:(((in @ X349 @ (powerset @ X348))<=>![X350:$i]:(((in @ X350 @ X349)=>(in @ X350 @ X348)))))=>(![X351:$i, X352:$i]:(((in @ X352 @ (setunion @ X351))<=>?[X353:$i]:(((in @ X352 @ X353)&(in @ X353 @ X351)))))=>((in @ emptyset @ omega)=>(![X354:$i]:(((in @ X354 @ omega)=>(in @ (setadjoin @ X354 @ X354) @ omega)))=>(![X355:$i]:((((in @ emptyset @ X355)&![X356:$i]:((((in @ X356 @ omega)&(in @ X356 @ X355))=>(in @ (setadjoin @ X356 @ X356) @ X355))))=>![X357:$i]:(((in @ X357 @ omega)=>(in @ X357 @ X355)))))=>(![X358:$i > $i > $o, X359:$i]:((![X360:$i]:(((in @ X360 @ X359)=>(exu @ (X358 @ X360))))=>?[X361:$i]:(![X362:$i]:(((in @ X362 @ X361)<=>?[X363:$i]:(((in @ X363 @ X359)&(X358 @ X363 @ X362))))))))=>(![X364:$i]:((?[X365:$i]:((in @ X365 @ X364))=>?[X366:$i]:(((in @ X366 @ X364)&~(?[X367:$i]:(((in @ X367 @ X366)&(in @ X367 @ X364))))))))=>((epred1_0)=>(![X387:$i > $o]:(((exu @ X387)=>(X387 @ (descr @ (^[Z0:$i]:(X387 @ Z0))))))=>(![X388:$i, X389:$i > $o, X390:$i]:(((in @ X390 @ X388)=>((X389 @ X390)=>(in @ X390 @ (dsetconstr @ X388 @ X389)))))=>(![X391:$i, X392:$i > $o, X393:$i]:(((in @ X393 @ (dsetconstr @ X391 @ X392))=>(in @ X393 @ X391)))=>(![X394:$i, X395:$i > $o, X396:$i]:(((in @ X396 @ (dsetconstr @ X394 @ X395))=>(X395 @ X396)))=>(![X397:$i > $o]:(((exu @ X397)=>?[X398:$i]:(((X397 @ X398)&![X399:$i]:(((X397 @ X399)=>((X398)=(X399))))))))=>(![X400:$o, X401:$i]:(((in @ X401 @ (prop2set @ ((X400))))=>(X400)))=>(![X402:$i]:(((in @ X402 @ emptyset)=>![X403:$o]:((X403))))=>(![X404:$i]:(((in @ X404 @ emptyset)=>~($true)))=>(![X405:$i]:(~(in @ X405 @ emptyset))=>(![X406:$i > $o]:(((exu @ X406)=>?[X407:$i]:((X406 @ X407))))=>(![X408:$i, X409:$i]:((![X410:$i]:(((in @ X410 @ X408)=>(in @ X410 @ X409)))=>(![X411:$i]:(((in @ X411 @ X409)=>(in @ X411 @ X408)))=>((X408)=(X409)))))=>(![X412:$i]:((![X413:$i]:(~(in @ X413 @ X412))=>((X412)=(emptyset))))=>(![X414:$i]:((![X415:$i]:(~(in @ X415 @ X414))=>((X414)=(emptyset))))=>(![X416:$i, X417:$i > $o, X418:$i]:(((in @ X418 @ X416)=>((in @ X418 @ (dsetconstr @ X416 @ X417))<=>(X417 @ X418))))=>(![X419:$i]:(((nonempty @ X419)=>?[X420:$i]:((in @ X420 @ X419))))=>(![X421:$i, X422:$i > $o, X423:$i]:(((in @ X423 @ X421)=>((X422 @ X423)=>(nonempty @ (dsetconstr @ X421 @ X422)))))=>(![X424:$i]:((?[X425:$i]:((in @ X425 @ X424))=>(nonempty @ X424)))=>(![X426:$i, X427:$i]:((in @ X426 @ (setadjoin @ X426 @ X427)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X428:$i, X429:$i, X430:$i]:(((in @ X430 @ X429)=>(in @ X430 @ (setadjoin @ X428 @ X429))))=>(![X431:$i, X432:$i, X433:$i]:(((in @ X433 @ (setadjoin @ X431 @ X432))=>![X434:$o]:(((((X433)=(X431))=>(X434))=>(((in @ X433 @ X432)=>(X434))=>(X434))))))=>(![X435:$i, X436:$i, X437:$i]:(((in @ X437 @ (setadjoin @ X435 @ X436))=>(((X437)=(X435))|(in @ X437 @ X436))))=>(![X438:$i]:(((dsetconstr @ X438 @ (^[Z0:$i]:($true)))=(X438)))=>(![X439:$i, X440:$i]:((![X441:$i]:(((in @ X441 @ X440)=>(in @ X441 @ X439)))=>(in @ X440 @ (powerset @ X439))))=>(![X442:$i]:((in @ emptyset @ (powerset @ X442)))=>(![X443:$i]:((in @ emptyset @ (powerset @ X443)))=>(![X444:$i, X445:$i, X446:$i]:(((in @ X445 @ (powerset @ X444))=>((in @ X446 @ X445)=>(in @ X446 @ X444))))=>(![X447:$i, X448:$i, X449:$i]:(((in @ X448 @ X449)=>((in @ X449 @ X447)=>(in @ X448 @ (setunion @ X447)))))=>(![X450:$i, X451:$i]:(((in @ X451 @ (setunion @ X450))=>![X452:$o]:((![X453:$i]:(((in @ X451 @ X453)=>((in @ X453 @ X450)=>(X452))))=>(X452)))))=>(![X454:$i, X455:$i]:(((in @ X455 @ X454)=>(in @ X455 @ (powerset @ (setunion @ X454)))))=>(![X456:$i > $o]:(((exu @ X456)=>?[X457:$i]:(![X458:$i]:(((X456 @ X458)<=>((X458)=(X457)))))))=>(![X459:$i]:(((nonempty @ X459)=>?[X460:$i]:(((in @ X460 @ X459)&$true))))=>(![X461:$i, X462:$i]:(((in @ X461 @ (setadjoin @ X462 @ emptyset))=>((X461)=(X462))))=>(![X463:$i, X464:$i]:((((X463)!=(X464))=>~(in @ X464 @ (setadjoin @ X463 @ emptyset))))=>(![X465:$i, X466:$i]:((((X465)=(X466))=>(in @ X465 @ (setadjoin @ X466 @ emptyset))))=>(![X467:$i, X468:$i]:(((in @ X467 @ (setadjoin @ X468 @ emptyset))=>(in @ X468 @ (setadjoin @ X467 @ emptyset))))=>(![X469:$i, X470:$i, X471:$i]:(((in @ X471 @ (setadjoin @ X469 @ (setadjoin @ X470 @ emptyset)))=>(((X471)=(X469))|((X471)=(X470)))))=>(![X472:$i, X473:$i]:((in @ X472 @ (setadjoin @ X472 @ (setadjoin @ X473 @ emptyset))))=>(![X474:$i, X475:$i]:((in @ X475 @ (setadjoin @ X474 @ (setadjoin @ X475 @ emptyset))))=>(![X476:$i, X477:$i > $o]:((?[X478:$i]:(((in @ X478 @ X476)&(X477 @ X478)))=>(((dsetconstr @ X476 @ X477)=(emptyset))=>~($true))))=>(![X479:$i > $o, X480:$i]:(((in @ X480 @ emptyset)=>(X479 @ X480)))=>(![X481:$i, X482:$i > $o]:((~(![X483:$i]:(((in @ X483 @ X481)=>(X482 @ X483))))=>?[X484:$i]:(((in @ X484 @ X481)&~((X482 @ X484))))))=>(![X485:$i, X486:$i > $o]:((![X487:$i]:(((in @ X487 @ X485)=>~((X486 @ X487))))=>~(?[X488:$i]:(((in @ X488 @ X485)&(X486 @ X488))))))=>(![X489:$i, X490:$i > $o]:((~(?[X491:$i]:(((in @ X491 @ X489)&(X490 @ X491))))=>![X492:$i]:(((in @ X492 @ X489)=>~((X490 @ X492))))))=>(![X493:$i, X494:$i > $o]:((?[X495:$i]:(((in @ X495 @ X493)&~((X494 @ X495))))=>~(![X496:$i]:(((in @ X496 @ X493)=>(X494 @ X496))))))=>(![X497:$o]:(((X497)=>(in @ emptyset @ (prop2set @ ((X497))))))=>((prop2set2propI)=>(![X498:$i, X499:$i > $o]:((~(?[X500:$i]:(((in @ X500 @ X498)&(X499 @ X500))))=>![X501:$i]:(((in @ X501 @ X498)=>~((X499 @ X501))))))=>(![X502:$i, X503:$i > $o]:((~(![X504:$i]:(((in @ X504 @ X502)=>(X503 @ X504))))=>?[X505:$i]:(((in @ X505 @ X502)&~((X503 @ X505))))))=>(![X506:$i > $o]:((?[X507:$i]:(((X506 @ X507)&![X508:$i]:(((X506 @ X508)=>((X507)=(X508))))))=>(exu @ X506)))=>(![X509:$i > $o]:((?[X510:$i]:((X509 @ X510))=>(![X511:$i, X512:$i]:(((X509 @ X511)=>((X509 @ X512)=>((X511)=(X512)))))=>(exu @ X509))))=>(![X513:$i > $o]:((?[X514:$i]:(![X515:$i]:(((X513 @ X515)<=>((X515)=(X514)))))=>(exu @ X513)))=>(![X516:$i, X517:$i]:((((X516)=(X517))=>![X518:$i, X519:$i]:((((X518)=(X519))=>((in @ X518 @ X516)=>(in @ X519 @ X517))))))=>(![X520:$i, X521:$i]:((((X520)=(X521))=>![X522:$i, X523:$i]:((((X522)=(X523))=>((in @ X522 @ X520)<=>(in @ X523 @ X521))))))=>(![X524:$i > $o]:(((exu @ X524)=>![X525:$i, X526:$i]:(((X524 @ X525)=>((X524 @ X526)=>((X525)=(X526)))))))=>(![X527:$i > $o, X528:$i > $o]:((![X529:$i, X530:$i]:((((X529)=(X530))=>((X527 @ X529)<=>(X528 @ X530))))=>((exu @ X527)<=>(exu @ X528))))=>(((emptyset)=(emptyset))=>(![X531:$i, X532:$i]:((((X531)=(X532))=>![X533:$i, X534:$i]:((((X533)=(X534))=>((setadjoin @ X531 @ X533)=(setadjoin @ X532 @ X534))))))=>(![X535:$i, X536:$i]:((((X535)=(X536))=>((powerset @ X535)=(powerset @ X536))))=>(![X537:$i, X538:$i]:((((X537)=(X538))=>((setunion @ X537)=(setunion @ X538))))=>(((omega)=(omega))=>(![X539:$i > $o]:(((exu @ X539)=>![X540:$i, X541:$i]:(((X539 @ X540)=>((X539 @ X541)=>((X540)=(X541)))))))=>(![X542:$i > $o, X543:$i > $o]:((![X544:$i, X545:$i]:((((X544)=(X545))=>((X542 @ X544)<=>(X543 @ X545))))=>((exu @ X542)=>((exu @ X543)=>((descr @ X542)=(descr @ X543))))))=>(![X546:$i, X547:$i]:((((X546)=(X547))=>![X548:$i > $o, X549:$i > $o]:((![X550:$i]:(((in @ X550 @ X546)=>![X551:$i]:(((in @ X551 @ X547)=>(((X550)=(X551))=>((X548 @ X550)<=>(X549 @ X551)))))))=>((dsetconstr @ X546 @ X548)=(dsetconstr @ X547 @ X549))))))=>(![X552:$i, X553:$i]:((![X554:$i]:(((in @ X554 @ X552)=>(in @ X554 @ X553)))=>(subset @ X552 @ X553)))=>(![X555:$i, X556:$i]:((((X555)=(X556))=>(subset @ X556 @ X555)))=>(![X557:$i, X558:$i]:((((X557)=(X558))=>(subset @ X557 @ X558)))=>(![X559:$i, X560:$i]:((![X561:$i]:(((in @ X561 @ X559)=>(in @ X561 @ X560)))=>(subset @ X559 @ X560)))=>(![X562:$i]:((subset @ emptyset @ X562))=>(![X563:$i, X564:$i, X565:$i]:(((subset @ X563 @ X564)=>((in @ X565 @ X563)=>(in @ X565 @ X564))))=>(![X566:$i, X567:$i, X568:$i]:(((subset @ X566 @ X567)=>(~(in @ X568 @ X567)=>~(in @ X568 @ X566))))=>(![X569:$i, X570:$i, X571:$i]:(((in @ X571 @ X569)=>(~(in @ X571 @ X570)=>~(subset @ X569 @ X570))))=>(![X572:$i, X573:$i]:((~(subset @ X572 @ X573)=>((X572)!=(X573))))=>(![X574:$i, X575:$i, X576:$i]:(((in @ X576 @ X574)=>(~(in @ X576 @ X575)=>((X574)!=(X575)))))=>(![X577:$i]:((subset @ X577 @ X577))=>(![X578:$i, X579:$i, X580:$i]:(((subset @ X578 @ X579)=>((subset @ X579 @ X580)=>(subset @ X578 @ X580))))=>(![X581:$i, X582:$i]:((subset @ X582 @ (setadjoin @ X581 @ X582)))=>(![X583:$i, X584:$i, X585:$i]:(((subset @ X583 @ X585)=>(subset @ X583 @ (setadjoin @ X584 @ X585))))=>(![X586:$i, X587:$i]:(((subset @ X586 @ X587)=>(in @ X586 @ (powerset @ X587))))=>(![X588:$i, X589:$i]:(((subset @ X588 @ X589)=>((subset @ X589 @ X588)=>((X588)=(X589)))))=>(![X590:$i]:(((subset @ X590 @ emptyset)=>((X590)=(emptyset))))=>(![X591:$i, X592:$i]:(((subset @ X592 @ X591)=>(in @ X592 @ (powerset @ X591))))=>(![X593:$i, X594:$i]:(((in @ X594 @ (powerset @ X593))=>(subset @ X594 @ X593)))=>(![X595:$i]:((in @ X595 @ (powerset @ X595)))=>(![X596:$i, X597:$i]:(((subset @ X596 @ X597)=>(subset @ (powerset @ X596) @ (powerset @ X597))))=>(![X598:$i, X599:$i > $o]:((in @ (dsetconstr @ X598 @ X599) @ (powerset @ X598)))=>(![X600:$i, X601:$i > $o]:((subset @ (dsetconstr @ X600 @ X601) @ X600))=>(![X602:$i, X603:$i, X604:$i]:(((in @ X604 @ X602)=>(in @ X604 @ (binunion @ X602 @ X603))))=>(![X605:$i, X606:$i]:((in @ X606 @ (setadjoin @ X605 @ (setadjoin @ X606 @ emptyset))))=>(![X607:$i, X608:$i, X609:$i]:(((in @ X609 @ X608)=>(in @ X609 @ (binunion @ X607 @ X608))))=>(![X610:$i, X611:$i, X612:$i, X613:$o]:(((in @ X612 @ (binunion @ X610 @ X611))=>(((in @ X612 @ X610)=>(X613))=>(((in @ X612 @ X611)=>(X613))=>(X613)))))=>(![X614:$i, X615:$i, X616:$i]:(((in @ X616 @ (binunion @ X614 @ X615))=>((in @ X616 @ X614)|(in @ X616 @ X615))))=>(![X617:$i, X618:$i]:((subset @ X617 @ (binunion @ X617 @ X618)))=>(![X619:$i, X620:$i]:((subset @ X620 @ (binunion @ X619 @ X620)))=>(![X621:$i, X622:$i, X623:$i]:(((in @ X623 @ X621)=>((in @ X623 @ X622)=>(in @ X623 @ (binintersect @ X621 @ X622)))))=>(![X624:$i, X625:$i, X626:$i]:(((subset @ X626 @ X624)=>((subset @ X626 @ X625)=>(subset @ X626 @ (binintersect @ X624 @ X625)))))=>(![X627:$i, X628:$i, X629:$i]:(((in @ X629 @ (binintersect @ X627 @ X628))=>(in @ X629 @ X627)))=>(![X630:$i, X631:$i]:((subset @ (binintersect @ X630 @ X631) @ X630))=>(![X632:$i, X633:$i]:(((subset @ X632 @ X633)=>((binintersect @ X632 @ X633)=(X632))))=>(![X634:$i, X635:$i]:((((binintersect @ X634 @ X635)=(X635))=>(subset @ X635 @ X634)))=>(![X636:$i, X637:$i, X638:$i]:(((in @ X638 @ (binintersect @ X636 @ X637))=>(in @ X638 @ X637)))=>(![X639:$i, X640:$i]:((~(?[X641:$i]:(((in @ X641 @ X639)&(in @ X641 @ X640))))=>((binintersect @ X639 @ X640)=(emptyset))))=>(![X642:$i, X643:$i]:((subset @ (binintersect @ X642 @ X643) @ X643))=>(![X644:$i, X645:$i]:(((subset @ X645 @ X644)=>((binintersect @ X644 @ X645)=(X645))))=>(![X646:$i, X647:$i]:((((binintersect @ X646 @ X647)=(X646))=>(subset @ X646 @ X647)))=>(![X648:$i, X649:$i, X650:$i]:(((binintersect @ X648 @ (binunion @ X649 @ X650))=(binunion @ (binintersect @ X648 @ X649) @ (binintersect @ X648 @ X650))))=>(![X651:$i, X652:$i, X653:$i]:(((in @ X653 @ X651)=>(~(in @ X653 @ X652)=>(in @ X653 @ (setminus @ X651 @ X652)))))=>(![X654:$i, X655:$i, X656:$i]:(((in @ X656 @ (setminus @ X654 @ X655))=>(in @ X656 @ X654)))=>(![X657:$i, X658:$i, X659:$i]:(((in @ X659 @ (setminus @ X657 @ X658))=>~(in @ X659 @ X658)))=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_120, c_0_121]), powersetsubset]), c_0_122]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), c_0_123]), binunionE]), noeltsimpempty]), binunionLsub]), emptyI]), binunionRsub]), setext]), binintersectI]), c_0_124]), binintersectSubset5]), notinemptyset]), binintersectEL]), emptysetimpfalse]), binintersectLsub]), nonemptyE1]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), nonemptyI1]), c_0_125]), c_0_126]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_127]), setextsub]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), nonemptyImpWitness]), upairsetIR]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_128]), notdexE]), c_0_129]), in__Cong]), inCongP]), c_0_130]), c_0_131]), c_0_132]), notdallE]), c_0_133]), c_0_134]), c_0_135]), omega__Cong]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_136]), subsetE2]), subsetE]), emptysetsubset]), subsetI2]), eqimpsubset1]), eqimpsubset2]), subsetI1]), notsubsetI]), subset2powerset]), setadjoinSub2]), setadjoinSub]), subsetTrans]), subsetRefl]), notequalI2]), notequalI1]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), emptysetE]), prop2setE]), c_0_137]), c_0_138]), c_0_139]), c_0_140]), c_0_141]), wellorderingAx]), foundationAx]), c_0_142]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_143])).
% 32.11/5.00 thf(c_0_145, negated_conjecture, ![X660:$i, X661:$i, X663:$i, X664:$i, X665:$i, X666:$i, X667:$i, X668:$i, X669:$i, X670:$i, X671:$i, X673:$i, X674:$i, X676:$i, X677:$i, X678:$i, X679:$i, X680:$i, X682:$i, X683:$i > $i > $o, X684:$i, X687:$i, X689:$i, X690:$i, X691:$i, X692:$i, X694:$i, X695:$i > $o, X696:$i, X697:$i > $o, X698:$i, X699:$i, X700:$i > $o, X701:$i, X702:$i, X703:$i > $o, X704:$i, X705:$i > $o, X707:$i, X708:$o, X709:$i, X710:$i, X711:$o, X712:$i, X713:$i, X714:$i > $o, X716:$i, X717:$i, X720:$i, X722:$i, X724:$i, X725:$i > $o, X726:$i, X727:$i, X729:$i, X730:$i > $o, X731:$i, X732:$i, X733:$i, X734:$i, X735:$i, X736:$i, X737:$i, X738:$i, X739:$i, X740:$i, X741:$i, X742:$o, X743:$i, X744:$i, X745:$i, X746:$i, X747:$i, X748:$i, X750:$i, X751:$i, X752:$i, X753:$i, X754:$i, X755:$i, X756:$i, X757:$i, X758:$i, X759:$i, X760:$o, X762:$i, X763:$i, X764:$i > $o, X766:$i, X767:$i, X768:$i, X770:$i, X771:$i, X772:$i, X773:$i, X774:$i, X775:$i, X776:$i, X777:$i, X778:$i, X779:$i, X780:$i, X781:$i, X782:$i, X783:$i, X784:$i, X785:$i, X786:$i > $o, X787:$i, X788:$i > $o, X789:$i, X790:$i, X791:$i > $o, X792:$i, X794:$i, X795:$i > $o, X797:$i, X798:$i, X799:$i > $o, X801:$i, X802:$i, X803:$i > $o, X804:$i, X806:$o, X807:$i, X808:$i > $o, X810:$i, X811:$i, X812:$i > $o, X813:$i, X815:$i > $o, X816:$i, X818:$i > $o, X819:$i, X822:$i > $o, X823:$i, X825:$i, X826:$i, X827:$i, X828:$i, X829:$i, X830:$i, X831:$i, X832:$i, X833:$i > $o, X834:$i, X835:$i, X836:$i > $o, X837:$i > $o, X840:$i, X841:$i, X842:$i, X843:$i, X844:$i, X845:$i, X846:$i, X847:$i, X848:$i > $o, X849:$i, X850:$i, X851:$i > $o, X852:$i > $o, X855:$i, X856:$i, X857:$i > $o, X858:$i > $o, X861:$i, X862:$i, X864:$i, X865:$i, X866:$i, X867:$i, X868:$i, X869:$i, X871:$i, X872:$i, X873:$i, X874:$i, X875:$i, X876:$i, X877:$i, X878:$i, X879:$i, X880:$i, X881:$i, X882:$i, X883:$i, X884:$i, X885:$i, X886:$i, X887:$i, X888:$i, X889:$i, X890:$i, X891:$i, X892:$i, X893:$i, X894:$i, X895:$i, X896:$i, X897:$i, X898:$i, X899:$i, X900:$i, X901:$i, X902:$i, X903:$i, X904:$i, X905:$i, X906:$i, X907:$i, X908:$i > $o, X909:$i, X910:$i > $o, X911:$i, X912:$i, X913:$i, X914:$i, X915:$i, X916:$i, X917:$i, X918:$i, X919:$i, X920:$i, X921:$i, X922:$o, X923:$i, X924:$i, X925:$i, X926:$i, X927:$i, X928:$i, X929:$i, X930:$i, X931:$i, X932:$i, X933:$i, X934:$i, X935:$i, X936:$i, X937:$i, X938:$i, X939:$i, X940:$i, X941:$i, X942:$i, X943:$i, X944:$i, X945:$i, X946:$i, X947:$i, X948:$i, X949:$i, 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:$i, X964:$i, X965:$i, X966:$i, X967:$i, X968:$i]:((((~(in @ (esk1_2 @ X660 @ X661) @ X660)|~(in @ (esk1_2 @ X660 @ X661) @ X661)|((X660)=(X661)))&((in @ (esk1_2 @ X660 @ X661) @ X660)|(in @ (esk1_2 @ X660 @ X661) @ X661)|((X660)=(X661))))&(~(in @ X663 @ emptyset)&(((~(in @ X666 @ (setadjoin @ X664 @ X665))|(((X666)=(X664))|(in @ X666 @ X665)))&((((X666)!=(X664))|(in @ X666 @ (setadjoin @ X664 @ X665)))&(~(in @ X666 @ X665)|(in @ X666 @ (setadjoin @ X664 @ X665)))))&(((~(in @ X668 @ (powerset @ X667))|(~(in @ X669 @ X668)|(in @ X669 @ X667)))&(((in @ (esk2_2 @ X670 @ X671) @ X671)|(in @ X671 @ (powerset @ X670)))&(~(in @ (esk2_2 @ X670 @ X671) @ X670)|(in @ X671 @ (powerset @ X670)))))&(((((in @ X674 @ (esk3_2 @ X673 @ X674))|~(in @ X674 @ (setunion @ X673)))&((in @ (esk3_2 @ X673 @ X674) @ X673)|~(in @ X674 @ (setunion @ X673))))&(~(in @ X677 @ X678)|~(in @ X678 @ X676)|(in @ X677 @ (setunion @ X676))))&((in @ emptyset @ omega)&((~(in @ X679 @ omega)|(in @ (setadjoin @ X679 @ X679) @ omega))&(((((in @ (esk4_1 @ X680) @ omega)|~(in @ emptyset @ X680)|(~(in @ X682 @ omega)|(in @ X682 @ X680)))&((in @ (esk4_1 @ X680) @ X680)|~(in @ emptyset @ X680)|(~(in @ X682 @ omega)|(in @ X682 @ X680))))&(~(in @ (setadjoin @ (esk4_1 @ X680) @ (esk4_1 @ X680)) @ X680)|~(in @ emptyset @ X680)|(~(in @ X682 @ omega)|(in @ X682 @ X680))))&((((((in @ (esk7_3 @ X683 @ X684 @ X687) @ X684)|~(in @ X687 @ (esk6_2 @ X683 @ X684))|(in @ (esk5_2 @ X683 @ X684) @ X684))&((X683 @ (esk7_3 @ X683 @ X684 @ X687) @ X687)|~(in @ X687 @ (esk6_2 @ X683 @ X684))|(in @ (esk5_2 @ X683 @ X684) @ X684)))&(~(in @ X690 @ X684)|~(X683 @ X690 @ X689)|(in @ X689 @ (esk6_2 @ X683 @ X684))|(in @ (esk5_2 @ X683 @ X684) @ X684)))&((((in @ (esk7_3 @ X683 @ X684 @ X687) @ X684)|~(in @ X687 @ (esk6_2 @ X683 @ X684))|~(exu @ (X683 @ (esk5_2 @ X683 @ X684))))&((X683 @ (esk7_3 @ X683 @ X684 @ X687) @ X687)|~(in @ X687 @ (esk6_2 @ X683 @ X684))|~(exu @ (X683 @ (esk5_2 @ X683 @ X684)))))&(~(in @ X690 @ X684)|~(X683 @ X690 @ X689)|(in @ X689 @ (esk6_2 @ X683 @ X684))|~(exu @ (X683 @ (esk5_2 @ X683 @ X684))))))&((((in @ (esk8_1 @ X691) @ X691)|~(in @ X692 @ X691))&(~(in @ X694 @ (esk8_1 @ X691))|~(in @ X694 @ X691)|~(in @ X692 @ X691)))&((epred1_0)&((~(exu @ X695)|(X695 @ (descr @ X695)))&((~(in @ X698 @ X696)|(~(X697 @ X698)|(in @ X698 @ (dsetconstr @ X696 @ X697))))&((~(in @ X701 @ (dsetconstr @ X699 @ X700))|(in @ X701 @ X699))&((~(in @ X704 @ (dsetconstr @ X702 @ X703))|(X703 @ X704))&((((X705 @ (esk9_1 @ X705))|~(exu @ X705))&(~(X705 @ X707)|((esk9_1 @ X705)=(X707))|~(exu @ X705)))&((~(in @ X709 @ (prop2set @ ((X708))))|(X708))&((~(in @ X710 @ emptyset)|(X711))&((~(in @ X712 @ emptyset)|~($true))&(~(in @ X713 @ emptyset)&((~(exu @ X714)|(X714 @ (esk10_1 @ X714)))&(((((in @ (esk12_2 @ X716 @ X717) @ X717)|((X716)=(X717))|(in @ (esk11_2 @ X716 @ X717) @ X716))&(~(in @ (esk12_2 @ X716 @ X717) @ X716)|((X716)=(X717))|(in @ (esk11_2 @ X716 @ X717) @ X716)))&(((in @ (esk12_2 @ X716 @ X717) @ X717)|((X716)=(X717))|~(in @ (esk11_2 @ X716 @ X717) @ X717))&(~(in @ (esk12_2 @ X716 @ X717) @ X716)|((X716)=(X717))|~(in @ (esk11_2 @ X716 @ X717) @ X717))))&(((in @ (esk13_1 @ X720) @ X720)|((X720)=(emptyset)))&(((in @ (esk14_1 @ X722) @ X722)|((X722)=(emptyset)))&(((~(in @ X726 @ (dsetconstr @ X724 @ X725))|(X725 @ X726)|~(in @ X726 @ X724))&(~(X725 @ X726)|(in @ X726 @ (dsetconstr @ X724 @ X725))|~(in @ X726 @ X724)))&((~(nonempty @ X727)|(in @ (esk15_1 @ X727) @ X727))&((~(in @ X731 @ X729)|(~(X730 @ X731)|(nonempty @ (dsetconstr @ X729 @ X730))))&((~(in @ X733 @ X732)|(nonempty @ X732))&((in @ X734 @ (setadjoin @ X734 @ X735))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X738 @ X737)|(in @ X738 @ (setadjoin @ X736 @ X737)))&(((((in @ X741 @ X740)|(X742)|((X741)=(X739))|~(in @ X741 @ (setadjoin @ X739 @ X740)))&(~(X742)|(X742)|((X741)=(X739))|~(in @ X741 @ (setadjoin @ X739 @ X740))))&(((in @ X741 @ X740)|(X742)|~(X742)|~(in @ X741 @ (setadjoin @ X739 @ X740)))&(~(X742)|(X742)|~(X742)|~(in @ X741 @ (setadjoin @ X739 @ X740)))))&((~(in @ X745 @ (setadjoin @ X743 @ X744))|(((X745)=(X743))|(in @ X745 @ X744)))&(((dsetconstr @ X746 @ (^[Z0:$i]:($true)))=(X746))&((((in @ (esk16_2 @ X747 @ X748) @ X748)|(in @ X748 @ (powerset @ X747)))&(~(in @ (esk16_2 @ X747 @ X748) @ X747)|(in @ X748 @ (powerset @ X747))))&((in @ emptyset @ (powerset @ X750))&((in @ emptyset @ (powerset @ X751))&((~(in @ X753 @ (powerset @ X752))|(~(in @ X754 @ X753)|(in @ X754 @ X752)))&((~(in @ X756 @ X757)|(~(in @ X757 @ X755)|(in @ X756 @ (setunion @ X755))))&((((in @ X759 @ (esk17_3 @ X758 @ X759 @ X760))|(X760)|~(in @ X759 @ (setunion @ X758)))&(((in @ (esk17_3 @ X758 @ X759 @ X760) @ X758)|(X760)|~(in @ X759 @ (setunion @ X758)))&(~(X760)|(X760)|~(in @ X759 @ (setunion @ X758)))))&((~(in @ X763 @ X762)|(in @ X763 @ (powerset @ (setunion @ X762))))&(((~(X764 @ X766)|((X766)=(esk18_1 @ X764))|~(exu @ X764))&(((X767)!=(esk18_1 @ X764))|(X764 @ X767)|~(exu @ X764)))&((((in @ (esk19_1 @ X768) @ X768)|~(nonempty @ X768))&(($true)|~(nonempty @ X768)))&((~(in @ X770 @ (setadjoin @ X771 @ emptyset))|((X770)=(X771)))&((((X772)=(X773))|~(in @ X773 @ (setadjoin @ X772 @ emptyset)))&((((X774)!=(X775))|(in @ X774 @ (setadjoin @ X775 @ emptyset)))&((~(in @ X776 @ (setadjoin @ X777 @ emptyset))|(in @ X777 @ (setadjoin @ X776 @ emptyset)))&((~(in @ X780 @ (setadjoin @ X778 @ (setadjoin @ X779 @ emptyset)))|(((X780)=(X778))|((X780)=(X779))))&((in @ X781 @ (setadjoin @ X781 @ (setadjoin @ X782 @ emptyset)))&((in @ X784 @ (setadjoin @ X783 @ (setadjoin @ X784 @ emptyset)))&((~(in @ X787 @ X785)|~(X786 @ X787)|(((dsetconstr @ X785 @ X786)!=(emptyset))|~($true)))&((~(in @ X789 @ emptyset)|(X788 @ X789))&((((in @ (esk20_2 @ X790 @ X791) @ X790)|(~(in @ X792 @ X790)|(X791 @ X792)))&(~(X791 @ (esk20_2 @ X790 @ X791))|(~(in @ X792 @ X790)|(X791 @ X792))))&((((in @ (esk21_2 @ X794 @ X795) @ X794)|(~(in @ X797 @ X794)|~(X795 @ X797)))&((X795 @ (esk21_2 @ X794 @ X795))|(~(in @ X797 @ X794)|~(X795 @ X797))))&((((in @ (esk22_2 @ X798 @ X799) @ X798)|(~(in @ X801 @ X798)|~(X799 @ X801)))&((X799 @ (esk22_2 @ X798 @ X799))|(~(in @ X801 @ X798)|~(X799 @ X801))))&((((in @ (esk23_2 @ X802 @ X803) @ X802)|(~(in @ X804 @ X802)|(X803 @ X804)))&(~(X803 @ (esk23_2 @ X802 @ X803))|(~(in @ X804 @ X802)|(X803 @ X804))))&((~(X806)|(in @ emptyset @ (prop2set @ ((X806)))))&((prop2set2propI)&((((in @ (esk24_2 @ X807 @ X808) @ X807)|(~(in @ X810 @ X807)|~(X808 @ X810)))&((X808 @ (esk24_2 @ X807 @ X808))|(~(in @ X810 @ X807)|~(X808 @ X810))))&((((in @ (esk25_2 @ X811 @ X812) @ X811)|(~(in @ X813 @ X811)|(X812 @ X813)))&(~(X812 @ (esk25_2 @ X811 @ X812))|(~(in @ X813 @ X811)|(X812 @ X813))))&((((X815 @ (esk26_2 @ X815 @ X816))|~(X815 @ X816)|(exu @ X815))&(((X816)!=(esk26_2 @ X815 @ X816))|~(X815 @ X816)|(exu @ X815)))&((((X818 @ (esk27_1 @ X818))|(exu @ X818)|~(X818 @ X819))&(((X818 @ (esk28_1 @ X818))|(exu @ X818)|~(X818 @ X819))&(((esk27_1 @ X818)!=(esk28_1 @ X818))|(exu @ X818)|~(X818 @ X819))))&(((~(X822 @ (esk29_2 @ X822 @ X823))|((esk29_2 @ X822 @ X823)!=(X823))|(exu @ X822))&((X822 @ (esk29_2 @ X822 @ X823))|((esk29_2 @ X822 @ X823)=(X823))|(exu @ X822)))&((((X825)!=(X826))|(((X827)!=(X828))|(~(in @ X827 @ X825)|(in @ X828 @ X826))))&(((~(in @ X831 @ X829)|(in @ X832 @ X830)|((X831)!=(X832))|((X829)!=(X830)))&(~(in @ X832 @ X830)|(in @ X831 @ X829)|((X831)!=(X832))|((X829)!=(X830))))&((~(exu @ X833)|(~(X833 @ X834)|(~(X833 @ X835)|((X834)=(X835)))))&((((~(exu @ X836)|(exu @ X837)|((esk30_2 @ X836 @ X837)=(esk31_2 @ X836 @ X837)))&(~(exu @ X837)|(exu @ X836)|((esk30_2 @ X836 @ X837)=(esk31_2 @ X836 @ X837))))&(((~(exu @ X836)|(exu @ X837)|(~(X836 @ (esk30_2 @ X836 @ X837))|~(X837 @ (esk31_2 @ X836 @ X837))))&(~(exu @ X837)|(exu @ X836)|(~(X836 @ (esk30_2 @ X836 @ X837))|~(X837 @ (esk31_2 @ X836 @ X837)))))&((~(exu @ X836)|(exu @ X837)|((X836 @ (esk30_2 @ X836 @ X837))|(X837 @ (esk31_2 @ X836 @ X837))))&(~(exu @ X837)|(exu @ X836)|((X836 @ (esk30_2 @ X836 @ X837))|(X837 @ (esk31_2 @ X836 @ X837)))))))&(((emptyset)=(emptyset))&((((X840)!=(X841))|(((X842)!=(X843))|((setadjoin @ X840 @ X842)=(setadjoin @ X841 @ X843))))&((((X844)!=(X845))|((powerset @ X844)=(powerset @ X845)))&((((X846)!=(X847))|((setunion @ X846)=(setunion @ X847)))&(((omega)=(omega))&((~(exu @ X848)|(~(X848 @ X849)|(~(X848 @ X850)|((X849)=(X850)))))&(((((esk32_2 @ X851 @ X852)=(esk33_2 @ X851 @ X852))|(~(exu @ X851)|(~(exu @ X852)|((descr @ X851)=(descr @ X852)))))&((~(X851 @ (esk32_2 @ X851 @ X852))|~(X852 @ (esk33_2 @ X851 @ X852))|(~(exu @ X851)|(~(exu @ X852)|((descr @ X851)=(descr @ X852)))))&((X851 @ (esk32_2 @ X851 @ X852))|(X852 @ (esk33_2 @ X851 @ X852))|(~(exu @ X851)|(~(exu @ X852)|((descr @ X851)=(descr @ X852)))))))&((((in @ (esk34_4 @ X855 @ X856 @ X857 @ X858) @ X855)|((dsetconstr @ X855 @ X857)=(dsetconstr @ X856 @ X858))|((X855)!=(X856)))&(((in @ (esk35_4 @ X855 @ X856 @ X857 @ X858) @ X856)|((dsetconstr @ X855 @ X857)=(dsetconstr @ X856 @ X858))|((X855)!=(X856)))&((((esk34_4 @ X855 @ X856 @ X857 @ X858)=(esk35_4 @ X855 @ X856 @ X857 @ X858))|((dsetconstr @ X855 @ X857)=(dsetconstr @ X856 @ X858))|((X855)!=(X856)))&((~(X857 @ (esk34_4 @ X855 @ X856 @ X857 @ X858))|~(X858 @ (esk35_4 @ X855 @ X856 @ X857 @ X858))|((dsetconstr @ X855 @ X857)=(dsetconstr @ X856 @ X858))|((X855)!=(X856)))&((X857 @ (esk34_4 @ X855 @ X856 @ X857 @ X858))|(X858 @ (esk35_4 @ X855 @ X856 @ X857 @ X858))|((dsetconstr @ X855 @ X857)=(dsetconstr @ X856 @ X858))|((X855)!=(X856)))))))&((((in @ (esk36_2 @ X861 @ X862) @ X861)|(subset @ X861 @ X862))&(~(in @ (esk36_2 @ X861 @ X862) @ X862)|(subset @ X861 @ X862)))&((((X864)!=(X865))|(subset @ X865 @ X864))&((((X866)!=(X867))|(subset @ X866 @ X867))&((((in @ (esk37_2 @ X868 @ X869) @ X868)|(subset @ X868 @ X869))&(~(in @ (esk37_2 @ X868 @ X869) @ X869)|(subset @ X868 @ X869)))&((subset @ emptyset @ X871)&((~(subset @ X872 @ X873)|(~(in @ X874 @ X872)|(in @ X874 @ X873)))&((~(subset @ X875 @ X876)|((in @ X877 @ X876)|~(in @ X877 @ X875)))&((~(in @ X880 @ X878)|((in @ X880 @ X879)|~(subset @ X878 @ X879)))&(((subset @ X881 @ X882)|((X881)!=(X882)))&((~(in @ X885 @ X883)|((in @ X885 @ X884)|((X883)!=(X884))))&((subset @ X886 @ X886)&((~(subset @ X887 @ X888)|(~(subset @ X888 @ X889)|(subset @ X887 @ X889)))&((subset @ X891 @ (setadjoin @ X890 @ X891))&((~(subset @ X892 @ X894)|(subset @ X892 @ (setadjoin @ X893 @ X894)))&((~(subset @ X895 @ X896)|(in @ X895 @ (powerset @ X896)))&((~(subset @ X897 @ X898)|(~(subset @ X898 @ X897)|((X897)=(X898))))&((~(subset @ X899 @ emptyset)|((X899)=(emptyset)))&((~(subset @ X901 @ X900)|(in @ X901 @ (powerset @ X900)))&((~(in @ X903 @ (powerset @ X902))|(subset @ X903 @ X902))&((in @ X904 @ (powerset @ X904))&((~(subset @ X905 @ X906)|(subset @ (powerset @ X905) @ (powerset @ X906)))&((in @ (dsetconstr @ X907 @ X908) @ (powerset @ X907))&((subset @ (dsetconstr @ X909 @ X910) @ X909)&((~(in @ X913 @ X911)|(in @ X913 @ (binunion @ X911 @ X912)))&((in @ X915 @ (setadjoin @ X914 @ (setadjoin @ X915 @ emptyset)))&((~(in @ X918 @ X917)|(in @ X918 @ (binunion @ X916 @ X917)))&(((((in @ X921 @ X920)|(X922)|(in @ X921 @ X919)|~(in @ X921 @ (binunion @ X919 @ X920)))&(~(X922)|(X922)|(in @ X921 @ X919)|~(in @ X921 @ (binunion @ X919 @ X920))))&(((in @ X921 @ X920)|(X922)|~(X922)|~(in @ X921 @ (binunion @ X919 @ X920)))&(~(X922)|(X922)|~(X922)|~(in @ X921 @ (binunion @ X919 @ X920)))))&((~(in @ X925 @ (binunion @ X923 @ X924))|((in @ X925 @ X923)|(in @ X925 @ X924)))&((subset @ X926 @ (binunion @ X926 @ X927))&((subset @ X929 @ (binunion @ X928 @ X929))&((~(in @ X932 @ X930)|(~(in @ X932 @ X931)|(in @ X932 @ (binintersect @ X930 @ X931))))&((~(subset @ X935 @ X933)|(~(subset @ X935 @ X934)|(subset @ X935 @ (binintersect @ X933 @ X934))))&((~(in @ X938 @ (binintersect @ X936 @ X937))|(in @ X938 @ X936))&((subset @ (binintersect @ X939 @ X940) @ X939)&((~(subset @ X941 @ X942)|((binintersect @ X941 @ X942)=(X941)))&((((binintersect @ X943 @ X944)!=(X944))|(subset @ X944 @ X943))&((~(in @ X947 @ (binintersect @ X945 @ X946))|(in @ X947 @ X946))&((((in @ (esk38_2 @ X948 @ X949) @ X948)|((binintersect @ X948 @ X949)=(emptyset)))&((in @ (esk38_2 @ X948 @ X949) @ X949)|((binintersect @ X948 @ X949)=(emptyset))))&((subset @ (binintersect @ X951 @ X952) @ X952)&((~(subset @ X954 @ X953)|((binintersect @ X953 @ X954)=(X954)))&((((binintersect @ X955 @ X956)!=(X955))|(subset @ X955 @ X956))&(((binintersect @ X957 @ (binunion @ X958 @ X959))=(binunion @ (binintersect @ X957 @ X958) @ (binintersect @ X957 @ X959)))&((~(in @ X962 @ X960)|((in @ X962 @ X961)|(in @ X962 @ (setminus @ X960 @ X961))))&((~(in @ X965 @ (setminus @ X963 @ X964))|(in @ X965 @ X963))&((~(in @ X968 @ (setminus @ X966 @ X967))|~(in @ X968 @ X967))&((subset @ esk39_0 @ esk40_0)&((setminus @ esk39_0 @ esk40_0)!=(emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_144])])])])])])])).
% 32.11/5.00 thf(c_0_146, negated_conjecture, ![X2:$i, X3:$i]:(((nonempty @ X3)|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 32.11/5.00 thf(c_0_147, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk36_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 32.11/5.00 thf(c_0_148, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((subset @ X2 @ X3))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 32.11/5.00 thf(c_0_149, negated_conjecture, (subset @ esk39_0 @ esk40_0), inference(split_conjunct,[status(thm)],[c_0_145])).
% 32.11/5.00 thf(c_0_150, negated_conjecture, ![X3:$i, X2:$i]:((((X2)=(X3))|~((subset @ X2 @ X3))|~((subset @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 32.11/5.00 thf(c_0_151, negated_conjecture, ![X3:$i, X2:$i]:(((subset @ X2 @ X3)|(nonempty @ X2))), inference(spm,[status(thm)],[c_0_146, c_0_147])).
% 32.11/5.00 thf(c_0_152, negated_conjecture, ![X3:$i, X2:$i]:(((in @ (esk8_1 @ X2) @ X2)|~((in @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 32.11/5.00 thf(c_0_153, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk37_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 32.11/5.00 thf(c_0_154, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk40_0)|~((in @ X2 @ esk39_0)))), inference(spm,[status(thm)],[c_0_148, c_0_149])).
% 32.11/5.00 thf(c_0_155, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X3)|~((in @ X2 @ (setminus @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 32.11/5.00 thf(c_0_156, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk37_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 32.11/5.00 thf(c_0_157, negated_conjecture, ![X2:$i, X3:$i]:((((X2)=(X3))|(nonempty @ X3)|~((subset @ X2 @ X3)))), inference(spm,[status(thm)],[c_0_150, c_0_151])).
% 32.11/5.00 thf(c_0_158, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk8_1 @ X2) @ X2)|(subset @ X2 @ X3))), inference(spm,[status(thm)],[c_0_152, c_0_147])).
% 32.11/5.00 thf(c_0_159, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 32.11/5.00 thf(c_0_160, negated_conjecture, ![X2:$i]:(((in @ (esk15_1 @ X2) @ X2)|~((nonempty @ X2)))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 32.11/5.00 thf(c_0_161, negated_conjecture, ![X2:$i]:(((subset @ X2 @ esk40_0)|~((in @ (esk37_2 @ X2 @ esk40_0) @ esk39_0)))), inference(spm,[status(thm)],[c_0_153, c_0_154])).
% 32.11/5.00 thf(c_0_162, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ (esk37_2 @ (setminus @ X2 @ X3) @ X4) @ X2)|(subset @ (setminus @ X2 @ X3) @ X4))), inference(spm,[status(thm)],[c_0_155, c_0_156])).
% 32.11/5.00 thf(c_0_163, negated_conjecture, ((setminus @ esk39_0 @ esk40_0)!=(emptyset)), inference(split_conjunct,[status(thm)],[c_0_145])).
% 32.11/5.00 thf(c_0_164, negated_conjecture, ![X2:$i, X3:$i]:((((X2)=(X3))|(in @ (esk8_1 @ X2) @ X2)|(nonempty @ X3))), inference(spm,[status(thm)],[c_0_157, c_0_158])).
% 32.11/5.00 thf(c_0_165, negated_conjecture, ~((nonempty @ emptyset)), inference(spm,[status(thm)],[c_0_159, c_0_160])).
% 32.11/5.00 thf(c_0_166, negated_conjecture, ![X2:$i]:((subset @ (setminus @ esk39_0 @ X2) @ esk40_0)), inference(spm,[status(thm)],[c_0_161, c_0_162])).
% 32.11/5.00 thf(c_0_167, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((~((in @ X2 @ (setminus @ X3 @ X4)))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_145])).
% 32.11/5.00 thf(c_0_168, negated_conjecture, (in @ (esk8_1 @ (setminus @ esk39_0 @ esk40_0)) @ (setminus @ esk39_0 @ esk40_0)), inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_163, c_0_164])]), c_0_165])).
% 32.11/5.00 thf(c_0_169, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ esk40_0)|~((in @ X2 @ (setminus @ esk39_0 @ X3))))), inference(spm,[status(thm)],[c_0_148, c_0_166])).
% 32.11/5.00 thf(c_0_170, negated_conjecture, ~((in @ (esk8_1 @ (setminus @ esk39_0 @ esk40_0)) @ esk40_0)), inference(spm,[status(thm)],[c_0_167, c_0_168])).
% 32.11/5.00 thf(c_0_171, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_169, c_0_168]), c_0_170]), ['proof']).
% 32.11/5.00 % SZS output end CNFRefutation
% 32.11/5.00 % Parsed axioms : 262
% 32.11/5.00 % Removed by relevancy pruning/SinE : 142
% 32.11/5.00 % Initial clauses : 193
% 32.11/5.00 % Removed in clause preprocessing : 18
% 32.11/5.00 % Initial clauses in saturation : 175
% 32.11/5.00 % Processed clauses : 21486
% 32.11/5.00 % ...of these trivial : 460
% 32.11/5.00 % ...subsumed : 16468
% 32.11/5.00 % ...remaining for further processing : 4557
% 32.11/5.00 % Other redundant clauses eliminated : 172
% 32.11/5.00 % Clauses deleted for lack of memory : 0
% 32.11/5.00 % Backward-subsumed : 687
% 32.11/5.00 % Backward-rewritten : 247
% 32.11/5.00 % Generated clauses : 493568
% 32.11/5.00 % ...of the previous two non-redundant : 426337
% 32.11/5.00 % ...aggressively subsumed : 0
% 32.11/5.00 % Contextual simplify-reflections : 9
% 32.11/5.00 % Paramodulations : 493217
% 32.11/5.00 % Factorizations : 158
% 32.11/5.00 % NegExts : 0
% 32.11/5.00 % Equation resolutions : 172
% 32.11/5.00 % Disequality decompositions : 0
% 32.11/5.00 % Total rewrite steps : 78152
% 32.11/5.00 % ...of those cached : 72500
% 32.11/5.00 % Propositional unsat checks : 0
% 32.11/5.00 % Propositional check models : 0
% 32.11/5.00 % Propositional check unsatisfiable : 0
% 32.11/5.00 % Propositional clauses : 0
% 32.11/5.00 % Propositional clauses after purity: 0
% 32.11/5.00 % Propositional unsat core size : 0
% 32.11/5.00 % Propositional preprocessing time : 0.000
% 32.11/5.00 % Propositional encoding time : 0.000
% 32.11/5.00 % Propositional solver time : 0.000
% 32.11/5.00 % Success case prop preproc time : 0.000
% 32.11/5.00 % Success case prop encoding time : 0.000
% 32.11/5.00 % Success case prop solver time : 0.000
% 32.11/5.00 % Current number of processed clauses : 3591
% 32.11/5.00 % Positive orientable unit clauses : 634
% 32.11/5.00 % Positive unorientable unit clauses: 0
% 32.11/5.00 % Negative unit clauses : 800
% 32.11/5.00 % Non-unit-clauses : 2157
% 32.11/5.00 % Current number of unprocessed clauses: 397583
% 32.11/5.00 % ...number of literals in the above : 1381486
% 32.11/5.00 % Current number of archived formulas : 0
% 32.11/5.00 % Current number of archived clauses : 955
% 32.11/5.00 % Clause-clause subsumption calls (NU) : 460751
% 32.11/5.00 % Rec. Clause-clause subsumption calls : 360736
% 32.11/5.00 % Non-unit clause-clause subsumptions : 10934
% 32.11/5.00 % Unit Clause-clause subsumption calls : 99371
% 32.11/5.00 % Rewrite failures with RHS unbound : 0
% 32.11/5.00 % BW rewrite match attempts : 3824
% 32.11/5.00 % BW rewrite match successes : 68
% 32.11/5.00 % Condensation attempts : 0
% 32.11/5.00 % Condensation successes : 0
% 32.11/5.00 % Termbank termtop insertions : 6713647
% 32.11/5.00 % Search garbage collected termcells : 10656
% 32.11/5.00
% 32.11/5.00 % -------------------------------------------------
% 32.11/5.00 % User time : 4.397 s
% 32.11/5.00 % System time : 0.193 s
% 32.11/5.00 % Total time : 4.590 s
% 32.11/5.00 % Maximum resident set size: 6408 pages
% 32.11/5.00
% 32.11/5.00 % -------------------------------------------------
% 32.11/5.00 % User time : 4.404 s
% 32.11/5.00 % System time : 0.199 s
% 32.11/5.00 % Total time : 4.603 s
% 32.11/5.00 % Maximum resident set size: 5120 pages
% 32.11/5.00 % E exiting
%------------------------------------------------------------------------------