%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU601^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:40 AM UTC 2026
% Result : Theorem 0.81s 0.40s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU601^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n002.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 13:59:22 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.24 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p
% 0.81/0.40 % Version: 3.5.1-ho
% 0.81/0.40 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.81/0.40 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.81/0.40 % Starting ehoh_best5 with 300s (1) cores
% 0.81/0.40 % Starting almost_fo_3_lam with 300s (1) cores
% 0.81/0.40 % Starting new_bool_5 with 300s (1) cores
% 0.81/0.40 % Starting pre_casc_3 with 300s (1) cores
% 0.81/0.40 % Starting ho_unfolding_8 with 300s (1) cores
% 0.81/0.40 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.81/0.40 % Starting new_bool_3 with 300s (1) cores
% 0.81/0.40 % Starting new_ho_5 with 300s (1) cores
% 0.81/0.40 % pre_casc_3 with pid 1325221 completed with status 9
% 0.81/0.40 % new_bool_3 with pid 1325228 completed with status 0
% 0.81/0.40 % Result found by new_bool_3
% 0.81/0.40 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.81/0.40 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.81/0.40 % Starting ehoh_best5 with 300s (1) cores
% 0.81/0.40 % Starting almost_fo_3_lam with 300s (1) cores
% 0.81/0.40 % Starting new_bool_5 with 300s (1) cores
% 0.81/0.40 % Starting pre_casc_3 with 300s (1) cores
% 0.81/0.40 % Starting ho_unfolding_8 with 300s (1) cores
% 0.81/0.40 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.81/0.40 % Starting new_bool_3 with 300s (1) cores
% 0.81/0.40 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.81/0.40 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.81/0.40 % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.81/0.40 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.81/0.40 % Starting SubtermCWHack with 28s (1) cores
% 0.81/0.40 % SubtermCWHack with pid 1325241 completed with status 0
% 0.81/0.40 % Result found by SubtermCWHack
% 0.81/0.40 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.81/0.40 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.81/0.40 % Starting ehoh_best5 with 300s (1) cores
% 0.81/0.40 % Starting almost_fo_3_lam with 300s (1) cores
% 0.81/0.40 % Starting new_bool_5 with 300s (1) cores
% 0.81/0.40 % Starting pre_casc_3 with 300s (1) cores
% 0.81/0.40 % Starting ho_unfolding_8 with 300s (1) cores
% 0.81/0.40 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.81/0.40 % Starting new_bool_3 with 300s (1) cores
% 0.81/0.40 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.81/0.40 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.81/0.40 % Search class: HGHSM-FSLM31-MHFMMSBN
% 0.81/0.40 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.81/0.40 % Starting SubtermCWHack with 28s (1) cores
% 0.81/0.40 % Preprocessing time : 0.004 s
% 0.81/0.40
% 0.81/0.40 % Proof found!
% 0.81/0.40 % SZS status Theorem
% 0.81/0.40 % SZS output start CNFRefutation
% 0.81/0.40 thf(decl_23, type, in: $i > $i > $o).
% 0.81/0.40 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.81/0.40 thf(decl_25, type, setextAx: $o).
% 0.81/0.40 thf(decl_26, type, emptyset: $i).
% 0.81/0.40 thf(decl_27, type, emptysetAx: $o).
% 0.81/0.40 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.81/0.40 thf(decl_29, type, setadjoinAx: $o).
% 0.81/0.40 thf(decl_30, type, powerset: $i > $i).
% 0.81/0.40 thf(decl_31, type, powersetAx: $o).
% 0.81/0.40 thf(decl_32, type, setunion: $i > $i).
% 0.81/0.40 thf(decl_33, type, setunionAx: $o).
% 0.81/0.40 thf(decl_34, type, omega: $i).
% 0.81/0.40 thf(decl_35, type, omega0Ax: $o).
% 0.81/0.40 thf(decl_36, type, omegaSAx: $o).
% 0.81/0.40 thf(decl_37, type, omegaIndAx: $o).
% 0.81/0.40 thf(decl_38, type, replAx: $o).
% 0.81/0.40 thf(decl_39, type, foundationAx: $o).
% 0.81/0.40 thf(decl_40, type, wellorderingAx: $o).
% 0.81/0.40 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.81/0.40 thf(decl_42, type, descrp: $o).
% 0.81/0.40 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.81/0.40 thf(decl_44, type, dsetconstrI: $o).
% 0.81/0.40 thf(decl_45, type, dsetconstrEL: $o).
% 0.81/0.40 thf(decl_46, type, dsetconstrER: $o).
% 0.81/0.40 thf(decl_47, type, exuE1: $o).
% 0.81/0.40 thf(decl_48, type, prop2set: $o > $i).
% 0.81/0.40 thf(decl_49, type, prop2setE: $o).
% 0.81/0.40 thf(decl_50, type, emptysetE: $o).
% 0.81/0.40 thf(decl_51, type, emptysetimpfalse: $o).
% 0.81/0.40 thf(decl_52, type, notinemptyset: $o).
% 0.81/0.40 thf(decl_53, type, exuE3e: $o).
% 0.81/0.40 thf(decl_54, type, setext: $o).
% 0.81/0.40 thf(decl_55, type, emptyI: $o).
% 0.81/0.40 thf(decl_56, type, noeltsimpempty: $o).
% 0.81/0.40 thf(decl_57, type, setbeta: $o).
% 0.81/0.40 thf(decl_58, type, nonempty: $i > $o).
% 0.81/0.40 thf(decl_59, type, nonemptyE1: $o).
% 0.81/0.40 thf(decl_60, type, nonemptyI: $o).
% 0.81/0.40 thf(decl_61, type, nonemptyI1: $o).
% 0.81/0.40 thf(decl_62, type, setadjoinIL: $o).
% 0.81/0.40 thf(decl_63, type, emptyinunitempty: $o).
% 0.81/0.40 thf(decl_64, type, setadjoinIR: $o).
% 0.81/0.40 thf(decl_65, type, setadjoinE: $o).
% 0.81/0.40 thf(decl_66, type, setadjoinOr: $o).
% 0.81/0.40 thf(decl_67, type, setoftrueEq: $o).
% 0.81/0.40 thf(decl_68, type, powersetI: $o).
% 0.81/0.40 thf(decl_69, type, emptyinPowerset: $o).
% 0.81/0.40 thf(decl_70, type, emptyInPowerset: $o).
% 0.81/0.40 thf(decl_71, type, powersetE: $o).
% 0.81/0.40 thf(decl_72, type, setunionI: $o).
% 0.81/0.40 thf(decl_73, type, setunionE: $o).
% 0.81/0.40 thf(decl_74, type, subPowSU: $o).
% 0.81/0.40 thf(decl_75, type, exuE2: $o).
% 0.81/0.40 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.81/0.40 thf(decl_77, type, uniqinunit: $o).
% 0.81/0.40 thf(decl_78, type, notinsingleton: $o).
% 0.81/0.40 thf(decl_79, type, eqinunit: $o).
% 0.81/0.40 thf(decl_80, type, singletonsswitch: $o).
% 0.81/0.40 thf(decl_81, type, upairsetE: $o).
% 0.81/0.40 thf(decl_82, type, upairsetIL: $o).
% 0.81/0.40 thf(decl_83, type, upairsetIR: $o).
% 0.81/0.40 thf(decl_84, type, emptyE1: $o).
% 0.81/0.40 thf(decl_85, type, vacuousDall: $o).
% 0.81/0.40 thf(decl_86, type, quantDeMorgan1: $o).
% 0.81/0.40 thf(decl_87, type, quantDeMorgan2: $o).
% 0.81/0.40 thf(decl_88, type, quantDeMorgan3: $o).
% 0.81/0.40 thf(decl_89, type, quantDeMorgan4: $o).
% 0.81/0.40 thf(decl_90, type, prop2setI: $o).
% 0.81/0.40 thf(decl_92, type, prop2set2propI: $o).
% 0.81/0.40 thf(decl_93, type, notdexE: $o).
% 0.81/0.40 thf(decl_94, type, notdallE: $o).
% 0.81/0.40 thf(decl_95, type, exuI1: $o).
% 0.81/0.40 thf(decl_96, type, exuI3: $o).
% 0.81/0.40 thf(decl_97, type, exuI2: $o).
% 0.81/0.40 thf(decl_98, type, inCongP: $o).
% 0.81/0.40 thf(decl_99, type, in__Cong: $o).
% 0.81/0.40 thf(decl_100, type, exuE3u: $o).
% 0.81/0.40 thf(decl_101, type, exu__Cong: $o).
% 0.81/0.40 thf(decl_102, type, emptyset__Cong: $o).
% 0.81/0.40 thf(decl_103, type, setadjoin__Cong: $o).
% 0.81/0.40 thf(decl_104, type, powerset__Cong: $o).
% 0.81/0.40 thf(decl_105, type, setunion__Cong: $o).
% 0.81/0.40 thf(decl_106, type, omega__Cong: $o).
% 0.81/0.40 thf(decl_107, type, exuEu: $o).
% 0.81/0.40 thf(decl_108, type, descr__Cong: $o).
% 0.81/0.40 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.81/0.40 thf(decl_110, type, subset: $i > $i > $o).
% 0.81/0.40 thf(decl_113, type, subsetI1: $o).
% 0.81/0.40 thf(decl_114, type, eqimpsubset2: $o).
% 0.81/0.40 thf(decl_115, type, eqimpsubset1: $o).
% 0.81/0.40 thf(decl_116, type, subsetI2: $o).
% 0.81/0.40 thf(decl_117, type, emptysetsubset: $o).
% 0.81/0.40 thf(decl_118, type, subsetE: $o).
% 0.81/0.40 thf(decl_119, type, subsetE2: $o).
% 0.81/0.40 thf(decl_120, type, notsubsetI: $o).
% 0.81/0.40 thf(decl_121, type, notequalI1: $o).
% 0.81/0.40 thf(decl_122, type, notequalI2: $o).
% 0.81/0.40 thf(decl_123, type, subsetRefl: $o).
% 0.81/0.40 thf(decl_124, type, subsetTrans: $o).
% 0.81/0.40 thf(decl_125, type, setadjoinSub: $o).
% 0.81/0.40 thf(decl_126, type, setadjoinSub2: $o).
% 0.81/0.40 thf(decl_127, type, subset2powerset: $o).
% 0.81/0.40 thf(decl_128, type, setextsub: $o).
% 0.81/0.40 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.81/0.40 thf(decl_130, type, powersetI1: $o).
% 0.81/0.40 thf(decl_131, type, powersetE1: $o).
% 0.81/0.40 thf(decl_132, type, inPowerset: $o).
% 0.81/0.40 thf(decl_133, type, powersetsubset: $o).
% 0.81/0.40 thf(decl_134, type, sepInPowerset: $o).
% 0.81/0.40 thf(decl_135, type, sepSubset: $o).
% 0.81/0.40 thf(decl_136, type, binunion: $i > $i > $i).
% 0.81/0.40 thf(decl_137, type, binunionIL: $o).
% 0.81/0.40 thf(decl_138, type, upairset2IR: $o).
% 0.81/0.40 thf(decl_139, type, binunionIR: $o).
% 0.81/0.40 thf(decl_140, type, binunionEcases: $o).
% 0.81/0.40 thf(decl_141, type, binunionE: $o).
% 0.81/0.40 thf(decl_142, type, binunionLsub: $o).
% 0.81/0.40 thf(decl_143, type, binunionRsub: $o).
% 0.81/0.40 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.81/0.40 thf(decl_145, type, binintersectI: $o).
% 0.81/0.40 thf(decl_146, type, binintersectSubset5: $o).
% 0.81/0.40 thf(decl_147, type, binintersectEL: $o).
% 0.81/0.40 thf(decl_148, type, binintersectLsub: $o).
% 0.81/0.40 thf(decl_149, type, binintersectSubset2: $o).
% 0.81/0.40 thf(decl_150, type, binintersectSubset3: $o).
% 0.81/0.40 thf(decl_151, type, binintersectER: $o).
% 0.81/0.40 thf(decl_152, type, disjointsetsI1: $o).
% 0.81/0.40 thf(decl_153, type, binintersectRsub: $o).
% 0.81/0.40 thf(decl_154, type, binintersectSubset4: $o).
% 0.81/0.40 thf(decl_155, type, binintersectSubset1: $o).
% 0.81/0.40 thf(decl_156, type, bs114d: $o).
% 0.81/0.40 thf(decl_158, type, setminus: $i > $i > $i).
% 0.81/0.40 thf(decl_159, type, epred1_0: $o).
% 0.81/0.40 thf(decl_160, type, esk1_2: $i > $i > $i).
% 0.81/0.40 thf(decl_161, type, esk2_2: $i > $i > $i).
% 0.81/0.40 thf(decl_162, type, esk3_2: $i > $i > $i).
% 0.81/0.40 thf(decl_163, type, esk4_1: $i > $i).
% 0.81/0.40 thf(decl_164, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.81/0.40 thf(decl_165, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.81/0.40 thf(decl_166, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.81/0.40 thf(decl_167, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.81/0.40 thf(decl_168, type, esk9_1: $i > $i).
% 0.81/0.40 thf(decl_169, type, esk10_2: ($i > $o) > $i > $i).
% 0.81/0.40 thf(decl_170, type, esk11_2: ($i > $o) > $i > $i).
% 0.81/0.40 thf(decl_171, type, esk12_1: ($i > $o) > $i).
% 0.81/0.40 thf(decl_172, type, esk13_2: ($i > $o) > $i > $i).
% 0.81/0.40 thf(decl_173, type, esk14_1: ($i > $o) > $i).
% 0.81/0.40 thf(decl_174, type, esk15_2: $i > $i > $i).
% 0.81/0.40 thf(decl_175, type, esk16_2: $i > $i > $i).
% 0.81/0.40 thf(decl_176, type, esk17_1: $i > $i).
% 0.81/0.40 thf(decl_177, type, esk18_1: $i > $i).
% 0.81/0.40 thf(decl_178, type, esk19_1: $i > $i).
% 0.81/0.40 thf(decl_179, type, esk20_2: $i > $i > $i).
% 0.81/0.40 thf(decl_180, type, esk21_3: $i > $i > $o > $i).
% 0.81/0.40 thf(decl_181, type, esk22_2: ($i > $o) > $i > $i).
% 0.81/0.40 thf(decl_182, type, esk23_1: ($i > $o) > $i).
% 0.81/0.40 thf(decl_183, type, esk24_1: $i > $i).
% 0.81/0.40 thf(decl_184, type, esk25_2: $i > ($i > $o) > $i).
% 0.81/0.40 thf(decl_185, type, esk26_2: $i > ($i > $o) > $i).
% 0.81/0.40 thf(decl_186, type, esk27_2: $i > ($i > $o) > $i).
% 0.81/0.40 thf(decl_187, type, esk28_2: $i > ($i > $o) > $i).
% 0.81/0.40 thf(decl_188, type, esk29_2: $i > ($i > $o) > $i).
% 0.81/0.40 thf(decl_189, type, esk30_2: $i > ($i > $o) > $i).
% 0.81/0.40 thf(decl_190, type, esk31_2: ($i > $o) > $i > $i).
% 0.81/0.40 thf(decl_191, type, esk32_1: ($i > $o) > $i).
% 0.81/0.40 thf(decl_192, type, esk33_1: ($i > $o) > $i).
% 0.81/0.40 thf(decl_193, type, esk34_1: ($i > $o) > $i).
% 0.81/0.40 thf(decl_194, type, esk35_1: ($i > $o) > $i).
% 0.81/0.40 thf(decl_195, type, esk36_2: ($i > $o) > $i > $i).
% 0.81/0.40 thf(decl_196, type, esk37_1: ($i > $o) > $i).
% 0.81/0.40 thf(decl_197, type, esk38_2: ($i > $o) > $i > $i).
% 0.81/0.40 thf(decl_198, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.81/0.40 thf(decl_199, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.81/0.40 thf(decl_200, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.81/0.40 thf(decl_201, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.81/0.40 thf(decl_202, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.81/0.40 thf(decl_203, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.81/0.40 thf(decl_204, type, esk45_2: ($i > $o) > $i > $i).
% 0.81/0.40 thf(decl_205, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.81/0.40 thf(decl_206, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.81/0.40 thf(decl_207, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.81/0.40 thf(decl_208, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.81/0.40 thf(decl_209, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.81/0.40 thf(decl_210, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.81/0.40 thf(decl_211, type, esk52_2: $i > $i > $i).
% 0.81/0.40 thf(decl_212, type, esk53_2: $i > $i > $i).
% 0.81/0.40 thf(decl_213, type, esk54_2: $i > $i > $i).
% 0.81/0.40 thf(decl_214, type, esk55_0: $i).
% 0.81/0.40 thf(decl_215, type, esk56_0: $i).
% 0.81/0.40 thf(decl_216, type, esk57_0: $i).
% 0.81/0.40 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', nonempty)).
% 0.81/0.40 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', nonemptyI)).
% 0.81/0.40 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', exuE2)).
% 0.81/0.40 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', exu)).
% 0.81/0.40 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', exuI2)).
% 0.81/0.40 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', exuI3)).
% 0.81/0.40 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', exuI1)).
% 0.81/0.40 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', exu__Cong)).
% 0.81/0.40 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', exuE3u)).
% 0.81/0.40 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', descr__Cong)).
% 0.81/0.40 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', exuEu)).
% 0.81/0.40 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', exuE3e)).
% 0.81/0.40 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', exuE1)).
% 0.81/0.40 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', descrp)).
% 0.81/0.40 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', replAx)).
% 0.81/0.40 thf(setminusI, 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)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setminusI)).
% 0.81/0.40 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', nonemptyI1)).
% 0.81/0.40 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', nonemptyE1)).
% 0.81/0.40 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setbeta)).
% 0.81/0.40 thf(setminus, axiom, ((setminus)=(^[X4:$i, X5:$i]:(dsetconstr @ X4 @ (^[X2:$i]:(~((in @ X2 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setminus)).
% 0.81/0.40 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setoftrueEq)).
% 0.81/0.40 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', nonemptyImpWitness)).
% 0.81/0.40 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', emptyE1)).
% 0.81/0.40 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', dsetconstr__Cong)).
% 0.81/0.40 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', sepInPowerset)).
% 0.81/0.40 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', sepSubset)).
% 0.81/0.40 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', dsetconstrER)).
% 0.81/0.40 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', dsetconstrEL)).
% 0.81/0.40 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', dsetconstrI)).
% 0.81/0.40 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', binunionIR)).
% 0.81/0.40 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', binunionEcases)).
% 0.81/0.40 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', binunionE)).
% 0.81/0.40 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', binunionLsub)).
% 0.81/0.40 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', binunionRsub)).
% 0.81/0.40 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', binintersectI)).
% 0.81/0.40 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', emptyinunitempty)).
% 0.81/0.40 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', binintersectSubset5)).
% 0.81/0.40 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setadjoinIL)).
% 0.81/0.40 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', binintersectEL)).
% 0.81/0.40 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', binintersectLsub)).
% 0.81/0.40 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', binintersectSubset2)).
% 0.81/0.40 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', binintersectSubset3)).
% 0.81/0.40 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', binintersectER)).
% 0.81/0.40 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', noeltsimpempty)).
% 0.81/0.40 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', disjointsetsI1)).
% 0.81/0.40 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setadjoinIR)).
% 0.81/0.40 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', binintersectRsub)).
% 0.81/0.40 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', binintersectSubset4)).
% 0.81/0.40 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', binintersectSubset1)).
% 0.81/0.40 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', bs114d)).
% 0.81/0.40 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', powersetE)).
% 0.81/0.40 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', emptyInPowerset)).
% 0.81/0.40 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', emptyinPowerset)).
% 0.81/0.40 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', powersetI)).
% 0.81/0.40 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setadjoinOr)).
% 0.81/0.40 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setadjoinE)).
% 0.81/0.40 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setunionI)).
% 0.81/0.40 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', eqinunit)).
% 0.81/0.40 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', notinsingleton)).
% 0.81/0.40 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', uniqinunit)).
% 0.81/0.40 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', subPowSU)).
% 0.81/0.40 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setunionE)).
% 0.81/0.40 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', singletonsswitch)).
% 0.81/0.40 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', quantDeMorgan2)).
% 0.81/0.40 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', quantDeMorgan1)).
% 0.81/0.40 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', vacuousDall)).
% 0.81/0.40 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', upairsetIR)).
% 0.81/0.40 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', upairsetIL)).
% 0.81/0.40 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', upairsetE)).
% 0.81/0.40 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', quantDeMorgan3)).
% 0.81/0.40 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', notdallE)).
% 0.81/0.40 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', notdexE)).
% 0.81/0.40 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', prop2setI)).
% 0.81/0.40 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', quantDeMorgan4)).
% 0.81/0.40 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', inCongP)).
% 0.81/0.40 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setunion__Cong)).
% 0.81/0.40 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', powerset__Cong)).
% 0.81/0.40 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setadjoin__Cong)).
% 0.81/0.40 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', emptyset__Cong)).
% 0.81/0.40 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', in__Cong)).
% 0.81/0.40 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', omega__Cong)).
% 0.81/0.40 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', subsetI2)).
% 0.81/0.40 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', eqimpsubset1)).
% 0.81/0.40 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', eqimpsubset2)).
% 0.81/0.40 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', subsetI1)).
% 0.81/0.40 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', emptysetsubset)).
% 0.81/0.40 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', subsetTrans)).
% 0.81/0.40 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', subsetRefl)).
% 0.81/0.40 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', notequalI2)).
% 0.81/0.40 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', notequalI1)).
% 0.81/0.40 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', notsubsetI)).
% 0.81/0.40 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', subsetE2)).
% 0.81/0.40 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', subsetE)).
% 0.81/0.40 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setadjoinSub)).
% 0.81/0.40 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', inPowerset)).
% 0.81/0.40 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', powersetE1)).
% 0.81/0.40 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', powersetI1)).
% 0.81/0.40 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', subsetemptysetimpeq)).
% 0.81/0.40 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setextsub)).
% 0.81/0.40 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', subset2powerset)).
% 0.81/0.40 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setadjoinSub2)).
% 0.81/0.40 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', powersetsubset)).
% 0.81/0.40 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', binunionIL)).
% 0.81/0.40 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', upairset2IR)).
% 0.81/0.40 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', emptyI)).
% 0.81/0.40 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setext)).
% 0.81/0.40 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', notinemptyset)).
% 0.81/0.40 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', emptysetimpfalse)).
% 0.81/0.40 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', emptysetE)).
% 0.81/0.40 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', prop2setE)).
% 0.81/0.40 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', wellorderingAx)).
% 0.81/0.40 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', foundationAx)).
% 0.81/0.40 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', omegaIndAx)).
% 0.81/0.40 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', omegaSAx)).
% 0.81/0.40 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', omega0Ax)).
% 0.81/0.40 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setunionAx)).
% 0.81/0.40 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', powersetAx)).
% 0.81/0.40 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setadjoinAx)).
% 0.81/0.40 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', emptysetAx)).
% 0.81/0.40 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.tKkP6jmQDC/E---3.1_1325184.p', setextAx)).
% 0.81/0.40 thf(c_0_120, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.81/0.40 thf(c_0_121, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.81/0.40 thf(c_0_122, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.81/0.40 thf(c_0_123, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.81/0.40 thf(c_0_124, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.81/0.40 thf(c_0_125, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.81/0.40 thf(c_0_126, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.81/0.40 thf(c_0_127, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.81/0.40 thf(c_0_128, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.81/0.40 thf(c_0_129, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.81/0.40 thf(c_0_130, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.81/0.40 thf(c_0_131, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.81/0.40 thf(c_0_132, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.81/0.40 thf(c_0_133, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.81/0.40 thf(c_0_134, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.81/0.40 thf(c_0_135, 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)=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setminusI])).
% 0.81/0.40 thf(c_0_136, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_120])).
% 0.81/0.40 thf(c_0_137, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_121, c_0_120])).
% 0.81/0.40 thf(c_0_138, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_120])).
% 0.81/0.40 thf(c_0_139, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.81/0.40 thf(c_0_140, plain, ((setminus)=(^[Z0:$i, Z1:$i]:(dsetconstr @ Z0 @ (^[Z2:$i]:(~((in @ Z2 @ Z1))))))), inference(fof_simplification,[status(thm)],[setminus])).
% 0.81/0.40 thf(c_0_141, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.81/0.40 thf(c_0_142, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_120])).
% 0.81/0.40 thf(c_0_143, plain, ((exuE2)=(![X1:$i > $o]:((((?[X341:$i]:(((((X1 @ X341)))&(![X342:$i]:(((((X1 @ X342)))=>(((X341)=(X342))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_122, c_0_123])).
% 0.81/0.40 thf(c_0_144, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 0.81/0.40 thf(c_0_145, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X347:$i]:(((((X1 @ X347)))&(![X348:$i]:(((((X1 @ X348)))=>(((X347)=(X348)))))))))))))), inference(apply_def,[status(thm)],[c_0_124, c_0_123])).
% 0.81/0.40 thf(c_0_146, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X345:$i]:(((((X1 @ X345)))&(![X346:$i]:(((((X1 @ X346)))=>(((X345)=(X346)))))))))))))))), inference(apply_def,[status(thm)],[c_0_125, c_0_123])).
% 0.81/0.40 thf(c_0_147, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X343:$i]:(((((X1 @ X343)))&(![X344:$i]:(((((X1 @ X344)))=>(((X343)=(X344)))))))))))))), inference(apply_def,[status(thm)],[c_0_126, c_0_123])).
% 0.81/0.40 thf(c_0_148, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X351:$i]:(((((X1 @ X351)))&(![X352:$i]:(((((X1 @ X352)))=>(((X351)=(X352))))))))))<=>((?[X353:$i]:(((((X17 @ X353)))&(![X354:$i]:(((((X17 @ X354)))=>(((X353)=(X354)))))))))))))))), inference(apply_def,[status(thm)],[c_0_127, c_0_123])).
% 0.81/0.40 thf(c_0_149, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X349:$i]:(((((X1 @ X349)))&(![X350:$i]:(((((X1 @ X350)))=>(((X349)=(X350))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_128, c_0_123])).
% 0.81/0.40 thf(c_0_150, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.81/0.40 thf(c_0_151, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X357:$i]:(((((X1 @ X357)))&(![X358:$i]:(((((X1 @ X358)))=>(((X357)=(X358))))))))))=>((((?[X359:$i]:(((((X17 @ X359)))&(![X360:$i]:(((((X17 @ X360)))=>(((X359)=(X360))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_129, c_0_123])).
% 0.81/0.40 thf(c_0_152, plain, ((exuEu)=(![X1:$i > $o]:((((?[X355:$i]:(((((X1 @ X355)))&(![X356:$i]:(((((X1 @ X356)))=>(((X355)=(X356))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_130, c_0_123])).
% 0.81/0.40 thf(c_0_153, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.81/0.40 thf(c_0_154, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.81/0.40 thf(c_0_155, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X339:$i]:(((((X1 @ X339)))&(![X340:$i]:(((((X1 @ X340)))=>(((X339)=(X340))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_131, c_0_123])).
% 0.81/0.40 thf(c_0_156, plain, ((exuE1)=(![X1:$i > $o]:((((?[X337:$i]:(((((X1 @ X337)))&(![X338:$i]:(((((X1 @ X338)))=>(((X337)=(X338))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_132, c_0_123])).
% 0.81/0.40 thf(c_0_157, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.81/0.40 thf(c_0_158, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.81/0.40 thf(c_0_159, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.81/0.40 thf(c_0_160, plain, ((descrp)=(![X1:$i > $o]:((((?[X335:$i]:(((((X1 @ X335)))&(![X336:$i]:(((((X1 @ X336)))=>(((X335)=(X336))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_133, c_0_123])).
% 0.81/0.40 thf(c_0_161, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X333:$i]:(((((X6 @ X2 @ X333)))&(![X334:$i]:(((((X6 @ X2 @ X334)))=>(((X333)=(X334)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_134, c_0_123])).
% 0.81/0.40 thf(c_0_162, plain, ((epred1_0)<=>![X390:$i]:(?[X391:$i]:((((![X392:$i]:(((in @ X392 @ X391)=>![X393:$i]:(((in @ X393 @ X392)=>(in @ X393 @ X390)))))&![X394:$i, X395:$i]:((((in @ X394 @ X390)&(in @ X395 @ X390))=>(![X396:$i]:(((in @ X396 @ X391)=>((in @ X394 @ X396)<=>(in @ X395 @ X396))))=>((X394)=(X395))))))&![X397:$i, X398:$i]:((((in @ X397 @ X391)&(in @ X398 @ X391))=>(![X399:$i]:(((in @ X399 @ X397)=>(in @ X399 @ X398)))|![X400:$i]:(((in @ X400 @ X398)=>(in @ X400 @ X397)))))))&![X401:$i]:(((![X402:$i]:(((in @ X402 @ X401)=>(in @ X402 @ X390)))&?[X403:$i]:((in @ X403 @ X401)))=>?[X404:$i, X405:$i]:(((((in @ X404 @ X391)&(in @ X405 @ X401))&~(?[X406:$i]:(((in @ X406 @ X404)&(in @ X406 @ X401)))))&![X407:$i]:(((in @ X407 @ X391)=>(![X408:$i]:(((in @ X408 @ X407)=>(in @ X408 @ X404)))|(in @ X405 @ X407)))))))))))), introduced(definition)).
% 0.81/0.40 thf(c_0_163, negated_conjecture, ~((![X361:$i, X362:$i]:((![X363:$i]:(((in @ X363 @ X361)<=>(in @ X363 @ X362)))=>((X361)=(X362))))=>(![X364:$i]:(~(in @ X364 @ emptyset))=>(![X365:$i, X366:$i, X367:$i]:(((in @ X367 @ (setadjoin @ X365 @ X366))<=>(((X367)=(X365))|(in @ X367 @ X366))))=>(![X368:$i, X369:$i]:(((in @ X369 @ (powerset @ X368))<=>![X370:$i]:(((in @ X370 @ X369)=>(in @ X370 @ X368)))))=>(![X371:$i, X372:$i]:(((in @ X372 @ (setunion @ X371))<=>?[X373:$i]:(((in @ X372 @ X373)&(in @ X373 @ X371)))))=>((in @ emptyset @ omega)=>(![X374:$i]:(((in @ X374 @ omega)=>(in @ (setadjoin @ X374 @ X374) @ omega)))=>(![X375:$i]:((((in @ emptyset @ X375)&![X376:$i]:((((in @ X376 @ omega)&(in @ X376 @ X375))=>(in @ (setadjoin @ X376 @ X376) @ X375))))=>![X377:$i]:(((in @ X377 @ omega)=>(in @ X377 @ X375)))))=>(![X378:$i > $i > $o, X379:$i]:((![X380:$i]:(((in @ X380 @ X379)=>?[X381:$i]:(((X378 @ X380 @ X381)&![X382:$i]:(((X378 @ X380 @ X382)=>((X381)=(X382))))))))=>?[X383:$i]:(![X384:$i]:(((in @ X384 @ X383)<=>?[X385:$i]:(((in @ X385 @ X379)&(X378 @ X385 @ X384))))))))=>(![X386:$i]:((?[X387:$i]:((in @ X387 @ X386))=>?[X388:$i]:(((in @ X388 @ X386)&~(?[X389:$i]:(((in @ X389 @ X388)&(in @ X389 @ X386))))))))=>((epred1_0)=>(![X409:$i > $o]:((?[X410:$i]:(((X409 @ X410)&![X411:$i]:(((X409 @ X411)=>((X410)=(X411))))))=>(X409 @ (descr @ (^[Z0:$i]:(X409 @ Z0))))))=>(![X412:$i, X413:$i > $o, X414:$i]:(((in @ X414 @ X412)=>((X413 @ X414)=>(in @ X414 @ (dsetconstr @ X412 @ X413)))))=>(![X415:$i, X416:$i > $o, X417:$i]:(((in @ X417 @ (dsetconstr @ X415 @ X416))=>(in @ X417 @ X415)))=>(![X418:$i, X419:$i > $o, X420:$i]:(((in @ X420 @ (dsetconstr @ X418 @ X419))=>(X419 @ X420)))=>(![X421:$i > $o]:((?[X422:$i]:(((X421 @ X422)&![X423:$i]:(((X421 @ X423)=>((X422)=(X423))))))=>?[X424:$i]:(((X421 @ X424)&![X425:$i]:(((X421 @ X425)=>((X424)=(X425))))))))=>(![X426:$o, X427:$i]:(((in @ X427 @ (prop2set @ ((X426))))=>(X426)))=>(![X428:$i]:(((in @ X428 @ emptyset)=>![X429:$o]:((X429))))=>(![X430:$i]:(((in @ X430 @ emptyset)=>~($true)))=>(![X431:$i]:(~(in @ X431 @ emptyset))=>(![X432:$i > $o]:((?[X433:$i]:(((X432 @ X433)&![X434:$i]:(((X432 @ X434)=>((X433)=(X434))))))=>?[X435:$i]:((X432 @ X435))))=>(![X436:$i, X437:$i]:((![X438:$i]:(((in @ X438 @ X436)=>(in @ X438 @ X437)))=>(![X439:$i]:(((in @ X439 @ X437)=>(in @ X439 @ X436)))=>((X436)=(X437)))))=>(![X440:$i]:((![X441:$i]:(~(in @ X441 @ X440))=>((X440)=(emptyset))))=>(![X442:$i]:((![X443:$i]:(~(in @ X443 @ X442))=>((X442)=(emptyset))))=>(![X444:$i, X445:$i > $o, X446:$i]:(((in @ X446 @ X444)=>((in @ X446 @ (dsetconstr @ X444 @ X445))<=>(X445 @ X446))))=>(![X447:$i]:((((X447)!=(emptyset))=>?[X448:$i]:((in @ X448 @ X447))))=>(![X449:$i, X450:$i > $o, X451:$i]:(((in @ X451 @ X449)=>((X450 @ X451)=>((dsetconstr @ X449 @ X450)!=(emptyset)))))=>(![X452:$i]:((?[X453:$i]:((in @ X453 @ X452))=>((X452)!=(emptyset))))=>(![X454:$i, X455:$i]:((in @ X454 @ (setadjoin @ X454 @ X455)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X456:$i, X457:$i, X458:$i]:(((in @ X458 @ X457)=>(in @ X458 @ (setadjoin @ X456 @ X457))))=>(![X459:$i, X460:$i, X461:$i]:(((in @ X461 @ (setadjoin @ X459 @ X460))=>![X462:$o]:(((((X461)=(X459))=>(X462))=>(((in @ X461 @ X460)=>(X462))=>(X462))))))=>(![X463:$i, X464:$i, X465:$i]:(((in @ X465 @ (setadjoin @ X463 @ X464))=>(((X465)=(X463))|(in @ X465 @ X464))))=>(![X466:$i]:(((dsetconstr @ X466 @ (^[Z0:$i]:($true)))=(X466)))=>(![X467:$i, X468:$i]:((![X469:$i]:(((in @ X469 @ X468)=>(in @ X469 @ X467)))=>(in @ X468 @ (powerset @ X467))))=>(![X470:$i]:((in @ emptyset @ (powerset @ X470)))=>(![X471:$i]:((in @ emptyset @ (powerset @ X471)))=>(![X472:$i, X473:$i, X474:$i]:(((in @ X473 @ (powerset @ X472))=>((in @ X474 @ X473)=>(in @ X474 @ X472))))=>(![X475:$i, X476:$i, X477:$i]:(((in @ X476 @ X477)=>((in @ X477 @ X475)=>(in @ X476 @ (setunion @ X475)))))=>(![X478:$i, X479:$i]:(((in @ X479 @ (setunion @ X478))=>![X480:$o]:((![X481:$i]:(((in @ X479 @ X481)=>((in @ X481 @ X478)=>(X480))))=>(X480)))))=>(![X482:$i, X483:$i]:(((in @ X483 @ X482)=>(in @ X483 @ (powerset @ (setunion @ X482)))))=>(![X484:$i > $o]:((?[X485:$i]:(((X484 @ X485)&![X486:$i]:(((X484 @ X486)=>((X485)=(X486))))))=>?[X487:$i]:(![X488:$i]:(((X484 @ X488)<=>((X488)=(X487)))))))=>(![X489:$i]:((((X489)!=(emptyset))=>?[X490:$i]:(((in @ X490 @ X489)&$true))))=>(![X491:$i, X492:$i]:(((in @ X491 @ (setadjoin @ X492 @ emptyset))=>((X491)=(X492))))=>(![X493:$i, X494:$i]:((((X493)!=(X494))=>~(in @ X494 @ (setadjoin @ X493 @ emptyset))))=>(![X495:$i, X496:$i]:((((X495)=(X496))=>(in @ X495 @ (setadjoin @ X496 @ emptyset))))=>(![X497:$i, X498:$i]:(((in @ X497 @ (setadjoin @ X498 @ emptyset))=>(in @ X498 @ (setadjoin @ X497 @ emptyset))))=>(![X499:$i, X500:$i, X501:$i]:(((in @ X501 @ (setadjoin @ X499 @ (setadjoin @ X500 @ emptyset)))=>(((X501)=(X499))|((X501)=(X500)))))=>(![X502:$i, X503:$i]:((in @ X502 @ (setadjoin @ X502 @ (setadjoin @ X503 @ emptyset))))=>(![X504:$i, X505:$i]:((in @ X505 @ (setadjoin @ X504 @ (setadjoin @ X505 @ emptyset))))=>(![X506:$i, X507:$i > $o]:((?[X508:$i]:(((in @ X508 @ X506)&(X507 @ X508)))=>(((dsetconstr @ X506 @ X507)=(emptyset))=>~($true))))=>(![X509:$i > $o, X510:$i]:(((in @ X510 @ emptyset)=>(X509 @ X510)))=>(![X511:$i, X512:$i > $o]:((~(![X513:$i]:(((in @ X513 @ X511)=>(X512 @ X513))))=>?[X514:$i]:(((in @ X514 @ X511)&~((X512 @ X514))))))=>(![X515:$i, X516:$i > $o]:((![X517:$i]:(((in @ X517 @ X515)=>~((X516 @ X517))))=>~(?[X518:$i]:(((in @ X518 @ X515)&(X516 @ X518))))))=>(![X519:$i, X520:$i > $o]:((~(?[X521:$i]:(((in @ X521 @ X519)&(X520 @ X521))))=>![X522:$i]:(((in @ X522 @ X519)=>~((X520 @ X522))))))=>(![X523:$i, X524:$i > $o]:((?[X525:$i]:(((in @ X525 @ X523)&~((X524 @ X525))))=>~(![X526:$i]:(((in @ X526 @ X523)=>(X524 @ X526))))))=>(![X527:$o]:(((X527)=>(in @ emptyset @ (prop2set @ ((X527))))))=>((prop2set2propI)=>(![X528:$i, X529:$i > $o]:((~(?[X530:$i]:(((in @ X530 @ X528)&(X529 @ X530))))=>![X531:$i]:(((in @ X531 @ X528)=>~((X529 @ X531))))))=>(![X532:$i, X533:$i > $o]:((~(![X534:$i]:(((in @ X534 @ X532)=>(X533 @ X534))))=>?[X535:$i]:(((in @ X535 @ X532)&~((X533 @ X535))))))=>(![X536:$i > $o]:((?[X537:$i]:(((X536 @ X537)&![X538:$i]:(((X536 @ X538)=>((X537)=(X538))))))=>?[X539:$i]:(((X536 @ X539)&![X540:$i]:(((X536 @ X540)=>((X539)=(X540))))))))=>(![X541:$i > $o]:((?[X542:$i]:((X541 @ X542))=>(![X543:$i, X544:$i]:(((X541 @ X543)=>((X541 @ X544)=>((X543)=(X544)))))=>?[X545:$i]:(((X541 @ X545)&![X546:$i]:(((X541 @ X546)=>((X545)=(X546)))))))))=>(![X547:$i > $o]:((?[X548:$i]:(![X549:$i]:(((X547 @ X549)<=>((X549)=(X548)))))=>?[X550:$i]:(((X547 @ X550)&![X551:$i]:(((X547 @ X551)=>((X550)=(X551))))))))=>(![X552:$i, X553:$i]:((((X552)=(X553))=>![X554:$i, X555:$i]:((((X554)=(X555))=>((in @ X554 @ X552)=>(in @ X555 @ X553))))))=>(![X556:$i, X557:$i]:((((X556)=(X557))=>![X558:$i, X559:$i]:((((X558)=(X559))=>((in @ X558 @ X556)<=>(in @ X559 @ X557))))))=>(![X560:$i > $o]:((?[X561:$i]:(((X560 @ X561)&![X562:$i]:(((X560 @ X562)=>((X561)=(X562))))))=>![X563:$i, X564:$i]:(((X560 @ X563)=>((X560 @ X564)=>((X563)=(X564)))))))=>(![X565:$i > $o, X566:$i > $o]:((![X567:$i, X568:$i]:((((X567)=(X568))=>((X565 @ X567)<=>(X566 @ X568))))=>(?[X569:$i]:(((X565 @ X569)&![X570:$i]:(((X565 @ X570)=>((X569)=(X570))))))<=>?[X571:$i]:(((X566 @ X571)&![X572:$i]:(((X566 @ X572)=>((X571)=(X572)))))))))=>(((emptyset)=(emptyset))=>(![X573:$i, X574:$i]:((((X573)=(X574))=>![X575:$i, X576:$i]:((((X575)=(X576))=>((setadjoin @ X573 @ X575)=(setadjoin @ X574 @ X576))))))=>(![X577:$i, X578:$i]:((((X577)=(X578))=>((powerset @ X577)=(powerset @ X578))))=>(![X579:$i, X580:$i]:((((X579)=(X580))=>((setunion @ X579)=(setunion @ X580))))=>(((omega)=(omega))=>(![X581:$i > $o]:((?[X582:$i]:(((X581 @ X582)&![X583:$i]:(((X581 @ X583)=>((X582)=(X583))))))=>![X584:$i, X585:$i]:(((X581 @ X584)=>((X581 @ X585)=>((X584)=(X585)))))))=>(![X586:$i > $o, X587:$i > $o]:((![X588:$i, X589:$i]:((((X588)=(X589))=>((X586 @ X588)<=>(X587 @ X589))))=>(?[X590:$i]:(((X586 @ X590)&![X591:$i]:(((X586 @ X591)=>((X590)=(X591))))))=>(?[X592:$i]:(((X587 @ X592)&![X593:$i]:(((X587 @ X593)=>((X592)=(X593))))))=>((descr @ X586)=(descr @ X587))))))=>(![X594:$i, X595:$i]:((((X594)=(X595))=>![X596:$i > $o, X597:$i > $o]:((![X598:$i]:(((in @ X598 @ X594)=>![X599:$i]:(((in @ X599 @ X595)=>(((X598)=(X599))=>((X596 @ X598)<=>(X597 @ X599)))))))=>((dsetconstr @ X594 @ X596)=(dsetconstr @ X595 @ X597))))))=>(![X600:$i, X601:$i]:((![X602:$i]:(((in @ X602 @ X600)=>(in @ X602 @ X601)))=>(subset @ X600 @ X601)))=>(![X603:$i, X604:$i]:((((X603)=(X604))=>(subset @ X604 @ X603)))=>(![X605:$i, X606:$i]:((((X605)=(X606))=>(subset @ X605 @ X606)))=>(![X607:$i, X608:$i]:((![X609:$i]:(((in @ X609 @ X607)=>(in @ X609 @ X608)))=>(subset @ X607 @ X608)))=>(![X610:$i]:((subset @ emptyset @ X610))=>(![X611:$i, X612:$i, X613:$i]:(((subset @ X611 @ X612)=>((in @ X613 @ X611)=>(in @ X613 @ X612))))=>(![X614:$i, X615:$i, X616:$i]:(((subset @ X614 @ X615)=>(~(in @ X616 @ X615)=>~(in @ X616 @ X614))))=>(![X617:$i, X618:$i, X619:$i]:(((in @ X619 @ X617)=>(~(in @ X619 @ X618)=>~(subset @ X617 @ X618))))=>(![X620:$i, X621:$i]:((~(subset @ X620 @ X621)=>((X620)!=(X621))))=>(![X622:$i, X623:$i, X624:$i]:(((in @ X624 @ X622)=>(~(in @ X624 @ X623)=>((X622)!=(X623)))))=>(![X625:$i]:((subset @ X625 @ X625))=>(![X626:$i, X627:$i, X628:$i]:(((subset @ X626 @ X627)=>((subset @ X627 @ X628)=>(subset @ X626 @ X628))))=>(![X629:$i, X630:$i]:((subset @ X630 @ (setadjoin @ X629 @ X630)))=>(![X631:$i, X632:$i, X633:$i]:(((subset @ X631 @ X633)=>(subset @ X631 @ (setadjoin @ X632 @ X633))))=>(![X634:$i, X635:$i]:(((subset @ X634 @ X635)=>(in @ X634 @ (powerset @ X635))))=>(![X636:$i, X637:$i]:(((subset @ X636 @ X637)=>((subset @ X637 @ X636)=>((X636)=(X637)))))=>(![X638:$i]:(((subset @ X638 @ emptyset)=>((X638)=(emptyset))))=>(![X639:$i, X640:$i]:(((subset @ X640 @ X639)=>(in @ X640 @ (powerset @ X639))))=>(![X641:$i, X642:$i]:(((in @ X642 @ (powerset @ X641))=>(subset @ X642 @ X641)))=>(![X643:$i]:((in @ X643 @ (powerset @ X643)))=>(![X644:$i, X645:$i]:(((subset @ X644 @ X645)=>(subset @ (powerset @ X644) @ (powerset @ X645))))=>(![X646:$i, X647:$i > $o]:((in @ (dsetconstr @ X646 @ X647) @ (powerset @ X646)))=>(![X648:$i, X649:$i > $o]:((subset @ (dsetconstr @ X648 @ X649) @ X648))=>(![X650:$i, X651:$i, X652:$i]:(((in @ X652 @ X650)=>(in @ X652 @ (binunion @ X650 @ X651))))=>(![X653:$i, X654:$i]:((in @ X654 @ (setadjoin @ X653 @ (setadjoin @ X654 @ emptyset))))=>(![X655:$i, X656:$i, X657:$i]:(((in @ X657 @ X656)=>(in @ X657 @ (binunion @ X655 @ X656))))=>(![X658:$i, X659:$i, X660:$i, X661:$o]:(((in @ X660 @ (binunion @ X658 @ X659))=>(((in @ X660 @ X658)=>(X661))=>(((in @ X660 @ X659)=>(X661))=>(X661)))))=>(![X662:$i, X663:$i, X664:$i]:(((in @ X664 @ (binunion @ X662 @ X663))=>((in @ X664 @ X662)|(in @ X664 @ X663))))=>(![X665:$i, X666:$i]:((subset @ X665 @ (binunion @ X665 @ X666)))=>(![X667:$i, X668:$i]:((subset @ X668 @ (binunion @ X667 @ X668)))=>(![X669:$i, X670:$i, X671:$i]:(((in @ X671 @ X669)=>((in @ X671 @ X670)=>(in @ X671 @ (binintersect @ X669 @ X670)))))=>(![X672:$i, X673:$i, X674:$i]:(((subset @ X674 @ X672)=>((subset @ X674 @ X673)=>(subset @ X674 @ (binintersect @ X672 @ X673)))))=>(![X675:$i, X676:$i, X677:$i]:(((in @ X677 @ (binintersect @ X675 @ X676))=>(in @ X677 @ X675)))=>(![X678:$i, X679:$i]:((subset @ (binintersect @ X678 @ X679) @ X678))=>(![X680:$i, X681:$i]:(((subset @ X680 @ X681)=>((binintersect @ X680 @ X681)=(X680))))=>(![X682:$i, X683:$i]:((((binintersect @ X682 @ X683)=(X683))=>(subset @ X683 @ X682)))=>(![X684:$i, X685:$i, X686:$i]:(((in @ X686 @ (binintersect @ X684 @ X685))=>(in @ X686 @ X685)))=>(![X687:$i, X688:$i]:((~(?[X689:$i]:(((in @ X689 @ X687)&(in @ X689 @ X688))))=>((binintersect @ X687 @ X688)=(emptyset))))=>(![X690:$i, X691:$i]:((subset @ (binintersect @ X690 @ X691) @ X691))=>(![X692:$i, X693:$i]:(((subset @ X693 @ X692)=>((binintersect @ X692 @ X693)=(X693))))=>(![X694:$i, X695:$i]:((((binintersect @ X694 @ X695)=(X694))=>(subset @ X694 @ X695)))=>(![X696:$i, X697:$i, X698:$i]:(((binintersect @ X696 @ (binunion @ X697 @ X698))=(binunion @ (binintersect @ X696 @ X697) @ (binintersect @ X696 @ X698))))=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~(in @ X2 @ X5)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:(~((in @ Z0 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_135, binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), emptyinunitempty]), binintersectSubset5]), setadjoinIL]), binintersectEL]), c_0_136]), binintersectLsub]), c_0_137]), binintersectSubset2]), c_0_138]), binintersectSubset3]), c_0_139]), binintersectER]), noeltsimpempty]), disjointsetsI1]), setadjoinIR]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), c_0_140]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_141]), setadjoinOr]), setadjoinE]), setunionI]), eqinunit]), notinsingleton]), uniqinunit]), c_0_142]), c_0_143]), subPowSU]), setunionE]), singletonsswitch]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_144]), upairsetIR]), upairsetIL]), upairsetE]), quantDeMorgan3]), c_0_145]), c_0_146]), c_0_147]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), inCongP]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_148]), c_0_149]), in__Cong]), omega__Cong]), subsetI2]), eqimpsubset1]), eqimpsubset2]), subsetI1]), c_0_150]), c_0_151]), c_0_152]), emptysetsubset]), subsetTrans]), subsetRefl]), notequalI2]), notequalI1]), notsubsetI]), subsetE2]), subsetE]), setadjoinSub]), inPowerset]), powersetE1]), powersetI1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), setadjoinSub2]), powersetsubset]), c_0_153]), c_0_154]), binunionIL]), upairset2IR]), emptyI]), setext]), c_0_155]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_156]), c_0_157]), c_0_158]), c_0_159]), c_0_160]), wellorderingAx]), foundationAx]), c_0_161]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_162])).
% 0.81/0.40 thf(c_0_164, negated_conjecture, ![X699:$i, X700:$i, X702:$i, X703:$i, X704:$i, X705:$i, X706:$i, X707:$i, X708:$i, X709:$i, X710:$i, X712:$i, X713:$i, X715:$i, X716:$i, X717:$i, X718:$i, X719:$i, X721:$i, X722:$i > $i > $o, X723:$i, X725:$i, X728:$i, X730:$i, X731:$i, X732:$i, X733:$i, X735:$i, X736:$i > $o, X737:$i, X739:$i, X740:$i > $o, X741:$i, X742:$i, X743:$i > $o, X744:$i, X745:$i, X746:$i > $o, X747:$i, X748:$i > $o, X749:$i, X752:$i, X753:$o, X754:$i, X755:$i, X756:$o, X757:$i, X758:$i, X759:$i > $o, X760:$i, X763:$i, X764:$i, X767:$i, X769:$i, X771:$i, X772:$i > $o, X773:$i, X774:$i, X776:$i, X777:$i > $o, X778:$i, X779:$i, X780:$i, X781:$i, X782:$i, X783:$i, X784:$i, X785:$i, X786:$i, X787:$i, X788:$i, X789:$o, X790:$i, X791:$i, X792:$i, X793:$i, X794:$i, X795:$i, X797:$i, X798:$i, X799:$i, X800:$i, X801:$i, X802:$i, X803:$i, X804:$i, X805:$i, X806:$i, X807:$o, X809:$i, X810:$i, X811:$i > $o, X812:$i, X815:$i, X816:$i, X817:$i, X819:$i, X820:$i, X821:$i, X822:$i, X823:$i, X824:$i, X825:$i, X826:$i, X827:$i, X828:$i, X829:$i, X830:$i, X831:$i, X832:$i, X833:$i, X834:$i, X835:$i > $o, X836:$i, X837:$i > $o, X838:$i, X839:$i, X840:$i > $o, X841:$i, X843:$i, X844:$i > $o, X846:$i, X847:$i, X848:$i > $o, X850:$i, X851:$i, X852:$i > $o, X853:$i, X855:$o, X856:$i, X857:$i > $o, X859:$i, X860:$i, X861:$i > $o, X862:$i, X864:$i > $o, X865:$i, X868:$i, X869:$i > $o, X870:$i, X874:$i, X875:$i > $o, X876:$i, X879:$i, X880:$i, X881:$i, X882:$i, X883:$i, X884:$i, X885:$i, X886:$i, X887:$i, X888:$i > $o, X889:$i, X891:$i, X892:$i, X893:$i > $o, X894:$i > $o, X897:$i, X900:$i, X901:$i, X904:$i, X905:$i, X906:$i, X907:$i, X908:$i, X909:$i, X910:$i, X911:$i, X912:$i, X913:$i > $o, X914:$i, X916:$i, X917:$i, X918:$i > $o, X919:$i > $o, X922:$i, X924:$i, X926:$i, X927:$i, X928:$i > $o, X929:$i > $o, X932:$i, X933:$i, X935:$i, X936:$i, X937:$i, X938:$i, X939:$i, X940:$i, X942:$i, X943:$i, X944:$i, X945:$i, X946:$i, X947:$i, X948:$i, X949:$i, X950:$i, X951:$i, X952:$i, X953:$i, X954:$i, X955:$i, X956:$i, X957:$i, X958:$i, X959:$i, X960:$i, X961:$i, X962:$i, X963:$i, X964:$i, X965:$i, X966:$i, X967:$i, X968:$i, X969:$i, X970:$i, X971:$i, X972:$i, X973:$i, X974:$i, X975:$i, X976:$i, X977:$i, X978:$i, X979:$i > $o, X980:$i, X981:$i > $o, X982:$i, X983:$i, X984:$i, X985:$i, X986:$i, X987:$i, X988:$i, X989:$i, X990:$i, X991:$i, X992:$i, X993:$o, X994:$i, X995:$i, X996:$i, X997:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i, X1003:$i, X1004:$i, X1005:$i, X1006:$i, X1007:$i, X1008:$i, X1009:$i, X1010:$i, X1011:$i, X1012:$i, X1013:$i, X1014:$i, X1015:$i, X1016:$i, X1017:$i, X1018:$i, X1019:$i, X1020:$i, X1022:$i, X1023:$i, X1024:$i, X1025:$i, X1026:$i, X1027:$i, X1028:$i, X1029:$i, X1030:$i]:((((~(in @ (esk1_2 @ X699 @ X700) @ X699)|~(in @ (esk1_2 @ X699 @ X700) @ X700)|((X699)=(X700)))&((in @ (esk1_2 @ X699 @ X700) @ X699)|(in @ (esk1_2 @ X699 @ X700) @ X700)|((X699)=(X700))))&(~(in @ X702 @ emptyset)&(((~(in @ X705 @ (setadjoin @ X703 @ X704))|(((X705)=(X703))|(in @ X705 @ X704)))&((((X705)!=(X703))|(in @ X705 @ (setadjoin @ X703 @ X704)))&(~(in @ X705 @ X704)|(in @ X705 @ (setadjoin @ X703 @ X704)))))&(((~(in @ X707 @ (powerset @ X706))|(~(in @ X708 @ X707)|(in @ X708 @ X706)))&(((in @ (esk2_2 @ X709 @ X710) @ X710)|(in @ X710 @ (powerset @ X709)))&(~(in @ (esk2_2 @ X709 @ X710) @ X709)|(in @ X710 @ (powerset @ X709)))))&(((((in @ X713 @ (esk3_2 @ X712 @ X713))|~(in @ X713 @ (setunion @ X712)))&((in @ (esk3_2 @ X712 @ X713) @ X712)|~(in @ X713 @ (setunion @ X712))))&(~(in @ X716 @ X717)|~(in @ X717 @ X715)|(in @ X716 @ (setunion @ X715))))&((in @ emptyset @ omega)&((~(in @ X718 @ omega)|(in @ (setadjoin @ X718 @ X718) @ omega))&(((((in @ (esk4_1 @ X719) @ omega)|~(in @ emptyset @ X719)|(~(in @ X721 @ omega)|(in @ X721 @ X719)))&((in @ (esk4_1 @ X719) @ X719)|~(in @ emptyset @ X719)|(~(in @ X721 @ omega)|(in @ X721 @ X719))))&(~(in @ (setadjoin @ (esk4_1 @ X719) @ (esk4_1 @ X719)) @ X719)|~(in @ emptyset @ X719)|(~(in @ X721 @ omega)|(in @ X721 @ X719))))&((((((in @ (esk8_3 @ X722 @ X723 @ X728) @ X723)|~(in @ X728 @ (esk7_2 @ X722 @ X723))|(in @ (esk5_2 @ X722 @ X723) @ X723))&((X722 @ (esk8_3 @ X722 @ X723 @ X728) @ X728)|~(in @ X728 @ (esk7_2 @ X722 @ X723))|(in @ (esk5_2 @ X722 @ X723) @ X723)))&(~(in @ X731 @ X723)|~(X722 @ X731 @ X730)|(in @ X730 @ (esk7_2 @ X722 @ X723))|(in @ (esk5_2 @ X722 @ X723) @ X723)))&(((((in @ (esk8_3 @ X722 @ X723 @ X728) @ X723)|~(in @ X728 @ (esk7_2 @ X722 @ X723))|((X722 @ (esk5_2 @ X722 @ X723) @ (esk6_3 @ X722 @ X723 @ X725))|~(X722 @ (esk5_2 @ X722 @ X723) @ X725)))&((X722 @ (esk8_3 @ X722 @ X723 @ X728) @ X728)|~(in @ X728 @ (esk7_2 @ X722 @ X723))|((X722 @ (esk5_2 @ X722 @ X723) @ (esk6_3 @ X722 @ X723 @ X725))|~(X722 @ (esk5_2 @ X722 @ X723) @ X725))))&(~(in @ X731 @ X723)|~(X722 @ X731 @ X730)|(in @ X730 @ (esk7_2 @ X722 @ X723))|((X722 @ (esk5_2 @ X722 @ X723) @ (esk6_3 @ X722 @ X723 @ X725))|~(X722 @ (esk5_2 @ X722 @ X723) @ X725))))&((((in @ (esk8_3 @ X722 @ X723 @ X728) @ X723)|~(in @ X728 @ (esk7_2 @ X722 @ X723))|(((X725)!=(esk6_3 @ X722 @ X723 @ X725))|~(X722 @ (esk5_2 @ X722 @ X723) @ X725)))&((X722 @ (esk8_3 @ X722 @ X723 @ X728) @ X728)|~(in @ X728 @ (esk7_2 @ X722 @ X723))|(((X725)!=(esk6_3 @ X722 @ X723 @ X725))|~(X722 @ (esk5_2 @ X722 @ X723) @ X725))))&(~(in @ X731 @ X723)|~(X722 @ X731 @ X730)|(in @ X730 @ (esk7_2 @ X722 @ X723))|(((X725)!=(esk6_3 @ X722 @ X723 @ X725))|~(X722 @ (esk5_2 @ X722 @ X723) @ X725))))))&((((in @ (esk9_1 @ X732) @ X732)|~(in @ X733 @ X732))&(~(in @ X735 @ (esk9_1 @ X732))|~(in @ X735 @ X732)|~(in @ X733 @ X732)))&((epred1_0)&((((X736 @ (esk10_2 @ X736 @ X737))|~(X736 @ X737)|(X736 @ (descr @ X736)))&(((X737)!=(esk10_2 @ X736 @ X737))|~(X736 @ X737)|(X736 @ (descr @ X736))))&((~(in @ X741 @ X739)|(~(X740 @ X741)|(in @ X741 @ (dsetconstr @ X739 @ X740))))&((~(in @ X744 @ (dsetconstr @ X742 @ X743))|(in @ X744 @ X742))&((~(in @ X747 @ (dsetconstr @ X745 @ X746))|(X746 @ X747))&(((((X748 @ (esk12_1 @ X748))|((X748 @ (esk11_2 @ X748 @ X749))|~(X748 @ X749)))&(~(X748 @ X752)|((esk12_1 @ X748)=(X752))|((X748 @ (esk11_2 @ X748 @ X749))|~(X748 @ X749))))&(((X748 @ (esk12_1 @ X748))|(((X749)!=(esk11_2 @ X748 @ X749))|~(X748 @ X749)))&(~(X748 @ X752)|((esk12_1 @ X748)=(X752))|(((X749)!=(esk11_2 @ X748 @ X749))|~(X748 @ X749)))))&((~(in @ X754 @ (prop2set @ ((X753))))|(X753))&((~(in @ X755 @ emptyset)|(X756))&((~(in @ X757 @ emptyset)|~($true))&(~(in @ X758 @ emptyset)&((((X759 @ (esk13_2 @ X759 @ X760))|~(X759 @ X760)|(X759 @ (esk14_1 @ X759)))&(((X760)!=(esk13_2 @ X759 @ X760))|~(X759 @ X760)|(X759 @ (esk14_1 @ X759))))&(((((in @ (esk16_2 @ X763 @ X764) @ X764)|((X763)=(X764))|(in @ (esk15_2 @ X763 @ X764) @ X763))&(~(in @ (esk16_2 @ X763 @ X764) @ X763)|((X763)=(X764))|(in @ (esk15_2 @ X763 @ X764) @ X763)))&(((in @ (esk16_2 @ X763 @ X764) @ X764)|((X763)=(X764))|~(in @ (esk15_2 @ X763 @ X764) @ X764))&(~(in @ (esk16_2 @ X763 @ X764) @ X763)|((X763)=(X764))|~(in @ (esk15_2 @ X763 @ X764) @ X764))))&(((in @ (esk17_1 @ X767) @ X767)|((X767)=(emptyset)))&(((in @ (esk18_1 @ X769) @ X769)|((X769)=(emptyset)))&(((~(in @ X773 @ (dsetconstr @ X771 @ X772))|(X772 @ X773)|~(in @ X773 @ X771))&(~(X772 @ X773)|(in @ X773 @ (dsetconstr @ X771 @ X772))|~(in @ X773 @ X771)))&((((X774)=(emptyset))|(in @ (esk19_1 @ X774) @ X774))&((~(in @ X778 @ X776)|(~(X777 @ X778)|((dsetconstr @ X776 @ X777)!=(emptyset))))&((~(in @ X780 @ X779)|((X779)!=(emptyset)))&((in @ X781 @ (setadjoin @ X781 @ X782))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X785 @ X784)|(in @ X785 @ (setadjoin @ X783 @ X784)))&(((((in @ X788 @ X787)|(X789)|((X788)=(X786))|~(in @ X788 @ (setadjoin @ X786 @ X787)))&(~(X789)|(X789)|((X788)=(X786))|~(in @ X788 @ (setadjoin @ X786 @ X787))))&(((in @ X788 @ X787)|(X789)|~(X789)|~(in @ X788 @ (setadjoin @ X786 @ X787)))&(~(X789)|(X789)|~(X789)|~(in @ X788 @ (setadjoin @ X786 @ X787)))))&((~(in @ X792 @ (setadjoin @ X790 @ X791))|(((X792)=(X790))|(in @ X792 @ X791)))&(((dsetconstr @ X793 @ (^[Z0:$i]:($true)))=(X793))&((((in @ (esk20_2 @ X794 @ X795) @ X795)|(in @ X795 @ (powerset @ X794)))&(~(in @ (esk20_2 @ X794 @ X795) @ X794)|(in @ X795 @ (powerset @ X794))))&((in @ emptyset @ (powerset @ X797))&((in @ emptyset @ (powerset @ X798))&((~(in @ X800 @ (powerset @ X799))|(~(in @ X801 @ X800)|(in @ X801 @ X799)))&((~(in @ X803 @ X804)|(~(in @ X804 @ X802)|(in @ X803 @ (setunion @ X802))))&((((in @ X806 @ (esk21_3 @ X805 @ X806 @ X807))|(X807)|~(in @ X806 @ (setunion @ X805)))&(((in @ (esk21_3 @ X805 @ X806 @ X807) @ X805)|(X807)|~(in @ X806 @ (setunion @ X805)))&(~(X807)|(X807)|~(in @ X806 @ (setunion @ X805)))))&((~(in @ X810 @ X809)|(in @ X810 @ (powerset @ (setunion @ X809))))&((((~(X811 @ X815)|((X815)=(esk23_1 @ X811))|((X811 @ (esk22_2 @ X811 @ X812))|~(X811 @ X812)))&(((X816)!=(esk23_1 @ X811))|(X811 @ X816)|((X811 @ (esk22_2 @ X811 @ X812))|~(X811 @ X812))))&((~(X811 @ X815)|((X815)=(esk23_1 @ X811))|(((X812)!=(esk22_2 @ X811 @ X812))|~(X811 @ X812)))&(((X816)!=(esk23_1 @ X811))|(X811 @ X816)|(((X812)!=(esk22_2 @ X811 @ X812))|~(X811 @ X812)))))&((((in @ (esk24_1 @ X817) @ X817)|((X817)=(emptyset)))&(($true)|((X817)=(emptyset))))&((~(in @ X819 @ (setadjoin @ X820 @ emptyset))|((X819)=(X820)))&((((X821)=(X822))|~(in @ X822 @ (setadjoin @ X821 @ emptyset)))&((((X823)!=(X824))|(in @ X823 @ (setadjoin @ X824 @ emptyset)))&((~(in @ X825 @ (setadjoin @ X826 @ emptyset))|(in @ X826 @ (setadjoin @ X825 @ emptyset)))&((~(in @ X829 @ (setadjoin @ X827 @ (setadjoin @ X828 @ emptyset)))|(((X829)=(X827))|((X829)=(X828))))&((in @ X830 @ (setadjoin @ X830 @ (setadjoin @ X831 @ emptyset)))&((in @ X833 @ (setadjoin @ X832 @ (setadjoin @ X833 @ emptyset)))&((~(in @ X836 @ X834)|~(X835 @ X836)|(((dsetconstr @ X834 @ X835)!=(emptyset))|~($true)))&((~(in @ X838 @ emptyset)|(X837 @ X838))&((((in @ (esk25_2 @ X839 @ X840) @ X839)|(~(in @ X841 @ X839)|(X840 @ X841)))&(~(X840 @ (esk25_2 @ X839 @ X840))|(~(in @ X841 @ X839)|(X840 @ X841))))&((((in @ (esk26_2 @ X843 @ X844) @ X843)|(~(in @ X846 @ X843)|~(X844 @ X846)))&((X844 @ (esk26_2 @ X843 @ X844))|(~(in @ X846 @ X843)|~(X844 @ X846))))&((((in @ (esk27_2 @ X847 @ X848) @ X847)|(~(in @ X850 @ X847)|~(X848 @ X850)))&((X848 @ (esk27_2 @ X847 @ X848))|(~(in @ X850 @ X847)|~(X848 @ X850))))&((((in @ (esk28_2 @ X851 @ X852) @ X851)|(~(in @ X853 @ X851)|(X852 @ X853)))&(~(X852 @ (esk28_2 @ X851 @ X852))|(~(in @ X853 @ X851)|(X852 @ X853))))&((~(X855)|(in @ emptyset @ (prop2set @ ((X855)))))&((prop2set2propI)&((((in @ (esk29_2 @ X856 @ X857) @ X856)|(~(in @ X859 @ X856)|~(X857 @ X859)))&((X857 @ (esk29_2 @ X856 @ X857))|(~(in @ X859 @ X856)|~(X857 @ X859))))&((((in @ (esk30_2 @ X860 @ X861) @ X860)|(~(in @ X862 @ X860)|(X861 @ X862)))&(~(X861 @ (esk30_2 @ X860 @ X861))|(~(in @ X862 @ X860)|(X861 @ X862))))&(((((X864 @ (esk32_1 @ X864))|((X864 @ (esk31_2 @ X864 @ X865))|~(X864 @ X865)))&(~(X864 @ X868)|((esk32_1 @ X864)=(X868))|((X864 @ (esk31_2 @ X864 @ X865))|~(X864 @ X865))))&(((X864 @ (esk32_1 @ X864))|(((X865)!=(esk31_2 @ X864 @ X865))|~(X864 @ X865)))&(~(X864 @ X868)|((esk32_1 @ X864)=(X868))|(((X865)!=(esk31_2 @ X864 @ X865))|~(X864 @ X865)))))&(((((X869 @ (esk35_1 @ X869))|(X869 @ (esk33_1 @ X869))|~(X869 @ X870))&(~(X869 @ X874)|((esk35_1 @ X869)=(X874))|(X869 @ (esk33_1 @ X869))|~(X869 @ X870)))&((((X869 @ (esk35_1 @ X869))|(X869 @ (esk34_1 @ X869))|~(X869 @ X870))&(~(X869 @ X874)|((esk35_1 @ X869)=(X874))|(X869 @ (esk34_1 @ X869))|~(X869 @ X870)))&(((X869 @ (esk35_1 @ X869))|((esk33_1 @ X869)!=(esk34_1 @ X869))|~(X869 @ X870))&(~(X869 @ X874)|((esk35_1 @ X869)=(X874))|((esk33_1 @ X869)!=(esk34_1 @ X869))|~(X869 @ X870)))))&(((((X875 @ (esk37_1 @ X875))|(~(X875 @ (esk36_2 @ X875 @ X876))|((esk36_2 @ X875 @ X876)!=(X876))))&(~(X875 @ X879)|((esk37_1 @ X875)=(X879))|(~(X875 @ (esk36_2 @ X875 @ X876))|((esk36_2 @ X875 @ X876)!=(X876)))))&(((X875 @ (esk37_1 @ X875))|((X875 @ (esk36_2 @ X875 @ X876))|((esk36_2 @ X875 @ X876)=(X876))))&(~(X875 @ X879)|((esk37_1 @ X875)=(X879))|((X875 @ (esk36_2 @ X875 @ X876))|((esk36_2 @ X875 @ X876)=(X876))))))&((((X880)!=(X881))|(((X882)!=(X883))|(~(in @ X882 @ X880)|(in @ X883 @ X881))))&(((~(in @ X886 @ X884)|(in @ X887 @ X885)|((X886)!=(X887))|((X884)!=(X885)))&(~(in @ X887 @ X885)|(in @ X886 @ X884)|((X886)!=(X887))|((X884)!=(X885))))&((((X888 @ (esk38_2 @ X888 @ X889))|~(X888 @ X889)|(~(X888 @ X891)|(~(X888 @ X892)|((X891)=(X892)))))&(((X889)!=(esk38_2 @ X888 @ X889))|~(X888 @ X889)|(~(X888 @ X891)|(~(X888 @ X892)|((X891)=(X892))))))&(((((((X894 @ (esk42_2 @ X893 @ X894))|((X893 @ (esk41_3 @ X893 @ X894 @ X897))|~(X893 @ X897))|((esk39_2 @ X893 @ X894)=(esk40_2 @ X893 @ X894)))&(~(X894 @ X900)|((esk42_2 @ X893 @ X894)=(X900))|((X893 @ (esk41_3 @ X893 @ X894 @ X897))|~(X893 @ X897))|((esk39_2 @ X893 @ X894)=(esk40_2 @ X893 @ X894))))&(((X894 @ (esk42_2 @ X893 @ X894))|(((X897)!=(esk41_3 @ X893 @ X894 @ X897))|~(X893 @ X897))|((esk39_2 @ X893 @ X894)=(esk40_2 @ X893 @ X894)))&(~(X894 @ X900)|((esk42_2 @ X893 @ X894)=(X900))|(((X897)!=(esk41_3 @ X893 @ X894 @ X897))|~(X893 @ X897))|((esk39_2 @ X893 @ X894)=(esk40_2 @ X893 @ X894)))))&((((X893 @ (esk44_2 @ X893 @ X894))|((X894 @ (esk43_3 @ X893 @ X894 @ X901))|~(X894 @ X901))|((esk39_2 @ X893 @ X894)=(esk40_2 @ X893 @ X894)))&(~(X893 @ X904)|((esk44_2 @ X893 @ X894)=(X904))|((X894 @ (esk43_3 @ X893 @ X894 @ X901))|~(X894 @ X901))|((esk39_2 @ X893 @ X894)=(esk40_2 @ X893 @ X894))))&(((X893 @ (esk44_2 @ X893 @ X894))|(((X901)!=(esk43_3 @ X893 @ X894 @ X901))|~(X894 @ X901))|((esk39_2 @ X893 @ X894)=(esk40_2 @ X893 @ X894)))&(~(X893 @ X904)|((esk44_2 @ X893 @ X894)=(X904))|(((X901)!=(esk43_3 @ X893 @ X894 @ X901))|~(X894 @ X901))|((esk39_2 @ X893 @ X894)=(esk40_2 @ X893 @ X894))))))&((((((X894 @ (esk42_2 @ X893 @ X894))|((X893 @ (esk41_3 @ X893 @ X894 @ X897))|~(X893 @ X897))|(~(X893 @ (esk39_2 @ X893 @ X894))|~(X894 @ (esk40_2 @ X893 @ X894))))&(~(X894 @ X900)|((esk42_2 @ X893 @ X894)=(X900))|((X893 @ (esk41_3 @ X893 @ X894 @ X897))|~(X893 @ X897))|(~(X893 @ (esk39_2 @ X893 @ X894))|~(X894 @ (esk40_2 @ X893 @ X894)))))&(((X894 @ (esk42_2 @ X893 @ X894))|(((X897)!=(esk41_3 @ X893 @ X894 @ X897))|~(X893 @ X897))|(~(X893 @ (esk39_2 @ X893 @ X894))|~(X894 @ (esk40_2 @ X893 @ X894))))&(~(X894 @ X900)|((esk42_2 @ X893 @ X894)=(X900))|(((X897)!=(esk41_3 @ X893 @ X894 @ X897))|~(X893 @ X897))|(~(X893 @ (esk39_2 @ X893 @ X894))|~(X894 @ (esk40_2 @ X893 @ X894))))))&((((X893 @ (esk44_2 @ X893 @ X894))|((X894 @ (esk43_3 @ X893 @ X894 @ X901))|~(X894 @ X901))|(~(X893 @ (esk39_2 @ X893 @ X894))|~(X894 @ (esk40_2 @ X893 @ X894))))&(~(X893 @ X904)|((esk44_2 @ X893 @ X894)=(X904))|((X894 @ (esk43_3 @ X893 @ X894 @ X901))|~(X894 @ X901))|(~(X893 @ (esk39_2 @ X893 @ X894))|~(X894 @ (esk40_2 @ X893 @ X894)))))&(((X893 @ (esk44_2 @ X893 @ X894))|(((X901)!=(esk43_3 @ X893 @ X894 @ X901))|~(X894 @ X901))|(~(X893 @ (esk39_2 @ X893 @ X894))|~(X894 @ (esk40_2 @ X893 @ X894))))&(~(X893 @ X904)|((esk44_2 @ X893 @ X894)=(X904))|(((X901)!=(esk43_3 @ X893 @ X894 @ X901))|~(X894 @ X901))|(~(X893 @ (esk39_2 @ X893 @ X894))|~(X894 @ (esk40_2 @ X893 @ X894)))))))&(((((X894 @ (esk42_2 @ X893 @ X894))|((X893 @ (esk41_3 @ X893 @ X894 @ X897))|~(X893 @ X897))|((X893 @ (esk39_2 @ X893 @ X894))|(X894 @ (esk40_2 @ X893 @ X894))))&(~(X894 @ X900)|((esk42_2 @ X893 @ X894)=(X900))|((X893 @ (esk41_3 @ X893 @ X894 @ X897))|~(X893 @ X897))|((X893 @ (esk39_2 @ X893 @ X894))|(X894 @ (esk40_2 @ X893 @ X894)))))&(((X894 @ (esk42_2 @ X893 @ X894))|(((X897)!=(esk41_3 @ X893 @ X894 @ X897))|~(X893 @ X897))|((X893 @ (esk39_2 @ X893 @ X894))|(X894 @ (esk40_2 @ X893 @ X894))))&(~(X894 @ X900)|((esk42_2 @ X893 @ X894)=(X900))|(((X897)!=(esk41_3 @ X893 @ X894 @ X897))|~(X893 @ X897))|((X893 @ (esk39_2 @ X893 @ X894))|(X894 @ (esk40_2 @ X893 @ X894))))))&((((X893 @ (esk44_2 @ X893 @ X894))|((X894 @ (esk43_3 @ X893 @ X894 @ X901))|~(X894 @ X901))|((X893 @ (esk39_2 @ X893 @ X894))|(X894 @ (esk40_2 @ X893 @ X894))))&(~(X893 @ X904)|((esk44_2 @ X893 @ X894)=(X904))|((X894 @ (esk43_3 @ X893 @ X894 @ X901))|~(X894 @ X901))|((X893 @ (esk39_2 @ X893 @ X894))|(X894 @ (esk40_2 @ X893 @ X894)))))&(((X893 @ (esk44_2 @ X893 @ X894))|(((X901)!=(esk43_3 @ X893 @ X894 @ X901))|~(X894 @ X901))|((X893 @ (esk39_2 @ X893 @ X894))|(X894 @ (esk40_2 @ X893 @ X894))))&(~(X893 @ X904)|((esk44_2 @ X893 @ X894)=(X904))|(((X901)!=(esk43_3 @ X893 @ X894 @ X901))|~(X894 @ X901))|((X893 @ (esk39_2 @ X893 @ X894))|(X894 @ (esk40_2 @ X893 @ X894)))))))))&(((emptyset)=(emptyset))&((((X905)!=(X906))|(((X907)!=(X908))|((setadjoin @ X905 @ X907)=(setadjoin @ X906 @ X908))))&((((X909)!=(X910))|((powerset @ X909)=(powerset @ X910)))&((((X911)!=(X912))|((setunion @ X911)=(setunion @ X912)))&(((omega)=(omega))&((((X913 @ (esk45_2 @ X913 @ X914))|~(X913 @ X914)|(~(X913 @ X916)|(~(X913 @ X917)|((X916)=(X917)))))&(((X914)!=(esk45_2 @ X913 @ X914))|~(X913 @ X914)|(~(X913 @ X916)|(~(X913 @ X917)|((X916)=(X917))))))&((((((X919 @ (esk49_3 @ X918 @ X919 @ X924))|~(X919 @ X924)|((descr @ X918)=(descr @ X919))|((X918 @ (esk48_3 @ X918 @ X919 @ X922))|~(X918 @ X922))|((esk46_2 @ X918 @ X919)=(esk47_2 @ X918 @ X919)))&(((X924)!=(esk49_3 @ X918 @ X919 @ X924))|~(X919 @ X924)|((descr @ X918)=(descr @ X919))|((X918 @ (esk48_3 @ X918 @ X919 @ X922))|~(X918 @ X922))|((esk46_2 @ X918 @ X919)=(esk47_2 @ X918 @ X919))))&(((X919 @ (esk49_3 @ X918 @ X919 @ X924))|~(X919 @ X924)|((descr @ X918)=(descr @ X919))|(((X922)!=(esk48_3 @ X918 @ X919 @ X922))|~(X918 @ X922))|((esk46_2 @ X918 @ X919)=(esk47_2 @ X918 @ X919)))&(((X924)!=(esk49_3 @ X918 @ X919 @ X924))|~(X919 @ X924)|((descr @ X918)=(descr @ X919))|(((X922)!=(esk48_3 @ X918 @ X919 @ X922))|~(X918 @ X922))|((esk46_2 @ X918 @ X919)=(esk47_2 @ X918 @ X919)))))&(((((X919 @ (esk49_3 @ X918 @ X919 @ X924))|~(X919 @ X924)|((descr @ X918)=(descr @ X919))|((X918 @ (esk48_3 @ X918 @ X919 @ X922))|~(X918 @ X922))|(~(X918 @ (esk46_2 @ X918 @ X919))|~(X919 @ (esk47_2 @ X918 @ X919))))&(((X924)!=(esk49_3 @ X918 @ X919 @ X924))|~(X919 @ X924)|((descr @ X918)=(descr @ X919))|((X918 @ (esk48_3 @ X918 @ X919 @ X922))|~(X918 @ X922))|(~(X918 @ (esk46_2 @ X918 @ X919))|~(X919 @ (esk47_2 @ X918 @ X919)))))&(((X919 @ (esk49_3 @ X918 @ X919 @ X924))|~(X919 @ X924)|((descr @ X918)=(descr @ X919))|(((X922)!=(esk48_3 @ X918 @ X919 @ X922))|~(X918 @ X922))|(~(X918 @ (esk46_2 @ X918 @ X919))|~(X919 @ (esk47_2 @ X918 @ X919))))&(((X924)!=(esk49_3 @ X918 @ X919 @ X924))|~(X919 @ X924)|((descr @ X918)=(descr @ X919))|(((X922)!=(esk48_3 @ X918 @ X919 @ X922))|~(X918 @ X922))|(~(X918 @ (esk46_2 @ X918 @ X919))|~(X919 @ (esk47_2 @ X918 @ X919))))))&((((X919 @ (esk49_3 @ X918 @ X919 @ X924))|~(X919 @ X924)|((descr @ X918)=(descr @ X919))|((X918 @ (esk48_3 @ X918 @ X919 @ X922))|~(X918 @ X922))|((X918 @ (esk46_2 @ X918 @ X919))|(X919 @ (esk47_2 @ X918 @ X919))))&(((X924)!=(esk49_3 @ X918 @ X919 @ X924))|~(X919 @ X924)|((descr @ X918)=(descr @ X919))|((X918 @ (esk48_3 @ X918 @ X919 @ X922))|~(X918 @ X922))|((X918 @ (esk46_2 @ X918 @ X919))|(X919 @ (esk47_2 @ X918 @ X919)))))&(((X919 @ (esk49_3 @ X918 @ X919 @ X924))|~(X919 @ X924)|((descr @ X918)=(descr @ X919))|(((X922)!=(esk48_3 @ X918 @ X919 @ X922))|~(X918 @ X922))|((X918 @ (esk46_2 @ X918 @ X919))|(X919 @ (esk47_2 @ X918 @ X919))))&(((X924)!=(esk49_3 @ X918 @ X919 @ X924))|~(X919 @ X924)|((descr @ X918)=(descr @ X919))|(((X922)!=(esk48_3 @ X918 @ X919 @ X922))|~(X918 @ X922))|((X918 @ (esk46_2 @ X918 @ X919))|(X919 @ (esk47_2 @ X918 @ X919))))))))&((((in @ (esk50_4 @ X926 @ X927 @ X928 @ X929) @ X926)|((dsetconstr @ X926 @ X928)=(dsetconstr @ X927 @ X929))|((X926)!=(X927)))&(((in @ (esk51_4 @ X926 @ X927 @ X928 @ X929) @ X927)|((dsetconstr @ X926 @ X928)=(dsetconstr @ X927 @ X929))|((X926)!=(X927)))&((((esk50_4 @ X926 @ X927 @ X928 @ X929)=(esk51_4 @ X926 @ X927 @ X928 @ X929))|((dsetconstr @ X926 @ X928)=(dsetconstr @ X927 @ X929))|((X926)!=(X927)))&((~(X928 @ (esk50_4 @ X926 @ X927 @ X928 @ X929))|~(X929 @ (esk51_4 @ X926 @ X927 @ X928 @ X929))|((dsetconstr @ X926 @ X928)=(dsetconstr @ X927 @ X929))|((X926)!=(X927)))&((X928 @ (esk50_4 @ X926 @ X927 @ X928 @ X929))|(X929 @ (esk51_4 @ X926 @ X927 @ X928 @ X929))|((dsetconstr @ X926 @ X928)=(dsetconstr @ X927 @ X929))|((X926)!=(X927)))))))&((((in @ (esk52_2 @ X932 @ X933) @ X932)|(subset @ X932 @ X933))&(~(in @ (esk52_2 @ X932 @ X933) @ X933)|(subset @ X932 @ X933)))&((((X935)!=(X936))|(subset @ X936 @ X935))&((((X937)!=(X938))|(subset @ X937 @ X938))&((((in @ (esk53_2 @ X939 @ X940) @ X939)|(subset @ X939 @ X940))&(~(in @ (esk53_2 @ X939 @ X940) @ X940)|(subset @ X939 @ X940)))&((subset @ emptyset @ X942)&((~(subset @ X943 @ X944)|(~(in @ X945 @ X943)|(in @ X945 @ X944)))&((~(subset @ X946 @ X947)|((in @ X948 @ X947)|~(in @ X948 @ X946)))&((~(in @ X951 @ X949)|((in @ X951 @ X950)|~(subset @ X949 @ X950)))&(((subset @ X952 @ X953)|((X952)!=(X953)))&((~(in @ X956 @ X954)|((in @ X956 @ X955)|((X954)!=(X955))))&((subset @ X957 @ X957)&((~(subset @ X958 @ X959)|(~(subset @ X959 @ X960)|(subset @ X958 @ X960)))&((subset @ X962 @ (setadjoin @ X961 @ X962))&((~(subset @ X963 @ X965)|(subset @ X963 @ (setadjoin @ X964 @ X965)))&((~(subset @ X966 @ X967)|(in @ X966 @ (powerset @ X967)))&((~(subset @ X968 @ X969)|(~(subset @ X969 @ X968)|((X968)=(X969))))&((~(subset @ X970 @ emptyset)|((X970)=(emptyset)))&((~(subset @ X972 @ X971)|(in @ X972 @ (powerset @ X971)))&((~(in @ X974 @ (powerset @ X973))|(subset @ X974 @ X973))&((in @ X975 @ (powerset @ X975))&((~(subset @ X976 @ X977)|(subset @ (powerset @ X976) @ (powerset @ X977)))&((in @ (dsetconstr @ X978 @ X979) @ (powerset @ X978))&((subset @ (dsetconstr @ X980 @ X981) @ X980)&((~(in @ X984 @ X982)|(in @ X984 @ (binunion @ X982 @ X983)))&((in @ X986 @ (setadjoin @ X985 @ (setadjoin @ X986 @ emptyset)))&((~(in @ X989 @ X988)|(in @ X989 @ (binunion @ X987 @ X988)))&(((((in @ X992 @ X991)|(X993)|(in @ X992 @ X990)|~(in @ X992 @ (binunion @ X990 @ X991)))&(~(X993)|(X993)|(in @ X992 @ X990)|~(in @ X992 @ (binunion @ X990 @ X991))))&(((in @ X992 @ X991)|(X993)|~(X993)|~(in @ X992 @ (binunion @ X990 @ X991)))&(~(X993)|(X993)|~(X993)|~(in @ X992 @ (binunion @ X990 @ X991)))))&((~(in @ X996 @ (binunion @ X994 @ X995))|((in @ X996 @ X994)|(in @ X996 @ X995)))&((subset @ X997 @ (binunion @ X997 @ X998))&((subset @ X1000 @ (binunion @ X999 @ X1000))&((~(in @ X1003 @ X1001)|(~(in @ X1003 @ X1002)|(in @ X1003 @ (binintersect @ X1001 @ X1002))))&((~(subset @ X1006 @ X1004)|(~(subset @ X1006 @ X1005)|(subset @ X1006 @ (binintersect @ X1004 @ X1005))))&((~(in @ X1009 @ (binintersect @ X1007 @ X1008))|(in @ X1009 @ X1007))&((subset @ (binintersect @ X1010 @ X1011) @ X1010)&((~(subset @ X1012 @ X1013)|((binintersect @ X1012 @ X1013)=(X1012)))&((((binintersect @ X1014 @ X1015)!=(X1015))|(subset @ X1015 @ X1014))&((~(in @ X1018 @ (binintersect @ X1016 @ X1017))|(in @ X1018 @ X1017))&((((in @ (esk54_2 @ X1019 @ X1020) @ X1019)|((binintersect @ X1019 @ X1020)=(emptyset)))&((in @ (esk54_2 @ X1019 @ X1020) @ X1020)|((binintersect @ X1019 @ X1020)=(emptyset))))&((subset @ (binintersect @ X1022 @ X1023) @ X1023)&((~(subset @ X1025 @ X1024)|((binintersect @ X1024 @ X1025)=(X1025)))&((((binintersect @ X1026 @ X1027)!=(X1026))|(subset @ X1026 @ X1027))&(((binintersect @ X1028 @ (binunion @ X1029 @ X1030))=(binunion @ (binintersect @ X1028 @ X1029) @ (binintersect @ X1028 @ X1030)))&((in @ esk57_0 @ esk55_0)&(~(in @ esk57_0 @ esk56_0)&~(in @ esk57_0 @ (dsetconstr @ esk55_0 @ (^[Z0:$i]:(~((in @ Z0 @ esk56_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_163])])])])])])])).
% 0.81/0.40 thf(c_0_165, negated_conjecture, ~((in @ esk57_0 @ (dsetconstr @ esk55_0 @ (^[Z0:$i]:(~((in @ Z0 @ esk56_0))))))), inference(split_conjunct,[status(thm)],[c_0_164])).
% 0.81/0.40 thf(c_0_166, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ X2 @ (dsetconstr @ X3 @ X1))|~((X1 @ X2))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_164])).
% 0.81/0.40 thf(c_0_167, negated_conjecture, (in @ esk57_0 @ esk55_0), inference(split_conjunct,[status(thm)],[c_0_164])).
% 0.81/0.40 thf(c_0_168, negated_conjecture, ~((in @ esk57_0 @ esk56_0)), inference(split_conjunct,[status(thm)],[c_0_164])).
% 0.81/0.40 thf(c_0_169, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_165, c_0_166])]), c_0_167])]), c_0_168]), ['proof']).
% 0.81/0.40 % SZS output end CNFRefutation
% 0.81/0.40 % Parsed axioms : 257
% 0.81/0.40 % Removed by relevancy pruning/SinE : 137
% 0.81/0.40 % Initial clauses : 234
% 0.81/0.40 % Removed in clause preprocessing : 17
% 0.81/0.40 % Initial clauses in saturation : 217
% 0.81/0.40 % Processed clauses : 484
% 0.81/0.40 % ...of these trivial : 7
% 0.81/0.40 % ...subsumed : 219
% 0.81/0.40 % ...remaining for further processing : 258
% 0.81/0.40 % Other redundant clauses eliminated : 20
% 0.81/0.40 % Clauses deleted for lack of memory : 0
% 0.81/0.40 % Backward-subsumed : 0
% 0.81/0.40 % Backward-rewritten : 4
% 0.81/0.40 % Generated clauses : 3988
% 0.81/0.40 % ...of the previous two non-redundant : 2965
% 0.81/0.40 % ...aggressively subsumed : 0
% 0.81/0.40 % Contextual simplify-reflections : 0
% 0.81/0.40 % Paramodulations : 3966
% 0.81/0.40 % Factorizations : 2
% 0.81/0.40 % NegExts : 0
% 0.81/0.40 % Equation resolutions : 20
% 0.81/0.40 % Disequality decompositions : 0
% 0.81/0.40 % Total rewrite steps : 1982
% 0.81/0.40 % ...of those cached : 1884
% 0.81/0.40 % Propositional unsat checks : 0
% 0.81/0.40 % Propositional check models : 0
% 0.81/0.40 % Propositional check unsatisfiable : 0
% 0.81/0.40 % Propositional clauses : 0
% 0.81/0.40 % Propositional clauses after purity: 0
% 0.81/0.40 % Propositional unsat core size : 0
% 0.81/0.40 % Propositional preprocessing time : 0.000
% 0.81/0.40 % Propositional encoding time : 0.000
% 0.81/0.40 % Propositional solver time : 0.000
% 0.81/0.40 % Success case prop preproc time : 0.000
% 0.81/0.40 % Success case prop encoding time : 0.000
% 0.81/0.40 % Success case prop solver time : 0.000
% 0.81/0.40 % Current number of processed clauses : 247
% 0.81/0.40 % Positive orientable unit clauses : 89
% 0.81/0.40 % Positive unorientable unit clauses: 0
% 0.81/0.40 % Negative unit clauses : 3
% 0.81/0.40 % Non-unit-clauses : 155
% 0.81/0.40 % Current number of unprocessed clauses: 2677
% 0.81/0.40 % ...number of literals in the above : 7570
% 0.81/0.40 % Current number of archived formulas : 0
% 0.81/0.40 % Current number of archived clauses : 4
% 0.81/0.40 % Clause-clause subsumption calls (NU) : 2679
% 0.81/0.40 % Rec. Clause-clause subsumption calls : 2311
% 0.81/0.40 % Non-unit clause-clause subsumptions : 134
% 0.81/0.40 % Unit Clause-clause subsumption calls : 48
% 0.81/0.40 % Rewrite failures with RHS unbound : 0
% 0.81/0.40 % BW rewrite match attempts : 269
% 0.81/0.40 % BW rewrite match successes : 3
% 0.81/0.40 % Condensation attempts : 0
% 0.81/0.40 % Condensation successes : 0
% 0.81/0.40 % Termbank termtop insertions : 78160
% 0.81/0.40 % Search garbage collected termcells : 11806
% 0.81/0.40
% 0.81/0.40 % -------------------------------------------------
% 0.81/0.40 % User time : 0.097 s
% 0.81/0.40 % System time : 0.013 s
% 0.81/0.40 % Total time : 0.110 s
% 0.81/0.40 % Maximum resident set size: 6440 pages
% 0.81/0.40
% 0.81/0.40 % -------------------------------------------------
% 0.81/0.40 % User time : 0.161 s
% 0.81/0.40 % System time : 0.053 s
% 0.81/0.40 % Total time : 0.214 s
% 0.81/0.40 % Maximum resident set size: 5120 pages
% 0.81/0.40 % E exiting
%------------------------------------------------------------------------------