%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU636^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:27:01 AM UTC 2026
% Result : Theorem 0.20s 0.31s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU636^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n004.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 14:00:37 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p
% 0.20/0.31 % Version: 3.5.1-ho
% 0.20/0.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.20/0.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.31 % Starting ehoh_best5 with 300s (1) cores
% 0.20/0.31 % Starting almost_fo_3_lam with 300s (1) cores
% 0.20/0.31 % Starting new_bool_5 with 300s (1) cores
% 0.20/0.31 % Starting pre_casc_3 with 300s (1) cores
% 0.20/0.31 % Starting ho_unfolding_8 with 300s (1) cores
% 0.20/0.31 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.20/0.31 % Starting new_bool_3 with 300s (1) cores
% 0.20/0.31 % Starting new_ho_5 with 300s (1) cores
% 0.20/0.31 % new_ho_10_cnf2 with pid 1331670 completed with status 0
% 0.20/0.31 % Result found by new_ho_10_cnf2
% 0.20/0.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.20/0.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.31 % Starting ehoh_best5 with 300s (1) cores
% 0.20/0.31 % Starting almost_fo_3_lam with 300s (1) cores
% 0.20/0.31 % Starting new_bool_5 with 300s (1) cores
% 0.20/0.31 % Starting pre_casc_3 with 300s (1) cores
% 0.20/0.31 % Starting ho_unfolding_8 with 300s (1) cores
% 0.20/0.31 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.20/0.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.31 % No SInE strategy applied
% 0.20/0.31 % Search class: HGHSM-FSLS31-MHFMMSBN
% 0.20/0.31 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.31 % Starting SubtermCWHack with 31s (1) cores
% 0.20/0.31 % SubtermCWHack with pid 1331675 completed with status 0
% 0.20/0.31 % Result found by SubtermCWHack
% 0.20/0.31 % Preprocessing class: HSLMSLSSLLLCHFA.
% 0.20/0.31 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.31 % Starting ehoh_best5 with 300s (1) cores
% 0.20/0.31 % Starting almost_fo_3_lam with 300s (1) cores
% 0.20/0.31 % Starting new_bool_5 with 300s (1) cores
% 0.20/0.31 % Starting pre_casc_3 with 300s (1) cores
% 0.20/0.31 % Starting ho_unfolding_8 with 300s (1) cores
% 0.20/0.31 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.20/0.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.31 % No SInE strategy applied
% 0.20/0.31 % Search class: HGHSM-FSLS31-MHFMMSBN
% 0.20/0.31 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.31 % Starting SubtermCWHack with 31s (1) cores
% 0.20/0.31 % Preprocessing time : 0.003 s
% 0.20/0.31
% 0.20/0.31 % Proof found!
% 0.20/0.31 % SZS status Theorem
% 0.20/0.31 % SZS output start CNFRefutation
% 0.20/0.31 thf(decl_23, type, in: $i > $i > $o).
% 0.20/0.31 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.20/0.31 thf(decl_25, type, setextAx: $o).
% 0.20/0.31 thf(decl_26, type, emptyset: $i).
% 0.20/0.31 thf(decl_27, type, emptysetAx: $o).
% 0.20/0.31 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.20/0.31 thf(decl_29, type, setadjoinAx: $o).
% 0.20/0.31 thf(decl_30, type, powerset: $i > $i).
% 0.20/0.31 thf(decl_31, type, powersetAx: $o).
% 0.20/0.31 thf(decl_32, type, setunion: $i > $i).
% 0.20/0.31 thf(decl_33, type, setunionAx: $o).
% 0.20/0.31 thf(decl_34, type, omega: $i).
% 0.20/0.31 thf(decl_35, type, omega0Ax: $o).
% 0.20/0.31 thf(decl_36, type, omegaSAx: $o).
% 0.20/0.31 thf(decl_37, type, omegaIndAx: $o).
% 0.20/0.31 thf(decl_38, type, replAx: $o).
% 0.20/0.31 thf(decl_39, type, foundationAx: $o).
% 0.20/0.31 thf(decl_40, type, wellorderingAx: $o).
% 0.20/0.31 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.20/0.31 thf(decl_42, type, descrp: $o).
% 0.20/0.31 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.20/0.31 thf(decl_44, type, dsetconstrI: $o).
% 0.20/0.31 thf(decl_45, type, dsetconstrEL: $o).
% 0.20/0.31 thf(decl_46, type, dsetconstrER: $o).
% 0.20/0.31 thf(decl_47, type, exuE1: $o).
% 0.20/0.31 thf(decl_48, type, prop2set: $o > $i).
% 0.20/0.31 thf(decl_49, type, prop2setE: $o).
% 0.20/0.31 thf(decl_50, type, emptysetE: $o).
% 0.20/0.31 thf(decl_51, type, emptysetimpfalse: $o).
% 0.20/0.31 thf(decl_52, type, notinemptyset: $o).
% 0.20/0.31 thf(decl_53, type, exuE3e: $o).
% 0.20/0.31 thf(decl_54, type, setext: $o).
% 0.20/0.31 thf(decl_55, type, emptyI: $o).
% 0.20/0.31 thf(decl_56, type, noeltsimpempty: $o).
% 0.20/0.31 thf(decl_57, type, setbeta: $o).
% 0.20/0.31 thf(decl_58, type, nonempty: $i > $o).
% 0.20/0.31 thf(decl_59, type, nonemptyE1: $o).
% 0.20/0.31 thf(decl_60, type, nonemptyI: $o).
% 0.20/0.31 thf(decl_61, type, nonemptyI1: $o).
% 0.20/0.31 thf(decl_62, type, setadjoinIL: $o).
% 0.20/0.31 thf(decl_63, type, emptyinunitempty: $o).
% 0.20/0.31 thf(decl_64, type, setadjoinIR: $o).
% 0.20/0.31 thf(decl_65, type, setadjoinE: $o).
% 0.20/0.31 thf(decl_66, type, setadjoinOr: $o).
% 0.20/0.31 thf(decl_67, type, setoftrueEq: $o).
% 0.20/0.31 thf(decl_68, type, powersetI: $o).
% 0.20/0.31 thf(decl_69, type, emptyinPowerset: $o).
% 0.20/0.31 thf(decl_70, type, emptyInPowerset: $o).
% 0.20/0.31 thf(decl_71, type, powersetE: $o).
% 0.20/0.31 thf(decl_72, type, setunionI: $o).
% 0.20/0.31 thf(decl_73, type, setunionE: $o).
% 0.20/0.31 thf(decl_74, type, subPowSU: $o).
% 0.20/0.31 thf(decl_75, type, exuE2: $o).
% 0.20/0.31 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.20/0.31 thf(decl_77, type, uniqinunit: $o).
% 0.20/0.31 thf(decl_78, type, notinsingleton: $o).
% 0.20/0.31 thf(decl_79, type, eqinunit: $o).
% 0.20/0.31 thf(decl_80, type, singletonsswitch: $o).
% 0.20/0.31 thf(decl_81, type, upairsetE: $o).
% 0.20/0.31 thf(decl_82, type, upairsetIL: $o).
% 0.20/0.31 thf(decl_83, type, upairsetIR: $o).
% 0.20/0.31 thf(decl_84, type, emptyE1: $o).
% 0.20/0.31 thf(decl_85, type, vacuousDall: $o).
% 0.20/0.31 thf(decl_86, type, quantDeMorgan1: $o).
% 0.20/0.31 thf(decl_87, type, quantDeMorgan2: $o).
% 0.20/0.31 thf(decl_88, type, quantDeMorgan3: $o).
% 0.20/0.31 thf(decl_89, type, quantDeMorgan4: $o).
% 0.20/0.31 thf(decl_90, type, prop2setI: $o).
% 0.20/0.31 thf(decl_91, type, set2prop: $i > $o).
% 0.20/0.31 thf(decl_92, type, prop2set2propI: $o).
% 0.20/0.31 thf(decl_93, type, notdexE: $o).
% 0.20/0.31 thf(decl_94, type, notdallE: $o).
% 0.20/0.31 thf(decl_95, type, exuI1: $o).
% 0.20/0.31 thf(decl_96, type, exuI3: $o).
% 0.20/0.31 thf(decl_97, type, exuI2: $o).
% 0.20/0.31 thf(decl_98, type, inCongP: $o).
% 0.20/0.31 thf(decl_99, type, in__Cong: $o).
% 0.20/0.31 thf(decl_100, type, exuE3u: $o).
% 0.20/0.31 thf(decl_101, type, exu__Cong: $o).
% 0.20/0.31 thf(decl_102, type, emptyset__Cong: $o).
% 0.20/0.31 thf(decl_103, type, setadjoin__Cong: $o).
% 0.20/0.31 thf(decl_104, type, powerset__Cong: $o).
% 0.20/0.31 thf(decl_105, type, setunion__Cong: $o).
% 0.20/0.31 thf(decl_106, type, omega__Cong: $o).
% 0.20/0.31 thf(decl_107, type, exuEu: $o).
% 0.20/0.31 thf(decl_108, type, descr__Cong: $o).
% 0.20/0.31 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.20/0.31 thf(decl_110, type, subset: $i > $i > $o).
% 0.20/0.31 thf(decl_113, type, subsetI1: $o).
% 0.20/0.31 thf(decl_114, type, eqimpsubset2: $o).
% 0.20/0.31 thf(decl_115, type, eqimpsubset1: $o).
% 0.20/0.31 thf(decl_116, type, subsetI2: $o).
% 0.20/0.31 thf(decl_117, type, emptysetsubset: $o).
% 0.20/0.31 thf(decl_118, type, subsetE: $o).
% 0.20/0.31 thf(decl_119, type, subsetE2: $o).
% 0.20/0.31 thf(decl_120, type, notsubsetI: $o).
% 0.20/0.31 thf(decl_121, type, notequalI1: $o).
% 0.20/0.31 thf(decl_122, type, notequalI2: $o).
% 0.20/0.31 thf(decl_123, type, subsetRefl: $o).
% 0.20/0.31 thf(decl_124, type, subsetTrans: $o).
% 0.20/0.31 thf(decl_125, type, setadjoinSub: $o).
% 0.20/0.31 thf(decl_126, type, setadjoinSub2: $o).
% 0.20/0.31 thf(decl_127, type, subset2powerset: $o).
% 0.20/0.31 thf(decl_128, type, setextsub: $o).
% 0.20/0.31 thf(decl_129, type, subsetemptysetimpeq: $o).
% 0.20/0.31 thf(decl_130, type, powersetI1: $o).
% 0.20/0.31 thf(decl_131, type, powersetE1: $o).
% 0.20/0.31 thf(decl_132, type, inPowerset: $o).
% 0.20/0.31 thf(decl_133, type, powersetsubset: $o).
% 0.20/0.31 thf(decl_134, type, sepInPowerset: $o).
% 0.20/0.31 thf(decl_135, type, sepSubset: $o).
% 0.20/0.31 thf(decl_136, type, binunion: $i > $i > $i).
% 0.20/0.31 thf(decl_137, type, binunionIL: $o).
% 0.20/0.31 thf(decl_138, type, upairset2IR: $o).
% 0.20/0.31 thf(decl_139, type, binunionIR: $o).
% 0.20/0.31 thf(decl_140, type, binunionEcases: $o).
% 0.20/0.31 thf(decl_141, type, binunionE: $o).
% 0.20/0.31 thf(decl_142, type, binunionLsub: $o).
% 0.20/0.31 thf(decl_143, type, binunionRsub: $o).
% 0.20/0.31 thf(decl_144, type, binintersect: $i > $i > $i).
% 0.20/0.31 thf(decl_145, type, binintersectI: $o).
% 0.20/0.31 thf(decl_146, type, binintersectSubset5: $o).
% 0.20/0.31 thf(decl_147, type, binintersectEL: $o).
% 0.20/0.31 thf(decl_148, type, binintersectLsub: $o).
% 0.20/0.31 thf(decl_149, type, binintersectSubset2: $o).
% 0.20/0.31 thf(decl_150, type, binintersectSubset3: $o).
% 0.20/0.31 thf(decl_151, type, binintersectER: $o).
% 0.20/0.31 thf(decl_152, type, disjointsetsI1: $o).
% 0.20/0.31 thf(decl_153, type, binintersectRsub: $o).
% 0.20/0.31 thf(decl_154, type, binintersectSubset4: $o).
% 0.20/0.31 thf(decl_155, type, binintersectSubset1: $o).
% 0.20/0.31 thf(decl_156, type, bs114d: $o).
% 0.20/0.31 thf(decl_158, type, setminus: $i > $i > $i).
% 0.20/0.31 thf(decl_159, type, setminusI: $o).
% 0.20/0.31 thf(decl_160, type, setminusEL: $o).
% 0.20/0.31 thf(decl_161, type, setminusER: $o).
% 0.20/0.31 thf(decl_162, type, setminusSubset2: $o).
% 0.20/0.31 thf(decl_163, type, setminusERneg: $o).
% 0.20/0.31 thf(decl_164, type, setminusELneg: $o).
% 0.20/0.31 thf(decl_165, type, setminusILneg: $o).
% 0.20/0.31 thf(decl_166, type, setminusIRneg: $o).
% 0.20/0.31 thf(decl_167, type, setminusLsub: $o).
% 0.20/0.31 thf(decl_168, type, setminusSubset1: $o).
% 0.20/0.31 thf(decl_169, type, symdiff: $i > $i > $i).
% 0.20/0.31 thf(decl_170, type, symdiffE: $o).
% 0.20/0.31 thf(decl_171, type, symdiffI1: $o).
% 0.20/0.31 thf(decl_172, type, symdiffI2: $o).
% 0.20/0.31 thf(decl_173, type, symdiffIneg1: $o).
% 0.20/0.31 thf(decl_174, type, symdiffIneg2: $o).
% 0.20/0.31 thf(decl_175, type, iskpair: $i > $o).
% 0.20/0.31 thf(decl_176, type, secondinupair: $o).
% 0.20/0.31 thf(decl_177, type, setukpairIL: $o).
% 0.20/0.31 thf(decl_178, type, setukpairIR: $o).
% 0.20/0.31 thf(decl_179, type, kpairiskpair: $o).
% 0.20/0.31 thf(decl_180, type, kpair: $i > $i > $i).
% 0.20/0.31 thf(decl_181, type, kpairp: $o).
% 0.20/0.31 thf(decl_182, type, cartprod: $i > $i > $i).
% 0.20/0.31 thf(decl_183, type, singletonsubset: $o).
% 0.20/0.31 thf(decl_184, type, singletoninpowerset: $o).
% 0.20/0.31 thf(decl_185, type, singletoninpowunion: $o).
% 0.20/0.31 thf(decl_186, type, upairset2E: $o).
% 0.20/0.31 thf(decl_187, type, upairsubunion: $o).
% 0.20/0.31 thf(decl_188, type, upairinpowunion: $o).
% 0.20/0.31 thf(decl_189, type, ubforcartprodlem1: $o).
% 0.20/0.31 thf(decl_190, type, ubforcartprodlem2: $o).
% 0.20/0.31 thf(decl_191, type, ubforcartprodlem3: $o).
% 0.20/0.31 thf(decl_192, type, cartprodpairin: $o).
% 0.20/0.31 thf(decl_193, type, cartprodmempair1: $o).
% 0.20/0.31 thf(decl_194, type, cartprodmempair: $o).
% 0.20/0.31 thf(decl_195, type, setunionE2: $o).
% 0.20/0.31 thf(decl_196, type, setunionsingleton1: $o).
% 0.20/0.31 thf(decl_197, type, setunionsingleton2: $o).
% 0.20/0.31 thf(decl_198, type, epred1_0: $o).
% 0.20/0.31 thf(decl_199, type, esk1_2: $i > $i > $i).
% 0.20/0.31 thf(decl_200, type, esk2_2: $i > $i > $i).
% 0.20/0.31 thf(decl_201, type, esk3_2: $i > $i > $i).
% 0.20/0.31 thf(decl_202, type, esk4_1: $i > $i).
% 0.20/0.31 thf(decl_203, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.20/0.31 thf(decl_204, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.20/0.31 thf(decl_205, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.20/0.31 thf(decl_206, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.20/0.31 thf(decl_207, type, esk9_1: $i > $i).
% 0.20/0.31 thf(decl_208, type, esk10_2: ($i > $o) > $i > $i).
% 0.20/0.31 thf(decl_209, type, esk11_2: ($i > $o) > $i > $i).
% 0.20/0.31 thf(decl_210, type, esk12_1: ($i > $o) > $i).
% 0.20/0.31 thf(decl_211, type, esk13_2: ($i > $o) > $i > $i).
% 0.20/0.31 thf(decl_212, type, esk14_1: ($i > $o) > $i).
% 0.20/0.31 thf(decl_213, type, esk15_2: $i > $i > $i).
% 0.20/0.31 thf(decl_214, type, esk16_2: $i > $i > $i).
% 0.20/0.31 thf(decl_215, type, esk17_1: $i > $i).
% 0.20/0.31 thf(decl_216, type, esk18_1: $i > $i).
% 0.20/0.31 thf(decl_217, type, esk19_1: $i > $i).
% 0.20/0.31 thf(decl_218, type, esk20_2: $i > $i > $i).
% 0.20/0.31 thf(decl_219, type, esk21_3: $i > $i > $o > $i).
% 0.20/0.31 thf(decl_220, type, esk22_2: ($i > $o) > $i > $i).
% 0.20/0.31 thf(decl_221, type, esk23_1: ($i > $o) > $i).
% 0.20/0.31 thf(decl_222, type, esk24_1: $i > $i).
% 0.20/0.31 thf(decl_223, type, esk25_2: $i > ($i > $o) > $i).
% 0.20/0.31 thf(decl_224, type, esk26_2: $i > ($i > $o) > $i).
% 0.20/0.31 thf(decl_225, type, esk27_2: $i > ($i > $o) > $i).
% 0.20/0.31 thf(decl_226, type, esk28_2: $i > ($i > $o) > $i).
% 0.20/0.31 thf(decl_227, type, esk29_2: $i > ($i > $o) > $i).
% 0.20/0.31 thf(decl_228, type, esk30_2: $i > ($i > $o) > $i).
% 0.20/0.31 thf(decl_229, type, esk31_2: ($i > $o) > $i > $i).
% 0.20/0.31 thf(decl_230, type, esk32_1: ($i > $o) > $i).
% 0.20/0.31 thf(decl_231, type, esk33_1: ($i > $o) > $i).
% 0.20/0.31 thf(decl_232, type, esk34_1: ($i > $o) > $i).
% 0.20/0.31 thf(decl_233, type, esk35_1: ($i > $o) > $i).
% 0.20/0.31 thf(decl_234, type, esk36_2: ($i > $o) > $i > $i).
% 0.20/0.31 thf(decl_235, type, esk37_1: ($i > $o) > $i).
% 0.20/0.31 thf(decl_236, type, esk38_2: ($i > $o) > $i > $i).
% 0.20/0.31 thf(decl_237, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.20/0.31 thf(decl_238, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.20/0.31 thf(decl_239, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.20/0.31 thf(decl_240, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.20/0.31 thf(decl_241, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.20/0.31 thf(decl_242, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.20/0.31 thf(decl_243, type, esk45_2: ($i > $o) > $i > $i).
% 0.20/0.31 thf(decl_244, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.20/0.31 thf(decl_245, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.20/0.31 thf(decl_246, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.20/0.31 thf(decl_247, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.20/0.31 thf(decl_248, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.20/0.31 thf(decl_249, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.20/0.31 thf(decl_250, type, esk52_2: $i > $i > $i).
% 0.20/0.31 thf(decl_251, type, esk53_2: $i > $i > $i).
% 0.20/0.31 thf(decl_252, type, esk54_2: $i > $i > $i).
% 0.20/0.31 thf(decl_253, type, esk55_2: $i > $i > $i).
% 0.20/0.31 thf(decl_254, type, esk56_2: $i > $i > $i).
% 0.20/0.31 thf(decl_255, type, esk57_2: $i > $i > $i).
% 0.20/0.31 thf(decl_256, type, esk58_2: $i > $i > $i).
% 0.20/0.31 thf(decl_257, type, esk59_3: $i > $i > $i > $i).
% 0.20/0.31 thf(decl_258, type, esk60_3: $i > $i > $i > $i).
% 0.20/0.31 thf(decl_259, type, esk61_3: $i > $i > $i > $i).
% 0.20/0.31 thf(decl_260, type, esk62_3: $i > $i > $i > $i).
% 0.20/0.31 thf(decl_261, type, esk63_2: $i > $i > $i).
% 0.20/0.31 thf(decl_262, type, esk64_0: $i).
% 0.20/0.31 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', replAx)).
% 0.20/0.31 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', exu)).
% 0.20/0.31 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', descrp)).
% 0.20/0.31 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', exuE1)).
% 0.20/0.31 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', exuE3e)).
% 0.20/0.31 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', nonempty)).
% 0.20/0.31 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', nonemptyI)).
% 0.20/0.31 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', exuE2)).
% 0.20/0.31 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', exuI1)).
% 0.20/0.31 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', exuI3)).
% 0.20/0.31 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', exuI2)).
% 0.20/0.31 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', exuE3u)).
% 0.20/0.31 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', exu__Cong)).
% 0.20/0.31 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', exuEu)).
% 0.20/0.31 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', descr__Cong)).
% 0.20/0.31 thf(iskpair, axiom, ((iskpair)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ (setunion @ X4)))&(?[X3:$i]:((((in @ X3 @ (setunion @ X4)))&(((X4)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', iskpair)).
% 0.20/0.31 thf(setunionsingleton, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setunionsingleton)).
% 0.20/0.31 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', dsetconstrI)).
% 0.20/0.31 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', dsetconstrEL)).
% 0.20/0.31 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', dsetconstrER)).
% 0.20/0.31 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setbeta)).
% 0.20/0.31 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', nonemptyE1)).
% 0.20/0.31 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', nonemptyI1)).
% 0.20/0.31 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setoftrueEq)).
% 0.20/0.31 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', nonemptyImpWitness)).
% 0.20/0.31 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', emptyE1)).
% 0.20/0.31 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', dsetconstr__Cong)).
% 0.20/0.31 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', sepInPowerset)).
% 0.20/0.31 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', sepSubset)).
% 0.20/0.31 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', kpairiskpair)).
% 0.20/0.31 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', kpairp)).
% 0.20/0.31 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', cartprodmempair)).
% 0.20/0.31 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setextAx)).
% 0.20/0.31 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', emptysetAx)).
% 0.20/0.31 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setadjoinAx)).
% 0.20/0.31 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', powersetAx)).
% 0.20/0.31 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setunionAx)).
% 0.20/0.31 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', omega0Ax)).
% 0.20/0.31 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', omegaSAx)).
% 0.20/0.31 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', omegaIndAx)).
% 0.20/0.31 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', foundationAx)).
% 0.20/0.31 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', wellorderingAx)).
% 0.20/0.31 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', prop2setE)).
% 0.20/0.31 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', emptysetE)).
% 0.20/0.31 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', emptysetimpfalse)).
% 0.20/0.31 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', notinemptyset)).
% 0.20/0.31 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setext)).
% 0.20/0.31 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', emptyI)).
% 0.20/0.31 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', noeltsimpempty)).
% 0.20/0.31 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setadjoinIL)).
% 0.20/0.31 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', emptyinunitempty)).
% 0.20/0.31 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setadjoinIR)).
% 0.20/0.31 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setadjoinE)).
% 0.20/0.31 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setadjoinOr)).
% 0.20/0.31 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', powersetI)).
% 0.20/0.31 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', emptyinPowerset)).
% 0.20/0.31 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', emptyInPowerset)).
% 0.20/0.31 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', powersetE)).
% 0.20/0.31 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setunionI)).
% 0.20/0.31 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setunionE)).
% 0.20/0.31 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', subPowSU)).
% 0.20/0.31 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', uniqinunit)).
% 0.20/0.31 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', notinsingleton)).
% 0.20/0.31 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', eqinunit)).
% 0.20/0.31 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', singletonsswitch)).
% 0.20/0.31 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', upairsetE)).
% 0.20/0.31 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', upairsetIL)).
% 0.20/0.31 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', upairsetIR)).
% 0.20/0.31 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', vacuousDall)).
% 0.20/0.31 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', quantDeMorgan1)).
% 0.20/0.31 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', quantDeMorgan2)).
% 0.20/0.31 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', quantDeMorgan3)).
% 0.20/0.31 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', quantDeMorgan4)).
% 0.20/0.31 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', prop2setI)).
% 0.20/0.31 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', prop2set2propI)).
% 0.20/0.31 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', notdexE)).
% 0.20/0.31 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', notdallE)).
% 0.20/0.31 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', inCongP)).
% 0.20/0.31 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', in__Cong)).
% 0.20/0.31 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', emptyset__Cong)).
% 0.20/0.31 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setadjoin__Cong)).
% 0.20/0.31 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', powerset__Cong)).
% 0.20/0.31 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setunion__Cong)).
% 0.20/0.31 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', omega__Cong)).
% 0.20/0.31 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', subsetI1)).
% 0.20/0.31 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', eqimpsubset2)).
% 0.20/0.31 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', eqimpsubset1)).
% 0.20/0.31 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', subsetI2)).
% 0.20/0.31 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', emptysetsubset)).
% 0.20/0.31 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', subsetE)).
% 0.20/0.31 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', subsetE2)).
% 0.20/0.31 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', notsubsetI)).
% 0.20/0.31 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', notequalI1)).
% 0.20/0.31 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', notequalI2)).
% 0.20/0.31 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', subsetRefl)).
% 0.20/0.31 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', subsetTrans)).
% 0.20/0.31 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setadjoinSub)).
% 0.20/0.31 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setadjoinSub2)).
% 0.20/0.31 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', subset2powerset)).
% 0.20/0.31 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setextsub)).
% 0.20/0.31 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', subsetemptysetimpeq)).
% 0.20/0.31 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', powersetI1)).
% 0.20/0.31 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', powersetE1)).
% 0.20/0.31 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', inPowerset)).
% 0.20/0.31 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', powersetsubset)).
% 0.20/0.31 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', binunionIL)).
% 0.20/0.31 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', upairset2IR)).
% 0.20/0.31 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', binunionIR)).
% 0.20/0.31 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', binunionEcases)).
% 0.20/0.31 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', binunionE)).
% 0.20/0.31 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', binunionLsub)).
% 0.20/0.31 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', binunionRsub)).
% 0.20/0.31 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', binintersectI)).
% 0.20/0.31 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', binintersectSubset5)).
% 0.20/0.31 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', binintersectEL)).
% 0.20/0.31 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', binintersectLsub)).
% 0.20/0.31 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', binintersectSubset2)).
% 0.20/0.31 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', binintersectSubset3)).
% 0.20/0.31 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', binintersectER)).
% 0.20/0.31 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', disjointsetsI1)).
% 0.20/0.31 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', binintersectRsub)).
% 0.20/0.31 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', binintersectSubset4)).
% 0.20/0.31 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', binintersectSubset1)).
% 0.20/0.31 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', bs114d)).
% 0.20/0.31 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setminusI)).
% 0.20/0.31 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setminusEL)).
% 0.20/0.31 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setminusER)).
% 0.20/0.31 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setminusSubset2)).
% 0.20/0.31 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setminusERneg)).
% 0.20/0.31 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setminusELneg)).
% 0.20/0.31 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setminusILneg)).
% 0.20/0.31 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setminusIRneg)).
% 0.20/0.31 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setminusLsub)).
% 0.20/0.31 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setminusSubset1)).
% 0.20/0.31 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', symdiffE)).
% 0.20/0.31 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', symdiffI1)).
% 0.20/0.31 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', symdiffI2)).
% 0.20/0.31 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', symdiffIneg1)).
% 0.20/0.31 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', symdiffIneg2)).
% 0.20/0.31 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', secondinupair)).
% 0.20/0.31 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setukpairIL)).
% 0.20/0.31 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setukpairIR)).
% 0.20/0.31 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', singletonsubset)).
% 0.20/0.31 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', singletoninpowerset)).
% 0.20/0.31 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', singletoninpowunion)).
% 0.20/0.31 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', upairset2E)).
% 0.20/0.31 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', upairsubunion)).
% 0.20/0.31 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', upairinpowunion)).
% 0.20/0.31 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', ubforcartprodlem1)).
% 0.20/0.31 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', ubforcartprodlem2)).
% 0.20/0.31 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', ubforcartprodlem3)).
% 0.20/0.31 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', cartprodpairin)).
% 0.20/0.31 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', cartprodmempair1)).
% 0.20/0.31 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setunionE2)).
% 0.20/0.31 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setunionsingleton1)).
% 0.20/0.31 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTrCSDKPQJ/E---3.1_1331652.p', setunionsingleton2)).
% 0.20/0.31 thf(c_0_156, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.20/0.31 thf(c_0_157, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.20/0.31 thf(c_0_158, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.20/0.31 thf(c_0_159, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.20/0.31 thf(c_0_160, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.20/0.31 thf(c_0_161, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.20/0.31 thf(c_0_162, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.20/0.31 thf(c_0_163, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.20/0.31 thf(c_0_164, 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])).
% 0.20/0.31 thf(c_0_165, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.20/0.31 thf(c_0_166, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.20/0.31 thf(c_0_167, 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])).
% 0.20/0.31 thf(c_0_168, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.20/0.31 thf(c_0_169, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.20/0.31 thf(c_0_170, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.20/0.31 thf(c_0_171, plain, ((iskpair)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ (setunion @ Z0)))&(?[X3:$i]:((((in @ X3 @ (setunion @ Z0)))&(((Z0)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))))), inference(fof_simplification,[status(thm)],[iskpair])).
% 0.20/0.31 thf(c_0_172, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setunionsingleton])).
% 0.20/0.31 thf(c_0_173, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X434:$i]:(((((X6 @ X2 @ X434)))&(![X435:$i]:(((((X6 @ X2 @ X435)))=>(((X434)=(X435)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_156, c_0_157])).
% 0.20/0.31 thf(c_0_174, plain, ((descrp)=(![X1:$i > $o]:((((?[X436:$i]:(((((X1 @ X436)))&(![X437:$i]:(((((X1 @ X437)))=>(((X436)=(X437))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_158, c_0_157])).
% 0.20/0.31 thf(c_0_175, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.20/0.31 thf(c_0_176, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.20/0.31 thf(c_0_177, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.20/0.31 thf(c_0_178, plain, ((exuE1)=(![X1:$i > $o]:((((?[X438:$i]:(((((X1 @ X438)))&(![X439:$i]:(((((X1 @ X439)))=>(((X438)=(X439))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_159, c_0_157])).
% 0.20/0.31 thf(c_0_179, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X440:$i]:(((((X1 @ X440)))&(![X441:$i]:(((((X1 @ X441)))=>(((X440)=(X441))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_160, c_0_157])).
% 0.20/0.31 thf(c_0_180, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.20/0.31 thf(c_0_181, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_161])).
% 0.20/0.31 thf(c_0_182, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_162, c_0_161])).
% 0.20/0.31 thf(c_0_183, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_161])).
% 0.20/0.31 thf(c_0_184, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.20/0.31 thf(c_0_185, plain, ((exuE2)=(![X1:$i > $o]:((((?[X442:$i]:(((((X1 @ X442)))&(![X443:$i]:(((((X1 @ X443)))=>(((X442)=(X443))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_163, c_0_157])).
% 0.20/0.31 thf(c_0_186, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_161])).
% 0.20/0.31 thf(c_0_187, 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])).
% 0.20/0.31 thf(c_0_188, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X444:$i]:(((((X1 @ X444)))&(![X445:$i]:(((((X1 @ X445)))=>(((X444)=(X445)))))))))))))), inference(apply_def,[status(thm)],[c_0_164, c_0_157])).
% 0.20/0.31 thf(c_0_189, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X446:$i]:(((((X1 @ X446)))&(![X447:$i]:(((((X1 @ X447)))=>(((X446)=(X447)))))))))))))))), inference(apply_def,[status(thm)],[c_0_165, c_0_157])).
% 0.20/0.31 thf(c_0_190, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X448:$i]:(((((X1 @ X448)))&(![X449:$i]:(((((X1 @ X449)))=>(((X448)=(X449)))))))))))))), inference(apply_def,[status(thm)],[c_0_166, c_0_157])).
% 0.20/0.31 thf(c_0_191, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X450:$i]:(((((X1 @ X450)))&(![X451:$i]:(((((X1 @ X451)))=>(((X450)=(X451))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_167, c_0_157])).
% 0.20/0.31 thf(c_0_192, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X452:$i]:(((((X1 @ X452)))&(![X453:$i]:(((((X1 @ X453)))=>(((X452)=(X453))))))))))<=>((?[X454:$i]:(((((X17 @ X454)))&(![X455:$i]:(((((X17 @ X455)))=>(((X454)=(X455)))))))))))))))), inference(apply_def,[status(thm)],[c_0_168, c_0_157])).
% 0.20/0.31 thf(c_0_193, plain, ((exuEu)=(![X1:$i > $o]:((((?[X456:$i]:(((((X1 @ X456)))&(![X457:$i]:(((((X1 @ X457)))=>(((X456)=(X457))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_169, c_0_157])).
% 0.20/0.31 thf(c_0_194, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X458:$i]:(((((X1 @ X458)))&(![X459:$i]:(((((X1 @ X459)))=>(((X458)=(X459))))))))))=>((((?[X460:$i]:(((((X17 @ X460)))&(![X461:$i]:(((((X17 @ X461)))=>(((X460)=(X461))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_170, c_0_157])).
% 0.20/0.31 thf(c_0_195, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.20/0.31 thf(c_0_196, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.20/0.31 thf(c_0_197, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.20/0.31 thf(c_0_198, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X462:$i]:((((in @ X462 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))&(?[X463:$i]:((((in @ X463 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))&(((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X462 @ emptyset) @ (setadjoin @ (setadjoin @ X462 @ (setadjoin @ X463 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_171])).
% 0.20/0.31 thf(c_0_199, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X464:$i]:((((in @ X464 @ (setunion @ (kpair @ X2 @ X3))))&(?[X465:$i]:((((in @ X465 @ (setunion @ (kpair @ X2 @ X3))))&(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X464 @ emptyset) @ (setadjoin @ (setadjoin @ X464 @ (setadjoin @ X465 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairp, c_0_171])).
% 0.20/0.31 thf(c_0_200, axiom, ((cartprodmempair)=(![X4:$i, X5:$i, X18:$i]:((((in @ X18 @ (cartprod @ X4 @ X5)))=>((?[X466:$i]:((((in @ X466 @ (setunion @ X18)))&(?[X467:$i]:((((in @ X467 @ (setunion @ X18)))&(((X18)=(setadjoin @ (setadjoin @ X466 @ emptyset) @ (setadjoin @ (setadjoin @ X466 @ (setadjoin @ X467 @ emptyset)) @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[cartprodmempair, c_0_171])).
% 0.20/0.31 thf(c_0_201, plain, ((epred1_0)<=>![X497:$i]:(?[X498:$i]:((((![X499:$i]:(((in @ X499 @ X498)=>![X500:$i]:(((in @ X500 @ X499)=>(in @ X500 @ X497)))))&![X501:$i, X502:$i]:((((in @ X501 @ X497)&(in @ X502 @ X497))=>(![X503:$i]:(((in @ X503 @ X498)=>((in @ X501 @ X503)<=>(in @ X502 @ X503))))=>((X501)=(X502))))))&![X504:$i, X505:$i]:((((in @ X504 @ X498)&(in @ X505 @ X498))=>(![X506:$i]:(((in @ X506 @ X504)=>(in @ X506 @ X505)))|![X507:$i]:(((in @ X507 @ X505)=>(in @ X507 @ X504)))))))&![X508:$i]:(((![X509:$i]:(((in @ X509 @ X508)=>(in @ X509 @ X497)))&?[X510:$i]:((in @ X510 @ X508)))=>?[X511:$i, X512:$i]:(((((in @ X511 @ X498)&(in @ X512 @ X508))&~(?[X513:$i]:(((in @ X513 @ X511)&(in @ X513 @ X508)))))&![X514:$i]:(((in @ X514 @ X498)=>(![X515:$i]:(((in @ X515 @ X514)=>(in @ X515 @ X511)))|(in @ X512 @ X514)))))))))))), introduced(definition)).
% 0.20/0.31 thf(c_0_202, negated_conjecture, ~((![X468:$i, X469:$i]:((![X470:$i]:(((in @ X470 @ X468)<=>(in @ X470 @ X469)))=>((X468)=(X469))))=>(![X471:$i]:(~(in @ X471 @ emptyset))=>(![X472:$i, X473:$i, X474:$i]:(((in @ X474 @ (setadjoin @ X472 @ X473))<=>(((X474)=(X472))|(in @ X474 @ X473))))=>(![X475:$i, X476:$i]:(((in @ X476 @ (powerset @ X475))<=>![X477:$i]:(((in @ X477 @ X476)=>(in @ X477 @ X475)))))=>(![X478:$i, X479:$i]:(((in @ X479 @ (setunion @ X478))<=>?[X480:$i]:(((in @ X479 @ X480)&(in @ X480 @ X478)))))=>((in @ emptyset @ omega)=>(![X481:$i]:(((in @ X481 @ omega)=>(in @ (setadjoin @ X481 @ X481) @ omega)))=>(![X482:$i]:((((in @ emptyset @ X482)&![X483:$i]:((((in @ X483 @ omega)&(in @ X483 @ X482))=>(in @ (setadjoin @ X483 @ X483) @ X482))))=>![X484:$i]:(((in @ X484 @ omega)=>(in @ X484 @ X482)))))=>(![X485:$i > $i > $o, X486:$i]:((![X487:$i]:(((in @ X487 @ X486)=>?[X488:$i]:(((X485 @ X487 @ X488)&![X489:$i]:(((X485 @ X487 @ X489)=>((X488)=(X489))))))))=>?[X490:$i]:(![X491:$i]:(((in @ X491 @ X490)<=>?[X492:$i]:(((in @ X492 @ X486)&(X485 @ X492 @ X491))))))))=>(![X493:$i]:((?[X494:$i]:((in @ X494 @ X493))=>?[X495:$i]:(((in @ X495 @ X493)&~(?[X496:$i]:(((in @ X496 @ X495)&(in @ X496 @ X493))))))))=>((epred1_0)=>(![X516:$i > $o]:((?[X517:$i]:(((X516 @ X517)&![X518:$i]:(((X516 @ X518)=>((X517)=(X518))))))=>(X516 @ (descr @ (^[Z0:$i]:(X516 @ Z0))))))=>(![X519:$i, X520:$i > $o, X521:$i]:(((in @ X521 @ X519)=>((X520 @ X521)=>(in @ X521 @ (dsetconstr @ X519 @ X520)))))=>(![X522:$i, X523:$i > $o, X524:$i]:(((in @ X524 @ (dsetconstr @ X522 @ X523))=>(in @ X524 @ X522)))=>(![X525:$i, X526:$i > $o, X527:$i]:(((in @ X527 @ (dsetconstr @ X525 @ X526))=>(X526 @ X527)))=>(![X528:$i > $o]:((?[X529:$i]:(((X528 @ X529)&![X530:$i]:(((X528 @ X530)=>((X529)=(X530))))))=>?[X531:$i]:(((X528 @ X531)&![X532:$i]:(((X528 @ X532)=>((X531)=(X532))))))))=>(![X533:$o, X534:$i]:(((in @ X534 @ (prop2set @ ((X533))))=>(X533)))=>(![X535:$i]:(((in @ X535 @ emptyset)=>![X536:$o]:((X536))))=>(![X537:$i]:(((in @ X537 @ emptyset)=>~($true)))=>(![X538:$i]:(~(in @ X538 @ emptyset))=>(![X539:$i > $o]:((?[X540:$i]:(((X539 @ X540)&![X541:$i]:(((X539 @ X541)=>((X540)=(X541))))))=>?[X542:$i]:((X539 @ X542))))=>(![X543:$i, X544:$i]:((![X545:$i]:(((in @ X545 @ X543)=>(in @ X545 @ X544)))=>(![X546:$i]:(((in @ X546 @ X544)=>(in @ X546 @ X543)))=>((X543)=(X544)))))=>(![X547:$i]:((![X548:$i]:(~(in @ X548 @ X547))=>((X547)=(emptyset))))=>(![X549:$i]:((![X550:$i]:(~(in @ X550 @ X549))=>((X549)=(emptyset))))=>(![X551:$i, X552:$i > $o, X553:$i]:(((in @ X553 @ X551)=>((in @ X553 @ (dsetconstr @ X551 @ X552))<=>(X552 @ X553))))=>(![X554:$i]:((((X554)!=(emptyset))=>?[X555:$i]:((in @ X555 @ X554))))=>(![X556:$i, X557:$i > $o, X558:$i]:(((in @ X558 @ X556)=>((X557 @ X558)=>((dsetconstr @ X556 @ X557)!=(emptyset)))))=>(![X559:$i]:((?[X560:$i]:((in @ X560 @ X559))=>((X559)!=(emptyset))))=>(![X561:$i, X562:$i]:((in @ X561 @ (setadjoin @ X561 @ X562)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X563:$i, X564:$i, X565:$i]:(((in @ X565 @ X564)=>(in @ X565 @ (setadjoin @ X563 @ X564))))=>(![X566:$i, X567:$i, X568:$i]:(((in @ X568 @ (setadjoin @ X566 @ X567))=>![X569:$o]:(((((X568)=(X566))=>(X569))=>(((in @ X568 @ X567)=>(X569))=>(X569))))))=>(![X570:$i, X571:$i, X572:$i]:(((in @ X572 @ (setadjoin @ X570 @ X571))=>(((X572)=(X570))|(in @ X572 @ X571))))=>(![X573:$i]:(((dsetconstr @ X573 @ (^[Z0:$i]:($true)))=(X573)))=>(![X574:$i, X575:$i]:((![X576:$i]:(((in @ X576 @ X575)=>(in @ X576 @ X574)))=>(in @ X575 @ (powerset @ X574))))=>(![X577:$i]:((in @ emptyset @ (powerset @ X577)))=>(![X578:$i]:((in @ emptyset @ (powerset @ X578)))=>(![X579:$i, X580:$i, X581:$i]:(((in @ X580 @ (powerset @ X579))=>((in @ X581 @ X580)=>(in @ X581 @ X579))))=>(![X582:$i, X583:$i, X584:$i]:(((in @ X583 @ X584)=>((in @ X584 @ X582)=>(in @ X583 @ (setunion @ X582)))))=>(![X585:$i, X586:$i]:(((in @ X586 @ (setunion @ X585))=>![X587:$o]:((![X588:$i]:(((in @ X586 @ X588)=>((in @ X588 @ X585)=>(X587))))=>(X587)))))=>(![X589:$i, X590:$i]:(((in @ X590 @ X589)=>(in @ X590 @ (powerset @ (setunion @ X589)))))=>(![X591:$i > $o]:((?[X592:$i]:(((X591 @ X592)&![X593:$i]:(((X591 @ X593)=>((X592)=(X593))))))=>?[X594:$i]:(![X595:$i]:(((X591 @ X595)<=>((X595)=(X594)))))))=>(![X596:$i]:((((X596)!=(emptyset))=>?[X597:$i]:(((in @ X597 @ X596)&$true))))=>(![X598:$i, X599:$i]:(((in @ X598 @ (setadjoin @ X599 @ emptyset))=>((X598)=(X599))))=>(![X600:$i, X601:$i]:((((X600)!=(X601))=>~(in @ X601 @ (setadjoin @ X600 @ emptyset))))=>(![X602:$i, X603:$i]:((((X602)=(X603))=>(in @ X602 @ (setadjoin @ X603 @ emptyset))))=>(![X604:$i, X605:$i]:(((in @ X604 @ (setadjoin @ X605 @ emptyset))=>(in @ X605 @ (setadjoin @ X604 @ emptyset))))=>(![X606:$i, X607:$i, X608:$i]:(((in @ X608 @ (setadjoin @ X606 @ (setadjoin @ X607 @ emptyset)))=>(((X608)=(X606))|((X608)=(X607)))))=>(![X609:$i, X610:$i]:((in @ X609 @ (setadjoin @ X609 @ (setadjoin @ X610 @ emptyset))))=>(![X611:$i, X612:$i]:((in @ X612 @ (setadjoin @ X611 @ (setadjoin @ X612 @ emptyset))))=>(![X613:$i, X614:$i > $o]:((?[X615:$i]:(((in @ X615 @ X613)&(X614 @ X615)))=>(((dsetconstr @ X613 @ X614)=(emptyset))=>~($true))))=>(![X616:$i > $o, X617:$i]:(((in @ X617 @ emptyset)=>(X616 @ X617)))=>(![X618:$i, X619:$i > $o]:((~(![X620:$i]:(((in @ X620 @ X618)=>(X619 @ X620))))=>?[X621:$i]:(((in @ X621 @ X618)&~((X619 @ X621))))))=>(![X622:$i, X623:$i > $o]:((![X624:$i]:(((in @ X624 @ X622)=>~((X623 @ X624))))=>~(?[X625:$i]:(((in @ X625 @ X622)&(X623 @ X625))))))=>(![X626:$i, X627:$i > $o]:((~(?[X628:$i]:(((in @ X628 @ X626)&(X627 @ X628))))=>![X629:$i]:(((in @ X629 @ X626)=>~((X627 @ X629))))))=>(![X630:$i, X631:$i > $o]:((?[X632:$i]:(((in @ X632 @ X630)&~((X631 @ X632))))=>~(![X633:$i]:(((in @ X633 @ X630)=>(X631 @ X633))))))=>(![X634:$o]:(((X634)=>(in @ emptyset @ (prop2set @ ((X634))))))=>(![X635:$o]:(((X635)=>(set2prop @ (prop2set @ ((X635))))))=>(![X636:$i, X637:$i > $o]:((~(?[X638:$i]:(((in @ X638 @ X636)&(X637 @ X638))))=>![X639:$i]:(((in @ X639 @ X636)=>~((X637 @ X639))))))=>(![X640:$i, X641:$i > $o]:((~(![X642:$i]:(((in @ X642 @ X640)=>(X641 @ X642))))=>?[X643:$i]:(((in @ X643 @ X640)&~((X641 @ X643))))))=>(![X644:$i > $o]:((?[X645:$i]:(((X644 @ X645)&![X646:$i]:(((X644 @ X646)=>((X645)=(X646))))))=>?[X647:$i]:(((X644 @ X647)&![X648:$i]:(((X644 @ X648)=>((X647)=(X648))))))))=>(![X649:$i > $o]:((?[X650:$i]:((X649 @ X650))=>(![X651:$i, X652:$i]:(((X649 @ X651)=>((X649 @ X652)=>((X651)=(X652)))))=>?[X653:$i]:(((X649 @ X653)&![X654:$i]:(((X649 @ X654)=>((X653)=(X654)))))))))=>(![X655:$i > $o]:((?[X656:$i]:(![X657:$i]:(((X655 @ X657)<=>((X657)=(X656)))))=>?[X658:$i]:(((X655 @ X658)&![X659:$i]:(((X655 @ X659)=>((X658)=(X659))))))))=>(![X660:$i, X661:$i]:((((X660)=(X661))=>![X662:$i, X663:$i]:((((X662)=(X663))=>((in @ X662 @ X660)=>(in @ X663 @ X661))))))=>(![X664:$i, X665:$i]:((((X664)=(X665))=>![X666:$i, X667:$i]:((((X666)=(X667))=>((in @ X666 @ X664)<=>(in @ X667 @ X665))))))=>(![X668:$i > $o]:((?[X669:$i]:(((X668 @ X669)&![X670:$i]:(((X668 @ X670)=>((X669)=(X670))))))=>![X671:$i, X672:$i]:(((X668 @ X671)=>((X668 @ X672)=>((X671)=(X672)))))))=>(![X673:$i > $o, X674:$i > $o]:((![X675:$i, X676:$i]:((((X675)=(X676))=>((X673 @ X675)<=>(X674 @ X676))))=>(?[X677:$i]:(((X673 @ X677)&![X678:$i]:(((X673 @ X678)=>((X677)=(X678))))))<=>?[X679:$i]:(((X674 @ X679)&![X680:$i]:(((X674 @ X680)=>((X679)=(X680)))))))))=>(((emptyset)=(emptyset))=>(![X681:$i, X682:$i]:((((X681)=(X682))=>![X683:$i, X684:$i]:((((X683)=(X684))=>((setadjoin @ X681 @ X683)=(setadjoin @ X682 @ X684))))))=>(![X685:$i, X686:$i]:((((X685)=(X686))=>((powerset @ X685)=(powerset @ X686))))=>(![X687:$i, X688:$i]:((((X687)=(X688))=>((setunion @ X687)=(setunion @ X688))))=>(((omega)=(omega))=>(![X689:$i > $o]:((?[X690:$i]:(((X689 @ X690)&![X691:$i]:(((X689 @ X691)=>((X690)=(X691))))))=>![X692:$i, X693:$i]:(((X689 @ X692)=>((X689 @ X693)=>((X692)=(X693)))))))=>(![X694:$i 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,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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_172, 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c_0_193]), c_0_194]), c_0_195]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_196]), c_0_197]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), c_0_198]), c_0_199]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), c_0_200]), setunionE2]), setunionsingleton1]), setunionsingleton2])])]), c_0_201])).
% 0.20/0.31 thf(c_0_203, negated_conjecture, ![X917:$i, X918:$i, X920:$i, X921:$i, X922:$i, X923:$i, X924:$i, X925:$i, X926:$i, X927:$i, X928:$i, X930:$i, X931:$i, X933:$i, X934:$i, X935:$i, X936:$i, X937:$i, X939:$i, X940:$i > $i > $o, X941:$i, X943:$i, X946:$i, X948:$i, X949:$i, X950:$i, X951:$i, X953:$i, X954:$i > $o, X955:$i, X957:$i, X958:$i > $o, X959:$i, X960:$i, X961:$i > $o, X962:$i, X963:$i, X964:$i > $o, X965:$i, X966:$i > $o, X967:$i, X970:$i, X971:$o, X972:$i, X973:$i, X974:$o, X975:$i, X976:$i, X977:$i > $o, X978:$i, X981:$i, X982:$i, X985:$i, X987:$i, X989:$i, X990:$i > $o, X991:$i, X992:$i, X994:$i, X995:$i > $o, X996:$i, X997:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i, X1003:$i, X1004:$i, X1005:$i, X1006:$i, X1007:$o, X1008:$i, X1009:$i, X1010:$i, X1011:$i, X1012:$i, X1013:$i, X1015:$i, X1016:$i, X1017:$i, X1018:$i, X1019:$i, X1020:$i, X1021:$i, X1022:$i, X1023:$i, X1024:$i, X1025:$o, X1027:$i, X1028:$i, X1029:$i > $o, X1030:$i, X1033:$i, X1034:$i, X1035:$i, X1037:$i, X1038:$i, X1039:$i, X1040:$i, X1041:$i, X1042:$i, X1043:$i, X1044:$i, X1045:$i, X1046:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$i, X1053:$i > $o, X1054:$i, X1055:$i > $o, X1056:$i, X1057:$i, X1058:$i > $o, X1059:$i, X1061:$i, X1062:$i > $o, X1064:$i, X1065:$i, X1066:$i > $o, X1068:$i, X1069:$i, X1070:$i > $o, X1071:$i, X1073:$o, X1074:$o, X1075:$i, X1076:$i > $o, X1078:$i, X1079:$i, X1080:$i > $o, X1081:$i, X1083:$i > $o, X1084:$i, X1087:$i, X1088:$i > $o, X1089:$i, X1093:$i, X1094:$i > $o, X1095:$i, X1098:$i, X1099:$i, X1100:$i, X1101:$i, X1102:$i, X1103:$i, X1104:$i, X1105:$i, X1106:$i, X1107:$i > $o, X1108:$i, X1110:$i, X1111:$i, X1112:$i > $o, X1113:$i > $o, X1116:$i, X1119:$i, X1120:$i, X1123:$i, X1124:$i, X1125:$i, X1126:$i, X1127:$i, X1128:$i, X1129:$i, X1130:$i, X1131:$i, X1132:$i > $o, X1133:$i, X1135:$i, X1136:$i, X1137:$i > $o, X1138:$i > $o, X1141:$i, X1143:$i, X1145:$i, X1146:$i, X1147:$i > $o, X1148:$i > $o, X1151:$i, X1152:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1161:$i, X1162:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$i, X1171:$i, X1172:$i, X1173:$i, X1174:$i, X1175:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i, X1198:$i > $o, X1199:$i, X1200:$i > $o, X1201:$i, X1202:$i, X1203:$i, X1204:$i, X1205:$i, X1206:$i, X1207:$i, X1208:$i, X1209:$i, X1210:$i, X1211:$i, X1212:$o, X1213:$i, X1214:$i, X1215:$i, X1216:$i, X1217:$i, X1218:$i, X1219:$i, X1220:$i, X1221:$i, X1222:$i, X1223:$i, X1224:$i, X1225:$i, X1226:$i, X1227:$i, X1228:$i, X1229:$i, X1230:$i, X1231:$i, X1232:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, X1241:$i, X1242:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i, X1251:$i, X1252:$i, X1253:$i, X1254:$i, X1255:$i, X1256:$i, X1257:$i, X1258:$i, X1259:$i, X1260:$i, X1261:$i, X1262:$i, X1263:$i, X1264:$i, X1265:$i, X1266:$i, X1267:$i, X1268:$i, X1269:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$i, X1278:$i, X1279:$i, X1280:$o, X1281:$i, X1282:$i, X1283:$i, X1284:$i, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$i, X1290:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1303:$i, X1304:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1326:$i, X1327:$i, X1328:$i, X1329:$i, X1330:$i, X1331:$i, X1332:$i, X1333:$i, X1334:$i, X1335:$i, X1336:$i, X1337:$i, X1338:$i, X1339:$i, X1340:$i, X1341:$i, X1342:$i, X1343:$i, X1346:$i, X1347:$i, X1348:$i, X1351:$i, X1352:$i, X1354:$i, X1355:$i]:((((~(in @ (esk1_2 @ X917 @ X918) @ X917)|~(in @ (esk1_2 @ X917 @ X918) @ X918)|((X917)=(X918)))&((in @ (esk1_2 @ X917 @ X918) @ X917)|(in @ (esk1_2 @ X917 @ X918) @ X918)|((X917)=(X918))))&(~(in @ X920 @ emptyset)&(((~(in @ X923 @ (setadjoin @ X921 @ X922))|(((X923)=(X921))|(in @ X923 @ X922)))&((((X923)!=(X921))|(in @ X923 @ (setadjoin @ X921 @ X922)))&(~(in @ X923 @ X922)|(in @ X923 @ (setadjoin @ X921 @ X922)))))&(((~(in @ X925 @ (powerset @ X924))|(~(in @ X926 @ X925)|(in @ X926 @ X924)))&(((in @ (esk2_2 @ X927 @ X928) @ X928)|(in @ X928 @ (powerset @ X927)))&(~(in @ (esk2_2 @ X927 @ X928) @ X927)|(in @ X928 @ (powerset @ X927)))))&(((((in @ X931 @ (esk3_2 @ X930 @ X931))|~(in @ X931 @ (setunion @ X930)))&((in @ (esk3_2 @ X930 @ X931) @ X930)|~(in @ X931 @ (setunion @ X930))))&(~(in @ X934 @ X935)|~(in @ X935 @ X933)|(in @ X934 @ (setunion @ X933))))&((in @ emptyset @ omega)&((~(in @ X936 @ omega)|(in @ (setadjoin @ X936 @ X936) @ omega))&(((((in @ (esk4_1 @ X937) @ omega)|~(in @ emptyset @ X937)|(~(in @ X939 @ omega)|(in @ X939 @ X937)))&((in @ (esk4_1 @ X937) @ X937)|~(in @ emptyset @ X937)|(~(in @ X939 @ omega)|(in @ X939 @ X937))))&(~(in @ (setadjoin @ (esk4_1 @ X937) @ (esk4_1 @ X937)) @ X937)|~(in @ emptyset @ X937)|(~(in @ X939 @ omega)|(in @ X939 @ X937))))&((((((in @ (esk8_3 @ X940 @ X941 @ X946) @ X941)|~(in @ X946 @ (esk7_2 @ X940 @ X941))|(in @ (esk5_2 @ X940 @ X941) @ X941))&((X940 @ (esk8_3 @ X940 @ X941 @ X946) @ X946)|~(in @ X946 @ (esk7_2 @ X940 @ X941))|(in @ (esk5_2 @ X940 @ X941) @ X941)))&(~(in @ X949 @ X941)|~(X940 @ X949 @ X948)|(in @ X948 @ (esk7_2 @ X940 @ X941))|(in @ (esk5_2 @ X940 @ X941) @ X941)))&(((((in @ (esk8_3 @ X940 @ X941 @ X946) @ X941)|~(in @ X946 @ (esk7_2 @ X940 @ X941))|((X940 @ (esk5_2 @ X940 @ X941) @ (esk6_3 @ X940 @ X941 @ X943))|~(X940 @ (esk5_2 @ X940 @ X941) @ X943)))&((X940 @ (esk8_3 @ X940 @ X941 @ X946) @ X946)|~(in @ X946 @ (esk7_2 @ X940 @ X941))|((X940 @ (esk5_2 @ X940 @ X941) @ (esk6_3 @ X940 @ X941 @ X943))|~(X940 @ (esk5_2 @ X940 @ X941) @ X943))))&(~(in @ X949 @ X941)|~(X940 @ X949 @ X948)|(in @ X948 @ (esk7_2 @ X940 @ X941))|((X940 @ (esk5_2 @ X940 @ X941) @ (esk6_3 @ X940 @ X941 @ X943))|~(X940 @ (esk5_2 @ X940 @ X941) @ X943))))&((((in @ (esk8_3 @ X940 @ X941 @ X946) @ X941)|~(in @ X946 @ (esk7_2 @ X940 @ X941))|(((X943)!=(esk6_3 @ X940 @ X941 @ X943))|~(X940 @ (esk5_2 @ X940 @ X941) @ X943)))&((X940 @ (esk8_3 @ X940 @ X941 @ X946) @ X946)|~(in @ X946 @ (esk7_2 @ X940 @ X941))|(((X943)!=(esk6_3 @ X940 @ X941 @ X943))|~(X940 @ (esk5_2 @ X940 @ X941) @ X943))))&(~(in @ X949 @ X941)|~(X940 @ X949 @ X948)|(in @ X948 @ (esk7_2 @ X940 @ X941))|(((X943)!=(esk6_3 @ X940 @ X941 @ X943))|~(X940 @ (esk5_2 @ X940 @ X941) @ X943))))))&((((in @ (esk9_1 @ X950) @ X950)|~(in @ X951 @ X950))&(~(in @ X953 @ (esk9_1 @ X950))|~(in @ X953 @ X950)|~(in @ X951 @ X950)))&((epred1_0)&((((X954 @ (esk10_2 @ X954 @ X955))|~(X954 @ X955)|(X954 @ (descr @ X954)))&(((X955)!=(esk10_2 @ X954 @ X955))|~(X954 @ X955)|(X954 @ (descr @ X954))))&((~(in @ X959 @ X957)|(~(X958 @ X959)|(in @ X959 @ (dsetconstr @ X957 @ X958))))&((~(in @ X962 @ (dsetconstr @ X960 @ X961))|(in @ X962 @ X960))&((~(in @ X965 @ (dsetconstr @ X963 @ X964))|(X964 @ X965))&(((((X966 @ (esk12_1 @ X966))|((X966 @ (esk11_2 @ X966 @ X967))|~(X966 @ X967)))&(~(X966 @ X970)|((esk12_1 @ X966)=(X970))|((X966 @ (esk11_2 @ X966 @ X967))|~(X966 @ X967))))&(((X966 @ (esk12_1 @ X966))|(((X967)!=(esk11_2 @ X966 @ X967))|~(X966 @ X967)))&(~(X966 @ X970)|((esk12_1 @ X966)=(X970))|(((X967)!=(esk11_2 @ X966 @ X967))|~(X966 @ X967)))))&((~(in @ X972 @ (prop2set @ ((X971))))|(X971))&((~(in @ X973 @ emptyset)|(X974))&((~(in @ X975 @ emptyset)|~($true))&(~(in @ X976 @ emptyset)&((((X977 @ (esk13_2 @ X977 @ X978))|~(X977 @ X978)|(X977 @ (esk14_1 @ X977)))&(((X978)!=(esk13_2 @ X977 @ X978))|~(X977 @ X978)|(X977 @ (esk14_1 @ X977))))&(((((in @ (esk16_2 @ X981 @ X982) @ X982)|((X981)=(X982))|(in @ (esk15_2 @ X981 @ X982) @ X981))&(~(in @ (esk16_2 @ X981 @ X982) @ X981)|((X981)=(X982))|(in @ (esk15_2 @ X981 @ X982) @ X981)))&(((in @ (esk16_2 @ X981 @ X982) @ X982)|((X981)=(X982))|~(in @ (esk15_2 @ X981 @ X982) @ X982))&(~(in @ (esk16_2 @ X981 @ X982) @ X981)|((X981)=(X982))|~(in @ (esk15_2 @ X981 @ X982) @ X982))))&(((in @ (esk17_1 @ X985) @ X985)|((X985)=(emptyset)))&(((in @ (esk18_1 @ X987) @ X987)|((X987)=(emptyset)))&(((~(in @ X991 @ (dsetconstr @ X989 @ X990))|(X990 @ X991)|~(in @ X991 @ X989))&(~(X990 @ X991)|(in @ X991 @ (dsetconstr @ X989 @ X990))|~(in @ X991 @ X989)))&((((X992)=(emptyset))|(in @ (esk19_1 @ X992) @ X992))&((~(in @ X996 @ X994)|(~(X995 @ X996)|((dsetconstr @ X994 @ X995)!=(emptyset))))&((~(in @ X998 @ X997)|((X997)!=(emptyset)))&((in @ X999 @ (setadjoin @ X999 @ X1000))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1003 @ X1002)|(in @ X1003 @ (setadjoin @ X1001 @ X1002)))&(((((in @ X1006 @ X1005)|(X1007)|((X1006)=(X1004))|~(in @ X1006 @ (setadjoin @ X1004 @ X1005)))&(~(X1007)|(X1007)|((X1006)=(X1004))|~(in @ X1006 @ (setadjoin @ X1004 @ X1005))))&(((in @ X1006 @ X1005)|(X1007)|~(X1007)|~(in @ X1006 @ (setadjoin @ X1004 @ X1005)))&(~(X1007)|(X1007)|~(X1007)|~(in @ X1006 @ (setadjoin @ X1004 @ X1005)))))&((~(in @ X1010 @ (setadjoin @ X1008 @ X1009))|(((X1010)=(X1008))|(in @ X1010 @ X1009)))&(((dsetconstr @ X1011 @ (^[Z0:$i]:($true)))=(X1011))&((((in @ (esk20_2 @ X1012 @ X1013) @ X1013)|(in @ X1013 @ (powerset @ X1012)))&(~(in @ (esk20_2 @ X1012 @ X1013) @ X1012)|(in @ X1013 @ (powerset @ X1012))))&((in @ emptyset @ (powerset @ X1015))&((in @ emptyset @ (powerset @ X1016))&((~(in @ X1018 @ (powerset @ X1017))|(~(in @ X1019 @ X1018)|(in @ X1019 @ X1017)))&((~(in @ X1021 @ X1022)|(~(in @ X1022 @ X1020)|(in @ X1021 @ (setunion @ X1020))))&((((in @ X1024 @ (esk21_3 @ X1023 @ X1024 @ X1025))|(X1025)|~(in @ X1024 @ (setunion @ X1023)))&(((in @ (esk21_3 @ X1023 @ X1024 @ X1025) @ X1023)|(X1025)|~(in @ X1024 @ (setunion @ X1023)))&(~(X1025)|(X1025)|~(in @ X1024 @ (setunion @ X1023)))))&((~(in @ X1028 @ X1027)|(in @ X1028 @ (powerset @ (setunion @ X1027))))&((((~(X1029 @ X1033)|((X1033)=(esk23_1 @ X1029))|((X1029 @ (esk22_2 @ X1029 @ X1030))|~(X1029 @ X1030)))&(((X1034)!=(esk23_1 @ X1029))|(X1029 @ X1034)|((X1029 @ (esk22_2 @ X1029 @ X1030))|~(X1029 @ X1030))))&((~(X1029 @ X1033)|((X1033)=(esk23_1 @ X1029))|(((X1030)!=(esk22_2 @ X1029 @ X1030))|~(X1029 @ X1030)))&(((X1034)!=(esk23_1 @ X1029))|(X1029 @ X1034)|(((X1030)!=(esk22_2 @ X1029 @ X1030))|~(X1029 @ X1030)))))&((((in @ (esk24_1 @ X1035) @ X1035)|((X1035)=(emptyset)))&(($true)|((X1035)=(emptyset))))&((~(in @ X1037 @ (setadjoin @ X1038 @ emptyset))|((X1037)=(X1038)))&((((X1039)=(X1040))|~(in @ X1040 @ (setadjoin @ X1039 @ emptyset)))&((((X1041)!=(X1042))|(in @ X1041 @ (setadjoin @ X1042 @ emptyset)))&((~(in @ X1043 @ (setadjoin @ X1044 @ emptyset))|(in @ X1044 @ (setadjoin @ X1043 @ emptyset)))&((~(in @ X1047 @ (setadjoin @ X1045 @ (setadjoin @ X1046 @ emptyset)))|(((X1047)=(X1045))|((X1047)=(X1046))))&((in @ X1048 @ (setadjoin @ X1048 @ (setadjoin @ X1049 @ emptyset)))&((in @ X1051 @ (setadjoin @ X1050 @ (setadjoin @ X1051 @ emptyset)))&((~(in @ X1054 @ X1052)|~(X1053 @ X1054)|(((dsetconstr @ X1052 @ X1053)!=(emptyset))|~($true)))&((~(in @ X1056 @ emptyset)|(X1055 @ X1056))&((((in @ (esk25_2 @ X1057 @ X1058) @ X1057)|(~(in @ X1059 @ X1057)|(X1058 @ X1059)))&(~(X1058 @ (esk25_2 @ X1057 @ X1058))|(~(in @ X1059 @ X1057)|(X1058 @ X1059))))&((((in @ (esk26_2 @ X1061 @ X1062) @ X1061)|(~(in @ X1064 @ X1061)|~(X1062 @ X1064)))&((X1062 @ (esk26_2 @ X1061 @ X1062))|(~(in @ X1064 @ X1061)|~(X1062 @ X1064))))&((((in @ (esk27_2 @ X1065 @ X1066) @ X1065)|(~(in @ X1068 @ X1065)|~(X1066 @ X1068)))&((X1066 @ (esk27_2 @ X1065 @ X1066))|(~(in @ X1068 @ X1065)|~(X1066 @ X1068))))&((((in @ (esk28_2 @ X1069 @ X1070) @ X1069)|(~(in @ X1071 @ X1069)|(X1070 @ X1071)))&(~(X1070 @ (esk28_2 @ X1069 @ X1070))|(~(in @ X1071 @ X1069)|(X1070 @ X1071))))&((~(X1073)|(in @ emptyset @ (prop2set @ ((X1073)))))&((~(X1074)|(set2prop @ (prop2set @ ((X1074)))))&((((in @ (esk29_2 @ X1075 @ 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X1250 @ X1251))))&((~(in @ X1255 @ (setminus @ X1253 @ X1254))|(in @ X1255 @ X1253))&((~(in @ X1258 @ (setminus @ X1256 @ X1257))|~(in @ X1258 @ X1257))&((~(subset @ X1259 @ X1260)|((setminus @ X1259 @ X1260)=(emptyset)))&(((in @ X1263 @ (setminus @ X1261 @ X1262))|(~(in @ X1263 @ X1261)|(in @ X1263 @ X1262)))&(((in @ X1266 @ (setminus @ X1264 @ X1265))|((in @ X1266 @ X1265)|~(in @ X1266 @ X1264)))&(((in @ X1269 @ X1267)|~(in @ X1269 @ (setminus @ X1267 @ X1268)))&((~(in @ X1272 @ X1271)|~(in @ X1272 @ (setminus @ X1270 @ X1271)))&((subset @ (setminus @ X1273 @ X1274) @ X1273)&((((setminus @ X1275 @ X1276)!=(emptyset))|(subset @ X1275 @ X1276))&((((~(in @ X1279 @ X1277)|(X1280)|(in @ X1279 @ X1277)|~(in @ X1279 @ (symdiff @ X1277 @ X1278)))&(((in @ X1279 @ X1278)|(X1280)|(in @ X1279 @ X1277)|~(in @ X1279 @ (symdiff @ X1277 @ X1278)))&(~(X1280)|(X1280)|(in @ X1279 @ X1277)|~(in @ X1279 @ (symdiff @ X1277 @ X1278)))))&(((~(in @ X1279 @ X1277)|(X1280)|~(in @ X1279 @ X1278)|~(in @ X1279 @ (symdiff @ X1277 @ X1278)))&(((in @ X1279 @ X1278)|(X1280)|~(in @ X1279 @ X1278)|~(in @ X1279 @ (symdiff @ X1277 @ X1278)))&(~(X1280)|(X1280)|~(in @ X1279 @ X1278)|~(in @ X1279 @ (symdiff @ X1277 @ X1278)))))&((~(in @ X1279 @ X1277)|(X1280)|~(X1280)|~(in @ X1279 @ (symdiff @ X1277 @ X1278)))&(((in @ X1279 @ X1278)|(X1280)|~(X1280)|~(in @ X1279 @ (symdiff @ X1277 @ X1278)))&(~(X1280)|(X1280)|~(X1280)|~(in @ X1279 @ (symdiff @ X1277 @ X1278)))))))&((~(in @ X1283 @ X1281)|((in @ X1283 @ X1282)|(in @ X1283 @ (symdiff @ X1281 @ X1282))))&(((in @ X1286 @ X1284)|(~(in @ X1286 @ X1285)|(in @ X1286 @ (symdiff @ X1284 @ X1285))))&((~(in @ X1289 @ X1287)|(~(in @ X1289 @ X1288)|~(in @ X1289 @ (symdiff @ X1287 @ X1288))))&(((in @ X1292 @ X1290)|((in @ X1292 @ X1291)|~(in @ X1292 @ (symdiff @ X1290 @ X1291))))&((in @ X1294 @ (setadjoin @ X1293 @ (setadjoin @ X1294 @ emptyset)))&((in @ X1295 @ (setunion @ (setadjoin @ (setadjoin @ X1295 @ emptyset) @ (setadjoin @ (setadjoin @ X1295 @ (setadjoin @ X1296 @ emptyset)) @ emptyset))))&((in @ X1298 @ (setunion @ (setadjoin @ (setadjoin @ X1297 @ emptyset) @ (setadjoin @ (setadjoin @ X1297 @ (setadjoin @ X1298 @ emptyset)) @ emptyset))))&(((in @ (esk55_2 @ X1299 @ X1300) @ (setunion @ (setadjoin @ (setadjoin @ X1299 @ emptyset) @ (setadjoin @ (setadjoin @ X1299 @ (setadjoin @ X1300 @ emptyset)) @ emptyset))))&((in @ (esk56_2 @ X1299 @ X1300) @ (setunion @ (setadjoin @ (setadjoin @ X1299 @ emptyset) @ (setadjoin @ (setadjoin @ X1299 @ (setadjoin @ X1300 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1299 @ emptyset) @ (setadjoin @ (setadjoin @ X1299 @ (setadjoin @ X1300 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk55_2 @ X1299 @ X1300) @ emptyset) @ (setadjoin @ (setadjoin @ (esk55_2 @ X1299 @ X1300) @ (setadjoin @ (esk56_2 @ X1299 @ X1300) @ emptyset)) @ emptyset)))))&(((in @ (esk57_2 @ X1303 @ X1304) @ (setunion @ (kpair @ X1303 @ X1304)))&((in @ (esk58_2 @ X1303 @ X1304) @ (setunion @ (kpair @ X1303 @ X1304)))&((kpair @ X1303 @ X1304)=(setadjoin @ (setadjoin @ (esk57_2 @ X1303 @ X1304) @ emptyset) @ (setadjoin @ (setadjoin @ (esk57_2 @ X1303 @ X1304) @ (setadjoin @ (esk58_2 @ X1303 @ X1304) @ emptyset)) @ emptyset)))))&((~(in @ X1308 @ X1307)|(subset @ (setadjoin @ X1308 @ emptyset) @ X1307))&((~(in @ X1310 @ X1309)|(in @ (setadjoin @ X1310 @ emptyset) @ (powerset @ X1309)))&((~(in @ X1313 @ X1311)|(in @ (setadjoin @ X1313 @ emptyset) @ (powerset @ (binunion @ X1311 @ X1312))))&((~(in @ X1316 @ (setadjoin @ X1314 @ (setadjoin @ X1315 @ emptyset)))|(((X1316)=(X1314))|((X1316)=(X1315))))&((~(in @ X1319 @ X1317)|(~(in @ X1320 @ X1318)|(subset @ (setadjoin @ X1319 @ (setadjoin @ X1320 @ emptyset)) @ (binunion @ X1317 @ X1318))))&((~(in @ X1323 @ X1321)|(~(in @ X1324 @ X1322)|(in @ (setadjoin @ X1323 @ (setadjoin @ X1324 @ emptyset)) @ (powerset @ (binunion @ X1321 @ X1322)))))&((~(in @ X1327 @ X1325)|(~(in @ X1328 @ X1326)|(subset @ (setadjoin @ (setadjoin @ X1327 @ emptyset) @ (setadjoin @ (setadjoin @ X1327 @ (setadjoin @ X1328 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1325 @ X1326)))))&((~(in @ X1331 @ X1329)|(~(in @ X1332 @ X1330)|(in @ (setadjoin @ (setadjoin @ X1331 @ emptyset) @ (setadjoin @ (setadjoin @ X1331 @ (setadjoin @ X1332 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1329 @ X1330))))))&((~(in @ X1335 @ X1333)|(~(in @ X1336 @ X1334)|(in @ (kpair @ X1335 @ X1336) @ (powerset @ (powerset @ (binunion @ X1333 @ X1334))))))&((~(in @ X1339 @ X1337)|(~(in @ X1340 @ X1338)|(in @ (kpair @ X1339 @ X1340) @ (cartprod @ X1337 @ X1338))))&((((in @ (esk59_3 @ X1341 @ X1342 @ X1343) @ X1341)|~(in @ X1343 @ (cartprod @ X1341 @ X1342)))&(((in @ (esk60_3 @ X1341 @ X1342 @ X1343) @ X1342)|~(in @ X1343 @ (cartprod @ X1341 @ X1342)))&(((X1343)=(kpair @ (esk59_3 @ X1341 @ X1342 @ X1343) @ (esk60_3 @ X1341 @ X1342 @ X1343)))|~(in @ X1343 @ (cartprod @ X1341 @ X1342)))))&((((in @ (esk61_3 @ X1346 @ X1347 @ X1348) @ (setunion @ X1348))|~(in @ X1348 @ (cartprod @ X1346 @ X1347)))&(((in @ (esk62_3 @ X1346 @ X1347 @ X1348) @ (setunion @ X1348))|~(in @ X1348 @ (cartprod @ X1346 @ X1347)))&(((X1348)=(setadjoin @ (setadjoin @ (esk61_3 @ X1346 @ X1347 @ X1348) @ emptyset) @ (setadjoin @ (setadjoin @ (esk61_3 @ X1346 @ X1347 @ X1348) @ (setadjoin @ (esk62_3 @ X1346 @ X1347 @ X1348) @ emptyset)) @ emptyset)))|~(in @ X1348 @ (cartprod @ X1346 @ X1347)))))&((((in @ (esk63_2 @ X1351 @ X1352) @ X1351)|~(in @ X1352 @ (setunion @ X1351)))&((in @ X1352 @ (esk63_2 @ X1351 @ X1352))|~(in @ X1352 @ (setunion @ X1351))))&((subset @ (setunion @ (setadjoin @ X1354 @ emptyset)) @ X1354)&((subset @ X1355 @ (setunion @ (setadjoin @ X1355 @ emptyset)))&((setunion @ (setadjoin @ esk64_0 @ emptyset))!=(esk64_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_202])])])])])])])).
% 0.20/0.31 thf(c_0_204, negated_conjecture, ![X3:$i, X2:$i]:((((X2)=(X3))|~((subset @ X2 @ X3))|~((subset @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_203])).
% 0.20/0.31 thf(c_0_205, negated_conjecture, ![X2:$i]:((subset @ (setunion @ (setadjoin @ X2 @ emptyset)) @ X2)), inference(split_conjunct,[status(thm)],[c_0_203])).
% 0.20/0.31 thf(c_0_206, negated_conjecture, ![X2:$i]:((subset @ X2 @ (setunion @ (setadjoin @ X2 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_203])).
% 0.20/0.31 thf(c_0_207, negated_conjecture, ((setunion @ (setadjoin @ esk64_0 @ emptyset))!=(esk64_0)), inference(split_conjunct,[status(thm)],[c_0_203])).
% 0.20/0.31 thf(c_0_208, negated_conjecture, ![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204, c_0_205]), c_0_206])])).
% 0.20/0.31 thf(c_0_209, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_207, c_0_208])]), ['proof']).
% 0.20/0.31 % SZS output end CNFRefutation
% 0.20/0.31 % Parsed axioms : 332
% 0.20/0.31 % Removed by relevancy pruning/SinE : 0
% 0.20/0.31 % Initial clauses : 462
% 0.20/0.31 % Removed in clause preprocessing : 200
% 0.20/0.31 % Initial clauses in saturation : 262
% 0.20/0.31 % Processed clauses : 89
% 0.20/0.31 % ...of these trivial : 6
% 0.20/0.31 % ...subsumed : 16
% 0.20/0.31 % ...remaining for further processing : 67
% 0.20/0.31 % Other redundant clauses eliminated : 10
% 0.20/0.31 % Clauses deleted for lack of memory : 0
% 0.20/0.31 % Backward-subsumed : 0
% 0.20/0.31 % Backward-rewritten : 6
% 0.20/0.31 % Generated clauses : 115
% 0.20/0.31 % ...of the previous two non-redundant : 61
% 0.20/0.31 % ...aggressively subsumed : 0
% 0.20/0.31 % Contextual simplify-reflections : 0
% 0.20/0.31 % Paramodulations : 105
% 0.20/0.31 % Factorizations : 0
% 0.20/0.31 % NegExts : 0
% 0.20/0.31 % Equation resolutions : 10
% 0.20/0.31 % Disequality decompositions : 0
% 0.20/0.31 % Total rewrite steps : 61
% 0.20/0.31 % ...of those cached : 36
% 0.20/0.31 % Propositional unsat checks : 0
% 0.20/0.31 % Propositional check models : 0
% 0.20/0.31 % Propositional check unsatisfiable : 0
% 0.20/0.31 % Propositional clauses : 0
% 0.20/0.31 % Propositional clauses after purity: 0
% 0.20/0.31 % Propositional unsat core size : 0
% 0.20/0.31 % Propositional preprocessing time : 0.000
% 0.20/0.31 % Propositional encoding time : 0.000
% 0.20/0.31 % Propositional solver time : 0.000
% 0.20/0.31 % Success case prop preproc time : 0.000
% 0.20/0.31 % Success case prop encoding time : 0.000
% 0.20/0.31 % Success case prop solver time : 0.000
% 0.20/0.31 % Current number of processed clauses : 55
% 0.20/0.31 % Positive orientable unit clauses : 31
% 0.20/0.31 % Positive unorientable unit clauses: 0
% 0.20/0.31 % Negative unit clauses : 1
% 0.20/0.31 % Non-unit-clauses : 23
% 0.20/0.31 % Current number of unprocessed clauses: 234
% 0.20/0.31 % ...number of literals in the above : 771
% 0.20/0.31 % Current number of archived formulas : 0
% 0.20/0.31 % Current number of archived clauses : 6
% 0.20/0.31 % Clause-clause subsumption calls (NU) : 53
% 0.20/0.31 % Rec. Clause-clause subsumption calls : 48
% 0.20/0.31 % Non-unit clause-clause subsumptions : 9
% 0.20/0.31 % Unit Clause-clause subsumption calls : 3
% 0.20/0.31 % Rewrite failures with RHS unbound : 0
% 0.20/0.31 % BW rewrite match attempts : 9
% 0.20/0.31 % BW rewrite match successes : 5
% 0.20/0.31 % Condensation attempts : 0
% 0.20/0.31 % Condensation successes : 0
% 0.20/0.31 % Termbank termtop insertions : 39556
% 0.20/0.31 % Search garbage collected termcells : 14639
% 0.20/0.31
% 0.20/0.31 % -------------------------------------------------
% 0.20/0.31 % User time : 0.037 s
% 0.20/0.31 % System time : 0.004 s
% 0.20/0.31 % Total time : 0.041 s
% 0.20/0.31 % Maximum resident set size: 7040 pages
% 0.20/0.31
% 0.20/0.31 % -------------------------------------------------
% 0.20/0.31 % User time : 0.049 s
% 0.20/0.31 % System time : 0.007 s
% 0.20/0.31 % Total time : 0.055 s
% 0.20/0.31 % Maximum resident set size: 5120 pages
% 0.20/0.31 % E exiting
%------------------------------------------------------------------------------