%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU650^1 : 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 : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:52 AM UTC 2026
% Result : Theorem 3.98s 1.25s
% Output : CNFRefutation 3.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU650^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.27 % Computer : n001.cluster.edu
% 0.12/0.27 % Model : x86_64 x86_64
% 0.12/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.27 % Memory : 8046.5625MB
% 0.12/0.27 % OS : Linux 6.8.0-71-generic
% 0.12/0.28 % CPULimit : 300
% 0.12/0.28 % WCLimit : 300
% 0.12/0.28 % DateTime : Tue Sep 29 14:08:35 UTC 2026
% 0.12/0.28 % CPUTime :
% 0.12/0.28 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.28/0.35 Running higher-order theorem proving
% 0.33/0.40 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.i1XFWEGaTR/E---3.1_1297253.p
% 3.98/1.25 % Version: 3.5.1-ho
% 3.98/1.25 % Preprocessing class: HSLMSLSSLLLCHFA.
% 3.98/1.25 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.98/1.25 % Starting ehoh_best5 with 300s (1) cores
% 3.98/1.25 % Starting almost_fo_3_lam with 300s (1) cores
% 3.98/1.25 % Starting new_bool_5 with 300s (1) cores
% 3.98/1.25 % Starting pre_casc_3 with 300s (1) cores
% 3.98/1.25 % Starting ho_unfolding_8 with 300s (1) cores
% 3.98/1.25 % Starting new_ho_10_cnf2 with 300s (1) cores
% 3.98/1.25 % Starting new_bool_3 with 300s (1) cores
% 3.98/1.25 % Starting new_ho_5 with 300s (1) cores
% 3.98/1.25 % new_bool_3 with pid 1297272 completed with status 0
% 3.98/1.25 % Result found by new_bool_3
% 3.98/1.25 % Preprocessing class: HSLMSLSSLLLCHFA.
% 3.98/1.25 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.98/1.25 % Starting ehoh_best5 with 300s (1) cores
% 3.98/1.25 % Starting almost_fo_3_lam with 300s (1) cores
% 3.98/1.25 % Starting new_bool_5 with 300s (1) cores
% 3.98/1.25 % Starting pre_casc_3 with 300s (1) cores
% 3.98/1.25 % Starting ho_unfolding_8 with 300s (1) cores
% 3.98/1.25 % Starting new_ho_10_cnf2 with 300s (1) cores
% 3.98/1.25 % Starting new_bool_3 with 300s (1) cores
% 3.98/1.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 3.98/1.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.98/1.25 % Search class: HGHSM-FSLM31-MHFMMSBN
% 3.98/1.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 3.98/1.25 % Starting SubtermCWHack with 28s (1) cores
% 3.98/1.25 % SubtermCWHack with pid 1297277 completed with status 0
% 3.98/1.25 % Result found by SubtermCWHack
% 3.98/1.25 % Preprocessing class: HSLMSLSSLLLCHFA.
% 3.98/1.25 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.98/1.25 % Starting ehoh_best5 with 300s (1) cores
% 3.98/1.25 % Starting almost_fo_3_lam with 300s (1) cores
% 3.98/1.25 % Starting new_bool_5 with 300s (1) cores
% 3.98/1.25 % Starting pre_casc_3 with 300s (1) cores
% 3.98/1.25 % Starting ho_unfolding_8 with 300s (1) cores
% 3.98/1.25 % Starting new_ho_10_cnf2 with 300s (1) cores
% 3.98/1.25 % Starting new_bool_3 with 300s (1) cores
% 3.98/1.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 3.98/1.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.98/1.25 % Search class: HGHSM-FSLM31-MHFMMSBN
% 3.98/1.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 3.98/1.25 % Starting SubtermCWHack with 28s (1) cores
% 3.98/1.25 % Preprocessing time : 0.009 s
% 3.98/1.25
% 3.98/1.25 % Proof found!
% 3.98/1.25 % SZS status Theorem
% 3.98/1.25 % SZS output start CNFRefutation
% 3.98/1.25 thf(decl_23, type, in: $i > $i > $o).
% 3.98/1.25 thf(decl_24, type, exu: ($i > $o) > $o).
% 3.98/1.25 thf(decl_25, type, setextAx: $o).
% 3.98/1.25 thf(decl_26, type, emptyset: $i).
% 3.98/1.25 thf(decl_27, type, emptysetAx: $o).
% 3.98/1.25 thf(decl_28, type, setadjoin: $i > $i > $i).
% 3.98/1.25 thf(decl_29, type, setadjoinAx: $o).
% 3.98/1.25 thf(decl_30, type, powerset: $i > $i).
% 3.98/1.25 thf(decl_31, type, powersetAx: $o).
% 3.98/1.25 thf(decl_32, type, setunion: $i > $i).
% 3.98/1.25 thf(decl_33, type, setunionAx: $o).
% 3.98/1.25 thf(decl_34, type, omega: $i).
% 3.98/1.25 thf(decl_35, type, omega0Ax: $o).
% 3.98/1.25 thf(decl_36, type, omegaSAx: $o).
% 3.98/1.25 thf(decl_37, type, omegaIndAx: $o).
% 3.98/1.25 thf(decl_38, type, replAx: $o).
% 3.98/1.25 thf(decl_39, type, foundationAx: $o).
% 3.98/1.25 thf(decl_40, type, wellorderingAx: $o).
% 3.98/1.25 thf(decl_41, type, descr: ($i > $o) > $i).
% 3.98/1.25 thf(decl_42, type, descrp: $o).
% 3.98/1.25 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 3.98/1.25 thf(decl_44, type, dsetconstrI: $o).
% 3.98/1.25 thf(decl_45, type, dsetconstrEL: $o).
% 3.98/1.25 thf(decl_46, type, dsetconstrER: $o).
% 3.98/1.25 thf(decl_47, type, exuE1: $o).
% 3.98/1.25 thf(decl_48, type, prop2set: $o > $i).
% 3.98/1.25 thf(decl_49, type, prop2setE: $o).
% 3.98/1.25 thf(decl_50, type, emptysetE: $o).
% 3.98/1.25 thf(decl_51, type, emptysetimpfalse: $o).
% 3.98/1.25 thf(decl_52, type, notinemptyset: $o).
% 3.98/1.25 thf(decl_53, type, exuE3e: $o).
% 3.98/1.25 thf(decl_54, type, setext: $o).
% 3.98/1.25 thf(decl_55, type, emptyI: $o).
% 3.98/1.25 thf(decl_56, type, noeltsimpempty: $o).
% 3.98/1.25 thf(decl_57, type, setbeta: $o).
% 3.98/1.25 thf(decl_58, type, nonempty: $i > $o).
% 3.98/1.25 thf(decl_59, type, nonemptyE1: $o).
% 3.98/1.25 thf(decl_60, type, nonemptyI: $o).
% 3.98/1.25 thf(decl_61, type, nonemptyI1: $o).
% 3.98/1.25 thf(decl_62, type, setadjoinIL: $o).
% 3.98/1.25 thf(decl_63, type, emptyinunitempty: $o).
% 3.98/1.25 thf(decl_64, type, setadjoinIR: $o).
% 3.98/1.25 thf(decl_65, type, setadjoinE: $o).
% 3.98/1.25 thf(decl_66, type, setadjoinOr: $o).
% 3.98/1.25 thf(decl_67, type, setoftrueEq: $o).
% 3.98/1.25 thf(decl_68, type, powersetI: $o).
% 3.98/1.25 thf(decl_69, type, emptyinPowerset: $o).
% 3.98/1.25 thf(decl_70, type, emptyInPowerset: $o).
% 3.98/1.25 thf(decl_71, type, powersetE: $o).
% 3.98/1.25 thf(decl_72, type, setunionI: $o).
% 3.98/1.25 thf(decl_73, type, setunionE: $o).
% 3.98/1.25 thf(decl_74, type, subPowSU: $o).
% 3.98/1.25 thf(decl_75, type, exuE2: $o).
% 3.98/1.25 thf(decl_76, type, nonemptyImpWitness: $o).
% 3.98/1.25 thf(decl_77, type, uniqinunit: $o).
% 3.98/1.25 thf(decl_78, type, notinsingleton: $o).
% 3.98/1.25 thf(decl_79, type, eqinunit: $o).
% 3.98/1.25 thf(decl_80, type, singletonsswitch: $o).
% 3.98/1.25 thf(decl_81, type, upairsetE: $o).
% 3.98/1.25 thf(decl_82, type, upairsetIL: $o).
% 3.98/1.25 thf(decl_83, type, upairsetIR: $o).
% 3.98/1.25 thf(decl_84, type, emptyE1: $o).
% 3.98/1.25 thf(decl_85, type, vacuousDall: $o).
% 3.98/1.25 thf(decl_86, type, quantDeMorgan1: $o).
% 3.98/1.25 thf(decl_87, type, quantDeMorgan2: $o).
% 3.98/1.25 thf(decl_88, type, quantDeMorgan3: $o).
% 3.98/1.25 thf(decl_89, type, quantDeMorgan4: $o).
% 3.98/1.25 thf(decl_90, type, prop2setI: $o).
% 3.98/1.25 thf(decl_92, type, prop2set2propI: $o).
% 3.98/1.25 thf(decl_93, type, notdexE: $o).
% 3.98/1.25 thf(decl_94, type, notdallE: $o).
% 3.98/1.25 thf(decl_95, type, exuI1: $o).
% 3.98/1.25 thf(decl_96, type, exuI3: $o).
% 3.98/1.25 thf(decl_97, type, exuI2: $o).
% 3.98/1.25 thf(decl_98, type, inCongP: $o).
% 3.98/1.25 thf(decl_99, type, in__Cong: $o).
% 3.98/1.25 thf(decl_100, type, exuE3u: $o).
% 3.98/1.25 thf(decl_101, type, exu__Cong: $o).
% 3.98/1.25 thf(decl_102, type, emptyset__Cong: $o).
% 3.98/1.25 thf(decl_103, type, setadjoin__Cong: $o).
% 3.98/1.25 thf(decl_104, type, powerset__Cong: $o).
% 3.98/1.25 thf(decl_105, type, setunion__Cong: $o).
% 3.98/1.25 thf(decl_106, type, omega__Cong: $o).
% 3.98/1.25 thf(decl_107, type, exuEu: $o).
% 3.98/1.25 thf(decl_108, type, descr__Cong: $o).
% 3.98/1.25 thf(decl_109, type, dsetconstr__Cong: $o).
% 3.98/1.25 thf(decl_110, type, subset: $i > $i > $o).
% 3.98/1.25 thf(decl_113, type, subsetI1: $o).
% 3.98/1.25 thf(decl_114, type, eqimpsubset2: $o).
% 3.98/1.25 thf(decl_115, type, eqimpsubset1: $o).
% 3.98/1.25 thf(decl_116, type, subsetI2: $o).
% 3.98/1.25 thf(decl_117, type, emptysetsubset: $o).
% 3.98/1.25 thf(decl_118, type, subsetE: $o).
% 3.98/1.25 thf(decl_119, type, subsetE2: $o).
% 3.98/1.25 thf(decl_120, type, notsubsetI: $o).
% 3.98/1.25 thf(decl_121, type, notequalI1: $o).
% 3.98/1.25 thf(decl_122, type, notequalI2: $o).
% 3.98/1.25 thf(decl_123, type, subsetRefl: $o).
% 3.98/1.25 thf(decl_124, type, subsetTrans: $o).
% 3.98/1.25 thf(decl_125, type, setadjoinSub: $o).
% 3.98/1.25 thf(decl_126, type, setadjoinSub2: $o).
% 3.98/1.25 thf(decl_127, type, subset2powerset: $o).
% 3.98/1.25 thf(decl_128, type, setextsub: $o).
% 3.98/1.25 thf(decl_129, type, subsetemptysetimpeq: $o).
% 3.98/1.25 thf(decl_130, type, powersetI1: $o).
% 3.98/1.25 thf(decl_131, type, powersetE1: $o).
% 3.98/1.25 thf(decl_132, type, inPowerset: $o).
% 3.98/1.25 thf(decl_133, type, powersetsubset: $o).
% 3.98/1.25 thf(decl_134, type, sepInPowerset: $o).
% 3.98/1.25 thf(decl_135, type, sepSubset: $o).
% 3.98/1.25 thf(decl_136, type, binunion: $i > $i > $i).
% 3.98/1.25 thf(decl_137, type, binunionIL: $o).
% 3.98/1.25 thf(decl_138, type, upairset2IR: $o).
% 3.98/1.25 thf(decl_139, type, binunionIR: $o).
% 3.98/1.25 thf(decl_140, type, binunionEcases: $o).
% 3.98/1.25 thf(decl_141, type, binunionE: $o).
% 3.98/1.25 thf(decl_142, type, binunionLsub: $o).
% 3.98/1.25 thf(decl_143, type, binunionRsub: $o).
% 3.98/1.25 thf(decl_144, type, binintersect: $i > $i > $i).
% 3.98/1.25 thf(decl_145, type, binintersectI: $o).
% 3.98/1.25 thf(decl_146, type, binintersectSubset5: $o).
% 3.98/1.25 thf(decl_147, type, binintersectEL: $o).
% 3.98/1.25 thf(decl_148, type, binintersectLsub: $o).
% 3.98/1.25 thf(decl_149, type, binintersectSubset2: $o).
% 3.98/1.25 thf(decl_150, type, binintersectSubset3: $o).
% 3.98/1.25 thf(decl_151, type, binintersectER: $o).
% 3.98/1.25 thf(decl_152, type, disjointsetsI1: $o).
% 3.98/1.25 thf(decl_153, type, binintersectRsub: $o).
% 3.98/1.25 thf(decl_154, type, binintersectSubset4: $o).
% 3.98/1.25 thf(decl_155, type, binintersectSubset1: $o).
% 3.98/1.25 thf(decl_156, type, bs114d: $o).
% 3.98/1.25 thf(decl_158, type, setminus: $i > $i > $i).
% 3.98/1.25 thf(decl_159, type, setminusI: $o).
% 3.98/1.25 thf(decl_160, type, setminusEL: $o).
% 3.98/1.25 thf(decl_161, type, setminusER: $o).
% 3.98/1.25 thf(decl_162, type, setminusSubset2: $o).
% 3.98/1.25 thf(decl_163, type, setminusERneg: $o).
% 3.98/1.25 thf(decl_164, type, setminusELneg: $o).
% 3.98/1.25 thf(decl_165, type, setminusILneg: $o).
% 3.98/1.25 thf(decl_166, type, setminusIRneg: $o).
% 3.98/1.25 thf(decl_167, type, setminusLsub: $o).
% 3.98/1.25 thf(decl_168, type, setminusSubset1: $o).
% 3.98/1.25 thf(decl_169, type, symdiff: $i > $i > $i).
% 3.98/1.25 thf(decl_170, type, symdiffE: $o).
% 3.98/1.25 thf(decl_171, type, symdiffI1: $o).
% 3.98/1.25 thf(decl_172, type, symdiffI2: $o).
% 3.98/1.25 thf(decl_173, type, symdiffIneg1: $o).
% 3.98/1.25 thf(decl_174, type, symdiffIneg2: $o).
% 3.98/1.25 thf(decl_175, type, iskpair: $i > $o).
% 3.98/1.25 thf(decl_176, type, secondinupair: $o).
% 3.98/1.25 thf(decl_177, type, setukpairIL: $o).
% 3.98/1.25 thf(decl_178, type, setukpairIR: $o).
% 3.98/1.25 thf(decl_179, type, kpairiskpair: $o).
% 3.98/1.25 thf(decl_180, type, kpair: $i > $i > $i).
% 3.98/1.25 thf(decl_181, type, kpairp: $o).
% 3.98/1.25 thf(decl_182, type, cartprod: $i > $i > $i).
% 3.98/1.25 thf(decl_183, type, singletonsubset: $o).
% 3.98/1.25 thf(decl_184, type, singletoninpowerset: $o).
% 3.98/1.25 thf(decl_185, type, singletoninpowunion: $o).
% 3.98/1.25 thf(decl_186, type, upairset2E: $o).
% 3.98/1.25 thf(decl_187, type, upairsubunion: $o).
% 3.98/1.25 thf(decl_188, type, upairinpowunion: $o).
% 3.98/1.25 thf(decl_189, type, ubforcartprodlem1: $o).
% 3.98/1.25 thf(decl_190, type, ubforcartprodlem2: $o).
% 3.98/1.25 thf(decl_191, type, ubforcartprodlem3: $o).
% 3.98/1.25 thf(decl_192, type, cartprodpairin: $o).
% 3.98/1.25 thf(decl_193, type, cartprodmempair1: $o).
% 3.98/1.25 thf(decl_194, type, cartprodmempair: $o).
% 3.98/1.25 thf(decl_195, type, setunionE2: $o).
% 3.98/1.25 thf(decl_196, type, setunionsingleton1: $o).
% 3.98/1.25 thf(decl_197, type, setunionsingleton2: $o).
% 3.98/1.25 thf(decl_198, type, setunionsingleton: $o).
% 3.98/1.25 thf(decl_199, type, singleton: $i > $o).
% 3.98/1.25 thf(decl_200, type, singletonprop: $o).
% 3.98/1.25 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 3.98/1.25 thf(decl_202, type, ex1E1: $o).
% 3.98/1.25 thf(decl_203, type, ex1I: $o).
% 3.98/1.25 thf(decl_204, type, ex1I2: $o).
% 3.98/1.25 thf(decl_205, type, singletonsuniq: $o).
% 3.98/1.25 thf(decl_210, type, setukpairinjL1: $o).
% 3.98/1.25 thf(decl_211, type, kfstsingleton: $o).
% 3.98/1.25 thf(decl_212, type, theprop: $o).
% 3.98/1.25 thf(decl_213, type, kfst: $i > $i).
% 3.98/1.25 thf(decl_214, type, kfstpairEq: $o).
% 3.98/1.25 thf(decl_215, type, cartprodfstin: $o).
% 3.98/1.25 thf(decl_216, type, setukpairinjL2: $o).
% 3.98/1.25 thf(decl_217, type, setukpairinjL: $o).
% 3.98/1.25 thf(decl_218, type, setukpairinjR11: $o).
% 3.98/1.25 thf(decl_219, type, epred1_0: $o).
% 3.98/1.25 thf(decl_220, type, esk1_2: $i > $i > $i).
% 3.98/1.25 thf(decl_221, type, esk2_2: $i > $i > $i).
% 3.98/1.25 thf(decl_222, type, esk3_2: $i > $i > $i).
% 3.98/1.25 thf(decl_223, type, esk4_1: $i > $i).
% 3.98/1.25 thf(decl_224, type, esk5_2: ($i > $i > $o) > $i > $i).
% 3.98/1.25 thf(decl_225, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 3.98/1.25 thf(decl_226, type, esk7_2: ($i > $i > $o) > $i > $i).
% 3.98/1.25 thf(decl_227, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 3.98/1.25 thf(decl_228, type, esk9_1: $i > $i).
% 3.98/1.25 thf(decl_229, type, esk10_2: ($i > $o) > $i > $i).
% 3.98/1.25 thf(decl_230, type, esk11_2: ($i > $o) > $i > $i).
% 3.98/1.25 thf(decl_231, type, esk12_1: ($i > $o) > $i).
% 3.98/1.25 thf(decl_232, type, esk13_2: ($i > $o) > $i > $i).
% 3.98/1.25 thf(decl_233, type, esk14_1: ($i > $o) > $i).
% 3.98/1.25 thf(decl_234, type, esk15_2: $i > $i > $i).
% 3.98/1.25 thf(decl_235, type, esk16_2: $i > $i > $i).
% 3.98/1.25 thf(decl_236, type, esk17_1: $i > $i).
% 3.98/1.25 thf(decl_237, type, esk18_1: $i > $i).
% 3.98/1.25 thf(decl_238, type, esk19_1: $i > $i).
% 3.98/1.25 thf(decl_239, type, esk20_2: $i > $i > $i).
% 3.98/1.25 thf(decl_240, type, esk21_3: $i > $i > $o > $i).
% 3.98/1.25 thf(decl_241, type, esk22_2: ($i > $o) > $i > $i).
% 3.98/1.25 thf(decl_242, type, esk23_1: ($i > $o) > $i).
% 3.98/1.25 thf(decl_243, type, esk24_1: $i > $i).
% 3.98/1.25 thf(decl_244, type, esk25_2: $i > ($i > $o) > $i).
% 3.98/1.25 thf(decl_245, type, esk26_2: $i > ($i > $o) > $i).
% 3.98/1.25 thf(decl_246, type, esk27_2: $i > ($i > $o) > $i).
% 3.98/1.25 thf(decl_247, type, esk28_2: $i > ($i > $o) > $i).
% 3.98/1.25 thf(decl_248, type, esk29_2: $i > ($i > $o) > $i).
% 3.98/1.25 thf(decl_249, type, esk30_2: $i > ($i > $o) > $i).
% 3.98/1.25 thf(decl_250, type, esk31_2: ($i > $o) > $i > $i).
% 3.98/1.25 thf(decl_251, type, esk32_1: ($i > $o) > $i).
% 3.98/1.25 thf(decl_252, type, esk33_1: ($i > $o) > $i).
% 3.98/1.25 thf(decl_253, type, esk34_1: ($i > $o) > $i).
% 3.98/1.25 thf(decl_254, type, esk35_1: ($i > $o) > $i).
% 3.98/1.25 thf(decl_255, type, esk36_2: ($i > $o) > $i > $i).
% 3.98/1.25 thf(decl_256, type, esk37_1: ($i > $o) > $i).
% 3.98/1.25 thf(decl_257, type, esk38_2: ($i > $o) > $i > $i).
% 3.98/1.25 thf(decl_258, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 3.98/1.25 thf(decl_259, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 3.98/1.25 thf(decl_260, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 3.98/1.25 thf(decl_261, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 3.98/1.25 thf(decl_262, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 3.98/1.25 thf(decl_263, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 3.98/1.25 thf(decl_264, type, esk45_2: ($i > $o) > $i > $i).
% 3.98/1.25 thf(decl_265, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 3.98/1.25 thf(decl_266, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 3.98/1.25 thf(decl_267, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 3.98/1.25 thf(decl_268, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 3.98/1.25 thf(decl_269, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 3.98/1.25 thf(decl_270, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 3.98/1.25 thf(decl_271, type, esk52_2: $i > $i > $i).
% 3.98/1.25 thf(decl_272, type, esk53_2: $i > $i > $i).
% 3.98/1.25 thf(decl_273, type, esk54_2: $i > $i > $i).
% 3.98/1.25 thf(decl_274, type, esk55_2: $i > $i > $i).
% 3.98/1.25 thf(decl_275, type, esk56_2: $i > $i > $i).
% 3.98/1.25 thf(decl_276, type, esk57_2: $i > $i > $i).
% 3.98/1.25 thf(decl_277, type, esk58_2: $i > $i > $i).
% 3.98/1.25 thf(decl_278, type, esk59_3: $i > $i > $i > $i).
% 3.98/1.25 thf(decl_279, type, esk60_3: $i > $i > $i > $i).
% 3.98/1.25 thf(decl_280, type, esk61_3: $i > $i > $i > $i).
% 3.98/1.25 thf(decl_281, type, esk62_3: $i > $i > $i > $i).
% 3.98/1.25 thf(decl_282, type, esk63_2: $i > $i > $i).
% 3.98/1.25 thf(decl_283, type, esk64_2: $i > ($i > $o) > $i).
% 3.98/1.25 thf(decl_284, type, esk65_2: $i > ($i > $o) > $i).
% 3.98/1.25 thf(decl_285, type, esk66_2: $i > ($i > $o) > $i).
% 3.98/1.25 thf(decl_286, type, esk67_2: $i > ($i > $o) > $i).
% 3.98/1.25 thf(decl_287, type, esk68_3: $i > ($i > $o) > $i > $i).
% 3.98/1.25 thf(decl_288, type, esk69_3: $i > ($i > $o) > $i > $i).
% 3.98/1.25 thf(decl_289, type, esk70_2: $i > ($i > $o) > $i).
% 3.98/1.25 thf(decl_290, type, esk71_2: $i > ($i > $o) > $i).
% 3.98/1.25 thf(decl_291, type, esk72_2: $i > ($i > $o) > $i).
% 3.98/1.25 thf(decl_292, type, esk73_1: $i > $i).
% 3.98/1.25 thf(decl_293, type, esk74_0: $i).
% 3.98/1.25 thf(decl_294, type, esk75_0: $i).
% 3.98/1.25 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', ex1)).
% 3.98/1.25 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ X4))&(((X4)=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', singleton)).
% 3.98/1.25 thf(kpair, axiom, ((kpair)=(^[X2:$i, X3:$i]:(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', kpair)).
% 3.98/1.25 thf(iskpair, axiom, ((iskpair)=(^[X4:$i]:(?[X2:$i]:((((in @ X2 @ (setunion @ X4)))&(?[X3:$i]:((((in @ X3 @ (setunion @ X4)))&(((X4)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', iskpair)).
% 3.98/1.25 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', singletonprop)).
% 3.98/1.25 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', ex1E1)).
% 3.98/1.25 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', ex1I)).
% 3.98/1.25 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', ex1I2)).
% 3.98/1.25 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', kfstsingleton)).
% 3.98/1.25 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', nonempty)).
% 3.98/1.25 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.i1XFWEGaTR/E---3.1_1297253.p', exuE2)).
% 3.98/1.25 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', exu)).
% 3.98/1.25 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', exuI2)).
% 3.98/1.25 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', exuI3)).
% 3.98/1.25 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', exuI1)).
% 3.98/1.25 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', exu__Cong)).
% 3.98/1.25 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', exuE3u)).
% 3.98/1.25 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.i1XFWEGaTR/E---3.1_1297253.p', exuEu)).
% 3.98/1.25 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', descr__Cong)).
% 3.98/1.25 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', nonemptyI)).
% 3.98/1.25 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', exuE3e)).
% 3.98/1.25 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', exuE1)).
% 3.98/1.25 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', descrp)).
% 3.98/1.25 thf(replAx, axiom, ((replAx)<=>![X6:$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.i1XFWEGaTR/E---3.1_1297253.p', replAx)).
% 3.98/1.25 thf(setukpairinjR12, 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)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setukpairinjR12)).
% 3.98/1.25 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', ubforcartprodlem3)).
% 3.98/1.25 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', cartprodpairin)).
% 3.98/1.25 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.i1XFWEGaTR/E---3.1_1297253.p', cartprodmempair1)).
% 3.98/1.25 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', cartprodmempair)).
% 3.98/1.25 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setoftrueEq)).
% 3.98/1.25 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', theprop)).
% 3.98/1.25 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', kfstpairEq)).
% 3.98/1.25 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setukpairinjL)).
% 3.98/1.25 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', nonemptyImpWitness)).
% 3.98/1.25 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.i1XFWEGaTR/E---3.1_1297253.p', emptyE1)).
% 3.98/1.25 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', dsetconstr__Cong)).
% 3.98/1.25 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', sepInPowerset)).
% 3.98/1.25 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', sepSubset)).
% 3.98/1.25 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.i1XFWEGaTR/E---3.1_1297253.p', kpairiskpair)).
% 3.98/1.25 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', kpairp)).
% 3.98/1.25 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', nonemptyI1)).
% 3.98/1.25 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', nonemptyE1)).
% 3.98/1.25 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setbeta)).
% 3.98/1.25 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', dsetconstrER)).
% 3.98/1.25 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', dsetconstrEL)).
% 3.98/1.25 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', dsetconstrI)).
% 3.98/1.25 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', upairset2E)).
% 3.98/1.25 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.i1XFWEGaTR/E---3.1_1297253.p', upairsubunion)).
% 3.98/1.25 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.i1XFWEGaTR/E---3.1_1297253.p', upairinpowunion)).
% 3.98/1.25 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.i1XFWEGaTR/E---3.1_1297253.p', ubforcartprodlem1)).
% 3.98/1.25 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.i1XFWEGaTR/E---3.1_1297253.p', ubforcartprodlem2)).
% 3.98/1.25 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setunionI)).
% 3.98/1.25 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', powersetE)).
% 3.98/1.25 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', emptyInPowerset)).
% 3.98/1.25 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setunionE2)).
% 3.98/1.25 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', emptyinPowerset)).
% 3.98/1.25 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setunionsingleton1)).
% 3.98/1.25 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', powersetI)).
% 3.98/1.25 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setunionsingleton2)).
% 3.98/1.25 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setunionsingleton)).
% 3.98/1.25 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setadjoinOr)).
% 3.98/1.25 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.i1XFWEGaTR/E---3.1_1297253.p', setunionE)).
% 3.98/1.25 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', singletonsuniq)).
% 3.98/1.25 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setukpairinjL1)).
% 3.98/1.25 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', cartprodfstin)).
% 3.98/1.25 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setukpairinjL2)).
% 3.98/1.25 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setukpairinjR11)).
% 3.98/1.25 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', singletonsswitch)).
% 3.98/1.25 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', eqinunit)).
% 3.98/1.25 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', notinsingleton)).
% 3.98/1.25 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', uniqinunit)).
% 3.98/1.25 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', subPowSU)).
% 3.98/1.25 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', upairsetE)).
% 3.98/1.25 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', quantDeMorgan3)).
% 3.98/1.25 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', quantDeMorgan2)).
% 3.98/1.25 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', quantDeMorgan1)).
% 3.98/1.25 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', vacuousDall)).
% 3.98/1.25 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', upairsetIR)).
% 3.98/1.25 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', upairsetIL)).
% 3.98/1.25 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', quantDeMorgan4)).
% 3.98/1.25 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', inCongP)).
% 3.98/1.25 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', notdallE)).
% 3.98/1.25 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', notdexE)).
% 3.98/1.25 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', prop2setI)).
% 3.98/1.25 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.i1XFWEGaTR/E---3.1_1297253.p', in__Cong)).
% 3.98/1.25 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', omega__Cong)).
% 3.98/1.25 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setunion__Cong)).
% 3.98/1.25 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', powerset__Cong)).
% 3.98/1.25 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.i1XFWEGaTR/E---3.1_1297253.p', setadjoin__Cong)).
% 3.98/1.25 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', emptyset__Cong)).
% 3.98/1.25 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', emptysetsubset)).
% 3.98/1.25 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', subsetI2)).
% 3.98/1.25 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', eqimpsubset1)).
% 3.98/1.25 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', eqimpsubset2)).
% 3.98/1.25 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', subsetI1)).
% 3.98/1.25 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', subsetE)).
% 3.98/1.25 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setadjoinSub)).
% 3.98/1.25 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', subsetTrans)).
% 3.98/1.25 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', subsetRefl)).
% 3.98/1.25 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', notequalI2)).
% 3.98/1.25 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', notequalI1)).
% 3.98/1.25 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', notsubsetI)).
% 3.98/1.25 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', subsetE2)).
% 3.98/1.25 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setadjoinSub2)).
% 3.98/1.25 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', powersetsubset)).
% 3.98/1.25 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', inPowerset)).
% 3.98/1.25 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', powersetE1)).
% 3.98/1.25 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', powersetI1)).
% 3.98/1.25 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', subsetemptysetimpeq)).
% 3.98/1.25 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setextsub)).
% 3.98/1.25 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', subset2powerset)).
% 3.98/1.25 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', binunionLsub)).
% 3.98/1.25 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', binunionE)).
% 3.98/1.25 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', binunionEcases)).
% 3.98/1.25 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', binunionIR)).
% 3.98/1.25 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', upairset2IR)).
% 3.98/1.25 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', binunionIL)).
% 3.98/1.25 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', binunionRsub)).
% 3.98/1.25 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', binintersectER)).
% 3.98/1.25 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', binintersectSubset3)).
% 3.98/1.25 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', binintersectSubset2)).
% 3.98/1.25 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', binintersectLsub)).
% 3.98/1.25 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', binintersectEL)).
% 3.98/1.25 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', binintersectSubset5)).
% 3.98/1.25 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', binintersectI)).
% 3.98/1.25 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', disjointsetsI1)).
% 3.98/1.25 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setminusER)).
% 3.98/1.25 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setminusEL)).
% 3.98/1.25 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setminusI)).
% 3.98/1.25 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', bs114d)).
% 3.98/1.25 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', binintersectSubset1)).
% 3.98/1.25 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', binintersectSubset4)).
% 3.98/1.25 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', binintersectRsub)).
% 3.98/1.25 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setminusSubset2)).
% 3.98/1.25 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.i1XFWEGaTR/E---3.1_1297253.p', symdiffE)).
% 3.98/1.25 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setminusSubset1)).
% 3.98/1.25 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setminusLsub)).
% 3.98/1.25 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setminusIRneg)).
% 3.98/1.25 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setminusILneg)).
% 3.98/1.25 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setminusELneg)).
% 3.98/1.25 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setminusERneg)).
% 3.98/1.25 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', symdiffI1)).
% 3.98/1.25 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setukpairIR)).
% 3.98/1.25 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setukpairIL)).
% 3.98/1.25 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', secondinupair)).
% 3.98/1.25 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', symdiffIneg2)).
% 3.98/1.25 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', symdiffIneg1)).
% 3.98/1.25 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', symdiffI2)).
% 3.98/1.25 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', singletonsubset)).
% 3.98/1.25 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', singletoninpowerset)).
% 3.98/1.25 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', singletoninpowunion)).
% 3.98/1.25 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setadjoinE)).
% 3.98/1.25 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setadjoinIR)).
% 3.98/1.25 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', emptyinunitempty)).
% 3.98/1.25 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setadjoinIL)).
% 3.98/1.25 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', noeltsimpempty)).
% 3.98/1.25 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', emptyI)).
% 3.98/1.25 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.i1XFWEGaTR/E---3.1_1297253.p', setext)).
% 3.98/1.25 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', notinemptyset)).
% 3.98/1.25 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', emptysetimpfalse)).
% 3.98/1.25 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', emptysetE)).
% 3.98/1.25 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', prop2setE)).
% 3.98/1.25 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.i1XFWEGaTR/E---3.1_1297253.p', wellorderingAx)).
% 3.98/1.25 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.i1XFWEGaTR/E---3.1_1297253.p', foundationAx)).
% 3.98/1.25 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', omegaIndAx)).
% 3.98/1.25 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', omegaSAx)).
% 3.98/1.25 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', omega0Ax)).
% 3.98/1.25 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setunionAx)).
% 3.98/1.25 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', powersetAx)).
% 3.98/1.25 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setadjoinAx)).
% 3.98/1.25 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', emptysetAx)).
% 3.98/1.25 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.i1XFWEGaTR/E---3.1_1297253.p', setextAx)).
% 3.98/1.25 thf(c_0_172, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X509:$i]:((((in @ X509 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X509 @ emptyset))))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 3.98/1.25 thf(c_0_173, plain, ((singleton)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ Z0))&(((Z0)=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 3.98/1.25 thf(c_0_174, plain, ((kpair)=(^[Z0:$i, Z1:$i]:(setadjoin @ (setadjoin @ Z0 @ emptyset) @ (setadjoin @ (setadjoin @ Z0 @ (setadjoin @ Z1 @ emptyset)) @ emptyset)))), inference(fof_simplification,[status(thm)],[kpair])).
% 3.98/1.25 thf(c_0_175, plain, ((iskpair)=(^[Z0:$i]:(?[X2:$i]:((((in @ X2 @ (setunion @ Z0)))&(?[X3:$i]:((((in @ X3 @ (setunion @ Z0)))&(((Z0)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))))), inference(fof_simplification,[status(thm)],[iskpair])).
% 3.98/1.25 thf(c_0_176, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 3.98/1.25 thf(c_0_177, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 3.98/1.25 thf(c_0_178, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((?[X509:$i]:((((in @ X509 @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))))&(((dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2))))=(setadjoin @ X509 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_172, c_0_173])).
% 3.98/1.25 thf(c_0_179, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
% 3.98/1.25 thf(c_0_180, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 3.98/1.25 thf(c_0_181, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 3.98/1.25 thf(c_0_182, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 3.98/1.25 thf(c_0_183, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 3.98/1.25 thf(c_0_184, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 3.98/1.25 thf(c_0_185, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 3.98/1.25 thf(c_0_186, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 3.98/1.25 thf(c_0_187, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 3.98/1.25 thf(c_0_188, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 3.98/1.25 thf(c_0_189, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 3.98/1.25 thf(c_0_190, 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])).
% 3.98/1.25 thf(c_0_191, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 3.98/1.25 thf(c_0_192, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 3.98/1.25 thf(c_0_193, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 3.98/1.25 thf(c_0_194, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 3.98/1.25 thf(c_0_195, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 3.98/1.25 thf(c_0_196, plain, ((replAx)<=>![X6:$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])).
% 3.98/1.25 thf(c_0_197, 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)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setukpairinjR12])).
% 3.98/1.25 thf(c_0_198, axiom, ((ubforcartprodlem3)=(![X4:$i, X5:$i, X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5)))))))))))), inference(apply_def,[status(thm)],[ubforcartprodlem3, c_0_174])).
% 3.98/1.25 thf(c_0_199, axiom, ((cartprodpairin)=(![X4:$i, X5:$i, X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (cartprod @ X4 @ X5)))))))))), inference(apply_def,[status(thm)],[cartprodpairin, c_0_174])).
% 3.98/1.25 thf(c_0_200, axiom, ((cartprodmempair1)=(![X4:$i, X5:$i, X18:$i]:((((in @ X18 @ (cartprod @ X4 @ X5)))=>(?[X2:$i]:((((in @ X2 @ X4))&(?[X3:$i]:((((in @ X3 @ X5))&(((X18)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))))))), inference(apply_def,[status(thm)],[cartprodmempair1, c_0_174])).
% 3.98/1.25 thf(c_0_201, axiom, ((cartprodmempair)=(![X4:$i, X5:$i, X18:$i]:((((in @ X18 @ (cartprod @ X4 @ X5)))=>((?[X506:$i]:((((in @ X506 @ (setunion @ X18)))&(?[X507:$i]:((((in @ X507 @ (setunion @ X18)))&(((X18)=(setadjoin @ (setadjoin @ X506 @ emptyset) @ (setadjoin @ (setadjoin @ X506 @ (setadjoin @ X507 @ emptyset)) @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[cartprodmempair, c_0_175])).
% 3.98/1.25 thf(c_0_202, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 3.98/1.25 thf(c_0_203, plain, ((singletonprop)=(![X4:$i, X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))))=>(((?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2)))))=>((?[X508:$i]:((((in @ X508 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(setadjoin @ X508 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_176, c_0_173])).
% 3.98/1.25 thf(c_0_204, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((?[X510:$i]:((((in @ X510 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X510 @ emptyset)))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_177, c_0_178])).
% 3.98/1.25 thf(c_0_205, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>((?[X511:$i]:((((in @ X511 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X511 @ emptyset))))))))))))))), inference(apply_def,[status(thm)],[c_0_179, c_0_178])).
% 3.98/1.25 thf(c_0_206, plain, ((ex1I2)=(![X4:$i, X1:$i > $o]:(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))))=>(((?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2)))))=>((?[X512:$i]:((((in @ X512 @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))&(((dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))=(setadjoin @ X512 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_180, c_0_178])).
% 3.98/1.25 thf(c_0_207, plain, ((kfstsingleton)=(![X18:$i]:((((?[X513:$i]:((((in @ X513 @ (setunion @ X18)))&(?[X514:$i]:((((in @ X514 @ (setunion @ X18)))&(((X18)=(setadjoin @ (setadjoin @ X513 @ emptyset) @ (setadjoin @ (setadjoin @ X513 @ (setadjoin @ X514 @ emptyset)) @ emptyset)))))))))))=>((?[X515:$i]:((((in @ X515 @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))))&(((dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X515 @ emptyset))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_181, c_0_173]), c_0_175])).
% 3.98/1.25 thf(c_0_208, axiom, ((theprop)=(![X21:$i]:((((?[X516:$i]:((((in @ X516 @ X21))&(((X21)=(setadjoin @ X516 @ emptyset)))))))=>((in @ (setunion @ X21) @ X21)))))), inference(apply_def,[status(thm)],[theprop, c_0_173])).
% 3.98/1.25 thf(c_0_209, axiom, ((kfstpairEq)=(![X2:$i, X3:$i]:(((kfst @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=(X2))))), inference(apply_def,[status(thm)],[kfstpairEq, c_0_174])).
% 3.98/1.25 thf(c_0_210, axiom, ((setukpairinjL)=(![X2:$i, X3:$i, X14:$i, X18:$i]:(((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset))))=>(((X2)=(X14))))))), inference(apply_def,[status(thm)],[setukpairinjL, c_0_174])).
% 3.98/1.25 thf(c_0_211, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_182])).
% 3.98/1.25 thf(c_0_212, plain, ((exuE2)=(![X1:$i > $o]:((((?[X482:$i]:(((((X1 @ X482)))&(![X483:$i]:(((((X1 @ X483)))=>(((X482)=(X483))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_183, c_0_184])).
% 3.98/1.25 thf(c_0_213, plain, ((emptyE1)<=>![X4:$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])).
% 3.98/1.25 thf(c_0_214, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X488:$i]:(((((X1 @ X488)))&(![X489:$i]:(((((X1 @ X489)))=>(((X488)=(X489)))))))))))))), inference(apply_def,[status(thm)],[c_0_185, c_0_184])).
% 3.98/1.25 thf(c_0_215, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X486:$i]:(((((X1 @ X486)))&(![X487:$i]:(((((X1 @ X487)))=>(((X486)=(X487)))))))))))))))), inference(apply_def,[status(thm)],[c_0_186, c_0_184])).
% 3.98/1.25 thf(c_0_216, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X484:$i]:(((((X1 @ X484)))&(![X485:$i]:(((((X1 @ X485)))=>(((X484)=(X485)))))))))))))), inference(apply_def,[status(thm)],[c_0_187, c_0_184])).
% 3.98/1.25 thf(c_0_217, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X492:$i]:(((((X1 @ X492)))&(![X493:$i]:(((((X1 @ X493)))=>(((X492)=(X493))))))))))<=>((?[X494:$i]:(((((X17 @ X494)))&(![X495:$i]:(((((X17 @ X495)))=>(((X494)=(X495)))))))))))))))), inference(apply_def,[status(thm)],[c_0_188, c_0_184])).
% 3.98/1.25 thf(c_0_218, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X490:$i]:(((((X1 @ X490)))&(![X491:$i]:(((((X1 @ X491)))=>(((X490)=(X491))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_189, c_0_184])).
% 3.98/1.25 thf(c_0_219, plain, ((exuEu)=(![X1:$i > $o]:((((?[X496:$i]:(((((X1 @ X496)))&(![X497:$i]:(((((X1 @ X497)))=>(((X496)=(X497))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_190, c_0_184])).
% 3.98/1.25 thf(c_0_220, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 3.98/1.25 thf(c_0_221, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X498:$i]:(((((X1 @ X498)))&(![X499:$i]:(((((X1 @ X499)))=>(((X498)=(X499))))))))))=>((((?[X500:$i]:(((((X17 @ X500)))&(![X501:$i]:(((((X17 @ X501)))=>(((X500)=(X501))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_191, c_0_184])).
% 3.98/1.25 thf(c_0_222, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 3.98/1.25 thf(c_0_223, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 3.98/1.25 thf(c_0_224, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X502:$i]:((((in @ X502 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))&(?[X503:$i]:((((in @ X503 @ (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 @ X502 @ emptyset) @ (setadjoin @ (setadjoin @ X502 @ (setadjoin @ X503 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_175])).
% 3.98/1.25 thf(c_0_225, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X504:$i]:((((in @ X504 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))&(?[X505:$i]:((((in @ X505 @ (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 @ X504 @ emptyset) @ (setadjoin @ (setadjoin @ X504 @ (setadjoin @ X505 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[kpairp, c_0_174]), c_0_175])).
% 3.98/1.25 thf(c_0_226, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_182])).
% 3.98/1.25 thf(c_0_227, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_192, c_0_182])).
% 3.98/1.25 thf(c_0_228, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_182])).
% 3.98/1.25 thf(c_0_229, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 3.98/1.25 thf(c_0_230, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X480:$i]:(((((X1 @ X480)))&(![X481:$i]:(((((X1 @ X481)))=>(((X480)=(X481))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_193, c_0_184])).
% 3.98/1.25 thf(c_0_231, plain, ((exuE1)=(![X1:$i > $o]:((((?[X478:$i]:(((((X1 @ X478)))&(![X479:$i]:(((((X1 @ X479)))=>(((X478)=(X479))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_194, c_0_184])).
% 3.98/1.25 thf(c_0_232, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 3.98/1.25 thf(c_0_233, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 3.98/1.25 thf(c_0_234, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 3.98/1.25 thf(c_0_235, plain, ((descrp)=(![X1:$i > $o]:((((?[X476:$i]:(((((X1 @ X476)))&(![X477:$i]:(((((X1 @ X477)))=>(((X476)=(X477))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_195, c_0_184])).
% 3.98/1.25 thf(c_0_236, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X474:$i]:(((((X6 @ X2 @ X474)))&(![X475:$i]:(((((X6 @ X2 @ X475)))=>(((X474)=(X475)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_196, c_0_184])).
% 3.98/1.25 thf(c_0_237, plain, ((epred1_0)<=>![X546:$i]:(?[X547:$i]:((((![X548:$i]:(((in @ X548 @ X547)=>![X549:$i]:(((in @ X549 @ X548)=>(in @ X549 @ X546)))))&![X550:$i, X551:$i]:((((in @ X550 @ X546)&(in @ X551 @ X546))=>(![X552:$i]:(((in @ X552 @ X547)=>((in @ X550 @ X552)<=>(in @ X551 @ X552))))=>((X550)=(X551))))))&![X553:$i, X554:$i]:((((in @ X553 @ X547)&(in @ X554 @ X547))=>(![X555:$i]:(((in @ X555 @ X553)=>(in @ X555 @ X554)))|![X556:$i]:(((in @ X556 @ X554)=>(in @ X556 @ X553)))))))&![X557:$i]:(((![X558:$i]:(((in @ X558 @ X557)=>(in @ X558 @ X546)))&?[X559:$i]:((in @ X559 @ X557)))=>?[X560:$i, X561:$i]:(((((in @ X560 @ X547)&(in @ X561 @ X557))&~(?[X562:$i]:(((in @ X562 @ X560)&(in @ X562 @ X557)))))&![X563:$i]:(((in @ X563 @ X547)=>(![X564:$i]:(((in @ X564 @ X563)=>(in @ X564 @ X560)))|(in @ X561 @ X563)))))))))))), introduced(definition)).
% 3.98/1.25 thf(c_0_238, negated_conjecture, ~((![X517:$i, X518:$i]:((![X519:$i]:(((in @ X519 @ X517)<=>(in @ X519 @ X518)))=>((X517)=(X518))))=>(![X520:$i]:(~(in @ X520 @ emptyset))=>(![X521:$i, X522:$i, X523:$i]:(((in @ X523 @ (setadjoin @ X521 @ X522))<=>(((X523)=(X521))|(in @ X523 @ X522))))=>(![X524:$i, X525:$i]:(((in @ X525 @ (powerset @ X524))<=>![X526:$i]:(((in @ X526 @ X525)=>(in @ X526 @ X524)))))=>(![X527:$i, X528:$i]:(((in @ X528 @ (setunion @ X527))<=>?[X529:$i]:(((in @ X528 @ X529)&(in @ X529 @ X527)))))=>((in @ emptyset @ omega)=>(![X530:$i]:(((in @ X530 @ omega)=>(in @ (setadjoin @ X530 @ X530) @ omega)))=>(![X531:$i]:((((in @ emptyset @ X531)&![X532:$i]:((((in @ X532 @ omega)&(in @ X532 @ X531))=>(in @ (setadjoin @ X532 @ X532) @ X531))))=>![X533:$i]:(((in @ X533 @ omega)=>(in @ X533 @ X531)))))=>(![X534:$i > $i > $o, X535:$i]:((![X536:$i]:(((in @ X536 @ X535)=>?[X537:$i]:(((X534 @ X536 @ X537)&![X538:$i]:(((X534 @ X536 @ X538)=>((X537)=(X538))))))))=>?[X539:$i]:(![X540:$i]:(((in @ X540 @ X539)<=>?[X541:$i]:(((in @ X541 @ X535)&(X534 @ X541 @ X540))))))))=>(![X542:$i]:((?[X543:$i]:((in @ X543 @ X542))=>?[X544:$i]:(((in @ X544 @ X542)&~(?[X545:$i]:(((in @ X545 @ X544)&(in @ X545 @ X542))))))))=>((epred1_0)=>(![X565:$i > $o]:((?[X566:$i]:(((X565 @ X566)&![X567:$i]:(((X565 @ X567)=>((X566)=(X567))))))=>(X565 @ (descr @ (^[Z0:$i]:(X565 @ Z0))))))=>(![X568:$i, X569:$i > $o, X570:$i]:(((in @ X570 @ X568)=>((X569 @ X570)=>(in @ X570 @ (dsetconstr @ X568 @ X569)))))=>(![X571:$i, X572:$i > $o, X573:$i]:(((in @ X573 @ (dsetconstr @ X571 @ X572))=>(in @ X573 @ X571)))=>(![X574:$i, X575:$i > $o, X576:$i]:(((in @ X576 @ (dsetconstr @ X574 @ X575))=>(X575 @ X576)))=>(![X577:$i > $o]:((?[X578:$i]:(((X577 @ X578)&![X579:$i]:(((X577 @ X579)=>((X578)=(X579))))))=>?[X580:$i]:(((X577 @ X580)&![X581:$i]:(((X577 @ X581)=>((X580)=(X581))))))))=>(![X582:$o, X583:$i]:(((in @ X583 @ (prop2set @ ((X582))))=>(X582)))=>(![X584:$i]:(((in @ X584 @ emptyset)=>![X585:$o]:((X585))))=>(![X586:$i]:(((in @ X586 @ emptyset)=>~($true)))=>(![X587:$i]:(~(in @ X587 @ emptyset))=>(![X588:$i > $o]:((?[X589:$i]:(((X588 @ X589)&![X590:$i]:(((X588 @ X590)=>((X589)=(X590))))))=>?[X591:$i]:((X588 @ X591))))=>(![X592:$i, X593:$i]:((![X594:$i]:(((in @ X594 @ X592)=>(in @ X594 @ X593)))=>(![X595:$i]:(((in @ X595 @ X593)=>(in @ X595 @ X592)))=>((X592)=(X593)))))=>(![X596:$i]:((![X597:$i]:(~(in @ X597 @ X596))=>((X596)=(emptyset))))=>(![X598:$i]:((![X599:$i]:(~(in @ X599 @ X598))=>((X598)=(emptyset))))=>(![X600:$i, X601:$i > $o, X602:$i]:(((in @ X602 @ X600)=>((in @ X602 @ (dsetconstr @ X600 @ X601))<=>(X601 @ X602))))=>(![X603:$i]:((((X603)!=(emptyset))=>?[X604:$i]:((in @ X604 @ X603))))=>(![X605:$i, X606:$i > $o, X607:$i]:(((in @ X607 @ X605)=>((X606 @ X607)=>((dsetconstr @ X605 @ X606)!=(emptyset)))))=>(![X608:$i]:((?[X609:$i]:((in @ X609 @ X608))=>((X608)!=(emptyset))))=>(![X610:$i, X611:$i]:((in @ X610 @ (setadjoin @ X610 @ X611)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X612:$i, X613:$i, X614:$i]:(((in @ X614 @ X613)=>(in @ X614 @ (setadjoin @ X612 @ X613))))=>(![X615:$i, X616:$i, X617:$i]:(((in @ X617 @ (setadjoin @ X615 @ X616))=>![X618:$o]:(((((X617)=(X615))=>(X618))=>(((in @ X617 @ X616)=>(X618))=>(X618))))))=>(![X619:$i, X620:$i, X621:$i]:(((in @ X621 @ (setadjoin @ X619 @ X620))=>(((X621)=(X619))|(in @ X621 @ X620))))=>(![X622:$i]:(((dsetconstr @ X622 @ (^[Z0:$i]:($true)))=(X622)))=>(![X623:$i, X624:$i]:((![X625:$i]:(((in @ X625 @ X624)=>(in @ X625 @ X623)))=>(in @ X624 @ (powerset @ X623))))=>(![X626:$i]:((in @ emptyset @ (powerset @ X626)))=>(![X627:$i]:((in @ emptyset @ (powerset @ X627)))=>(![X628:$i, X629:$i, X630:$i]:(((in @ X629 @ (powerset @ X628))=>((in @ X630 @ X629)=>(in @ X630 @ X628))))=>(![X631:$i, X632:$i, X633:$i]:(((in @ X632 @ X633)=>((in @ X633 @ X631)=>(in @ X632 @ (setunion @ X631)))))=>(![X634:$i, X635:$i]:(((in @ X635 @ (setunion @ X634))=>![X636:$o]:((![X637:$i]:(((in @ X635 @ X637)=>((in @ X637 @ X634)=>(X636))))=>(X636)))))=>(![X638:$i, X639:$i]:(((in @ X639 @ X638)=>(in @ X639 @ (powerset @ (setunion @ X638)))))=>(![X640:$i > $o]:((?[X641:$i]:(((X640 @ X641)&![X642:$i]:(((X640 @ X642)=>((X641)=(X642))))))=>?[X643:$i]:(![X644:$i]:(((X640 @ X644)<=>((X644)=(X643)))))))=>(![X645:$i]:((((X645)!=(emptyset))=>?[X646:$i]:(((in @ X646 @ X645)&$true))))=>(![X647:$i, X648:$i]:(((in @ X647 @ (setadjoin @ X648 @ emptyset))=>((X647)=(X648))))=>(![X649:$i, X650:$i]:((((X649)!=(X650))=>~(in @ X650 @ (setadjoin @ X649 @ emptyset))))=>(![X651:$i, X652:$i]:((((X651)=(X652))=>(in @ X651 @ (setadjoin @ X652 @ emptyset))))=>(![X653:$i, X654:$i]:(((in @ X653 @ (setadjoin @ X654 @ emptyset))=>(in @ X654 @ (setadjoin @ X653 @ emptyset))))=>(![X655:$i, X656:$i, X657:$i]:(((in @ X657 @ (setadjoin @ X655 @ (setadjoin @ X656 @ emptyset)))=>(((X657)=(X655))|((X657)=(X656)))))=>(![X658:$i, X659:$i]:((in @ X658 @ (setadjoin @ X658 @ (setadjoin @ X659 @ emptyset))))=>(![X660:$i, X661:$i]:((in @ X661 @ (setadjoin @ X660 @ (setadjoin @ X661 @ emptyset))))=>(![X662:$i, X663:$i > $o]:((?[X664:$i]:(((in @ X664 @ X662)&(X663 @ X664)))=>(((dsetconstr @ X662 @ X663)=(emptyset))=>~($true))))=>(![X665:$i > $o, X666:$i]:(((in @ X666 @ emptyset)=>(X665 @ X666)))=>(![X667:$i, X668:$i > $o]:((~(![X669:$i]:(((in @ X669 @ X667)=>(X668 @ X669))))=>?[X670:$i]:(((in @ X670 @ X667)&~((X668 @ X670))))))=>(![X671:$i, X672:$i > $o]:((![X673:$i]:(((in @ X673 @ X671)=>~((X672 @ X673))))=>~(?[X674:$i]:(((in @ X674 @ X671)&(X672 @ X674))))))=>(![X675:$i, X676:$i > $o]:((~(?[X677:$i]:(((in @ X677 @ X675)&(X676 @ X677))))=>![X678:$i]:(((in @ X678 @ X675)=>~((X676 @ X678))))))=>(![X679:$i, X680:$i > $o]:((?[X681:$i]:(((in @ X681 @ X679)&~((X680 @ X681))))=>~(![X682:$i]:(((in @ X682 @ X679)=>(X680 @ X682))))))=>(![X683:$o]:(((X683)=>(in @ emptyset @ (prop2set @ ((X683))))))=>((prop2set2propI)=>(![X684:$i, X685:$i > $o]:((~(?[X686:$i]:(((in @ X686 @ X684)&(X685 @ X686))))=>![X687:$i]:(((in @ X687 @ X684)=>~((X685 @ X687))))))=>(![X688:$i, X689:$i > $o]:((~(![X690:$i]:(((in @ X690 @ X688)=>(X689 @ X690))))=>?[X691:$i]:(((in @ X691 @ X688)&~((X689 @ X691))))))=>(![X692:$i > $o]:((?[X693:$i]:(((X692 @ X693)&![X694:$i]:(((X692 @ X694)=>((X693)=(X694))))))=>?[X695:$i]:(((X692 @ X695)&![X696:$i]:(((X692 @ X696)=>((X695)=(X696))))))))=>(![X697:$i > $o]:((?[X698:$i]:((X697 @ X698))=>(![X699:$i, X700:$i]:(((X697 @ X699)=>((X697 @ X700)=>((X699)=(X700)))))=>?[X701:$i]:(((X697 @ X701)&![X702:$i]:(((X697 @ X702)=>((X701)=(X702)))))))))=>(![X703:$i > $o]:((?[X704:$i]:(![X705:$i]:(((X703 @ X705)<=>((X705)=(X704)))))=>?[X706:$i]:(((X703 @ X706)&![X707:$i]:(((X703 @ X707)=>((X706)=(X707))))))))=>(![X708:$i, X709:$i]:((((X708)=(X709))=>![X710:$i, X711:$i]:((((X710)=(X711))=>((in @ X710 @ X708)=>(in @ X711 @ X709))))))=>(![X712:$i, X713:$i]:((((X712)=(X713))=>![X714:$i, X715:$i]:((((X714)=(X715))=>((in @ X714 @ X712)<=>(in @ X715 @ X713))))))=>(![X716:$i > $o]:((?[X717:$i]:(((X716 @ X717)&![X718:$i]:(((X716 @ X718)=>((X717)=(X718))))))=>![X719:$i, X720:$i]:(((X716 @ X719)=>((X716 @ X720)=>((X719)=(X720)))))))=>(![X721:$i > $o, X722:$i > $o]:((![X723:$i, X724:$i]:((((X723)=(X724))=>((X721 @ X723)<=>(X722 @ X724))))=>(?[X725:$i]:(((X721 @ X725)&![X726:$i]:(((X721 @ X726)=>((X725)=(X726))))))<=>?[X727:$i]:(((X722 @ X727)&![X728:$i]:(((X722 @ X728)=>((X727)=(X728)))))))))=>(((emptyset)=(emptyset))=>(![X729:$i, X730:$i]:((((X729)=(X730))=>![X731:$i, X732:$i]:((((X731)=(X732))=>((setadjoin @ X729 @ X731)=(setadjoin @ X730 @ X732))))))=>(![X733:$i, X734:$i]:((((X733)=(X734))=>((powerset @ X733)=(powerset @ X734))))=>(![X735:$i, X736:$i]:((((X735)=(X736))=>((setunion @ X735)=(setunion @ X736))))=>(((omega)=(omega))=>(![X737:$i > $o]:((?[X738:$i]:(((X737 @ X738)&![X739:$i]:(((X737 @ X739)=>((X738)=(X739))))))=>![X740:$i, X741:$i]:(((X737 @ X740)=>((X737 @ X741)=>((X740)=(X741)))))))=>(![X742:$i > $o, X743:$i > $o]:((![X744:$i, X745:$i]:((((X744)=(X745))=>((X742 @ X744)<=>(X743 @ X745))))=>(?[X746:$i]:(((X742 @ X746)&![X747:$i]:(((X742 @ X747)=>((X746)=(X747))))))=>(?[X748:$i]:(((X743 @ X748)&![X749:$i]:(((X743 @ X749)=>((X748)=(X749))))))=>((descr @ X742)=(descr @ X743))))))=>(![X750:$i, X751:$i]:((((X750)=(X751))=>![X752:$i > $o, X753:$i > $o]:((![X754:$i]:(((in @ X754 @ X750)=>![X755:$i]:(((in @ X755 @ X751)=>(((X754)=(X755))=>((X752 @ X754)<=>(X753 @ X755)))))))=>((dsetconstr @ X750 @ X752)=(dsetconstr @ X751 @ X753))))))=>(![X756:$i, X757:$i]:((![X758:$i]:(((in @ X758 @ X756)=>(in @ X758 @ X757)))=>(subset @ X756 @ X757)))=>(![X759:$i, X760:$i]:((((X759)=(X760))=>(subset @ X760 @ X759)))=>(![X761:$i, X762:$i]:((((X761)=(X762))=>(subset @ X761 @ X762)))=>(![X763:$i, X764:$i]:((![X765:$i]:(((in @ X765 @ X763)=>(in @ X765 @ X764)))=>(subset @ X763 @ X764)))=>(![X766:$i]:((subset @ emptyset @ X766))=>(![X767:$i, X768:$i, X769:$i]:(((subset @ X767 @ X768)=>((in @ X769 @ X767)=>(in @ X769 @ X768))))=>(![X770:$i, X771:$i, X772:$i]:(((subset @ X770 @ X771)=>(~(in @ X772 @ X771)=>~(in @ X772 @ X770))))=>(![X773:$i, X774:$i, X775:$i]:(((in @ X775 @ X773)=>(~(in @ X775 @ X774)=>~(subset @ X773 @ X774))))=>(![X776:$i, X777:$i]:((~(subset @ X776 @ X777)=>((X776)!=(X777))))=>(![X778:$i, X779:$i, X780:$i]:(((in @ X780 @ X778)=>(~(in @ X780 @ X779)=>((X778)!=(X779)))))=>(![X781:$i]:((subset @ X781 @ X781))=>(![X782:$i, X783:$i, X784:$i]:(((subset @ X782 @ X783)=>((subset @ X783 @ X784)=>(subset @ X782 @ X784))))=>(![X785:$i, X786:$i]:((subset @ X786 @ (setadjoin @ X785 @ X786)))=>(![X787:$i, X788:$i, X789:$i]:(((subset @ X787 @ X789)=>(subset @ X787 @ (setadjoin @ X788 @ X789))))=>(![X790:$i, X791:$i]:(((subset @ X790 @ X791)=>(in @ X790 @ (powerset @ X791))))=>(![X792:$i, X793:$i]:(((subset @ X792 @ X793)=>((subset @ X793 @ X792)=>((X792)=(X793)))))=>(![X794:$i]:(((subset @ X794 @ emptyset)=>((X794)=(emptyset))))=>(![X795:$i, X796:$i]:(((subset @ X796 @ X795)=>(in @ X796 @ 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emptyset)))=>((X999)=(X1001))))=>(![X1003:$i, X1004:$i, X1005:$i, X1006:$i]:((((setadjoin @ (setadjoin @ X1003 @ emptyset) @ (setadjoin @ (setadjoin @ X1003 @ (setadjoin @ X1004 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1005 @ emptyset) @ (setadjoin @ (setadjoin @ X1005 @ (setadjoin @ X1006 @ emptyset)) @ emptyset)))=>((X1003)=(X1005))))=>(![X1007:$i, X1008:$i]:((((X1007)=(X1008))=>((setadjoin @ X1007 @ (setadjoin @ X1008 @ emptyset))=(setadjoin @ X1007 @ emptyset))))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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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)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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_197, upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), c_0_198]), c_0_199]), setunionI]), c_0_200]), powersetE]), c_0_201]), emptyInPowerset]), setunionE2]), emptyinPowerset]), setunionsingleton1]), powersetI]), setunionsingleton2]), c_0_202]), setunionsingleton]), setadjoinOr]), c_0_203]), c_0_204]), setunionE]), c_0_205]), c_0_206]), singletonsuniq]), setukpairinjL1]), c_0_207]), c_0_208]), c_0_209]), cartprodfstin]), setukpairinjL2]), c_0_210]), setukpairinjR11]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), c_0_211]), c_0_212]), subPowSU]), upairsetE]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_213]), upairsetIR]), upairsetIL]), quantDeMorgan4]), inCongP]), c_0_214]), c_0_215]), c_0_216]), notdallE]), notdexE]), prop2setI]), in__Cong]), omega__Cong]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_217]), c_0_218]), c_0_219]), emptysetsubset]), subsetI2]), eqimpsubset1]), eqimpsubset2]), subsetI1]), c_0_220]), c_0_221]), subsetE]), setadjoinSub]), subsetTrans]), subsetRefl]), notequalI2]), notequalI1]), notsubsetI]), subsetE2]), setadjoinSub2]), powersetsubset]), inPowerset]), powersetE1]), powersetI1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), c_0_222]), binunionLsub]), binunionE]), binunionEcases]), binunionIR]), upairset2IR]), binunionIL]), c_0_223]), binunionRsub]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectI]), disjointsetsI1]), setminusER]), setminusEL]), setminusI]), bs114d]), binintersectSubset1]), binintersectSubset4]), binintersectRsub]), setminusSubset2]), symdiffE]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusERneg]), symdiffI1]), c_0_224]), setukpairIR]), setukpairIL]), secondinupair]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), c_0_225]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_226]), c_0_227]), c_0_228]), c_0_229]), noeltsimpempty]), emptyI]), setext]), c_0_230]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_231]), c_0_232]), c_0_233]), c_0_234]), c_0_235]), wellorderingAx]), foundationAx]), c_0_236]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_237])).
% 3.98/1.25 thf(c_0_239, negated_conjecture, ![X1009:$i, X1010:$i, X1012:$i, X1013:$i, X1014:$i, X1015:$i, X1016:$i, X1017:$i, X1018:$i, X1019:$i, X1020:$i, X1022:$i, X1023:$i, X1025:$i, X1026:$i, X1027:$i, X1028:$i, X1029:$i, X1031:$i, X1032:$i > $i > $o, X1033:$i, X1035:$i, X1038:$i, X1040:$i, X1041:$i, X1042:$i, X1043:$i, X1045:$i, X1046:$i > $o, X1047:$i, X1049:$i, X1050:$i > $o, X1051:$i, X1052:$i, X1053:$i > $o, X1054:$i, X1055:$i, X1056:$i > $o, X1057:$i, X1058:$i > $o, X1059:$i, X1062:$i, X1063:$o, X1064:$i, X1065:$i, X1066:$o, X1067:$i, X1068:$i, X1069:$i > $o, X1070:$i, X1073:$i, X1074:$i, X1077:$i, X1079:$i, X1081:$i, X1082:$i > $o, X1083:$i, X1084:$i, X1086:$i, X1087:$i > $o, X1088:$i, X1089:$i, X1090:$i, X1091:$i, X1092:$i, X1093:$i, X1094:$i, X1095:$i, X1096:$i, X1097:$i, X1098:$i, X1099:$o, X1100:$i, X1101:$i, X1102:$i, X1103:$i, X1104:$i, X1105:$i, X1107:$i, X1108:$i, X1109:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1114:$i, X1115:$i, X1116:$i, X1117:$o, X1119:$i, X1120:$i, X1121:$i > $o, X1122:$i, X1125:$i, X1126:$i, X1127:$i, X1129:$i, X1130:$i, X1131:$i, X1132:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i > $o, X1146:$i, X1147:$i > $o, X1148:$i, X1149:$i, X1150:$i > $o, X1151:$i, X1153:$i, X1154:$i > $o, X1156:$i, X1157:$i, X1158:$i > $o, X1160:$i, X1161:$i, X1162:$i > $o, X1163:$i, X1165:$o, X1166:$i, X1167:$i > $o, X1169:$i, X1170:$i, X1171:$i > $o, X1172:$i, X1174:$i > $o, X1175:$i, X1178:$i, X1179:$i > $o, X1180:$i, X1184:$i, X1185:$i > $o, X1186:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i, X1198:$i > $o, X1199:$i, X1201:$i, X1202:$i, X1203:$i > $o, X1204:$i > $o, X1207:$i, X1210:$i, X1211:$i, X1214:$i, X1215:$i, X1216:$i, X1217:$i, X1218:$i, X1219:$i, X1220:$i, X1221:$i, X1222:$i, X1223:$i > $o, X1224:$i, X1226:$i, X1227:$i, X1228:$i > $o, X1229:$i > $o, X1232:$i, X1234:$i, X1236:$i, X1237:$i, X1238:$i > $o, X1239:$i > $o, X1242:$i, X1243:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i, X1252:$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:$i, X1280:$i, X1281:$i, X1282:$i, X1283:$i, X1284:$i, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$i > $o, X1290:$i, X1291:$i > $o, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$o, X1304:$i, X1305:$i, X1306:$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, X1332:$i, X1333:$i, X1334:$i, X1335:$i, X1336:$i, X1337:$i, X1338:$i, X1339:$i, X1340:$i, X1341:$i, X1342:$i, X1343:$i, X1344:$i, X1345:$i, X1346:$i, X1347:$i, X1348:$i, X1349:$i, X1350:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i, X1356:$i, X1357:$i, X1358:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i, X1365:$i, X1366:$i, X1367:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$o, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i, X1381:$i, X1382:$i, X1383:$i, X1384:$i, X1385:$i, X1386:$i, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1394:$i, X1395:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i, X1403:$i, X1404:$i, X1405:$i, X1406:$i, X1407:$i, X1408:$i, X1409:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1417:$i, X1418:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1423:$i, X1424:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$i, X1432:$i, X1433:$i, X1434:$i, X1437:$i, X1438:$i, X1439:$i, X1442:$i, X1443:$i, X1445:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$i > $o, X1452:$i, X1454:$i, X1455:$i > $o, X1456:$i, X1458:$i, X1459:$i > $o, X1460:$i, X1463:$i, X1464:$i > $o, X1467:$i, X1469:$i, X1470:$i, X1471:$i, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$i, X1483:$i, X1484:$i, X1485:$i, X1486:$i, X1487:$i, X1488:$i, X1489:$i, X1490:$i, X1491:$i, X1492:$i, X1493:$i, X1494:$i]:((((~(in @ (esk1_2 @ X1009 @ X1010) @ X1009)|~(in @ (esk1_2 @ X1009 @ X1010) @ X1010)|((X1009)=(X1010)))&((in @ (esk1_2 @ X1009 @ X1010) @ X1009)|(in @ (esk1_2 @ X1009 @ X1010) @ X1010)|((X1009)=(X1010))))&(~(in @ X1012 @ emptyset)&(((~(in @ X1015 @ (setadjoin @ X1013 @ X1014))|(((X1015)=(X1013))|(in @ X1015 @ X1014)))&((((X1015)!=(X1013))|(in @ X1015 @ (setadjoin @ X1013 @ X1014)))&(~(in @ X1015 @ X1014)|(in @ X1015 @ (setadjoin @ X1013 @ X1014)))))&(((~(in @ X1017 @ (powerset @ X1016))|(~(in @ X1018 @ X1017)|(in @ X1018 @ X1016)))&(((in @ (esk2_2 @ X1019 @ X1020) @ X1020)|(in @ X1020 @ (powerset @ X1019)))&(~(in @ (esk2_2 @ X1019 @ X1020) @ X1019)|(in @ X1020 @ (powerset @ X1019)))))&(((((in @ X1023 @ (esk3_2 @ X1022 @ X1023))|~(in @ X1023 @ (setunion @ X1022)))&((in @ (esk3_2 @ X1022 @ X1023) @ X1022)|~(in @ X1023 @ (setunion @ X1022))))&(~(in @ X1026 @ X1027)|~(in @ X1027 @ X1025)|(in @ X1026 @ (setunion @ X1025))))&((in @ emptyset @ omega)&((~(in @ X1028 @ omega)|(in @ (setadjoin @ X1028 @ X1028) @ omega))&(((((in @ (esk4_1 @ X1029) @ omega)|~(in @ emptyset @ X1029)|(~(in @ X1031 @ omega)|(in @ X1031 @ X1029)))&((in @ (esk4_1 @ X1029) @ X1029)|~(in @ emptyset @ X1029)|(~(in @ X1031 @ omega)|(in @ X1031 @ X1029))))&(~(in @ (setadjoin @ (esk4_1 @ X1029) @ (esk4_1 @ X1029)) @ X1029)|~(in @ emptyset @ X1029)|(~(in @ X1031 @ omega)|(in @ X1031 @ X1029))))&((((((in @ (esk8_3 @ X1032 @ X1033 @ X1038) @ X1033)|~(in @ X1038 @ (esk7_2 @ X1032 @ X1033))|(in @ (esk5_2 @ X1032 @ X1033) @ X1033))&((X1032 @ (esk8_3 @ X1032 @ X1033 @ X1038) @ X1038)|~(in @ X1038 @ (esk7_2 @ X1032 @ X1033))|(in @ (esk5_2 @ X1032 @ X1033) @ X1033)))&(~(in @ X1041 @ X1033)|~(X1032 @ X1041 @ X1040)|(in @ X1040 @ (esk7_2 @ X1032 @ X1033))|(in @ (esk5_2 @ X1032 @ X1033) @ X1033)))&(((((in @ (esk8_3 @ X1032 @ X1033 @ X1038) @ X1033)|~(in @ X1038 @ (esk7_2 @ X1032 @ X1033))|((X1032 @ (esk5_2 @ X1032 @ X1033) @ (esk6_3 @ X1032 @ X1033 @ X1035))|~(X1032 @ (esk5_2 @ X1032 @ X1033) @ X1035)))&((X1032 @ (esk8_3 @ X1032 @ X1033 @ X1038) @ X1038)|~(in @ X1038 @ (esk7_2 @ X1032 @ X1033))|((X1032 @ (esk5_2 @ X1032 @ X1033) @ (esk6_3 @ X1032 @ X1033 @ X1035))|~(X1032 @ (esk5_2 @ X1032 @ X1033) @ X1035))))&(~(in @ X1041 @ X1033)|~(X1032 @ X1041 @ X1040)|(in @ X1040 @ (esk7_2 @ X1032 @ X1033))|((X1032 @ (esk5_2 @ X1032 @ X1033) @ (esk6_3 @ X1032 @ X1033 @ X1035))|~(X1032 @ (esk5_2 @ X1032 @ X1033) @ X1035))))&((((in @ (esk8_3 @ X1032 @ X1033 @ X1038) @ X1033)|~(in @ X1038 @ (esk7_2 @ X1032 @ X1033))|(((X1035)!=(esk6_3 @ X1032 @ X1033 @ X1035))|~(X1032 @ (esk5_2 @ X1032 @ X1033) @ X1035)))&((X1032 @ (esk8_3 @ X1032 @ X1033 @ X1038) @ X1038)|~(in @ X1038 @ (esk7_2 @ X1032 @ X1033))|(((X1035)!=(esk6_3 @ X1032 @ X1033 @ X1035))|~(X1032 @ (esk5_2 @ X1032 @ X1033) @ X1035))))&(~(in @ X1041 @ X1033)|~(X1032 @ X1041 @ X1040)|(in @ X1040 @ (esk7_2 @ X1032 @ X1033))|(((X1035)!=(esk6_3 @ X1032 @ X1033 @ X1035))|~(X1032 @ (esk5_2 @ X1032 @ X1033) @ X1035))))))&((((in @ (esk9_1 @ X1042) @ X1042)|~(in @ X1043 @ X1042))&(~(in @ X1045 @ (esk9_1 @ X1042))|~(in @ X1045 @ X1042)|~(in @ X1043 @ X1042)))&((epred1_0)&((((X1046 @ (esk10_2 @ X1046 @ X1047))|~(X1046 @ X1047)|(X1046 @ (descr @ X1046)))&(((X1047)!=(esk10_2 @ X1046 @ X1047))|~(X1046 @ X1047)|(X1046 @ (descr @ X1046))))&((~(in @ X1051 @ X1049)|(~(X1050 @ X1051)|(in @ X1051 @ (dsetconstr @ X1049 @ X1050))))&((~(in @ X1054 @ (dsetconstr @ X1052 @ X1053))|(in @ X1054 @ X1052))&((~(in @ X1057 @ (dsetconstr @ X1055 @ X1056))|(X1056 @ X1057))&(((((X1058 @ (esk12_1 @ X1058))|((X1058 @ (esk11_2 @ X1058 @ X1059))|~(X1058 @ X1059)))&(~(X1058 @ X1062)|((esk12_1 @ 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X1448 @ X1449)=(setadjoin @ (esk66_2 @ X1448 @ X1449) @ emptyset))|(~(in @ X1452 @ X1448)|~(X1449 @ X1452))|(X1449 @ (esk64_2 @ X1448 @ X1449))))&((((in @ (esk66_2 @ X1448 @ X1449) @ (dsetconstr @ X1448 @ X1449))|(~(in @ X1452 @ X1448)|~(X1449 @ X1452))|(X1449 @ (esk65_2 @ X1448 @ X1449)))&(((dsetconstr @ X1448 @ X1449)=(setadjoin @ (esk66_2 @ X1448 @ X1449) @ emptyset))|(~(in @ X1452 @ X1448)|~(X1449 @ X1452))|(X1449 @ (esk65_2 @ X1448 @ X1449))))&(((in @ (esk66_2 @ X1448 @ X1449) @ (dsetconstr @ X1448 @ X1449))|(~(in @ X1452 @ X1448)|~(X1449 @ X1452))|((esk64_2 @ X1448 @ X1449)!=(esk65_2 @ X1448 @ X1449)))&(((dsetconstr @ X1448 @ X1449)=(setadjoin @ (esk66_2 @ X1448 @ X1449) @ emptyset))|(~(in @ X1452 @ X1448)|~(X1449 @ X1452))|((esk64_2 @ X1448 @ X1449)!=(esk65_2 @ X1448 @ X1449))))))))&((((in @ (esk67_2 @ X1454 @ X1455) @ X1454)|(~(in @ X1456 @ (dsetconstr @ X1454 @ X1455))|((dsetconstr @ X1454 @ X1455)!=(setadjoin @ X1456 @ emptyset))))&((X1455 @ (esk67_2 @ X1454 @ X1455))|(~(in @ X1456 @ (dsetconstr @ X1454 @ X1455))|((dsetconstr @ X1454 @ X1455)!=(setadjoin @ X1456 @ emptyset)))))&(((((in @ (esk69_3 @ X1458 @ X1459 @ X1460) @ (dsetconstr @ X1458 @ X1459))|(in @ (esk68_3 @ X1458 @ X1459 @ X1460) @ X1458)|~(X1459 @ X1460)|~(in @ X1460 @ X1458))&(((dsetconstr @ X1458 @ X1459)=(setadjoin @ (esk69_3 @ X1458 @ X1459 @ X1460) @ emptyset))|(in @ (esk68_3 @ X1458 @ X1459 @ X1460) @ X1458)|~(X1459 @ X1460)|~(in @ X1460 @ X1458)))&((((in @ (esk69_3 @ X1458 @ X1459 @ X1460) @ (dsetconstr @ X1458 @ X1459))|(X1459 @ (esk68_3 @ X1458 @ X1459 @ X1460))|~(X1459 @ X1460)|~(in @ X1460 @ X1458))&(((dsetconstr @ X1458 @ X1459)=(setadjoin @ (esk69_3 @ X1458 @ X1459 @ X1460) @ emptyset))|(X1459 @ (esk68_3 @ X1458 @ X1459 @ X1460))|~(X1459 @ X1460)|~(in @ X1460 @ X1458)))&(((in @ (esk69_3 @ X1458 @ X1459 @ X1460) @ (dsetconstr @ X1458 @ X1459))|((esk68_3 @ X1458 @ X1459 @ X1460)!=(X1460))|~(X1459 @ X1460)|~(in @ X1460 @ X1458))&(((dsetconstr @ X1458 @ X1459)=(setadjoin @ (esk69_3 @ X1458 @ X1459 @ X1460) @ emptyset))|((esk68_3 @ X1458 @ X1459 @ X1460)!=(X1460))|~(X1459 @ X1460)|~(in @ X1460 @ X1458)))))&(((((in @ (esk72_2 @ X1463 @ X1464) @ (dsetconstr @ X1463 @ X1464))|(~(in @ X1467 @ X1463)|~(X1464 @ X1467))|(in @ (esk70_2 @ X1463 @ X1464) @ X1463))&(((dsetconstr @ X1463 @ X1464)=(setadjoin @ (esk72_2 @ X1463 @ X1464) @ emptyset))|(~(in @ X1467 @ X1463)|~(X1464 @ X1467))|(in @ (esk70_2 @ X1463 @ X1464) @ X1463)))&((((in @ (esk72_2 @ X1463 @ X1464) @ (dsetconstr @ X1463 @ X1464))|(~(in @ X1467 @ X1463)|~(X1464 @ X1467))|(in @ (esk71_2 @ X1463 @ X1464) @ X1463))&(((dsetconstr @ X1463 @ X1464)=(setadjoin @ (esk72_2 @ X1463 @ X1464) @ emptyset))|(~(in @ X1467 @ X1463)|~(X1464 @ X1467))|(in @ (esk71_2 @ X1463 @ X1464) @ X1463)))&((((in @ (esk72_2 @ X1463 @ X1464) @ (dsetconstr @ X1463 @ X1464))|(~(in @ X1467 @ X1463)|~(X1464 @ X1467))|(X1464 @ (esk70_2 @ X1463 @ X1464)))&(((dsetconstr @ X1463 @ X1464)=(setadjoin @ (esk72_2 @ X1463 @ X1464) @ emptyset))|(~(in @ X1467 @ X1463)|~(X1464 @ X1467))|(X1464 @ (esk70_2 @ X1463 @ X1464))))&((((in @ (esk72_2 @ X1463 @ X1464) @ (dsetconstr @ X1463 @ X1464))|(~(in @ X1467 @ X1463)|~(X1464 @ X1467))|(X1464 @ (esk71_2 @ X1463 @ X1464)))&(((dsetconstr @ X1463 @ X1464)=(setadjoin @ (esk72_2 @ X1463 @ X1464) @ emptyset))|(~(in @ X1467 @ X1463)|~(X1464 @ X1467))|(X1464 @ (esk71_2 @ X1463 @ X1464))))&(((in @ (esk72_2 @ X1463 @ X1464) @ (dsetconstr @ X1463 @ X1464))|(~(in @ X1467 @ X1463)|~(X1464 @ X1467))|((esk70_2 @ X1463 @ X1464)!=(esk71_2 @ X1463 @ X1464)))&(((dsetconstr @ X1463 @ X1464)=(setadjoin @ (esk72_2 @ X1463 @ X1464) @ emptyset))|(~(in @ X1467 @ X1463)|~(X1464 @ X1467))|((esk70_2 @ X1463 @ X1464)!=(esk71_2 @ X1463 @ X1464))))))))&((((setadjoin @ X1469 @ emptyset)!=(setadjoin @ X1470 @ emptyset))|((X1469)=(X1470)))&((~(in @ (setadjoin @ X1473 @ emptyset) @ (setadjoin @ (setadjoin @ X1471 @ emptyset) @ (setadjoin @ (setadjoin @ X1471 @ (setadjoin @ X1472 @ emptyset)) @ emptyset)))|((X1471)=(X1473)))&((((in @ (esk73_1 @ X1474) @ (dsetconstr @ (setunion @ X1474) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1474)))))|(~(in @ X1475 @ (setunion @ X1474))|(~(in @ X1476 @ (setunion @ X1474))|((X1474)!=(setadjoin @ (setadjoin @ X1475 @ emptyset) @ (setadjoin @ (setadjoin @ X1475 @ (setadjoin @ X1476 @ emptyset)) @ emptyset))))))&(((dsetconstr @ (setunion @ X1474) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1474))))=(setadjoin @ (esk73_1 @ X1474) @ emptyset))|(~(in @ X1475 @ (setunion @ X1474))|(~(in @ X1476 @ (setunion @ X1474))|((X1474)!=(setadjoin @ (setadjoin @ X1475 @ emptyset) @ (setadjoin @ (setadjoin @ X1475 @ (setadjoin @ X1476 @ emptyset)) @ emptyset)))))))&((~(in @ X1479 @ X1478)|((X1478)!=(setadjoin @ X1479 @ emptyset))|(in @ (setunion @ X1478) @ X1478))&(((kfst @ (setadjoin @ (setadjoin @ X1480 @ emptyset) @ (setadjoin @ (setadjoin @ X1480 @ (setadjoin @ X1481 @ emptyset)) @ emptyset)))=(X1480))&((~(in @ X1484 @ (cartprod @ X1482 @ X1483))|(in @ (kfst @ X1484) @ X1482))&((((setadjoin @ (setadjoin @ X1485 @ emptyset) @ (setadjoin @ (setadjoin @ X1485 @ (setadjoin @ X1486 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1487 @ emptyset) @ (setadjoin @ (setadjoin @ X1487 @ (setadjoin @ X1488 @ emptyset)) @ emptyset)))|((X1485)=(X1487)))&((((setadjoin @ (setadjoin @ X1489 @ emptyset) @ (setadjoin @ (setadjoin @ X1489 @ (setadjoin @ X1490 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1491 @ emptyset) @ (setadjoin @ (setadjoin @ X1491 @ (setadjoin @ X1492 @ emptyset)) @ emptyset)))|((X1489)=(X1491)))&((((X1493)!=(X1494))|((setadjoin @ X1493 @ (setadjoin @ X1494 @ emptyset))=(setadjoin @ X1493 @ emptyset)))&(((esk74_0)=(esk75_0))&((setadjoin @ (setadjoin @ esk74_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk74_0 @ (setadjoin @ esk75_0 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ esk74_0 @ emptyset) @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_238])])])])])])])).
% 3.98/1.25 thf(c_0_240, negated_conjecture, ![X2:$i, X3:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))|((X2)!=(X3)))), inference(split_conjunct,[status(thm)],[c_0_239])).
% 3.98/1.25 thf(c_0_241, negated_conjecture, ((setadjoin @ (setadjoin @ esk74_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk74_0 @ (setadjoin @ esk75_0 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ esk74_0 @ emptyset) @ emptyset)), inference(split_conjunct,[status(thm)],[c_0_239])).
% 3.98/1.25 thf(c_0_242, negated_conjecture, ((esk74_0)=(esk75_0)), inference(split_conjunct,[status(thm)],[c_0_239])).
% 3.98/1.25 thf(c_0_243, negated_conjecture, ![X2:$i]:(((setadjoin @ X2 @ (setadjoin @ X2 @ emptyset))=(setadjoin @ X2 @ emptyset))), inference(er,[status(thm)],[c_0_240])).
% 3.98/1.25 thf(c_0_244, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_241, c_0_242]), c_0_243]), c_0_243])]), ['proof']).
% 3.98/1.25 % SZS output end CNFRefutation
% 3.98/1.25 % Parsed axioms : 369
% 3.98/1.25 % Removed by relevancy pruning/SinE : 197
% 3.98/1.25 % Initial clauses : 324
% 3.98/1.25 % Removed in clause preprocessing : 24
% 3.98/1.25 % Initial clauses in saturation : 300
% 3.98/1.25 % Processed clauses : 1837
% 3.98/1.25 % ...of these trivial : 14
% 3.98/1.25 % ...subsumed : 1221
% 3.98/1.25 % ...remaining for further processing : 601
% 3.98/1.25 % Other redundant clauses eliminated : 24
% 3.98/1.25 % Clauses deleted for lack of memory : 0
% 3.98/1.25 % Backward-subsumed : 1
% 3.98/1.25 % Backward-rewritten : 12
% 3.98/1.25 % Generated clauses : 21284
% 3.98/1.25 % ...of the previous two non-redundant : 18744
% 3.98/1.25 % ...aggressively subsumed : 0
% 3.98/1.25 % Contextual simplify-reflections : 1
% 3.98/1.25 % Paramodulations : 21257
% 3.98/1.25 % Factorizations : 2
% 3.98/1.25 % NegExts : 0
% 3.98/1.25 % Equation resolutions : 25
% 3.98/1.25 % Disequality decompositions : 0
% 3.98/1.25 % Total rewrite steps : 6860
% 3.98/1.25 % ...of those cached : 6611
% 3.98/1.25 % Propositional unsat checks : 0
% 3.98/1.25 % Propositional check models : 0
% 3.98/1.25 % Propositional check unsatisfiable : 0
% 3.98/1.25 % Propositional clauses : 0
% 3.98/1.25 % Propositional clauses after purity: 0
% 3.98/1.25 % Propositional unsat core size : 0
% 3.98/1.25 % Propositional preprocessing time : 0.000
% 3.98/1.25 % Propositional encoding time : 0.000
% 3.98/1.25 % Propositional solver time : 0.000
% 3.98/1.25 % Success case prop preproc time : 0.000
% 3.98/1.25 % Success case prop encoding time : 0.000
% 3.98/1.25 % Success case prop solver time : 0.000
% 3.98/1.25 % Current number of processed clauses : 578
% 3.98/1.25 % Positive orientable unit clauses : 195
% 3.98/1.25 % Positive unorientable unit clauses: 0
% 3.98/1.25 % Negative unit clauses : 2
% 3.98/1.25 % Non-unit-clauses : 381
% 3.98/1.25 % Current number of unprocessed clauses: 17074
% 3.98/1.25 % ...number of literals in the above : 60084
% 3.98/1.25 % Current number of archived formulas : 0
% 3.98/1.25 % Current number of archived clauses : 13
% 3.98/1.25 % Clause-clause subsumption calls (NU) : 13581
% 3.98/1.25 % Rec. Clause-clause subsumption calls : 8213
% 3.98/1.25 % Non-unit clause-clause subsumptions : 803
% 3.98/1.25 % Unit Clause-clause subsumption calls : 451
% 3.98/1.25 % Rewrite failures with RHS unbound : 0
% 3.98/1.25 % BW rewrite match attempts : 951
% 3.98/1.25 % BW rewrite match successes : 10
% 3.98/1.25 % Condensation attempts : 0
% 3.98/1.25 % Condensation successes : 0
% 3.98/1.25 % Termbank termtop insertions : 414007
% 3.98/1.25 % Search garbage collected termcells : 16472
% 3.98/1.25
% 3.98/1.25 % -------------------------------------------------
% 3.98/1.25 % User time : 0.741 s
% 3.98/1.25 % System time : 0.043 s
% 3.98/1.25 % Total time : 0.783 s
% 3.98/1.25 % Maximum resident set size: 7840 pages
% 3.98/1.25
% 3.98/1.25 % -------------------------------------------------
% 3.98/1.25 % User time : 0.755 s
% 3.98/1.25 % System time : 0.057 s
% 3.98/1.25 % Total time : 0.811 s
% 3.98/1.25 % Maximum resident set size: 5376 pages
% 3.98/1.25 % E exiting
%------------------------------------------------------------------------------