%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU748^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:25:28 AM UTC 2026
% Result : Theorem 1.35s 0.54s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU748^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n019.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:20:42 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.22/0.29 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p
% 1.35/0.54 % Version: 3.5.1-ho
% 1.35/0.54 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.35/0.54 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.35/0.54 % Starting ehoh_best5 with 300s (1) cores
% 1.35/0.54 % Starting almost_fo_3_lam with 300s (1) cores
% 1.35/0.54 % Starting new_bool_5 with 300s (1) cores
% 1.35/0.54 % Starting pre_casc_3 with 300s (1) cores
% 1.35/0.54 % Starting ho_unfolding_8 with 300s (1) cores
% 1.35/0.54 % Starting new_ho_10_cnf2 with 300s (1) cores
% 1.35/0.54 % Starting new_bool_3 with 300s (1) cores
% 1.35/0.54 % Starting new_ho_5 with 300s (1) cores
% 1.35/0.54 % pre_casc_3 with pid 846329 completed with status 9
% 1.35/0.54 % new_ho_5 with pid 846333 completed with status 9
% 1.35/0.54 % new_bool_5 with pid 846328 completed with status 0
% 1.35/0.54 % Result found by new_bool_5
% 1.35/0.54 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.35/0.54 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.35/0.54 % Starting ehoh_best5 with 300s (1) cores
% 1.35/0.54 % Starting almost_fo_3_lam with 300s (1) cores
% 1.35/0.54 % Starting new_bool_5 with 300s (1) cores
% 1.35/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 1.35/0.54 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 1.35/0.54 % Search class: HGHSM-FSLM32-MHFMMSBN
% 1.35/0.54 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 1.35/0.54 % Starting SubtermCWHack with 28s (1) cores
% 1.35/0.54 % SubtermCWHack with pid 846355 completed with status 0
% 1.35/0.54 % Result found by SubtermCWHack
% 1.35/0.54 % Preprocessing class: HSLMSLSSLLLCHFA.
% 1.35/0.54 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.35/0.54 % Starting ehoh_best5 with 300s (1) cores
% 1.35/0.54 % Starting almost_fo_3_lam with 300s (1) cores
% 1.35/0.54 % Starting new_bool_5 with 300s (1) cores
% 1.35/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 1.35/0.54 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 1.35/0.54 % Search class: HGHSM-FSLM32-MHFMMSBN
% 1.35/0.54 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 1.35/0.54 % Starting SubtermCWHack with 28s (1) cores
% 1.35/0.54 % Preprocessing time : 0.008 s
% 1.35/0.54
% 1.35/0.54 % Proof found!
% 1.35/0.54 % SZS status Theorem
% 1.35/0.54 % SZS output start CNFRefutation
% 1.35/0.54 thf(decl_23, type, in: $i > $i > $o).
% 1.35/0.54 thf(decl_24, type, exu: ($i > $o) > $o).
% 1.35/0.54 thf(decl_25, type, setextAx: $o).
% 1.35/0.54 thf(decl_26, type, emptyset: $i).
% 1.35/0.54 thf(decl_27, type, emptysetAx: $o).
% 1.35/0.54 thf(decl_28, type, setadjoin: $i > $i > $i).
% 1.35/0.54 thf(decl_29, type, setadjoinAx: $o).
% 1.35/0.54 thf(decl_30, type, powerset: $i > $i).
% 1.35/0.54 thf(decl_31, type, powersetAx: $o).
% 1.35/0.54 thf(decl_32, type, setunion: $i > $i).
% 1.35/0.54 thf(decl_33, type, setunionAx: $o).
% 1.35/0.54 thf(decl_34, type, omega: $i).
% 1.35/0.54 thf(decl_35, type, omega0Ax: $o).
% 1.35/0.54 thf(decl_36, type, omegaSAx: $o).
% 1.35/0.54 thf(decl_37, type, omegaIndAx: $o).
% 1.35/0.54 thf(decl_38, type, replAx: $o).
% 1.35/0.54 thf(decl_39, type, foundationAx: $o).
% 1.35/0.54 thf(decl_40, type, wellorderingAx: $o).
% 1.35/0.54 thf(decl_41, type, descr: ($i > $o) > $i).
% 1.35/0.54 thf(decl_42, type, descrp: $o).
% 1.35/0.54 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 1.35/0.54 thf(decl_44, type, dsetconstrI: $o).
% 1.35/0.54 thf(decl_45, type, dsetconstrEL: $o).
% 1.35/0.54 thf(decl_46, type, dsetconstrER: $o).
% 1.35/0.54 thf(decl_47, type, exuE1: $o).
% 1.35/0.54 thf(decl_48, type, prop2set: $o > $i).
% 1.35/0.54 thf(decl_49, type, prop2setE: $o).
% 1.35/0.54 thf(decl_50, type, emptysetE: $o).
% 1.35/0.54 thf(decl_51, type, emptysetimpfalse: $o).
% 1.35/0.54 thf(decl_52, type, notinemptyset: $o).
% 1.35/0.54 thf(decl_53, type, exuE3e: $o).
% 1.35/0.54 thf(decl_54, type, setext: $o).
% 1.35/0.54 thf(decl_55, type, emptyI: $o).
% 1.35/0.54 thf(decl_56, type, noeltsimpempty: $o).
% 1.35/0.54 thf(decl_57, type, setbeta: $o).
% 1.35/0.54 thf(decl_58, type, nonempty: $i > $o).
% 1.35/0.54 thf(decl_59, type, nonemptyE1: $o).
% 1.35/0.54 thf(decl_60, type, nonemptyI: $o).
% 1.35/0.54 thf(decl_61, type, nonemptyI1: $o).
% 1.35/0.54 thf(decl_62, type, setadjoinIL: $o).
% 1.35/0.54 thf(decl_63, type, emptyinunitempty: $o).
% 1.35/0.54 thf(decl_64, type, setadjoinIR: $o).
% 1.35/0.54 thf(decl_65, type, setadjoinE: $o).
% 1.35/0.54 thf(decl_66, type, setadjoinOr: $o).
% 1.35/0.54 thf(decl_67, type, setoftrueEq: $o).
% 1.35/0.54 thf(decl_68, type, powersetI: $o).
% 1.35/0.54 thf(decl_69, type, emptyinPowerset: $o).
% 1.35/0.54 thf(decl_70, type, emptyInPowerset: $o).
% 1.35/0.54 thf(decl_71, type, powersetE: $o).
% 1.35/0.54 thf(decl_72, type, setunionI: $o).
% 1.35/0.54 thf(decl_73, type, setunionE: $o).
% 1.35/0.54 thf(decl_74, type, subPowSU: $o).
% 1.35/0.54 thf(decl_75, type, exuE2: $o).
% 1.35/0.54 thf(decl_76, type, nonemptyImpWitness: $o).
% 1.35/0.54 thf(decl_77, type, uniqinunit: $o).
% 1.35/0.54 thf(decl_78, type, notinsingleton: $o).
% 1.35/0.54 thf(decl_79, type, eqinunit: $o).
% 1.35/0.54 thf(decl_80, type, singletonsswitch: $o).
% 1.35/0.54 thf(decl_81, type, upairsetE: $o).
% 1.35/0.54 thf(decl_82, type, upairsetIL: $o).
% 1.35/0.54 thf(decl_83, type, upairsetIR: $o).
% 1.35/0.54 thf(decl_84, type, emptyE1: $o).
% 1.35/0.54 thf(decl_85, type, vacuousDall: $o).
% 1.35/0.54 thf(decl_86, type, quantDeMorgan1: $o).
% 1.35/0.54 thf(decl_87, type, quantDeMorgan2: $o).
% 1.35/0.54 thf(decl_88, type, quantDeMorgan3: $o).
% 1.35/0.54 thf(decl_89, type, quantDeMorgan4: $o).
% 1.35/0.54 thf(decl_90, type, prop2setI: $o).
% 1.35/0.54 thf(decl_92, type, prop2set2propI: $o).
% 1.35/0.54 thf(decl_93, type, notdexE: $o).
% 1.35/0.54 thf(decl_94, type, notdallE: $o).
% 1.35/0.54 thf(decl_95, type, exuI1: $o).
% 1.35/0.54 thf(decl_96, type, exuI3: $o).
% 1.35/0.54 thf(decl_97, type, exuI2: $o).
% 1.35/0.54 thf(decl_98, type, inCongP: $o).
% 1.35/0.54 thf(decl_99, type, in__Cong: $o).
% 1.35/0.54 thf(decl_100, type, exuE3u: $o).
% 1.35/0.54 thf(decl_101, type, exu__Cong: $o).
% 1.35/0.54 thf(decl_102, type, emptyset__Cong: $o).
% 1.35/0.54 thf(decl_103, type, setadjoin__Cong: $o).
% 1.35/0.54 thf(decl_104, type, powerset__Cong: $o).
% 1.35/0.54 thf(decl_105, type, setunion__Cong: $o).
% 1.35/0.54 thf(decl_106, type, omega__Cong: $o).
% 1.35/0.54 thf(decl_107, type, exuEu: $o).
% 1.35/0.54 thf(decl_108, type, descr__Cong: $o).
% 1.35/0.54 thf(decl_109, type, dsetconstr__Cong: $o).
% 1.35/0.54 thf(decl_110, type, subset: $i > $i > $o).
% 1.35/0.54 thf(decl_113, type, subsetI1: $o).
% 1.35/0.54 thf(decl_114, type, eqimpsubset2: $o).
% 1.35/0.54 thf(decl_115, type, eqimpsubset1: $o).
% 1.35/0.54 thf(decl_116, type, subsetI2: $o).
% 1.35/0.54 thf(decl_117, type, emptysetsubset: $o).
% 1.35/0.54 thf(decl_118, type, subsetE: $o).
% 1.35/0.54 thf(decl_119, type, subsetE2: $o).
% 1.35/0.54 thf(decl_120, type, notsubsetI: $o).
% 1.35/0.54 thf(decl_121, type, notequalI1: $o).
% 1.35/0.54 thf(decl_122, type, notequalI2: $o).
% 1.35/0.54 thf(decl_123, type, subsetRefl: $o).
% 1.35/0.54 thf(decl_124, type, subsetTrans: $o).
% 1.35/0.54 thf(decl_125, type, setadjoinSub: $o).
% 1.35/0.54 thf(decl_126, type, setadjoinSub2: $o).
% 1.35/0.54 thf(decl_127, type, subset2powerset: $o).
% 1.35/0.54 thf(decl_128, type, setextsub: $o).
% 1.35/0.54 thf(decl_129, type, subsetemptysetimpeq: $o).
% 1.35/0.54 thf(decl_130, type, powersetI1: $o).
% 1.35/0.54 thf(decl_131, type, powersetE1: $o).
% 1.35/0.54 thf(decl_132, type, inPowerset: $o).
% 1.35/0.54 thf(decl_133, type, powersetsubset: $o).
% 1.35/0.54 thf(decl_134, type, sepInPowerset: $o).
% 1.35/0.54 thf(decl_135, type, sepSubset: $o).
% 1.35/0.54 thf(decl_136, type, binunion: $i > $i > $i).
% 1.35/0.54 thf(decl_137, type, binunionIL: $o).
% 1.35/0.54 thf(decl_138, type, upairset2IR: $o).
% 1.35/0.54 thf(decl_139, type, binunionIR: $o).
% 1.35/0.54 thf(decl_140, type, binunionEcases: $o).
% 1.35/0.54 thf(decl_141, type, binunionE: $o).
% 1.35/0.54 thf(decl_142, type, binunionLsub: $o).
% 1.35/0.54 thf(decl_143, type, binunionRsub: $o).
% 1.35/0.54 thf(decl_144, type, binintersect: $i > $i > $i).
% 1.35/0.54 thf(decl_145, type, binintersectI: $o).
% 1.35/0.54 thf(decl_146, type, binintersectSubset5: $o).
% 1.35/0.54 thf(decl_147, type, binintersectEL: $o).
% 1.35/0.54 thf(decl_148, type, binintersectLsub: $o).
% 1.35/0.54 thf(decl_149, type, binintersectSubset2: $o).
% 1.35/0.54 thf(decl_150, type, binintersectSubset3: $o).
% 1.35/0.54 thf(decl_151, type, binintersectER: $o).
% 1.35/0.54 thf(decl_152, type, disjointsetsI1: $o).
% 1.35/0.54 thf(decl_153, type, binintersectRsub: $o).
% 1.35/0.54 thf(decl_154, type, binintersectSubset4: $o).
% 1.35/0.54 thf(decl_155, type, binintersectSubset1: $o).
% 1.35/0.54 thf(decl_156, type, bs114d: $o).
% 1.35/0.54 thf(decl_158, type, setminus: $i > $i > $i).
% 1.35/0.54 thf(decl_159, type, setminusI: $o).
% 1.35/0.54 thf(decl_160, type, setminusEL: $o).
% 1.35/0.54 thf(decl_161, type, setminusER: $o).
% 1.35/0.54 thf(decl_162, type, setminusSubset2: $o).
% 1.35/0.54 thf(decl_163, type, setminusERneg: $o).
% 1.35/0.54 thf(decl_164, type, setminusELneg: $o).
% 1.35/0.54 thf(decl_165, type, setminusILneg: $o).
% 1.35/0.54 thf(decl_166, type, setminusIRneg: $o).
% 1.35/0.54 thf(decl_167, type, setminusLsub: $o).
% 1.35/0.54 thf(decl_168, type, setminusSubset1: $o).
% 1.35/0.54 thf(decl_169, type, symdiff: $i > $i > $i).
% 1.35/0.54 thf(decl_170, type, symdiffE: $o).
% 1.35/0.54 thf(decl_171, type, symdiffI1: $o).
% 1.35/0.54 thf(decl_172, type, symdiffI2: $o).
% 1.35/0.54 thf(decl_173, type, symdiffIneg1: $o).
% 1.35/0.54 thf(decl_174, type, symdiffIneg2: $o).
% 1.35/0.54 thf(decl_175, type, iskpair: $i > $o).
% 1.35/0.54 thf(decl_176, type, secondinupair: $o).
% 1.35/0.54 thf(decl_177, type, setukpairIL: $o).
% 1.35/0.54 thf(decl_178, type, setukpairIR: $o).
% 1.35/0.54 thf(decl_179, type, kpairiskpair: $o).
% 1.35/0.54 thf(decl_180, type, kpair: $i > $i > $i).
% 1.35/0.54 thf(decl_181, type, kpairp: $o).
% 1.35/0.54 thf(decl_182, type, cartprod: $i > $i > $i).
% 1.35/0.54 thf(decl_183, type, singletonsubset: $o).
% 1.35/0.54 thf(decl_184, type, singletoninpowerset: $o).
% 1.35/0.54 thf(decl_185, type, singletoninpowunion: $o).
% 1.35/0.54 thf(decl_186, type, upairset2E: $o).
% 1.35/0.54 thf(decl_187, type, upairsubunion: $o).
% 1.35/0.54 thf(decl_188, type, upairinpowunion: $o).
% 1.35/0.54 thf(decl_189, type, ubforcartprodlem1: $o).
% 1.35/0.54 thf(decl_190, type, ubforcartprodlem2: $o).
% 1.35/0.54 thf(decl_191, type, ubforcartprodlem3: $o).
% 1.35/0.54 thf(decl_192, type, cartprodpairin: $o).
% 1.35/0.54 thf(decl_193, type, cartprodmempair1: $o).
% 1.35/0.54 thf(decl_194, type, cartprodmempair: $o).
% 1.35/0.54 thf(decl_195, type, setunionE2: $o).
% 1.35/0.54 thf(decl_196, type, setunionsingleton1: $o).
% 1.35/0.54 thf(decl_197, type, setunionsingleton2: $o).
% 1.35/0.54 thf(decl_198, type, setunionsingleton: $o).
% 1.35/0.54 thf(decl_199, type, singleton: $i > $o).
% 1.35/0.54 thf(decl_200, type, singletonprop: $o).
% 1.35/0.54 thf(decl_201, type, ex1: $i > ($i > $o) > $o).
% 1.35/0.54 thf(decl_202, type, ex1E1: $o).
% 1.35/0.54 thf(decl_203, type, ex1I: $o).
% 1.35/0.54 thf(decl_204, type, ex1I2: $o).
% 1.35/0.54 thf(decl_205, type, singletonsuniq: $o).
% 1.35/0.54 thf(decl_210, type, setukpairinjL1: $o).
% 1.35/0.54 thf(decl_211, type, kfstsingleton: $o).
% 1.35/0.54 thf(decl_212, type, theprop: $o).
% 1.35/0.54 thf(decl_213, type, kfst: $i > $i).
% 1.35/0.54 thf(decl_214, type, kfstpairEq: $o).
% 1.35/0.54 thf(decl_215, type, cartprodfstin: $o).
% 1.35/0.54 thf(decl_216, type, setukpairinjL2: $o).
% 1.35/0.54 thf(decl_217, type, setukpairinjL: $o).
% 1.35/0.54 thf(decl_218, type, setukpairinjR11: $o).
% 1.35/0.54 thf(decl_219, type, setukpairinjR12: $o).
% 1.35/0.54 thf(decl_220, type, setukpairinjR1: $o).
% 1.35/0.54 thf(decl_221, type, upairequniteq: $o).
% 1.35/0.54 thf(decl_222, type, setukpairinjR2: $o).
% 1.35/0.54 thf(decl_223, type, setukpairinjR: $o).
% 1.35/0.54 thf(decl_224, type, ksndsingleton: $o).
% 1.35/0.54 thf(decl_225, type, ksnd: $i > $i).
% 1.35/0.54 thf(decl_226, type, ksndpairEq: $o).
% 1.35/0.54 thf(decl_227, type, kpairsurjEq: $o).
% 1.35/0.54 thf(decl_228, type, cartprodsndin: $o).
% 1.35/0.54 thf(decl_229, type, cartprodpairmemEL: $o).
% 1.35/0.54 thf(decl_230, type, cartprodpairmemER: $o).
% 1.35/0.54 thf(decl_231, type, cartprodmempaircEq: $o).
% 1.35/0.54 thf(decl_232, type, cartprodfstpairEq: $o).
% 1.35/0.54 thf(decl_233, type, cartprodsndpairEq: $o).
% 1.35/0.54 thf(decl_234, type, cartprodpairsurjEq: $o).
% 1.35/0.54 thf(decl_235, type, breln: $i > $i > $i > $o).
% 1.35/0.54 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.35/0.54 thf(decl_237, type, dpsetconstrI: $o).
% 1.35/0.54 thf(decl_238, type, dpsetconstrSub: $o).
% 1.35/0.54 thf(decl_239, type, setOfPairsIsBReln: $o).
% 1.35/0.54 thf(decl_240, type, dpsetconstrERa: $o).
% 1.35/0.54 thf(decl_241, type, dpsetconstrEL1: $o).
% 1.35/0.54 thf(decl_242, type, dpsetconstrEL2: $o).
% 1.35/0.54 thf(decl_243, type, dpsetconstrER: $o).
% 1.35/0.54 thf(decl_244, type, func: $i > $i > $i > $o).
% 1.35/0.54 thf(decl_245, type, funcSet: $i > $i > $i).
% 1.35/0.54 thf(decl_246, type, funcImageSingleton: $o).
% 1.35/0.54 thf(decl_247, type, apProp: $o).
% 1.35/0.54 thf(decl_248, type, ap: $i > $i > $i > $i > $i).
% 1.35/0.54 thf(decl_249, type, app: $o).
% 1.35/0.54 thf(decl_250, type, infuncsetfunc: $o).
% 1.35/0.54 thf(decl_251, type, ap2p: $o).
% 1.35/0.54 thf(decl_252, type, funcinfuncset: $o).
% 1.35/0.54 thf(decl_253, type, lamProp: $o).
% 1.35/0.54 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
% 1.35/0.54 thf(decl_255, type, lamp: $o).
% 1.35/0.54 thf(decl_256, type, lam2p: $o).
% 1.35/0.54 thf(decl_257, type, brelnall1: $o).
% 1.35/0.54 thf(decl_258, type, brelnall2: $o).
% 1.35/0.54 thf(decl_259, type, ex1E2: $o).
% 1.35/0.54 thf(decl_260, type, funcGraphProp1: $o).
% 1.35/0.54 thf(decl_261, type, funcGraphProp3: $o).
% 1.35/0.54 thf(decl_262, type, funcGraphProp2: $o).
% 1.35/0.54 thf(decl_263, type, funcextLem: $o).
% 1.35/0.54 thf(decl_264, type, funcGraphProp4: $o).
% 1.35/0.54 thf(decl_265, type, subbreln: $o).
% 1.35/0.54 thf(decl_266, type, eqbreln: $o).
% 1.35/0.54 thf(decl_267, type, funcext: $o).
% 1.35/0.54 thf(decl_268, type, funcext2: $o).
% 1.35/0.54 thf(decl_269, type, ap2apEq1: $o).
% 1.35/0.54 thf(decl_270, type, ap2apEq2: $o).
% 1.35/0.54 thf(decl_271, type, beta1: $o).
% 1.35/0.54 thf(decl_272, type, eta1: $o).
% 1.35/0.54 thf(decl_273, type, lam2lamEq: $o).
% 1.35/0.54 thf(decl_274, type, beta2: $o).
% 1.35/0.54 thf(decl_275, type, eta2: $o).
% 1.35/0.54 thf(decl_276, type, iffalseProp1: $o).
% 1.35/0.54 thf(decl_277, type, iffalseProp2: $o).
% 1.35/0.54 thf(decl_278, type, iftrueProp1: $o).
% 1.35/0.54 thf(decl_279, type, iftrueProp2: $o).
% 1.35/0.54 thf(decl_280, type, ifSingleton: $o).
% 1.35/0.54 thf(decl_281, type, if: $i > $o > $i > $i > $i).
% 1.35/0.54 thf(decl_282, type, ifp: $o).
% 1.35/0.54 thf(decl_283, type, theeq: $o).
% 1.35/0.54 thf(decl_284, type, iftrue: $o).
% 1.35/0.54 thf(decl_285, type, iffalse: $o).
% 1.35/0.54 thf(decl_286, type, iftrueorfalse: $o).
% 1.35/0.54 thf(decl_287, type, binintersectT_lem: $o).
% 1.35/0.54 thf(decl_288, type, binunionT_lem: $o).
% 1.35/0.54 thf(decl_289, type, powersetT_lem: $o).
% 1.35/0.54 thf(decl_290, type, setminusT_lem: $o).
% 1.35/0.54 thf(decl_291, type, complementT_lem: $o).
% 1.35/0.54 thf(decl_292, type, setextT: $o).
% 1.35/0.54 thf(decl_293, type, subsetTI: $o).
% 1.35/0.54 thf(decl_294, type, powersetTI1: $o).
% 1.35/0.54 thf(decl_295, type, powersetTE1: $o).
% 1.35/0.54 thf(decl_296, type, complementTI1: $o).
% 1.35/0.54 thf(decl_297, type, complementTE1: $o).
% 1.35/0.55 thf(decl_298, type, binintersectTELcontra: $o).
% 1.35/0.55 thf(decl_299, type, binintersectTERcontra: $o).
% 1.35/0.55 thf(decl_300, type, contrasubsetT: $o).
% 1.35/0.55 thf(decl_301, type, contrasubsetT1: $o).
% 1.35/0.55 thf(decl_302, type, contrasubsetT2: $o).
% 1.35/0.55 thf(decl_303, type, contrasubsetT3: $o).
% 1.35/0.55 thf(decl_304, type, doubleComplementI1: $o).
% 1.35/0.55 thf(decl_305, type, doubleComplementE1: $o).
% 1.35/0.55 thf(decl_306, type, doubleComplementSub1: $o).
% 1.35/0.55 thf(decl_307, type, doubleComplementSub2: $o).
% 1.35/0.55 thf(decl_308, type, doubleComplementEq: $o).
% 1.35/0.55 thf(decl_309, type, complementTnotintersectT: $o).
% 1.35/0.55 thf(decl_310, type, complementImpComplementIntersect: $o).
% 1.35/0.55 thf(decl_311, type, complementSubsetComplementIntersect: $o).
% 1.35/0.55 thf(decl_312, type, complementInPowersetComplementIntersect: $o).
% 1.35/0.55 thf(decl_313, type, contraSubsetComplement: $o).
% 1.35/0.55 thf(decl_314, type, complementTcontraSubset: $o).
% 1.35/0.55 thf(decl_315, type, binunionTILcontra: $o).
% 1.35/0.55 thf(decl_316, type, binunionTIRcontra: $o).
% 1.35/0.55 thf(decl_317, type, inIntersectImpInUnion: $o).
% 1.35/0.55 thf(decl_318, type, inIntersectImpInUnion2: $o).
% 1.35/0.55 thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
% 1.35/0.55 thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
% 1.35/0.55 thf(decl_321, type, inComplementUnionImpNotIn1: $o).
% 1.35/0.55 thf(decl_322, type, inComplementUnionImpInComplement1: $o).
% 1.35/0.55 thf(decl_323, type, binunionTE: $o).
% 1.35/0.55 thf(decl_324, type, binunionTEcontra: $o).
% 1.35/0.55 thf(decl_325, type, epred1_0: $o).
% 1.35/0.55 thf(decl_326, type, esk1_2: $i > $i > $i).
% 1.35/0.55 thf(decl_327, type, esk2_2: $i > $i > $i).
% 1.35/0.55 thf(decl_328, type, esk3_2: $i > $i > $i).
% 1.35/0.55 thf(decl_329, type, esk4_1: $i > $i).
% 1.35/0.55 thf(decl_330, type, esk5_2: ($i > $i > $o) > $i > $i).
% 1.35/0.55 thf(decl_331, type, esk6_2: ($i > $i > $o) > $i > $i).
% 1.35/0.55 thf(decl_332, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 1.35/0.55 thf(decl_333, type, esk8_1: $i > $i).
% 1.35/0.55 thf(decl_334, type, esk9_1: ($i > $o) > $i).
% 1.35/0.55 thf(decl_335, type, esk10_1: ($i > $o) > $i).
% 1.35/0.55 thf(decl_336, type, esk11_2: $i > $i > $i).
% 1.35/0.55 thf(decl_337, type, esk12_2: $i > $i > $i).
% 1.35/0.55 thf(decl_338, type, esk13_1: $i > $i).
% 1.35/0.55 thf(decl_339, type, esk14_1: $i > $i).
% 1.35/0.55 thf(decl_340, type, esk15_1: $i > $i).
% 1.35/0.55 thf(decl_341, type, esk16_2: $i > $i > $i).
% 1.35/0.55 thf(decl_342, type, esk17_3: $i > $i > $o > $i).
% 1.35/0.55 thf(decl_343, type, esk18_1: ($i > $o) > $i).
% 1.35/0.55 thf(decl_344, type, esk19_1: $i > $i).
% 1.35/0.55 thf(decl_345, type, esk20_2: $i > ($i > $o) > $i).
% 1.35/0.55 thf(decl_346, type, esk21_2: $i > ($i > $o) > $i).
% 1.35/0.55 thf(decl_347, type, esk22_2: $i > ($i > $o) > $i).
% 1.35/0.55 thf(decl_348, type, esk23_2: $i > ($i > $o) > $i).
% 1.35/0.55 thf(decl_349, type, esk24_2: $i > ($i > $o) > $i).
% 1.35/0.55 thf(decl_350, type, esk25_2: $i > ($i > $o) > $i).
% 1.35/0.55 thf(decl_351, type, esk26_2: ($i > $o) > $i > $i).
% 1.35/0.55 thf(decl_352, type, esk27_1: ($i > $o) > $i).
% 1.35/0.55 thf(decl_353, type, esk28_1: ($i > $o) > $i).
% 1.35/0.55 thf(decl_354, type, esk29_2: ($i > $o) > $i > $i).
% 1.35/0.55 thf(decl_355, type, esk30_2: ($i > $o) > ($i > $o) > $i).
% 1.35/0.55 thf(decl_356, type, esk31_2: ($i > $o) > ($i > $o) > $i).
% 1.35/0.55 thf(decl_357, type, esk32_2: ($i > $o) > ($i > $o) > $i).
% 1.35/0.55 thf(decl_358, type, esk33_2: ($i > $o) > ($i > $o) > $i).
% 1.35/0.55 thf(decl_359, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.35/0.55 thf(decl_360, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.35/0.55 thf(decl_361, type, esk36_2: $i > $i > $i).
% 1.35/0.55 thf(decl_362, type, esk37_2: $i > $i > $i).
% 1.35/0.55 thf(decl_363, type, esk38_2: $i > $i > $i).
% 1.35/0.55 thf(decl_364, type, esk39_3: $i > $i > $i > $i).
% 1.35/0.55 thf(decl_365, type, esk40_3: $i > $i > $i > $i).
% 1.35/0.55 thf(decl_366, type, esk41_2: $i > $i > $i).
% 1.35/0.55 thf(decl_367, type, esk42_2: $i > ($i > $o) > $i).
% 1.35/0.55 thf(decl_368, type, esk43_2: $i > ($i > $o) > $i).
% 1.35/0.55 thf(decl_369, type, esk44_2: $i > ($i > $o) > $i).
% 1.35/0.55 thf(decl_370, type, esk45_3: $i > ($i > $o) > $i > $i).
% 1.35/0.55 thf(decl_371, type, esk46_2: $i > ($i > $o) > $i).
% 1.35/0.55 thf(decl_372, type, esk47_2: $i > ($i > $o) > $i).
% 1.35/0.55 thf(decl_373, type, esk48_3: $i > $i > ($i > $i) > $i).
% 1.35/0.55 thf(decl_374, type, esk49_3: $i > $i > ($i > $i) > $i).
% 1.35/0.55 thf(decl_375, type, esk50_3: $i > $i > ($i > $i) > $i).
% 1.35/0.55 thf(decl_376, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
% 1.35/0.55 thf(decl_377, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
% 1.35/0.55 thf(decl_378, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
% 1.35/0.55 thf(decl_379, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
% 1.35/0.55 thf(decl_380, type, esk55_4: $i > $i > $i > $i > $i).
% 1.35/0.55 thf(decl_381, type, esk56_4: $i > $i > $i > $i > $i).
% 1.35/0.55 thf(decl_382, type, esk57_4: $i > $i > $i > $i > $i).
% 1.35/0.55 thf(decl_383, type, esk58_4: $i > $i > $i > $i > $i).
% 1.35/0.55 thf(decl_384, type, esk59_4: $i > $i > $i > $i > $i).
% 1.35/0.55 thf(decl_385, type, esk60_4: $i > $i > $i > $i > $i).
% 1.35/0.55 thf(decl_386, type, esk61_4: $i > $i > $i > $i > $i).
% 1.35/0.55 thf(decl_387, type, esk62_4: $i > $i > $i > $i > $i).
% 1.35/0.55 thf(decl_388, type, esk63_4: $i > $i > $i > $i > $i).
% 1.35/0.55 thf(decl_389, type, esk64_3: $i > $i > ($i > $i) > $i).
% 1.35/0.55 thf(decl_390, type, esk65_3: $i > $i > ($i > $i) > $i).
% 1.35/0.55 thf(decl_391, type, esk66_3: $i > $i > ($i > $i) > $i).
% 1.35/0.55 thf(decl_392, type, esk67_3: $i > $i > $i > $i).
% 1.35/0.55 thf(decl_393, type, esk68_3: $i > $i > $i > $i).
% 1.35/0.55 thf(decl_394, type, esk69_3: $i > $i > $i > $i).
% 1.35/0.55 thf(decl_395, type, esk70_3: $i > $i > $i > $i).
% 1.35/0.55 thf(decl_396, type, esk71_0: $i).
% 1.35/0.55 thf(decl_397, type, esk72_0: $i).
% 1.35/0.55 thf(decl_398, type, esk73_0: $i).
% 1.35/0.55 thf(decl_399, type, esk74_0: $i).
% 1.35/0.55 thf(demorgan2a1, 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)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', demorgan2a1)).
% 1.35/0.55 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', ifSingleton)).
% 1.35/0.55 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', iftrueProp2)).
% 1.35/0.55 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', exuI3)).
% 1.35/0.55 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', exuI1)).
% 1.35/0.55 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', exuI2)).
% 1.35/0.55 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', exu__Cong)).
% 1.35/0.55 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', exuE3u)).
% 1.35/0.55 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', dsetconstr__Cong)).
% 1.35/0.55 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', descr__Cong)).
% 1.35/0.55 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', exuEu)).
% 1.35/0.55 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', sepSubset)).
% 1.35/0.55 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', sepInPowerset)).
% 1.35/0.55 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', ex1I2)).
% 1.35/0.55 thf(ex1I, axiom, ((ex1I)<=>![X4:$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/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', ex1I)).
% 1.35/0.55 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', ex1E1)).
% 1.35/0.55 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', singletonprop)).
% 1.35/0.55 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', kfstsingleton)).
% 1.35/0.55 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', ksndsingleton)).
% 1.35/0.55 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', dpsetconstrI)).
% 1.35/0.55 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', dpsetconstrSub)).
% 1.35/0.55 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', apProp)).
% 1.35/0.55 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', funcImageSingleton)).
% 1.35/0.55 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', dpsetconstrER)).
% 1.35/0.55 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', dpsetconstrEL2)).
% 1.35/0.55 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', dpsetconstrEL1)).
% 1.35/0.55 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', dpsetconstrERa)).
% 1.35/0.55 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setOfPairsIsBReln)).
% 1.35/0.55 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', lam2p)).
% 1.35/0.55 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', lamp)).
% 1.35/0.55 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', lamProp)).
% 1.35/0.55 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', ex1E2)).
% 1.35/0.55 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', lam2lamEq)).
% 1.35/0.55 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', eta1)).
% 1.35/0.55 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', beta1)).
% 1.35/0.55 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', eta2)).
% 1.35/0.55 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', iffalseProp1)).
% 1.35/0.55 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', iffalseProp2)).
% 1.35/0.55 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', iftrueProp1)).
% 1.35/0.55 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', beta2)).
% 1.35/0.55 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', emptyE1)).
% 1.35/0.55 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', exuE2)).
% 1.35/0.55 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setoftrueEq)).
% 1.35/0.55 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', nonemptyI)).
% 1.35/0.55 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setbeta)).
% 1.35/0.55 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', exuE3e)).
% 1.35/0.55 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', exuE1)).
% 1.35/0.55 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', dsetconstrER)).
% 1.35/0.55 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', dsetconstrEL)).
% 1.35/0.55 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', dsetconstrI)).
% 1.35/0.55 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', descrp)).
% 1.35/0.55 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', replAx)).
% 1.35/0.55 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', ifp)).
% 1.35/0.55 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', theeq)).
% 1.35/0.55 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', iftrue)).
% 1.35/0.55 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', iffalse)).
% 1.35/0.55 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', iftrueorfalse)).
% 1.35/0.55 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', notdallE)).
% 1.35/0.55 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binintersectT_lem)).
% 1.35/0.55 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', notdexE)).
% 1.35/0.55 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binunionT_lem)).
% 1.35/0.55 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', prop2setI)).
% 1.35/0.55 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', powersetT_lem)).
% 1.35/0.55 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', quantDeMorgan4)).
% 1.35/0.55 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setminusT_lem)).
% 1.35/0.55 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', quantDeMorgan3)).
% 1.35/0.55 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', complementT_lem)).
% 1.35/0.55 thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setextT)).
% 1.35/0.55 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', subsetTI)).
% 1.35/0.55 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', powersetTI1)).
% 1.35/0.55 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', powersetTE1)).
% 1.35/0.55 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', complementTI1)).
% 1.35/0.55 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', complementTE1)).
% 1.35/0.55 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binintersectTELcontra)).
% 1.35/0.55 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binintersectTERcontra)).
% 1.35/0.55 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', contrasubsetT)).
% 1.35/0.55 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', contrasubsetT1)).
% 1.35/0.55 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', contrasubsetT2)).
% 1.35/0.55 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', contrasubsetT3)).
% 1.35/0.55 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', doubleComplementI1)).
% 1.35/0.55 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', doubleComplementE1)).
% 1.35/0.55 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', powerset__Cong)).
% 1.35/0.55 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', doubleComplementSub1)).
% 1.35/0.55 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setadjoin__Cong)).
% 1.35/0.55 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', doubleComplementSub2)).
% 1.35/0.55 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', emptyset__Cong)).
% 1.35/0.55 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', doubleComplementEq)).
% 1.35/0.55 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', complementTnotintersectT)).
% 1.35/0.55 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', complementImpComplementIntersect)).
% 1.35/0.55 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', in__Cong)).
% 1.35/0.55 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', complementSubsetComplementIntersect)).
% 1.35/0.55 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', inCongP)).
% 1.35/0.55 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', complementInPowersetComplementIntersect)).
% 1.35/0.55 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setunion__Cong)).
% 1.35/0.55 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', contraSubsetComplement)).
% 1.35/0.55 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', complementTcontraSubset)).
% 1.35/0.55 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binunionTILcontra)).
% 1.35/0.55 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binunionTIRcontra)).
% 1.35/0.55 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', inIntersectImpInUnion)).
% 1.35/0.55 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', inIntersectImpInUnion2)).
% 1.35/0.55 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', inIntersectImpInIntersectUnions)).
% 1.35/0.55 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', intersectInPowersetIntersectUnions)).
% 1.35/0.55 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', inComplementUnionImpNotIn1)).
% 1.35/0.55 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', inComplementUnionImpInComplement1)).
% 1.35/0.55 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binunionTE)).
% 1.35/0.55 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binunionTEcontra)).
% 1.35/0.55 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', eqimpsubset1)).
% 1.35/0.55 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', eqimpsubset2)).
% 1.35/0.55 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', subsetI1)).
% 1.35/0.55 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', omega__Cong)).
% 1.35/0.55 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', subsetI2)).
% 1.35/0.55 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', subsetRefl)).
% 1.35/0.55 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', notequalI2)).
% 1.35/0.55 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', notequalI1)).
% 1.35/0.55 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', notsubsetI)).
% 1.35/0.55 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', subsetE2)).
% 1.35/0.55 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', subsetE)).
% 1.35/0.55 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', emptysetsubset)).
% 1.35/0.55 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', subsetTrans)).
% 1.35/0.55 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', powersetE1)).
% 1.35/0.55 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', powersetI1)).
% 1.35/0.55 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', subsetemptysetimpeq)).
% 1.35/0.55 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setextsub)).
% 1.35/0.55 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', subset2powerset)).
% 1.35/0.55 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setadjoinSub2)).
% 1.35/0.55 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setadjoinSub)).
% 1.35/0.55 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', inPowerset)).
% 1.35/0.55 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binunionEcases)).
% 1.35/0.55 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binunionIR)).
% 1.35/0.55 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', upairset2IR)).
% 1.35/0.55 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binunionIL)).
% 1.35/0.55 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', powersetsubset)).
% 1.35/0.55 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binunionE)).
% 1.35/0.55 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binintersectSubset2)).
% 1.35/0.55 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binintersectLsub)).
% 1.35/0.55 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binintersectEL)).
% 1.35/0.55 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binintersectSubset5)).
% 1.35/0.55 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binintersectI)).
% 1.35/0.55 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binunionRsub)).
% 1.35/0.55 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binunionLsub)).
% 1.35/0.55 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binintersectSubset3)).
% 1.35/0.55 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', ap2apEq2)).
% 1.35/0.55 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', ap2apEq1)).
% 1.35/0.55 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', funcext2)).
% 1.35/0.55 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', funcext)).
% 1.35/0.55 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setminusI)).
% 1.35/0.55 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', bs114d)).
% 1.35/0.55 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binintersectSubset1)).
% 1.35/0.55 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binintersectSubset4)).
% 1.35/0.55 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binintersectRsub)).
% 1.35/0.55 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', disjointsetsI1)).
% 1.35/0.55 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', binintersectER)).
% 1.35/0.55 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setminusEL)).
% 1.35/0.55 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setminusLsub)).
% 1.35/0.55 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setminusIRneg)).
% 1.35/0.55 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setminusILneg)).
% 1.35/0.55 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setminusELneg)).
% 1.35/0.55 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setminusERneg)).
% 1.35/0.55 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setminusSubset2)).
% 1.35/0.55 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setminusER)).
% 1.35/0.55 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setminusSubset1)).
% 1.35/0.55 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setukpairIL)).
% 1.35/0.55 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', secondinupair)).
% 1.35/0.55 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', symdiffIneg2)).
% 1.35/0.55 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', symdiffIneg1)).
% 1.35/0.55 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', symdiffI2)).
% 1.35/0.55 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', symdiffI1)).
% 1.35/0.55 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', symdiffE)).
% 1.35/0.55 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setukpairIR)).
% 1.35/0.55 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', upairsubunion)).
% 1.35/0.55 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', upairset2E)).
% 1.35/0.55 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', singletoninpowunion)).
% 1.35/0.55 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', singletoninpowerset)).
% 1.35/0.55 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', singletonsubset)).
% 1.35/0.55 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', kpairp)).
% 1.35/0.55 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', kpairiskpair)).
% 1.35/0.55 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', upairinpowunion)).
% 1.35/0.55 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setunionE2)).
% 1.35/0.55 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', cartprodmempair)).
% 1.35/0.55 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', cartprodmempair1)).
% 1.35/0.55 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/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', cartprodpairin)).
% 1.35/0.55 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/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', ubforcartprodlem3)).
% 1.35/0.55 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/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', ubforcartprodlem2)).
% 1.35/0.55 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/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', ubforcartprodlem1)).
% 1.35/0.55 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setunionsingleton1)).
% 1.35/0.55 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', singletonsuniq)).
% 1.35/0.55 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setunionsingleton)).
% 1.35/0.55 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setunionsingleton2)).
% 1.35/0.55 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setukpairinjL1)).
% 1.35/0.55 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setukpairinjR11)).
% 1.35/0.55 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setukpairinjL)).
% 1.35/0.55 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/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setukpairinjL2)).
% 1.35/0.55 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', cartprodfstin)).
% 1.35/0.55 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', kfstpairEq)).
% 1.35/0.55 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', theprop)).
% 1.35/0.55 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![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/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setukpairinjR12)).
% 1.35/0.55 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', kpairsurjEq)).
% 1.35/0.55 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', ksndpairEq)).
% 1.35/0.55 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setukpairinjR)).
% 1.35/0.55 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setukpairinjR2)).
% 1.35/0.55 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', upairequniteq)).
% 1.35/0.55 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![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)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setukpairinjR1)).
% 1.35/0.55 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', cartprodsndin)).
% 1.35/0.55 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', cartprodpairsurjEq)).
% 1.35/0.55 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', cartprodsndpairEq)).
% 1.35/0.55 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', cartprodfstpairEq)).
% 1.35/0.55 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', cartprodmempaircEq)).
% 1.35/0.55 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', cartprodpairmemER)).
% 1.35/0.55 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', cartprodpairmemEL)).
% 1.35/0.55 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', app)).
% 1.35/0.55 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', brelnall1)).
% 1.35/0.55 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', funcinfuncset)).
% 1.35/0.55 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', ap2p)).
% 1.35/0.55 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', infuncsetfunc)).
% 1.35/0.55 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', brelnall2)).
% 1.35/0.55 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', subbreln)).
% 1.35/0.55 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', funcGraphProp4)).
% 1.35/0.55 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', funcextLem)).
% 1.35/0.55 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', funcGraphProp2)).
% 1.35/0.55 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', funcGraphProp3)).
% 1.35/0.55 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', funcGraphProp1)).
% 1.35/0.55 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', eqbreln)).
% 1.35/0.55 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', quantDeMorgan2)).
% 1.35/0.55 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', quantDeMorgan1)).
% 1.35/0.55 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', vacuousDall)).
% 1.35/0.55 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', upairsetIR)).
% 1.35/0.55 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', upairsetIL)).
% 1.35/0.55 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', upairsetE)).
% 1.35/0.55 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', singletonsswitch)).
% 1.35/0.55 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', eqinunit)).
% 1.35/0.55 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', notinsingleton)).
% 1.35/0.55 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', uniqinunit)).
% 1.35/0.55 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', nonemptyImpWitness)).
% 1.35/0.55 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', subPowSU)).
% 1.35/0.55 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setunionE)).
% 1.35/0.55 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setunionI)).
% 1.35/0.55 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', powersetE)).
% 1.35/0.55 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', emptyInPowerset)).
% 1.35/0.55 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', emptyinPowerset)).
% 1.35/0.55 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', powersetI)).
% 1.35/0.55 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setadjoinOr)).
% 1.35/0.55 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setadjoinE)).
% 1.35/0.55 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setadjoinIR)).
% 1.35/0.55 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', emptyinunitempty)).
% 1.35/0.55 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setadjoinIL)).
% 1.35/0.55 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', nonemptyI1)).
% 1.35/0.55 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', nonemptyE1)).
% 1.35/0.55 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', noeltsimpempty)).
% 1.35/0.55 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', emptyI)).
% 1.35/0.55 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setext)).
% 1.35/0.55 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', notinemptyset)).
% 1.35/0.55 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', emptysetimpfalse)).
% 1.35/0.55 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', emptysetE)).
% 1.35/0.55 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', prop2setE)).
% 1.35/0.55 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', wellorderingAx)).
% 1.35/0.55 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', foundationAx)).
% 1.35/0.55 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', omegaIndAx)).
% 1.35/0.55 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', omegaSAx)).
% 1.35/0.55 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', omega0Ax)).
% 1.35/0.55 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setunionAx)).
% 1.35/0.55 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', powersetAx)).
% 1.35/0.55 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setadjoinAx)).
% 1.35/0.55 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', emptysetAx)).
% 1.35/0.55 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.zflmNNdeSC/E---3.1_846313.p', setextAx)).
% 1.35/0.55 thf(c_0_264, 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)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[demorgan2a1])).
% 1.35/0.55 thf(c_0_265, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 1.35/0.55 thf(c_0_266, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X42))&(((Z0)=(X2)))))|(((~((X42)))&(((Z0)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
% 1.35/0.55 thf(c_0_267, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 1.35/0.55 thf(c_0_268, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 1.35/0.55 thf(c_0_269, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 1.35/0.55 thf(c_0_270, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 1.35/0.55 thf(c_0_271, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 1.35/0.55 thf(c_0_272, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 1.35/0.55 thf(c_0_273, plain, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 1.35/0.55 thf(c_0_274, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 1.35/0.55 thf(c_0_275, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 1.35/0.55 thf(c_0_276, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 1.35/0.55 thf(c_0_277, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 1.35/0.55 thf(c_0_278, plain, ((ex1I)<=>![X4:$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])).
% 1.35/0.55 thf(c_0_279, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 1.35/0.55 thf(c_0_280, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 1.35/0.55 thf(c_0_281, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 1.35/0.55 thf(c_0_282, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 1.35/0.55 thf(c_0_283, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 1.35/0.55 thf(c_0_284, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 1.35/0.55 thf(c_0_285, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 1.35/0.55 thf(c_0_286, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 1.35/0.55 thf(c_0_287, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 1.35/0.55 thf(c_0_288, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 1.35/0.55 thf(c_0_289, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 1.35/0.55 thf(c_0_290, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 1.35/0.55 thf(c_0_291, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 1.35/0.55 thf(c_0_292, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 1.35/0.55 thf(c_0_293, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 1.35/0.55 thf(c_0_294, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
% 1.35/0.55 thf(c_0_295, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
% 1.35/0.55 thf(c_0_296, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
% 1.35/0.55 thf(c_0_297, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
% 1.35/0.55 thf(c_0_298, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
% 1.35/0.55 thf(c_0_299, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
% 1.35/0.55 thf(c_0_300, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 1.35/0.55 thf(c_0_301, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
% 1.35/0.55 thf(c_0_302, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 1.35/0.55 thf(c_0_303, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
% 1.35/0.55 thf(c_0_304, 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])).
% 1.35/0.55 thf(c_0_305, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 1.35/0.55 thf(c_0_306, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 1.35/0.55 thf(c_0_307, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 1.35/0.55 thf(c_0_308, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 1.35/0.55 thf(c_0_309, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 1.35/0.55 thf(c_0_310, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 1.35/0.55 thf(c_0_311, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 1.35/0.55 thf(c_0_312, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 1.35/0.55 thf(c_0_313, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 1.35/0.55 thf(c_0_314, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 1.35/0.55 thf(c_0_315, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 1.35/0.55 thf(c_0_316, plain, ((epred1_0)<=>![X912:$i]:(?[X913:$i]:((((![X914:$i]:(((in @ X914 @ X913)=>![X915:$i]:(((in @ X915 @ X914)=>(in @ X915 @ X912)))))&![X916:$i, X917:$i]:((((in @ X916 @ X912)&(in @ X917 @ X912))=>(![X918:$i]:(((in @ X918 @ X913)=>((in @ X916 @ X918)<=>(in @ X917 @ X918))))=>((X916)=(X917))))))&![X919:$i, X920:$i]:((((in @ X919 @ X913)&(in @ X920 @ X913))=>(![X921:$i]:(((in @ X921 @ X919)=>(in @ X921 @ X920)))|![X922:$i]:(((in @ X922 @ X920)=>(in @ X922 @ X919)))))))&![X923:$i]:(((![X924:$i]:(((in @ X924 @ X923)=>(in @ X924 @ X912)))&?[X925:$i]:((in @ X925 @ X923)))=>?[X926:$i, X927:$i]:(((((in @ X926 @ X913)&(in @ X927 @ X923))&~(?[X928:$i]:(((in @ X928 @ X926)&(in @ X928 @ X923)))))&![X929:$i]:(((in @ X929 @ X913)=>(![X930:$i]:(((in @ X930 @ X929)=>(in @ X930 @ X926)))|(in @ X927 @ X929)))))))))))), introduced(definition)).
% 1.35/0.55 thf(c_0_317, negated_conjecture, ~((![X885:$i, X886:$i]:((![X887:$i]:(((in @ X887 @ X885)<=>(in @ X887 @ X886)))=>((X885)=(X886))))=>(![X888:$i]:(~(in @ X888 @ emptyset))=>(![X889:$i, X890:$i, X891:$i]:(((in @ X891 @ (setadjoin @ X889 @ X890))<=>(((X891)=(X889))|(in @ X891 @ X890))))=>(![X892:$i, X893:$i]:(((in @ X893 @ (powerset @ X892))<=>![X894:$i]:(((in @ X894 @ X893)=>(in @ X894 @ X892)))))=>(![X895:$i, X896:$i]:(((in @ X896 @ (setunion @ X895))<=>?[X897:$i]:(((in @ X896 @ X897)&(in @ X897 @ X895)))))=>((in @ emptyset @ omega)=>(![X898:$i]:(((in @ X898 @ omega)=>(in @ (setadjoin @ X898 @ X898) @ omega)))=>(![X899:$i]:((((in @ emptyset @ X899)&![X900:$i]:((((in @ X900 @ omega)&(in @ X900 @ X899))=>(in @ (setadjoin @ X900 @ X900) @ X899))))=>![X901:$i]:(((in @ X901 @ omega)=>(in @ X901 @ X899)))))=>(![X902:$i > $i > $o, X903:$i]:((![X904:$i]:(((in @ X904 @ X903)=>(exu @ (X902 @ X904))))=>?[X905:$i]:(![X906:$i]:(((in @ X906 @ X905)<=>?[X907:$i]:(((in @ X907 @ X903)&(X902 @ X907 @ X906))))))))=>(![X908:$i]:((?[X909:$i]:((in @ X909 @ X908))=>?[X910:$i]:(((in @ X910 @ X908)&~(?[X911:$i]:(((in @ X911 @ X910)&(in @ X911 @ X908))))))))=>((epred1_0)=>(![X931:$i > $o]:(((exu @ X931)=>(X931 @ (descr @ (^[Z0:$i]:(X931 @ Z0))))))=>(![X932:$i, X933:$i > $o, X934:$i]:(((in @ X934 @ X932)=>((X933 @ X934)=>(in @ X934 @ (dsetconstr @ X932 @ X933)))))=>(![X935:$i, X936:$i > $o, X937:$i]:(((in @ X937 @ (dsetconstr @ X935 @ X936))=>(in @ X937 @ X935)))=>(![X938:$i, X939:$i > $o, X940:$i]:(((in @ X940 @ (dsetconstr @ X938 @ X939))=>(X939 @ X940)))=>(![X941:$i > $o]:(((exu @ X941)=>?[X942:$i]:(((X941 @ X942)&![X943:$i]:(((X941 @ X943)=>((X942)=(X943))))))))=>(![X944:$o, X945:$i]:(((in @ X945 @ (prop2set @ ((X944))))=>(X944)))=>(![X946:$i]:(((in @ X946 @ emptyset)=>![X947:$o]:((X947))))=>(![X948:$i]:(((in @ X948 @ emptyset)=>~($true)))=>(![X949:$i]:(~(in @ X949 @ emptyset))=>(![X950:$i > $o]:(((exu @ X950)=>?[X951:$i]:((X950 @ X951))))=>(![X952:$i, X953:$i]:((![X954:$i]:(((in @ X954 @ X952)=>(in @ X954 @ X953)))=>(![X955:$i]:(((in @ X955 @ X953)=>(in @ X955 @ X952)))=>((X952)=(X953)))))=>(![X956:$i]:((![X957:$i]:(~(in @ X957 @ X956))=>((X956)=(emptyset))))=>(![X958:$i]:((![X959:$i]:(~(in @ X959 @ X958))=>((X958)=(emptyset))))=>(![X960:$i, X961:$i > $o, X962:$i]:(((in @ X962 @ X960)=>((in @ X962 @ (dsetconstr @ X960 @ X961))<=>(X961 @ X962))))=>(![X963:$i]:(((nonempty @ X963)=>?[X964:$i]:((in @ X964 @ X963))))=>(![X965:$i, X966:$i > $o, X967:$i]:(((in @ X967 @ X965)=>((X966 @ X967)=>(nonempty @ (dsetconstr @ X965 @ X966)))))=>(![X968:$i]:((?[X969:$i]:((in @ X969 @ X968))=>(nonempty @ X968)))=>(![X970:$i, X971:$i]:((in @ X970 @ (setadjoin @ X970 @ X971)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X972:$i, X973:$i, X974:$i]:(((in @ X974 @ X973)=>(in @ X974 @ (setadjoin @ X972 @ X973))))=>(![X975:$i, X976:$i, X977:$i]:(((in @ X977 @ (setadjoin @ X975 @ X976))=>![X978:$o]:(((((X977)=(X975))=>(X978))=>(((in @ X977 @ X976)=>(X978))=>(X978))))))=>(![X979:$i, X980:$i, X981:$i]:(((in @ X981 @ (setadjoin @ X979 @ X980))=>(((X981)=(X979))|(in @ X981 @ X980))))=>(![X982:$i]:(((dsetconstr @ X982 @ (^[Z0:$i]:($true)))=(X982)))=>(![X983:$i, X984:$i]:((![X985:$i]:(((in @ X985 @ X984)=>(in @ X985 @ X983)))=>(in @ X984 @ (powerset @ X983))))=>(![X986:$i]:((in @ emptyset @ (powerset @ X986)))=>(![X987:$i]:((in @ emptyset @ (powerset @ X987)))=>(![X988:$i, X989:$i, X990:$i]:(((in @ X989 @ (powerset @ X988))=>((in @ X990 @ X989)=>(in @ X990 @ X988))))=>(![X991:$i, X992:$i, X993:$i]:(((in @ X992 @ X993)=>((in @ X993 @ X991)=>(in @ X992 @ (setunion @ X991)))))=>(![X994:$i, X995:$i]:(((in @ X995 @ (setunion @ X994))=>![X996:$o]:((![X997:$i]:(((in @ X995 @ X997)=>((in @ X997 @ X994)=>(X996))))=>(X996)))))=>(![X998:$i, X999:$i]:(((in @ X999 @ X998)=>(in @ X999 @ (powerset @ (setunion @ X998)))))=>(![X1000:$i > $o]:(((exu @ X1000)=>?[X1001:$i]:(![X1002:$i]:(((X1000 @ X1002)<=>((X1002)=(X1001)))))))=>(![X1003:$i]:(((nonempty @ X1003)=>?[X1004:$i]:(((in @ X1004 @ X1003)&$true))))=>(![X1005:$i, X1006:$i]:(((in @ X1005 @ (setadjoin @ X1006 @ emptyset))=>((X1005)=(X1006))))=>(![X1007:$i, X1008:$i]:((((X1007)!=(X1008))=>~(in @ X1008 @ (setadjoin @ X1007 @ emptyset))))=>(![X1009:$i, X1010:$i]:((((X1009)=(X1010))=>(in @ X1009 @ (setadjoin @ X1010 @ emptyset))))=>(![X1011:$i, X1012:$i]:(((in @ X1011 @ (setadjoin @ X1012 @ emptyset))=>(in @ X1012 @ (setadjoin @ X1011 @ emptyset))))=>(![X1013:$i, X1014:$i, X1015:$i]:(((in @ X1015 @ (setadjoin @ X1013 @ (setadjoin @ X1014 @ emptyset)))=>(((X1015)=(X1013))|((X1015)=(X1014)))))=>(![X1016:$i, X1017:$i]:((in @ X1016 @ (setadjoin @ X1016 @ (setadjoin @ X1017 @ emptyset))))=>(![X1018:$i, X1019:$i]:((in @ X1019 @ (setadjoin @ X1018 @ (setadjoin @ X1019 @ emptyset))))=>(![X1020:$i, X1021:$i > $o]:((?[X1022:$i]:(((in @ X1022 @ X1020)&(X1021 @ X1022)))=>(((dsetconstr @ X1020 @ X1021)=(emptyset))=>~($true))))=>(![X1023:$i > $o, X1024:$i]:(((in @ X1024 @ emptyset)=>(X1023 @ X1024)))=>(![X1025:$i, X1026:$i > $o]:((~(![X1027:$i]:(((in @ X1027 @ X1025)=>(X1026 @ X1027))))=>?[X1028:$i]:(((in @ X1028 @ X1025)&~((X1026 @ X1028))))))=>(![X1029:$i, X1030:$i > $o]:((![X1031:$i]:(((in @ X1031 @ X1029)=>~((X1030 @ X1031))))=>~(?[X1032:$i]:(((in @ X1032 @ X1029)&(X1030 @ X1032))))))=>(![X1033:$i, X1034:$i > $o]:((~(?[X1035:$i]:(((in @ X1035 @ X1033)&(X1034 @ X1035))))=>![X1036:$i]:(((in @ X1036 @ X1033)=>~((X1034 @ X1036))))))=>(![X1037:$i, X1038:$i > $o]:((?[X1039:$i]:(((in @ X1039 @ X1037)&~((X1038 @ X1039))))=>~(![X1040:$i]:(((in @ X1040 @ X1037)=>(X1038 @ X1040))))))=>(![X1041:$o]:(((X1041)=>(in @ emptyset @ (prop2set @ ((X1041))))))=>((prop2set2propI)=>(![X1042:$i, X1043:$i > $o]:((~(?[X1044:$i]:(((in @ X1044 @ X1042)&(X1043 @ X1044))))=>![X1045:$i]:(((in @ X1045 @ X1042)=>~((X1043 @ X1045))))))=>(![X1046:$i, X1047:$i > $o]:((~(![X1048:$i]:(((in @ X1048 @ X1046)=>(X1047 @ X1048))))=>?[X1049:$i]:(((in @ X1049 @ X1046)&~((X1047 @ X1049))))))=>(![X1050:$i > $o]:((?[X1051:$i]:(((X1050 @ X1051)&![X1052:$i]:(((X1050 @ X1052)=>((X1051)=(X1052))))))=>(exu @ X1050)))=>(![X1053:$i > $o]:((?[X1054:$i]:((X1053 @ X1054))=>(![X1055:$i, X1056:$i]:(((X1053 @ X1055)=>((X1053 @ X1056)=>((X1055)=(X1056)))))=>(exu @ X1053))))=>(![X1057:$i > $o]:((?[X1058:$i]:(![X1059:$i]:(((X1057 @ X1059)<=>((X1059)=(X1058)))))=>(exu @ X1057)))=>(![X1060:$i, X1061:$i]:((((X1060)=(X1061))=>![X1062:$i, X1063:$i]:((((X1062)=(X1063))=>((in @ X1062 @ X1060)=>(in @ X1063 @ X1061))))))=>(![X1064:$i, X1065:$i]:((((X1064)=(X1065))=>![X1066:$i, X1067:$i]:((((X1066)=(X1067))=>((in @ X1066 @ X1064)<=>(in @ X1067 @ X1065))))))=>(![X1068:$i > $o]:(((exu @ X1068)=>![X1069:$i, X1070:$i]:(((X1068 @ X1069)=>((X1068 @ X1070)=>((X1069)=(X1070)))))))=>(![X1071:$i > $o, X1072:$i > $o]:((![X1073:$i, X1074:$i]:((((X1073)=(X1074))=>((X1071 @ X1073)<=>(X1072 @ X1074))))=>((exu @ X1071)<=>(exu @ 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X1662 @ X1663))))))))=>(![X1664:$i, X1665:$i]:(((in @ X1665 @ (powerset @ X1664))=>![X1666:$i]:(((in @ X1666 @ (powerset @ X1664))=>((subset @ X1665 @ (setminus @ X1664 @ X1666))=>![X1667:$i]:(((in @ X1667 @ X1664)=>((in @ X1667 @ X1666)=>(in @ X1667 @ (setminus @ X1664 @ X1665))))))))))=>(![X1668:$i, X1669:$i]:(((in @ X1669 @ (powerset @ X1668))=>![X1670:$i]:(((in @ X1670 @ (powerset @ X1668))=>((subset @ X1669 @ (setminus @ X1668 @ X1670))=>(subset @ X1670 @ (setminus @ X1668 @ X1669)))))))=>(![X1671:$i, X1672:$i]:(((in @ X1672 @ (powerset @ X1671))=>![X1673:$i]:(((in @ X1673 @ (powerset @ X1671))=>![X1674:$i]:(((in @ X1674 @ X1671)=>(~(in @ X1674 @ (binunion @ X1672 @ X1673))=>~(in @ X1674 @ X1672))))))))=>(![X1675:$i, X1676:$i]:(((in @ X1676 @ (powerset @ X1675))=>![X1677:$i]:(((in @ X1677 @ (powerset @ X1675))=>![X1678:$i]:(((in @ X1678 @ X1675)=>(~(in @ X1678 @ (binunion @ X1676 @ X1677))=>~(in @ X1678 @ X1677))))))))=>(![X1679:$i, X1680:$i]:(((in @ X1680 @ (powerset @ X1679))=>![X1681:$i]:(((in @ X1681 @ (powerset @ X1679))=>![X1682:$i]:(((in @ X1682 @ (powerset @ X1679))=>![X1683:$i]:(((in @ X1683 @ X1679)=>((in @ X1683 @ (binintersect @ X1680 @ X1681))=>(in @ X1683 @ (binunion @ X1680 @ X1682)))))))))))=>(![X1684:$i, X1685:$i]:(((in @ X1685 @ (powerset @ X1684))=>![X1686:$i]:(((in @ X1686 @ (powerset @ X1684))=>![X1687:$i]:(((in @ X1687 @ (powerset @ X1684))=>![X1688:$i]:(((in @ X1688 @ X1684)=>((in @ X1688 @ (binintersect @ X1685 @ X1686))=>(in @ X1688 @ (binunion @ X1686 @ X1687)))))))))))=>(![X1689:$i, X1690:$i]:(((in @ X1690 @ (powerset @ X1689))=>![X1691:$i]:(((in @ X1691 @ (powerset @ X1689))=>![X1692:$i]:(((in @ X1692 @ (powerset @ X1689))=>![X1693:$i]:(((in @ X1693 @ X1689)=>((in @ X1693 @ (binintersect @ X1690 @ X1691))=>(in @ X1693 @ (binintersect @ (binunion @ X1690 @ X1692) @ (binunion @ X1691 @ X1692))))))))))))=>(![X1694:$i, X1695:$i]:(((in @ X1695 @ (powerset @ X1694))=>![X1696:$i]:(((in @ X1696 @ (powerset @ X1694))=>![X1697:$i]:(((in @ X1697 @ (powerset @ X1694))=>(in @ (binintersect @ X1695 @ X1696) @ (powerset @ (binintersect @ (binunion @ X1695 @ X1697) @ (binunion @ X1696 @ X1697))))))))))=>(![X1698:$i, X1699:$i]:(((in @ X1699 @ (powerset @ X1698))=>![X1700:$i]:(((in @ X1700 @ (powerset @ X1698))=>![X1701:$i]:(((in @ X1701 @ X1698)=>((in @ X1701 @ (setminus @ X1698 @ (binunion @ X1699 @ X1700)))=>~(in @ X1701 @ X1699))))))))=>(![X1702:$i, X1703:$i]:(((in @ X1703 @ (powerset @ X1702))=>![X1704:$i]:(((in @ X1704 @ (powerset @ X1702))=>![X1705:$i]:(((in @ X1705 @ X1702)=>((in @ X1705 @ (setminus @ X1702 @ (binunion @ X1703 @ X1704)))=>(in @ X1705 @ (setminus @ X1702 @ X1703)))))))))=>(![X1706:$i, X1707:$i]:(((in @ X1707 @ (powerset @ X1706))=>![X1708:$i]:(((in @ X1708 @ (powerset @ X1706))=>![X1709:$o, X1710:$i]:(((in @ X1710 @ X1706)=>((in @ X1710 @ (binunion @ X1707 @ X1708))=>(((in @ X1710 @ X1707)=>(X1709))=>(((in @ X1710 @ X1708)=>(X1709))=>(X1709))))))))))=>(![X1711:$i, X1712:$i]:(((in @ X1712 @ (powerset @ X1711))=>![X1713:$i]:(((in @ X1713 @ (powerset @ X1711))=>![X1714:$i]:(((in @ X1714 @ X1711)=>(~(in @ X1714 @ X1712)=>(~(in @ X1714 @ X1713)=>~(in @ X1714 @ (binunion @ X1712 @ X1713))))))))))=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(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_264, c_0_265]), c_0_266]), ifp]), theeq]), iftrue]), c_0_267]), iffalse]), c_0_268]), iftrueorfalse]), notdallE]), binintersectT_lem]), notdexE]), binunionT_lem]), prop2setI]), powersetT_lem]), quantDeMorgan4]), setminusT_lem]), quantDeMorgan3]), complementT_lem]), c_0_269]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), powerset__Cong]), doubleComplementSub1]), setadjoin__Cong]), doubleComplementSub2]), emptyset__Cong]), doubleComplementEq]), c_0_270]), complementTnotintersectT]), c_0_271]), complementImpComplementIntersect]), in__Cong]), complementSubsetComplementIntersect]), inCongP]), complementInPowersetComplementIntersect]), setunion__Cong]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), eqimpsubset1]), eqimpsubset2]), subsetI1]), c_0_272]), c_0_273]), c_0_274]), omega__Cong]), subsetI2]), subsetRefl]), notequalI2]), notequalI1]), notsubsetI]), subsetE2]), subsetE]), emptysetsubset]), subsetTrans]), powersetE1]), powersetI1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), setadjoinSub2]), setadjoinSub]), inPowerset]), binunionEcases]), binunionIR]), upairset2IR]), binunionIL]), c_0_275]), c_0_276]), powersetsubset]), binunionE]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectI]), binunionRsub]), binunionLsub]), binintersectSubset3]), ap2apEq2]), ap2apEq1]), funcext2]), funcext]), setminusI]), bs114d]), binintersectSubset1]), binintersectSubset4]), binintersectRsub]), disjointsetsI1]), binintersectER]), setminusEL]), setminusLsub]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusERneg]), setminusSubset2]), setminusER]), setminusSubset1]), setukpairIL]), secondinupair]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), symdiffI1]), symdiffE]), setukpairIR]), upairsubunion]), upairset2E]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), kpairp]), kpairiskpair]), upairinpowunion]), setunionE2]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), ubforcartprodlem3]), ubforcartprodlem2]), ubforcartprodlem1]), setunionsingleton1]), singletonsuniq]), c_0_277]), c_0_278]), c_0_279]), c_0_280]), setunionsingleton]), setunionsingleton2]), setukpairinjL1]), setukpairinjR11]), setukpairinjL]), setukpairinjL2]), cartprodfstin]), kfstpairEq]), theprop]), c_0_281]), setukpairinjR12]), kpairsurjEq]), ksndpairEq]), c_0_282]), setukpairinjR]), setukpairinjR2]), upairequniteq]), setukpairinjR1]), cartprodsndin]), c_0_283]), cartprodpairsurjEq]), cartprodsndpairEq]), cartprodfstpairEq]), cartprodmempaircEq]), cartprodpairmemER]), cartprodpairmemEL]), c_0_284]), c_0_285]), c_0_286]), c_0_287]), c_0_288]), c_0_289]), c_0_290]), c_0_291]), app]), brelnall1]), c_0_292]), c_0_293]), c_0_294]), funcinfuncset]), ap2p]), infuncsetfunc]), brelnall2]), subbreln]), funcGraphProp4]), funcextLem]), funcGraphProp2]), funcGraphProp3]), funcGraphProp1]), c_0_295]), eqbreln]), c_0_296]), c_0_297]), c_0_298]), c_0_299]), c_0_300]), c_0_301]), c_0_302]), c_0_303]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_304]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), nonemptyImpWitness]), c_0_305]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_306]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), nonemptyI1]), c_0_307]), nonemptyE1]), c_0_308]), noeltsimpempty]), emptyI]), setext]), c_0_309]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_310]), c_0_311]), c_0_312]), c_0_313]), c_0_314]), wellorderingAx]), foundationAx]), c_0_315]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_316])).
% 1.35/0.55 thf(c_0_318, negated_conjecture, ![X1715:$i, X1716:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$i, X1725:$i, X1726:$i, X1728:$i, X1729:$i, X1731:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i, X1737:$i, X1738:$i > $i > $o, X1739:$i, X1742:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1749:$i, X1750:$i > $o, X1751:$i, X1752:$i > $o, X1753:$i, X1754:$i, X1755:$i > $o, X1756:$i, X1757:$i, X1758:$i > $o, X1759:$i, X1760:$i > $o, X1762:$i, X1763:$o, X1764:$i, X1765:$i, X1766:$o, X1767:$i, X1768:$i, X1769:$i > $o, X1771:$i, X1772:$i, X1775:$i, X1777:$i, X1779:$i, X1780:$i > $o, X1781:$i, X1782:$i, X1784:$i, X1785:$i > $o, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$o, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$o, X1817:$i, X1818:$i, X1819:$i > $o, X1821:$i, X1822:$i, X1823:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i > $o, X1842:$i, X1843:$i > $o, X1844:$i, X1845:$i, X1846:$i > $o, X1847:$i, X1849:$i, X1850:$i > $o, X1852:$i, X1853:$i, X1854:$i > $o, X1856:$i, X1857:$i, X1858:$i > $o, X1859:$i, X1861:$o, X1862:$i, X1863:$i > $o, X1865:$i, X1866:$i, X1867:$i > $o, X1868:$i, X1870:$i > $o, X1871:$i, X1873:$i > $o, X1874:$i, X1877:$i > $o, X1878:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i > $o, X1889:$i, X1890:$i, X1891:$i > $o, X1892:$i > $o, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i > $o, X1904:$i, X1905:$i, X1906:$i > $o, X1907:$i > $o, X1910:$i, X1911:$i, X1912:$i > $o, X1913:$i > $o, X1916:$i, X1917:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i > $o, X1964:$i, X1965:$i > $o, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$o, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$o, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i > $o, X2120:$i, X2121:$i, X2122:$i > $o, X2124:$i, X2125:$i > $o, X2126:$i, X2128:$i, X2129:$i > $o, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i > $i > $o, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i > $i > $o, X2210:$i, X2211:$i, X2212:$i > $i > $o, X2213:$i, X2214:$i, X2215:$i > $i > $o, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i > $i > $o, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i > $i > $o, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2230:$i > $i > $o, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i > $i, X2259:$i, X2260:$i, X2261:$i > $i, X2263:$i, X2264:$i, X2265:$i > $i, X2267:$i, X2268:$i, X2269:$i, X2270:$i > $o, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i > $o, X2280:$i, X2281:$i, X2282:$i > $o, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2324:$i, X2325:$i, X2326:$i, X2327:$i, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i > $i, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i > $i, X2354:$i, X2355:$i, X2356:$i > $i, X2358:$i, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$o, X2364:$i, X2365:$i, X2366:$i, X2367:$o, X2368:$i, X2369:$i, X2370:$i, X2371:$o, X2372:$i, X2373:$i, X2374:$i, X2375:$o, X2376:$i, X2377:$i, X2378:$i, X2379:$o, X2380:$i, X2381:$i, X2382:$i, X2383:$o, X2384:$i, X2385:$i, X2386:$i, X2387:$i, X2388:$i, X2389:$o, X2390:$i, X2391:$i, X2392:$i, X2393:$o, X2394:$i, X2395:$i, X2396:$i, X2397:$o, X2398:$i, X2399:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$i, X2404:$i, X2405:$i, X2406:$i, X2407:$i, X2408:$i, X2409:$i, X2410:$i, X2411:$i, X2412:$i, X2413:$i, X2414:$i, X2415:$i, X2418:$i, X2419:$i, X2420:$i, X2422:$i, X2423:$i, X2424:$i, X2426:$i, X2427:$i, X2428:$i, X2429:$i, X2430:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2435:$i, X2436:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, X2442:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$i, X2455:$i, X2456:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i, X2463:$i, X2464:$i, X2465:$i, X2466:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2471:$i, X2472:$i, X2473:$i, X2474:$i, X2475:$i, X2476:$i, X2477:$i, X2478:$i, X2479:$i, X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$i, X2486:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2493:$i, X2494:$i, X2495:$i, X2496:$i, X2497:$i, X2498:$i, X2499:$i, X2500:$i, X2501:$i, X2502:$i, X2503:$i, X2504:$i, X2505:$i, X2506:$i, X2507:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$o, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i]:((((~(in @ (esk1_2 @ X1715 @ X1716) @ X1715)|~(in @ (esk1_2 @ X1715 @ X1716) @ X1716)|((X1715)=(X1716)))&((in @ (esk1_2 @ X1715 @ X1716) @ X1715)|(in @ (esk1_2 @ X1715 @ X1716) @ X1716)|((X1715)=(X1716))))&(~(in @ X1718 @ emptyset)&(((~(in @ X1721 @ (setadjoin @ X1719 @ X1720))|(((X1721)=(X1719))|(in @ X1721 @ X1720)))&((((X1721)!=(X1719))|(in @ X1721 @ (setadjoin @ X1719 @ X1720)))&(~(in @ X1721 @ X1720)|(in @ X1721 @ (setadjoin @ X1719 @ X1720)))))&(((~(in @ X1723 @ (powerset @ X1722))|(~(in @ X1724 @ X1723)|(in @ X1724 @ X1722)))&(((in @ (esk2_2 @ X1725 @ X1726) @ X1726)|(in @ X1726 @ (powerset @ X1725)))&(~(in @ (esk2_2 @ X1725 @ X1726) @ X1725)|(in @ X1726 @ (powerset @ X1725)))))&(((((in @ X1729 @ (esk3_2 @ X1728 @ X1729))|~(in @ X1729 @ (setunion @ X1728)))&((in @ (esk3_2 @ X1728 @ X1729) @ X1728)|~(in @ X1729 @ (setunion @ X1728))))&(~(in @ X1732 @ X1733)|~(in @ X1733 @ X1731)|(in @ X1732 @ (setunion @ X1731))))&((in @ emptyset @ omega)&((~(in @ X1734 @ omega)|(in @ (setadjoin @ X1734 @ X1734) @ omega))&(((((in @ (esk4_1 @ X1735) @ omega)|~(in @ emptyset @ X1735)|(~(in @ X1737 @ omega)|(in @ X1737 @ X1735)))&((in @ (esk4_1 @ X1735) @ X1735)|~(in @ emptyset @ X1735)|(~(in @ X1737 @ omega)|(in @ X1737 @ X1735))))&(~(in @ (setadjoin @ (esk4_1 @ X1735) @ (esk4_1 @ X1735)) @ X1735)|~(in @ emptyset @ X1735)|(~(in @ X1737 @ omega)|(in @ X1737 @ X1735))))&((((((in @ (esk7_3 @ X1738 @ X1739 @ X1742) @ X1739)|~(in @ X1742 @ (esk6_2 @ X1738 @ X1739))|(in @ (esk5_2 @ X1738 @ X1739) @ X1739))&((X1738 @ (esk7_3 @ X1738 @ X1739 @ X1742) @ X1742)|~(in @ X1742 @ (esk6_2 @ X1738 @ X1739))|(in @ (esk5_2 @ X1738 @ X1739) @ X1739)))&(~(in @ X1745 @ X1739)|~(X1738 @ X1745 @ X1744)|(in @ X1744 @ (esk6_2 @ X1738 @ X1739))|(in @ (esk5_2 @ X1738 @ X1739) @ X1739)))&((((in @ (esk7_3 @ X1738 @ X1739 @ X1742) @ X1739)|~(in @ X1742 @ (esk6_2 @ X1738 @ X1739))|~(exu @ (X1738 @ (esk5_2 @ X1738 @ X1739))))&((X1738 @ (esk7_3 @ X1738 @ X1739 @ X1742) @ X1742)|~(in @ X1742 @ (esk6_2 @ X1738 @ X1739))|~(exu @ (X1738 @ (esk5_2 @ X1738 @ X1739)))))&(~(in @ X1745 @ X1739)|~(X1738 @ X1745 @ X1744)|(in @ X1744 @ (esk6_2 @ X1738 @ X1739))|~(exu @ (X1738 @ (esk5_2 @ X1738 @ X1739))))))&((((in @ (esk8_1 @ X1746) @ X1746)|~(in @ X1747 @ X1746))&(~(in @ X1749 @ (esk8_1 @ X1746))|~(in @ X1749 @ X1746)|~(in @ X1747 @ X1746)))&((epred1_0)&((~(exu @ X1750)|(X1750 @ (descr @ X1750)))&((~(in @ X1753 @ X1751)|(~(X1752 @ X1753)|(in @ X1753 @ (dsetconstr @ X1751 @ X1752))))&((~(in @ X1756 @ (dsetconstr @ X1754 @ X1755))|(in @ X1756 @ X1754))&((~(in @ X1759 @ (dsetconstr @ X1757 @ X1758))|(X1758 @ X1759))&((((X1760 @ (esk9_1 @ X1760))|~(exu @ X1760))&(~(X1760 @ X1762)|((esk9_1 @ X1760)=(X1762))|~(exu @ X1760)))&((~(in @ X1764 @ (prop2set @ ((X1763))))|(X1763))&((~(in @ X1765 @ emptyset)|(X1766))&((~(in @ X1767 @ emptyset)|~($true))&(~(in @ X1768 @ emptyset)&((~(exu @ X1769)|(X1769 @ (esk10_1 @ X1769)))&(((((in @ (esk12_2 @ X1771 @ X1772) @ X1772)|((X1771)=(X1772))|(in @ (esk11_2 @ X1771 @ X1772) @ X1771))&(~(in @ (esk12_2 @ X1771 @ X1772) @ X1771)|((X1771)=(X1772))|(in @ (esk11_2 @ X1771 @ X1772) @ X1771)))&(((in @ (esk12_2 @ X1771 @ X1772) @ X1772)|((X1771)=(X1772))|~(in @ (esk11_2 @ X1771 @ X1772) @ X1772))&(~(in @ (esk12_2 @ X1771 @ X1772) @ X1771)|((X1771)=(X1772))|~(in @ (esk11_2 @ X1771 @ X1772) @ X1772))))&(((in @ (esk13_1 @ X1775) @ X1775)|((X1775)=(emptyset)))&(((in @ (esk14_1 @ X1777) @ X1777)|((X1777)=(emptyset)))&(((~(in @ X1781 @ (dsetconstr @ X1779 @ X1780))|(X1780 @ X1781)|~(in @ X1781 @ X1779))&(~(X1780 @ X1781)|(in @ X1781 @ (dsetconstr @ X1779 @ X1780))|~(in @ X1781 @ X1779)))&((~(nonempty @ X1782)|(in @ (esk15_1 @ X1782) @ X1782))&((~(in @ X1786 @ X1784)|(~(X1785 @ X1786)|(nonempty @ (dsetconstr @ X1784 @ X1785))))&((~(in @ X1788 @ X1787)|(nonempty @ X1787))&((in @ X1789 @ (setadjoin @ X1789 @ X1790))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1793 @ X1792)|(in @ X1793 @ (setadjoin @ X1791 @ X1792)))&(((((in @ X1796 @ X1795)|(X1797)|((X1796)=(X1794))|~(in @ X1796 @ (setadjoin @ X1794 @ X1795)))&(~(X1797)|(X1797)|((X1796)=(X1794))|~(in @ X1796 @ (setadjoin @ X1794 @ X1795))))&(((in @ X1796 @ X1795)|(X1797)|~(X1797)|~(in @ X1796 @ (setadjoin @ X1794 @ X1795)))&(~(X1797)|(X1797)|~(X1797)|~(in @ X1796 @ (setadjoin @ X1794 @ X1795)))))&((~(in @ X1800 @ (setadjoin @ X1798 @ X1799))|(((X1800)=(X1798))|(in @ X1800 @ X1799)))&(((dsetconstr @ X1801 @ (^[Z0:$i]:($true)))=(X1801))&((((in @ (esk16_2 @ X1802 @ X1803) @ X1803)|(in @ X1803 @ (powerset @ X1802)))&(~(in @ (esk16_2 @ X1802 @ X1803) @ X1802)|(in @ X1803 @ (powerset @ X1802))))&((in @ emptyset @ (powerset @ X1805))&((in @ emptyset @ (powerset @ X1806))&((~(in @ X1808 @ (powerset @ X1807))|(~(in @ X1809 @ X1808)|(in @ X1809 @ X1807)))&((~(in @ X1811 @ X1812)|(~(in @ X1812 @ X1810)|(in @ X1811 @ (setunion @ X1810))))&((((in @ X1814 @ (esk17_3 @ X1813 @ X1814 @ X1815))|(X1815)|~(in @ X1814 @ (setunion @ X1813)))&(((in @ (esk17_3 @ X1813 @ X1814 @ X1815) @ X1813)|(X1815)|~(in @ X1814 @ (setunion @ X1813)))&(~(X1815)|(X1815)|~(in @ X1814 @ (setunion @ X1813)))))&((~(in @ X1818 @ X1817)|(in @ X1818 @ 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emptyset)))))&((~(in @ X2380 @ X2378)|(~(in @ X2381 @ X2378)|(singleton @ (dsetconstr @ X2378 @ (^[Z0:$i]:((((((X2379))&(((Z0)=(X2380)))))|(((~((X2379)))&(((Z0)=(X2381))))))))))))&((~(in @ X2384 @ X2382)|(~(in @ X2385 @ X2382)|(in @ (if @ X2382 @ ((X2383)) @ X2384 @ X2385) @ X2382)))&((~(singleton @ X2386)|(~(in @ X2387 @ X2386)|((setunion @ X2386)=(X2387))))&((~(in @ X2390 @ X2388)|(~(in @ X2391 @ X2388)|(~(X2389)|((if @ X2388 @ ((X2389)) @ X2390 @ X2391)=(X2390)))))&((~(in @ X2394 @ X2392)|(~(in @ X2395 @ X2392)|((X2393)|((if @ X2392 @ ((X2393)) @ X2394 @ X2395)=(X2395)))))&((~(in @ X2398 @ X2396)|(~(in @ X2399 @ X2396)|(in @ (if @ X2396 @ ((X2397)) @ X2398 @ X2399) @ (setadjoin @ X2398 @ (setadjoin @ X2399 @ emptyset)))))&((~(in @ X2401 @ (powerset @ X2400))|(~(in @ X2402 @ (powerset @ X2400))|(in @ (binintersect @ X2401 @ X2402) @ (powerset @ X2400))))&((~(in @ X2404 @ (powerset @ X2403))|(~(in @ X2405 @ (powerset @ X2403))|(in @ (binunion @ X2404 @ X2405) @ (powerset @ X2403))))&((~(in @ X2407 @ (powerset @ X2406))|(in @ (powerset @ X2407) @ (powerset @ (powerset @ X2406))))&((~(in @ X2409 @ (powerset @ X2408))|(~(in @ X2410 @ (powerset @ X2408))|(in @ (setminus @ X2409 @ X2410) @ (powerset @ X2408))))&((~(in @ X2412 @ (powerset @ X2411))|(in @ (setminus @ X2411 @ X2412) @ (powerset @ X2411)))&(((((in @ (esk68_3 @ X2413 @ X2414 @ X2415) @ X2413)|((X2414)=(X2415))|(in @ (esk67_3 @ X2413 @ X2414 @ X2415) @ X2413)|~(in @ X2415 @ (powerset @ X2413))|~(in @ X2414 @ (powerset @ X2413)))&(((in @ (esk68_3 @ X2413 @ X2414 @ X2415) @ X2415)|((X2414)=(X2415))|(in @ (esk67_3 @ X2413 @ X2414 @ X2415) @ X2413)|~(in @ X2415 @ (powerset @ X2413))|~(in @ X2414 @ (powerset @ X2413)))&(~(in @ (esk68_3 @ X2413 @ X2414 @ X2415) @ X2414)|((X2414)=(X2415))|(in @ (esk67_3 @ X2413 @ X2414 @ X2415) @ X2413)|~(in @ X2415 @ (powerset @ X2413))|~(in @ X2414 @ (powerset @ X2413)))))&((((in @ (esk68_3 @ X2413 @ X2414 @ X2415) @ X2413)|((X2414)=(X2415))|(in @ (esk67_3 @ X2413 @ X2414 @ X2415) @ X2414)|~(in @ X2415 @ (powerset @ X2413))|~(in @ X2414 @ (powerset @ X2413)))&(((in @ (esk68_3 @ X2413 @ X2414 @ X2415) @ X2415)|((X2414)=(X2415))|(in @ (esk67_3 @ X2413 @ X2414 @ X2415) @ X2414)|~(in @ X2415 @ (powerset @ X2413))|~(in @ X2414 @ (powerset @ X2413)))&(~(in @ (esk68_3 @ X2413 @ X2414 @ X2415) @ X2414)|((X2414)=(X2415))|(in @ (esk67_3 @ X2413 @ X2414 @ X2415) @ X2414)|~(in @ X2415 @ (powerset @ X2413))|~(in @ X2414 @ (powerset @ X2413)))))&(((in @ (esk68_3 @ X2413 @ X2414 @ X2415) @ X2413)|((X2414)=(X2415))|~(in @ (esk67_3 @ X2413 @ X2414 @ X2415) @ X2415)|~(in @ X2415 @ (powerset @ X2413))|~(in @ X2414 @ (powerset @ X2413)))&(((in @ (esk68_3 @ X2413 @ X2414 @ X2415) @ X2415)|((X2414)=(X2415))|~(in @ (esk67_3 @ X2413 @ X2414 @ X2415) @ X2415)|~(in @ X2415 @ (powerset @ X2413))|~(in @ X2414 @ (powerset @ X2413)))&(~(in @ (esk68_3 @ X2413 @ X2414 @ X2415) @ X2414)|((X2414)=(X2415))|~(in @ (esk67_3 @ X2413 @ X2414 @ X2415) @ X2415)|~(in @ X2415 @ (powerset @ X2413))|~(in @ X2414 @ (powerset @ X2413)))))))&((((in @ (esk69_3 @ X2418 @ X2419 @ X2420) @ X2418)|(subset @ X2419 @ X2420)|~(in @ X2420 @ (powerset @ X2418))|~(in @ X2419 @ (powerset @ X2418)))&(((in @ (esk69_3 @ X2418 @ X2419 @ X2420) @ X2419)|(subset @ X2419 @ X2420)|~(in @ X2420 @ (powerset @ X2418))|~(in @ X2419 @ (powerset @ X2418)))&(~(in @ (esk69_3 @ X2418 @ X2419 @ X2420) @ X2420)|(subset @ X2419 @ X2420)|~(in @ X2420 @ (powerset @ X2418))|~(in @ X2419 @ (powerset @ X2418)))))&((((in @ (esk70_3 @ X2422 @ X2423 @ X2424) @ X2422)|(in @ X2423 @ (powerset @ X2424))|~(in @ X2424 @ (powerset @ X2422))|~(in @ X2423 @ (powerset @ X2422)))&(((in @ (esk70_3 @ X2422 @ X2423 @ X2424) @ X2423)|(in @ X2423 @ (powerset @ X2424))|~(in @ X2424 @ (powerset @ X2422))|~(in @ X2423 @ (powerset @ X2422)))&(~(in @ (esk70_3 @ X2422 @ X2423 @ X2424) @ X2424)|(in @ X2423 @ (powerset @ X2424))|~(in @ X2424 @ (powerset @ X2422))|~(in @ X2423 @ (powerset @ X2422)))))&((~(in @ X2427 @ (powerset @ X2426))|(~(in @ X2428 @ (powerset @ X2426))|(~(in @ X2429 @ X2426)|(~(in @ X2427 @ (powerset @ X2428))|(~(in @ X2429 @ X2427)|(in @ X2429 @ X2428))))))&((~(in @ X2431 @ (powerset @ X2430))|(~(in @ X2432 @ X2430)|(~(in @ X2432 @ X2431)|~(in @ X2432 @ (setminus @ X2430 @ X2431)))))&((~(in @ X2434 @ (powerset @ X2433))|(~(in @ X2435 @ X2433)|((in @ X2435 @ (setminus @ X2433 @ X2434))|(in @ X2435 @ X2434))))&((~(in @ X2437 @ (powerset @ X2436))|(~(in @ X2438 @ (powerset @ X2436))|(~(in @ X2439 @ X2436)|((in @ X2439 @ X2437)|~(in @ X2439 @ (binintersect @ X2437 @ X2438))))))&((~(in @ X2441 @ (powerset @ X2440))|(~(in @ X2442 @ (powerset @ X2440))|(~(in @ X2443 @ X2440)|((in @ X2443 @ X2442)|~(in @ X2443 @ (binintersect @ X2441 @ X2442))))))&((~(in @ X2445 @ (powerset @ X2444))|(~(in @ X2446 @ (powerset @ X2444))|(~(in @ X2447 @ X2444)|(~(subset @ X2445 @ (setminus @ X2444 @ X2446))|(~(in @ X2447 @ X2446)|~(in @ X2447 @ X2445))))))&((~(in @ X2449 @ (powerset @ X2448))|(~(in @ X2450 @ (powerset @ X2448))|(~(in @ X2451 @ X2448)|(~(subset @ X2449 @ X2450)|((in @ X2451 @ X2450)|~(in @ X2451 @ X2449))))))&((~(in @ X2453 @ (powerset @ X2452))|(~(in @ X2454 @ (powerset @ X2452))|(~(subset @ X2453 @ X2454)|(subset @ (setminus @ X2452 @ X2454) @ (setminus @ X2452 @ X2453)))))&((~(in @ X2456 @ (powerset @ X2455))|(~(in @ X2457 @ (powerset @ X2455))|(~(subset @ (setminus @ X2455 @ X2457) @ (setminus @ X2455 @ X2456))|(subset @ X2456 @ X2457))))&((~(in @ X2459 @ (powerset @ X2458))|(~(in @ X2460 @ X2458)|(~(in @ X2460 @ X2459)|(in @ X2460 @ (setminus @ X2458 @ (setminus @ X2458 @ X2459))))))&((~(in @ X2462 @ (powerset @ X2461))|(~(in @ X2463 @ X2461)|(~(in @ X2463 @ (setminus @ X2461 @ (setminus @ X2461 @ X2462)))|(in @ X2463 @ X2462))))&((~(in @ X2465 @ (powerset @ X2464))|(subset @ X2465 @ (setminus @ X2464 @ (setminus @ X2464 @ X2465))))&((~(in @ X2467 @ (powerset @ X2466))|(subset @ (setminus @ X2466 @ (setminus @ X2466 @ X2467)) @ X2467))&((~(in @ X2469 @ (powerset @ X2468))|((X2469)=(setminus @ X2468 @ (setminus @ X2468 @ X2469))))&((~(in @ X2471 @ (powerset @ X2470))|(~(in @ X2472 @ (powerset @ X2470))|(~(in @ X2473 @ X2470)|(~(in @ X2473 @ (setminus @ X2470 @ X2471))|~(in @ X2473 @ (binintersect @ X2471 @ X2472))))))&((~(in @ X2475 @ (powerset @ X2474))|(~(in @ X2476 @ (powerset @ X2474))|(~(in @ X2477 @ X2474)|(~(in @ X2477 @ (setminus @ X2474 @ X2475))|(in @ X2477 @ (setminus @ X2474 @ (binintersect @ X2475 @ X2476)))))))&((~(in @ X2479 @ (powerset @ X2478))|(~(in @ X2480 @ (powerset @ X2478))|(subset @ (setminus @ X2478 @ X2479) @ (setminus @ X2478 @ (binintersect @ X2479 @ X2480)))))&((~(in @ X2482 @ (powerset @ X2481))|(~(in @ X2483 @ (powerset @ X2481))|(in @ (setminus @ X2481 @ X2482) @ (powerset @ (setminus @ X2481 @ (binintersect @ X2482 @ X2483))))))&((~(in @ X2485 @ (powerset @ X2484))|(~(in @ X2486 @ (powerset @ X2484))|(~(subset @ X2485 @ (setminus @ X2484 @ X2486))|(~(in @ X2487 @ X2484)|(~(in @ X2487 @ X2486)|(in @ X2487 @ (setminus @ X2484 @ X2485)))))))&((~(in @ X2489 @ (powerset @ X2488))|(~(in @ X2490 @ (powerset @ X2488))|(~(subset @ X2489 @ (setminus @ X2488 @ X2490))|(subset @ X2490 @ (setminus @ X2488 @ X2489)))))&((~(in @ X2492 @ (powerset @ X2491))|(~(in @ X2493 @ (powerset @ X2491))|(~(in @ X2494 @ X2491)|((in @ X2494 @ (binunion @ X2492 @ X2493))|~(in @ X2494 @ X2492)))))&((~(in @ X2496 @ (powerset @ X2495))|(~(in @ X2497 @ (powerset @ X2495))|(~(in @ X2498 @ X2495)|((in @ X2498 @ (binunion @ X2496 @ X2497))|~(in @ X2498 @ X2497)))))&((~(in @ X2500 @ (powerset @ X2499))|(~(in @ X2501 @ (powerset @ X2499))|(~(in @ X2502 @ (powerset @ X2499))|(~(in @ X2503 @ X2499)|(~(in @ X2503 @ (binintersect @ X2500 @ X2501))|(in @ X2503 @ (binunion @ X2500 @ X2502)))))))&((~(in @ X2505 @ (powerset @ X2504))|(~(in @ X2506 @ (powerset @ X2504))|(~(in @ X2507 @ (powerset @ X2504))|(~(in @ X2508 @ X2504)|(~(in @ X2508 @ (binintersect @ X2505 @ X2506))|(in @ X2508 @ (binunion @ X2506 @ X2507)))))))&((~(in @ X2510 @ (powerset @ X2509))|(~(in @ X2511 @ (powerset @ X2509))|(~(in @ X2512 @ (powerset @ X2509))|(~(in @ X2513 @ X2509)|(~(in @ X2513 @ (binintersect @ X2510 @ X2511))|(in @ X2513 @ (binintersect @ (binunion @ X2510 @ X2512) @ (binunion @ X2511 @ X2512))))))))&((~(in @ X2515 @ (powerset @ X2514))|(~(in @ X2516 @ (powerset @ X2514))|(~(in @ X2517 @ (powerset @ X2514))|(in @ (binintersect @ X2515 @ X2516) @ (powerset @ (binintersect @ (binunion @ X2515 @ X2517) @ (binunion @ X2516 @ X2517)))))))&((~(in @ X2519 @ (powerset @ X2518))|(~(in @ X2520 @ (powerset @ X2518))|(~(in @ X2521 @ X2518)|(~(in @ X2521 @ (setminus @ X2518 @ (binunion @ X2519 @ X2520)))|~(in @ X2521 @ X2519)))))&((~(in @ X2523 @ (powerset @ X2522))|(~(in @ X2524 @ (powerset @ X2522))|(~(in @ X2525 @ X2522)|(~(in @ X2525 @ (setminus @ X2522 @ (binunion @ X2523 @ X2524)))|(in @ X2525 @ (setminus @ X2522 @ X2523))))))&(((((in @ X2530 @ X2528)|(X2529)|(in @ X2530 @ X2527)|~(in @ X2530 @ (binunion @ X2527 @ X2528))|~(in @ X2530 @ X2526)|~(in @ X2528 @ (powerset @ X2526))|~(in @ X2527 @ (powerset @ X2526)))&(~(X2529)|(X2529)|(in @ X2530 @ X2527)|~(in @ X2530 @ (binunion @ X2527 @ X2528))|~(in @ X2530 @ X2526)|~(in @ X2528 @ (powerset @ X2526))|~(in @ X2527 @ (powerset @ X2526))))&(((in @ X2530 @ X2528)|(X2529)|~(X2529)|~(in @ X2530 @ (binunion @ X2527 @ X2528))|~(in @ X2530 @ X2526)|~(in @ X2528 @ (powerset @ X2526))|~(in @ X2527 @ (powerset @ X2526)))&(~(X2529)|(X2529)|~(X2529)|~(in @ X2530 @ (binunion @ X2527 @ X2528))|~(in @ X2530 @ X2526)|~(in @ X2528 @ (powerset @ X2526))|~(in @ X2527 @ (powerset @ X2526)))))&((~(in @ X2532 @ (powerset @ X2531))|(~(in @ X2533 @ (powerset @ X2531))|(~(in @ X2534 @ X2531)|((in @ X2534 @ X2532)|((in @ X2534 @ X2533)|~(in @ X2534 @ (binunion @ X2532 @ X2533)))))))&((in @ esk72_0 @ (powerset @ esk71_0))&((in @ esk73_0 @ (powerset @ esk71_0))&((in @ esk74_0 @ esk71_0)&((in @ esk74_0 @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0)))&~(in @ esk74_0 @ (setminus @ esk71_0 @ esk72_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_317])])])])])])])).
% 1.35/0.55 thf(c_0_319, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((~((in @ X2 @ (setminus @ X3 @ X4)))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_318])).
% 1.35/0.55 thf(c_0_320, negated_conjecture, (in @ esk74_0 @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0))), inference(split_conjunct,[status(thm)],[c_0_318])).
% 1.35/0.55 thf(c_0_321, negated_conjecture, ~((in @ esk74_0 @ (binunion @ esk72_0 @ esk73_0))), inference(spm,[status(thm)],[c_0_319, c_0_320])).
% 1.35/0.55 thf(c_0_322, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X3 @ X4))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_318])).
% 1.35/0.55 thf(c_0_323, negated_conjecture, ~((in @ esk74_0 @ (setminus @ esk71_0 @ esk72_0))), inference(split_conjunct,[status(thm)],[c_0_318])).
% 1.35/0.55 thf(c_0_324, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setminus @ X3 @ X4))|(in @ X2 @ X4)|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_318])).
% 1.35/0.55 thf(c_0_325, negated_conjecture, (in @ esk74_0 @ esk71_0), inference(split_conjunct,[status(thm)],[c_0_318])).
% 1.35/0.55 thf(c_0_326, negated_conjecture, ~((in @ esk74_0 @ esk72_0)), inference(spm,[status(thm)],[c_0_321, c_0_322])).
% 1.35/0.55 thf(c_0_327, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_323, c_0_324]), c_0_325])]), c_0_326]), ['proof']).
% 1.35/0.55 % SZS output end CNFRefutation
% 1.35/0.55 % Parsed axioms : 571
% 1.35/0.55 % Removed by relevancy pruning/SinE : 307
% 1.35/0.55 % Initial clauses : 429
% 1.35/0.55 % Removed in clause preprocessing : 37
% 1.35/0.55 % Initial clauses in saturation : 392
% 1.35/0.55 % Processed clauses : 704
% 1.35/0.55 % ...of these trivial : 48
% 1.35/0.55 % ...subsumed : 310
% 1.35/0.55 % ...remaining for further processing : 346
% 1.35/0.55 % Other redundant clauses eliminated : 29
% 1.35/0.55 % Clauses deleted for lack of memory : 0
% 1.35/0.55 % Backward-subsumed : 1
% 1.35/0.55 % Backward-rewritten : 13
% 1.35/0.55 % Generated clauses : 2669
% 1.35/0.55 % ...of the previous two non-redundant : 2287
% 1.35/0.55 % ...aggressively subsumed : 0
% 1.35/0.55 % Contextual simplify-reflections : 0
% 1.35/0.55 % Paramodulations : 2636
% 1.35/0.55 % Factorizations : 0
% 1.35/0.55 % NegExts : 0
% 1.35/0.55 % Equation resolutions : 32
% 1.35/0.55 % Disequality decompositions : 0
% 1.35/0.55 % Total rewrite steps : 412
% 1.35/0.55 % ...of those cached : 318
% 1.35/0.55 % Propositional unsat checks : 0
% 1.35/0.55 % Propositional check models : 0
% 1.35/0.55 % Propositional check unsatisfiable : 0
% 1.35/0.55 % Propositional clauses : 0
% 1.35/0.55 % Propositional clauses after purity: 0
% 1.35/0.55 % Propositional unsat core size : 0
% 1.35/0.55 % Propositional preprocessing time : 0.000
% 1.35/0.55 % Propositional encoding time : 0.000
% 1.35/0.55 % Propositional solver time : 0.000
% 1.35/0.55 % Success case prop preproc time : 0.000
% 1.35/0.55 % Success case prop encoding time : 0.000
% 1.35/0.55 % Success case prop solver time : 0.000
% 1.35/0.55 % Current number of processed clauses : 322
% 1.35/0.55 % Positive orientable unit clauses : 75
% 1.35/0.55 % Positive unorientable unit clauses: 0
% 1.35/0.55 % Negative unit clauses : 10
% 1.35/0.55 % Non-unit-clauses : 237
% 1.35/0.55 % Current number of unprocessed clauses: 1908
% 1.35/0.55 % ...number of literals in the above : 5220
% 1.35/0.55 % Current number of archived formulas : 0
% 1.35/0.55 % Current number of archived clauses : 14
% 1.35/0.55 % Clause-clause subsumption calls (NU) : 13815
% 1.35/0.55 % Rec. Clause-clause subsumption calls : 11104
% 1.35/0.55 % Non-unit clause-clause subsumptions : 273
% 1.35/0.55 % Unit Clause-clause subsumption calls : 635
% 1.35/0.55 % Rewrite failures with RHS unbound : 0
% 1.35/0.55 % BW rewrite match attempts : 24
% 1.35/0.55 % BW rewrite match successes : 9
% 1.35/0.55 % Condensation attempts : 0
% 1.35/0.55 % Condensation successes : 0
% 1.35/0.55 % Termbank termtop insertions : 94014
% 1.35/0.55 % Search garbage collected termcells : 26712
% 1.35/0.55
% 1.35/0.55 % -------------------------------------------------
% 1.35/0.55 % User time : 0.195 s
% 1.35/0.55 % System time : 0.015 s
% 1.35/0.55 % Total time : 0.210 s
% 1.35/0.55 % Maximum resident set size: 9908 pages
% 1.35/0.55
% 1.35/0.55 % -------------------------------------------------
% 1.35/0.55 % User time : 0.413 s
% 1.35/0.55 % System time : 0.119 s
% 1.35/0.55 % Total time : 0.532 s
% 1.35/0.55 % Maximum resident set size: 5632 pages
% 1.35/0.55 % E exiting
%------------------------------------------------------------------------------