0.00/0.04	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.07	% Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.16/0.42	% Computer : n022.cluster.edu
0.16/0.42	% Model    : x86_64 x86_64
0.16/0.42	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.16/0.42	% Memory   : 8046.5625MB
0.16/0.42	% OS       : Linux 6.8.0-71-generic
0.16/0.42	% CPULimit : 1440
0.16/0.42	% WCLimit  : 180
0.16/0.42	% DateTime : Mon Jul 27 12:27:58 UTC 2026
0.16/0.43	% CPUTime  : 
0.16/0.43	Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.16/0.48	Running higher-order theorem proving
0.24/0.59	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=180 /export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p
122.23/18.49	% Version: 3.5.1-ho
122.23/18.49	% Preprocessing class: HSLMSLSSLLLCHFA.
122.23/18.49	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
122.23/18.49	% Starting ehoh_best5 with 180s (1) cores
122.23/18.49	% Starting almost_fo_3_lam with 180s (1) cores
122.23/18.49	% Starting new_bool_5 with 180s (1) cores
122.23/18.49	% Starting pre_casc_3 with 180s (1) cores
122.23/18.49	% Starting ho_unfolding_8 with 180s (1) cores
122.23/18.49	% Starting new_ho_10_cnf2 with 180s (1) cores
122.23/18.49	% Starting new_bool_3 with 180s (1) cores
122.23/18.49	% Starting new_ho_5 with 180s (1) cores
122.23/18.49	% almost_fo_3_lam with pid 888114 completed with status 0
122.23/18.49	% Result found by almost_fo_3_lam
122.23/18.49	% Preprocessing class: HSLMSLSSLLLCHFA.
122.23/18.49	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
122.23/18.49	% Starting ehoh_best5 with 180s (1) cores
122.23/18.49	% Starting almost_fo_3_lam with 180s (1) cores
122.23/18.49	% (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
122.23/18.49	% No SInE strategy applied
122.23/18.49	% Search class: HGHSM-FSLM32-MHFMMSBN
122.23/18.49	% Scheduled 11 strats onto 1 cores with 180 seconds (180 total)
122.23/18.49	% Starting SubtermCWHack with 17s (1) cores
122.23/18.49	% SubtermCWHack with pid 888126 completed with status 8
122.23/18.50	% Starting almost_fo_3_lam with 19s (1) cores
122.23/18.50	% almost_fo_3_lam with pid 888131 completed with status 0
122.23/18.50	% Result found by almost_fo_3_lam
122.23/18.50	% Preprocessing class: HSLMSLSSLLLCHFA.
122.23/18.50	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
122.23/18.50	% Starting ehoh_best5 with 180s (1) cores
122.23/18.50	% Starting almost_fo_3_lam with 180s (1) cores
122.23/18.50	% (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
122.23/18.50	% No SInE strategy applied
122.23/18.50	% Search class: HGHSM-FSLM32-MHFMMSBN
122.23/18.50	% Scheduled 11 strats onto 1 cores with 180 seconds (180 total)
122.23/18.50	% Starting SubtermCWHack with 17s (1) cores
122.23/18.50	% SubtermCWHack with pid 888126 completed with status 8
122.23/18.50	% Starting almost_fo_3_lam with 19s (1) cores
122.23/18.50	% Preprocessing time       : 0.017 s
122.23/18.50	% Presaturation interreduction done
122.23/18.50	
122.23/18.50	% Proof found!
122.23/18.50	% SZS status Theorem
122.23/18.50	% SZS output start CNFRefutation
122.23/18.50	thf(decl_23, type, in: $i > $i > $o).
122.23/18.50	thf(decl_24, type, exu: ($i > $o) > $o).
122.23/18.50	thf(decl_25, type, setextAx: $o).
122.23/18.50	thf(decl_26, type, emptyset: $i).
122.23/18.50	thf(decl_27, type, emptysetAx: $o).
122.23/18.50	thf(decl_28, type, setadjoin: $i > $i > $i).
122.23/18.50	thf(decl_29, type, setadjoinAx: $o).
122.23/18.50	thf(decl_30, type, powerset: $i > $i).
122.23/18.50	thf(decl_31, type, powersetAx: $o).
122.23/18.50	thf(decl_32, type, setunion: $i > $i).
122.23/18.50	thf(decl_33, type, setunionAx: $o).
122.23/18.50	thf(decl_34, type, omega: $i).
122.23/18.50	thf(decl_35, type, omega0Ax: $o).
122.23/18.50	thf(decl_36, type, omegaSAx: $o).
122.23/18.50	thf(decl_37, type, omegaIndAx: $o).
122.23/18.50	thf(decl_38, type, replAx: $o).
122.23/18.50	thf(decl_39, type, foundationAx: $o).
122.23/18.50	thf(decl_40, type, wellorderingAx: $o).
122.23/18.50	thf(decl_41, type, descr: ($i > $o) > $i).
122.23/18.50	thf(decl_42, type, descrp: $o).
122.23/18.50	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
122.23/18.50	thf(decl_44, type, dsetconstrI: $o).
122.23/18.50	thf(decl_45, type, dsetconstrEL: $o).
122.23/18.50	thf(decl_46, type, dsetconstrER: $o).
122.23/18.50	thf(decl_47, type, exuE1: $o).
122.23/18.50	thf(decl_48, type, prop2set: $o > $i).
122.23/18.50	thf(decl_49, type, prop2setE: $o).
122.23/18.50	thf(decl_50, type, emptysetE: $o).
122.23/18.50	thf(decl_51, type, emptysetimpfalse: $o).
122.23/18.50	thf(decl_52, type, notinemptyset: $o).
122.23/18.50	thf(decl_53, type, exuE3e: $o).
122.23/18.50	thf(decl_54, type, setext: $o).
122.23/18.50	thf(decl_55, type, emptyI: $o).
122.23/18.50	thf(decl_56, type, noeltsimpempty: $o).
122.23/18.50	thf(decl_57, type, setbeta: $o).
122.23/18.50	thf(decl_58, type, nonempty: $i > $o).
122.23/18.50	thf(decl_59, type, nonemptyE1: $o).
122.23/18.50	thf(decl_60, type, nonemptyI: $o).
122.23/18.50	thf(decl_61, type, nonemptyI1: $o).
122.23/18.50	thf(decl_62, type, setadjoinIL: $o).
122.23/18.50	thf(decl_63, type, emptyinunitempty: $o).
122.23/18.50	thf(decl_64, type, setadjoinIR: $o).
122.23/18.50	thf(decl_65, type, setadjoinE: $o).
122.23/18.50	thf(decl_66, type, setadjoinOr: $o).
122.23/18.50	thf(decl_67, type, setoftrueEq: $o).
122.23/18.50	thf(decl_68, type, powersetI: $o).
122.23/18.50	thf(decl_69, type, emptyinPowerset: $o).
122.23/18.50	thf(decl_70, type, emptyInPowerset: $o).
122.23/18.50	thf(decl_71, type, powersetE: $o).
122.23/18.50	thf(decl_72, type, setunionI: $o).
122.23/18.50	thf(decl_73, type, setunionE: $o).
122.23/18.50	thf(decl_74, type, subPowSU: $o).
122.23/18.50	thf(decl_75, type, exuE2: $o).
122.23/18.50	thf(decl_76, type, nonemptyImpWitness: $o).
122.23/18.50	thf(decl_77, type, uniqinunit: $o).
122.23/18.50	thf(decl_78, type, notinsingleton: $o).
122.23/18.50	thf(decl_79, type, eqinunit: $o).
122.23/18.50	thf(decl_80, type, singletonsswitch: $o).
122.23/18.50	thf(decl_81, type, upairsetE: $o).
122.23/18.50	thf(decl_82, type, upairsetIL: $o).
122.23/18.50	thf(decl_83, type, upairsetIR: $o).
122.23/18.50	thf(decl_84, type, emptyE1: $o).
122.23/18.50	thf(decl_85, type, vacuousDall: $o).
122.23/18.50	thf(decl_86, type, quantDeMorgan1: $o).
122.23/18.50	thf(decl_87, type, quantDeMorgan2: $o).
122.23/18.50	thf(decl_88, type, quantDeMorgan3: $o).
122.23/18.50	thf(decl_89, type, quantDeMorgan4: $o).
122.23/18.50	thf(decl_90, type, prop2setI: $o).
122.23/18.50	thf(decl_91, type, set2prop: $i > $o).
122.23/18.50	thf(decl_92, type, prop2set2propI: $o).
122.23/18.50	thf(decl_93, type, notdexE: $o).
122.23/18.50	thf(decl_94, type, notdallE: $o).
122.23/18.50	thf(decl_95, type, exuI1: $o).
122.23/18.50	thf(decl_96, type, exuI3: $o).
122.23/18.50	thf(decl_97, type, exuI2: $o).
122.23/18.50	thf(decl_98, type, inCongP: $o).
122.23/18.50	thf(decl_99, type, in__Cong: $o).
122.23/18.50	thf(decl_100, type, exuE3u: $o).
122.23/18.50	thf(decl_101, type, exu__Cong: $o).
122.23/18.50	thf(decl_102, type, emptyset__Cong: $o).
122.23/18.50	thf(decl_103, type, setadjoin__Cong: $o).
122.23/18.50	thf(decl_104, type, powerset__Cong: $o).
122.23/18.50	thf(decl_105, type, setunion__Cong: $o).
122.23/18.50	thf(decl_106, type, omega__Cong: $o).
122.23/18.50	thf(decl_107, type, exuEu: $o).
122.23/18.50	thf(decl_108, type, descr__Cong: $o).
122.23/18.50	thf(decl_109, type, dsetconstr__Cong: $o).
122.23/18.50	thf(decl_110, type, subset: $i > $i > $o).
122.23/18.50	thf(decl_113, type, subsetI1: $o).
122.23/18.50	thf(decl_114, type, eqimpsubset2: $o).
122.23/18.50	thf(decl_115, type, eqimpsubset1: $o).
122.23/18.50	thf(decl_116, type, subsetI2: $o).
122.23/18.50	thf(decl_117, type, emptysetsubset: $o).
122.23/18.50	thf(decl_118, type, subsetE: $o).
122.23/18.50	thf(decl_119, type, subsetE2: $o).
122.23/18.50	thf(decl_120, type, notsubsetI: $o).
122.23/18.50	thf(decl_121, type, notequalI1: $o).
122.23/18.50	thf(decl_122, type, notequalI2: $o).
122.23/18.50	thf(decl_123, type, subsetRefl: $o).
122.23/18.50	thf(decl_124, type, subsetTrans: $o).
122.23/18.50	thf(decl_125, type, setadjoinSub: $o).
122.23/18.50	thf(decl_126, type, setadjoinSub2: $o).
122.23/18.50	thf(decl_127, type, subset2powerset: $o).
122.23/18.50	thf(decl_128, type, setextsub: $o).
122.23/18.50	thf(decl_129, type, subsetemptysetimpeq: $o).
122.23/18.50	thf(decl_130, type, powersetI1: $o).
122.23/18.50	thf(decl_131, type, powersetE1: $o).
122.23/18.50	thf(decl_132, type, inPowerset: $o).
122.23/18.50	thf(decl_133, type, powersetsubset: $o).
122.23/18.50	thf(decl_134, type, sepInPowerset: $o).
122.23/18.50	thf(decl_135, type, sepSubset: $o).
122.23/18.50	thf(decl_136, type, binunion: $i > $i > $i).
122.23/18.50	thf(decl_137, type, binunionIL: $o).
122.23/18.50	thf(decl_138, type, upairset2IR: $o).
122.23/18.50	thf(decl_139, type, binunionIR: $o).
122.23/18.50	thf(decl_140, type, binunionEcases: $o).
122.23/18.50	thf(decl_141, type, binunionE: $o).
122.23/18.50	thf(decl_142, type, binunionLsub: $o).
122.23/18.50	thf(decl_143, type, binunionRsub: $o).
122.23/18.50	thf(decl_144, type, binintersect: $i > $i > $i).
122.23/18.50	thf(decl_145, type, binintersectI: $o).
122.23/18.50	thf(decl_146, type, binintersectSubset5: $o).
122.23/18.50	thf(decl_147, type, binintersectEL: $o).
122.23/18.50	thf(decl_148, type, binintersectLsub: $o).
122.23/18.50	thf(decl_149, type, binintersectSubset2: $o).
122.23/18.50	thf(decl_150, type, binintersectSubset3: $o).
122.23/18.50	thf(decl_151, type, binintersectER: $o).
122.23/18.50	thf(decl_152, type, disjointsetsI1: $o).
122.23/18.50	thf(decl_153, type, binintersectRsub: $o).
122.23/18.50	thf(decl_154, type, binintersectSubset4: $o).
122.23/18.50	thf(decl_155, type, binintersectSubset1: $o).
122.23/18.50	thf(decl_156, type, bs114d: $o).
122.23/18.50	thf(decl_158, type, setminus: $i > $i > $i).
122.23/18.50	thf(decl_159, type, setminusI: $o).
122.23/18.50	thf(decl_160, type, setminusEL: $o).
122.23/18.50	thf(decl_161, type, setminusER: $o).
122.23/18.50	thf(decl_162, type, setminusSubset2: $o).
122.23/18.50	thf(decl_163, type, setminusERneg: $o).
122.23/18.50	thf(decl_164, type, setminusELneg: $o).
122.23/18.50	thf(decl_165, type, setminusILneg: $o).
122.23/18.50	thf(decl_166, type, setminusIRneg: $o).
122.23/18.50	thf(decl_167, type, setminusLsub: $o).
122.23/18.50	thf(decl_168, type, setminusSubset1: $o).
122.23/18.50	thf(decl_169, type, symdiff: $i > $i > $i).
122.23/18.50	thf(decl_170, type, symdiffE: $o).
122.23/18.50	thf(decl_171, type, symdiffI1: $o).
122.23/18.50	thf(decl_172, type, symdiffI2: $o).
122.23/18.50	thf(decl_173, type, symdiffIneg1: $o).
122.23/18.50	thf(decl_174, type, symdiffIneg2: $o).
122.23/18.50	thf(decl_175, type, iskpair: $i > $o).
122.23/18.50	thf(decl_176, type, secondinupair: $o).
122.23/18.50	thf(decl_177, type, setukpairIL: $o).
122.23/18.50	thf(decl_178, type, setukpairIR: $o).
122.23/18.50	thf(decl_179, type, kpairiskpair: $o).
122.23/18.50	thf(decl_180, type, kpair: $i > $i > $i).
122.23/18.50	thf(decl_181, type, kpairp: $o).
122.23/18.50	thf(decl_182, type, cartprod: $i > $i > $i).
122.23/18.50	thf(decl_183, type, singletonsubset: $o).
122.23/18.50	thf(decl_184, type, singletoninpowerset: $o).
122.23/18.50	thf(decl_185, type, singletoninpowunion: $o).
122.23/18.50	thf(decl_186, type, upairset2E: $o).
122.23/18.50	thf(decl_187, type, upairsubunion: $o).
122.23/18.50	thf(decl_188, type, upairinpowunion: $o).
122.23/18.50	thf(decl_189, type, ubforcartprodlem1: $o).
122.23/18.50	thf(decl_190, type, ubforcartprodlem2: $o).
122.23/18.50	thf(decl_191, type, ubforcartprodlem3: $o).
122.23/18.50	thf(decl_192, type, cartprodpairin: $o).
122.23/18.50	thf(decl_193, type, cartprodmempair1: $o).
122.23/18.50	thf(decl_194, type, cartprodmempair: $o).
122.23/18.50	thf(decl_195, type, setunionE2: $o).
122.23/18.50	thf(decl_196, type, setunionsingleton1: $o).
122.23/18.50	thf(decl_197, type, setunionsingleton2: $o).
122.23/18.50	thf(decl_198, type, setunionsingleton: $o).
122.23/18.50	thf(decl_199, type, singleton: $i > $o).
122.23/18.50	thf(decl_200, type, singletonprop: $o).
122.23/18.50	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
122.23/18.50	thf(decl_202, type, ex1E1: $o).
122.23/18.50	thf(decl_203, type, ex1I: $o).
122.23/18.50	thf(decl_204, type, ex1I2: $o).
122.23/18.50	thf(decl_205, type, singletonsuniq: $o).
122.23/18.50	thf(decl_210, type, setukpairinjL1: $o).
122.23/18.50	thf(decl_211, type, kfstsingleton: $o).
122.23/18.50	thf(decl_212, type, theprop: $o).
122.23/18.50	thf(decl_213, type, kfst: $i > $i).
122.23/18.50	thf(decl_214, type, kfstpairEq: $o).
122.23/18.50	thf(decl_215, type, cartprodfstin: $o).
122.23/18.50	thf(decl_216, type, setukpairinjL2: $o).
122.23/18.50	thf(decl_217, type, setukpairinjL: $o).
122.23/18.50	thf(decl_218, type, setukpairinjR11: $o).
122.23/18.50	thf(decl_219, type, setukpairinjR12: $o).
122.23/18.50	thf(decl_220, type, setukpairinjR1: $o).
122.23/18.50	thf(decl_221, type, upairequniteq: $o).
122.23/18.50	thf(decl_222, type, setukpairinjR2: $o).
122.23/18.50	thf(decl_223, type, setukpairinjR: $o).
122.23/18.50	thf(decl_224, type, ksndsingleton: $o).
122.23/18.50	thf(decl_225, type, ksnd: $i > $i).
122.23/18.50	thf(decl_226, type, ksndpairEq: $o).
122.23/18.50	thf(decl_227, type, kpairsurjEq: $o).
122.23/18.50	thf(decl_228, type, cartprodsndin: $o).
122.23/18.50	thf(decl_229, type, cartprodpairmemEL: $o).
122.23/18.50	thf(decl_230, type, cartprodpairmemER: $o).
122.23/18.50	thf(decl_231, type, cartprodmempaircEq: $o).
122.23/18.50	thf(decl_232, type, cartprodfstpairEq: $o).
122.23/18.50	thf(decl_233, type, cartprodsndpairEq: $o).
122.23/18.50	thf(decl_234, type, cartprodpairsurjEq: $o).
122.23/18.50	thf(decl_235, type, breln: $i > $i > $i > $o).
122.23/18.50	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
122.23/18.50	thf(decl_237, type, dpsetconstrI: $o).
122.23/18.50	thf(decl_238, type, dpsetconstrSub: $o).
122.23/18.50	thf(decl_239, type, setOfPairsIsBReln: $o).
122.23/18.50	thf(decl_240, type, dpsetconstrERa: $o).
122.23/18.50	thf(decl_241, type, dpsetconstrEL1: $o).
122.23/18.50	thf(decl_242, type, dpsetconstrEL2: $o).
122.23/18.50	thf(decl_243, type, dpsetconstrER: $o).
122.23/18.50	thf(decl_244, type, func: $i > $i > $i > $o).
122.23/18.50	thf(decl_245, type, funcSet: $i > $i > $i).
122.23/18.50	thf(decl_246, type, funcImageSingleton: $o).
122.23/18.50	thf(decl_247, type, apProp: $o).
122.23/18.50	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
122.23/18.50	thf(decl_249, type, app: $o).
122.23/18.50	thf(decl_250, type, infuncsetfunc: $o).
122.23/18.50	thf(decl_251, type, ap2p: $o).
122.23/18.50	thf(decl_252, type, funcinfuncset: $o).
122.23/18.50	thf(decl_253, type, lamProp: $o).
122.23/18.50	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
122.23/18.50	thf(decl_255, type, lamp: $o).
122.23/18.50	thf(decl_256, type, lam2p: $o).
122.23/18.50	thf(decl_257, type, brelnall1: $o).
122.23/18.50	thf(decl_258, type, brelnall2: $o).
122.23/18.50	thf(decl_259, type, ex1E2: $o).
122.23/18.50	thf(decl_260, type, funcGraphProp1: $o).
122.23/18.50	thf(decl_261, type, funcGraphProp3: $o).
122.23/18.50	thf(decl_262, type, funcGraphProp2: $o).
122.23/18.50	thf(decl_263, type, funcextLem: $o).
122.23/18.50	thf(decl_264, type, funcGraphProp4: $o).
122.23/18.50	thf(decl_265, type, subbreln: $o).
122.23/18.50	thf(decl_266, type, eqbreln: $o).
122.23/18.50	thf(decl_267, type, funcext: $o).
122.23/18.50	thf(decl_268, type, funcext2: $o).
122.23/18.50	thf(decl_269, type, ap2apEq1: $o).
122.23/18.50	thf(decl_270, type, ap2apEq2: $o).
122.23/18.50	thf(decl_271, type, beta1: $o).
122.23/18.50	thf(decl_272, type, eta1: $o).
122.23/18.50	thf(decl_273, type, lam2lamEq: $o).
122.23/18.50	thf(decl_274, type, beta2: $o).
122.23/18.50	thf(decl_275, type, eta2: $o).
122.23/18.50	thf(decl_276, type, iffalseProp1: $o).
122.23/18.50	thf(decl_277, type, iffalseProp2: $o).
122.23/18.50	thf(decl_278, type, iftrueProp1: $o).
122.23/18.50	thf(decl_279, type, iftrueProp2: $o).
122.23/18.50	thf(decl_280, type, ifSingleton: $o).
122.23/18.50	thf(decl_281, type, if: $i > $o > $i > $i > $i).
122.23/18.50	thf(decl_282, type, ifp: $o).
122.23/18.50	thf(decl_283, type, theeq: $o).
122.23/18.50	thf(decl_284, type, iftrue: $o).
122.23/18.50	thf(decl_285, type, iffalse: $o).
122.23/18.50	thf(decl_286, type, iftrueorfalse: $o).
122.23/18.50	thf(decl_287, type, binintersectT_lem: $o).
122.23/18.50	thf(decl_288, type, binunionT_lem: $o).
122.23/18.50	thf(decl_289, type, powersetT_lem: $o).
122.23/18.50	thf(decl_290, type, setminusT_lem: $o).
122.23/18.50	thf(decl_291, type, complementT_lem: $o).
122.23/18.50	thf(decl_292, type, setextT: $o).
122.23/18.50	thf(decl_293, type, subsetTI: $o).
122.23/18.50	thf(decl_294, type, powersetTI1: $o).
122.23/18.50	thf(decl_295, type, powersetTE1: $o).
122.23/18.50	thf(decl_296, type, complementTI1: $o).
122.23/18.50	thf(decl_297, type, complementTE1: $o).
122.23/18.50	thf(decl_298, type, binintersectTELcontra: $o).
122.23/18.50	thf(decl_299, type, binintersectTERcontra: $o).
122.23/18.50	thf(decl_300, type, contrasubsetT: $o).
122.23/18.50	thf(decl_301, type, contrasubsetT1: $o).
122.23/18.50	thf(decl_302, type, contrasubsetT2: $o).
122.23/18.50	thf(decl_303, type, contrasubsetT3: $o).
122.23/18.50	thf(decl_304, type, doubleComplementI1: $o).
122.23/18.50	thf(decl_305, type, doubleComplementE1: $o).
122.23/18.50	thf(decl_306, type, doubleComplementSub1: $o).
122.23/18.50	thf(decl_307, type, doubleComplementSub2: $o).
122.23/18.50	thf(decl_308, type, doubleComplementEq: $o).
122.23/18.50	thf(decl_309, type, complementTnotintersectT: $o).
122.23/18.50	thf(decl_310, type, complementImpComplementIntersect: $o).
122.23/18.50	thf(decl_311, type, complementSubsetComplementIntersect: $o).
122.23/18.50	thf(decl_312, type, complementInPowersetComplementIntersect: $o).
122.23/18.50	thf(decl_313, type, contraSubsetComplement: $o).
122.23/18.50	thf(decl_314, type, complementTcontraSubset: $o).
122.23/18.50	thf(decl_315, type, binunionTILcontra: $o).
122.23/18.50	thf(decl_316, type, binunionTIRcontra: $o).
122.23/18.50	thf(decl_317, type, inIntersectImpInUnion: $o).
122.23/18.50	thf(decl_318, type, inIntersectImpInUnion2: $o).
122.23/18.50	thf(decl_319, type, epred1_0: $o).
122.23/18.50	thf(decl_320, type, esk1_2: $i > $i > $i).
140.50/18.50	thf(decl_321, type, esk2_2: $i > $i > $i).
140.50/18.50	thf(decl_322, type, esk3_2: $i > $i > $i).
140.50/18.50	thf(decl_323, type, esk4_1: $i > $i).
140.50/18.50	thf(decl_324, type, esk5_2: ($i > $i > $o) > $i > $i).
140.50/18.50	thf(decl_325, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
140.50/18.50	thf(decl_326, type, esk7_2: ($i > $i > $o) > $i > $i).
140.50/18.50	thf(decl_327, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
140.50/18.50	thf(decl_328, type, esk9_1: $i > $i).
140.50/18.50	thf(decl_329, type, esk10_2: ($i > $o) > $i > $i).
140.50/18.50	thf(decl_330, type, esk11_2: ($i > $o) > $i > $i).
140.50/18.50	thf(decl_331, type, esk12_1: ($i > $o) > $i).
140.50/18.50	thf(decl_332, type, esk13_2: ($i > $o) > $i > $i).
140.50/18.50	thf(decl_333, type, esk14_1: ($i > $o) > $i).
140.50/18.50	thf(decl_334, type, esk15_2: $i > $i > $i).
140.50/18.50	thf(decl_335, type, esk16_2: $i > $i > $i).
140.50/18.50	thf(decl_336, type, esk17_1: $i > $i).
140.50/18.50	thf(decl_337, type, esk18_1: $i > $i).
140.50/18.50	thf(decl_338, type, esk19_1: $i > $i).
140.50/18.50	thf(decl_339, type, esk20_2: $i > $i > $i).
140.50/18.50	thf(decl_340, type, esk21_3: $i > $i > $o > $i).
140.50/18.50	thf(decl_341, type, esk22_2: ($i > $o) > $i > $i).
140.50/18.50	thf(decl_342, type, esk23_1: ($i > $o) > $i).
140.50/18.50	thf(decl_343, type, esk24_1: $i > $i).
140.50/18.50	thf(decl_344, type, esk25_2: $i > ($i > $o) > $i).
140.50/18.50	thf(decl_345, type, esk26_2: $i > ($i > $o) > $i).
140.50/18.50	thf(decl_346, type, esk27_2: $i > ($i > $o) > $i).
140.50/18.50	thf(decl_347, type, esk28_2: $i > ($i > $o) > $i).
140.50/18.50	thf(decl_348, type, esk29_2: $i > ($i > $o) > $i).
140.50/18.50	thf(decl_349, type, esk30_2: $i > ($i > $o) > $i).
140.50/18.50	thf(decl_350, type, esk31_2: ($i > $o) > $i > $i).
140.50/18.50	thf(decl_351, type, esk32_1: ($i > $o) > $i).
140.50/18.50	thf(decl_352, type, esk33_1: ($i > $o) > $i).
140.50/18.50	thf(decl_353, type, esk34_1: ($i > $o) > $i).
140.50/18.50	thf(decl_354, type, esk35_1: ($i > $o) > $i).
140.50/18.50	thf(decl_355, type, esk36_2: ($i > $o) > $i > $i).
140.50/18.50	thf(decl_356, type, esk37_1: ($i > $o) > $i).
140.50/18.50	thf(decl_357, type, esk38_2: ($i > $o) > $i > $i).
140.50/18.50	thf(decl_358, type, esk39_2: ($i > $o) > ($i > $o) > $i).
140.50/18.50	thf(decl_359, type, esk40_2: ($i > $o) > ($i > $o) > $i).
140.50/18.50	thf(decl_360, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
140.50/18.50	thf(decl_361, type, esk42_2: ($i > $o) > ($i > $o) > $i).
140.50/18.50	thf(decl_362, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
140.50/18.50	thf(decl_363, type, esk44_2: ($i > $o) > ($i > $o) > $i).
140.50/18.50	thf(decl_364, type, esk45_2: ($i > $o) > $i > $i).
140.50/18.50	thf(decl_365, type, esk46_2: ($i > $o) > ($i > $o) > $i).
140.50/18.50	thf(decl_366, type, esk47_2: ($i > $o) > ($i > $o) > $i).
140.50/18.50	thf(decl_367, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
140.50/18.50	thf(decl_368, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
140.50/18.50	thf(decl_369, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
140.50/18.50	thf(decl_370, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
140.50/18.50	thf(decl_371, type, esk52_2: $i > $i > $i).
140.50/18.50	thf(decl_372, type, esk53_2: $i > $i > $i).
140.50/18.50	thf(decl_373, type, esk54_2: $i > $i > $i).
140.50/18.50	thf(decl_374, type, esk55_3: $i > $i > $i > $i).
140.50/18.50	thf(decl_375, type, esk56_3: $i > $i > $i > $i).
140.50/18.50	thf(decl_376, type, esk57_2: $i > $i > $i).
140.50/18.50	thf(decl_377, type, esk58_2: $i > ($i > $o) > $i).
140.50/18.50	thf(decl_378, type, esk59_2: $i > ($i > $o) > $i).
140.50/18.50	thf(decl_379, type, esk60_2: $i > ($i > $o) > $i).
140.50/18.50	thf(decl_380, type, esk61_3: $i > ($i > $o) > $i > $i).
140.50/18.50	thf(decl_381, type, esk62_2: $i > ($i > $o) > $i).
140.50/18.50	thf(decl_382, type, esk63_2: $i > ($i > $o) > $i).
140.50/18.50	thf(decl_383, type, esk64_3: $i > $i > ($i > $i) > $i).
140.50/18.50	thf(decl_384, type, esk65_3: $i > $i > ($i > $i) > $i).
140.50/18.50	thf(decl_385, type, esk66_3: $i > $i > ($i > $i) > $i).
140.50/18.50	thf(decl_386, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
140.50/18.50	thf(decl_387, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
140.50/18.50	thf(decl_388, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
140.50/18.50	thf(decl_389, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
140.50/18.50	thf(decl_390, type, esk71_4: $i > $i > $i > $i > $i).
140.50/18.50	thf(decl_391, type, esk72_4: $i > $i > $i > $i > $i).
140.50/18.50	thf(decl_392, type, esk73_4: $i > $i > $i > $i > $i).
140.50/18.50	thf(decl_393, type, esk74_4: $i > $i > $i > $i > $i).
140.50/18.50	thf(decl_394, type, esk75_4: $i > $i > $i > $i > $i).
140.50/18.50	thf(decl_395, type, esk76_4: $i > $i > $i > $i > $i).
140.50/18.50	thf(decl_396, type, esk77_4: $i > $i > $i > $i > $i).
140.50/18.50	thf(decl_397, type, esk78_4: $i > $i > $i > $i > $i).
140.50/18.50	thf(decl_398, type, esk79_4: $i > $i > $i > $i > $i).
140.50/18.50	thf(decl_399, type, esk80_3: $i > $i > ($i > $i) > $i).
140.50/18.50	thf(decl_400, type, esk81_3: $i > $i > ($i > $i) > $i).
140.50/18.50	thf(decl_401, type, esk82_3: $i > $i > ($i > $i) > $i).
140.50/18.50	thf(decl_402, type, esk83_3: $i > $i > $i > $i).
140.50/18.50	thf(decl_403, type, esk84_3: $i > $i > $i > $i).
140.50/18.50	thf(decl_404, type, esk85_3: $i > $i > $i > $i).
140.50/18.50	thf(decl_405, type, esk86_3: $i > $i > $i > $i).
140.50/18.50	thf(decl_406, type, esk87_0: $i).
140.50/18.50	thf(decl_407, type, esk88_0: $i).
140.50/18.50	thf(decl_408, type, esk89_0: $i).
140.50/18.50	thf(decl_409, type, esk90_0: $i).
140.50/18.50	thf(decl_410, type, esk91_0: $i).
140.50/18.50	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', replAx)).
140.50/18.50	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', exu)).
140.50/18.50	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', descrp)).
140.50/18.50	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', exuE1)).
140.50/18.50	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', exuE3e)).
140.50/18.50	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', nonempty)).
140.50/18.50	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', nonemptyI)).
140.50/18.50	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', exuE2)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', exuI1)).
140.50/18.50	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', exuI3)).
140.50/18.50	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', exuI2)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', exuE3u)).
140.50/18.50	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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', exu__Cong)).
140.50/18.50	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', exuEu)).
140.50/18.50	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', descr__Cong)).
140.50/18.50	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', ex1E1)).
140.50/18.50	thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', ex1)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', ex1I)).
140.50/18.50	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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', ex1I2)).
140.50/18.50	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setOfPairsIsBReln)).
140.50/18.50	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', breln)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', ex1E2)).
140.50/18.50	thf(inIntersectImpInIntersectUnions, conjecture, (((emptysetAx)=>((((setunionAx)=>((((omegaIndAx)=>(((foundationAx)=>((((dsetconstrI)=>(((((((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((((noeltsimpempty)=>((setbeta)=>(((nonemptyI)=>(((setadjoinIL)=>(((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>(((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((((upairsetE)=>(((((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>(((prop2setI)=>((prop2set2propI)=>(((notdallE)=>(((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>(((emptyset__Cong)=>(((powerset__Cong)=>((setunion__Cong)=>(((exuEu)=>((descr__Cong)=>((((eqimpsubset2)=>((((emptysetsubset)=>(((subsetE2)=>((notsubsetI)=>(((notequalI2)=>((((setadjoinSub)=>((((setextsub)=>(((powersetI1)=>(((inPowerset)=>((powersetsubset)=>((((binunionIL)=>((upairset2IR)=>((((binunionE)=>(((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>(((binintersectSubset3)=>(((disjointsetsI1)=>(((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>(((((((setminusILneg)=>((setminusIRneg)=>(((setminusSubset1)=>(((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>(((setukpairIL)=>(((kpairiskpair)=>((((singletoninpowerset)=>(((upairset2E)=>((((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>(((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>(((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((((((((kfstpairEq)=>((((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((((ksndsingleton)=>((ksndpairEq)=>(((cartprodsndin)=>((((cartprodmempaircEq)=>((cartprodfstpairEq)=>(((cartprodpairsurjEq)=>((dpsetconstrI)=>(((((dpsetconstrEL1)=>((dpsetconstrEL2)=>(((funcImageSingleton)=>(((app)=>((((((lamp)=>(((((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>(((funcGraphProp4)=>((subbreln)=>(((funcext)=>((funcext2)=>((ap2apEq1)=>((((((beta2)=>(((iffalseProp1)=>((((((ifp)=>((theeq)=>(((iffalse)=>((iftrueorfalse)=>((((powersetT_lem)=>(((complementT_lem)=>(((subsetTI)=>((powersetTI1)=>((powersetTE1)=>(((complementTE1)=>(((((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((((doubleComplementSub2)=>(((complementTnotintersectT)=>((((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>(((binunionTILcontra)=>(((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:((![X49:$i]:((![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49)))<=(in @ X2 @ (binintersect @ X21 @ X48)))))<=(in @ X49 @ (powerset @ X4))))<=(in @ X48 @ (powerset @ X4))))))))<=(binunionTIRcontra)))<=(complementTcontraSubset))))<=(complementSubsetComplementIntersect))<=(complementImpComplementIntersect)))<=(doubleComplementEq)))<=(doubleComplementSub1))<=(doubleComplementE1))))))<=(contrasubsetT))<=(binintersectTERcontra))<=(binintersectTELcontra)))<=(complementTI1)))))<=(setextT)))<=(setminusT_lem)))<=(binunionT_lem))<=(binintersectT_lem))))<=(iftrue))))<=(ifSingleton))<=(iftrueProp2))<=(iftrueProp1))<=(iffalseProp2)))<=(eta2)))<=(lam2lamEq))<=(eta1))<=(beta1))<=(ap2apEq2)))))<=(eqbreln))))<=(funcextLem))))))<=(brelnall2))<=(brelnall1))<=(lam2p)))<=(lamProp))<=(funcinfuncset))<=(ap2p))<=(infuncsetfunc)))<=(apProp)))<=(dpsetconstrER))))<=(dpsetconstrERa))<=(setOfPairsIsBReln))<=(dpsetconstrSub))))<=(cartprodsndpairEq))))<=(cartprodpairmemER))<=(cartprodpairmemEL)))<=(kpairsurjEq))))<=(setukpairinjR))<=(setukpairinjR2)))))))<=(setukpairinjL2))<=(cartprodfstin)))<=(theprop))<=(kfstsingleton))<=(setukpairinjL1))<=(singletonsuniq))<=(ex1I2))<=(ex1I)))))<=(setunionsingleton2)))))<=(cartprodmempair1))))))<=(upairinpowunion))<=(upairsubunion)))<=(singletoninpowunion)))<=(singletonsubset))<=(kpairp)))<=(setukpairIR)))<=(secondinupair))))))<=(symdiffE)))<=(setminusLsub))))<=(setminusELneg))<=(setminusERneg))<=(setminusSubset2))<=(setminusER))<=(setminusEL))))))<=(binintersectRsub)))<=(binintersectER)))<=(binintersectSubset2)))))))<=(binunionLsub)))<=(binunionEcases))<=(binunionIR))))<=(sepSubset))<=(sepInPowerset))))<=(powersetE1)))<=(subsetemptysetimpeq)))<=(subset2powerset))<=(setadjoinSub2)))<=(subsetTrans))<=(subsetRefl)))<=(notequalI1))))<=(subsetE)))<=(subsetI2))<=(eqimpsubset1)))<=(subsetI1))<=(dsetconstr__Cong))))<=(omega__Cong))))<=(setadjoin__Cong)))<=(exu__Cong)))))))<=(exuI1)))<=(notdexE))))<=(quantDeMorgan4))))))<=(emptyE1))<=(upairsetIR))<=(upairsetIL)))<=(singletonsswitch))<=(eqinunit)))))))))<=(powersetE)))))))))<=(emptyinunitempty)))<=(nonemptyI1)))<=(nonemptyE1))))<=(emptyI))<=(setext)))))<=(emptysetE))<=(prop2setE))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL)))<=(descrp))<=(wellorderingAx)))<=(replAx)))<=(omegaSAx))<=(omega0Ax)))<=(powersetAx))<=(setadjoinAx)))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', inIntersectImpInIntersectUnions)).
140.50/18.50	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', dsetconstrI)).
140.50/18.50	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', dsetconstrEL)).
140.50/18.50	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', dsetconstrER)).
140.50/18.50	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setbeta)).
140.50/18.50	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', nonemptyE1)).
140.50/18.50	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', nonemptyI1)).
140.50/18.50	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setoftrueEq)).
140.50/18.50	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', nonemptyImpWitness)).
140.50/18.50	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.rokxLt3tjd/E---3.1_888100.p', emptyE1)).
140.50/18.50	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', dsetconstr__Cong)).
140.50/18.50	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', sepInPowerset)).
140.50/18.50	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', sepSubset)).
140.50/18.50	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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', singletonprop)).
140.50/18.50	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', kfstsingleton)).
140.50/18.50	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', ksndsingleton)).
140.50/18.50	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', dpsetconstrI)).
140.50/18.50	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', dpsetconstrSub)).
140.50/18.50	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', dpsetconstrERa)).
140.50/18.50	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', dpsetconstrEL1)).
140.50/18.50	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', dpsetconstrEL2)).
140.50/18.50	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', dpsetconstrER)).
140.50/18.50	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.rokxLt3tjd/E---3.1_888100.p', funcImageSingleton)).
140.50/18.50	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', apProp)).
140.50/18.50	thf(lamProp, axiom, ((lamProp)<=>![X4:$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.rokxLt3tjd/E---3.1_888100.p', lamProp)).
140.50/18.50	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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', lamp)).
140.50/18.50	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', lam2p)).
140.50/18.50	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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.rokxLt3tjd/E---3.1_888100.p', brelnall1)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', brelnall2)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', subbreln)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', eqbreln)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', beta1)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', eta1)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', lam2lamEq)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', beta2)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', eta2)).
140.50/18.50	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', iffalseProp1)).
140.50/18.50	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.rokxLt3tjd/E---3.1_888100.p', iffalseProp2)).
140.50/18.50	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', iftrueProp1)).
140.50/18.50	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.rokxLt3tjd/E---3.1_888100.p', iftrueProp2)).
140.50/18.50	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', ifSingleton)).
140.50/18.50	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setextAx)).
140.50/18.50	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', emptysetAx)).
140.50/18.50	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setadjoinAx)).
140.50/18.50	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', powersetAx)).
140.50/18.50	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setunionAx)).
140.50/18.50	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', omega0Ax)).
140.50/18.50	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', omegaSAx)).
140.50/18.50	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.rokxLt3tjd/E---3.1_888100.p', omegaIndAx)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', foundationAx)).
140.50/18.50	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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', wellorderingAx)).
140.50/18.50	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', prop2setE)).
140.50/18.50	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', emptysetE)).
140.50/18.50	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', emptysetimpfalse)).
140.50/18.50	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', notinemptyset)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', setext)).
140.50/18.50	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', emptyI)).
140.50/18.50	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', noeltsimpempty)).
140.50/18.50	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setadjoinIL)).
140.50/18.50	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', emptyinunitempty)).
140.50/18.50	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setadjoinIR)).
140.50/18.50	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setadjoinE)).
140.50/18.50	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setadjoinOr)).
140.50/18.50	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', powersetI)).
140.50/18.50	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', emptyinPowerset)).
140.50/18.50	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', emptyInPowerset)).
140.50/18.50	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', powersetE)).
140.50/18.50	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setunionI)).
140.50/18.50	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setunionE)).
140.50/18.50	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', subPowSU)).
140.50/18.50	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', uniqinunit)).
140.50/18.50	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', notinsingleton)).
140.50/18.50	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', eqinunit)).
140.50/18.50	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', singletonsswitch)).
140.50/18.50	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', upairsetE)).
140.50/18.50	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', upairsetIL)).
140.50/18.50	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', upairsetIR)).
140.50/18.50	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', vacuousDall)).
140.50/18.50	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', quantDeMorgan1)).
140.50/18.50	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', quantDeMorgan2)).
140.50/18.50	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', quantDeMorgan3)).
140.50/18.50	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', quantDeMorgan4)).
140.50/18.50	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', prop2setI)).
140.50/18.50	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', prop2set2propI)).
140.50/18.50	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', notdexE)).
140.50/18.50	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', notdallE)).
140.50/18.50	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', inCongP)).
140.50/18.50	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', in__Cong)).
140.50/18.50	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', emptyset__Cong)).
140.50/18.50	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setadjoin__Cong)).
140.50/18.50	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', powerset__Cong)).
140.50/18.50	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setunion__Cong)).
140.50/18.50	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', omega__Cong)).
140.50/18.50	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', subsetI1)).
140.50/18.50	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', eqimpsubset2)).
140.50/18.50	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', eqimpsubset1)).
140.50/18.50	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', subsetI2)).
140.50/18.50	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', emptysetsubset)).
140.50/18.50	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', subsetE)).
140.50/18.50	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', subsetE2)).
140.50/18.50	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', notsubsetI)).
140.50/18.50	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', notequalI1)).
140.50/18.50	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', notequalI2)).
140.50/18.50	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', subsetRefl)).
140.50/18.50	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', subsetTrans)).
140.50/18.50	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setadjoinSub)).
140.50/18.50	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setadjoinSub2)).
140.50/18.50	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', subset2powerset)).
140.50/18.50	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setextsub)).
140.50/18.50	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', subsetemptysetimpeq)).
140.50/18.50	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', powersetI1)).
140.50/18.50	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', powersetE1)).
140.50/18.50	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', inPowerset)).
140.50/18.50	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', powersetsubset)).
140.50/18.50	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binunionIL)).
140.50/18.50	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', upairset2IR)).
140.50/18.50	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binunionIR)).
140.50/18.50	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binunionEcases)).
140.50/18.50	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binunionE)).
140.50/18.50	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binunionLsub)).
140.50/18.50	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binunionRsub)).
140.50/18.50	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binintersectI)).
140.50/18.50	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binintersectSubset5)).
140.50/18.50	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binintersectEL)).
140.50/18.50	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binintersectLsub)).
140.50/18.50	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binintersectSubset2)).
140.50/18.50	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binintersectSubset3)).
140.50/18.50	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binintersectER)).
140.50/18.50	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', disjointsetsI1)).
140.50/18.50	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binintersectRsub)).
140.50/18.50	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binintersectSubset4)).
140.50/18.50	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binintersectSubset1)).
140.50/18.50	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', bs114d)).
140.50/18.50	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setminusI)).
140.50/18.50	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setminusEL)).
140.50/18.50	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setminusER)).
140.50/18.50	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setminusSubset2)).
140.50/18.50	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setminusERneg)).
140.50/18.50	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setminusELneg)).
140.50/18.50	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setminusILneg)).
140.50/18.50	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setminusIRneg)).
140.50/18.50	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setminusLsub)).
140.50/18.50	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setminusSubset1)).
140.50/18.50	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', symdiffE)).
140.50/18.50	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', symdiffI1)).
140.50/18.50	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', symdiffI2)).
140.50/18.50	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', symdiffIneg1)).
140.50/18.50	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', symdiffIneg2)).
140.50/18.50	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', secondinupair)).
140.50/18.50	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setukpairIL)).
140.50/18.50	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setukpairIR)).
140.50/18.50	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', kpairiskpair)).
140.50/18.50	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', kpairp)).
140.50/18.50	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', singletonsubset)).
140.50/18.50	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', singletoninpowerset)).
140.50/18.50	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', singletoninpowunion)).
140.50/18.50	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', upairset2E)).
140.50/18.50	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', upairsubunion)).
140.50/18.50	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', upairinpowunion)).
140.50/18.50	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', ubforcartprodlem1)).
140.50/18.50	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', ubforcartprodlem2)).
140.50/18.50	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', ubforcartprodlem3)).
140.50/18.50	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', cartprodpairin)).
140.50/18.50	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.rokxLt3tjd/E---3.1_888100.p', cartprodmempair1)).
140.50/18.50	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', cartprodmempair)).
140.50/18.50	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setunionE2)).
140.50/18.50	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setunionsingleton1)).
140.50/18.50	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setunionsingleton2)).
140.50/18.50	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setunionsingleton)).
140.50/18.50	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', singletonsuniq)).
140.50/18.50	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.rokxLt3tjd/E---3.1_888100.p', setukpairinjL1)).
140.50/18.50	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', theprop)).
140.50/18.50	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', kfstpairEq)).
140.50/18.50	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', cartprodfstin)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', setukpairinjL2)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', setukpairinjL)).
140.50/18.50	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setukpairinjR11)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', setukpairinjR12)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', setukpairinjR1)).
140.50/18.50	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', upairequniteq)).
140.50/18.50	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setukpairinjR2)).
140.50/18.50	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setukpairinjR)).
140.50/18.50	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', ksndpairEq)).
140.50/18.50	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', kpairsurjEq)).
140.50/18.50	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', cartprodsndin)).
140.50/18.50	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', cartprodpairmemEL)).
140.50/18.50	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', cartprodpairmemER)).
140.50/18.50	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', cartprodmempaircEq)).
140.50/18.50	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', cartprodfstpairEq)).
140.50/18.50	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', cartprodsndpairEq)).
140.50/18.50	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', cartprodpairsurjEq)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', app)).
140.50/18.50	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', infuncsetfunc)).
140.50/18.50	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', ap2p)).
140.50/18.50	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', funcinfuncset)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', funcGraphProp1)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', funcGraphProp3)).
140.50/18.50	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', funcGraphProp2)).
140.50/18.50	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.rokxLt3tjd/E---3.1_888100.p', funcextLem)).
140.50/18.50	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', funcGraphProp4)).
140.50/18.50	thf(funcext, axiom, ((funcext)<=>![X4:$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.rokxLt3tjd/E---3.1_888100.p', funcext)).
140.50/18.50	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', funcext2)).
140.50/18.50	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', ap2apEq1)).
140.50/18.50	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', ap2apEq2)).
140.50/18.50	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', ifp)).
140.50/18.50	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', theeq)).
140.50/18.50	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', iftrue)).
140.50/18.50	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', iffalse)).
140.50/18.50	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', iftrueorfalse)).
140.50/18.50	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$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.rokxLt3tjd/E---3.1_888100.p', binintersectT_lem)).
140.50/18.50	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binunionT_lem)).
140.50/18.50	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', powersetT_lem)).
140.50/18.50	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.rokxLt3tjd/E---3.1_888100.p', setminusT_lem)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', complementT_lem)).
140.50/18.50	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', setextT)).
140.50/18.50	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', subsetTI)).
140.50/18.50	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', powersetTI1)).
140.50/18.50	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', powersetTE1)).
140.50/18.50	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$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.rokxLt3tjd/E---3.1_888100.p', complementTI1)).
140.50/18.50	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', complementTE1)).
140.50/18.50	thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binintersectTELcontra)).
140.50/18.50	thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', binintersectTERcontra)).
140.50/18.50	thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', contrasubsetT)).
140.50/18.50	thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', contrasubsetT1)).
140.50/18.50	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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.rokxLt3tjd/E---3.1_888100.p', contrasubsetT2)).
140.50/18.50	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', contrasubsetT3)).
140.50/18.50	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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.rokxLt3tjd/E---3.1_888100.p', doubleComplementI1)).
140.50/18.50	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', doubleComplementE1)).
140.50/18.50	thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', doubleComplementSub1)).
140.50/18.50	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', doubleComplementSub2)).
140.50/18.50	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', doubleComplementEq)).
140.50/18.50	thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', complementTnotintersectT)).
140.50/18.50	thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', complementImpComplementIntersect)).
140.50/18.50	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$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.rokxLt3tjd/E---3.1_888100.p', complementSubsetComplementIntersect)).
140.50/18.50	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', complementInPowersetComplementIntersect)).
140.50/18.50	thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', contraSubsetComplement)).
140.50/18.50	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$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.rokxLt3tjd/E---3.1_888100.p', complementTcontraSubset)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', binunionTILcontra)).
140.50/18.50	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.rokxLt3tjd/E---3.1_888100.p', binunionTIRcontra)).
140.50/18.50	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rokxLt3tjd/E---3.1_888100.p', inIntersectImpInUnion)).
140.50/18.50	thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$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.rokxLt3tjd/E---3.1_888100.p', inIntersectImpInUnion2)).
140.50/18.50	thf(c_0_263, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
140.50/18.50	thf(c_0_264, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
140.50/18.50	thf(c_0_265, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
140.50/18.50	thf(c_0_266, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
140.50/18.50	thf(c_0_267, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
140.50/18.50	thf(c_0_268, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
140.50/18.50	thf(c_0_269, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
140.50/18.50	thf(c_0_270, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
140.50/18.50	thf(c_0_271, 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])).
140.50/18.50	thf(c_0_272, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
140.50/18.50	thf(c_0_273, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
140.50/18.50	thf(c_0_274, 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])).
140.50/18.50	thf(c_0_275, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
140.50/18.50	thf(c_0_276, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
140.50/18.50	thf(c_0_277, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
140.50/18.50	thf(c_0_278, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
140.50/18.50	thf(c_0_279, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])).
140.50/18.50	thf(c_0_280, 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])).
140.50/18.50	thf(c_0_281, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
140.50/18.50	thf(c_0_282, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
140.50/18.50	thf(c_0_283, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
140.50/18.50	thf(c_0_284, 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])).
140.50/18.50	thf(c_0_285, negated_conjecture, ~((((emptysetAx)=>((((setunionAx)=>((((omegaIndAx)=>(((foundationAx)=>((((dsetconstrI)=>(((((((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((((noeltsimpempty)=>((setbeta)=>(((nonemptyI)=>(((setadjoinIL)=>(((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>(((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((((upairsetE)=>(((((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>(((prop2setI)=>((prop2set2propI)=>(((notdallE)=>(((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>(((emptyset__Cong)=>(((powerset__Cong)=>((setunion__Cong)=>(((exuEu)=>((descr__Cong)=>((((eqimpsubset2)=>((((emptysetsubset)=>(((subsetE2)=>((notsubsetI)=>(((notequalI2)=>((((setadjoinSub)=>((((setextsub)=>(((powersetI1)=>(((inPowerset)=>((powersetsubset)=>((((binunionIL)=>((upairset2IR)=>((((binunionE)=>(((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>(((binintersectSubset3)=>(((disjointsetsI1)=>(((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>(((((((setminusILneg)=>((setminusIRneg)=>(((setminusSubset1)=>(((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>(((setukpairIL)=>(((kpairiskpair)=>((((singletoninpowerset)=>(((upairset2E)=>((((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>(((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>(((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((((((((kfstpairEq)=>((((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((((ksndsingleton)=>((ksndpairEq)=>(((cartprodsndin)=>((((cartprodmempaircEq)=>((cartprodfstpairEq)=>(((cartprodpairsurjEq)=>((dpsetconstrI)=>(((((dpsetconstrEL1)=>((dpsetconstrEL2)=>(((funcImageSingleton)=>(((app)=>((((((lamp)=>(((((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>(((funcGraphProp4)=>((subbreln)=>(((funcext)=>((funcext2)=>((ap2apEq1)=>((((((beta2)=>(((iffalseProp1)=>((((((ifp)=>((theeq)=>(((iffalse)=>((iftrueorfalse)=>((((powersetT_lem)=>(((complementT_lem)=>(((subsetTI)=>((powersetTI1)=>((powersetTE1)=>(((complementTE1)=>(((((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((((doubleComplementSub2)=>(((complementTnotintersectT)=>((((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>(((binunionTILcontra)=>(((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:((![X49:$i]:((![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49)))<=(in @ X2 @ (binintersect @ X21 @ X48)))))<=(in @ X49 @ (powerset @ X4))))<=(in @ X48 @ (powerset @ X4))))))))<=(binunionTIRcontra)))<=(complementTcontraSubset))))<=(complementSubsetComplementIntersect))<=(complementImpComplementIntersect)))<=(doubleComplementEq)))<=(doubleComplementSub1))<=(doubleComplementE1))))))<=(contrasubsetT))<=(binintersectTERcontra))<=(binintersectTELcontra)))<=(complementTI1)))))<=(setextT)))<=(setminusT_lem)))<=(binunionT_lem))<=(binintersectT_lem))))<=(iftrue))))<=(ifSingleton))<=(iftrueProp2))<=(iftrueProp1))<=(iffalseProp2)))<=(eta2)))<=(lam2lamEq))<=(eta1))<=(beta1))<=(ap2apEq2)))))<=(eqbreln))))<=(funcextLem))))))<=(brelnall2))<=(brelnall1))<=(lam2p)))<=(lamProp))<=(funcinfuncset))<=(ap2p))<=(infuncsetfunc)))<=(apProp)))<=(dpsetconstrER))))<=(dpsetconstrERa))<=(setOfPairsIsBReln))<=(dpsetconstrSub))))<=(cartprodsndpairEq))))<=(cartprodpairmemER))<=(cartprodpairmemEL)))<=(kpairsurjEq))))<=(setukpairinjR))<=(setukpairinjR2)))))))<=(setukpairinjL2))<=(cartprodfstin)))<=(theprop))<=(kfstsingleton))<=(setukpairinjL1))<=(singletonsuniq))<=(ex1I2))<=(ex1I)))))<=(setunionsingleton2)))))<=(cartprodmempair1))))))<=(upairinpowunion))<=(upairsubunion)))<=(singletoninpowunion)))<=(singletonsubset))<=(kpairp)))<=(setukpairIR)))<=(secondinupair))))))<=(symdiffE)))<=(setminusLsub))))<=(setminusELneg))<=(setminusERneg))<=(setminusSubset2))<=(setminusER))<=(setminusEL))))))<=(binintersectRsub)))<=(binintersectER)))<=(binintersectSubset2)))))))<=(binunionLsub)))<=(binunionEcases))<=(binunionIR))))<=(sepSubset))<=(sepInPowerset))))<=(powersetE1)))<=(subsetemptysetimpeq)))<=(subset2powerset))<=(setadjoinSub2)))<=(subsetTrans))<=(subsetRefl)))<=(notequalI1))))<=(subsetE)))<=(subsetI2))<=(eqimpsubset1)))<=(subsetI1))<=(dsetconstr__Cong))))<=(omega__Cong))))<=(setadjoin__Cong)))<=(exu__Cong)))))))<=(exuI1)))<=(notdexE))))<=(quantDeMorgan4))))))<=(emptyE1))<=(upairsetIR))<=(upairsetIL)))<=(singletonsswitch))<=(eqinunit)))))))))<=(powersetE)))))))))<=(emptyinunitempty)))<=(nonemptyI1)))<=(nonemptyE1))))<=(emptyI))<=(setext)))))<=(emptysetE))<=(prop2setE))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL)))<=(descrp))<=(wellorderingAx)))<=(replAx)))<=(omegaSAx))<=(omega0Ax)))<=(powersetAx))<=(setadjoinAx)))<=(setextAx))), inference(assume_negation,[status(cth)],[inIntersectImpInIntersectUnions])).
140.50/18.50	thf(c_0_286, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X860:$i]:(((((X6 @ X2 @ X860)))&(![X861:$i]:(((((X6 @ X2 @ X861)))=>(((X860)=(X861)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_263, c_0_264])).
140.50/18.50	thf(c_0_287, plain, ((descrp)=(![X1:$i > $o]:((((?[X862:$i]:(((((X1 @ X862)))&(![X863:$i]:(((((X1 @ X863)))=>(((X862)=(X863))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_265, c_0_264])).
140.50/18.50	thf(c_0_288, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
140.50/18.50	thf(c_0_289, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
140.50/18.50	thf(c_0_290, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
140.50/18.50	thf(c_0_291, plain, ((exuE1)=(![X1:$i > $o]:((((?[X864:$i]:(((((X1 @ X864)))&(![X865:$i]:(((((X1 @ X865)))=>(((X864)=(X865))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_266, c_0_264])).
140.50/18.50	thf(c_0_292, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X866:$i]:(((((X1 @ X866)))&(![X867:$i]:(((((X1 @ X867)))=>(((X866)=(X867))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_267, c_0_264])).
140.50/18.50	thf(c_0_293, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
140.50/18.50	thf(c_0_294, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_268])).
140.50/18.50	thf(c_0_295, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_269, c_0_268])).
140.50/18.50	thf(c_0_296, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_268])).
140.50/18.50	thf(c_0_297, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
140.50/18.50	thf(c_0_298, plain, ((exuE2)=(![X1:$i > $o]:((((?[X868:$i]:(((((X1 @ X868)))&(![X869:$i]:(((((X1 @ X869)))=>(((X868)=(X869))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_270, c_0_264])).
140.50/18.50	thf(c_0_299, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_268])).
140.50/18.50	thf(c_0_300, 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])).
140.50/18.50	thf(c_0_301, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X870:$i]:(((((X1 @ X870)))&(![X871:$i]:(((((X1 @ X871)))=>(((X870)=(X871)))))))))))))), inference(apply_def,[status(thm)],[c_0_271, c_0_264])).
140.50/18.50	thf(c_0_302, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X872:$i]:(((((X1 @ X872)))&(![X873:$i]:(((((X1 @ X873)))=>(((X872)=(X873)))))))))))))))), inference(apply_def,[status(thm)],[c_0_272, c_0_264])).
140.50/18.50	thf(c_0_303, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X874:$i]:(((((X1 @ X874)))&(![X875:$i]:(((((X1 @ X875)))=>(((X874)=(X875)))))))))))))), inference(apply_def,[status(thm)],[c_0_273, c_0_264])).
140.50/18.50	thf(c_0_304, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X876:$i]:(((((X1 @ X876)))&(![X877:$i]:(((((X1 @ X877)))=>(((X876)=(X877))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_274, c_0_264])).
140.50/18.50	thf(c_0_305, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X878:$i]:(((((X1 @ X878)))&(![X879:$i]:(((((X1 @ X879)))=>(((X878)=(X879))))))))))<=>((?[X880:$i]:(((((X17 @ X880)))&(![X881:$i]:(((((X17 @ X881)))=>(((X880)=(X881)))))))))))))))), inference(apply_def,[status(thm)],[c_0_275, c_0_264])).
140.50/18.50	thf(c_0_306, plain, ((exuEu)=(![X1:$i > $o]:((((?[X882:$i]:(((((X1 @ X882)))&(![X883:$i]:(((((X1 @ X883)))=>(((X882)=(X883))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_276, c_0_264])).
140.50/18.50	thf(c_0_307, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X884:$i]:(((((X1 @ X884)))&(![X885:$i]:(((((X1 @ X885)))=>(((X884)=(X885))))))))))=>((((?[X886:$i]:(((((X17 @ X886)))&(![X887:$i]:(((((X17 @ X887)))=>(((X886)=(X887))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_277, c_0_264])).
140.50/18.50	thf(c_0_308, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
140.50/18.50	thf(c_0_309, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
140.50/18.50	thf(c_0_310, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
140.50/18.50	thf(c_0_311, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
140.50/18.50	thf(c_0_312, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_278, c_0_279])).
140.50/18.50	thf(c_0_313, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>(((![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X3))=>(((X3)=(X2))))))))=>(((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))))))))))), inference(apply_def,[status(thm)],[c_0_280, c_0_279])).
140.50/18.50	thf(c_0_314, 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)))))=>(((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_281, c_0_279])).
140.50/18.50	thf(c_0_315, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
140.50/18.50	thf(c_0_316, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
140.50/18.50	thf(c_0_317, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
140.50/18.50	thf(c_0_318, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
140.50/18.50	thf(c_0_319, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_282, c_0_283])).
140.50/18.50	thf(c_0_320, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
140.50/18.50	thf(c_0_321, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
140.50/18.50	thf(c_0_322, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
140.50/18.50	thf(c_0_323, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
140.50/18.50	thf(c_0_324, plain, ((funcImageSingleton)<=>![X4:$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])).
140.50/18.50	thf(c_0_325, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
140.50/18.50	thf(c_0_326, plain, ((lamProp)<=>![X4:$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])).
140.50/18.50	thf(c_0_327, 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:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
140.50/18.50	thf(c_0_328, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
140.50/18.50	thf(c_0_329, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![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)))))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_283])).
140.50/18.50	thf(c_0_330, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X1:$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)))))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_283])).
140.50/18.50	thf(c_0_331, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X4))=>((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))))))))))), inference(apply_def,[status(thm)],[c_0_284, c_0_279])).
140.50/18.50	thf(c_0_332, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![X2:$i]:((((in @ X2 @ X4))=>(![X3:$i]:((((in @ X3 @ X5))=>((((in @ (kpair @ X2 @ X3) @ X33))=>((in @ (kpair @ X2 @ X3) @ X35))))))))))=>((subset @ X33 @ X35))))))))))), inference(apply_def,[status(thm)],[subbreln, c_0_283])).
140.50/18.50	thf(c_0_333, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:(((((subset @ X33 @ (cartprod @ X4 @ X5))))=>(![X35:$i]:(((((subset @ X35 @ (cartprod @ X4 @ X5))))=>(((![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)))))))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_283])).
140.50/18.50	thf(c_0_334, 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])).
140.50/18.50	thf(c_0_335, 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])).
140.50/18.50	thf(c_0_336, 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])).
140.50/18.50	thf(c_0_337, 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])).
140.50/18.50	thf(c_0_338, 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])).
140.50/18.50	thf(c_0_339, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
140.50/18.50	thf(c_0_340, plain, ((iffalseProp2)<=>![X4:$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])).
140.50/18.50	thf(c_0_341, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
140.50/18.50	thf(c_0_342, plain, ((iftrueProp2)<=>![X4:$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])).
140.50/18.50	thf(c_0_343, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
140.50/18.50	thf(c_0_344, plain, ((epred1_0)<=>![X1684:$i]:(?[X1685:$i]:((((![X1686:$i]:(((in @ X1686 @ X1685)=>![X1687:$i]:(((in @ X1687 @ X1686)=>(in @ X1687 @ X1684)))))&![X1688:$i, X1689:$i]:((((in @ X1688 @ X1684)&(in @ X1689 @ X1684))=>(![X1690:$i]:(((in @ X1690 @ X1685)=>((in @ X1688 @ X1690)<=>(in @ X1689 @ X1690))))=>((X1688)=(X1689))))))&![X1691:$i, X1692:$i]:((((in @ X1691 @ X1685)&(in @ X1692 @ X1685))=>(![X1693:$i]:(((in @ X1693 @ X1691)=>(in @ X1693 @ X1692)))|![X1694:$i]:(((in @ X1694 @ X1692)=>(in @ X1694 @ X1691)))))))&![X1695:$i]:(((![X1696:$i]:(((in @ X1696 @ X1695)=>(in @ X1696 @ X1684)))&?[X1697:$i]:((in @ X1697 @ X1695)))=>?[X1698:$i, X1699:$i]:(((((in @ X1698 @ X1685)&(in @ X1699 @ X1695))&~(?[X1700:$i]:(((in @ X1700 @ X1698)&(in @ X1700 @ X1695)))))&![X1701:$i]:(((in @ X1701 @ X1685)=>(![X1702:$i]:(((in @ X1702 @ X1701)=>(in @ X1702 @ X1698)))|(in @ X1699 @ X1701)))))))))))), introduced(definition)).
140.50/18.50	thf(c_0_345, negated_conjecture, ~((![X1718:$i, X1719:$i]:((![X1720:$i]:(((in @ X1720 @ X1718)<=>(in @ X1720 @ X1719)))=>((X1718)=(X1719))))=>(![X888:$i]:(~(in @ X888 @ emptyset))=>(![X1715:$i, X1716:$i, X1717:$i]:(((in @ X1717 @ (setadjoin @ X1715 @ X1716))<=>(((X1717)=(X1715))|(in @ X1717 @ X1716))))=>(![X1712:$i, X1713:$i]:(((in @ X1713 @ (powerset @ X1712))<=>![X1714:$i]:(((in @ X1714 @ X1713)=>(in @ X1714 @ X1712)))))=>(![X889:$i, X890:$i]:(((in @ X890 @ (setunion @ X889))<=>?[X891:$i]:(((in @ X890 @ X891)&(in @ X891 @ X889)))))=>((in @ emptyset @ omega)=>(![X1711:$i]:(((in @ X1711 @ omega)=>(in @ (setadjoin @ X1711 @ X1711) @ omega)))=>(![X892:$i]:((((in @ emptyset @ X892)&![X893:$i]:((((in @ X893 @ omega)&(in @ X893 @ X892))=>(in @ (setadjoin @ X893 @ X893) @ X892))))=>![X894:$i]:(((in @ X894 @ omega)=>(in @ X894 @ X892)))))=>(![X1703:$i > $i > $o, X1704:$i]:((![X1705:$i]:(((in @ X1705 @ X1704)=>?[X1706:$i]:(((X1703 @ X1705 @ X1706)&![X1707:$i]:(((X1703 @ X1705 @ X1707)=>((X1706)=(X1707))))))))=>?[X1708:$i]:(![X1709:$i]:(((in @ X1709 @ X1708)<=>?[X1710:$i]:(((in @ X1710 @ X1704)&(X1703 @ X1710 @ X1709))))))))=>(![X895:$i]:((?[X896:$i]:((in @ X896 @ X895))=>?[X897:$i]:(((in @ X897 @ X895)&~(?[X898:$i]:(((in @ X898 @ X897)&(in @ X898 @ X895))))))))=>((epred1_0)=>(![X1681:$i > $o]:((?[X1682:$i]:(((X1681 @ X1682)&![X1683:$i]:(((X1681 @ X1683)=>((X1682)=(X1683))))))=>(X1681 @ (descr @ (^[Z0:$i]:(X1681 @ Z0))))))=>(![X899:$i, X900:$i > $o, X901:$i]:(((in @ X901 @ X899)=>((X900 @ X901)=>(in @ X901 @ (dsetconstr @ X899 @ X900)))))=>(![X1678:$i, X1679:$i > $o, X1680:$i]:(((in @ X1680 @ (dsetconstr @ X1678 @ X1679))=>(in @ X1680 @ X1678)))=>(![X1675:$i, X1676:$i > $o, X1677:$i]:(((in @ X1677 @ (dsetconstr @ X1675 @ X1676))=>(X1676 @ X1677)))=>(![X1670:$i > $o]:((?[X1671:$i]:(((X1670 @ X1671)&![X1672:$i]:(((X1670 @ X1672)=>((X1671)=(X1672))))))=>?[X1673:$i]:(((X1670 @ X1673)&![X1674:$i]:(((X1670 @ X1674)=>((X1673)=(X1674))))))))=>(![X1668:$o, X1669:$i]:(((in @ X1669 @ (prop2set @ ((X1668))))=>(X1668)))=>(![X1666:$i]:(((in @ X1666 @ emptyset)=>![X1667:$o]:((X1667))))=>(![X902:$i]:(((in @ X902 @ emptyset)=>~($true)))=>(![X903:$i]:(~(in @ X903 @ emptyset))=>(![X904:$i > $o]:((?[X905:$i]:(((X904 @ X905)&![X906:$i]:(((X904 @ X906)=>((X905)=(X906))))))=>?[X907:$i]:((X904 @ X907))))=>(![X1662:$i, X1663:$i]:((![X1664:$i]:(((in @ X1664 @ X1662)=>(in @ X1664 @ X1663)))=>(![X1665:$i]:(((in @ X1665 @ X1663)=>(in @ X1665 @ X1662)))=>((X1662)=(X1663)))))=>(![X1660:$i]:((![X1661:$i]:(~(in @ X1661 @ X1660))=>((X1660)=(emptyset))))=>(![X908:$i]:((![X909:$i]:(~(in @ X909 @ X908))=>((X908)=(emptyset))))=>(![X910:$i, X911:$i > $o, X912:$i]:(((in @ X912 @ X910)=>((in @ X912 @ (dsetconstr @ X910 @ X911))<=>(X911 @ X912))))=>(![X1658:$i]:((((X1658)!=(emptyset))=>?[X1659:$i]:((in @ X1659 @ X1658))))=>(![X913:$i, X914:$i > $o, X915:$i]:(((in @ X915 @ X913)=>((X914 @ X915)=>((dsetconstr @ X913 @ X914)!=(emptyset)))))=>(![X1656:$i]:((?[X1657:$i]:((in @ X1657 @ X1656))=>((X1656)!=(emptyset))))=>(![X916:$i, X917:$i]:((in @ X916 @ (setadjoin @ X916 @ X917)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X918:$i, X919:$i, X920:$i]:(((in @ X920 @ X919)=>(in @ X920 @ (setadjoin @ X918 @ X919))))=>(![X921:$i, X922:$i, X923:$i]:(((in @ X923 @ (setadjoin @ X921 @ X922))=>![X924:$o]:(((((X923)=(X921))=>(X924))=>(((in @ X923 @ X922)=>(X924))=>(X924))))))=>(![X925:$i, X926:$i, X927:$i]:(((in @ X927 @ (setadjoin @ X925 @ X926))=>(((X927)=(X925))|(in @ X927 @ X926))))=>(![X928:$i]:(((dsetconstr @ X928 @ (^[Z0:$i]:($true)))=(X928)))=>(![X929:$i, X930:$i]:((![X931:$i]:(((in @ X931 @ X930)=>(in @ X931 @ X929)))=>(in @ X930 @ (powerset @ X929))))=>(![X932:$i]:((in @ emptyset @ (powerset @ X932)))=>(![X933:$i]:((in @ emptyset @ (powerset @ X933)))=>(![X1653:$i, X1654:$i, X1655:$i]:(((in @ X1654 @ (powerset @ X1653))=>((in @ X1655 @ X1654)=>(in @ X1655 @ X1653))))=>(![X934:$i, X935:$i, X936:$i]:(((in @ X935 @ X936)=>((in @ X936 @ X934)=>(in @ X935 @ (setunion @ X934)))))=>(![X937:$i, X938:$i]:(((in @ X938 @ (setunion @ X937))=>![X939:$o]:((![X940:$i]:(((in @ X938 @ X940)=>((in @ X940 @ X937)=>(X939))))=>(X939)))))=>(![X941:$i, X942:$i]:(((in @ X942 @ X941)=>(in @ X942 @ (powerset @ (setunion @ X941)))))=>(![X943:$i > $o]:((?[X944:$i]:(((X943 @ X944)&![X945:$i]:(((X943 @ X945)=>((X944)=(X945))))))=>?[X946:$i]:(![X947:$i]:(((X943 @ X947)<=>((X947)=(X946)))))))=>(![X948:$i]:((((X948)!=(emptyset))=>?[X949:$i]:(((in @ X949 @ X948)&$true))))=>(![X950:$i, X951:$i]:(((in @ X950 @ (setadjoin @ X951 @ emptyset))=>((X950)=(X951))))=>(![X952:$i, X953:$i]:((((X952)!=(X953))=>~(in @ X953 @ (setadjoin @ X952 @ emptyset))))=>(![X1651:$i, X1652:$i]:((((X1651)=(X1652))=>(in @ X1651 @ (setadjoin @ X1652 @ emptyset))))=>(![X1649:$i, X1650:$i]:(((in @ X1649 @ (setadjoin @ X1650 @ emptyset))=>(in @ X1650 @ (setadjoin @ X1649 @ emptyset))))=>(![X954:$i, X955:$i, X956:$i]:(((in @ X956 @ (setadjoin @ X954 @ (setadjoin @ X955 @ emptyset)))=>(((X956)=(X954))|((X956)=(X955)))))=>(![X1647:$i, X1648:$i]:((in @ X1647 @ (setadjoin @ X1647 @ (setadjoin @ X1648 @ emptyset))))=>(![X1645:$i, X1646:$i]:((in @ X1646 @ (setadjoin @ X1645 @ (setadjoin @ X1646 @ emptyset))))=>(![X1642:$i, X1643:$i > $o]:((?[X1644:$i]:(((in @ X1644 @ X1642)&(X1643 @ X1644)))=>(((dsetconstr @ X1642 @ X1643)=(emptyset))=>~($true))))=>(![X957:$i > $o, X958:$i]:(((in @ X958 @ emptyset)=>(X957 @ X958)))=>(![X959:$i, X960:$i > $o]:((~(![X961:$i]:(((in @ X961 @ X959)=>(X960 @ X961))))=>?[X962:$i]:(((in @ X962 @ X959)&~((X960 @ X962))))))=>(![X963:$i, X964:$i > $o]:((![X965:$i]:(((in @ X965 @ X963)=>~((X964 @ X965))))=>~(?[X966:$i]:(((in @ X966 @ X963)&(X964 @ X966))))))=>(![X967:$i, X968:$i > $o]:((~(?[X969:$i]:(((in @ X969 @ X967)&(X968 @ X969))))=>![X970:$i]:(((in @ X970 @ X967)=>~((X968 @ X970))))))=>(![X1638:$i, X1639:$i > $o]:((?[X1640:$i]:(((in @ X1640 @ X1638)&~((X1639 @ X1640))))=>~(![X1641:$i]:(((in @ X1641 @ X1638)=>(X1639 @ X1641))))))=>(![X971:$o]:(((X971)=>(in @ emptyset @ (prop2set @ ((X971))))))=>(![X972:$o]:(((X972)=>(set2prop @ (prop2set @ ((X972))))))=>(![X1634:$i, X1635:$i > $o]:((~(?[X1636:$i]:(((in @ X1636 @ X1634)&(X1635 @ X1636))))=>![X1637:$i]:(((in @ X1637 @ X1634)=>~((X1635 @ X1637))))))=>(![X973:$i, X974:$i > $o]:((~(![X975:$i]:(((in @ X975 @ X973)=>(X974 @ X975))))=>?[X976:$i]:(((in @ X976 @ X973)&~((X974 @ X976))))))=>(![X1629:$i > $o]:((?[X1630:$i]:(((X1629 @ X1630)&![X1631:$i]:(((X1629 @ X1631)=>((X1630)=(X1631))))))=>?[X1632:$i]:(((X1629 @ X1632)&![X1633:$i]:(((X1629 @ X1633)=>((X1632)=(X1633))))))))=>(![X977:$i > $o]:((?[X978:$i]:((X977 @ X978))=>(![X979:$i, X980:$i]:(((X977 @ X979)=>((X977 @ X980)=>((X979)=(X980)))))=>?[X981:$i]:(((X977 @ X981)&![X982:$i]:(((X977 @ X982)=>((X981)=(X982)))))))))=>(![X983:$i > $o]:((?[X984:$i]:(![X985:$i]:(((X983 @ X985)<=>((X985)=(X984)))))=>?[X986:$i]:(((X983 @ X986)&![X987:$i]:(((X983 @ X987)=>((X986)=(X987))))))))=>(![X988:$i, X989:$i]:((((X988)=(X989))=>![X990:$i, X991:$i]:((((X990)=(X991))=>((in @ X990 @ X988)=>(in @ X991 @ X989))))))=>(![X992:$i, X993:$i]:((((X992)=(X993))=>![X994:$i, X995:$i]:((((X994)=(X995))=>((in @ X994 @ X992)<=>(in @ X995 @ X993))))))=>(![X996:$i > $o]:((?[X997:$i]:(((X996 @ X997)&![X998:$i]:(((X996 @ X998)=>((X997)=(X998))))))=>![X999:$i, X1000:$i]:(((X996 @ X999)=>((X996 @ X1000)=>((X999)=(X1000)))))))=>(![X1621:$i > $o, X1622:$i > $o]:((![X1623:$i, X1624:$i]:((((X1623)=(X1624))=>((X1621 @ X1623)<=>(X1622 @ X1624))))=>(?[X1625:$i]:(((X1621 @ X1625)&![X1626:$i]:(((X1621 @ X1626)=>((X1625)=(X1626))))))<=>?[X1627:$i]:(((X1622 @ X1627)&![X1628:$i]:(((X1622 @ X1628)=>((X1627)=(X1628)))))))))=>(((emptyset)=(emptyset))=>(![X1617:$i, X1618:$i]:((((X1617)=(X1618))=>![X1619:$i, X1620:$i]:((((X1619)=(X1620))=>((setadjoin @ X1617 @ X1619)=(setadjoin @ X1618 @ X1620))))))=>(![X1001:$i, X1002:$i]:((((X1001)=(X1002))=>((powerset @ X1001)=(powerset @ X1002))))=>(![X1003:$i, X1004:$i]:((((X1003)=(X1004))=>((setunion @ X1003)=(setunion @ X1004))))=>(((omega)=(omega))=>(![X1005:$i > $o]:((?[X1006:$i]:(((X1005 @ X1006)&![X1007:$i]:(((X1005 @ X1007)=>((X1006)=(X1007))))))=>![X1008:$i, X1009:$i]:(((X1005 @ X1008)=>((X1005 @ X1009)=>((X1008)=(X1009)))))))=>(![X1010:$i > $o, X1011:$i > $o]:((![X1012:$i, X1013:$i]:((((X1012)=(X1013))=>((X1010 @ X1012)<=>(X1011 @ X1013))))=>(?[X1014:$i]:(((X1010 @ X1014)&![X1015:$i]:(((X1010 @ X1015)=>((X1014)=(X1015))))))=>(?[X1016:$i]:(((X1011 @ X1016)&![X1017:$i]:(((X1011 @ X1017)=>((X1016)=(X1017))))))=>((descr @ X1010)=(descr @ X1011))))))=>(![X1611:$i, X1612:$i]:((((X1611)=(X1612))=>![X1613:$i > $o, X1614:$i > $o]:((![X1615:$i]:(((in @ X1615 @ X1611)=>![X1616:$i]:(((in @ X1616 @ X1612)=>(((X1615)=(X1616))=>((X1613 @ X1615)<=>(X1614 @ X1616)))))))=>((dsetconstr @ X1611 @ X1613)=(dsetconstr @ X1612 @ X1614))))))=>(![X1608:$i, X1609:$i]:((![X1610:$i]:(((in @ X1610 @ X1608)=>(in @ X1610 @ X1609)))=>(subset @ X1608 @ X1609)))=>(![X1018:$i, X1019:$i]:((((X1018)=(X1019))=>(subset @ X1019 @ X1018)))=>(![X1606:$i, X1607:$i]:((((X1606)=(X1607))=>(subset @ X1606 @ X1607)))=>(![X1603:$i, X1604:$i]:((![X1605:$i]:(((in @ X1605 @ X1603)=>(in @ X1605 @ X1604)))=>(subset @ X1603 @ X1604)))=>(![X1020:$i]:((subset @ emptyset @ X1020))=>(![X1600:$i, X1601:$i, X1602:$i]:(((subset @ X1600 @ X1601)=>((in @ X1602 @ X1600)=>(in @ X1602 @ X1601))))=>(![X1021:$i, X1022:$i, X1023:$i]:(((subset @ X1021 @ X1022)=>(~(in @ X1023 @ X1022)=>~(in @ X1023 @ X1021))))=>(![X1024:$i, X1025:$i, X1026:$i]:(((in @ X1026 @ X1024)=>(~(in @ X1026 @ X1025)=>~(subset @ X1024 @ X1025))))=>(![X1598:$i, X1599:$i]:((~(subset @ X1598 @ X1599)=>((X1598)!=(X1599))))=>(![X1027:$i, X1028:$i, X1029:$i]:(((in @ X1029 @ X1027)=>(~(in @ X1029 @ X1028)=>((X1027)!=(X1028)))))=>(![X1597:$i]:((subset @ X1597 @ X1597))=>(![X1594:$i, X1595:$i, X1596:$i]:(((subset @ X1594 @ X1595)=>((subset @ X1595 @ X1596)=>(subset @ X1594 @ X1596))))=>(![X1030:$i, X1031:$i]:((subset @ X1031 @ (setadjoin @ X1030 @ X1031)))=>(![X1591:$i, X1592:$i, X1593:$i]:(((subset @ X1591 @ X1593)=>(subset @ X1591 @ (setadjoin @ X1592 @ X1593))))=>(![X1589:$i, X1590:$i]:(((subset @ X1589 @ X1590)=>(in @ X1589 @ (powerset @ X1590))))=>(![X1032:$i, X1033:$i]:(((subset @ X1032 @ X1033)=>((subset @ X1033 @ X1032)=>((X1032)=(X1033)))))=>(![X1588:$i]:(((subset @ X1588 @ emptyset)=>((X1588)=(emptyset))))=>(![X1034:$i, X1035:$i]:(((subset @ X1035 @ X1034)=>(in @ X1035 @ (powerset @ X1034))))=>(![X1586:$i, X1587:$i]:(((in @ X1587 @ (powerset @ X1586))=>(subset @ X1587 @ X1586)))=>(![X1036:$i]:((in @ X1036 @ (powerset @ X1036)))=>(![X1037:$i, X1038:$i]:(((subset @ X1037 @ X1038)=>(subset @ (powerset @ X1037) @ (powerset @ X1038))))=>(![X1584:$i, X1585:$i > $o]:((in @ (dsetconstr @ X1584 @ X1585) @ (powerset @ X1584)))=>(![X1582:$i, X1583:$i > $o]:((subset @ (dsetconstr @ X1582 @ X1583) @ X1582))=>(![X1039:$i, X1040:$i, X1041:$i]:(((in @ X1041 @ X1039)=>(in @ X1041 @ (binunion @ X1039 @ X1040))))=>(![X1042:$i, X1043:$i]:((in @ X1043 @ (setadjoin @ X1042 @ (setadjoin @ X1043 @ emptyset))))=>(![X1579:$i, X1580:$i, X1581:$i]:(((in @ X1581 @ X1580)=>(in @ X1581 @ (binunion @ X1579 @ X1580))))=>(![X1575:$i, X1576:$i, X1577:$i, X1578:$o]:(((in @ X1577 @ (binunion @ X1575 @ X1576))=>(((in @ X1577 @ X1575)=>(X1578))=>(((in @ X1577 @ X1576)=>(X1578))=>(X1578)))))=>(![X1044:$i, X1045:$i, X1046:$i]:(((in @ X1046 @ (binunion @ X1044 @ X1045))=>((in @ X1046 @ X1044)|(in @ X1046 @ X1045))))=>(![X1573:$i, X1574:$i]:((subset @ X1573 @ (binunion @ X1573 @ X1574)))=>(![X1047:$i, X1048:$i]:((subset @ X1048 @ (binunion @ X1047 @ X1048)))=>(![X1049:$i, X1050:$i, X1051:$i]:(((in @ X1051 @ X1049)=>((in @ X1051 @ X1050)=>(in @ X1051 @ (binintersect @ X1049 @ X1050)))))=>(![X1052:$i, X1053:$i, X1054:$i]:(((subset @ X1054 @ X1052)=>((subset @ X1054 @ X1053)=>(subset @ X1054 @ (binintersect @ X1052 @ X1053)))))=>(![X1055:$i, X1056:$i, X1057:$i]:(((in @ X1057 @ (binintersect @ X1055 @ X1056))=>(in @ X1057 @ X1055)))=>(![X1058:$i, X1059:$i]:((subset @ (binintersect @ X1058 @ X1059) @ X1058))=>(![X1571:$i, X1572:$i]:(((subset @ X1571 @ X1572)=>((binintersect @ X1571 @ X1572)=(X1571))))=>(![X1060:$i, X1061:$i]:((((binintersect @ X1060 @ X1061)=(X1061))=>(subset @ X1061 @ X1060)))=>(![X1568:$i, X1569:$i, X1570:$i]:(((in @ X1570 @ (binintersect @ X1568 @ X1569))=>(in @ X1570 @ X1569)))=>(![X1062:$i, X1063:$i]:((~(?[X1064:$i]:(((in @ X1064 @ X1062)&(in @ X1064 @ X1063))))=>((binintersect @ X1062 @ X1063)=(emptyset))))=>(![X1566:$i, X1567:$i]:((subset @ (binintersect @ X1566 @ X1567) @ X1567))=>(![X1065:$i, X1066:$i]:(((subset @ X1066 @ X1065)=>((binintersect @ X1065 @ X1066)=(X1066))))=>(![X1067:$i, X1068:$i]:((((binintersect @ X1067 @ X1068)=(X1067))=>(subset @ X1067 @ X1068)))=>(![X1069:$i, X1070:$i, X1071:$i]:(((binintersect @ X1069 @ (binunion @ X1070 @ X1071))=(binunion @ (binintersect @ X1069 @ X1070) @ (binintersect @ X1069 @ X1071))))=>(![X1072:$i, X1073:$i, X1074:$i]:(((in @ X1074 @ X1072)=>(~(in @ X1074 @ X1073)=>(in @ X1074 @ (setminus @ X1072 @ X1073)))))=>(![X1563:$i, X1564:$i, X1565:$i]:(((in @ X1565 @ (setminus @ X1563 @ X1564))=>(in @ X1565 @ X1563)))=>(![X1560:$i, X1561:$i, X1562:$i]:(((in @ X1562 @ (setminus @ X1560 @ X1561))=>~(in @ X1562 @ X1561)))=>(![X1558:$i, X1559:$i]:(((subset @ X1558 @ X1559)=>((setminus @ X1558 @ X1559)=(emptyset))))=>(![X1555:$i, X1556:$i, X1557:$i]:((~(in @ X1557 @ (setminus @ X1555 @ X1556))=>((in @ X1557 @ X1555)=>(in @ X1557 @ X1556))))=>(![X1552:$i, X1553:$i, X1554:$i]:((~(in @ X1554 @ (setminus @ X1552 @ X1553))=>(~(in @ X1554 @ X1553)=>~(in @ X1554 @ X1552))))=>(![X1075:$i, X1076:$i, X1077:$i]:((~(in @ X1077 @ X1075)=>~(in @ X1077 @ (setminus @ X1075 @ X1076))))=>(![X1078:$i, X1079:$i, X1080:$i]:(((in @ X1080 @ X1079)=>~(in @ X1080 @ (setminus @ X1078 @ X1079))))=>(![X1550:$i, X1551:$i]:((subset @ (setminus @ X1550 @ X1551) @ X1550))=>(![X1081:$i, X1082:$i]:((((setminus @ X1081 @ 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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_286]), foundationAx]), wellorderingAx]), c_0_287]), c_0_288]), c_0_289]), c_0_290]), c_0_291]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_292]), setext]), emptyI]), noeltsimpempty]), c_0_293]), c_0_294]), c_0_295]), c_0_296]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_297]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_298]), c_0_299]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_300]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_301]), c_0_302]), c_0_303]), inCongP]), in__Cong]), c_0_304]), c_0_305]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_306]), c_0_307]), c_0_308]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_309]), c_0_310]), 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]), c_0_311]), c_0_312]), c_0_313]), c_0_314]), singletonsuniq]), setukpairinjL1]), c_0_315]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_316]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_317]), c_0_318]), c_0_319]), c_0_320]), c_0_321]), c_0_322]), c_0_323]), c_0_324]), c_0_325]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_326]), c_0_327]), c_0_328]), c_0_329]), c_0_330]), c_0_331]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_332]), c_0_333]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_334]), c_0_335]), c_0_336]), c_0_337]), c_0_338]), c_0_339]), c_0_340]), c_0_341]), c_0_342]), c_0_343]), 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])])]), c_0_344])).
140.50/18.50	thf(c_0_346, negated_conjecture, ![X1721:$i, X1722:$i, X1724:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1734:$i, X1735:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1743:$i, X1744:$i > $i > $o, X1745:$i, X1747:$i, X1750:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1757:$i, X1758:$i > $o, X1759:$i, X1761:$i, X1762:$i > $o, X1763:$i, X1764:$i, X1765:$i > $o, X1766:$i, X1767:$i, X1768:$i > $o, X1769:$i, X1770:$i > $o, X1771:$i, X1774:$i, X1775:$o, X1776:$i, X1777:$i, X1778:$o, X1779:$i, X1780:$i, X1781:$i > $o, X1782:$i, X1785:$i, X1786:$i, X1789:$i, X1791:$i, X1793:$i, X1794:$i > $o, X1795:$i, X1796:$i, X1798:$i, X1799:$i > $o, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$o, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$o, X1831:$i, X1832:$i, X1833:$i > $o, X1834:$i, X1837:$i, X1838:$i, X1839:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i > $o, X1858:$i, X1859:$i > $o, X1860:$i, X1861:$i, X1862:$i > $o, X1863:$i, X1865:$i, X1866:$i > $o, X1868:$i, X1869:$i, X1870:$i > $o, X1872:$i, X1873:$i, X1874:$i > $o, X1875:$i, X1877:$o, X1878:$o, X1879:$i, X1880:$i > $o, X1882:$i, X1883:$i, X1884:$i > $o, X1885:$i, X1887:$i > $o, X1888:$i, X1891:$i, X1892:$i > $o, X1893:$i, X1897:$i, X1898:$i > $o, X1899:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i > $o, X1912:$i, X1914:$i, X1915:$i, X1916:$i > $o, X1917:$i > $o, X1920:$i, X1923:$i, X1924:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i > $o, X1937:$i, X1939:$i, X1940:$i, X1941:$i > $o, X1942:$i > $o, X1945:$i, X1947:$i, X1949:$i, X1950:$i, X1951:$i > $o, X1952:$i > $o, X1955:$i, X1956:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, 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 > $o, X2003:$i, X2004:$i > $o, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$o, X2017:$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, X2045:$i, X2046:$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:$i, X2084:$o, 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, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i > $o, X2159:$i, X2160:$i, X2161:$i > $o, X2163:$i, X2164:$i > $o, X2165:$i, X2167:$i, X2168:$i > $o, X2171:$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:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2230:$i, X2231:$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 > $i > $o, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i > $i > $o, X2249:$i, X2250:$i, X2251:$i > $i > $o, X2252:$i, X2253:$i, X2254:$i > $i > $o, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i > $i > $o, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i > $i > $o, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i > $i > $o, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i, X2282:$i, 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 > $i, X2298:$i, X2299:$i, X2300:$i > $i, X2302:$i, X2303:$i, X2304:$i > $i, X2306:$i, X2307:$i, X2308:$i, X2309:$i > $o, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i > $o, X2319:$i, X2320:$i, X2321:$i > $o, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2327:$i, X2328:$i, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2342:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2363:$i, X2364:$i, X2365:$i, X2366:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$i, X2373:$i, X2374:$i, X2375:$i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2383:$i > $i, X2385:$i, X2386:$i, X2387:$i, X2388:$i, X2389:$i, X2390:$i, X2391:$i > $i, X2393:$i, X2394:$i, X2395:$i > $i, X2397:$i, X2398:$i, X2399:$i, X2400:$i, X2401:$i, X2402:$o, X2403:$i, X2404:$i, X2405:$i, X2406:$o, X2407:$i, X2408:$i, X2409:$i, X2410:$o, X2411:$i, X2412:$i, X2413:$i, X2414:$o, X2415:$i, X2416:$i, X2417:$i, X2418:$o, X2419:$i, X2420:$i, X2421:$i, X2422:$o, X2423:$i, X2424:$i, X2425:$i, X2426:$i, X2427:$i, X2428:$o, X2429:$i, X2430:$i, X2431:$i, X2432:$o, X2433:$i, X2434:$i, X2435:$i, X2436:$o, X2437:$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:$i, X2457:$i, X2458:$i, X2459:$i, X2461:$i, X2462:$i, X2463:$i, X2465:$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:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i, X2546:$i, X2547:$i]:((((~(in @ (esk1_2 @ X1721 @ X1722) @ X1721)|~(in @ (esk1_2 @ X1721 @ X1722) @ X1722)|((X1721)=(X1722)))&((in @ (esk1_2 @ X1721 @ X1722) @ X1721)|(in @ (esk1_2 @ X1721 @ X1722) @ X1722)|((X1721)=(X1722))))&(~(in @ X1724 @ emptyset)&(((~(in 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X2358)|~(subset @ X2358 @ (cartprod @ X2355 @ X2356))|~(subset @ X2357 @ (cartprod @ X2355 @ X2356)))&(((in @ (kpair @ (esk76_4 @ X2355 @ X2356 @ X2357 @ X2358) @ (esk77_4 @ X2355 @ X2356 @ X2357 @ X2358)) @ X2358)|((X2357)=(X2358))|~(in @ (kpair @ (esk74_4 @ X2355 @ X2356 @ X2357 @ X2358) @ (esk75_4 @ X2355 @ X2356 @ X2357 @ X2358)) @ X2358)|~(subset @ X2358 @ (cartprod @ X2355 @ X2356))|~(subset @ X2357 @ (cartprod @ X2355 @ X2356)))&(~(in @ (kpair @ (esk76_4 @ X2355 @ X2356 @ X2357 @ X2358) @ (esk77_4 @ X2355 @ X2356 @ X2357 @ X2358)) @ X2357)|((X2357)=(X2358))|~(in @ (kpair @ (esk74_4 @ X2355 @ X2356 @ X2357 @ X2358) @ (esk75_4 @ X2355 @ X2356 @ X2357 @ X2358)) @ X2358)|~(subset @ X2358 @ (cartprod @ X2355 @ X2356))|~(subset @ X2357 @ (cartprod @ X2355 @ X2356)))))))))&((((in @ (esk78_4 @ X2363 @ X2364 @ X2365 @ X2366) @ X2363)|((X2365)=(X2366))|~(func @ X2363 @ X2364 @ X2366)|~(func @ X2363 @ X2364 @ X2365))&(((ap @ X2363 @ X2364 @ X2365 @ (esk78_4 @ X2363 @ X2364 @ X2365 @ X2366))!=(ap @ X2363 @ X2364 @ X2366 @ (esk78_4 @ X2363 @ X2364 @ X2365 @ X2366)))|((X2365)=(X2366))|~(func @ X2363 @ X2364 @ X2366)|~(func @ X2363 @ X2364 @ X2365)))&((((in @ (esk79_4 @ X2368 @ X2369 @ X2370 @ X2371) @ X2368)|((X2370)=(X2371))|~(in @ X2371 @ (funcSet @ X2368 @ X2369))|~(in @ X2370 @ (funcSet @ X2368 @ X2369)))&(((ap @ X2368 @ X2369 @ X2370 @ (esk79_4 @ X2368 @ X2369 @ X2370 @ X2371))!=(ap @ X2368 @ X2369 @ X2371 @ (esk79_4 @ X2368 @ X2369 @ X2370 @ X2371)))|((X2370)=(X2371))|~(in @ X2371 @ (funcSet @ X2368 @ X2369))|~(in @ X2370 @ (funcSet @ X2368 @ X2369))))&((~(in @ X2375 @ (funcSet @ X2373 @ X2374))|(~(in @ X2376 @ X2373)|((ap @ X2373 @ X2374 @ X2375 @ X2376)=(ap @ X2373 @ X2374 @ X2375 @ X2376))))&((~(func @ X2377 @ X2378 @ X2379)|(~(in @ X2380 @ X2377)|((ap @ X2377 @ X2378 @ X2379 @ X2380)=(ap @ X2377 @ X2378 @ X2379 @ X2380))))&((((in @ (esk80_3 @ X2381 @ X2382 @ X2383) @ X2381)|(~(in @ X2385 @ X2381)|((ap @ X2381 @ X2382 @ (lam @ X2381 @ X2382 @ X2383) @ X2385)=(X2383 @ X2385))))&(~(in @ (X2383 @ (esk80_3 @ X2381 @ X2382 @ X2383)) @ X2382)|(~(in @ X2385 @ X2381)|((ap @ X2381 @ X2382 @ (lam @ X2381 @ X2382 @ X2383) @ X2385)=(X2383 @ X2385)))))&((~(func @ X2386 @ X2387 @ X2388)|((lam @ X2386 @ X2387 @ (ap @ X2386 @ X2387 @ X2388))=(X2388)))&((((in @ (esk81_3 @ X2389 @ X2390 @ X2391) @ X2389)|((lam @ X2389 @ X2390 @ X2391)=(lam @ X2389 @ X2390 @ X2391)))&(~(in @ (X2391 @ (esk81_3 @ X2389 @ X2390 @ X2391)) @ X2390)|((lam @ X2389 @ X2390 @ X2391)=(lam @ X2389 @ X2390 @ X2391))))&((((in @ (esk82_3 @ X2393 @ X2394 @ X2395) @ X2393)|(~(in @ X2397 @ X2393)|((ap @ X2393 @ X2394 @ (lam @ X2393 @ X2394 @ X2395) @ X2397)=(X2395 @ X2397))))&(~(in @ (X2395 @ (esk82_3 @ X2393 @ X2394 @ X2395)) @ X2394)|(~(in @ X2397 @ X2393)|((ap @ X2393 @ X2394 @ (lam @ X2393 @ X2394 @ X2395) @ X2397)=(X2395 @ X2397)))))&((~(in @ X2400 @ (funcSet @ X2398 @ X2399))|((lam @ X2398 @ X2399 @ (ap @ X2398 @ X2399 @ X2400))=(X2400)))&((~(in @ X2403 @ X2401)|(~(in @ X2404 @ X2401)|((X2402)|(in @ X2404 @ (dsetconstr @ X2401 @ (^[Z0:$i]:((((((X2402))&(((Z0)=(X2403)))))|(((~((X2402)))&(((Z0)=(X2404)))))))))))))&((~(in @ X2407 @ X2405)|(~(in @ X2408 @ X2405)|((X2406)|((dsetconstr @ X2405 @ (^[Z0:$i]:((((((X2406))&(((Z0)=(X2407)))))|(((~((X2406)))&(((Z0)=(X2408)))))))))=(setadjoin @ X2408 @ emptyset)))))&((~(in @ X2411 @ X2409)|(~(in @ X2412 @ X2409)|(~(X2410)|(in @ X2411 @ (dsetconstr @ X2409 @ (^[Z0:$i]:((((((X2410))&(((Z0)=(X2411)))))|(((~((X2410)))&(((Z0)=(X2412)))))))))))))&((~(in @ X2415 @ X2413)|(~(in @ X2416 @ X2413)|(~(X2414)|((dsetconstr @ X2413 @ (^[Z0:$i]:((((((X2414))&(((Z0)=(X2415)))))|(((~((X2414)))&(((Z0)=(X2416)))))))))=(setadjoin @ X2415 @ emptyset)))))&((~(in @ X2419 @ X2417)|(~(in @ X2420 @ X2417)|(singleton @ (dsetconstr @ X2417 @ (^[Z0:$i]:((((((X2418))&(((Z0)=(X2419)))))|(((~((X2418)))&(((Z0)=(X2420))))))))))))&((~(in @ X2423 @ X2421)|(~(in @ X2424 @ X2421)|(in @ (if @ X2421 @ ((X2422)) @ X2423 @ X2424) @ X2421)))&((~(singleton @ X2425)|(~(in @ X2426 @ X2425)|((setunion @ X2425)=(X2426))))&((~(in @ X2429 @ X2427)|(~(in @ X2430 @ X2427)|(~(X2428)|((if @ X2427 @ ((X2428)) @ X2429 @ X2430)=(X2429)))))&((~(in @ X2433 @ X2431)|(~(in @ X2434 @ X2431)|((X2432)|((if @ X2431 @ ((X2432)) @ X2433 @ X2434)=(X2434)))))&((~(in @ X2437 @ X2435)|(~(in @ X2438 @ X2435)|(in @ (if @ X2435 @ ((X2436)) @ X2437 @ X2438) @ (setadjoin @ X2437 @ (setadjoin @ X2438 @ emptyset)))))&((~(in @ X2440 @ (powerset @ X2439))|(~(in @ X2441 @ (powerset @ X2439))|(in @ (binintersect @ X2440 @ X2441) @ (powerset @ X2439))))&((~(in @ X2443 @ (powerset @ X2442))|(~(in @ X2444 @ (powerset @ X2442))|(in @ (binunion @ X2443 @ X2444) @ (powerset @ X2442))))&((~(in @ X2446 @ (powerset @ X2445))|(in @ (powerset @ X2446) @ (powerset @ (powerset @ X2445))))&((~(in @ X2448 @ (powerset @ X2447))|(~(in @ X2449 @ (powerset @ X2447))|(in @ (setminus @ X2448 @ X2449) @ (powerset @ X2447))))&((~(in @ X2451 @ (powerset @ X2450))|(in @ (setminus @ X2450 @ X2451) @ (powerset @ X2450)))&(((((in @ (esk84_3 @ X2452 @ X2453 @ X2454) @ X2452)|((X2453)=(X2454))|(in @ (esk83_3 @ X2452 @ X2453 @ X2454) @ X2452)|~(in @ X2454 @ (powerset @ X2452))|~(in @ X2453 @ (powerset @ X2452)))&(((in @ (esk84_3 @ X2452 @ X2453 @ X2454) @ X2454)|((X2453)=(X2454))|(in @ (esk83_3 @ X2452 @ X2453 @ X2454) @ X2452)|~(in @ X2454 @ (powerset @ X2452))|~(in @ X2453 @ (powerset @ X2452)))&(~(in @ (esk84_3 @ X2452 @ X2453 @ X2454) @ X2453)|((X2453)=(X2454))|(in @ (esk83_3 @ X2452 @ X2453 @ X2454) @ X2452)|~(in @ X2454 @ (powerset @ X2452))|~(in @ X2453 @ (powerset @ X2452)))))&((((in @ (esk84_3 @ X2452 @ X2453 @ X2454) @ X2452)|((X2453)=(X2454))|(in @ (esk83_3 @ X2452 @ X2453 @ X2454) @ X2453)|~(in @ X2454 @ (powerset @ X2452))|~(in @ X2453 @ (powerset @ X2452)))&(((in @ (esk84_3 @ X2452 @ X2453 @ X2454) @ X2454)|((X2453)=(X2454))|(in @ (esk83_3 @ X2452 @ X2453 @ X2454) @ X2453)|~(in @ X2454 @ (powerset @ X2452))|~(in @ X2453 @ (powerset @ X2452)))&(~(in @ (esk84_3 @ X2452 @ X2453 @ X2454) @ X2453)|((X2453)=(X2454))|(in @ (esk83_3 @ X2452 @ X2453 @ X2454) @ X2453)|~(in @ X2454 @ (powerset @ X2452))|~(in @ X2453 @ (powerset @ X2452)))))&(((in @ (esk84_3 @ X2452 @ X2453 @ X2454) @ X2452)|((X2453)=(X2454))|~(in @ (esk83_3 @ X2452 @ X2453 @ X2454) @ X2454)|~(in @ X2454 @ (powerset @ X2452))|~(in @ X2453 @ (powerset @ X2452)))&(((in @ (esk84_3 @ X2452 @ X2453 @ X2454) @ X2454)|((X2453)=(X2454))|~(in @ (esk83_3 @ X2452 @ X2453 @ X2454) @ X2454)|~(in @ X2454 @ (powerset @ X2452))|~(in @ X2453 @ (powerset @ X2452)))&(~(in @ (esk84_3 @ X2452 @ X2453 @ X2454) @ X2453)|((X2453)=(X2454))|~(in @ (esk83_3 @ X2452 @ X2453 @ X2454) @ X2454)|~(in @ X2454 @ (powerset @ X2452))|~(in @ X2453 @ (powerset @ X2452)))))))&((((in @ (esk85_3 @ X2457 @ X2458 @ X2459) @ X2457)|(subset @ X2458 @ X2459)|~(in @ X2459 @ (powerset @ X2457))|~(in @ X2458 @ (powerset @ X2457)))&(((in @ (esk85_3 @ X2457 @ X2458 @ X2459) @ X2458)|(subset @ X2458 @ X2459)|~(in @ X2459 @ (powerset @ X2457))|~(in @ X2458 @ (powerset @ X2457)))&(~(in @ (esk85_3 @ X2457 @ X2458 @ X2459) @ X2459)|(subset @ X2458 @ X2459)|~(in @ X2459 @ (powerset @ X2457))|~(in @ X2458 @ (powerset @ X2457)))))&((((in @ (esk86_3 @ X2461 @ X2462 @ X2463) @ X2461)|(in @ X2462 @ (powerset @ X2463))|~(in @ X2463 @ (powerset @ X2461))|~(in @ X2462 @ (powerset @ X2461)))&(((in @ (esk86_3 @ X2461 @ X2462 @ X2463) @ X2462)|(in @ X2462 @ (powerset @ X2463))|~(in @ X2463 @ (powerset @ X2461))|~(in @ X2462 @ (powerset @ X2461)))&(~(in @ (esk86_3 @ X2461 @ X2462 @ X2463) @ X2463)|(in @ X2462 @ (powerset @ X2463))|~(in @ X2463 @ (powerset @ X2461))|~(in @ X2462 @ (powerset @ X2461)))))&((~(in @ X2466 @ (powerset @ X2465))|(~(in @ X2467 @ (powerset @ X2465))|(~(in @ X2468 @ X2465)|(~(in @ X2466 @ (powerset @ X2467))|(~(in @ X2468 @ X2466)|(in @ X2468 @ X2467))))))&((~(in @ X2470 @ (powerset @ X2469))|(~(in @ X2471 @ X2469)|(~(in @ X2471 @ X2470)|~(in @ X2471 @ (setminus @ X2469 @ X2470)))))&((~(in @ X2473 @ (powerset @ X2472))|(~(in @ X2474 @ X2472)|((in @ X2474 @ (setminus @ X2472 @ X2473))|(in @ X2474 @ X2473))))&((~(in @ X2476 @ (powerset @ X2475))|(~(in @ X2477 @ (powerset @ X2475))|(~(in @ X2478 @ X2475)|((in @ X2478 @ X2476)|~(in @ X2478 @ (binintersect @ X2476 @ X2477))))))&((~(in @ X2480 @ (powerset @ X2479))|(~(in @ X2481 @ (powerset @ X2479))|(~(in @ X2482 @ X2479)|((in @ X2482 @ X2481)|~(in @ X2482 @ (binintersect @ X2480 @ X2481))))))&((~(in @ X2484 @ (powerset @ X2483))|(~(in @ X2485 @ (powerset @ X2483))|(~(in @ X2486 @ X2483)|(~(subset @ X2484 @ (setminus @ X2483 @ X2485))|(~(in @ X2486 @ X2485)|~(in @ X2486 @ X2484))))))&((~(in @ X2488 @ (powerset @ X2487))|(~(in @ X2489 @ (powerset @ X2487))|(~(in @ X2490 @ X2487)|(~(subset @ X2488 @ X2489)|((in @ X2490 @ X2489)|~(in @ X2490 @ X2488))))))&((~(in @ X2492 @ (powerset @ X2491))|(~(in @ X2493 @ (powerset @ X2491))|(~(subset @ X2492 @ X2493)|(subset @ (setminus @ X2491 @ X2493) @ (setminus @ X2491 @ X2492)))))&((~(in @ X2495 @ (powerset @ X2494))|(~(in @ X2496 @ (powerset @ X2494))|(~(subset @ (setminus @ X2494 @ X2496) @ (setminus @ X2494 @ X2495))|(subset @ X2495 @ X2496))))&((~(in @ X2498 @ (powerset @ X2497))|(~(in @ X2499 @ X2497)|(~(in @ X2499 @ X2498)|(in @ X2499 @ (setminus @ X2497 @ (setminus @ X2497 @ X2498))))))&((~(in @ X2501 @ (powerset @ X2500))|(~(in @ X2502 @ X2500)|(~(in @ X2502 @ (setminus @ X2500 @ (setminus @ X2500 @ X2501)))|(in @ X2502 @ X2501))))&((~(in @ X2504 @ (powerset @ X2503))|(subset @ X2504 @ (setminus @ X2503 @ (setminus @ X2503 @ X2504))))&((~(in @ X2506 @ (powerset @ X2505))|(subset @ (setminus @ X2505 @ (setminus @ X2505 @ X2506)) @ X2506))&((~(in @ X2508 @ (powerset @ X2507))|((X2508)=(setminus @ X2507 @ (setminus @ X2507 @ X2508))))&((~(in @ X2510 @ (powerset @ X2509))|(~(in @ X2511 @ (powerset @ X2509))|(~(in @ X2512 @ X2509)|(~(in @ X2512 @ (setminus @ X2509 @ X2510))|~(in @ X2512 @ (binintersect @ X2510 @ X2511))))))&((~(in @ X2514 @ (powerset @ X2513))|(~(in @ X2515 @ (powerset @ X2513))|(~(in @ X2516 @ X2513)|(~(in @ X2516 @ (setminus @ X2513 @ X2514))|(in @ X2516 @ (setminus @ X2513 @ (binintersect @ X2514 @ X2515)))))))&((~(in @ X2518 @ (powerset @ X2517))|(~(in @ X2519 @ (powerset @ X2517))|(subset @ (setminus @ X2517 @ X2518) @ (setminus @ X2517 @ (binintersect @ X2518 @ X2519)))))&((~(in @ X2521 @ (powerset @ X2520))|(~(in @ X2522 @ (powerset @ X2520))|(in @ (setminus @ X2520 @ X2521) @ (powerset @ (setminus @ X2520 @ (binintersect @ X2521 @ X2522))))))&((~(in @ X2524 @ (powerset @ X2523))|(~(in @ X2525 @ (powerset @ X2523))|(~(subset @ X2524 @ (setminus @ X2523 @ X2525))|(~(in @ X2526 @ X2523)|(~(in @ X2526 @ X2525)|(in @ X2526 @ (setminus @ X2523 @ X2524)))))))&((~(in @ X2528 @ (powerset @ X2527))|(~(in @ X2529 @ (powerset @ X2527))|(~(subset @ X2528 @ (setminus @ X2527 @ X2529))|(subset @ X2529 @ (setminus @ X2527 @ X2528)))))&((~(in @ X2531 @ (powerset @ X2530))|(~(in @ X2532 @ (powerset @ X2530))|(~(in @ X2533 @ X2530)|((in @ X2533 @ (binunion @ X2531 @ X2532))|~(in @ X2533 @ X2531)))))&((~(in @ X2535 @ (powerset @ X2534))|(~(in @ X2536 @ (powerset @ X2534))|(~(in @ X2537 @ X2534)|((in @ X2537 @ (binunion @ X2535 @ X2536))|~(in @ X2537 @ X2536)))))&((~(in @ X2539 @ (powerset @ X2538))|(~(in @ X2540 @ (powerset @ X2538))|(~(in @ X2541 @ (powerset @ X2538))|(~(in @ X2542 @ X2538)|(~(in @ X2542 @ (binintersect @ X2539 @ X2540))|(in @ X2542 @ (binunion @ X2539 @ X2541)))))))&((~(in @ X2544 @ (powerset @ X2543))|(~(in @ X2545 @ (powerset @ X2543))|(~(in @ X2546 @ (powerset @ X2543))|(~(in @ X2547 @ X2543)|(~(in @ X2547 @ (binintersect @ X2544 @ X2545))|(in @ X2547 @ (binunion @ X2545 @ X2546)))))))&((in @ esk88_0 @ (powerset @ esk87_0))&((in @ esk89_0 @ (powerset @ esk87_0))&((in @ esk90_0 @ (powerset @ esk87_0))&((in @ esk91_0 @ esk87_0)&((in @ esk91_0 @ (binintersect @ esk88_0 @ esk89_0))&~(in @ esk91_0 @ (binintersect @ (binunion @ esk88_0 @ esk90_0) @ (binunion @ esk89_0 @ esk90_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_345])])])])])])])).
140.50/18.50	thf(c_0_347, negated_conjecture, ~((in @ esk91_0 @ (binintersect @ (binunion @ esk88_0 @ esk90_0) @ (binunion @ esk89_0 @ esk90_0)))), inference(split_conjunct,[status(thm)],[c_0_346])).
140.50/18.50	thf(c_0_348, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ (binintersect @ X3 @ X4))|~((in @ X2 @ X3))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_346])).
140.50/18.50	thf(c_0_349, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X4)|~((in @ X2 @ (binintersect @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_346])).
140.50/18.50	thf(c_0_350, negated_conjecture, (in @ esk91_0 @ (binintersect @ esk88_0 @ esk89_0)), inference(split_conjunct,[status(thm)],[c_0_346])).
140.50/18.50	thf(c_0_351, negated_conjecture, (~((in @ esk91_0 @ (binunion @ esk89_0 @ esk90_0)))|~((in @ esk91_0 @ (binunion @ esk88_0 @ esk90_0)))), inference(spm,[status(thm)],[c_0_347, c_0_348])).
140.50/18.50	thf(c_0_352, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X3 @ X4))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_346])).
140.50/18.50	thf(c_0_353, negated_conjecture, (in @ esk91_0 @ esk89_0), inference(spm,[status(thm)],[c_0_349, c_0_350])).
140.50/18.50	thf(c_0_354, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X3)|~((in @ X2 @ (binintersect @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_346])).
140.50/18.50	thf(c_0_355, negated_conjecture, ~((in @ esk91_0 @ (binunion @ esk88_0 @ esk90_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_351, c_0_352]), c_0_353])])).
140.50/18.50	thf(c_0_356, negated_conjecture, (in @ esk91_0 @ esk88_0), inference(spm,[status(thm)],[c_0_354, c_0_350])).
140.50/18.50	thf(c_0_357, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_355, c_0_352]), c_0_356])]), ['proof']).
140.50/18.50	% SZS output end CNFRefutation
140.50/18.50	% Parsed axioms                        : 559
140.50/18.50	% Removed by relevancy pruning/SinE    : 0
140.50/18.50	% Initial clauses                      : 741
140.50/18.50	% Removed in clause preprocessing      : 325
140.50/18.50	% Initial clauses in saturation        : 416
140.50/18.50	% Processed clauses                    : 999
140.50/18.50	% ...of these trivial                  : 31
140.50/18.50	% ...subsumed                          : 239
140.50/18.50	% ...remaining for further processing  : 729
140.50/18.50	% Other redundant clauses eliminated   : 20
140.50/18.50	% Clauses deleted for lack of memory   : 0
140.50/18.50	% Backward-subsumed                    : 2
140.50/18.50	% Backward-rewritten                   : 9
140.50/18.50	% Generated clauses                    : 2220
140.50/18.50	% ...of the previous two non-redundant : 1891
140.50/18.50	% ...aggressively subsumed             : 0
140.50/18.50	% Contextual simplify-reflections      : 6
140.50/18.50	% Paramodulations                      : 2194
140.50/18.50	% Factorizations                       : 0
140.50/18.50	% NegExts                              : 0
140.50/18.50	% Equation resolutions                 : 23
140.50/18.50	% Disequality decompositions           : 0
140.50/18.50	% Total rewrite steps                  : 623
140.50/18.50	% ...of those cached                   : 455
140.50/18.50	% Propositional unsat checks           : 0
140.50/18.50	%    Propositional check models        : 0
140.50/18.50	%    Propositional check unsatisfiable : 0
140.50/18.50	%    Propositional clauses             : 0
140.50/18.50	%    Propositional clauses after purity: 0
140.50/18.50	%    Propositional unsat core size     : 0
140.50/18.50	%    Propositional preprocessing time  : 0.000
140.50/18.50	%    Propositional encoding time       : 0.000
140.50/18.50	%    Propositional solver time         : 0.000
140.50/18.50	%    Success case prop preproc time    : 0.000
140.50/18.50	%    Success case prop encoding time   : 0.000
140.50/18.50	%    Success case prop solver time     : 0.000
140.50/18.50	% Current number of processed clauses  : 340
140.50/18.50	%    Positive orientable unit clauses  : 105
140.50/18.50	%    Positive unorientable unit clauses: 0
140.50/18.50	%    Negative unit clauses             : 6
140.50/18.50	%    Non-unit-clauses                  : 229
140.50/18.50	% Current number of unprocessed clauses: 1664
140.50/18.50	% ...number of literals in the above   : 4359
140.50/18.50	% Current number of archived formulas  : 0
140.50/18.50	% Current number of archived clauses   : 374
140.50/18.50	% Clause-clause subsumption calls (NU) : 33312
140.50/18.50	% Rec. Clause-clause subsumption calls : 14300
140.50/18.50	% Non-unit clause-clause subsumptions  : 82
140.50/18.50	% Unit Clause-clause subsumption calls : 869
140.50/18.50	% Rewrite failures with RHS unbound    : 0
140.50/18.50	% BW rewrite match attempts            : 40
140.50/18.50	% BW rewrite match successes           : 9
140.50/18.50	% Condensation attempts                : 0
140.50/18.50	% Condensation successes               : 0
140.50/18.50	% Termbank termtop insertions          : 129289
140.50/18.50	% Search garbage collected termcells   : 27050
140.50/18.50	
140.50/18.50	% -------------------------------------------------
140.50/18.50	% User time                : 16.969 s
140.50/18.50	% System time              : 0.541 s
140.50/18.50	% Total time               : 17.510 s
140.50/18.50	% Maximum resident set size: 10340 pages
140.50/18.50	
140.50/18.50	% -------------------------------------------------
140.50/18.50	% User time                : 16.996 s
140.50/18.50	% System time              : 0.555 s
140.50/18.50	% Total time               : 17.551 s
140.50/18.50	% Maximum resident set size: 5632 pages
140.50/18.50	% E exiting
140.50/18.51	EOF