0.00/0.03	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.05	% Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.12/0.36	% Computer : n006.cluster.edu
0.12/0.36	% Model    : x86_64 x86_64
0.12/0.36	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.36	% Memory   : 8046.5625MB
0.12/0.36	% OS       : Linux 6.8.0-71-generic
0.12/0.36	% CPULimit : 1440
0.12/0.36	% WCLimit  : 180
0.12/0.37	% DateTime : Mon Jul 27 13:47:49 UTC 2026
0.12/0.37	% CPUTime  : 
0.12/0.37	Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.12/0.43	Running higher-order theorem proving
0.21/0.48	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.caduz1V4uW/E---3.1_2881760.p
10.99/1.99	% Version: 3.5.1-ho
10.99/1.99	% Preprocessing class: HSLMSLSSLLLCHFA.
10.99/1.99	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
10.99/1.99	% Starting ehoh_best5 with 180s (1) cores
10.99/1.99	% Starting almost_fo_3_lam with 180s (1) cores
10.99/1.99	% Starting new_bool_5 with 180s (1) cores
10.99/1.99	% Starting pre_casc_3 with 180s (1) cores
10.99/1.99	% Starting ho_unfolding_8 with 180s (1) cores
10.99/1.99	% Starting new_ho_10_cnf2 with 180s (1) cores
10.99/1.99	% Starting new_bool_3 with 180s (1) cores
10.99/1.99	% Starting new_ho_5 with 180s (1) cores
10.99/1.99	% ho_unfolding_8 with pid 2881777 completed with status 0
10.99/1.99	% Result found by ho_unfolding_8
10.99/1.99	% Preprocessing class: HSLMSLSSLLLCHFA.
10.99/1.99	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
10.99/1.99	% Starting ehoh_best5 with 180s (1) cores
10.99/1.99	% Starting almost_fo_3_lam with 180s (1) cores
10.99/1.99	% Starting new_bool_5 with 180s (1) cores
10.99/1.99	% Starting pre_casc_3 with 180s (1) cores
10.99/1.99	% Starting ho_unfolding_8 with 180s (1) cores
10.99/1.99	% (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
10.99/1.99	% No SInE strategy applied
10.99/1.99	% Search class: HGHSM-FSLM32-MHFMMSBN
10.99/1.99	% Scheduled 9 strats onto 1 cores with 180 seconds (180 total)
10.99/1.99	% Starting SubtermCWHack with 19s (1) cores
10.99/1.99	% SubtermCWHack with pid 2881783 completed with status 0
10.99/1.99	% Result found by SubtermCWHack
10.99/1.99	% Preprocessing class: HSLMSLSSLLLCHFA.
10.99/1.99	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
10.99/1.99	% Starting ehoh_best5 with 180s (1) cores
10.99/1.99	% Starting almost_fo_3_lam with 180s (1) cores
10.99/1.99	% Starting new_bool_5 with 180s (1) cores
10.99/1.99	% Starting pre_casc_3 with 180s (1) cores
10.99/1.99	% Starting ho_unfolding_8 with 180s (1) cores
10.99/1.99	% (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
10.99/1.99	% No SInE strategy applied
10.99/1.99	% Search class: HGHSM-FSLM32-MHFMMSBN
10.99/1.99	% Scheduled 9 strats onto 1 cores with 180 seconds (180 total)
10.99/1.99	% Starting SubtermCWHack with 19s (1) cores
10.99/1.99	% Preprocessing time       : 0.007 s
10.99/1.99	
10.99/1.99	% Proof found!
10.99/1.99	% SZS status Theorem
10.99/1.99	% SZS output start CNFRefutation
10.99/1.99	thf(decl_23, type, in: $i > $i > $o).
10.99/1.99	thf(decl_24, type, exu: ($i > $o) > $o).
10.99/1.99	thf(decl_25, type, setextAx: $o).
10.99/1.99	thf(decl_26, type, emptyset: $i).
10.99/1.99	thf(decl_27, type, emptysetAx: $o).
10.99/1.99	thf(decl_28, type, setadjoin: $i > $i > $i).
10.99/1.99	thf(decl_29, type, setadjoinAx: $o).
10.99/1.99	thf(decl_30, type, powerset: $i > $i).
10.99/1.99	thf(decl_31, type, powersetAx: $o).
10.99/1.99	thf(decl_32, type, setunion: $i > $i).
10.99/1.99	thf(decl_33, type, setunionAx: $o).
10.99/1.99	thf(decl_34, type, omega: $i).
10.99/1.99	thf(decl_35, type, omega0Ax: $o).
10.99/1.99	thf(decl_36, type, omegaSAx: $o).
10.99/1.99	thf(decl_37, type, omegaIndAx: $o).
10.99/1.99	thf(decl_38, type, replAx: $o).
10.99/1.99	thf(decl_39, type, foundationAx: $o).
10.99/1.99	thf(decl_40, type, wellorderingAx: $o).
10.99/1.99	thf(decl_41, type, descr: ($i > $o) > $i).
10.99/1.99	thf(decl_42, type, descrp: $o).
10.99/1.99	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
10.99/1.99	thf(decl_44, type, dsetconstrI: $o).
10.99/1.99	thf(decl_45, type, dsetconstrEL: $o).
10.99/1.99	thf(decl_46, type, dsetconstrER: $o).
10.99/1.99	thf(decl_47, type, exuE1: $o).
10.99/1.99	thf(decl_48, type, prop2set: $o > $i).
10.99/1.99	thf(decl_49, type, prop2setE: $o).
10.99/1.99	thf(decl_50, type, emptysetE: $o).
10.99/1.99	thf(decl_51, type, emptysetimpfalse: $o).
10.99/1.99	thf(decl_52, type, notinemptyset: $o).
10.99/1.99	thf(decl_53, type, exuE3e: $o).
10.99/1.99	thf(decl_54, type, setext: $o).
10.99/1.99	thf(decl_55, type, emptyI: $o).
10.99/1.99	thf(decl_56, type, noeltsimpempty: $o).
10.99/1.99	thf(decl_57, type, setbeta: $o).
10.99/1.99	thf(decl_58, type, nonempty: $i > $o).
10.99/1.99	thf(decl_59, type, nonemptyE1: $o).
10.99/1.99	thf(decl_60, type, nonemptyI: $o).
10.99/1.99	thf(decl_61, type, nonemptyI1: $o).
10.99/1.99	thf(decl_62, type, setadjoinIL: $o).
10.99/1.99	thf(decl_63, type, emptyinunitempty: $o).
10.99/1.99	thf(decl_64, type, setadjoinIR: $o).
10.99/1.99	thf(decl_65, type, setadjoinE: $o).
10.99/1.99	thf(decl_66, type, setadjoinOr: $o).
10.99/1.99	thf(decl_67, type, setoftrueEq: $o).
10.99/1.99	thf(decl_68, type, powersetI: $o).
10.99/1.99	thf(decl_69, type, emptyinPowerset: $o).
10.99/1.99	thf(decl_70, type, emptyInPowerset: $o).
10.99/1.99	thf(decl_71, type, powersetE: $o).
10.99/1.99	thf(decl_72, type, setunionI: $o).
10.99/1.99	thf(decl_73, type, setunionE: $o).
10.99/1.99	thf(decl_74, type, subPowSU: $o).
10.99/1.99	thf(decl_75, type, exuE2: $o).
10.99/1.99	thf(decl_76, type, nonemptyImpWitness: $o).
10.99/1.99	thf(decl_77, type, uniqinunit: $o).
10.99/1.99	thf(decl_78, type, notinsingleton: $o).
10.99/1.99	thf(decl_79, type, eqinunit: $o).
10.99/1.99	thf(decl_80, type, singletonsswitch: $o).
10.99/1.99	thf(decl_81, type, upairsetE: $o).
10.99/1.99	thf(decl_82, type, upairsetIL: $o).
10.99/1.99	thf(decl_83, type, upairsetIR: $o).
10.99/1.99	thf(decl_84, type, emptyE1: $o).
10.99/1.99	thf(decl_85, type, vacuousDall: $o).
10.99/1.99	thf(decl_86, type, quantDeMorgan1: $o).
10.99/1.99	thf(decl_87, type, quantDeMorgan2: $o).
10.99/1.99	thf(decl_88, type, quantDeMorgan3: $o).
10.99/1.99	thf(decl_89, type, quantDeMorgan4: $o).
10.99/1.99	thf(decl_90, type, prop2setI: $o).
10.99/1.99	thf(decl_91, type, set2prop: $i > $o).
10.99/1.99	thf(decl_92, type, prop2set2propI: $o).
10.99/1.99	thf(decl_93, type, notdexE: $o).
10.99/1.99	thf(decl_94, type, notdallE: $o).
10.99/1.99	thf(decl_95, type, exuI1: $o).
10.99/1.99	thf(decl_96, type, exuI3: $o).
10.99/1.99	thf(decl_97, type, exuI2: $o).
10.99/1.99	thf(decl_98, type, inCongP: $o).
10.99/1.99	thf(decl_99, type, in__Cong: $o).
10.99/1.99	thf(decl_100, type, exuE3u: $o).
10.99/1.99	thf(decl_101, type, exu__Cong: $o).
10.99/1.99	thf(decl_102, type, emptyset__Cong: $o).
10.99/1.99	thf(decl_103, type, setadjoin__Cong: $o).
10.99/1.99	thf(decl_104, type, powerset__Cong: $o).
10.99/1.99	thf(decl_105, type, setunion__Cong: $o).
10.99/1.99	thf(decl_106, type, omega__Cong: $o).
10.99/1.99	thf(decl_107, type, exuEu: $o).
10.99/1.99	thf(decl_108, type, descr__Cong: $o).
10.99/1.99	thf(decl_109, type, dsetconstr__Cong: $o).
10.99/1.99	thf(decl_110, type, subset: $i > $i > $o).
10.99/1.99	thf(decl_113, type, subsetI1: $o).
10.99/1.99	thf(decl_114, type, eqimpsubset2: $o).
10.99/1.99	thf(decl_115, type, eqimpsubset1: $o).
10.99/1.99	thf(decl_116, type, subsetI2: $o).
10.99/1.99	thf(decl_117, type, emptysetsubset: $o).
10.99/1.99	thf(decl_118, type, subsetE: $o).
10.99/1.99	thf(decl_119, type, subsetE2: $o).
10.99/1.99	thf(decl_120, type, notsubsetI: $o).
10.99/1.99	thf(decl_121, type, notequalI1: $o).
10.99/1.99	thf(decl_122, type, notequalI2: $o).
10.99/1.99	thf(decl_123, type, subsetRefl: $o).
10.99/1.99	thf(decl_124, type, subsetTrans: $o).
10.99/1.99	thf(decl_125, type, setadjoinSub: $o).
10.99/1.99	thf(decl_126, type, setadjoinSub2: $o).
10.99/1.99	thf(decl_127, type, subset2powerset: $o).
10.99/1.99	thf(decl_128, type, setextsub: $o).
10.99/1.99	thf(decl_129, type, subsetemptysetimpeq: $o).
10.99/1.99	thf(decl_130, type, powersetI1: $o).
10.99/1.99	thf(decl_131, type, powersetE1: $o).
10.99/1.99	thf(decl_132, type, inPowerset: $o).
10.99/1.99	thf(decl_133, type, powersetsubset: $o).
10.99/1.99	thf(decl_134, type, sepInPowerset: $o).
10.99/1.99	thf(decl_135, type, sepSubset: $o).
10.99/1.99	thf(decl_136, type, binunion: $i > $i > $i).
10.99/1.99	thf(decl_137, type, binunionIL: $o).
10.99/1.99	thf(decl_138, type, upairset2IR: $o).
10.99/1.99	thf(decl_139, type, binunionIR: $o).
10.99/1.99	thf(decl_140, type, binunionEcases: $o).
10.99/1.99	thf(decl_141, type, binunionE: $o).
10.99/1.99	thf(decl_142, type, binunionLsub: $o).
10.99/1.99	thf(decl_143, type, binunionRsub: $o).
10.99/1.99	thf(decl_144, type, binintersect: $i > $i > $i).
10.99/1.99	thf(decl_145, type, binintersectI: $o).
10.99/1.99	thf(decl_146, type, binintersectSubset5: $o).
10.99/1.99	thf(decl_147, type, binintersectEL: $o).
10.99/1.99	thf(decl_148, type, binintersectLsub: $o).
10.99/1.99	thf(decl_149, type, binintersectSubset2: $o).
10.99/1.99	thf(decl_150, type, binintersectSubset3: $o).
10.99/1.99	thf(decl_151, type, binintersectER: $o).
10.99/1.99	thf(decl_152, type, disjointsetsI1: $o).
10.99/1.99	thf(decl_153, type, binintersectRsub: $o).
10.99/1.99	thf(decl_154, type, binintersectSubset4: $o).
10.99/1.99	thf(decl_155, type, binintersectSubset1: $o).
10.99/1.99	thf(decl_156, type, bs114d: $o).
10.99/1.99	thf(decl_158, type, setminus: $i > $i > $i).
10.99/1.99	thf(decl_159, type, setminusI: $o).
10.99/1.99	thf(decl_160, type, setminusEL: $o).
10.99/1.99	thf(decl_161, type, setminusER: $o).
10.99/1.99	thf(decl_162, type, setminusSubset2: $o).
10.99/1.99	thf(decl_163, type, setminusERneg: $o).
10.99/1.99	thf(decl_164, type, setminusELneg: $o).
10.99/1.99	thf(decl_165, type, setminusILneg: $o).
10.99/1.99	thf(decl_166, type, setminusIRneg: $o).
10.99/1.99	thf(decl_167, type, setminusLsub: $o).
10.99/1.99	thf(decl_168, type, setminusSubset1: $o).
10.99/1.99	thf(decl_169, type, symdiff: $i > $i > $i).
10.99/1.99	thf(decl_170, type, symdiffE: $o).
10.99/1.99	thf(decl_171, type, symdiffI1: $o).
10.99/1.99	thf(decl_172, type, symdiffI2: $o).
10.99/1.99	thf(decl_173, type, symdiffIneg1: $o).
10.99/1.99	thf(decl_174, type, symdiffIneg2: $o).
10.99/1.99	thf(decl_175, type, iskpair: $i > $o).
10.99/1.99	thf(decl_176, type, secondinupair: $o).
10.99/1.99	thf(decl_177, type, setukpairIL: $o).
10.99/1.99	thf(decl_178, type, setukpairIR: $o).
10.99/1.99	thf(decl_179, type, kpairiskpair: $o).
10.99/1.99	thf(decl_180, type, kpair: $i > $i > $i).
10.99/1.99	thf(decl_181, type, kpairp: $o).
10.99/1.99	thf(decl_182, type, cartprod: $i > $i > $i).
10.99/1.99	thf(decl_183, type, singletonsubset: $o).
10.99/1.99	thf(decl_184, type, singletoninpowerset: $o).
10.99/1.99	thf(decl_185, type, singletoninpowunion: $o).
10.99/1.99	thf(decl_186, type, upairset2E: $o).
10.99/1.99	thf(decl_187, type, upairsubunion: $o).
10.99/1.99	thf(decl_188, type, upairinpowunion: $o).
10.99/1.99	thf(decl_189, type, ubforcartprodlem1: $o).
10.99/1.99	thf(decl_190, type, ubforcartprodlem2: $o).
10.99/1.99	thf(decl_191, type, ubforcartprodlem3: $o).
10.99/1.99	thf(decl_192, type, cartprodpairin: $o).
10.99/1.99	thf(decl_193, type, cartprodmempair1: $o).
10.99/1.99	thf(decl_194, type, cartprodmempair: $o).
10.99/1.99	thf(decl_195, type, setunionE2: $o).
10.99/1.99	thf(decl_196, type, setunionsingleton1: $o).
10.99/1.99	thf(decl_197, type, setunionsingleton2: $o).
10.99/1.99	thf(decl_198, type, setunionsingleton: $o).
10.99/1.99	thf(decl_199, type, singleton: $i > $o).
10.99/1.99	thf(decl_200, type, singletonprop: $o).
10.99/1.99	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
10.99/1.99	thf(decl_202, type, ex1E1: $o).
10.99/1.99	thf(decl_203, type, ex1I: $o).
10.99/1.99	thf(decl_204, type, ex1I2: $o).
10.99/1.99	thf(decl_205, type, singletonsuniq: $o).
10.99/1.99	thf(decl_210, type, setukpairinjL1: $o).
10.99/1.99	thf(decl_211, type, kfstsingleton: $o).
10.99/1.99	thf(decl_212, type, theprop: $o).
10.99/1.99	thf(decl_213, type, kfst: $i > $i).
10.99/1.99	thf(decl_214, type, kfstpairEq: $o).
10.99/1.99	thf(decl_215, type, cartprodfstin: $o).
10.99/1.99	thf(decl_216, type, setukpairinjL2: $o).
10.99/1.99	thf(decl_217, type, setukpairinjL: $o).
10.99/1.99	thf(decl_218, type, setukpairinjR11: $o).
10.99/1.99	thf(decl_219, type, setukpairinjR12: $o).
10.99/1.99	thf(decl_220, type, setukpairinjR1: $o).
10.99/1.99	thf(decl_221, type, upairequniteq: $o).
10.99/1.99	thf(decl_222, type, setukpairinjR2: $o).
10.99/1.99	thf(decl_223, type, setukpairinjR: $o).
10.99/1.99	thf(decl_224, type, ksndsingleton: $o).
10.99/1.99	thf(decl_225, type, ksnd: $i > $i).
10.99/1.99	thf(decl_226, type, ksndpairEq: $o).
10.99/1.99	thf(decl_227, type, kpairsurjEq: $o).
10.99/1.99	thf(decl_228, type, cartprodsndin: $o).
10.99/1.99	thf(decl_229, type, cartprodpairmemEL: $o).
10.99/1.99	thf(decl_230, type, cartprodpairmemER: $o).
10.99/1.99	thf(decl_231, type, cartprodmempaircEq: $o).
10.99/1.99	thf(decl_232, type, cartprodfstpairEq: $o).
10.99/1.99	thf(decl_233, type, cartprodsndpairEq: $o).
10.99/1.99	thf(decl_234, type, cartprodpairsurjEq: $o).
10.99/1.99	thf(decl_235, type, breln: $i > $i > $i > $o).
10.99/1.99	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
10.99/1.99	thf(decl_237, type, dpsetconstrI: $o).
10.99/1.99	thf(decl_238, type, dpsetconstrSub: $o).
10.99/1.99	thf(decl_239, type, setOfPairsIsBReln: $o).
10.99/1.99	thf(decl_240, type, dpsetconstrERa: $o).
10.99/1.99	thf(decl_241, type, dpsetconstrEL1: $o).
10.99/1.99	thf(decl_242, type, dpsetconstrEL2: $o).
10.99/1.99	thf(decl_243, type, dpsetconstrER: $o).
10.99/1.99	thf(decl_244, type, func: $i > $i > $i > $o).
10.99/1.99	thf(decl_245, type, funcSet: $i > $i > $i).
10.99/1.99	thf(decl_246, type, funcImageSingleton: $o).
10.99/1.99	thf(decl_247, type, apProp: $o).
10.99/1.99	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
10.99/1.99	thf(decl_249, type, app: $o).
10.99/1.99	thf(decl_250, type, infuncsetfunc: $o).
10.99/1.99	thf(decl_251, type, ap2p: $o).
10.99/1.99	thf(decl_252, type, funcinfuncset: $o).
10.99/1.99	thf(decl_253, type, lamProp: $o).
10.99/1.99	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
10.99/1.99	thf(decl_255, type, lamp: $o).
10.99/1.99	thf(decl_256, type, lam2p: $o).
10.99/1.99	thf(decl_257, type, brelnall1: $o).
10.99/1.99	thf(decl_258, type, brelnall2: $o).
10.99/1.99	thf(decl_259, type, ex1E2: $o).
10.99/1.99	thf(decl_260, type, funcGraphProp1: $o).
10.99/1.99	thf(decl_261, type, funcGraphProp3: $o).
10.99/1.99	thf(decl_262, type, funcGraphProp2: $o).
10.99/1.99	thf(decl_263, type, funcextLem: $o).
10.99/1.99	thf(decl_264, type, funcGraphProp4: $o).
10.99/1.99	thf(decl_265, type, subbreln: $o).
10.99/1.99	thf(decl_266, type, eqbreln: $o).
10.99/1.99	thf(decl_267, type, funcext: $o).
10.99/1.99	thf(decl_268, type, funcext2: $o).
10.99/1.99	thf(decl_269, type, ap2apEq1: $o).
10.99/1.99	thf(decl_270, type, ap2apEq2: $o).
10.99/1.99	thf(decl_271, type, beta1: $o).
10.99/1.99	thf(decl_272, type, eta1: $o).
10.99/1.99	thf(decl_273, type, lam2lamEq: $o).
10.99/1.99	thf(decl_274, type, beta2: $o).
10.99/1.99	thf(decl_275, type, eta2: $o).
10.99/1.99	thf(decl_276, type, iffalseProp1: $o).
10.99/1.99	thf(decl_277, type, iffalseProp2: $o).
10.99/1.99	thf(decl_278, type, iftrueProp1: $o).
10.99/1.99	thf(decl_279, type, iftrueProp2: $o).
10.99/1.99	thf(decl_280, type, ifSingleton: $o).
10.99/1.99	thf(decl_281, type, if: $i > $o > $i > $i > $i).
10.99/1.99	thf(decl_282, type, ifp: $o).
10.99/1.99	thf(decl_283, type, theeq: $o).
10.99/1.99	thf(decl_284, type, iftrue: $o).
10.99/1.99	thf(decl_285, type, iffalse: $o).
10.99/1.99	thf(decl_286, type, iftrueorfalse: $o).
10.99/1.99	thf(decl_287, type, binintersectT_lem: $o).
10.99/1.99	thf(decl_288, type, binunionT_lem: $o).
10.99/1.99	thf(decl_289, type, powersetT_lem: $o).
10.99/1.99	thf(decl_290, type, setminusT_lem: $o).
10.99/1.99	thf(decl_291, type, complementT_lem: $o).
10.99/1.99	thf(decl_292, type, setextT: $o).
10.99/1.99	thf(decl_293, type, epred1_0: $o).
10.99/1.99	thf(decl_294, type, esk1_2: $i > $i > $i).
10.99/1.99	thf(decl_295, type, esk2_2: $i > $i > $i).
10.99/1.99	thf(decl_296, type, esk3_2: $i > $i > $i).
10.99/1.99	thf(decl_297, type, esk4_1: $i > $i).
10.99/1.99	thf(decl_298, type, esk5_2: ($i > $i > $o) > $i > $i).
10.99/1.99	thf(decl_299, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
10.99/1.99	thf(decl_300, type, esk7_2: ($i > $i > $o) > $i > $i).
10.99/1.99	thf(decl_301, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
10.99/1.99	thf(decl_302, type, esk9_1: $i > $i).
10.99/1.99	thf(decl_303, type, esk10_2: ($i > $o) > $i > $i).
10.99/1.99	thf(decl_304, type, esk11_2: ($i > $o) > $i > $i).
10.99/1.99	thf(decl_305, type, esk12_1: ($i > $o) > $i).
10.99/1.99	thf(decl_306, type, esk13_2: ($i > $o) > $i > $i).
10.99/1.99	thf(decl_307, type, esk14_1: ($i > $o) > $i).
10.99/1.99	thf(decl_308, type, esk15_2: $i > $i > $i).
10.99/1.99	thf(decl_309, type, esk16_2: $i > $i > $i).
10.99/1.99	thf(decl_310, type, esk17_1: $i > $i).
10.99/1.99	thf(decl_311, type, esk18_1: $i > $i).
10.99/1.99	thf(decl_312, type, esk19_1: $i > $i).
10.99/1.99	thf(decl_313, type, esk20_2: $i > $i > $i).
10.99/1.99	thf(decl_314, type, esk21_3: $i > $i > $o > $i).
10.99/1.99	thf(decl_315, type, esk22_2: ($i > $o) > $i > $i).
10.99/1.99	thf(decl_316, type, esk23_1: ($i > $o) > $i).
10.99/1.99	thf(decl_317, type, esk24_1: $i > $i).
10.99/1.99	thf(decl_318, type, esk25_2: $i > ($i > $o) > $i).
10.99/1.99	thf(decl_319, type, esk26_2: $i > ($i > $o) > $i).
10.99/1.99	thf(decl_320, type, esk27_2: $i > ($i > $o) > $i).
10.99/1.99	thf(decl_321, type, esk28_2: $i > ($i > $o) > $i).
10.99/1.99	thf(decl_322, type, esk29_2: $i > ($i > $o) > $i).
10.99/1.99	thf(decl_323, type, esk30_2: $i > ($i > $o) > $i).
10.99/1.99	thf(decl_324, type, esk31_2: ($i > $o) > $i > $i).
10.99/1.99	thf(decl_325, type, esk32_1: ($i > $o) > $i).
10.99/1.99	thf(decl_326, type, esk33_1: ($i > $o) > $i).
10.99/1.99	thf(decl_327, type, esk34_1: ($i > $o) > $i).
10.99/1.99	thf(decl_328, type, esk35_1: ($i > $o) > $i).
10.99/1.99	thf(decl_329, type, esk36_2: ($i > $o) > $i > $i).
10.99/1.99	thf(decl_330, type, esk37_1: ($i > $o) > $i).
10.99/1.99	thf(decl_331, type, esk38_2: ($i > $o) > $i > $i).
10.99/1.99	thf(decl_332, type, esk39_2: ($i > $o) > ($i > $o) > $i).
10.99/1.99	thf(decl_333, type, esk40_2: ($i > $o) > ($i > $o) > $i).
10.99/1.99	thf(decl_334, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
10.99/1.99	thf(decl_335, type, esk42_2: ($i > $o) > ($i > $o) > $i).
10.99/1.99	thf(decl_336, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
10.99/1.99	thf(decl_337, type, esk44_2: ($i > $o) > ($i > $o) > $i).
10.99/1.99	thf(decl_338, type, esk45_2: ($i > $o) > $i > $i).
10.99/1.99	thf(decl_339, type, esk46_2: ($i > $o) > ($i > $o) > $i).
10.99/1.99	thf(decl_340, type, esk47_2: ($i > $o) > ($i > $o) > $i).
10.99/1.99	thf(decl_341, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
10.99/1.99	thf(decl_342, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
10.99/1.99	thf(decl_343, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
10.99/1.99	thf(decl_344, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
10.99/1.99	thf(decl_345, type, esk52_2: $i > $i > $i).
10.99/1.99	thf(decl_346, type, esk53_2: $i > $i > $i).
10.99/1.99	thf(decl_347, type, esk54_2: $i > $i > $i).
10.99/1.99	thf(decl_348, type, esk55_3: $i > $i > $i > $i).
10.99/1.99	thf(decl_349, type, esk56_3: $i > $i > $i > $i).
10.99/1.99	thf(decl_350, type, esk57_2: $i > $i > $i).
10.99/1.99	thf(decl_351, type, esk58_2: $i > ($i > $o) > $i).
10.99/1.99	thf(decl_352, type, esk59_2: $i > ($i > $o) > $i).
10.99/1.99	thf(decl_353, type, esk60_2: $i > ($i > $o) > $i).
10.99/1.99	thf(decl_354, type, esk61_3: $i > ($i > $o) > $i > $i).
10.99/1.99	thf(decl_355, type, esk62_2: $i > ($i > $o) > $i).
10.99/1.99	thf(decl_356, type, esk63_2: $i > ($i > $o) > $i).
10.99/1.99	thf(decl_357, type, esk64_3: $i > $i > ($i > $i) > $i).
10.99/1.99	thf(decl_358, type, esk65_3: $i > $i > ($i > $i) > $i).
10.99/1.99	thf(decl_359, type, esk66_3: $i > $i > ($i > $i) > $i).
10.99/1.99	thf(decl_360, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
10.99/1.99	thf(decl_361, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
10.99/1.99	thf(decl_362, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
10.99/1.99	thf(decl_363, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
10.99/1.99	thf(decl_364, type, esk71_4: $i > $i > $i > $i > $i).
10.99/1.99	thf(decl_365, type, esk72_4: $i > $i > $i > $i > $i).
10.99/1.99	thf(decl_366, type, esk73_4: $i > $i > $i > $i > $i).
10.99/1.99	thf(decl_367, type, esk74_4: $i > $i > $i > $i > $i).
10.99/1.99	thf(decl_368, type, esk75_4: $i > $i > $i > $i > $i).
10.99/1.99	thf(decl_369, type, esk76_4: $i > $i > $i > $i > $i).
10.99/1.99	thf(decl_370, type, esk77_4: $i > $i > $i > $i > $i).
10.99/1.99	thf(decl_371, type, esk78_4: $i > $i > $i > $i > $i).
10.99/1.99	thf(decl_372, type, esk79_4: $i > $i > $i > $i > $i).
10.99/1.99	thf(decl_373, type, esk80_3: $i > $i > ($i > $i) > $i).
10.99/1.99	thf(decl_374, type, esk81_3: $i > $i > ($i > $i) > $i).
10.99/1.99	thf(decl_375, type, esk82_3: $i > $i > ($i > $i) > $i).
10.99/1.99	thf(decl_376, type, esk83_3: $i > $i > $i > $i).
10.99/1.99	thf(decl_377, type, esk84_3: $i > $i > $i > $i).
10.99/1.99	thf(decl_378, type, esk85_0: $i).
10.99/1.99	thf(decl_379, type, esk86_0: $i).
10.99/1.99	thf(decl_380, type, esk87_0: $i).
10.99/1.99	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', replAx)).
10.99/1.99	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', exu)).
10.99/1.99	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', descrp)).
10.99/1.99	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', exuE1)).
10.99/1.99	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', exuE3e)).
10.99/1.99	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', nonempty)).
10.99/1.99	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', nonemptyI)).
10.99/1.99	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', exuE2)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', exuI1)).
10.99/1.99	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', exuI3)).
10.99/1.99	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', exuI2)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', exuE3u)).
10.99/1.99	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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', exu__Cong)).
10.99/1.99	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', exuEu)).
10.99/1.99	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', descr__Cong)).
10.99/1.99	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', ex1E1)).
10.99/1.99	thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', ex1)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', ex1I)).
10.99/1.99	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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', ex1I2)).
10.99/1.99	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setOfPairsIsBReln)).
10.99/1.99	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', breln)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', ex1E2)).
10.99/1.99	thf(subsetTI, conjecture, ((setextAx)=>((((powersetAx)=>((setunionAx)=>((omega0Ax)=>(((((foundationAx)=>((((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>(((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>(((emptyI)=>((noeltsimpempty)=>((((nonemptyI)=>((nonemptyI1)=>(((((setadjoinE)=>((((powersetI)=>((((((setunionE)=>((subPowSU)=>((((uniqinunit)=>(((eqinunit)=>((singletonsswitch)=>((((((vacuousDall)=>((quantDeMorgan1)=>(((quantDeMorgan3)=>((((((((exuI3)=>((exuI2)=>((inCongP)=>(((((((powerset__Cong)=>((((exuEu)=>(((dsetconstr__Cong)=>(((eqimpsubset2)=>(((subsetI2)=>((((subsetE2)=>((notsubsetI)=>(((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>(((((powersetI1)=>((powersetE1)=>(((powersetsubset)=>((sepInPowerset)=>(((binunionIL)=>(((binunionIR)=>((binunionEcases)=>(((binunionLsub)=>((binunionRsub)=>(((((binintersectLsub)=>((binintersectSubset2)=>(((binintersectER)=>((disjointsetsI1)=>(((((bs114d)=>(((((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>(((((((((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>(((ubforcartprodlem1)=>(((ubforcartprodlem3)=>((cartprodpairin)=>(((cartprodmempair)=>((((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((((((setukpairinjL1)=>((kfstsingleton)=>(((((setukpairinjL2)=>((setukpairinjL)=>(((setukpairinjR12)=>(((((((((cartprodsndin)=>(((((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>(((((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>(((funcImageSingleton)=>(((((((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((((((((funcext2)=>(((((eta1)=>(((((iffalseProp1)=>(((((ifSingleton)=>((ifp)=>(((iftrue)=>((((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)<=(in @ X2 @ X21))))=>(subset @ X21 @ X48))<=(in @ X48 @ (powerset @ X4))))))<=(setextT))<=(complementT_lem))))))<=(iftrueorfalse))<=(iffalse)))<=(theeq))))<=(iftrueProp2))<=(iftrueProp1))<=(iffalseProp2)))<=(eta2))<=(beta2))<=(lam2lamEq)))<=(beta1))<=(ap2apEq2))<=(ap2apEq1)))<=(funcext))<=(eqbreln))<=(subbreln))<=(funcGraphProp4))<=(funcextLem))<=(funcGraphProp2))))))))))<=(funcinfuncset))<=(ap2p))<=(infuncsetfunc))<=(app))<=(apProp)))<=(dpsetconstrER)))))<=(setOfPairsIsBReln))<=(dpsetconstrSub))<=(dpsetconstrI)))))<=(cartprodmempaircEq))<=(cartprodpairmemER))<=(cartprodpairmemEL)))<=(kpairsurjEq))<=(ksndpairEq))<=(ksndsingleton))<=(setukpairinjR))<=(setukpairinjR2))<=(upairequniteq))<=(setukpairinjR1)))<=(setukpairinjR11))))<=(cartprodfstin))<=(kfstpairEq))<=(theprop))))<=(singletonsuniq))<=(ex1I2))<=(ex1I))<=(ex1E1)))))<=(setunionsingleton1))<=(setunionE2)))<=(cartprodmempair1))))<=(ubforcartprodlem2)))<=(upairinpowunion)))))<=(singletoninpowerset))<=(singletonsubset))<=(kpairp))<=(kpairiskpair))<=(setukpairIR))<=(setukpairIL))<=(secondinupair))))))<=(symdiffE))<=(setminusSubset1))))))))<=(setminusER))<=(setminusEL))<=(setminusI)))<=(binintersectSubset1))<=(binintersectSubset4))<=(binintersectRsub))))<=(binintersectSubset3))))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI))))<=(binunionE))))<=(upairset2IR)))<=(sepSubset))))<=(inPowerset))))<=(subsetemptysetimpeq))<=(setextsub))<=(subset2powerset)))))))<=(notequalI1))))<=(subsetE))<=(emptysetsubset)))<=(eqimpsubset1)))<=(subsetI1)))<=(descr__Cong)))<=(omega__Cong))<=(setunion__Cong)))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong))<=(exuE3u))<=(in__Cong)))))<=(exuI1))<=(notdallE))<=(notdexE))<=(prop2set2propI))<=(prop2setI))<=(quantDeMorgan4)))<=(quantDeMorgan2))))<=(emptyE1))<=(upairsetIR))<=(upairsetIL))<=(upairsetE))))<=(notinsingleton)))<=(nonemptyImpWitness))<=(exuE2))))<=(setunionI))<=(powersetE))<=(emptyInPowerset))<=(emptyinPowerset)))<=(setoftrueEq))<=(setadjoinOr)))<=(setadjoinIR))<=(emptyinunitempty))<=(setadjoinIL))))<=(nonemptyE1))<=(setbeta))))<=(setext))))))<=(prop2setE))))))<=(descrp))<=(wellorderingAx)))<=(replAx))<=(omegaIndAx))<=(omegaSAx)))))<=(setadjoinAx))<=(emptysetAx))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', subsetTI)).
10.99/1.99	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', dsetconstrI)).
10.99/1.99	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', dsetconstrEL)).
10.99/1.99	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', dsetconstrER)).
10.99/1.99	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setbeta)).
10.99/1.99	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', nonemptyE1)).
10.99/1.99	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', nonemptyI1)).
10.99/1.99	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setoftrueEq)).
10.99/1.99	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', nonemptyImpWitness)).
10.99/1.99	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.caduz1V4uW/E---3.1_2881760.p', emptyE1)).
10.99/1.99	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', dsetconstr__Cong)).
10.99/1.99	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', sepInPowerset)).
10.99/1.99	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', sepSubset)).
10.99/1.99	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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', singletonprop)).
10.99/1.99	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', kfstsingleton)).
10.99/1.99	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', ksndsingleton)).
10.99/1.99	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', dpsetconstrI)).
10.99/1.99	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', dpsetconstrSub)).
10.99/1.99	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', dpsetconstrERa)).
10.99/1.99	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', dpsetconstrEL1)).
10.99/1.99	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', dpsetconstrEL2)).
10.99/1.99	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', dpsetconstrER)).
10.99/1.99	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.caduz1V4uW/E---3.1_2881760.p', funcImageSingleton)).
10.99/1.99	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', apProp)).
10.99/1.99	thf(lamProp, axiom, ((lamProp)<=>![X4:$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.caduz1V4uW/E---3.1_2881760.p', lamProp)).
10.99/1.99	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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', lamp)).
10.99/1.99	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', lam2p)).
10.99/1.99	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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.caduz1V4uW/E---3.1_2881760.p', brelnall1)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', brelnall2)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', subbreln)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', eqbreln)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', beta1)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', eta1)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', lam2lamEq)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', beta2)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', eta2)).
10.99/1.99	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', iffalseProp1)).
10.99/1.99	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.caduz1V4uW/E---3.1_2881760.p', iffalseProp2)).
10.99/1.99	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', iftrueProp1)).
10.99/1.99	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.caduz1V4uW/E---3.1_2881760.p', iftrueProp2)).
10.99/1.99	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', ifSingleton)).
10.99/1.99	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setextAx)).
10.99/1.99	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', emptysetAx)).
10.99/1.99	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setadjoinAx)).
10.99/1.99	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', powersetAx)).
10.99/1.99	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setunionAx)).
10.99/1.99	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', omega0Ax)).
10.99/1.99	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', omegaSAx)).
10.99/1.99	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.caduz1V4uW/E---3.1_2881760.p', omegaIndAx)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', foundationAx)).
10.99/1.99	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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', wellorderingAx)).
10.99/1.99	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', prop2setE)).
10.99/1.99	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', emptysetE)).
10.99/1.99	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', emptysetimpfalse)).
10.99/1.99	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', notinemptyset)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', setext)).
10.99/1.99	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', emptyI)).
10.99/1.99	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', noeltsimpempty)).
10.99/1.99	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setadjoinIL)).
10.99/1.99	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', emptyinunitempty)).
10.99/1.99	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setadjoinIR)).
10.99/1.99	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setadjoinE)).
10.99/1.99	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setadjoinOr)).
10.99/1.99	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', powersetI)).
10.99/1.99	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', emptyinPowerset)).
10.99/1.99	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', emptyInPowerset)).
10.99/1.99	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', powersetE)).
10.99/1.99	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setunionI)).
10.99/1.99	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setunionE)).
10.99/1.99	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', subPowSU)).
10.99/1.99	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', uniqinunit)).
10.99/1.99	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', notinsingleton)).
10.99/1.99	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', eqinunit)).
10.99/1.99	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', singletonsswitch)).
10.99/1.99	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', upairsetE)).
10.99/1.99	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', upairsetIL)).
10.99/1.99	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', upairsetIR)).
10.99/1.99	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', vacuousDall)).
10.99/1.99	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', quantDeMorgan1)).
10.99/1.99	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', quantDeMorgan2)).
10.99/1.99	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', quantDeMorgan3)).
10.99/1.99	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', quantDeMorgan4)).
10.99/1.99	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', prop2setI)).
10.99/1.99	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', prop2set2propI)).
10.99/1.99	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', notdexE)).
10.99/1.99	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', notdallE)).
10.99/1.99	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', inCongP)).
10.99/1.99	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', in__Cong)).
10.99/1.99	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', emptyset__Cong)).
10.99/1.99	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setadjoin__Cong)).
10.99/1.99	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', powerset__Cong)).
10.99/1.99	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setunion__Cong)).
10.99/1.99	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', omega__Cong)).
10.99/1.99	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', subsetI1)).
10.99/1.99	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', eqimpsubset2)).
10.99/1.99	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', eqimpsubset1)).
10.99/1.99	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', subsetI2)).
10.99/1.99	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', emptysetsubset)).
10.99/1.99	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', subsetE)).
10.99/1.99	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', subsetE2)).
10.99/1.99	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', notsubsetI)).
10.99/1.99	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', notequalI1)).
10.99/1.99	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', notequalI2)).
10.99/1.99	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', subsetRefl)).
10.99/1.99	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', subsetTrans)).
10.99/1.99	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setadjoinSub)).
10.99/1.99	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setadjoinSub2)).
10.99/1.99	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', subset2powerset)).
10.99/1.99	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setextsub)).
10.99/1.99	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', subsetemptysetimpeq)).
10.99/1.99	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', powersetI1)).
10.99/1.99	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', powersetE1)).
10.99/1.99	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', inPowerset)).
10.99/1.99	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', powersetsubset)).
10.99/1.99	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', binunionIL)).
10.99/1.99	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', upairset2IR)).
10.99/1.99	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', binunionIR)).
10.99/1.99	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', binunionEcases)).
10.99/1.99	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', binunionE)).
10.99/1.99	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', binunionLsub)).
10.99/1.99	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', binunionRsub)).
10.99/1.99	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', binintersectI)).
10.99/1.99	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', binintersectSubset5)).
10.99/1.99	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', binintersectEL)).
10.99/1.99	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', binintersectLsub)).
10.99/1.99	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', binintersectSubset2)).
10.99/1.99	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', binintersectSubset3)).
10.99/1.99	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', binintersectER)).
10.99/1.99	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', disjointsetsI1)).
10.99/1.99	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', binintersectRsub)).
10.99/1.99	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', binintersectSubset4)).
10.99/1.99	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', binintersectSubset1)).
10.99/1.99	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', bs114d)).
10.99/1.99	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setminusI)).
10.99/1.99	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setminusEL)).
10.99/1.99	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setminusER)).
10.99/1.99	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setminusSubset2)).
10.99/1.99	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setminusERneg)).
10.99/1.99	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setminusELneg)).
10.99/1.99	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setminusILneg)).
10.99/1.99	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setminusIRneg)).
10.99/1.99	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setminusLsub)).
10.99/1.99	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setminusSubset1)).
10.99/1.99	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', symdiffE)).
10.99/1.99	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', symdiffI1)).
10.99/1.99	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', symdiffI2)).
10.99/1.99	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', symdiffIneg1)).
10.99/1.99	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', symdiffIneg2)).
10.99/1.99	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', secondinupair)).
10.99/1.99	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setukpairIL)).
10.99/1.99	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setukpairIR)).
10.99/1.99	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', kpairiskpair)).
10.99/1.99	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', kpairp)).
10.99/1.99	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', singletonsubset)).
10.99/1.99	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', singletoninpowerset)).
10.99/1.99	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', singletoninpowunion)).
10.99/1.99	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', upairset2E)).
10.99/1.99	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', upairsubunion)).
10.99/1.99	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', upairinpowunion)).
10.99/1.99	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', ubforcartprodlem1)).
10.99/1.99	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', ubforcartprodlem2)).
10.99/1.99	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', ubforcartprodlem3)).
10.99/1.99	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', cartprodpairin)).
10.99/1.99	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.caduz1V4uW/E---3.1_2881760.p', cartprodmempair1)).
10.99/1.99	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', cartprodmempair)).
10.99/1.99	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setunionE2)).
10.99/1.99	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setunionsingleton1)).
10.99/1.99	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setunionsingleton2)).
10.99/1.99	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setunionsingleton)).
10.99/1.99	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', singletonsuniq)).
10.99/1.99	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.caduz1V4uW/E---3.1_2881760.p', setukpairinjL1)).
10.99/1.99	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', theprop)).
10.99/1.99	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', kfstpairEq)).
10.99/1.99	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', cartprodfstin)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', setukpairinjL2)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', setukpairinjL)).
10.99/1.99	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setukpairinjR11)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', setukpairinjR12)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', setukpairinjR1)).
10.99/1.99	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', upairequniteq)).
10.99/1.99	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setukpairinjR2)).
10.99/1.99	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setukpairinjR)).
10.99/1.99	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', ksndpairEq)).
10.99/1.99	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', kpairsurjEq)).
10.99/1.99	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', cartprodsndin)).
10.99/1.99	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', cartprodpairmemEL)).
10.99/1.99	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', cartprodpairmemER)).
10.99/1.99	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', cartprodmempaircEq)).
10.99/1.99	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', cartprodfstpairEq)).
10.99/1.99	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', cartprodsndpairEq)).
10.99/1.99	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', cartprodpairsurjEq)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', app)).
10.99/1.99	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', infuncsetfunc)).
10.99/1.99	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', ap2p)).
10.99/1.99	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', funcinfuncset)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', funcGraphProp1)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', funcGraphProp3)).
10.99/1.99	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', funcGraphProp2)).
10.99/1.99	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.caduz1V4uW/E---3.1_2881760.p', funcextLem)).
10.99/1.99	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', funcGraphProp4)).
10.99/1.99	thf(funcext, axiom, ((funcext)<=>![X4:$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.caduz1V4uW/E---3.1_2881760.p', funcext)).
10.99/1.99	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', funcext2)).
10.99/1.99	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', ap2apEq1)).
10.99/1.99	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', ap2apEq2)).
10.99/1.99	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', ifp)).
10.99/1.99	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', theeq)).
10.99/1.99	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', iftrue)).
10.99/1.99	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', iffalse)).
10.99/1.99	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', iftrueorfalse)).
10.99/1.99	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$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.caduz1V4uW/E---3.1_2881760.p', binintersectT_lem)).
10.99/1.99	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', binunionT_lem)).
10.99/1.99	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', powersetT_lem)).
10.99/1.99	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.caduz1V4uW/E---3.1_2881760.p', setminusT_lem)).
10.99/1.99	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.caduz1V4uW/E---3.1_2881760.p', complementT_lem)).
10.99/1.99	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.caduz1V4uW/E---3.1_2881760.p', setextT)).
10.99/1.99	thf(c_0_237, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
10.99/1.99	thf(c_0_238, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
10.99/1.99	thf(c_0_239, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
10.99/1.99	thf(c_0_240, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
10.99/1.99	thf(c_0_241, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
10.99/1.99	thf(c_0_242, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
10.99/1.99	thf(c_0_243, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
10.99/1.99	thf(c_0_244, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
10.99/1.99	thf(c_0_245, 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])).
10.99/1.99	thf(c_0_246, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
10.99/1.99	thf(c_0_247, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
10.99/1.99	thf(c_0_248, 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])).
10.99/1.99	thf(c_0_249, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
10.99/1.99	thf(c_0_250, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
10.99/1.99	thf(c_0_251, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
10.99/1.99	thf(c_0_252, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
10.99/1.99	thf(c_0_253, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])).
10.99/1.99	thf(c_0_254, 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])).
10.99/1.99	thf(c_0_255, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
10.99/1.99	thf(c_0_256, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
10.99/1.99	thf(c_0_257, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
10.99/1.99	thf(c_0_258, 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])).
10.99/1.99	thf(c_0_259, negated_conjecture, ~(((setextAx)=>((((powersetAx)=>((setunionAx)=>((omega0Ax)=>(((((foundationAx)=>((((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>(((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>(((emptyI)=>((noeltsimpempty)=>((((nonemptyI)=>((nonemptyI1)=>(((((setadjoinE)=>((((powersetI)=>((((((setunionE)=>((subPowSU)=>((((uniqinunit)=>(((eqinunit)=>((singletonsswitch)=>((((((vacuousDall)=>((quantDeMorgan1)=>(((quantDeMorgan3)=>((((((((exuI3)=>((exuI2)=>((inCongP)=>(((((((powerset__Cong)=>((((exuEu)=>(((dsetconstr__Cong)=>(((eqimpsubset2)=>(((subsetI2)=>((((subsetE2)=>((notsubsetI)=>(((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>(((((powersetI1)=>((powersetE1)=>(((powersetsubset)=>((sepInPowerset)=>(((binunionIL)=>(((binunionIR)=>((binunionEcases)=>(((binunionLsub)=>((binunionRsub)=>(((((binintersectLsub)=>((binintersectSubset2)=>(((binintersectER)=>((disjointsetsI1)=>(((((bs114d)=>(((((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>(((((((((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>(((ubforcartprodlem1)=>(((ubforcartprodlem3)=>((cartprodpairin)=>(((cartprodmempair)=>((((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((((((setukpairinjL1)=>((kfstsingleton)=>(((((setukpairinjL2)=>((setukpairinjL)=>(((setukpairinjR12)=>(((((((((cartprodsndin)=>(((((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>(((((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>(((funcImageSingleton)=>(((((((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((((((((funcext2)=>(((((eta1)=>(((((iffalseProp1)=>(((((ifSingleton)=>((ifp)=>(((iftrue)=>((((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)<=(in @ X2 @ X21))))=>(subset @ X21 @ X48))<=(in @ X48 @ (powerset @ X4))))))<=(setextT))<=(complementT_lem))))))<=(iftrueorfalse))<=(iffalse)))<=(theeq))))<=(iftrueProp2))<=(iftrueProp1))<=(iffalseProp2)))<=(eta2))<=(beta2))<=(lam2lamEq)))<=(beta1))<=(ap2apEq2))<=(ap2apEq1)))<=(funcext))<=(eqbreln))<=(subbreln))<=(funcGraphProp4))<=(funcextLem))<=(funcGraphProp2))))))))))<=(funcinfuncset))<=(ap2p))<=(infuncsetfunc))<=(app))<=(apProp)))<=(dpsetconstrER)))))<=(setOfPairsIsBReln))<=(dpsetconstrSub))<=(dpsetconstrI)))))<=(cartprodmempaircEq))<=(cartprodpairmemER))<=(cartprodpairmemEL)))<=(kpairsurjEq))<=(ksndpairEq))<=(ksndsingleton))<=(setukpairinjR))<=(setukpairinjR2))<=(upairequniteq))<=(setukpairinjR1)))<=(setukpairinjR11))))<=(cartprodfstin))<=(kfstpairEq))<=(theprop))))<=(singletonsuniq))<=(ex1I2))<=(ex1I))<=(ex1E1)))))<=(setunionsingleton1))<=(setunionE2)))<=(cartprodmempair1))))<=(ubforcartprodlem2)))<=(upairinpowunion)))))<=(singletoninpowerset))<=(singletonsubset))<=(kpairp))<=(kpairiskpair))<=(setukpairIR))<=(setukpairIL))<=(secondinupair))))))<=(symdiffE))<=(setminusSubset1))))))))<=(setminusER))<=(setminusEL))<=(setminusI)))<=(binintersectSubset1))<=(binintersectSubset4))<=(binintersectRsub))))<=(binintersectSubset3))))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI))))<=(binunionE))))<=(upairset2IR)))<=(sepSubset))))<=(inPowerset))))<=(subsetemptysetimpeq))<=(setextsub))<=(subset2powerset)))))))<=(notequalI1))))<=(subsetE))<=(emptysetsubset)))<=(eqimpsubset1)))<=(subsetI1)))<=(descr__Cong)))<=(omega__Cong))<=(setunion__Cong)))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong))<=(exuE3u))<=(in__Cong)))))<=(exuI1))<=(notdallE))<=(notdexE))<=(prop2set2propI))<=(prop2setI))<=(quantDeMorgan4)))<=(quantDeMorgan2))))<=(emptyE1))<=(upairsetIR))<=(upairsetIL))<=(upairsetE))))<=(notinsingleton)))<=(nonemptyImpWitness))<=(exuE2))))<=(setunionI))<=(powersetE))<=(emptyInPowerset))<=(emptyinPowerset)))<=(setoftrueEq))<=(setadjoinOr)))<=(setadjoinIR))<=(emptyinunitempty))<=(setadjoinIL))))<=(nonemptyE1))<=(setbeta))))<=(setext))))))<=(prop2setE))))))<=(descrp))<=(wellorderingAx)))<=(replAx))<=(omegaIndAx))<=(omegaSAx)))))<=(setadjoinAx))<=(emptysetAx)))), inference(assume_negation,[status(cth)],[subsetTI])).
10.99/1.99	thf(c_0_260, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X767:$i]:(((((X6 @ X2 @ X767)))&(![X768:$i]:(((((X6 @ X2 @ X768)))=>(((X767)=(X768)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_237, c_0_238])).
10.99/1.99	thf(c_0_261, plain, ((descrp)=(![X1:$i > $o]:((((?[X769:$i]:(((((X1 @ X769)))&(![X770:$i]:(((((X1 @ X770)))=>(((X769)=(X770))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_239, c_0_238])).
10.99/1.99	thf(c_0_262, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
10.99/1.99	thf(c_0_263, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
10.99/1.99	thf(c_0_264, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
10.99/1.99	thf(c_0_265, plain, ((exuE1)=(![X1:$i > $o]:((((?[X771:$i]:(((((X1 @ X771)))&(![X772:$i]:(((((X1 @ X772)))=>(((X771)=(X772))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_240, c_0_238])).
10.99/1.99	thf(c_0_266, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X773:$i]:(((((X1 @ X773)))&(![X774:$i]:(((((X1 @ X774)))=>(((X773)=(X774))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_241, c_0_238])).
10.99/1.99	thf(c_0_267, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
10.99/1.99	thf(c_0_268, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_242])).
10.99/1.99	thf(c_0_269, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_243, c_0_242])).
10.99/1.99	thf(c_0_270, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_242])).
10.99/1.99	thf(c_0_271, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
10.99/1.99	thf(c_0_272, plain, ((exuE2)=(![X1:$i > $o]:((((?[X775:$i]:(((((X1 @ X775)))&(![X776:$i]:(((((X1 @ X776)))=>(((X775)=(X776))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_244, c_0_238])).
10.99/1.99	thf(c_0_273, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_242])).
10.99/1.99	thf(c_0_274, 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])).
10.99/1.99	thf(c_0_275, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X777:$i]:(((((X1 @ X777)))&(![X778:$i]:(((((X1 @ X778)))=>(((X777)=(X778)))))))))))))), inference(apply_def,[status(thm)],[c_0_245, c_0_238])).
10.99/1.99	thf(c_0_276, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X779:$i]:(((((X1 @ X779)))&(![X780:$i]:(((((X1 @ X780)))=>(((X779)=(X780)))))))))))))))), inference(apply_def,[status(thm)],[c_0_246, c_0_238])).
10.99/1.99	thf(c_0_277, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X781:$i]:(((((X1 @ X781)))&(![X782:$i]:(((((X1 @ X782)))=>(((X781)=(X782)))))))))))))), inference(apply_def,[status(thm)],[c_0_247, c_0_238])).
10.99/1.99	thf(c_0_278, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X783:$i]:(((((X1 @ X783)))&(![X784:$i]:(((((X1 @ X784)))=>(((X783)=(X784))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_248, c_0_238])).
10.99/1.99	thf(c_0_279, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X785:$i]:(((((X1 @ X785)))&(![X786:$i]:(((((X1 @ X786)))=>(((X785)=(X786))))))))))<=>((?[X787:$i]:(((((X17 @ X787)))&(![X788:$i]:(((((X17 @ X788)))=>(((X787)=(X788)))))))))))))))), inference(apply_def,[status(thm)],[c_0_249, c_0_238])).
10.99/1.99	thf(c_0_280, plain, ((exuEu)=(![X1:$i > $o]:((((?[X789:$i]:(((((X1 @ X789)))&(![X790:$i]:(((((X1 @ X790)))=>(((X789)=(X790))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_250, c_0_238])).
10.99/1.99	thf(c_0_281, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X791:$i]:(((((X1 @ X791)))&(![X792:$i]:(((((X1 @ X792)))=>(((X791)=(X792))))))))))=>((((?[X793:$i]:(((((X17 @ X793)))&(![X794:$i]:(((((X17 @ X794)))=>(((X793)=(X794))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_251, c_0_238])).
10.99/1.99	thf(c_0_282, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
10.99/1.99	thf(c_0_283, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
10.99/1.99	thf(c_0_284, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
10.99/1.99	thf(c_0_285, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
10.99/1.99	thf(c_0_286, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_252, c_0_253])).
10.99/1.99	thf(c_0_287, plain, ((ex1I)=(![X4:$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_254, c_0_253])).
10.99/1.99	thf(c_0_288, 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:$i]:(((X1 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_255, c_0_253])).
10.99/1.99	thf(c_0_289, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
10.99/1.99	thf(c_0_290, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
10.99/1.99	thf(c_0_291, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
10.99/1.99	thf(c_0_292, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
10.99/1.99	thf(c_0_293, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_256, c_0_257])).
10.99/1.99	thf(c_0_294, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
10.99/1.99	thf(c_0_295, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
10.99/1.99	thf(c_0_296, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
10.99/1.99	thf(c_0_297, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
10.99/1.99	thf(c_0_298, plain, ((funcImageSingleton)<=>![X4:$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])).
10.99/1.99	thf(c_0_299, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
10.99/1.99	thf(c_0_300, plain, ((lamProp)<=>![X4:$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])).
10.99/1.99	thf(c_0_301, 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:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
10.99/1.99	thf(c_0_302, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
10.99/1.99	thf(c_0_303, axiom, ((brelnall1)=(![X4:$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_257])).
10.99/1.99	thf(c_0_304, 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_257])).
10.99/1.99	thf(c_0_305, 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_258, c_0_253])).
10.99/1.99	thf(c_0_306, 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_257])).
10.99/1.99	thf(c_0_307, 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_257])).
10.99/1.99	thf(c_0_308, 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])).
10.99/1.99	thf(c_0_309, 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])).
10.99/1.99	thf(c_0_310, 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])).
10.99/1.99	thf(c_0_311, 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])).
10.99/1.99	thf(c_0_312, 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])).
10.99/1.99	thf(c_0_313, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
10.99/1.99	thf(c_0_314, plain, ((iffalseProp2)<=>![X4:$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])).
10.99/1.99	thf(c_0_315, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
10.99/1.99	thf(c_0_316, plain, ((iftrueProp2)<=>![X4:$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])).
10.99/1.99	thf(c_0_317, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
10.99/1.99	thf(c_0_318, plain, ((epred1_0)<=>![X1502:$i]:(?[X1503:$i]:((((![X1504:$i]:(((in @ X1504 @ X1503)=>![X1505:$i]:(((in @ X1505 @ X1504)=>(in @ X1505 @ X1502)))))&![X1506:$i, X1507:$i]:((((in @ X1506 @ X1502)&(in @ X1507 @ X1502))=>(![X1508:$i]:(((in @ X1508 @ X1503)=>((in @ X1506 @ X1508)<=>(in @ X1507 @ X1508))))=>((X1506)=(X1507))))))&![X1509:$i, X1510:$i]:((((in @ X1509 @ X1503)&(in @ X1510 @ X1503))=>(![X1511:$i]:(((in @ X1511 @ X1509)=>(in @ X1511 @ X1510)))|![X1512:$i]:(((in @ X1512 @ X1510)=>(in @ X1512 @ X1509)))))))&![X1513:$i]:(((![X1514:$i]:(((in @ X1514 @ X1513)=>(in @ X1514 @ X1502)))&?[X1515:$i]:((in @ X1515 @ X1513)))=>?[X1516:$i, X1517:$i]:(((((in @ X1516 @ X1503)&(in @ X1517 @ X1513))&~(?[X1518:$i]:(((in @ X1518 @ X1516)&(in @ X1518 @ X1513)))))&![X1519:$i]:(((in @ X1519 @ X1503)=>(![X1520:$i]:(((in @ X1520 @ X1519)=>(in @ X1520 @ X1516)))|(in @ X1517 @ X1519)))))))))))), introduced(definition)).
10.99/1.99	thf(c_0_319, negated_conjecture, ~((![X795:$i, X796:$i]:((![X797:$i]:(((in @ X797 @ X795)<=>(in @ X797 @ X796)))=>((X795)=(X796))))=>(![X1536:$i]:(~(in @ X1536 @ emptyset))=>(![X1533:$i, X1534:$i, X1535:$i]:(((in @ X1535 @ (setadjoin @ X1533 @ X1534))<=>(((X1535)=(X1533))|(in @ X1535 @ X1534))))=>(![X798:$i, X799:$i]:(((in @ X799 @ (powerset @ X798))<=>![X800:$i]:(((in @ X800 @ X799)=>(in @ X800 @ X798)))))=>(![X801:$i, X802:$i]:(((in @ X802 @ (setunion @ X801))<=>?[X803:$i]:(((in @ X802 @ X803)&(in @ X803 @ X801)))))=>((in @ emptyset @ omega)=>(![X1532:$i]:(((in @ X1532 @ omega)=>(in @ (setadjoin @ X1532 @ X1532) @ omega)))=>(![X1529:$i]:((((in @ emptyset @ X1529)&![X1530:$i]:((((in @ X1530 @ omega)&(in @ X1530 @ X1529))=>(in @ (setadjoin @ X1530 @ X1530) @ X1529))))=>![X1531:$i]:(((in @ X1531 @ omega)=>(in @ X1531 @ X1529)))))=>(![X1521:$i > $i > $o, X1522:$i]:((![X1523:$i]:(((in @ X1523 @ X1522)=>?[X1524:$i]:(((X1521 @ X1523 @ X1524)&![X1525:$i]:(((X1521 @ X1523 @ X1525)=>((X1524)=(X1525))))))))=>?[X1526:$i]:(![X1527:$i]:(((in @ X1527 @ X1526)<=>?[X1528:$i]:(((in @ X1528 @ X1522)&(X1521 @ X1528 @ X1527))))))))=>(![X804:$i]:((?[X805:$i]:((in @ X805 @ X804))=>?[X806:$i]:(((in @ X806 @ X804)&~(?[X807:$i]:(((in @ X807 @ X806)&(in @ X807 @ X804))))))))=>((epred1_0)=>(![X1499:$i > $o]:((?[X1500:$i]:(((X1499 @ X1500)&![X1501:$i]:(((X1499 @ X1501)=>((X1500)=(X1501))))))=>(X1499 @ (descr @ (^[Z0:$i]:(X1499 @ Z0))))))=>(![X808:$i, X809:$i > $o, X810:$i]:(((in @ X810 @ X808)=>((X809 @ X810)=>(in @ X810 @ (dsetconstr @ X808 @ X809)))))=>(![X811:$i, X812:$i > $o, X813:$i]:(((in @ X813 @ (dsetconstr @ X811 @ X812))=>(in @ X813 @ X811)))=>(![X814:$i, X815:$i > $o, X816:$i]:(((in @ X816 @ (dsetconstr @ X814 @ X815))=>(X815 @ X816)))=>(![X817:$i > $o]:((?[X818:$i]:(((X817 @ X818)&![X819:$i]:(((X817 @ X819)=>((X818)=(X819))))))=>?[X820:$i]:(((X817 @ X820)&![X821:$i]:(((X817 @ X821)=>((X820)=(X821))))))))=>(![X1497:$o, X1498:$i]:(((in @ X1498 @ (prop2set @ ((X1497))))=>(X1497)))=>(![X822:$i]:(((in @ X822 @ emptyset)=>![X823:$o]:((X823))))=>(![X824:$i]:(((in @ X824 @ emptyset)=>~($true)))=>(![X825:$i]:(~(in @ X825 @ emptyset))=>(![X826:$i > $o]:((?[X827:$i]:(((X826 @ X827)&![X828:$i]:(((X826 @ X828)=>((X827)=(X828))))))=>?[X829:$i]:((X826 @ X829))))=>(![X1493:$i, X1494:$i]:((![X1495:$i]:(((in @ X1495 @ X1493)=>(in @ X1495 @ X1494)))=>(![X1496:$i]:(((in @ X1496 @ X1494)=>(in @ X1496 @ X1493)))=>((X1493)=(X1494)))))=>(![X830:$i]:((![X831:$i]:(~(in @ X831 @ X830))=>((X830)=(emptyset))))=>(![X832:$i]:((![X833:$i]:(~(in @ X833 @ X832))=>((X832)=(emptyset))))=>(![X1490:$i, X1491:$i > $o, X1492:$i]:(((in @ X1492 @ X1490)=>((in @ X1492 @ (dsetconstr @ X1490 @ X1491))<=>(X1491 @ X1492))))=>(![X1488:$i]:((((X1488)!=(emptyset))=>?[X1489:$i]:((in @ X1489 @ X1488))))=>(![X834:$i, X835:$i > $o, X836:$i]:(((in @ X836 @ X834)=>((X835 @ X836)=>((dsetconstr @ X834 @ X835)!=(emptyset)))))=>(![X837:$i]:((?[X838:$i]:((in @ X838 @ X837))=>((X837)!=(emptyset))))=>(![X1486:$i, X1487:$i]:((in @ X1486 @ (setadjoin @ X1486 @ X1487)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1483:$i, X1484:$i, X1485:$i]:(((in @ X1485 @ X1484)=>(in @ X1485 @ (setadjoin @ X1483 @ X1484))))=>(![X839:$i, X840:$i, X841:$i]:(((in @ X841 @ (setadjoin @ X839 @ X840))=>![X842:$o]:(((((X841)=(X839))=>(X842))=>(((in @ X841 @ X840)=>(X842))=>(X842))))))=>(![X1480:$i, X1481:$i, X1482:$i]:(((in @ X1482 @ (setadjoin @ X1480 @ X1481))=>(((X1482)=(X1480))|(in @ X1482 @ X1481))))=>(![X1479:$i]:(((dsetconstr @ X1479 @ (^[Z0:$i]:($true)))=(X1479)))=>(![X843:$i, X844:$i]:((![X845:$i]:(((in @ X845 @ X844)=>(in @ X845 @ X843)))=>(in @ X844 @ (powerset @ X843))))=>(![X1478:$i]:((in @ emptyset @ (powerset @ X1478)))=>(![X1477:$i]:((in @ emptyset @ (powerset @ X1477)))=>(![X1474:$i, X1475:$i, X1476:$i]:(((in @ X1475 @ (powerset @ X1474))=>((in @ X1476 @ X1475)=>(in @ X1476 @ X1474))))=>(![X1471:$i, X1472:$i, X1473:$i]:(((in @ X1472 @ X1473)=>((in @ X1473 @ X1471)=>(in @ X1472 @ (setunion @ X1471)))))=>(![X846:$i, X847:$i]:(((in @ X847 @ (setunion @ X846))=>![X848:$o]:((![X849:$i]:(((in @ X847 @ X849)=>((in @ X849 @ X846)=>(X848))))=>(X848)))))=>(![X850:$i, X851:$i]:(((in @ X851 @ X850)=>(in @ X851 @ (powerset @ (setunion @ X850)))))=>(![X1466:$i > $o]:((?[X1467:$i]:(((X1466 @ X1467)&![X1468:$i]:(((X1466 @ X1468)=>((X1467)=(X1468))))))=>?[X1469:$i]:(![X1470:$i]:(((X1466 @ X1470)<=>((X1470)=(X1469)))))))=>(![X1464:$i]:((((X1464)!=(emptyset))=>?[X1465:$i]:(((in @ X1465 @ X1464)&$true))))=>(![X852:$i, X853:$i]:(((in @ X852 @ (setadjoin @ X853 @ emptyset))=>((X852)=(X853))))=>(![X1462:$i, X1463:$i]:((((X1462)!=(X1463))=>~(in @ X1463 @ (setadjoin @ X1462 @ emptyset))))=>(![X854:$i, X855:$i]:((((X854)=(X855))=>(in @ X854 @ (setadjoin @ X855 @ emptyset))))=>(![X856:$i, X857:$i]:(((in @ X856 @ (setadjoin @ X857 @ emptyset))=>(in @ X857 @ (setadjoin @ X856 @ emptyset))))=>(![X1459:$i, X1460:$i, X1461:$i]:(((in @ X1461 @ (setadjoin @ X1459 @ (setadjoin @ X1460 @ emptyset)))=>(((X1461)=(X1459))|((X1461)=(X1460)))))=>(![X1457:$i, X1458:$i]:((in @ X1457 @ (setadjoin @ X1457 @ (setadjoin @ X1458 @ emptyset))))=>(![X1455:$i, X1456:$i]:((in @ X1456 @ (setadjoin @ X1455 @ (setadjoin @ X1456 @ emptyset))))=>(![X1452:$i, X1453:$i > $o]:((?[X1454:$i]:(((in @ X1454 @ X1452)&(X1453 @ X1454)))=>(((dsetconstr @ X1452 @ X1453)=(emptyset))=>~($true))))=>(![X858:$i > $o, X859:$i]:(((in @ X859 @ emptyset)=>(X858 @ X859)))=>(![X860:$i, X861:$i > $o]:((~(![X862:$i]:(((in @ X862 @ X860)=>(X861 @ X862))))=>?[X863:$i]:(((in @ X863 @ X860)&~((X861 @ X863))))))=>(![X1448:$i, X1449:$i > $o]:((![X1450:$i]:(((in @ X1450 @ X1448)=>~((X1449 @ X1450))))=>~(?[X1451:$i]:(((in @ X1451 @ X1448)&(X1449 @ X1451))))))=>(![X864:$i, X865:$i > $o]:((~(?[X866:$i]:(((in @ X866 @ X864)&(X865 @ X866))))=>![X867:$i]:(((in @ X867 @ X864)=>~((X865 @ X867))))))=>(![X1444:$i, X1445:$i > $o]:((?[X1446:$i]:(((in @ X1446 @ X1444)&~((X1445 @ X1446))))=>~(![X1447:$i]:(((in @ X1447 @ X1444)=>(X1445 @ X1447))))))=>(![X1443:$o]:(((X1443)=>(in @ emptyset @ (prop2set @ ((X1443))))))=>(![X1442:$o]:(((X1442)=>(set2prop @ (prop2set @ ((X1442))))))=>(![X1438:$i, X1439:$i > $o]:((~(?[X1440:$i]:(((in @ X1440 @ X1438)&(X1439 @ X1440))))=>![X1441:$i]:(((in @ X1441 @ X1438)=>~((X1439 @ X1441))))))=>(![X1434:$i, X1435:$i > $o]:((~(![X1436:$i]:(((in @ X1436 @ X1434)=>(X1435 @ X1436))))=>?[X1437:$i]:(((in @ X1437 @ X1434)&~((X1435 @ X1437))))))=>(![X1429:$i > $o]:((?[X1430:$i]:(((X1429 @ X1430)&![X1431:$i]:(((X1429 @ X1431)=>((X1430)=(X1431))))))=>?[X1432:$i]:(((X1429 @ X1432)&![X1433:$i]:(((X1429 @ X1433)=>((X1432)=(X1433))))))))=>(![X868:$i > $o]:((?[X869:$i]:((X868 @ X869))=>(![X870:$i, X871:$i]:(((X868 @ X870)=>((X868 @ X871)=>((X870)=(X871)))))=>?[X872:$i]:(((X868 @ X872)&![X873:$i]:(((X868 @ X873)=>((X872)=(X873)))))))))=>(![X874:$i > $o]:((?[X875:$i]:(![X876:$i]:(((X874 @ X876)<=>((X876)=(X875)))))=>?[X877:$i]:(((X874 @ X877)&![X878:$i]:(((X874 @ X878)=>((X877)=(X878))))))))=>(![X879:$i, X880:$i]:((((X879)=(X880))=>![X881:$i, X882:$i]:((((X881)=(X882))=>((in @ X881 @ X879)=>(in @ X882 @ X880))))))=>(![X1425:$i, X1426:$i]:((((X1425)=(X1426))=>![X1427:$i, X1428:$i]:((((X1427)=(X1428))=>((in @ X1427 @ X1425)<=>(in @ X1428 @ X1426))))))=>(![X1420:$i > $o]:((?[X1421:$i]:(((X1420 @ X1421)&![X1422:$i]:(((X1420 @ X1422)=>((X1421)=(X1422))))))=>![X1423:$i, X1424:$i]:(((X1420 @ X1423)=>((X1420 @ X1424)=>((X1423)=(X1424)))))))=>(![X1412:$i > $o, X1413:$i > $o]:((![X1414:$i, X1415:$i]:((((X1414)=(X1415))=>((X1412 @ X1414)<=>(X1413 @ X1415))))=>(?[X1416:$i]:(((X1412 @ X1416)&![X1417:$i]:(((X1412 @ X1417)=>((X1416)=(X1417))))))<=>?[X1418:$i]:(((X1413 @ X1418)&![X1419:$i]:(((X1413 @ X1419)=>((X1418)=(X1419)))))))))=>(((emptyset)=(emptyset))=>(![X1408:$i, X1409:$i]:((((X1408)=(X1409))=>![X1410:$i, X1411:$i]:((((X1410)=(X1411))=>((setadjoin @ X1408 @ X1410)=(setadjoin @ X1409 @ X1411))))))=>(![X883:$i, 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X48))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_259, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_260]), foundationAx]), wellorderingAx]), c_0_261]), c_0_262]), c_0_263]), c_0_264]), c_0_265]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_266]), setext]), emptyI]), noeltsimpempty]), c_0_267]), c_0_268]), c_0_269]), c_0_270]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_271]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_272]), c_0_273]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_274]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_275]), c_0_276]), c_0_277]), inCongP]), in__Cong]), c_0_278]), c_0_279]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_280]), c_0_281]), c_0_282]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_283]), c_0_284]), 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_285]), c_0_286]), c_0_287]), c_0_288]), singletonsuniq]), setukpairinjL1]), c_0_289]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_290]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_291]), c_0_292]), c_0_293]), c_0_294]), c_0_295]), c_0_296]), c_0_297]), c_0_298]), c_0_299]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_300]), c_0_301]), c_0_302]), c_0_303]), c_0_304]), c_0_305]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_306]), c_0_307]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_308]), c_0_309]), c_0_310]), c_0_311]), c_0_312]), c_0_313]), c_0_314]), c_0_315]), c_0_316]), c_0_317]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT])])]), c_0_318])).
10.99/1.99	thf(c_0_320, negated_conjecture, ![X1537:$i, X1538:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1550:$i, X1551:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1559:$i, X1560:$i > $i > $o, X1561:$i, X1563:$i, X1566:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i, X1573:$i, X1574:$i > $o, X1575:$i, X1577:$i, X1578:$i > $o, X1579:$i, X1580:$i, X1581:$i > $o, X1582:$i, X1583:$i, X1584:$i > $o, X1585:$i, X1586:$i > $o, X1587:$i, X1590:$i, X1591:$o, X1592:$i, X1593:$i, X1594:$o, X1595:$i, X1596:$i, X1597:$i > $o, X1598:$i, X1601:$i, X1602:$i, X1605:$i, X1607:$i, X1609:$i, X1610:$i > $o, X1611:$i, X1612:$i, X1614:$i, X1615:$i > $o, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i, X1626:$i, X1627:$o, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i, X1633:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i, X1643:$i, X1644:$i, X1645:$o, X1647:$i, X1648:$i, X1649:$i > $o, X1650:$i, X1653:$i, X1654:$i, X1655:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i > $o, X1674:$i, X1675:$i > $o, X1676:$i, X1677:$i, X1678:$i > $o, X1679:$i, X1681:$i, X1682:$i > $o, X1684:$i, X1685:$i, X1686:$i > $o, X1688:$i, X1689:$i, X1690:$i > $o, X1691:$i, X1693:$o, X1694:$o, X1695:$i, X1696:$i > $o, X1698:$i, X1699:$i, X1700:$i > $o, X1701:$i, X1703:$i > $o, X1704:$i, X1707:$i, X1708:$i > $o, X1709:$i, X1713:$i, X1714:$i > $o, X1715:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$i, X1725:$i, X1726:$i, X1727:$i > $o, X1728:$i, X1730:$i, X1731:$i, X1732:$i > $o, X1733:$i > $o, X1736:$i, X1739:$i, X1740:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i > $o, X1753:$i, X1755:$i, X1756:$i, X1757:$i > $o, X1758:$i > $o, X1761:$i, X1763:$i, X1765:$i, X1766:$i, X1767:$i > $o, X1768:$i > $o, X1771:$i, X1772:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i > $o, X1819:$i, X1820:$i > $o, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$o, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$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, X1858:$i, X1859:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$o, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i > $o, X1975:$i, X1976:$i, X1977:$i > $o, X1979:$i, X1980:$i > $o, X1981:$i, X1983:$i, X1984:$i > $o, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$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 > $i > $o, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i > $i > $o, X2065:$i, X2066:$i, X2067:$i > $i > $o, X2068:$i, X2069:$i, X2070:$i > $i > $o, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i > $i > $o, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i > $i > $o, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i > $i > $o, X2086:$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 > $i, X2114:$i, X2115:$i, X2116:$i > $i, X2118:$i, X2119:$i, X2120:$i > $i, X2122:$i, X2123:$i, X2124:$i, X2125:$i > $o, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i > $o, X2135:$i, X2136:$i, X2137:$i > $o, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i > $i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i > $i, X2209:$i, X2210:$i, X2211:$i > $i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$o, X2219:$i, X2220:$i, X2221:$i, X2222:$o, X2223:$i, X2224:$i, X2225:$i, X2226:$o, X2227:$i, X2228:$i, X2229:$i, X2230:$o, X2231:$i, X2232:$i, X2233:$i, X2234:$o, X2235:$i, X2236:$i, X2237:$i, X2238:$o, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$o, X2245:$i, X2246:$i, X2247:$i, X2248:$o, X2249:$i, X2250:$i, X2251:$i, X2252:$o, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2276:$i]:((((~(in @ (esk1_2 @ X1537 @ X1538) @ X1537)|~(in @ (esk1_2 @ X1537 @ X1538) @ X1538)|((X1537)=(X1538)))&((in @ (esk1_2 @ 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X2174 @ (cartprod @ X2171 @ X2172))|~(subset @ X2173 @ (cartprod @ X2171 @ X2172)))&(((in @ (kpair @ (esk76_4 @ X2171 @ X2172 @ X2173 @ X2174) @ (esk77_4 @ X2171 @ X2172 @ X2173 @ X2174)) @ X2174)|((X2173)=(X2174))|(in @ (kpair @ (esk74_4 @ X2171 @ X2172 @ X2173 @ X2174) @ (esk75_4 @ X2171 @ X2172 @ X2173 @ X2174)) @ X2173)|~(subset @ X2174 @ (cartprod @ X2171 @ X2172))|~(subset @ X2173 @ (cartprod @ X2171 @ X2172)))&(~(in @ (kpair @ (esk76_4 @ X2171 @ X2172 @ X2173 @ X2174) @ (esk77_4 @ X2171 @ X2172 @ X2173 @ X2174)) @ X2173)|((X2173)=(X2174))|(in @ (kpair @ (esk74_4 @ X2171 @ X2172 @ X2173 @ X2174) @ (esk75_4 @ X2171 @ X2172 @ X2173 @ X2174)) @ X2173)|~(subset @ X2174 @ (cartprod @ X2171 @ X2172))|~(subset @ X2173 @ (cartprod @ X2171 @ X2172))))))&(((in @ (esk76_4 @ X2171 @ X2172 @ X2173 @ X2174) @ X2171)|((X2173)=(X2174))|~(in @ (kpair @ (esk74_4 @ X2171 @ X2172 @ X2173 @ X2174) @ (esk75_4 @ X2171 @ X2172 @ X2173 @ X2174)) @ X2174)|~(subset @ X2174 @ (cartprod @ X2171 @ X2172))|~(subset @ X2173 @ (cartprod @ X2171 @ X2172)))&(((in @ (esk77_4 @ X2171 @ X2172 @ X2173 @ X2174) @ X2172)|((X2173)=(X2174))|~(in @ (kpair @ (esk74_4 @ X2171 @ X2172 @ X2173 @ X2174) @ (esk75_4 @ X2171 @ X2172 @ X2173 @ X2174)) @ X2174)|~(subset @ X2174 @ (cartprod @ X2171 @ X2172))|~(subset @ X2173 @ (cartprod @ X2171 @ X2172)))&(((in @ (kpair @ (esk76_4 @ X2171 @ X2172 @ X2173 @ X2174) @ (esk77_4 @ X2171 @ X2172 @ X2173 @ X2174)) @ X2174)|((X2173)=(X2174))|~(in @ (kpair @ (esk74_4 @ X2171 @ X2172 @ X2173 @ X2174) @ (esk75_4 @ X2171 @ X2172 @ X2173 @ X2174)) @ X2174)|~(subset @ X2174 @ (cartprod @ X2171 @ X2172))|~(subset @ X2173 @ (cartprod @ X2171 @ X2172)))&(~(in @ (kpair @ (esk76_4 @ X2171 @ X2172 @ X2173 @ X2174) @ (esk77_4 @ X2171 @ X2172 @ X2173 @ X2174)) @ X2173)|((X2173)=(X2174))|~(in @ (kpair @ (esk74_4 @ X2171 @ X2172 @ X2173 @ X2174) @ (esk75_4 @ X2171 @ X2172 @ X2173 @ X2174)) @ X2174)|~(subset @ X2174 @ (cartprod @ X2171 @ X2172))|~(subset @ X2173 @ (cartprod @ X2171 @ X2172)))))))))&((((in @ (esk78_4 @ X2179 @ X2180 @ X2181 @ X2182) @ X2179)|((X2181)=(X2182))|~(func @ X2179 @ X2180 @ X2182)|~(func @ X2179 @ X2180 @ X2181))&(((ap @ X2179 @ X2180 @ X2181 @ (esk78_4 @ X2179 @ X2180 @ X2181 @ X2182))!=(ap @ X2179 @ X2180 @ X2182 @ (esk78_4 @ X2179 @ X2180 @ X2181 @ X2182)))|((X2181)=(X2182))|~(func @ X2179 @ X2180 @ X2182)|~(func @ X2179 @ X2180 @ X2181)))&((((in @ (esk79_4 @ X2184 @ X2185 @ X2186 @ X2187) @ X2184)|((X2186)=(X2187))|~(in @ X2187 @ (funcSet @ X2184 @ X2185))|~(in @ X2186 @ (funcSet @ X2184 @ X2185)))&(((ap @ X2184 @ X2185 @ X2186 @ (esk79_4 @ X2184 @ X2185 @ X2186 @ X2187))!=(ap @ X2184 @ X2185 @ X2187 @ (esk79_4 @ X2184 @ X2185 @ X2186 @ X2187)))|((X2186)=(X2187))|~(in @ X2187 @ (funcSet @ X2184 @ X2185))|~(in @ X2186 @ (funcSet @ X2184 @ X2185))))&((~(in @ X2191 @ (funcSet @ X2189 @ X2190))|(~(in @ X2192 @ X2189)|((ap @ X2189 @ X2190 @ X2191 @ X2192)=(ap @ X2189 @ X2190 @ X2191 @ X2192))))&((~(func @ X2193 @ X2194 @ X2195)|(~(in @ X2196 @ X2193)|((ap @ X2193 @ X2194 @ X2195 @ X2196)=(ap @ X2193 @ X2194 @ X2195 @ X2196))))&((((in @ (esk80_3 @ X2197 @ X2198 @ X2199) @ X2197)|(~(in @ X2201 @ X2197)|((ap @ X2197 @ X2198 @ (lam @ X2197 @ X2198 @ X2199) @ X2201)=(X2199 @ X2201))))&(~(in @ (X2199 @ (esk80_3 @ X2197 @ X2198 @ X2199)) @ X2198)|(~(in @ X2201 @ X2197)|((ap @ X2197 @ X2198 @ (lam @ X2197 @ X2198 @ X2199) @ X2201)=(X2199 @ X2201)))))&((~(func @ X2202 @ X2203 @ X2204)|((lam @ X2202 @ X2203 @ (ap @ X2202 @ X2203 @ X2204))=(X2204)))&((((in @ (esk81_3 @ X2205 @ X2206 @ X2207) @ X2205)|((lam @ X2205 @ X2206 @ X2207)=(lam @ X2205 @ X2206 @ X2207)))&(~(in @ (X2207 @ (esk81_3 @ X2205 @ X2206 @ X2207)) @ X2206)|((lam @ X2205 @ X2206 @ X2207)=(lam @ X2205 @ X2206 @ X2207))))&((((in @ (esk82_3 @ X2209 @ X2210 @ X2211) @ X2209)|(~(in @ X2213 @ X2209)|((ap @ X2209 @ X2210 @ (lam @ X2209 @ X2210 @ X2211) @ X2213)=(X2211 @ X2213))))&(~(in @ (X2211 @ (esk82_3 @ X2209 @ X2210 @ X2211)) @ X2210)|(~(in @ X2213 @ X2209)|((ap @ X2209 @ X2210 @ (lam @ X2209 @ X2210 @ X2211) @ X2213)=(X2211 @ X2213)))))&((~(in @ X2216 @ (funcSet @ X2214 @ X2215))|((lam @ X2214 @ X2215 @ (ap @ X2214 @ X2215 @ X2216))=(X2216)))&((~(in @ X2219 @ X2217)|(~(in @ X2220 @ X2217)|((X2218)|(in @ X2220 @ (dsetconstr @ X2217 @ (^[Z0:$i]:((((((X2218))&(((Z0)=(X2219)))))|(((~((X2218)))&(((Z0)=(X2220)))))))))))))&((~(in @ X2223 @ X2221)|(~(in @ X2224 @ X2221)|((X2222)|((dsetconstr @ X2221 @ (^[Z0:$i]:((((((X2222))&(((Z0)=(X2223)))))|(((~((X2222)))&(((Z0)=(X2224)))))))))=(setadjoin @ X2224 @ emptyset)))))&((~(in @ X2227 @ X2225)|(~(in @ X2228 @ X2225)|(~(X2226)|(in @ X2227 @ (dsetconstr @ X2225 @ (^[Z0:$i]:((((((X2226))&(((Z0)=(X2227)))))|(((~((X2226)))&(((Z0)=(X2228)))))))))))))&((~(in @ X2231 @ X2229)|(~(in @ X2232 @ X2229)|(~(X2230)|((dsetconstr @ X2229 @ (^[Z0:$i]:((((((X2230))&(((Z0)=(X2231)))))|(((~((X2230)))&(((Z0)=(X2232)))))))))=(setadjoin @ X2231 @ emptyset)))))&((~(in @ X2235 @ X2233)|(~(in @ X2236 @ X2233)|(singleton @ (dsetconstr @ X2233 @ (^[Z0:$i]:((((((X2234))&(((Z0)=(X2235)))))|(((~((X2234)))&(((Z0)=(X2236))))))))))))&((~(in @ X2239 @ X2237)|(~(in @ X2240 @ X2237)|(in @ (if @ X2237 @ ((X2238)) @ X2239 @ X2240) @ X2237)))&((~(singleton @ X2241)|(~(in @ X2242 @ X2241)|((setunion @ X2241)=(X2242))))&((~(in @ X2245 @ X2243)|(~(in @ X2246 @ X2243)|(~(X2244)|((if @ X2243 @ ((X2244)) @ X2245 @ X2246)=(X2245)))))&((~(in @ X2249 @ X2247)|(~(in @ X2250 @ X2247)|((X2248)|((if @ X2247 @ ((X2248)) @ X2249 @ X2250)=(X2250)))))&((~(in @ X2253 @ X2251)|(~(in @ X2254 @ X2251)|(in @ (if @ X2251 @ ((X2252)) @ X2253 @ X2254) @ (setadjoin @ X2253 @ (setadjoin @ X2254 @ emptyset)))))&((~(in @ X2256 @ (powerset @ X2255))|(~(in @ X2257 @ (powerset @ X2255))|(in @ (binintersect @ X2256 @ X2257) @ (powerset @ X2255))))&((~(in @ X2259 @ (powerset @ X2258))|(~(in @ X2260 @ (powerset @ X2258))|(in @ (binunion @ X2259 @ X2260) @ (powerset @ X2258))))&((~(in @ X2262 @ (powerset @ X2261))|(in @ (powerset @ X2262) @ (powerset @ (powerset @ X2261))))&((~(in @ X2264 @ (powerset @ X2263))|(~(in @ X2265 @ (powerset @ X2263))|(in @ (setminus @ X2264 @ X2265) @ (powerset @ X2263))))&((~(in @ X2267 @ (powerset @ X2266))|(in @ (setminus @ X2266 @ X2267) @ (powerset @ X2266)))&(((((in @ (esk84_3 @ X2268 @ X2269 @ X2270) @ X2268)|((X2269)=(X2270))|(in @ (esk83_3 @ X2268 @ X2269 @ X2270) @ X2268)|~(in @ X2270 @ (powerset @ X2268))|~(in @ X2269 @ (powerset @ X2268)))&(((in @ (esk84_3 @ X2268 @ X2269 @ X2270) @ X2270)|((X2269)=(X2270))|(in @ (esk83_3 @ X2268 @ X2269 @ X2270) @ X2268)|~(in @ X2270 @ (powerset @ X2268))|~(in @ X2269 @ (powerset @ X2268)))&(~(in @ (esk84_3 @ X2268 @ X2269 @ X2270) @ X2269)|((X2269)=(X2270))|(in @ (esk83_3 @ X2268 @ X2269 @ X2270) @ X2268)|~(in @ X2270 @ (powerset @ X2268))|~(in @ X2269 @ (powerset @ X2268)))))&((((in @ (esk84_3 @ X2268 @ X2269 @ X2270) @ X2268)|((X2269)=(X2270))|(in @ (esk83_3 @ X2268 @ X2269 @ X2270) @ X2269)|~(in @ X2270 @ (powerset @ X2268))|~(in @ X2269 @ (powerset @ X2268)))&(((in @ (esk84_3 @ X2268 @ X2269 @ X2270) @ X2270)|((X2269)=(X2270))|(in @ (esk83_3 @ X2268 @ X2269 @ X2270) @ X2269)|~(in @ X2270 @ (powerset @ X2268))|~(in @ X2269 @ (powerset @ X2268)))&(~(in @ (esk84_3 @ X2268 @ X2269 @ X2270) @ X2269)|((X2269)=(X2270))|(in @ (esk83_3 @ X2268 @ X2269 @ X2270) @ X2269)|~(in @ X2270 @ (powerset @ X2268))|~(in @ X2269 @ (powerset @ X2268)))))&(((in @ (esk84_3 @ X2268 @ X2269 @ X2270) @ X2268)|((X2269)=(X2270))|~(in @ (esk83_3 @ X2268 @ X2269 @ X2270) @ X2270)|~(in @ X2270 @ (powerset @ X2268))|~(in @ X2269 @ (powerset @ X2268)))&(((in @ (esk84_3 @ X2268 @ X2269 @ X2270) @ X2270)|((X2269)=(X2270))|~(in @ (esk83_3 @ X2268 @ X2269 @ X2270) @ X2270)|~(in @ X2270 @ (powerset @ X2268))|~(in @ X2269 @ (powerset @ X2268)))&(~(in @ (esk84_3 @ X2268 @ X2269 @ X2270) @ X2269)|((X2269)=(X2270))|~(in @ (esk83_3 @ X2268 @ X2269 @ X2270) @ X2270)|~(in @ X2270 @ (powerset @ X2268))|~(in @ X2269 @ (powerset @ X2268)))))))&((in @ esk86_0 @ (powerset @ esk85_0))&((in @ esk87_0 @ (powerset @ esk85_0))&((~(in @ X2276 @ esk85_0)|(~(in @ X2276 @ esk86_0)|(in @ X2276 @ esk87_0)))&~(subset @ esk86_0 @ esk87_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_319])])])])])])])).
10.99/1.99	thf(c_0_321, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ X2 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_320])).
10.99/1.99	thf(c_0_322, negated_conjecture, (in @ esk86_0 @ (powerset @ esk85_0)), inference(split_conjunct,[status(thm)],[c_0_320])).
10.99/1.99	thf(c_0_323, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((subset @ X2 @ X3))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_320])).
10.99/1.99	thf(c_0_324, negated_conjecture, (subset @ esk86_0 @ esk85_0), inference(spm,[status(thm)],[c_0_321, c_0_322])).
10.99/1.99	thf(c_0_325, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk53_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_320])).
10.99/1.99	thf(c_0_326, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk87_0)|~((in @ X2 @ esk85_0))|~((in @ X2 @ esk86_0)))), inference(split_conjunct,[status(thm)],[c_0_320])).
10.99/1.99	thf(c_0_327, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk85_0)|~((in @ X2 @ esk86_0)))), inference(spm,[status(thm)],[c_0_323, c_0_324])).
10.99/1.99	thf(c_0_328, negated_conjecture, ![X2:$i]:(((subset @ X2 @ esk87_0)|~((in @ (esk53_2 @ X2 @ esk87_0) @ esk86_0)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_325, c_0_326]), c_0_327])).
10.99/1.99	thf(c_0_329, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk53_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_320])).
10.99/1.99	thf(c_0_330, negated_conjecture, ~((subset @ esk86_0 @ esk87_0)), inference(split_conjunct,[status(thm)],[c_0_320])).
10.99/1.99	thf(c_0_331, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_328, c_0_329]), c_0_330]), ['proof']).
10.99/1.99	% SZS output end CNFRefutation
10.99/1.99	% Parsed axioms                        : 507
10.99/1.99	% Removed by relevancy pruning/SinE    : 0
10.99/1.99	% Initial clauses                      : 683
10.99/1.99	% Removed in clause preprocessing      : 299
10.99/1.99	% Initial clauses in saturation        : 384
10.99/1.99	% Processed clauses                    : 5665
10.99/1.99	% ...of these trivial                  : 199
10.99/1.99	% ...subsumed                          : 3646
10.99/1.99	% ...remaining for further processing  : 1820
10.99/1.99	% Other redundant clauses eliminated   : 330
10.99/1.99	% Clauses deleted for lack of memory   : 0
10.99/1.99	% Backward-subsumed                    : 81
10.99/1.99	% Backward-rewritten                   : 38
10.99/1.99	% Generated clauses                    : 105538
10.99/1.99	% ...of the previous two non-redundant : 97297
10.99/1.99	% ...aggressively subsumed             : 0
10.99/1.99	% Contextual simplify-reflections      : 2
10.99/1.99	% Paramodulations                      : 105195
10.99/1.99	% Factorizations                       : 6
10.99/1.99	% NegExts                              : 0
10.99/1.99	% Equation resolutions                 : 337
10.99/1.99	% Disequality decompositions           : 0
10.99/1.99	% Total rewrite steps                  : 18281
10.99/1.99	% ...of those cached                   : 17557
10.99/1.99	% Propositional unsat checks           : 0
10.99/1.99	%    Propositional check models        : 0
10.99/1.99	%    Propositional check unsatisfiable : 0
10.99/1.99	%    Propositional clauses             : 0
10.99/1.99	%    Propositional clauses after purity: 0
10.99/1.99	%    Propositional unsat core size     : 0
10.99/1.99	%    Propositional preprocessing time  : 0.000
10.99/1.99	%    Propositional encoding time       : 0.000
10.99/1.99	%    Propositional solver time         : 0.000
10.99/1.99	%    Success case prop preproc time    : 0.000
10.99/1.99	%    Success case prop encoding time   : 0.000
10.99/1.99	%    Success case prop solver time     : 0.000
10.99/1.99	% Current number of processed clauses  : 1686
10.99/1.99	%    Positive orientable unit clauses  : 559
10.99/1.99	%    Positive unorientable unit clauses: 0
10.99/1.99	%    Negative unit clauses             : 13
10.99/1.99	%    Non-unit-clauses                  : 1114
10.99/1.99	% Current number of unprocessed clauses: 85224
10.99/1.99	% ...number of literals in the above   : 289818
10.99/1.99	% Current number of archived formulas  : 0
10.99/1.99	% Current number of archived clauses   : 119
10.99/1.99	% Clause-clause subsumption calls (NU) : 133444
10.99/1.99	% Rec. Clause-clause subsumption calls : 82701
10.99/1.99	% Non-unit clause-clause subsumptions  : 2602
10.99/1.99	% Unit Clause-clause subsumption calls : 7313
10.99/1.99	% Rewrite failures with RHS unbound    : 0
10.99/1.99	% BW rewrite match attempts            : 5642
10.99/1.99	% BW rewrite match successes           : 23
10.99/1.99	% Condensation attempts                : 0
10.99/1.99	% Condensation successes               : 0
10.99/1.99	% Termbank termtop insertions          : 1746033
10.99/1.99	% Search garbage collected termcells   : 23904
10.99/1.99	
10.99/1.99	% -------------------------------------------------
10.99/1.99	% User time                : 1.300 s
10.99/1.99	% System time              : 0.055 s
10.99/1.99	% Total time               : 1.355 s
10.99/1.99	% Maximum resident set size: 9300 pages
10.99/1.99	
10.99/1.99	% -------------------------------------------------
10.99/1.99	% User time                : 1.313 s
10.99/1.99	% System time              : 0.063 s
10.99/1.99	% Total time               : 1.376 s
10.99/1.99	% Maximum resident set size: 5632 pages
10.99/1.99	% E exiting
10.99/2.00	EOF