0.00/0.03	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.05	% Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.14/0.38	% Computer : n007.cluster.edu
0.14/0.38	% Model    : x86_64 x86_64
0.14/0.38	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.38	% Memory   : 8046.5625MB
0.14/0.38	% OS       : Linux 6.8.0-71-generic
0.14/0.38	% CPULimit : 1440
0.14/0.38	% WCLimit  : 180
0.14/0.38	% DateTime : Mon Jul 27 13:15:03 UTC 2026
0.14/0.38	% CPUTime  : 
0.14/0.38	Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.14/0.42	Running higher-order theorem proving
0.21/0.49	Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p
130.12/19.42	% Version: 3.5.1-ho
130.12/19.42	% Preprocessing class: HSLMSLSSLLLCHFA.
130.12/19.42	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
130.12/19.42	% Starting ehoh_best5 with 180s (1) cores
130.12/19.42	% Starting almost_fo_3_lam with 180s (1) cores
130.12/19.42	% Starting new_bool_5 with 180s (1) cores
130.12/19.42	% Starting pre_casc_3 with 180s (1) cores
130.12/19.42	% Starting ho_unfolding_8 with 180s (1) cores
130.12/19.42	% Starting new_ho_10_cnf2 with 180s (1) cores
130.12/19.42	% Starting new_bool_3 with 180s (1) cores
130.12/19.42	% Starting new_ho_5 with 180s (1) cores
130.12/19.42	% ehoh_best5 with pid 1091440 completed with status 0
130.12/19.42	% Result found by ehoh_best5
130.12/19.42	% Preprocessing class: HSLMSLSSLLLCHFA.
130.12/19.42	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
130.12/19.42	% Starting ehoh_best5 with 180s (1) cores
130.12/19.42	% (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
130.12/19.42	% No SInE strategy applied
130.12/19.42	% Search class: HGHSM-FSLM32-MHFMMSBN
130.12/19.42	% Scheduled 11 strats onto 1 cores with 180 seconds (180 total)
130.12/19.42	% Starting SubtermCWHack with 17s (1) cores
130.12/19.42	% SubtermCWHack with pid 1091451 completed with status 8
130.12/19.42	% Starting ehoh_best5 with 19s (1) cores
130.12/19.42	% ehoh_best5 with pid 1091458 completed with status 0
130.12/19.42	% Result found by ehoh_best5
130.12/19.42	% Preprocessing class: HSLMSLSSLLLCHFA.
130.12/19.42	% Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
130.12/19.42	% Starting ehoh_best5 with 180s (1) cores
130.12/19.42	% (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
130.12/19.42	% No SInE strategy applied
130.12/19.42	% Search class: HGHSM-FSLM32-MHFMMSBN
130.12/19.42	% Scheduled 11 strats onto 1 cores with 180 seconds (180 total)
130.12/19.42	% Starting SubtermCWHack with 17s (1) cores
130.12/19.42	% SubtermCWHack with pid 1091451 completed with status 8
130.12/19.42	% Starting ehoh_best5 with 19s (1) cores
130.12/19.42	% Preprocessing time       : 0.011 s
130.12/19.42	% Presaturation interreduction done
130.12/19.42	
130.12/19.42	% Proof found!
130.12/19.42	% SZS status Theorem
130.12/19.42	% SZS output start CNFRefutation
130.12/19.42	thf(decl_23, type, in: $i > $i > $o).
130.12/19.42	thf(decl_24, type, exu: ($i > $o) > $o).
130.12/19.42	thf(decl_25, type, setextAx: $o).
130.12/19.42	thf(decl_26, type, emptyset: $i).
130.12/19.42	thf(decl_27, type, emptysetAx: $o).
130.12/19.42	thf(decl_28, type, setadjoin: $i > $i > $i).
130.12/19.42	thf(decl_29, type, setadjoinAx: $o).
130.12/19.42	thf(decl_30, type, powerset: $i > $i).
130.12/19.42	thf(decl_31, type, powersetAx: $o).
130.12/19.42	thf(decl_32, type, setunion: $i > $i).
130.12/19.42	thf(decl_33, type, setunionAx: $o).
130.12/19.42	thf(decl_34, type, omega: $i).
130.12/19.42	thf(decl_35, type, omega0Ax: $o).
130.12/19.42	thf(decl_36, type, omegaSAx: $o).
130.12/19.42	thf(decl_37, type, omegaIndAx: $o).
130.12/19.42	thf(decl_38, type, replAx: $o).
130.12/19.42	thf(decl_39, type, foundationAx: $o).
130.12/19.42	thf(decl_40, type, wellorderingAx: $o).
130.12/19.42	thf(decl_41, type, descr: ($i > $o) > $i).
130.12/19.42	thf(decl_42, type, descrp: $o).
130.12/19.42	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
130.12/19.42	thf(decl_44, type, dsetconstrI: $o).
130.12/19.42	thf(decl_45, type, dsetconstrEL: $o).
130.12/19.42	thf(decl_46, type, dsetconstrER: $o).
130.12/19.42	thf(decl_47, type, exuE1: $o).
130.12/19.42	thf(decl_48, type, prop2set: $o > $i).
130.12/19.42	thf(decl_49, type, prop2setE: $o).
130.12/19.42	thf(decl_50, type, emptysetE: $o).
130.12/19.42	thf(decl_51, type, emptysetimpfalse: $o).
130.12/19.42	thf(decl_52, type, notinemptyset: $o).
130.12/19.42	thf(decl_53, type, exuE3e: $o).
130.12/19.42	thf(decl_54, type, setext: $o).
130.12/19.42	thf(decl_55, type, emptyI: $o).
130.12/19.42	thf(decl_56, type, noeltsimpempty: $o).
130.12/19.42	thf(decl_57, type, setbeta: $o).
130.12/19.42	thf(decl_58, type, nonempty: $i > $o).
130.12/19.42	thf(decl_59, type, nonemptyE1: $o).
130.12/19.42	thf(decl_60, type, nonemptyI: $o).
130.12/19.42	thf(decl_61, type, nonemptyI1: $o).
130.12/19.42	thf(decl_62, type, setadjoinIL: $o).
130.12/19.42	thf(decl_63, type, emptyinunitempty: $o).
130.12/19.42	thf(decl_64, type, setadjoinIR: $o).
130.12/19.42	thf(decl_65, type, setadjoinE: $o).
130.12/19.42	thf(decl_66, type, setadjoinOr: $o).
130.12/19.42	thf(decl_67, type, setoftrueEq: $o).
130.12/19.42	thf(decl_68, type, powersetI: $o).
130.12/19.42	thf(decl_69, type, emptyinPowerset: $o).
130.12/19.42	thf(decl_70, type, emptyInPowerset: $o).
130.12/19.42	thf(decl_71, type, powersetE: $o).
130.12/19.42	thf(decl_72, type, setunionI: $o).
130.12/19.42	thf(decl_73, type, setunionE: $o).
130.12/19.42	thf(decl_74, type, subPowSU: $o).
130.12/19.42	thf(decl_75, type, exuE2: $o).
130.12/19.42	thf(decl_76, type, nonemptyImpWitness: $o).
130.12/19.42	thf(decl_77, type, uniqinunit: $o).
130.12/19.42	thf(decl_78, type, notinsingleton: $o).
130.12/19.42	thf(decl_79, type, eqinunit: $o).
130.12/19.42	thf(decl_80, type, singletonsswitch: $o).
130.12/19.42	thf(decl_81, type, upairsetE: $o).
130.12/19.42	thf(decl_82, type, upairsetIL: $o).
130.12/19.42	thf(decl_83, type, upairsetIR: $o).
130.12/19.42	thf(decl_84, type, emptyE1: $o).
130.12/19.42	thf(decl_85, type, vacuousDall: $o).
130.12/19.42	thf(decl_86, type, quantDeMorgan1: $o).
130.12/19.42	thf(decl_87, type, quantDeMorgan2: $o).
130.12/19.42	thf(decl_88, type, quantDeMorgan3: $o).
130.12/19.42	thf(decl_89, type, quantDeMorgan4: $o).
130.12/19.42	thf(decl_90, type, prop2setI: $o).
130.12/19.42	thf(decl_91, type, set2prop: $i > $o).
130.12/19.42	thf(decl_92, type, prop2set2propI: $o).
130.12/19.42	thf(decl_93, type, notdexE: $o).
130.12/19.42	thf(decl_94, type, notdallE: $o).
130.12/19.42	thf(decl_95, type, exuI1: $o).
130.12/19.42	thf(decl_96, type, exuI3: $o).
130.12/19.42	thf(decl_97, type, exuI2: $o).
130.12/19.42	thf(decl_98, type, inCongP: $o).
130.12/19.42	thf(decl_99, type, in__Cong: $o).
130.12/19.42	thf(decl_100, type, exuE3u: $o).
130.12/19.42	thf(decl_101, type, exu__Cong: $o).
130.12/19.42	thf(decl_102, type, emptyset__Cong: $o).
130.12/19.42	thf(decl_103, type, setadjoin__Cong: $o).
130.12/19.42	thf(decl_104, type, powerset__Cong: $o).
130.12/19.42	thf(decl_105, type, setunion__Cong: $o).
130.12/19.42	thf(decl_106, type, omega__Cong: $o).
130.12/19.42	thf(decl_107, type, exuEu: $o).
130.12/19.42	thf(decl_108, type, descr__Cong: $o).
130.12/19.42	thf(decl_109, type, dsetconstr__Cong: $o).
130.12/19.42	thf(decl_110, type, subset: $i > $i > $o).
130.12/19.42	thf(decl_113, type, subsetI1: $o).
130.12/19.42	thf(decl_114, type, eqimpsubset2: $o).
130.12/19.42	thf(decl_115, type, eqimpsubset1: $o).
130.12/19.42	thf(decl_116, type, subsetI2: $o).
130.12/19.42	thf(decl_117, type, emptysetsubset: $o).
130.12/19.42	thf(decl_118, type, subsetE: $o).
130.12/19.42	thf(decl_119, type, subsetE2: $o).
130.12/19.42	thf(decl_120, type, notsubsetI: $o).
130.12/19.42	thf(decl_121, type, notequalI1: $o).
130.12/19.42	thf(decl_122, type, notequalI2: $o).
130.12/19.42	thf(decl_123, type, subsetRefl: $o).
130.12/19.42	thf(decl_124, type, subsetTrans: $o).
130.12/19.42	thf(decl_125, type, setadjoinSub: $o).
130.12/19.42	thf(decl_126, type, setadjoinSub2: $o).
130.12/19.42	thf(decl_127, type, subset2powerset: $o).
130.12/19.42	thf(decl_128, type, setextsub: $o).
130.12/19.42	thf(decl_129, type, subsetemptysetimpeq: $o).
130.12/19.42	thf(decl_130, type, powersetI1: $o).
130.12/19.42	thf(decl_131, type, powersetE1: $o).
130.12/19.42	thf(decl_132, type, inPowerset: $o).
130.12/19.42	thf(decl_133, type, powersetsubset: $o).
130.12/19.42	thf(decl_134, type, sepInPowerset: $o).
130.12/19.42	thf(decl_135, type, sepSubset: $o).
130.12/19.42	thf(decl_136, type, binunion: $i > $i > $i).
130.12/19.42	thf(decl_137, type, binunionIL: $o).
130.12/19.42	thf(decl_138, type, upairset2IR: $o).
130.12/19.42	thf(decl_139, type, binunionIR: $o).
130.12/19.42	thf(decl_140, type, binunionEcases: $o).
130.12/19.42	thf(decl_141, type, binunionE: $o).
130.12/19.42	thf(decl_142, type, binunionLsub: $o).
130.12/19.42	thf(decl_143, type, binunionRsub: $o).
130.12/19.42	thf(decl_144, type, binintersect: $i > $i > $i).
130.12/19.42	thf(decl_145, type, binintersectI: $o).
130.12/19.42	thf(decl_146, type, binintersectSubset5: $o).
130.12/19.42	thf(decl_147, type, binintersectEL: $o).
130.12/19.42	thf(decl_148, type, binintersectLsub: $o).
130.12/19.42	thf(decl_149, type, binintersectSubset2: $o).
130.12/19.42	thf(decl_150, type, binintersectSubset3: $o).
130.12/19.42	thf(decl_151, type, binintersectER: $o).
130.12/19.42	thf(decl_152, type, disjointsetsI1: $o).
130.12/19.42	thf(decl_153, type, binintersectRsub: $o).
130.12/19.42	thf(decl_154, type, binintersectSubset4: $o).
130.12/19.42	thf(decl_155, type, binintersectSubset1: $o).
130.12/19.42	thf(decl_156, type, bs114d: $o).
130.12/19.42	thf(decl_158, type, setminus: $i > $i > $i).
130.12/19.42	thf(decl_159, type, setminusI: $o).
130.12/19.42	thf(decl_160, type, setminusEL: $o).
130.12/19.42	thf(decl_161, type, setminusER: $o).
130.12/19.42	thf(decl_162, type, setminusSubset2: $o).
130.12/19.42	thf(decl_163, type, setminusERneg: $o).
130.12/19.42	thf(decl_164, type, setminusELneg: $o).
130.12/19.42	thf(decl_165, type, setminusILneg: $o).
130.12/19.42	thf(decl_166, type, setminusIRneg: $o).
130.12/19.42	thf(decl_167, type, setminusLsub: $o).
130.12/19.42	thf(decl_168, type, setminusSubset1: $o).
130.12/19.42	thf(decl_169, type, symdiff: $i > $i > $i).
130.12/19.42	thf(decl_170, type, symdiffE: $o).
130.12/19.42	thf(decl_171, type, symdiffI1: $o).
130.12/19.42	thf(decl_172, type, symdiffI2: $o).
130.12/19.42	thf(decl_173, type, symdiffIneg1: $o).
130.12/19.42	thf(decl_174, type, symdiffIneg2: $o).
130.12/19.42	thf(decl_175, type, iskpair: $i > $o).
130.12/19.42	thf(decl_176, type, secondinupair: $o).
130.12/19.42	thf(decl_177, type, setukpairIL: $o).
130.12/19.42	thf(decl_178, type, setukpairIR: $o).
130.12/19.42	thf(decl_179, type, kpairiskpair: $o).
130.12/19.42	thf(decl_180, type, kpair: $i > $i > $i).
130.12/19.42	thf(decl_181, type, kpairp: $o).
130.12/19.42	thf(decl_182, type, cartprod: $i > $i > $i).
130.12/19.42	thf(decl_183, type, singletonsubset: $o).
130.12/19.42	thf(decl_184, type, singletoninpowerset: $o).
130.12/19.42	thf(decl_185, type, singletoninpowunion: $o).
130.12/19.42	thf(decl_186, type, upairset2E: $o).
130.12/19.42	thf(decl_187, type, upairsubunion: $o).
130.12/19.42	thf(decl_188, type, upairinpowunion: $o).
130.12/19.42	thf(decl_189, type, ubforcartprodlem1: $o).
130.12/19.42	thf(decl_190, type, ubforcartprodlem2: $o).
130.12/19.42	thf(decl_191, type, ubforcartprodlem3: $o).
130.12/19.42	thf(decl_192, type, cartprodpairin: $o).
130.12/19.42	thf(decl_193, type, cartprodmempair1: $o).
130.12/19.42	thf(decl_194, type, cartprodmempair: $o).
130.12/19.42	thf(decl_195, type, setunionE2: $o).
130.12/19.42	thf(decl_196, type, setunionsingleton1: $o).
130.12/19.42	thf(decl_197, type, setunionsingleton2: $o).
130.12/19.42	thf(decl_198, type, setunionsingleton: $o).
130.12/19.42	thf(decl_199, type, singleton: $i > $o).
130.12/19.42	thf(decl_200, type, singletonprop: $o).
130.12/19.42	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
130.12/19.42	thf(decl_202, type, ex1E1: $o).
130.12/19.42	thf(decl_203, type, ex1I: $o).
130.12/19.42	thf(decl_204, type, ex1I2: $o).
130.12/19.42	thf(decl_205, type, singletonsuniq: $o).
130.12/19.42	thf(decl_210, type, setukpairinjL1: $o).
130.12/19.42	thf(decl_211, type, kfstsingleton: $o).
130.12/19.42	thf(decl_212, type, theprop: $o).
130.12/19.42	thf(decl_213, type, kfst: $i > $i).
130.12/19.42	thf(decl_214, type, kfstpairEq: $o).
130.12/19.42	thf(decl_215, type, cartprodfstin: $o).
130.12/19.42	thf(decl_216, type, setukpairinjL2: $o).
130.12/19.42	thf(decl_217, type, setukpairinjL: $o).
130.12/19.42	thf(decl_218, type, setukpairinjR11: $o).
130.12/19.42	thf(decl_219, type, setukpairinjR12: $o).
130.12/19.42	thf(decl_220, type, setukpairinjR1: $o).
130.12/19.42	thf(decl_221, type, upairequniteq: $o).
130.12/19.42	thf(decl_222, type, setukpairinjR2: $o).
130.12/19.42	thf(decl_223, type, setukpairinjR: $o).
130.12/19.42	thf(decl_224, type, ksndsingleton: $o).
130.12/19.42	thf(decl_225, type, ksnd: $i > $i).
130.12/19.42	thf(decl_226, type, ksndpairEq: $o).
130.12/19.42	thf(decl_227, type, kpairsurjEq: $o).
130.12/19.42	thf(decl_228, type, cartprodsndin: $o).
130.12/19.42	thf(decl_229, type, cartprodpairmemEL: $o).
130.12/19.42	thf(decl_230, type, cartprodpairmemER: $o).
130.12/19.42	thf(decl_231, type, cartprodmempaircEq: $o).
130.12/19.42	thf(decl_232, type, cartprodfstpairEq: $o).
130.12/19.42	thf(decl_233, type, cartprodsndpairEq: $o).
130.12/19.42	thf(decl_234, type, cartprodpairsurjEq: $o).
130.12/19.42	thf(decl_235, type, breln: $i > $i > $i > $o).
130.12/19.42	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
130.12/19.42	thf(decl_237, type, dpsetconstrI: $o).
130.12/19.42	thf(decl_238, type, dpsetconstrSub: $o).
130.12/19.42	thf(decl_239, type, setOfPairsIsBReln: $o).
130.12/19.42	thf(decl_240, type, dpsetconstrERa: $o).
130.12/19.42	thf(decl_241, type, dpsetconstrEL1: $o).
130.12/19.42	thf(decl_242, type, dpsetconstrEL2: $o).
130.12/19.42	thf(decl_243, type, dpsetconstrER: $o).
130.12/19.42	thf(decl_244, type, func: $i > $i > $i > $o).
130.12/19.42	thf(decl_245, type, funcSet: $i > $i > $i).
130.12/19.42	thf(decl_246, type, funcImageSingleton: $o).
130.12/19.42	thf(decl_247, type, apProp: $o).
130.12/19.42	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
130.12/19.42	thf(decl_249, type, app: $o).
130.12/19.42	thf(decl_250, type, infuncsetfunc: $o).
130.12/19.42	thf(decl_251, type, ap2p: $o).
130.12/19.42	thf(decl_252, type, funcinfuncset: $o).
130.12/19.42	thf(decl_253, type, lamProp: $o).
130.12/19.42	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
130.12/19.42	thf(decl_255, type, lamp: $o).
130.12/19.42	thf(decl_256, type, lam2p: $o).
130.12/19.42	thf(decl_257, type, brelnall1: $o).
130.12/19.42	thf(decl_258, type, brelnall2: $o).
130.12/19.42	thf(decl_259, type, ex1E2: $o).
130.12/19.42	thf(decl_260, type, funcGraphProp1: $o).
130.12/19.42	thf(decl_261, type, funcGraphProp3: $o).
130.12/19.42	thf(decl_262, type, funcGraphProp2: $o).
130.12/19.42	thf(decl_263, type, funcextLem: $o).
130.12/19.42	thf(decl_264, type, funcGraphProp4: $o).
130.12/19.42	thf(decl_265, type, subbreln: $o).
130.12/19.42	thf(decl_266, type, eqbreln: $o).
130.12/19.42	thf(decl_267, type, funcext: $o).
130.12/19.42	thf(decl_268, type, funcext2: $o).
130.12/19.42	thf(decl_269, type, ap2apEq1: $o).
130.12/19.42	thf(decl_270, type, ap2apEq2: $o).
130.12/19.42	thf(decl_271, type, beta1: $o).
130.12/19.42	thf(decl_272, type, eta1: $o).
130.12/19.42	thf(decl_273, type, lam2lamEq: $o).
130.12/19.42	thf(decl_274, type, beta2: $o).
130.12/19.42	thf(decl_275, type, eta2: $o).
130.12/19.42	thf(decl_276, type, iffalseProp1: $o).
130.12/19.42	thf(decl_277, type, iffalseProp2: $o).
130.12/19.42	thf(decl_278, type, iftrueProp1: $o).
130.12/19.42	thf(decl_279, type, iftrueProp2: $o).
130.12/19.42	thf(decl_280, type, ifSingleton: $o).
130.12/19.42	thf(decl_281, type, if: $i > $o > $i > $i > $i).
130.12/19.42	thf(decl_282, type, ifp: $o).
130.12/19.42	thf(decl_283, type, theeq: $o).
130.12/19.42	thf(decl_284, type, iftrue: $o).
130.12/19.42	thf(decl_285, type, iffalse: $o).
130.12/19.42	thf(decl_286, type, iftrueorfalse: $o).
130.12/19.42	thf(decl_287, type, binintersectT_lem: $o).
130.12/19.42	thf(decl_288, type, binunionT_lem: $o).
130.12/19.42	thf(decl_289, type, powersetT_lem: $o).
130.12/19.42	thf(decl_290, type, setminusT_lem: $o).
130.12/19.42	thf(decl_291, type, complementT_lem: $o).
130.12/19.42	thf(decl_292, type, setextT: $o).
130.12/19.42	thf(decl_293, type, subsetTI: $o).
130.12/19.42	thf(decl_294, type, powersetTI1: $o).
130.12/19.42	thf(decl_295, type, powersetTE1: $o).
130.12/19.42	thf(decl_296, type, complementTI1: $o).
130.12/19.42	thf(decl_297, type, complementTE1: $o).
130.12/19.42	thf(decl_298, type, binintersectTELcontra: $o).
130.12/19.42	thf(decl_299, type, binintersectTERcontra: $o).
130.12/19.42	thf(decl_300, type, contrasubsetT: $o).
130.12/19.42	thf(decl_301, type, contrasubsetT1: $o).
130.12/19.42	thf(decl_302, type, contrasubsetT2: $o).
130.12/19.42	thf(decl_303, type, contrasubsetT3: $o).
130.12/19.42	thf(decl_304, type, doubleComplementI1: $o).
130.12/19.42	thf(decl_305, type, doubleComplementE1: $o).
130.12/19.42	thf(decl_306, type, doubleComplementSub1: $o).
130.12/19.42	thf(decl_307, type, doubleComplementSub2: $o).
130.12/19.42	thf(decl_308, type, doubleComplementEq: $o).
130.12/19.42	thf(decl_309, type, complementTnotintersectT: $o).
130.12/19.42	thf(decl_310, type, complementImpComplementIntersect: $o).
130.12/19.42	thf(decl_311, type, complementSubsetComplementIntersect: $o).
130.12/19.42	thf(decl_312, type, complementInPowersetComplementIntersect: $o).
130.12/19.42	thf(decl_313, type, contraSubsetComplement: $o).
130.12/19.42	thf(decl_314, type, complementTcontraSubset: $o).
130.12/19.42	thf(decl_315, type, binunionTILcontra: $o).
130.12/19.42	thf(decl_316, type, binunionTIRcontra: $o).
130.12/19.42	thf(decl_317, type, inIntersectImpInUnion: $o).
130.12/19.42	thf(decl_318, type, inIntersectImpInUnion2: $o).
130.12/19.42	thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
130.12/19.42	thf(decl_320, type, epred1_0: $o).
130.12/19.42	thf(decl_321, type, esk1_2: $i > $i > $i).
130.12/19.42	thf(decl_322, type, esk2_2: $i > $i > $i).
130.12/19.42	thf(decl_323, type, esk3_2: $i > $i > $i).
130.12/19.42	thf(decl_324, type, esk4_1: $i > $i).
130.12/19.42	thf(decl_325, type, esk5_2: ($i > $i > $o) > $i > $i).
130.12/19.42	thf(decl_326, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
130.12/19.42	thf(decl_327, type, esk7_2: ($i > $i > $o) > $i > $i).
130.12/19.42	thf(decl_328, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
130.12/19.42	thf(decl_329, type, esk9_1: $i > $i).
130.12/19.42	thf(decl_330, type, esk10_2: ($i > $o) > $i > $i).
130.12/19.42	thf(decl_331, type, esk11_2: ($i > $o) > $i > $i).
130.12/19.42	thf(decl_332, type, esk12_1: ($i > $o) > $i).
130.12/19.42	thf(decl_333, type, esk13_2: ($i > $o) > $i > $i).
130.12/19.42	thf(decl_334, type, esk14_1: ($i > $o) > $i).
130.12/19.42	thf(decl_335, type, esk15_2: $i > $i > $i).
130.12/19.42	thf(decl_336, type, esk16_2: $i > $i > $i).
130.12/19.42	thf(decl_337, type, esk17_1: $i > $i).
130.12/19.42	thf(decl_338, type, esk18_1: $i > $i).
130.12/19.42	thf(decl_339, type, esk19_1: $i > $i).
130.12/19.42	thf(decl_340, type, esk20_2: $i > $i > $i).
130.12/19.42	thf(decl_341, type, esk21_3: $i > $i > $o > $i).
130.12/19.42	thf(decl_342, type, esk22_2: ($i > $o) > $i > $i).
130.12/19.42	thf(decl_343, type, esk23_1: ($i > $o) > $i).
130.12/19.42	thf(decl_344, type, esk24_1: $i > $i).
130.12/19.42	thf(decl_345, type, esk25_2: $i > ($i > $o) > $i).
130.12/19.42	thf(decl_346, type, esk26_2: $i > ($i > $o) > $i).
130.12/19.42	thf(decl_347, type, esk27_2: $i > ($i > $o) > $i).
130.12/19.42	thf(decl_348, type, esk28_2: $i > ($i > $o) > $i).
130.12/19.42	thf(decl_349, type, esk29_2: $i > ($i > $o) > $i).
130.12/19.42	thf(decl_350, type, esk30_2: $i > ($i > $o) > $i).
130.12/19.42	thf(decl_351, type, esk31_2: ($i > $o) > $i > $i).
130.12/19.42	thf(decl_352, type, esk32_1: ($i > $o) > $i).
130.12/19.42	thf(decl_353, type, esk33_1: ($i > $o) > $i).
130.12/19.42	thf(decl_354, type, esk34_1: ($i > $o) > $i).
130.12/19.42	thf(decl_355, type, esk35_1: ($i > $o) > $i).
130.12/19.42	thf(decl_356, type, esk36_2: ($i > $o) > $i > $i).
130.12/19.42	thf(decl_357, type, esk37_1: ($i > $o) > $i).
130.12/19.42	thf(decl_358, type, esk38_2: ($i > $o) > $i > $i).
130.12/19.42	thf(decl_359, type, esk39_2: ($i > $o) > ($i > $o) > $i).
130.12/19.42	thf(decl_360, type, esk40_2: ($i > $o) > ($i > $o) > $i).
130.12/19.42	thf(decl_361, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
130.12/19.42	thf(decl_362, type, esk42_2: ($i > $o) > ($i > $o) > $i).
130.12/19.42	thf(decl_363, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
130.12/19.42	thf(decl_364, type, esk44_2: ($i > $o) > ($i > $o) > $i).
130.12/19.42	thf(decl_365, type, esk45_2: ($i > $o) > $i > $i).
130.12/19.42	thf(decl_366, type, esk46_2: ($i > $o) > ($i > $o) > $i).
130.12/19.42	thf(decl_367, type, esk47_2: ($i > $o) > ($i > $o) > $i).
130.12/19.42	thf(decl_368, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
130.12/19.42	thf(decl_369, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
130.12/19.42	thf(decl_370, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
130.12/19.42	thf(decl_371, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
130.12/19.42	thf(decl_372, type, esk52_2: $i > $i > $i).
130.12/19.42	thf(decl_373, type, esk53_2: $i > $i > $i).
130.12/19.42	thf(decl_374, type, esk54_2: $i > $i > $i).
130.12/19.42	thf(decl_375, type, esk55_3: $i > $i > $i > $i).
130.12/19.42	thf(decl_376, type, esk56_3: $i > $i > $i > $i).
130.12/19.42	thf(decl_377, type, esk57_2: $i > $i > $i).
130.12/19.42	thf(decl_378, type, esk58_2: $i > ($i > $o) > $i).
130.12/19.42	thf(decl_379, type, esk59_2: $i > ($i > $o) > $i).
130.12/19.42	thf(decl_380, type, esk60_2: $i > ($i > $o) > $i).
130.12/19.42	thf(decl_381, type, esk61_3: $i > ($i > $o) > $i > $i).
130.12/19.42	thf(decl_382, type, esk62_2: $i > ($i > $o) > $i).
130.12/19.42	thf(decl_383, type, esk63_2: $i > ($i > $o) > $i).
130.12/19.42	thf(decl_384, type, esk64_3: $i > $i > ($i > $i) > $i).
130.12/19.42	thf(decl_385, type, esk65_3: $i > $i > ($i > $i) > $i).
130.12/19.42	thf(decl_386, type, esk66_3: $i > $i > ($i > $i) > $i).
130.12/19.42	thf(decl_387, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
130.12/19.42	thf(decl_388, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
130.12/19.42	thf(decl_389, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
130.12/19.42	thf(decl_390, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
130.12/19.42	thf(decl_391, type, esk71_4: $i > $i > $i > $i > $i).
130.12/19.42	thf(decl_392, type, esk72_4: $i > $i > $i > $i > $i).
130.12/19.42	thf(decl_393, type, esk73_4: $i > $i > $i > $i > $i).
130.12/19.42	thf(decl_394, type, esk74_4: $i > $i > $i > $i > $i).
130.12/19.42	thf(decl_395, type, esk75_4: $i > $i > $i > $i > $i).
130.12/19.42	thf(decl_396, type, esk76_4: $i > $i > $i > $i > $i).
130.12/19.42	thf(decl_397, type, esk77_4: $i > $i > $i > $i > $i).
130.12/19.42	thf(decl_398, type, esk78_4: $i > $i > $i > $i > $i).
130.12/19.42	thf(decl_399, type, esk79_4: $i > $i > $i > $i > $i).
130.12/19.42	thf(decl_400, type, esk80_3: $i > $i > ($i > $i) > $i).
130.12/19.42	thf(decl_401, type, esk81_3: $i > $i > ($i > $i) > $i).
130.12/19.42	thf(decl_402, type, esk82_3: $i > $i > ($i > $i) > $i).
130.12/19.42	thf(decl_403, type, esk83_3: $i > $i > $i > $i).
130.12/19.42	thf(decl_404, type, esk84_3: $i > $i > $i > $i).
130.12/19.42	thf(decl_405, type, esk85_3: $i > $i > $i > $i).
130.12/19.42	thf(decl_406, type, esk86_3: $i > $i > $i > $i).
130.12/19.42	thf(decl_407, type, esk87_0: $i).
130.12/19.42	thf(decl_408, type, esk88_0: $i).
130.12/19.42	thf(decl_409, type, esk89_0: $i).
130.12/19.42	thf(decl_410, type, esk90_0: $i).
130.12/19.42	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', replAx)).
130.12/19.42	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', exu)).
130.12/19.42	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', descrp)).
130.12/19.42	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', exuE1)).
130.12/19.42	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', exuE3e)).
130.12/19.42	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', nonempty)).
130.12/19.42	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', nonemptyI)).
130.12/19.42	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', exuE2)).
130.12/19.42	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', exuI1)).
130.12/19.42	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', exuI3)).
130.12/19.42	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', exuI2)).
130.12/19.42	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', exuE3u)).
130.12/19.42	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', exu__Cong)).
130.12/19.42	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', exuEu)).
130.12/19.42	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', descr__Cong)).
130.12/19.42	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', ex1E1)).
130.12/19.42	thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', ex1)).
130.12/19.42	thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', ex1I)).
130.12/19.42	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', ex1I2)).
130.12/19.42	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setOfPairsIsBReln)).
130.12/19.42	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', breln)).
130.12/19.42	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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', ex1E2)).
130.12/19.42	thf(intersectInPowersetIntersectUnions, conjecture, ((setextAx)=>(((((setunionAx)=>((((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>(((dsetconstrEL)=>((dsetconstrER)=>((((emptysetE)=>(((((setext)=>((emptyI)=>(((setbeta)=>((nonemptyE1)=>((((((setadjoinIR)=>((setadjoinE)=>((((powersetI)=>((emptyinPowerset)=>((((setunionI)=>((setunionE)=>(((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>(((eqinunit)=>((singletonsswitch)=>(((upairsetIL)=>((upairsetIR)=>(((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>(((((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>(((exuI2)=>((inCongP)=>((in__Cong)=>(((exu__Cong)=>(((setadjoin__Cong)=>((powerset__Cong)=>(((((descr__Cong)=>(((((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>(((((notequalI2)=>(((subsetTrans)=>(((setadjoinSub2)=>(((setextsub)=>(((powersetI1)=>(((inPowerset)=>((((sepSubset)=>((((((((((((binintersectLsub)=>((((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((((bs114d)=>((((((setminusERneg)=>((((setminusIRneg)=>(((setminusSubset1)=>((symdiffE)=>(((symdiffI2)=>((((secondinupair)=>((setukpairIL)=>((setukpairIR)=>(((((singletoninpowerset)=>((((((((ubforcartprodlem3)=>((cartprodpairin)=>(((cartprodmempair)=>((setunionE2)=>(((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>(((ex1I)=>((ex1I2)=>(((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((((setukpairinjL2)=>((setukpairinjL)=>((((setukpairinjR1)=>((upairequniteq)=>(((setukpairinjR)=>((ksndsingleton)=>((((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>(((((dpsetconstrERa)=>(((dpsetconstrEL2)=>((dpsetconstrER)=>(((((infuncsetfunc)=>(((funcinfuncset)=>(((lamp)=>((lam2p)=>(((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>(((((subbreln)=>((eqbreln)=>((funcext)=>(((ap2apEq1)=>(((((((eta2)=>((iffalseProp1)=>(((((ifSingleton)=>(((theeq)=>((iftrue)=>(((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>(((((setextT)=>(((((((((contrasubsetT)=>(((((((doubleComplementSub1)=>(((((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((((complementTcontraSubset)=>((binunionTILcontra)=>(((inIntersectImpInUnion)=>((![X4:$i, X21:$i]:((![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))<=(in @ X21 @ (powerset @ X4))))<=(inIntersectImpInIntersectUnions))<=(inIntersectImpInUnion2)))<=(binunionTIRcontra))))<=(contraSubsetComplement))<=(complementInPowersetComplementIntersect))))<=(complementTnotintersectT))<=(doubleComplementEq))<=(doubleComplementSub2)))<=(doubleComplementE1))<=(doubleComplementI1))<=(contrasubsetT3))<=(contrasubsetT2))<=(contrasubsetT1)))<=(binintersectTERcontra))<=(binintersectTELcontra))<=(complementTE1))<=(complementTI1))<=(powersetTE1))<=(powersetTI1))<=(subsetTI)))<=(complementT_lem))<=(setminusT_lem))<=(powersetT_lem)))))<=(iffalse))))<=(ifp)))<=(iftrueProp2))<=(iftrueProp1))<=(iffalseProp2))))<=(beta2))<=(lam2lamEq))<=(eta1))<=(beta1))<=(ap2apEq2)))<=(funcext2)))))<=(funcGraphProp4))<=(funcextLem))<=(funcGraphProp2))))))<=(brelnall1))))<=(lamProp)))<=(ap2p)))<=(app))<=(apProp))<=(funcImageSingleton))))<=(dpsetconstrEL1)))<=(setOfPairsIsBReln))<=(dpsetconstrSub))<=(dpsetconstrI)))))))))<=(kpairsurjEq))<=(ksndpairEq))))<=(setukpairinjR2))))<=(setukpairinjR12))<=(setukpairinjR11))))<=(cartprodfstin))<=(kfstpairEq)))))<=(singletonsuniq))))<=(ex1E1)))))<=(setunionsingleton1))))<=(cartprodmempair1))))<=(ubforcartprodlem2))<=(ubforcartprodlem1))<=(upairinpowunion))<=(upairsubunion))<=(upairset2E))<=(singletoninpowunion)))<=(singletonsubset))<=(kpairp))<=(kpairiskpair)))))<=(symdiffIneg2))<=(symdiffIneg1)))<=(symdiffI1))))<=(setminusLsub)))<=(setminusILneg))<=(setminusELneg)))<=(setminusSubset2))<=(setminusER))<=(setminusEL))<=(setminusI)))<=(binintersectSubset1))<=(binintersectSubset4)))))<=(binintersectSubset3))<=(binintersectSubset2)))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI))<=(binunionRsub))<=(binunionLsub))<=(binunionE))<=(binunionEcases))<=(binunionIR))<=(upairset2IR))<=(binunionIL)))<=(sepInPowerset))<=(powersetsubset)))<=(powersetE1)))<=(subsetemptysetimpeq)))<=(subset2powerset)))<=(setadjoinSub)))<=(subsetRefl)))<=(notequalI1))<=(notsubsetI))<=(subsetE2))))))<=(eqimpsubset2))<=(subsetI1))<=(dsetconstr__Cong)))<=(exuEu))<=(omega__Cong))<=(setunion__Cong))))<=(emptyset__Cong)))<=(exuE3u)))))<=(exuI3))))))<=(prop2setI))<=(quantDeMorgan4))<=(quantDeMorgan3)))))<=(emptyE1))))<=(upairsetE))))<=(notinsingleton)))))<=(subPowSU))))<=(powersetE))<=(emptyInPowerset))))<=(setoftrueEq))<=(setadjoinOr))))<=(emptyinunitempty))<=(setadjoinIL))<=(nonemptyI1))<=(nonemptyI))))<=(noeltsimpempty))))<=(exuE3e))<=(notinemptyset))<=(emptysetimpfalse)))<=(prop2setE))<=(exuE1))))<=(dsetconstrI)))))))<=(omegaSAx))<=(omega0Ax)))<=(powersetAx))<=(setadjoinAx))<=(emptysetAx))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', intersectInPowersetIntersectUnions)).
130.12/19.42	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', dsetconstrI)).
130.12/19.42	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', dsetconstrEL)).
130.12/19.42	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', dsetconstrER)).
130.12/19.42	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setbeta)).
130.12/19.42	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', nonemptyE1)).
130.12/19.42	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', nonemptyI1)).
130.12/19.42	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setoftrueEq)).
130.12/19.42	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', nonemptyImpWitness)).
130.12/19.42	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', emptyE1)).
130.12/19.42	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', dsetconstr__Cong)).
130.12/19.42	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', sepInPowerset)).
130.12/19.42	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', sepSubset)).
130.12/19.42	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', singletonprop)).
130.12/19.42	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', kfstsingleton)).
130.12/19.42	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', ksndsingleton)).
130.12/19.42	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', dpsetconstrI)).
130.12/19.42	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', dpsetconstrSub)).
130.12/19.42	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', dpsetconstrERa)).
130.12/19.42	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', dpsetconstrEL1)).
130.12/19.42	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', dpsetconstrEL2)).
130.12/19.42	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', dpsetconstrER)).
130.12/19.42	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', funcImageSingleton)).
130.12/19.42	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', apProp)).
130.12/19.42	thf(lamProp, axiom, ((lamProp)<=>![X4:$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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', lamProp)).
130.12/19.42	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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', lamp)).
130.12/19.42	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', lam2p)).
130.12/19.42	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', brelnall1)).
130.12/19.42	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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', brelnall2)).
130.12/19.42	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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', subbreln)).
130.12/19.42	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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', eqbreln)).
130.12/19.42	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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', beta1)).
130.12/19.42	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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', eta1)).
130.12/19.42	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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', lam2lamEq)).
130.12/19.42	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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', beta2)).
130.12/19.42	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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', eta2)).
130.12/19.42	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', iffalseProp1)).
130.12/19.42	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', iffalseProp2)).
130.12/19.42	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', iftrueProp1)).
130.12/19.42	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', iftrueProp2)).
130.12/19.42	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', ifSingleton)).
130.12/19.42	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setextAx)).
130.12/19.42	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', emptysetAx)).
130.12/19.42	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setadjoinAx)).
130.12/19.42	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', powersetAx)).
130.12/19.42	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setunionAx)).
130.12/19.42	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', omega0Ax)).
130.12/19.42	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', omegaSAx)).
130.12/19.42	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', omegaIndAx)).
130.12/19.42	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', foundationAx)).
130.12/19.42	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', wellorderingAx)).
130.12/19.42	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', prop2setE)).
130.12/19.42	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', emptysetE)).
130.12/19.42	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', emptysetimpfalse)).
130.12/19.42	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', notinemptyset)).
130.12/19.42	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setext)).
130.12/19.42	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', emptyI)).
130.12/19.42	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', noeltsimpempty)).
130.12/19.42	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setadjoinIL)).
130.12/19.42	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', emptyinunitempty)).
130.12/19.42	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setadjoinIR)).
130.12/19.42	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setadjoinE)).
130.12/19.42	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setadjoinOr)).
130.12/19.42	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', powersetI)).
130.12/19.42	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', emptyinPowerset)).
130.12/19.42	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', emptyInPowerset)).
130.12/19.42	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', powersetE)).
130.12/19.42	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setunionI)).
130.12/19.42	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setunionE)).
130.12/19.42	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', subPowSU)).
130.12/19.42	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', uniqinunit)).
130.12/19.42	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', notinsingleton)).
130.12/19.42	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', eqinunit)).
130.12/19.42	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', singletonsswitch)).
130.12/19.42	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', upairsetE)).
130.12/19.42	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', upairsetIL)).
130.12/19.42	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', upairsetIR)).
130.12/19.42	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', vacuousDall)).
130.12/19.42	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', quantDeMorgan1)).
130.12/19.42	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', quantDeMorgan2)).
130.12/19.42	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', quantDeMorgan3)).
130.12/19.42	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', quantDeMorgan4)).
130.12/19.42	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', prop2setI)).
130.12/19.42	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', prop2set2propI)).
130.12/19.42	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', notdexE)).
130.12/19.42	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', notdallE)).
130.12/19.42	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', inCongP)).
130.12/19.42	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', in__Cong)).
130.12/19.42	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', emptyset__Cong)).
130.12/19.42	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setadjoin__Cong)).
130.12/19.42	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', powerset__Cong)).
130.12/19.42	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setunion__Cong)).
130.12/19.42	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', omega__Cong)).
130.12/19.42	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', subsetI1)).
130.12/19.42	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', eqimpsubset2)).
130.12/19.42	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', eqimpsubset1)).
130.12/19.42	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', subsetI2)).
130.12/19.42	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', emptysetsubset)).
130.12/19.42	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', subsetE)).
130.12/19.42	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', subsetE2)).
130.12/19.42	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', notsubsetI)).
130.12/19.42	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', notequalI1)).
130.12/19.42	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', notequalI2)).
130.12/19.42	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', subsetRefl)).
130.12/19.42	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', subsetTrans)).
130.12/19.42	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setadjoinSub)).
130.12/19.42	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setadjoinSub2)).
130.12/19.42	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', subset2powerset)).
130.12/19.42	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setextsub)).
130.12/19.42	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', subsetemptysetimpeq)).
130.12/19.42	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', powersetI1)).
130.12/19.42	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', powersetE1)).
130.12/19.42	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', inPowerset)).
130.12/19.42	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', powersetsubset)).
130.12/19.42	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binunionIL)).
130.12/19.42	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', upairset2IR)).
130.12/19.42	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binunionIR)).
130.12/19.42	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binunionEcases)).
130.12/19.42	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binunionE)).
130.12/19.42	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binunionLsub)).
130.12/19.42	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binunionRsub)).
130.12/19.42	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binintersectI)).
130.12/19.42	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binintersectSubset5)).
130.12/19.42	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binintersectEL)).
130.12/19.42	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binintersectLsub)).
130.12/19.42	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binintersectSubset2)).
130.12/19.42	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binintersectSubset3)).
130.12/19.42	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binintersectER)).
130.12/19.42	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', disjointsetsI1)).
130.12/19.42	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binintersectRsub)).
130.12/19.42	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binintersectSubset4)).
130.12/19.42	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binintersectSubset1)).
130.12/19.42	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', bs114d)).
130.12/19.42	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setminusI)).
130.12/19.42	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setminusEL)).
130.12/19.42	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setminusER)).
130.12/19.42	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setminusSubset2)).
130.12/19.42	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setminusERneg)).
130.12/19.42	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setminusELneg)).
130.12/19.42	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setminusILneg)).
130.12/19.42	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setminusIRneg)).
130.12/19.42	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setminusLsub)).
130.12/19.42	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setminusSubset1)).
130.12/19.42	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', symdiffE)).
130.12/19.42	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', symdiffI1)).
130.12/19.42	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', symdiffI2)).
130.12/19.42	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', symdiffIneg1)).
130.12/19.42	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', symdiffIneg2)).
130.12/19.42	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', secondinupair)).
130.12/19.42	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setukpairIL)).
130.12/19.42	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setukpairIR)).
130.12/19.42	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', kpairiskpair)).
130.12/19.42	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', kpairp)).
130.12/19.42	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', singletonsubset)).
130.12/19.42	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', singletoninpowerset)).
130.12/19.42	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', singletoninpowunion)).
130.12/19.42	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', upairset2E)).
130.12/19.42	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', upairsubunion)).
130.12/19.42	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', upairinpowunion)).
130.12/19.42	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', ubforcartprodlem1)).
130.12/19.42	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', ubforcartprodlem2)).
130.12/19.42	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', ubforcartprodlem3)).
130.12/19.42	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', cartprodpairin)).
130.12/19.42	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', cartprodmempair1)).
130.12/19.42	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', cartprodmempair)).
130.12/19.42	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setunionE2)).
130.12/19.42	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setunionsingleton1)).
130.12/19.42	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setunionsingleton2)).
130.12/19.42	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setunionsingleton)).
130.12/19.42	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', singletonsuniq)).
130.12/19.42	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setukpairinjL1)).
130.12/19.42	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', theprop)).
130.12/19.42	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', kfstpairEq)).
130.12/19.42	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', cartprodfstin)).
130.12/19.42	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setukpairinjL2)).
130.12/19.42	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setukpairinjL)).
130.12/19.42	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setukpairinjR11)).
130.12/19.42	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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setukpairinjR12)).
130.12/19.42	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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setukpairinjR1)).
130.12/19.42	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', upairequniteq)).
130.12/19.42	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setukpairinjR2)).
130.12/19.42	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setukpairinjR)).
130.12/19.42	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', ksndpairEq)).
130.12/19.42	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', kpairsurjEq)).
130.12/19.42	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', cartprodsndin)).
130.12/19.42	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', cartprodpairmemEL)).
130.12/19.42	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', cartprodpairmemER)).
130.12/19.42	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', cartprodmempaircEq)).
130.12/19.42	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', cartprodfstpairEq)).
130.12/19.42	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', cartprodsndpairEq)).
130.12/19.42	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', cartprodpairsurjEq)).
130.12/19.42	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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', app)).
130.12/19.42	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', infuncsetfunc)).
130.12/19.42	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', ap2p)).
130.12/19.42	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', funcinfuncset)).
130.12/19.42	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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', funcGraphProp1)).
130.12/19.42	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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', funcGraphProp3)).
130.12/19.42	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', funcGraphProp2)).
130.12/19.42	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', funcextLem)).
130.12/19.42	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', funcGraphProp4)).
130.12/19.42	thf(funcext, axiom, ((funcext)<=>![X4:$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/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', funcext)).
130.12/19.42	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', funcext2)).
130.12/19.42	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', ap2apEq1)).
130.12/19.42	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', ap2apEq2)).
130.12/19.42	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', ifp)).
130.12/19.42	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', theeq)).
130.12/19.42	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', iftrue)).
130.12/19.42	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', iffalse)).
130.12/19.42	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', iftrueorfalse)).
130.12/19.42	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binintersectT_lem)).
130.12/19.42	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binunionT_lem)).
130.12/19.42	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', powersetT_lem)).
130.12/19.42	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setminusT_lem)).
130.12/19.42	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', complementT_lem)).
130.12/19.42	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', setextT)).
130.12/19.42	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', subsetTI)).
130.12/19.42	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', powersetTI1)).
130.12/19.42	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', powersetTE1)).
130.12/19.42	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', complementTI1)).
130.12/19.42	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', complementTE1)).
130.12/19.42	thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binintersectTELcontra)).
130.12/19.42	thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binintersectTERcontra)).
130.12/19.42	thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', contrasubsetT)).
130.12/19.42	thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', contrasubsetT1)).
130.12/19.42	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', contrasubsetT2)).
130.12/19.42	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', contrasubsetT3)).
130.12/19.42	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', doubleComplementI1)).
130.12/19.42	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', doubleComplementE1)).
130.12/19.42	thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', doubleComplementSub1)).
130.12/19.42	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', doubleComplementSub2)).
130.12/19.42	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', doubleComplementEq)).
130.12/19.42	thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', complementTnotintersectT)).
130.12/19.42	thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', complementImpComplementIntersect)).
130.12/19.42	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', complementSubsetComplementIntersect)).
130.12/19.42	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', complementInPowersetComplementIntersect)).
130.12/19.42	thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', contraSubsetComplement)).
130.12/19.42	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', complementTcontraSubset)).
130.12/19.42	thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binunionTILcontra)).
130.12/19.42	thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', binunionTIRcontra)).
130.12/19.42	thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', inIntersectImpInUnion)).
130.12/19.42	thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', inIntersectImpInUnion2)).
130.12/19.42	thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.A2bOKPxGX0/E---3.1_1091427.p', inIntersectImpInIntersectUnions)).
130.12/19.42	thf(c_0_264, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
130.12/19.42	thf(c_0_265, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
130.12/19.42	thf(c_0_266, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
130.12/19.42	thf(c_0_267, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
130.12/19.42	thf(c_0_268, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
130.12/19.42	thf(c_0_269, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
130.12/19.42	thf(c_0_270, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
130.12/19.42	thf(c_0_271, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
130.12/19.42	thf(c_0_272, 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])).
130.12/19.42	thf(c_0_273, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
130.12/19.42	thf(c_0_274, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
130.12/19.42	thf(c_0_275, 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])).
130.12/19.42	thf(c_0_276, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
130.12/19.42	thf(c_0_277, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
130.12/19.42	thf(c_0_278, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
130.12/19.42	thf(c_0_279, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
130.12/19.42	thf(c_0_280, plain, ((ex1)=(^[Z0:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])).
130.12/19.42	thf(c_0_281, 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])).
130.12/19.42	thf(c_0_282, 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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
130.12/19.42	thf(c_0_283, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
130.12/19.42	thf(c_0_284, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
130.12/19.42	thf(c_0_285, 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])).
130.12/19.42	thf(c_0_286, negated_conjecture, ~(((setextAx)=>(((((setunionAx)=>((((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>(((dsetconstrEL)=>((dsetconstrER)=>((((emptysetE)=>(((((setext)=>((emptyI)=>(((setbeta)=>((nonemptyE1)=>((((((setadjoinIR)=>((setadjoinE)=>((((powersetI)=>((emptyinPowerset)=>((((setunionI)=>((setunionE)=>(((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>(((eqinunit)=>((singletonsswitch)=>(((upairsetIL)=>((upairsetIR)=>(((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>(((((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>(((exuI2)=>((inCongP)=>((in__Cong)=>(((exu__Cong)=>(((setadjoin__Cong)=>((powerset__Cong)=>(((((descr__Cong)=>(((((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>(((((notequalI2)=>(((subsetTrans)=>(((setadjoinSub2)=>(((setextsub)=>(((powersetI1)=>(((inPowerset)=>((((sepSubset)=>((((((((((((binintersectLsub)=>((((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((((bs114d)=>((((((setminusERneg)=>((((setminusIRneg)=>(((setminusSubset1)=>((symdiffE)=>(((symdiffI2)=>((((secondinupair)=>((setukpairIL)=>((setukpairIR)=>(((((singletoninpowerset)=>((((((((ubforcartprodlem3)=>((cartprodpairin)=>(((cartprodmempair)=>((setunionE2)=>(((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>(((ex1I)=>((ex1I2)=>(((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((((setukpairinjL2)=>((setukpairinjL)=>((((setukpairinjR1)=>((upairequniteq)=>(((setukpairinjR)=>((ksndsingleton)=>((((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>(((((dpsetconstrERa)=>(((dpsetconstrEL2)=>((dpsetconstrER)=>(((((infuncsetfunc)=>(((funcinfuncset)=>(((lamp)=>((lam2p)=>(((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>(((((subbreln)=>((eqbreln)=>((funcext)=>(((ap2apEq1)=>(((((((eta2)=>((iffalseProp1)=>(((((ifSingleton)=>(((theeq)=>((iftrue)=>(((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>(((((setextT)=>(((((((((contrasubsetT)=>(((((((doubleComplementSub1)=>(((((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((((complementTcontraSubset)=>((binunionTILcontra)=>(((inIntersectImpInUnion)=>((![X4:$i, X21:$i]:((![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))<=(in @ X21 @ (powerset @ X4))))<=(inIntersectImpInIntersectUnions))<=(inIntersectImpInUnion2)))<=(binunionTIRcontra))))<=(contraSubsetComplement))<=(complementInPowersetComplementIntersect))))<=(complementTnotintersectT))<=(doubleComplementEq))<=(doubleComplementSub2)))<=(doubleComplementE1))<=(doubleComplementI1))<=(contrasubsetT3))<=(contrasubsetT2))<=(contrasubsetT1)))<=(binintersectTERcontra))<=(binintersectTELcontra))<=(complementTE1))<=(complementTI1))<=(powersetTE1))<=(powersetTI1))<=(subsetTI)))<=(complementT_lem))<=(setminusT_lem))<=(powersetT_lem)))))<=(iffalse))))<=(ifp)))<=(iftrueProp2))<=(iftrueProp1))<=(iffalseProp2))))<=(beta2))<=(lam2lamEq))<=(eta1))<=(beta1))<=(ap2apEq2)))<=(funcext2)))))<=(funcGraphProp4))<=(funcextLem))<=(funcGraphProp2))))))<=(brelnall1))))<=(lamProp)))<=(ap2p)))<=(app))<=(apProp))<=(funcImageSingleton))))<=(dpsetconstrEL1)))<=(setOfPairsIsBReln))<=(dpsetconstrSub))<=(dpsetconstrI)))))))))<=(kpairsurjEq))<=(ksndpairEq))))<=(setukpairinjR2))))<=(setukpairinjR12))<=(setukpairinjR11))))<=(cartprodfstin))<=(kfstpairEq)))))<=(singletonsuniq))))<=(ex1E1)))))<=(setunionsingleton1))))<=(cartprodmempair1))))<=(ubforcartprodlem2))<=(ubforcartprodlem1))<=(upairinpowunion))<=(upairsubunion))<=(upairset2E))<=(singletoninpowunion)))<=(singletonsubset))<=(kpairp))<=(kpairiskpair)))))<=(symdiffIneg2))<=(symdiffIneg1)))<=(symdiffI1))))<=(setminusLsub)))<=(setminusILneg))<=(setminusELneg)))<=(setminusSubset2))<=(setminusER))<=(setminusEL))<=(setminusI)))<=(binintersectSubset1))<=(binintersectSubset4)))))<=(binintersectSubset3))<=(binintersectSubset2)))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI))<=(binunionRsub))<=(binunionLsub))<=(binunionE))<=(binunionEcases))<=(binunionIR))<=(upairset2IR))<=(binunionIL)))<=(sepInPowerset))<=(powersetsubset)))<=(powersetE1)))<=(subsetemptysetimpeq)))<=(subset2powerset)))<=(setadjoinSub)))<=(subsetRefl)))<=(notequalI1))<=(notsubsetI))<=(subsetE2))))))<=(eqimpsubset2))<=(subsetI1))<=(dsetconstr__Cong)))<=(exuEu))<=(omega__Cong))<=(setunion__Cong))))<=(emptyset__Cong)))<=(exuE3u)))))<=(exuI3))))))<=(prop2setI))<=(quantDeMorgan4))<=(quantDeMorgan3)))))<=(emptyE1))))<=(upairsetE))))<=(notinsingleton)))))<=(subPowSU))))<=(powersetE))<=(emptyInPowerset))))<=(setoftrueEq))<=(setadjoinOr))))<=(emptyinunitempty))<=(setadjoinIL))<=(nonemptyI1))<=(nonemptyI))))<=(noeltsimpempty))))<=(exuE3e))<=(notinemptyset))<=(emptysetimpfalse)))<=(prop2setE))<=(exuE1))))<=(dsetconstrI)))))))<=(omegaSAx))<=(omega0Ax)))<=(powersetAx))<=(setadjoinAx))<=(emptysetAx)))), inference(assume_negation,[status(cth)],[intersectInPowersetIntersectUnions])).
130.12/19.42	thf(c_0_287, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X864:$i]:(((((X6 @ X2 @ X864)))&(![X865:$i]:(((((X6 @ X2 @ X865)))=>(((X864)=(X865)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_264, c_0_265])).
130.12/19.42	thf(c_0_288, plain, ((descrp)=(![X1:$i > $o]:((((?[X866:$i]:(((((X1 @ X866)))&(![X867:$i]:(((((X1 @ X867)))=>(((X866)=(X867))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_266, c_0_265])).
130.12/19.42	thf(c_0_289, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
130.12/19.42	thf(c_0_290, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
130.12/19.42	thf(c_0_291, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
130.12/19.42	thf(c_0_292, plain, ((exuE1)=(![X1:$i > $o]:((((?[X868:$i]:(((((X1 @ X868)))&(![X869:$i]:(((((X1 @ X869)))=>(((X868)=(X869))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_267, c_0_265])).
130.12/19.42	thf(c_0_293, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X870:$i]:(((((X1 @ X870)))&(![X871:$i]:(((((X1 @ X871)))=>(((X870)=(X871))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_268, c_0_265])).
130.12/19.42	thf(c_0_294, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
130.12/19.42	thf(c_0_295, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_269])).
130.12/19.42	thf(c_0_296, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_270, c_0_269])).
130.12/19.42	thf(c_0_297, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_269])).
130.12/19.42	thf(c_0_298, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
130.12/19.42	thf(c_0_299, plain, ((exuE2)=(![X1:$i > $o]:((((?[X872:$i]:(((((X1 @ X872)))&(![X873:$i]:(((((X1 @ X873)))=>(((X872)=(X873))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_271, c_0_265])).
130.12/19.42	thf(c_0_300, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_269])).
130.12/19.42	thf(c_0_301, 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])).
130.12/19.42	thf(c_0_302, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X874:$i]:(((((X1 @ X874)))&(![X875:$i]:(((((X1 @ X875)))=>(((X874)=(X875)))))))))))))), inference(apply_def,[status(thm)],[c_0_272, c_0_265])).
130.12/19.42	thf(c_0_303, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X876:$i]:(((((X1 @ X876)))&(![X877:$i]:(((((X1 @ X877)))=>(((X876)=(X877)))))))))))))))), inference(apply_def,[status(thm)],[c_0_273, c_0_265])).
130.12/19.42	thf(c_0_304, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X878:$i]:(((((X1 @ X878)))&(![X879:$i]:(((((X1 @ X879)))=>(((X878)=(X879)))))))))))))), inference(apply_def,[status(thm)],[c_0_274, c_0_265])).
130.12/19.42	thf(c_0_305, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X880:$i]:(((((X1 @ X880)))&(![X881:$i]:(((((X1 @ X881)))=>(((X880)=(X881))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_275, c_0_265])).
130.12/19.42	thf(c_0_306, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X882:$i]:(((((X1 @ X882)))&(![X883:$i]:(((((X1 @ X883)))=>(((X882)=(X883))))))))))<=>((?[X884:$i]:(((((X17 @ X884)))&(![X885:$i]:(((((X17 @ X885)))=>(((X884)=(X885)))))))))))))))), inference(apply_def,[status(thm)],[c_0_276, c_0_265])).
130.12/19.42	thf(c_0_307, plain, ((exuEu)=(![X1:$i > $o]:((((?[X886:$i]:(((((X1 @ X886)))&(![X887:$i]:(((((X1 @ X887)))=>(((X886)=(X887))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_277, c_0_265])).
130.12/19.42	thf(c_0_308, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X888:$i]:(((((X1 @ X888)))&(![X889:$i]:(((((X1 @ X889)))=>(((X888)=(X889))))))))))=>((((?[X890:$i]:(((((X17 @ X890)))&(![X891:$i]:(((((X17 @ X891)))=>(((X890)=(X891))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_278, c_0_265])).
130.12/19.42	thf(c_0_309, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
130.12/19.42	thf(c_0_310, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
130.12/19.42	thf(c_0_311, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
130.12/19.42	thf(c_0_312, 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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
130.12/19.42	thf(c_0_313, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((((singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:(((X1 @ Z0))))))))=>(?[X2:$i]:((((in @ X2 @ X4))&((X1 @ X2))))))))), inference(apply_def,[status(thm)],[c_0_279, c_0_280])).
130.12/19.42	thf(c_0_314, plain, ((ex1I)=(![X4:$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_281, c_0_280])).
130.12/19.42	thf(c_0_315, 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:$i]:(((X1 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_282, c_0_280])).
130.12/19.42	thf(c_0_316, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
130.12/19.42	thf(c_0_317, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
130.12/19.42	thf(c_0_318, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
130.12/19.42	thf(c_0_319, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
130.12/19.42	thf(c_0_320, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_283, c_0_284])).
130.12/19.42	thf(c_0_321, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
130.12/19.42	thf(c_0_322, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
130.12/19.42	thf(c_0_323, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
130.12/19.42	thf(c_0_324, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
130.12/19.42	thf(c_0_325, plain, ((funcImageSingleton)<=>![X4:$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])).
130.12/19.42	thf(c_0_326, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
130.12/19.42	thf(c_0_327, plain, ((lamProp)<=>![X4:$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])).
130.12/19.42	thf(c_0_328, 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:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
130.12/19.42	thf(c_0_329, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
130.12/19.42	thf(c_0_330, axiom, ((brelnall1)=(![X4:$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_284])).
130.12/19.42	thf(c_0_331, 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_284])).
130.12/19.42	thf(c_0_332, 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_285, c_0_280])).
130.12/19.42	thf(c_0_333, 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_284])).
130.12/19.42	thf(c_0_334, 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_284])).
130.12/19.42	thf(c_0_335, 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])).
130.12/19.42	thf(c_0_336, 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])).
130.12/19.42	thf(c_0_337, 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])).
130.12/19.42	thf(c_0_338, 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])).
130.12/19.42	thf(c_0_339, 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])).
130.12/19.42	thf(c_0_340, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
130.12/19.42	thf(c_0_341, plain, ((iffalseProp2)<=>![X4:$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])).
130.12/19.42	thf(c_0_342, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
130.12/19.42	thf(c_0_343, plain, ((iftrueProp2)<=>![X4:$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])).
130.12/19.42	thf(c_0_344, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
130.12/19.42	thf(c_0_345, plain, ((epred1_0)<=>![X913:$i]:(?[X914:$i]:((((![X915:$i]:(((in @ X915 @ X914)=>![X916:$i]:(((in @ X916 @ X915)=>(in @ X916 @ X913)))))&![X917:$i, X918:$i]:((((in @ X917 @ X913)&(in @ X918 @ X913))=>(![X919:$i]:(((in @ X919 @ X914)=>((in @ X917 @ X919)<=>(in @ X918 @ X919))))=>((X917)=(X918))))))&![X920:$i, X921:$i]:((((in @ X920 @ X914)&(in @ X921 @ X914))=>(![X922:$i]:(((in @ X922 @ X920)=>(in @ X922 @ X921)))|![X923:$i]:(((in @ X923 @ X921)=>(in @ X923 @ X920)))))))&![X924:$i]:(((![X925:$i]:(((in @ X925 @ X924)=>(in @ X925 @ X913)))&?[X926:$i]:((in @ X926 @ X924)))=>?[X927:$i, X928:$i]:(((((in @ X927 @ X914)&(in @ X928 @ X924))&~(?[X929:$i]:(((in @ X929 @ X927)&(in @ X929 @ X924)))))&![X930:$i]:(((in @ X930 @ X914)=>(![X931:$i]:(((in @ X931 @ X930)=>(in @ X931 @ X927)))|(in @ X928 @ X930)))))))))))), introduced(definition)).
130.12/19.42	thf(c_0_346, negated_conjecture, ~((![X892:$i, X893:$i]:((![X894:$i]:(((in @ X894 @ X892)<=>(in @ X894 @ X893)))=>((X892)=(X893))))=>(![X1729:$i]:(~(in @ X1729 @ emptyset))=>(![X1726:$i, X1727:$i, X1728:$i]:(((in @ X1728 @ (setadjoin @ X1726 @ X1727))<=>(((X1728)=(X1726))|(in @ X1728 @ X1727))))=>(![X1723:$i, X1724:$i]:(((in @ X1724 @ (powerset @ X1723))<=>![X1725:$i]:(((in @ X1725 @ X1724)=>(in @ X1725 @ X1723)))))=>(![X895:$i, X896:$i]:(((in @ X896 @ (setunion @ X895))<=>?[X897:$i]:(((in @ X896 @ X897)&(in @ X897 @ X895)))))=>((in @ emptyset @ omega)=>(![X1722:$i]:(((in @ X1722 @ omega)=>(in @ (setadjoin @ X1722 @ X1722) @ omega)))=>(![X898:$i]:((((in @ emptyset @ X898)&![X899:$i]:((((in @ X899 @ omega)&(in @ X899 @ X898))=>(in @ (setadjoin @ X899 @ X899) @ X898))))=>![X900:$i]:(((in @ X900 @ omega)=>(in @ X900 @ X898)))))=>(![X901:$i > $i > $o, X902:$i]:((![X903:$i]:(((in @ X903 @ X902)=>?[X904:$i]:(((X901 @ X903 @ X904)&![X905:$i]:(((X901 @ X903 @ X905)=>((X904)=(X905))))))))=>?[X906:$i]:(![X907:$i]:(((in @ X907 @ X906)<=>?[X908:$i]:(((in @ X908 @ X902)&(X901 @ X908 @ X907))))))))=>(![X909:$i]:((?[X910:$i]:((in @ X910 @ X909))=>?[X911:$i]:(((in @ X911 @ X909)&~(?[X912:$i]:(((in @ X912 @ X911)&(in @ X912 @ X909))))))))=>((epred1_0)=>(![X932:$i > $o]:((?[X933:$i]:(((X932 @ X933)&![X934:$i]:(((X932 @ X934)=>((X933)=(X934))))))=>(X932 @ (descr @ (^[Z0:$i]:(X932 @ Z0))))))=>(![X1719:$i, X1720:$i > $o, X1721:$i]:(((in @ X1721 @ X1719)=>((X1720 @ X1721)=>(in @ X1721 @ (dsetconstr @ X1719 @ X1720)))))=>(![X935:$i, X936:$i > $o, X937:$i]:(((in @ X937 @ (dsetconstr @ X935 @ X936))=>(in @ X937 @ X935)))=>(![X938:$i, X939:$i > $o, X940:$i]:(((in @ X940 @ (dsetconstr @ X938 @ X939))=>(X939 @ X940)))=>(![X1714:$i > $o]:((?[X1715:$i]:(((X1714 @ X1715)&![X1716:$i]:(((X1714 @ X1716)=>((X1715)=(X1716))))))=>?[X1717:$i]:(((X1714 @ X1717)&![X1718:$i]:(((X1714 @ X1718)=>((X1717)=(X1718))))))))=>(![X1712:$o, X1713:$i]:(((in @ X1713 @ (prop2set @ ((X1712))))=>(X1712)))=>(![X941:$i]:(((in @ X941 @ emptyset)=>![X942:$o]:((X942))))=>(![X1711:$i]:(((in @ X1711 @ emptyset)=>~($true)))=>(![X1710:$i]:(~(in @ X1710 @ emptyset))=>(![X1706:$i > $o]:((?[X1707:$i]:(((X1706 @ X1707)&![X1708:$i]:(((X1706 @ X1708)=>((X1707)=(X1708))))))=>?[X1709:$i]:((X1706 @ X1709))))=>(![X943:$i, X944:$i]:((![X945:$i]:(((in @ X945 @ X943)=>(in @ X945 @ X944)))=>(![X946:$i]:(((in @ X946 @ X944)=>(in @ X946 @ X943)))=>((X943)=(X944)))))=>(![X947:$i]:((![X948:$i]:(~(in @ X948 @ X947))=>((X947)=(emptyset))))=>(![X1704:$i]:((![X1705:$i]:(~(in @ X1705 @ X1704))=>((X1704)=(emptyset))))=>(![X949:$i, X950:$i > $o, X951:$i]:(((in @ X951 @ X949)=>((in @ X951 @ (dsetconstr @ X949 @ X950))<=>(X950 @ X951))))=>(![X952:$i]:((((X952)!=(emptyset))=>?[X953:$i]:((in @ X953 @ X952))))=>(![X1701:$i, X1702:$i > $o, X1703:$i]:(((in @ X1703 @ X1701)=>((X1702 @ X1703)=>((dsetconstr @ X1701 @ X1702)!=(emptyset)))))=>(![X1699:$i]:((?[X1700:$i]:((in @ X1700 @ X1699))=>((X1699)!=(emptyset))))=>(![X1697:$i, X1698:$i]:((in @ X1697 @ (setadjoin @ X1697 @ X1698)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X954:$i, X955:$i, X956:$i]:(((in @ X956 @ X955)=>(in @ X956 @ (setadjoin @ X954 @ X955))))=>(![X957:$i, X958:$i, X959:$i]:(((in @ X959 @ (setadjoin @ X957 @ X958))=>![X960:$o]:(((((X959)=(X957))=>(X960))=>(((in @ X959 @ X958)=>(X960))=>(X960))))))=>(![X1694:$i, X1695:$i, X1696:$i]:(((in @ X1696 @ (setadjoin @ X1694 @ X1695))=>(((X1696)=(X1694))|(in @ X1696 @ X1695))))=>(![X1693:$i]:(((dsetconstr @ X1693 @ (^[Z0:$i]:($true)))=(X1693)))=>(![X961:$i, X962:$i]:((![X963:$i]:(((in @ X963 @ X962)=>(in @ X963 @ X961)))=>(in @ X962 @ (powerset @ X961))))=>(![X964:$i]:((in @ emptyset @ (powerset @ X964)))=>(![X1692:$i]:((in @ emptyset @ (powerset @ X1692)))=>(![X1689:$i, X1690:$i, X1691:$i]:(((in @ X1690 @ (powerset @ X1689))=>((in @ X1691 @ X1690)=>(in @ X1691 @ X1689))))=>(![X965:$i, X966:$i, X967:$i]:(((in @ X966 @ X967)=>((in @ X967 @ X965)=>(in @ X966 @ (setunion @ X965)))))=>(![X968:$i, X969:$i]:(((in @ X969 @ (setunion @ X968))=>![X970:$o]:((![X971:$i]:(((in @ X969 @ X971)=>((in @ X971 @ X968)=>(X970))))=>(X970)))))=>(![X1687:$i, X1688:$i]:(((in @ X1688 @ X1687)=>(in @ X1688 @ (powerset @ (setunion @ X1687)))))=>(![X972:$i > $o]:((?[X973:$i]:(((X972 @ X973)&![X974:$i]:(((X972 @ X974)=>((X973)=(X974))))))=>?[X975:$i]:(![X976:$i]:(((X972 @ X976)<=>((X976)=(X975)))))))=>(![X977:$i]:((((X977)!=(emptyset))=>?[X978:$i]:(((in @ X978 @ X977)&$true))))=>(![X979:$i, X980:$i]:(((in @ X979 @ (setadjoin @ X980 @ emptyset))=>((X979)=(X980))))=>(![X1685:$i, X1686:$i]:((((X1685)!=(X1686))=>~(in @ X1686 @ (setadjoin @ X1685 @ emptyset))))=>(![X981:$i, X982:$i]:((((X981)=(X982))=>(in @ X981 @ (setadjoin @ X982 @ emptyset))))=>(![X983:$i, X984:$i]:(((in @ X983 @ (setadjoin @ X984 @ emptyset))=>(in @ X984 @ (setadjoin @ X983 @ emptyset))))=>(![X1682:$i, X1683:$i, X1684:$i]:(((in @ X1684 @ (setadjoin @ X1682 @ (setadjoin @ X1683 @ emptyset)))=>(((X1684)=(X1682))|((X1684)=(X1683)))))=>(![X985:$i, X986:$i]:((in @ X985 @ (setadjoin @ X985 @ (setadjoin @ X986 @ emptyset))))=>(![X987:$i, X988:$i]:((in @ X988 @ (setadjoin @ X987 @ (setadjoin @ X988 @ emptyset))))=>(![X1679:$i, X1680:$i > $o]:((?[X1681:$i]:(((in @ X1681 @ X1679)&(X1680 @ X1681)))=>(((dsetconstr @ X1679 @ X1680)=(emptyset))=>~($true))))=>(![X989:$i > $o, X990:$i]:(((in @ X990 @ emptyset)=>(X989 @ X990)))=>(![X991:$i, X992:$i > $o]:((~(![X993:$i]:(((in @ X993 @ X991)=>(X992 @ X993))))=>?[X994:$i]:(((in @ X994 @ X991)&~((X992 @ X994))))))=>(![X995:$i, X996:$i > $o]:((![X997:$i]:(((in @ X997 @ X995)=>~((X996 @ X997))))=>~(?[X998:$i]:(((in @ X998 @ X995)&(X996 @ X998))))))=>(![X1675:$i, X1676:$i > $o]:((~(?[X1677:$i]:(((in @ X1677 @ X1675)&(X1676 @ X1677))))=>![X1678:$i]:(((in @ X1678 @ X1675)=>~((X1676 @ X1678))))))=>(![X1671:$i, X1672:$i > $o]:((?[X1673:$i]:(((in @ X1673 @ X1671)&~((X1672 @ X1673))))=>~(![X1674:$i]:(((in @ X1674 @ X1671)=>(X1672 @ X1674))))))=>(![X1670:$o]:(((X1670)=>(in @ emptyset @ (prop2set @ ((X1670))))))=>(![X999:$o]:(((X999)=>(set2prop @ (prop2set @ ((X999))))))=>(![X1000:$i, X1001:$i > $o]:((~(?[X1002:$i]:(((in @ X1002 @ X1000)&(X1001 @ X1002))))=>![X1003:$i]:(((in @ X1003 @ X1000)=>~((X1001 @ X1003))))))=>(![X1004:$i, X1005:$i > $o]:((~(![X1006:$i]:(((in @ X1006 @ X1004)=>(X1005 @ X1006))))=>?[X1007:$i]:(((in @ X1007 @ X1004)&~((X1005 @ X1007))))))=>(![X1008:$i > $o]:((?[X1009:$i]:(((X1008 @ X1009)&![X1010:$i]:(((X1008 @ X1010)=>((X1009)=(X1010))))))=>?[X1011:$i]:(((X1008 @ X1011)&![X1012:$i]:(((X1008 @ X1012)=>((X1011)=(X1012))))))))=>(![X1664:$i > $o]:((?[X1665:$i]:((X1664 @ X1665))=>(![X1666:$i, X1667:$i]:(((X1664 @ X1666)=>((X1664 @ X1667)=>((X1666)=(X1667)))))=>?[X1668:$i]:(((X1664 @ X1668)&![X1669:$i]:(((X1664 @ X1669)=>((X1668)=(X1669)))))))))=>(![X1013:$i > $o]:((?[X1014:$i]:(![X1015:$i]:(((X1013 @ X1015)<=>((X1015)=(X1014)))))=>?[X1016:$i]:(((X1013 @ X1016)&![X1017:$i]:(((X1013 @ X1017)=>((X1016)=(X1017))))))))=>(![X1018:$i, X1019:$i]:((((X1018)=(X1019))=>![X1020:$i, X1021:$i]:((((X1020)=(X1021))=>((in @ X1020 @ X1018)=>(in @ X1021 @ X1019))))))=>(![X1022:$i, X1023:$i]:((((X1022)=(X1023))=>![X1024:$i, X1025:$i]:((((X1024)=(X1025))=>((in @ X1024 @ X1022)<=>(in @ X1025 @ X1023))))))=>(![X1659:$i > $o]:((?[X1660:$i]:(((X1659 @ X1660)&![X1661:$i]:(((X1659 @ X1661)=>((X1660)=(X1661))))))=>![X1662:$i, X1663:$i]:(((X1659 @ X1662)=>((X1659 @ X1663)=>((X1662)=(X1663)))))))=>(![X1026:$i > $o, X1027:$i > $o]:((![X1028:$i, X1029:$i]:((((X1028)=(X1029))=>((X1026 @ X1028)<=>(X1027 @ X1029))))=>(?[X1030:$i]:(((X1026 @ X1030)&![X1031:$i]:(((X1026 @ X1031)=>((X1030)=(X1031))))))<=>?[X1032:$i]:(((X1027 @ X1032)&![X1033:$i]:(((X1027 @ X1033)=>((X1032)=(X1033)))))))))=>(((emptyset)=(emptyset))=>(![X1034:$i, X1035:$i]:((((X1034)=(X1035))=>![X1036:$i, X1037:$i]:((((X1036)=(X1037))=>((setadjoin @ X1034 @ X1036)=(setadjoin @ X1035 @ X1037))))))=>(![X1038:$i, X1039:$i]:((((X1038)=(X1039))=>((powerset @ X1038)=(powerset @ X1039))))=>(![X1657:$i, X1658:$i]:((((X1657)=(X1658))=>((setunion @ X1657)=(setunion @ X1658))))=>(((omega)=(omega))=>(![X1652:$i > $o]:((?[X1653:$i]:(((X1652 @ X1653)&![X1654:$i]:(((X1652 @ X1654)=>((X1653)=(X1654))))))=>![X1655:$i, X1656:$i]:(((X1652 @ X1655)=>((X1652 @ X1656)=>((X1655)=(X1656)))))))=>(![X1040:$i > $o, X1041:$i > $o]:((![X1042:$i, X1043:$i]:((((X1042)=(X1043))=>((X1040 @ X1042)<=>(X1041 @ X1043))))=>(?[X1044:$i]:(((X1040 @ X1044)&![X1045:$i]:(((X1040 @ X1045)=>((X1044)=(X1045))))))=>(?[X1046:$i]:(((X1041 @ X1046)&![X1047:$i]:(((X1041 @ X1047)=>((X1046)=(X1047))))))=>((descr @ X1040)=(descr @ X1041))))))=>(![X1646:$i, X1647:$i]:((((X1646)=(X1647))=>![X1648:$i > $o, X1649:$i > $o]:((![X1650:$i]:(((in @ X1650 @ X1646)=>![X1651:$i]:(((in @ X1651 @ X1647)=>(((X1650)=(X1651))=>((X1648 @ X1650)<=>(X1649 @ X1651)))))))=>((dsetconstr @ X1646 @ X1648)=(dsetconstr @ X1647 @ X1649))))))=>(![X1643:$i, X1644:$i]:((![X1645:$i]:(((in @ X1645 @ X1643)=>(in @ X1645 @ X1644)))=>(subset @ X1643 @ X1644)))=>(![X1641:$i, X1642:$i]:((((X1641)=(X1642))=>(subset @ X1642 @ X1641)))=>(![X1048:$i, X1049:$i]:((((X1048)=(X1049))=>(subset @ X1048 @ X1049)))=>(![X1050:$i, X1051:$i]:((![X1052:$i]:(((in @ X1052 @ X1050)=>(in @ X1052 @ X1051)))=>(subset @ X1050 @ X1051)))=>(![X1053:$i]:((subset @ emptyset @ X1053))=>(![X1054:$i, X1055:$i, X1056:$i]:(((subset @ X1054 @ X1055)=>((in @ X1056 @ X1054)=>(in @ X1056 @ X1055))))=>(![X1638:$i, X1639:$i, X1640:$i]:(((subset @ X1638 @ X1639)=>(~(in @ X1640 @ X1639)=>~(in @ X1640 @ X1638))))=>(![X1635:$i, X1636:$i, X1637:$i]:(((in @ X1637 @ X1635)=>(~(in @ X1637 @ X1636)=>~(subset @ X1635 @ X1636))))=>(![X1633:$i, X1634:$i]:((~(subset @ X1633 @ X1634)=>((X1633)!=(X1634))))=>(![X1057:$i, X1058:$i, X1059:$i]:(((in @ X1059 @ X1057)=>(~(in @ X1059 @ X1058)=>((X1057)!=(X1058)))))=>(![X1632:$i]:((subset @ X1632 @ X1632))=>(![X1060:$i, X1061:$i, X1062:$i]:(((subset @ X1060 @ X1061)=>((subset @ X1061 @ X1062)=>(subset @ X1060 @ X1062))))=>(![X1630:$i, X1631:$i]:((subset @ X1631 @ (setadjoin @ X1630 @ X1631)))=>(![X1063:$i, X1064:$i, X1065:$i]:(((subset @ X1063 @ X1065)=>(subset @ X1063 @ (setadjoin @ X1064 @ X1065))))=>(![X1628:$i, X1629:$i]:(((subset @ X1628 @ X1629)=>(in @ X1628 @ (powerset @ X1629))))=>(![X1066:$i, X1067:$i]:(((subset @ X1066 @ X1067)=>((subset @ X1067 @ X1066)=>((X1066)=(X1067)))))=>(![X1627:$i]:(((subset @ X1627 @ emptyset)=>((X1627)=(emptyset))))=>(![X1068:$i, X1069:$i]:(((subset @ X1069 @ X1068)=>(in @ X1069 @ (powerset @ X1068))))=>(![X1625:$i, X1626:$i]:(((in @ X1626 @ (powerset @ X1625))=>(subset @ X1626 @ X1625)))=>(![X1070:$i]:((in @ X1070 @ (powerset @ X1070)))=>(![X1623:$i, X1624:$i]:(((subset @ X1623 @ X1624)=>(subset @ (powerset @ X1623) @ (powerset @ X1624))))=>(![X1621:$i, X1622:$i > $o]:((in @ (dsetconstr @ X1621 @ X1622) @ (powerset @ X1621)))=>(![X1071:$i, X1072:$i > $o]:((subset @ (dsetconstr @ X1071 @ X1072) @ 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inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_286, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_287]), foundationAx]), wellorderingAx]), c_0_288]), c_0_289]), c_0_290]), c_0_291]), c_0_292]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_293]), setext]), emptyI]), noeltsimpempty]), c_0_294]), c_0_295]), c_0_296]), c_0_297]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_298]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_299]), c_0_300]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_301]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_302]), c_0_303]), c_0_304]), inCongP]), in__Cong]), c_0_305]), c_0_306]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_307]), c_0_308]), c_0_309]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_310]), c_0_311]), 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_312]), c_0_313]), c_0_314]), c_0_315]), singletonsuniq]), setukpairinjL1]), c_0_316]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_317]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_318]), c_0_319]), c_0_320]), c_0_321]), c_0_322]), c_0_323]), c_0_324]), c_0_325]), c_0_326]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_327]), c_0_328]), c_0_329]), c_0_330]), c_0_331]), c_0_332]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_333]), c_0_334]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_335]), c_0_336]), c_0_337]), c_0_338]), c_0_339]), c_0_340]), c_0_341]), c_0_342]), c_0_343]), c_0_344]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions])])]), c_0_345])).
130.12/19.42	thf(c_0_347, negated_conjecture, ![X1730:$i, X1731:$i, X1733:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1743:$i, X1744:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1752:$i, X1753:$i > $i > $o, X1754:$i, X1756:$i, X1759:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1766:$i, X1767:$i > $o, X1768:$i, X1770:$i, X1771:$i > $o, X1772:$i, X1773:$i, X1774:$i > $o, X1775:$i, X1776:$i, X1777:$i > $o, X1778:$i, X1779:$i > $o, X1780:$i, X1783:$i, X1784:$o, X1785:$i, X1786:$i, X1787:$o, X1788:$i, X1789:$i, X1790:$i > $o, X1791:$i, X1794:$i, X1795:$i, X1798:$i, X1800:$i, X1802:$i, X1803:$i > $o, X1804:$i, X1805:$i, X1807:$i, X1808:$i > $o, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$o, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$o, X1840:$i, X1841:$i, X1842:$i > $o, X1843:$i, X1846:$i, X1847:$i, X1848:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i > $o, X1867:$i, X1868:$i > $o, X1869:$i, X1870:$i, X1871:$i > $o, X1872:$i, X1874:$i, X1875:$i > $o, X1877:$i, X1878:$i, X1879:$i > $o, X1881:$i, X1882:$i, X1883:$i > $o, X1884:$i, X1886:$o, X1887:$o, X1888:$i, X1889:$i > $o, X1891:$i, X1892:$i, X1893:$i > $o, X1894:$i, X1896:$i > $o, X1897:$i, X1900:$i, X1901:$i > $o, X1902:$i, X1906:$i, X1907:$i > $o, X1908:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i > $o, X1921:$i, X1923:$i, X1924:$i, X1925:$i > $o, X1926:$i > $o, X1929:$i, X1932:$i, X1933:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i > $o, X1946:$i, X1948:$i, X1949:$i, X1950:$i > $o, X1951:$i > $o, X1954:$i, X1956:$i, X1958:$i, X1959:$i, X1960:$i > $o, X1961:$i > $o, X1964:$i, X1965:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i > $o, X2012:$i, X2013:$i > $o, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$o, X2026:$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, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$o, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i > $o, X2168:$i, X2169:$i, X2170:$i > $o, X2172:$i, X2173:$i > $o, X2174:$i, X2176:$i, X2177:$i > $o, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i > $i > $o, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i > $i > $o, X2258:$i, X2259:$i, X2260:$i > $i > $o, X2261:$i, X2262:$i, X2263:$i > $i > $o, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i > $i > $o, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i > $i > $o, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i > $i > $o, X2279:$i, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i > $i, X2307:$i, X2308:$i, X2309:$i > $i, X2311:$i, X2312:$i, X2313:$i > $i, X2315:$i, X2316:$i, X2317:$i, X2318:$i > $o, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i > $o, X2328:$i, X2329:$i, X2330:$i > $o, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i, X2360:$i, X2361:$i, X2364:$i, X2365:$i, X2366:$i, X2367:$i, X2372:$i, X2373:$i, X2374:$i, X2375:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2382:$i, X2383:$i, X2384:$i, X2385:$i, X2386:$i, X2387:$i, X2388:$i, X2389:$i, X2390:$i, X2391:$i, X2392:$i > $i, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i > $i, X2402:$i, X2403:$i, X2404:$i > $i, X2406:$i, X2407:$i, X2408:$i, X2409:$i, X2410:$i, X2411:$o, X2412:$i, X2413:$i, X2414:$i, X2415:$o, X2416:$i, X2417:$i, X2418:$i, X2419:$o, X2420:$i, X2421:$i, X2422:$i, X2423:$o, X2424:$i, X2425:$i, X2426:$i, X2427:$o, X2428:$i, X2429:$i, X2430:$i, X2431:$o, X2432:$i, X2433:$i, X2434:$i, X2435:$i, X2436:$i, X2437:$o, X2438:$i, X2439:$i, X2440:$i, X2441:$o, X2442:$i, X2443:$i, X2444:$i, X2445:$o, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$i, X2455:$i, X2456:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i, X2463:$i, X2466:$i, X2467:$i, X2468:$i, X2470:$i, X2471:$i, X2472:$i, X2474:$i, X2475:$i, X2476:$i, X2477:$i, X2478:$i, X2479:$i, X2480:$i, 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X2367 @ (cartprod @ X2364 @ X2365))|~(subset @ X2366 @ (cartprod @ X2364 @ X2365)))&(((in @ (kpair @ (esk76_4 @ X2364 @ X2365 @ X2366 @ X2367) @ (esk77_4 @ X2364 @ X2365 @ X2366 @ X2367)) @ X2367)|((X2366)=(X2367))|(in @ (kpair @ (esk74_4 @ X2364 @ X2365 @ X2366 @ X2367) @ (esk75_4 @ X2364 @ X2365 @ X2366 @ X2367)) @ X2366)|~(subset @ X2367 @ (cartprod @ X2364 @ X2365))|~(subset @ X2366 @ (cartprod @ X2364 @ X2365)))&(~(in @ (kpair @ (esk76_4 @ X2364 @ X2365 @ X2366 @ X2367) @ (esk77_4 @ X2364 @ X2365 @ X2366 @ X2367)) @ X2366)|((X2366)=(X2367))|(in @ (kpair @ (esk74_4 @ X2364 @ X2365 @ X2366 @ X2367) @ (esk75_4 @ X2364 @ X2365 @ X2366 @ X2367)) @ X2366)|~(subset @ X2367 @ (cartprod @ X2364 @ X2365))|~(subset @ X2366 @ (cartprod @ X2364 @ X2365))))))&(((in @ (esk76_4 @ X2364 @ X2365 @ X2366 @ X2367) @ X2364)|((X2366)=(X2367))|~(in @ (kpair @ (esk74_4 @ X2364 @ X2365 @ X2366 @ X2367) @ (esk75_4 @ X2364 @ X2365 @ X2366 @ X2367)) @ X2367)|~(subset @ X2367 @ (cartprod @ X2364 @ X2365))|~(subset @ X2366 @ (cartprod @ X2364 @ X2365)))&(((in @ (esk77_4 @ X2364 @ X2365 @ X2366 @ X2367) @ X2365)|((X2366)=(X2367))|~(in @ (kpair @ (esk74_4 @ X2364 @ X2365 @ X2366 @ X2367) @ (esk75_4 @ X2364 @ X2365 @ X2366 @ X2367)) @ X2367)|~(subset @ X2367 @ (cartprod @ X2364 @ X2365))|~(subset @ X2366 @ (cartprod @ X2364 @ X2365)))&(((in @ (kpair @ (esk76_4 @ X2364 @ X2365 @ X2366 @ X2367) @ (esk77_4 @ X2364 @ X2365 @ X2366 @ X2367)) @ X2367)|((X2366)=(X2367))|~(in @ (kpair @ (esk74_4 @ X2364 @ X2365 @ X2366 @ X2367) @ (esk75_4 @ X2364 @ X2365 @ X2366 @ X2367)) @ X2367)|~(subset @ X2367 @ (cartprod @ X2364 @ X2365))|~(subset @ X2366 @ (cartprod @ X2364 @ X2365)))&(~(in @ (kpair @ (esk76_4 @ X2364 @ X2365 @ X2366 @ X2367) @ (esk77_4 @ X2364 @ X2365 @ X2366 @ X2367)) @ X2366)|((X2366)=(X2367))|~(in @ (kpair @ (esk74_4 @ X2364 @ X2365 @ X2366 @ X2367) @ (esk75_4 @ X2364 @ X2365 @ X2366 @ X2367)) @ X2367)|~(subset @ X2367 @ (cartprod @ X2364 @ X2365))|~(subset @ X2366 @ (cartprod @ X2364 @ X2365)))))))))&((((in @ (esk78_4 @ X2372 @ X2373 @ X2374 @ X2375) @ X2372)|((X2374)=(X2375))|~(func @ X2372 @ X2373 @ X2375)|~(func @ X2372 @ X2373 @ X2374))&(((ap @ X2372 @ X2373 @ X2374 @ (esk78_4 @ X2372 @ X2373 @ X2374 @ X2375))!=(ap @ X2372 @ X2373 @ X2375 @ (esk78_4 @ X2372 @ X2373 @ X2374 @ X2375)))|((X2374)=(X2375))|~(func @ X2372 @ X2373 @ X2375)|~(func @ X2372 @ X2373 @ X2374)))&((((in @ (esk79_4 @ X2377 @ X2378 @ X2379 @ X2380) @ X2377)|((X2379)=(X2380))|~(in @ X2380 @ (funcSet @ X2377 @ X2378))|~(in @ X2379 @ (funcSet @ X2377 @ X2378)))&(((ap @ X2377 @ X2378 @ X2379 @ (esk79_4 @ X2377 @ X2378 @ X2379 @ X2380))!=(ap @ X2377 @ X2378 @ X2380 @ (esk79_4 @ X2377 @ X2378 @ X2379 @ X2380)))|((X2379)=(X2380))|~(in @ X2380 @ (funcSet @ X2377 @ X2378))|~(in @ X2379 @ (funcSet @ X2377 @ X2378))))&((~(in @ X2384 @ (funcSet @ X2382 @ X2383))|(~(in @ X2385 @ X2382)|((ap @ X2382 @ X2383 @ X2384 @ X2385)=(ap @ X2382 @ X2383 @ X2384 @ X2385))))&((~(func @ X2386 @ X2387 @ X2388)|(~(in @ X2389 @ X2386)|((ap @ X2386 @ X2387 @ X2388 @ X2389)=(ap @ X2386 @ X2387 @ X2388 @ X2389))))&((((in @ (esk80_3 @ X2390 @ X2391 @ X2392) @ X2390)|(~(in @ X2394 @ X2390)|((ap @ X2390 @ X2391 @ (lam @ X2390 @ X2391 @ X2392) @ X2394)=(X2392 @ X2394))))&(~(in @ (X2392 @ (esk80_3 @ X2390 @ X2391 @ X2392)) @ X2391)|(~(in @ X2394 @ X2390)|((ap @ X2390 @ X2391 @ (lam @ X2390 @ X2391 @ X2392) @ X2394)=(X2392 @ X2394)))))&((~(func @ X2395 @ X2396 @ X2397)|((lam @ X2395 @ X2396 @ (ap @ X2395 @ X2396 @ X2397))=(X2397)))&((((in @ (esk81_3 @ X2398 @ X2399 @ X2400) @ X2398)|((lam @ X2398 @ X2399 @ X2400)=(lam @ X2398 @ X2399 @ X2400)))&(~(in @ (X2400 @ (esk81_3 @ X2398 @ X2399 @ X2400)) @ X2399)|((lam @ X2398 @ X2399 @ X2400)=(lam @ X2398 @ X2399 @ X2400))))&((((in @ (esk82_3 @ X2402 @ X2403 @ X2404) @ X2402)|(~(in @ X2406 @ X2402)|((ap @ X2402 @ X2403 @ (lam @ X2402 @ X2403 @ X2404) @ X2406)=(X2404 @ X2406))))&(~(in @ (X2404 @ (esk82_3 @ X2402 @ X2403 @ X2404)) @ X2403)|(~(in @ X2406 @ X2402)|((ap @ X2402 @ X2403 @ (lam @ X2402 @ X2403 @ X2404) @ X2406)=(X2404 @ X2406)))))&((~(in @ X2409 @ (funcSet @ X2407 @ X2408))|((lam @ X2407 @ X2408 @ (ap @ X2407 @ X2408 @ X2409))=(X2409)))&((~(in @ X2412 @ X2410)|(~(in @ X2413 @ X2410)|((X2411)|(in @ X2413 @ (dsetconstr @ X2410 @ (^[Z0:$i]:((((((X2411))&(((Z0)=(X2412)))))|(((~((X2411)))&(((Z0)=(X2413)))))))))))))&((~(in @ X2416 @ X2414)|(~(in @ X2417 @ X2414)|((X2415)|((dsetconstr @ X2414 @ (^[Z0:$i]:((((((X2415))&(((Z0)=(X2416)))))|(((~((X2415)))&(((Z0)=(X2417)))))))))=(setadjoin @ X2417 @ emptyset)))))&((~(in @ X2420 @ X2418)|(~(in @ X2421 @ X2418)|(~(X2419)|(in @ X2420 @ (dsetconstr @ X2418 @ (^[Z0:$i]:((((((X2419))&(((Z0)=(X2420)))))|(((~((X2419)))&(((Z0)=(X2421)))))))))))))&((~(in @ X2424 @ X2422)|(~(in @ X2425 @ X2422)|(~(X2423)|((dsetconstr @ X2422 @ (^[Z0:$i]:((((((X2423))&(((Z0)=(X2424)))))|(((~((X2423)))&(((Z0)=(X2425)))))))))=(setadjoin @ X2424 @ emptyset)))))&((~(in @ X2428 @ X2426)|(~(in @ X2429 @ X2426)|(singleton @ (dsetconstr @ X2426 @ (^[Z0:$i]:((((((X2427))&(((Z0)=(X2428)))))|(((~((X2427)))&(((Z0)=(X2429))))))))))))&((~(in @ X2432 @ X2430)|(~(in @ X2433 @ X2430)|(in @ (if @ X2430 @ ((X2431)) @ X2432 @ X2433) @ X2430)))&((~(singleton @ X2434)|(~(in @ X2435 @ X2434)|((setunion @ X2434)=(X2435))))&((~(in @ X2438 @ X2436)|(~(in @ X2439 @ X2436)|(~(X2437)|((if @ X2436 @ ((X2437)) @ X2438 @ X2439)=(X2438)))))&((~(in @ X2442 @ X2440)|(~(in @ X2443 @ X2440)|((X2441)|((if @ X2440 @ ((X2441)) @ X2442 @ X2443)=(X2443)))))&((~(in @ X2446 @ X2444)|(~(in @ X2447 @ X2444)|(in @ (if @ X2444 @ ((X2445)) @ X2446 @ X2447) @ (setadjoin @ X2446 @ (setadjoin @ X2447 @ emptyset)))))&((~(in @ X2449 @ (powerset @ X2448))|(~(in @ X2450 @ (powerset @ X2448))|(in @ (binintersect @ X2449 @ X2450) @ (powerset @ X2448))))&((~(in @ X2452 @ (powerset @ X2451))|(~(in @ X2453 @ (powerset @ X2451))|(in @ (binunion @ X2452 @ X2453) @ (powerset @ X2451))))&((~(in @ X2455 @ (powerset @ X2454))|(in @ (powerset @ X2455) @ (powerset @ (powerset @ X2454))))&((~(in @ X2457 @ (powerset @ X2456))|(~(in @ X2458 @ (powerset @ X2456))|(in @ (setminus @ X2457 @ X2458) @ (powerset @ X2456))))&((~(in @ X2460 @ (powerset @ X2459))|(in @ (setminus @ X2459 @ X2460) @ (powerset @ X2459)))&(((((in @ (esk84_3 @ X2461 @ X2462 @ X2463) @ X2461)|((X2462)=(X2463))|(in @ (esk83_3 @ X2461 @ X2462 @ X2463) @ X2461)|~(in @ X2463 @ (powerset @ X2461))|~(in @ X2462 @ (powerset @ X2461)))&(((in @ (esk84_3 @ X2461 @ X2462 @ X2463) @ X2463)|((X2462)=(X2463))|(in @ (esk83_3 @ X2461 @ X2462 @ X2463) @ X2461)|~(in @ X2463 @ (powerset @ X2461))|~(in @ X2462 @ (powerset @ X2461)))&(~(in @ (esk84_3 @ X2461 @ X2462 @ X2463) @ X2462)|((X2462)=(X2463))|(in @ (esk83_3 @ X2461 @ X2462 @ X2463) @ X2461)|~(in @ X2463 @ (powerset @ X2461))|~(in @ X2462 @ (powerset @ X2461)))))&((((in @ (esk84_3 @ X2461 @ X2462 @ X2463) @ X2461)|((X2462)=(X2463))|(in @ (esk83_3 @ X2461 @ X2462 @ X2463) @ X2462)|~(in @ X2463 @ (powerset @ X2461))|~(in @ X2462 @ (powerset @ X2461)))&(((in @ (esk84_3 @ X2461 @ X2462 @ X2463) @ X2463)|((X2462)=(X2463))|(in @ (esk83_3 @ X2461 @ X2462 @ X2463) @ X2462)|~(in @ X2463 @ (powerset @ X2461))|~(in @ X2462 @ (powerset @ X2461)))&(~(in @ (esk84_3 @ X2461 @ X2462 @ X2463) @ X2462)|((X2462)=(X2463))|(in @ (esk83_3 @ X2461 @ X2462 @ X2463) @ X2462)|~(in @ X2463 @ (powerset @ X2461))|~(in @ X2462 @ (powerset @ X2461)))))&(((in @ (esk84_3 @ X2461 @ X2462 @ X2463) @ X2461)|((X2462)=(X2463))|~(in @ (esk83_3 @ X2461 @ X2462 @ X2463) @ X2463)|~(in @ X2463 @ (powerset @ X2461))|~(in @ X2462 @ (powerset @ X2461)))&(((in @ (esk84_3 @ X2461 @ X2462 @ X2463) @ X2463)|((X2462)=(X2463))|~(in @ (esk83_3 @ X2461 @ X2462 @ X2463) @ X2463)|~(in @ X2463 @ (powerset @ X2461))|~(in @ X2462 @ (powerset @ X2461)))&(~(in @ (esk84_3 @ X2461 @ X2462 @ X2463) @ X2462)|((X2462)=(X2463))|~(in @ (esk83_3 @ X2461 @ X2462 @ X2463) @ X2463)|~(in @ X2463 @ (powerset @ X2461))|~(in @ X2462 @ (powerset @ X2461)))))))&((((in @ (esk85_3 @ X2466 @ X2467 @ X2468) @ X2466)|(subset @ X2467 @ X2468)|~(in @ X2468 @ (powerset @ X2466))|~(in @ X2467 @ (powerset @ X2466)))&(((in @ (esk85_3 @ X2466 @ X2467 @ X2468) @ X2467)|(subset @ X2467 @ X2468)|~(in @ X2468 @ (powerset @ X2466))|~(in @ X2467 @ (powerset @ X2466)))&(~(in @ (esk85_3 @ X2466 @ X2467 @ X2468) @ X2468)|(subset @ X2467 @ X2468)|~(in @ X2468 @ (powerset @ X2466))|~(in @ X2467 @ (powerset @ X2466)))))&((((in @ (esk86_3 @ X2470 @ X2471 @ X2472) @ X2470)|(in @ X2471 @ (powerset @ X2472))|~(in @ X2472 @ (powerset @ X2470))|~(in @ X2471 @ (powerset @ X2470)))&(((in @ (esk86_3 @ X2470 @ X2471 @ X2472) @ X2471)|(in @ X2471 @ (powerset @ X2472))|~(in @ X2472 @ (powerset @ X2470))|~(in @ X2471 @ (powerset @ X2470)))&(~(in @ (esk86_3 @ X2470 @ X2471 @ X2472) @ X2472)|(in @ X2471 @ (powerset @ X2472))|~(in @ X2472 @ (powerset @ X2470))|~(in @ X2471 @ (powerset @ X2470)))))&((~(in @ X2475 @ (powerset @ X2474))|(~(in @ X2476 @ (powerset @ X2474))|(~(in @ X2477 @ X2474)|(~(in @ X2475 @ (powerset @ X2476))|(~(in @ X2477 @ X2475)|(in @ X2477 @ X2476))))))&((~(in @ X2479 @ (powerset @ X2478))|(~(in @ X2480 @ X2478)|(~(in @ X2480 @ X2479)|~(in @ X2480 @ (setminus @ X2478 @ X2479)))))&((~(in @ X2482 @ (powerset @ X2481))|(~(in @ X2483 @ X2481)|((in @ X2483 @ (setminus @ X2481 @ X2482))|(in @ X2483 @ X2482))))&((~(in @ X2485 @ (powerset @ X2484))|(~(in @ X2486 @ (powerset @ X2484))|(~(in @ X2487 @ X2484)|((in @ X2487 @ X2485)|~(in @ X2487 @ (binintersect @ X2485 @ X2486))))))&((~(in @ X2489 @ (powerset @ X2488))|(~(in @ X2490 @ (powerset @ X2488))|(~(in @ X2491 @ X2488)|((in @ X2491 @ X2490)|~(in @ X2491 @ (binintersect @ X2489 @ X2490))))))&((~(in @ X2493 @ (powerset @ X2492))|(~(in @ X2494 @ (powerset @ X2492))|(~(in @ X2495 @ X2492)|(~(subset @ X2493 @ (setminus @ X2492 @ X2494))|(~(in @ X2495 @ X2494)|~(in @ X2495 @ X2493))))))&((~(in @ X2497 @ (powerset @ X2496))|(~(in @ X2498 @ (powerset @ X2496))|(~(in @ X2499 @ X2496)|(~(subset @ X2497 @ X2498)|((in @ X2499 @ X2498)|~(in @ X2499 @ X2497))))))&((~(in @ X2501 @ (powerset @ X2500))|(~(in @ X2502 @ (powerset @ X2500))|(~(subset @ X2501 @ X2502)|(subset @ (setminus @ X2500 @ X2502) @ (setminus @ X2500 @ X2501)))))&((~(in @ X2504 @ (powerset @ X2503))|(~(in @ X2505 @ (powerset @ X2503))|(~(subset @ (setminus @ X2503 @ X2505) @ (setminus @ X2503 @ X2504))|(subset @ X2504 @ X2505))))&((~(in @ X2507 @ (powerset @ X2506))|(~(in @ X2508 @ X2506)|(~(in @ X2508 @ X2507)|(in @ X2508 @ (setminus @ X2506 @ (setminus @ X2506 @ X2507))))))&((~(in @ X2510 @ (powerset @ X2509))|(~(in @ X2511 @ X2509)|(~(in @ X2511 @ (setminus @ X2509 @ (setminus @ X2509 @ X2510)))|(in @ X2511 @ X2510))))&((~(in @ X2513 @ (powerset @ X2512))|(subset @ X2513 @ (setminus @ X2512 @ (setminus @ X2512 @ X2513))))&((~(in @ X2515 @ (powerset @ X2514))|(subset @ (setminus @ X2514 @ (setminus @ X2514 @ X2515)) @ X2515))&((~(in @ X2517 @ (powerset @ X2516))|((X2517)=(setminus @ X2516 @ (setminus @ X2516 @ X2517))))&((~(in @ X2519 @ (powerset @ X2518))|(~(in @ X2520 @ (powerset @ X2518))|(~(in @ X2521 @ X2518)|(~(in @ X2521 @ (setminus @ X2518 @ X2519))|~(in @ X2521 @ (binintersect @ X2519 @ X2520))))))&((~(in @ X2523 @ (powerset @ X2522))|(~(in @ X2524 @ (powerset @ X2522))|(~(in @ X2525 @ X2522)|(~(in @ X2525 @ (setminus @ X2522 @ X2523))|(in @ X2525 @ (setminus @ X2522 @ (binintersect @ X2523 @ X2524)))))))&((~(in @ X2527 @ (powerset @ X2526))|(~(in @ X2528 @ (powerset @ X2526))|(subset @ (setminus @ X2526 @ X2527) @ (setminus @ X2526 @ (binintersect @ X2527 @ X2528)))))&((~(in @ X2530 @ (powerset @ X2529))|(~(in @ X2531 @ (powerset @ X2529))|(in @ (setminus @ X2529 @ X2530) @ (powerset @ (setminus @ X2529 @ (binintersect @ X2530 @ X2531))))))&((~(in @ X2533 @ (powerset @ X2532))|(~(in @ X2534 @ (powerset @ X2532))|(~(subset @ X2533 @ (setminus @ X2532 @ X2534))|(~(in @ X2535 @ X2532)|(~(in @ X2535 @ X2534)|(in @ X2535 @ (setminus @ X2532 @ X2533)))))))&((~(in @ X2537 @ (powerset @ X2536))|(~(in @ X2538 @ (powerset @ X2536))|(~(subset @ X2537 @ (setminus @ X2536 @ X2538))|(subset @ X2538 @ (setminus @ X2536 @ X2537)))))&((~(in @ X2540 @ (powerset @ X2539))|(~(in @ X2541 @ (powerset @ X2539))|(~(in @ X2542 @ X2539)|((in @ X2542 @ (binunion @ X2540 @ X2541))|~(in @ X2542 @ X2540)))))&((~(in @ X2544 @ (powerset @ X2543))|(~(in @ X2545 @ (powerset @ X2543))|(~(in @ X2546 @ X2543)|((in @ X2546 @ (binunion @ X2544 @ X2545))|~(in @ X2546 @ X2545)))))&((~(in @ X2548 @ (powerset @ X2547))|(~(in @ X2549 @ (powerset @ X2547))|(~(in @ X2550 @ (powerset @ X2547))|(~(in @ X2551 @ X2547)|(~(in @ X2551 @ (binintersect @ X2548 @ X2549))|(in @ X2551 @ (binunion @ X2548 @ X2550)))))))&((~(in @ X2553 @ (powerset @ X2552))|(~(in @ X2554 @ (powerset @ X2552))|(~(in @ X2555 @ (powerset @ X2552))|(~(in @ X2556 @ X2552)|(~(in @ X2556 @ (binintersect @ X2553 @ X2554))|(in @ X2556 @ (binunion @ X2554 @ X2555)))))))&((~(in @ X2558 @ (powerset @ X2557))|(~(in @ X2559 @ (powerset @ X2557))|(~(in @ X2560 @ (powerset @ X2557))|(~(in @ X2561 @ X2557)|(~(in @ X2561 @ (binintersect @ X2558 @ X2559))|(in @ X2561 @ (binintersect @ (binunion @ X2558 @ X2560) @ (binunion @ X2559 @ X2560))))))))&((in @ esk88_0 @ (powerset @ esk87_0))&((in @ esk89_0 @ (powerset @ esk87_0))&((in @ esk90_0 @ (powerset @ esk87_0))&~(in @ (binintersect @ esk88_0 @ esk89_0) @ (powerset @ (binintersect @ (binunion @ esk88_0 @ esk90_0) @ (binunion @ esk89_0 @ esk90_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_346])])])])])])])).
130.12/19.42	thf(c_0_348, negated_conjecture, ~((in @ (binintersect @ esk88_0 @ esk89_0) @ (powerset @ (binintersect @ (binunion @ esk88_0 @ esk90_0) @ (binunion @ esk89_0 @ esk90_0))))), inference(split_conjunct,[status(thm)],[c_0_347])).
130.12/19.42	thf(c_0_349, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ X3))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_347])).
130.12/19.42	thf(c_0_350, negated_conjecture, ~((subset @ (binintersect @ esk88_0 @ esk89_0) @ (binintersect @ (binunion @ esk88_0 @ esk90_0) @ (binunion @ esk89_0 @ esk90_0)))), inference(spm,[status(thm)],[c_0_348, c_0_349])).
130.12/19.42	thf(c_0_351, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((subset @ X2 @ (binintersect @ X3 @ X4))|~((subset @ X2 @ X3))|~((subset @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_347])).
130.12/19.42	thf(c_0_352, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((subset @ X2 @ X4)|~((subset @ X2 @ X3))|~((subset @ X3 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_347])).
130.12/19.42	thf(c_0_353, negated_conjecture, ![X2:$i, X3:$i]:((subset @ X2 @ (binunion @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_347])).
130.12/19.42	thf(c_0_354, negated_conjecture, (~((subset @ (binintersect @ esk88_0 @ esk89_0) @ (binunion @ esk89_0 @ esk90_0)))|~((subset @ (binintersect @ esk88_0 @ esk89_0) @ (binunion @ esk88_0 @ esk90_0)))), inference(spm,[status(thm)],[c_0_350, c_0_351])).
130.12/19.42	thf(c_0_355, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((subset @ X2 @ (binunion @ X3 @ X4))|~((subset @ X2 @ X3)))), inference(spm,[status(thm)],[c_0_352, c_0_353])).
130.12/19.42	thf(c_0_356, negated_conjecture, ![X2:$i, X3:$i]:((subset @ (binintersect @ X2 @ X3) @ X3)), inference(split_conjunct,[status(thm)],[c_0_347])).
130.12/19.42	thf(c_0_357, negated_conjecture, ~((subset @ (binintersect @ esk88_0 @ esk89_0) @ (binunion @ esk88_0 @ esk90_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_354, c_0_355]), c_0_356])])).
130.12/19.42	thf(c_0_358, negated_conjecture, ![X3:$i, X2:$i]:((subset @ (binintersect @ X2 @ X3) @ X2)), inference(split_conjunct,[status(thm)],[c_0_347])).
130.12/19.42	thf(c_0_359, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_357, c_0_355]), c_0_358])]), ['proof']).
130.12/19.42	% SZS output end CNFRefutation
130.12/19.42	% Parsed axioms                        : 561
130.12/19.42	% Removed by relevancy pruning/SinE    : 0
130.12/19.42	% Initial clauses                      : 762
130.12/19.42	% Removed in clause preprocessing      : 331
130.12/19.42	% Initial clauses in saturation        : 431
130.12/19.42	% Processed clauses                    : 6547
130.12/19.42	% ...of these trivial                  : 24
130.12/19.42	% ...subsumed                          : 4364
130.12/19.42	% ...remaining for further processing  : 2159
130.12/19.42	% Other redundant clauses eliminated   : 90
130.12/19.42	% Clauses deleted for lack of memory   : 0
130.12/19.42	% Backward-subsumed                    : 193
130.12/19.42	% Backward-rewritten                   : 22
130.12/19.42	% Generated clauses                    : 44235
130.12/19.42	% ...of the previous two non-redundant : 42724
130.12/19.42	% ...aggressively subsumed             : 0
130.12/19.42	% Contextual simplify-reflections      : 12
130.12/19.42	% Paramodulations                      : 44049
130.12/19.42	% Factorizations                       : 37
130.12/19.42	% NegExts                              : 26
130.12/19.42	% Equation resolutions                 : 97
130.12/19.42	% Disequality decompositions           : 0
130.12/19.42	% Total rewrite steps                  : 3532
130.12/19.42	% ...of those cached                   : 3023
130.12/19.42	% Propositional unsat checks           : 0
130.12/19.42	%    Propositional check models        : 0
130.12/19.42	%    Propositional check unsatisfiable : 0
130.12/19.42	%    Propositional clauses             : 0
130.12/19.42	%    Propositional clauses after purity: 0
130.12/19.42	%    Propositional unsat core size     : 0
130.12/19.42	%    Propositional preprocessing time  : 0.000
130.12/19.42	%    Propositional encoding time       : 0.000
130.12/19.42	%    Propositional solver time         : 0.000
130.12/19.42	%    Success case prop preproc time    : 0.000
130.12/19.42	%    Success case prop encoding time   : 0.000
130.12/19.42	%    Success case prop solver time     : 0.000
130.12/19.42	% Current number of processed clauses  : 1546
130.12/19.42	%    Positive orientable unit clauses  : 129
130.12/19.42	%    Positive unorientable unit clauses: 0
130.12/19.42	%    Negative unit clauses             : 31
130.12/19.42	%    Non-unit-clauses                  : 1386
130.12/19.42	% Current number of unprocessed clauses: 36797
130.12/19.42	% ...number of literals in the above   : 135677
130.12/19.42	% Current number of archived formulas  : 0
130.12/19.42	% Current number of archived clauses   : 595
130.12/19.42	% Clause-clause subsumption calls (NU) : 192754
130.12/19.42	% Rec. Clause-clause subsumption calls : 103550
130.12/19.42	% Non-unit clause-clause subsumptions  : 2232
130.12/19.42	% Unit Clause-clause subsumption calls : 4520
130.12/19.42	% Rewrite failures with RHS unbound    : 0
130.12/19.42	% BW rewrite match attempts            : 70
130.12/19.42	% BW rewrite match successes           : 18
130.12/19.42	% Condensation attempts                : 0
130.12/19.42	% Condensation successes               : 0
130.12/19.42	% Termbank termtop insertions          : 815061
130.12/19.42	% Search garbage collected termcells   : 27510
130.12/19.42	
130.12/19.42	% -------------------------------------------------
130.12/19.42	% User time                : 17.707 s
130.12/19.42	% System time              : 0.646 s
130.12/19.42	% Total time               : 18.352 s
130.12/19.42	% Maximum resident set size: 9884 pages
130.12/19.42	
130.12/19.42	% -------------------------------------------------
130.12/19.42	% User time                : 17.720 s
130.12/19.42	% System time              : 0.658 s
130.12/19.42	% Total time               : 18.379 s
130.12/19.42	% Maximum resident set size: 5632 pages
130.12/19.42	% E exiting
130.12/19.43	EOF