0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : run_E %s %d THM
0.13/0.33	% Computer : n028.cluster.edu
0.13/0.33	% Model    : x86_64 x86_64
0.13/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory   : 8042.1875MB
0.13/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.33	% CPULimit   : 1440
0.13/0.33	% WCLimit    : 180
0.13/0.33	% DateTime   : Thu Jul  4 10:14:08 EDT 2024
0.13/0.33	% CPUTime    : 
0.20/0.49	Running higher-order theorem proving
0.37/0.55	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.OzmfPJvcVc/E---3.1_25410.p
279.00/50.34	# Version: 3.2.0-ho
279.00/50.34	# Preprocessing class: HSLMSLSSLLLCHFA.
279.00/50.34	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
279.00/50.34	# Starting ehoh_best5 with 180s (1) cores
279.00/50.34	# Starting almost_fo_3_lam with 180s (1) cores
279.00/50.34	# Starting new_bool_5 with 180s (1) cores
279.00/50.34	# Starting pre_casc_3 with 180s (1) cores
279.00/50.34	# Starting ho_unfolding_8 with 180s (1) cores
279.00/50.34	# Starting new_ho_10_cnf2 with 180s (1) cores
279.00/50.34	# Starting new_bool_3 with 180s (1) cores
279.00/50.34	# Starting new_ho_5 with 180s (1) cores
279.00/50.34	# new_bool_5 with pid 25490 completed with status 0
279.00/50.34	# Result found by new_bool_5
279.00/50.34	# Preprocessing class: HSLMSLSSLLLCHFA.
279.00/50.34	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
279.00/50.34	# Starting ehoh_best5 with 180s (1) cores
279.00/50.34	# Starting almost_fo_3_lam with 180s (1) cores
279.00/50.34	# Starting new_bool_5 with 180s (1) cores
279.00/50.34	# SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
279.00/50.34	# Search class: HGHSM-FSLM32-MHFMMSBN
279.00/50.34	# Scheduled 10 strats onto 1 cores with 180 seconds (180 total)
279.00/50.34	# Starting ho_unfolding_8 with 33s (1) cores
279.00/50.34	# ho_unfolding_8 with pid 25499 completed with status 7
279.00/50.34	# Starting new_bool_5 with 19s (1) cores
279.00/50.34	# new_bool_5 with pid 25507 completed with status 0
279.00/50.34	# Result found by new_bool_5
279.00/50.34	# Preprocessing class: HSLMSLSSLLLCHFA.
279.00/50.34	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
279.00/50.34	# Starting ehoh_best5 with 180s (1) cores
279.00/50.34	# Starting almost_fo_3_lam with 180s (1) cores
279.00/50.34	# Starting new_bool_5 with 180s (1) cores
279.00/50.34	# SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
279.00/50.34	# Search class: HGHSM-FSLM32-MHFMMSBN
279.00/50.34	# Scheduled 10 strats onto 1 cores with 180 seconds (180 total)
279.00/50.34	# Starting ho_unfolding_8 with 33s (1) cores
279.00/50.34	# ho_unfolding_8 with pid 25499 completed with status 7
279.00/50.34	# Starting new_bool_5 with 19s (1) cores
279.00/50.34	# Preprocessing time       : 0.006 s
279.00/50.34	# Presaturation interreduction done
279.00/50.34	
279.00/50.34	# Proof found!
279.00/50.34	# SZS status Theorem
279.00/50.34	# SZS output start CNFRefutation
279.00/50.34	thf(decl_22, type, in: $i > $i > $o).
279.00/50.34	thf(decl_23, type, exu: ($i > $o) > $o).
279.00/50.34	thf(decl_24, type, setextAx: $o).
279.00/50.34	thf(decl_25, type, emptyset: $i).
279.00/50.34	thf(decl_26, type, emptysetAx: $o).
279.00/50.34	thf(decl_27, type, setadjoin: $i > $i > $i).
279.00/50.34	thf(decl_28, type, setadjoinAx: $o).
279.00/50.34	thf(decl_29, type, powerset: $i > $i).
279.00/50.34	thf(decl_30, type, powersetAx: $o).
279.00/50.34	thf(decl_31, type, setunion: $i > $i).
279.00/50.34	thf(decl_32, type, setunionAx: $o).
279.00/50.34	thf(decl_33, type, omega: $i).
279.00/50.34	thf(decl_34, type, omega0Ax: $o).
279.00/50.34	thf(decl_35, type, omegaSAx: $o).
279.00/50.34	thf(decl_36, type, omegaIndAx: $o).
279.00/50.34	thf(decl_37, type, replAx: $o).
279.00/50.34	thf(decl_38, type, foundationAx: $o).
279.00/50.34	thf(decl_39, type, wellorderingAx: $o).
279.00/50.34	thf(decl_40, type, descr: ($i > $o) > $i).
279.00/50.34	thf(decl_41, type, descrp: $o).
279.00/50.34	thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
279.00/50.34	thf(decl_43, type, dsetconstrI: $o).
279.00/50.34	thf(decl_44, type, dsetconstrEL: $o).
279.00/50.34	thf(decl_45, type, dsetconstrER: $o).
279.00/50.34	thf(decl_46, type, exuE1: $o).
279.00/50.34	thf(decl_47, type, prop2set: $o > $i).
279.00/50.34	thf(decl_48, type, prop2setE: $o).
279.00/50.34	thf(decl_49, type, emptysetE: $o).
279.00/50.34	thf(decl_50, type, emptysetimpfalse: $o).
279.00/50.34	thf(decl_51, type, notinemptyset: $o).
279.00/50.34	thf(decl_52, type, exuE3e: $o).
279.00/50.34	thf(decl_53, type, setext: $o).
279.00/50.34	thf(decl_54, type, emptyI: $o).
279.00/50.34	thf(decl_55, type, noeltsimpempty: $o).
279.00/50.34	thf(decl_56, type, setbeta: $o).
279.00/50.34	thf(decl_57, type, nonempty: $i > $o).
279.00/50.34	thf(decl_58, type, nonemptyE1: $o).
279.00/50.34	thf(decl_59, type, nonemptyI: $o).
279.00/50.34	thf(decl_60, type, nonemptyI1: $o).
279.00/50.34	thf(decl_61, type, setadjoinIL: $o).
279.00/50.34	thf(decl_62, type, emptyinunitempty: $o).
279.00/50.34	thf(decl_63, type, setadjoinIR: $o).
279.00/50.34	thf(decl_64, type, setadjoinE: $o).
279.00/50.34	thf(decl_65, type, setadjoinOr: $o).
279.00/50.34	thf(decl_66, type, setoftrueEq: $o).
279.00/50.34	thf(decl_67, type, powersetI: $o).
279.00/50.34	thf(decl_68, type, emptyinPowerset: $o).
279.00/50.34	thf(decl_69, type, emptyInPowerset: $o).
279.00/50.34	thf(decl_70, type, powersetE: $o).
279.00/50.34	thf(decl_71, type, setunionI: $o).
279.00/50.34	thf(decl_72, type, setunionE: $o).
279.00/50.34	thf(decl_73, type, subPowSU: $o).
279.00/50.34	thf(decl_74, type, exuE2: $o).
279.00/50.34	thf(decl_75, type, nonemptyImpWitness: $o).
279.00/50.34	thf(decl_76, type, uniqinunit: $o).
279.00/50.34	thf(decl_77, type, notinsingleton: $o).
279.00/50.34	thf(decl_78, type, eqinunit: $o).
279.00/50.34	thf(decl_79, type, singletonsswitch: $o).
279.00/50.34	thf(decl_80, type, upairsetE: $o).
279.00/50.34	thf(decl_81, type, upairsetIL: $o).
279.00/50.34	thf(decl_82, type, upairsetIR: $o).
279.00/50.34	thf(decl_83, type, emptyE1: $o).
279.00/50.34	thf(decl_84, type, vacuousDall: $o).
279.00/50.34	thf(decl_85, type, quantDeMorgan1: $o).
279.00/50.34	thf(decl_86, type, quantDeMorgan2: $o).
279.00/50.34	thf(decl_87, type, quantDeMorgan3: $o).
279.00/50.34	thf(decl_88, type, quantDeMorgan4: $o).
279.00/50.34	thf(decl_89, type, prop2setI: $o).
279.00/50.34	thf(decl_91, type, prop2set2propI: $o).
279.00/50.34	thf(decl_92, type, notdexE: $o).
279.00/50.34	thf(decl_93, type, notdallE: $o).
279.00/50.34	thf(decl_94, type, exuI1: $o).
279.00/50.34	thf(decl_95, type, exuI3: $o).
279.00/50.34	thf(decl_96, type, exuI2: $o).
279.00/50.34	thf(decl_97, type, inCongP: $o).
279.00/50.34	thf(decl_98, type, in__Cong: $o).
279.00/50.34	thf(decl_99, type, exuE3u: $o).
279.00/50.34	thf(decl_100, type, exu__Cong: $o).
279.00/50.34	thf(decl_101, type, emptyset__Cong: $o).
279.00/50.34	thf(decl_102, type, setadjoin__Cong: $o).
279.00/50.34	thf(decl_103, type, powerset__Cong: $o).
279.00/50.34	thf(decl_104, type, setunion__Cong: $o).
279.00/50.34	thf(decl_105, type, omega__Cong: $o).
279.00/50.34	thf(decl_106, type, exuEu: $o).
279.00/50.34	thf(decl_107, type, descr__Cong: $o).
279.00/50.34	thf(decl_108, type, dsetconstr__Cong: $o).
279.00/50.34	thf(decl_109, type, subset: $i > $i > $o).
279.00/50.34	thf(decl_112, type, subsetI1: $o).
279.00/50.34	thf(decl_113, type, eqimpsubset2: $o).
279.00/50.34	thf(decl_114, type, eqimpsubset1: $o).
279.00/50.34	thf(decl_115, type, subsetI2: $o).
279.00/50.34	thf(decl_116, type, emptysetsubset: $o).
279.00/50.34	thf(decl_117, type, subsetE: $o).
279.00/50.34	thf(decl_118, type, subsetE2: $o).
279.00/50.34	thf(decl_119, type, notsubsetI: $o).
279.00/50.34	thf(decl_120, type, notequalI1: $o).
279.00/50.34	thf(decl_121, type, notequalI2: $o).
279.00/50.34	thf(decl_122, type, subsetRefl: $o).
279.00/50.34	thf(decl_123, type, subsetTrans: $o).
279.00/50.34	thf(decl_124, type, setadjoinSub: $o).
279.00/50.34	thf(decl_125, type, setadjoinSub2: $o).
279.00/50.34	thf(decl_126, type, subset2powerset: $o).
279.00/50.34	thf(decl_127, type, setextsub: $o).
279.00/50.34	thf(decl_128, type, subsetemptysetimpeq: $o).
279.00/50.34	thf(decl_129, type, powersetI1: $o).
279.00/50.34	thf(decl_130, type, powersetE1: $o).
279.00/50.34	thf(decl_131, type, inPowerset: $o).
279.00/50.34	thf(decl_132, type, powersetsubset: $o).
279.00/50.34	thf(decl_133, type, sepInPowerset: $o).
279.00/50.34	thf(decl_134, type, sepSubset: $o).
279.00/50.34	thf(decl_135, type, binunion: $i > $i > $i).
279.00/50.34	thf(decl_136, type, binunionIL: $o).
279.00/50.34	thf(decl_137, type, upairset2IR: $o).
279.00/50.34	thf(decl_138, type, binunionIR: $o).
279.00/50.34	thf(decl_139, type, binunionEcases: $o).
279.00/50.34	thf(decl_140, type, binunionE: $o).
279.00/50.34	thf(decl_141, type, binunionLsub: $o).
279.00/50.34	thf(decl_142, type, binunionRsub: $o).
279.00/50.34	thf(decl_143, type, binintersect: $i > $i > $i).
279.00/50.34	thf(decl_144, type, binintersectI: $o).
279.00/50.34	thf(decl_145, type, binintersectSubset5: $o).
279.00/50.34	thf(decl_146, type, binintersectEL: $o).
279.00/50.34	thf(decl_147, type, binintersectLsub: $o).
279.00/50.34	thf(decl_148, type, binintersectSubset2: $o).
279.00/50.34	thf(decl_149, type, binintersectSubset3: $o).
279.00/50.34	thf(decl_150, type, binintersectER: $o).
279.00/50.34	thf(decl_151, type, disjointsetsI1: $o).
279.00/50.34	thf(decl_152, type, binintersectRsub: $o).
279.00/50.34	thf(decl_153, type, binintersectSubset4: $o).
279.00/50.34	thf(decl_154, type, binintersectSubset1: $o).
279.00/50.34	thf(decl_155, type, bs114d: $o).
279.00/50.34	thf(decl_157, type, setminus: $i > $i > $i).
279.00/50.34	thf(decl_158, type, setminusI: $o).
279.00/50.34	thf(decl_159, type, setminusEL: $o).
279.00/50.34	thf(decl_160, type, setminusER: $o).
279.00/50.34	thf(decl_161, type, setminusSubset2: $o).
279.00/50.34	thf(decl_162, type, setminusERneg: $o).
279.00/50.34	thf(decl_163, type, setminusELneg: $o).
279.00/50.34	thf(decl_164, type, setminusILneg: $o).
279.00/50.34	thf(decl_165, type, setminusIRneg: $o).
279.00/50.34	thf(decl_166, type, setminusLsub: $o).
279.00/50.34	thf(decl_167, type, setminusSubset1: $o).
279.00/50.34	thf(decl_168, type, symdiff: $i > $i > $i).
279.00/50.34	thf(decl_169, type, symdiffE: $o).
279.00/50.34	thf(decl_170, type, symdiffI1: $o).
279.00/50.34	thf(decl_171, type, symdiffI2: $o).
279.00/50.34	thf(decl_172, type, symdiffIneg1: $o).
279.00/50.34	thf(decl_173, type, symdiffIneg2: $o).
279.00/50.34	thf(decl_174, type, iskpair: $i > $o).
279.00/50.34	thf(decl_175, type, secondinupair: $o).
279.00/50.34	thf(decl_176, type, setukpairIL: $o).
279.00/50.34	thf(decl_177, type, setukpairIR: $o).
279.00/50.34	thf(decl_178, type, kpairiskpair: $o).
279.00/50.34	thf(decl_179, type, kpair: $i > $i > $i).
279.00/50.34	thf(decl_180, type, kpairp: $o).
279.00/50.34	thf(decl_181, type, cartprod: $i > $i > $i).
279.00/50.34	thf(decl_182, type, singletonsubset: $o).
279.00/50.34	thf(decl_183, type, singletoninpowerset: $o).
279.00/50.34	thf(decl_184, type, singletoninpowunion: $o).
279.00/50.34	thf(decl_185, type, upairset2E: $o).
279.00/50.34	thf(decl_186, type, upairsubunion: $o).
279.00/50.34	thf(decl_187, type, upairinpowunion: $o).
279.00/50.34	thf(decl_188, type, ubforcartprodlem1: $o).
279.00/50.34	thf(decl_189, type, ubforcartprodlem2: $o).
279.00/50.34	thf(decl_190, type, ubforcartprodlem3: $o).
279.00/50.34	thf(decl_191, type, cartprodpairin: $o).
279.00/50.34	thf(decl_192, type, cartprodmempair1: $o).
279.00/50.34	thf(decl_193, type, cartprodmempair: $o).
279.00/50.34	thf(decl_194, type, setunionE2: $o).
279.00/50.34	thf(decl_195, type, setunionsingleton1: $o).
279.00/50.34	thf(decl_196, type, setunionsingleton2: $o).
279.00/50.34	thf(decl_197, type, setunionsingleton: $o).
279.00/50.34	thf(decl_198, type, singleton: $i > $o).
279.00/50.34	thf(decl_199, type, singletonprop: $o).
279.00/50.34	thf(decl_200, type, ex1: $i > ($i > $o) > $o).
279.00/50.34	thf(decl_201, type, ex1E1: $o).
279.00/50.34	thf(decl_202, type, ex1I: $o).
279.00/50.34	thf(decl_203, type, ex1I2: $o).
279.00/50.34	thf(decl_204, type, singletonsuniq: $o).
279.00/50.34	thf(decl_209, type, setukpairinjL1: $o).
279.00/50.34	thf(decl_210, type, kfstsingleton: $o).
279.00/50.34	thf(decl_211, type, theprop: $o).
279.00/50.34	thf(decl_212, type, kfst: $i > $i).
279.00/50.34	thf(decl_213, type, kfstpairEq: $o).
279.00/50.34	thf(decl_214, type, cartprodfstin: $o).
279.00/50.34	thf(decl_215, type, setukpairinjL2: $o).
279.00/50.34	thf(decl_216, type, setukpairinjL: $o).
279.00/50.34	thf(decl_217, type, setukpairinjR11: $o).
279.00/50.34	thf(decl_218, type, setukpairinjR12: $o).
279.00/50.34	thf(decl_219, type, setukpairinjR1: $o).
279.00/50.34	thf(decl_220, type, upairequniteq: $o).
279.00/50.34	thf(decl_221, type, setukpairinjR2: $o).
279.00/50.34	thf(decl_222, type, setukpairinjR: $o).
279.00/50.34	thf(decl_223, type, ksndsingleton: $o).
279.00/50.34	thf(decl_224, type, ksnd: $i > $i).
279.00/50.34	thf(decl_225, type, ksndpairEq: $o).
279.00/50.34	thf(decl_226, type, kpairsurjEq: $o).
279.00/50.34	thf(decl_227, type, cartprodsndin: $o).
279.00/50.34	thf(decl_228, type, cartprodpairmemEL: $o).
279.00/50.34	thf(decl_229, type, cartprodpairmemER: $o).
279.00/50.34	thf(decl_230, type, cartprodmempaircEq: $o).
279.00/50.34	thf(decl_231, type, cartprodfstpairEq: $o).
279.00/50.34	thf(decl_232, type, cartprodsndpairEq: $o).
279.00/50.34	thf(decl_233, type, cartprodpairsurjEq: $o).
279.00/50.34	thf(decl_234, type, breln: $i > $i > $i > $o).
279.00/50.34	thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
279.00/50.34	thf(decl_236, type, dpsetconstrI: $o).
279.00/50.34	thf(decl_237, type, dpsetconstrSub: $o).
279.00/50.34	thf(decl_238, type, setOfPairsIsBReln: $o).
279.00/50.34	thf(decl_239, type, dpsetconstrERa: $o).
279.00/50.34	thf(decl_240, type, dpsetconstrEL1: $o).
279.00/50.34	thf(decl_241, type, dpsetconstrEL2: $o).
279.00/50.34	thf(decl_242, type, dpsetconstrER: $o).
279.00/50.34	thf(decl_243, type, func: $i > $i > $i > $o).
279.00/50.34	thf(decl_244, type, funcSet: $i > $i > $i).
279.00/50.34	thf(decl_245, type, funcImageSingleton: $o).
279.00/50.34	thf(decl_246, type, apProp: $o).
279.00/50.34	thf(decl_247, type, ap: $i > $i > $i > $i > $i).
279.00/50.34	thf(decl_248, type, app: $o).
279.00/50.34	thf(decl_249, type, infuncsetfunc: $o).
279.00/50.34	thf(decl_250, type, ap2p: $o).
279.00/50.34	thf(decl_251, type, funcinfuncset: $o).
279.00/50.34	thf(decl_252, type, lamProp: $o).
279.00/50.34	thf(decl_253, type, lam: $i > $i > ($i > $i) > $i).
279.00/50.34	thf(decl_254, type, lamp: $o).
279.00/50.34	thf(decl_255, type, lam2p: $o).
279.00/50.34	thf(decl_256, type, brelnall1: $o).
279.00/50.34	thf(decl_257, type, brelnall2: $o).
279.00/50.34	thf(decl_258, type, ex1E2: $o).
279.00/50.34	thf(decl_259, type, funcGraphProp1: $o).
279.00/50.34	thf(decl_260, type, funcGraphProp3: $o).
279.00/50.34	thf(decl_261, type, funcGraphProp2: $o).
279.00/50.34	thf(decl_262, type, funcextLem: $o).
279.00/50.34	thf(decl_263, type, funcGraphProp4: $o).
279.00/50.34	thf(decl_264, type, subbreln: $o).
279.00/50.34	thf(decl_265, type, eqbreln: $o).
279.00/50.34	thf(decl_266, type, funcext: $o).
279.00/50.34	thf(decl_267, type, funcext2: $o).
279.00/50.34	thf(decl_268, type, ap2apEq1: $o).
279.00/50.34	thf(decl_269, type, ap2apEq2: $o).
279.00/50.34	thf(decl_270, type, beta1: $o).
279.00/50.34	thf(decl_271, type, eta1: $o).
279.00/50.34	thf(decl_272, type, lam2lamEq: $o).
279.00/50.34	thf(decl_273, type, beta2: $o).
279.00/50.34	thf(decl_274, type, eta2: $o).
279.00/50.34	thf(decl_275, type, iffalseProp1: $o).
279.00/50.34	thf(decl_276, type, iffalseProp2: $o).
279.00/50.34	thf(decl_277, type, iftrueProp1: $o).
279.00/50.34	thf(decl_278, type, iftrueProp2: $o).
279.00/50.34	thf(decl_279, type, ifSingleton: $o).
279.00/50.34	thf(decl_280, type, if: $i > $o > $i > $i > $i).
279.00/50.34	thf(decl_281, type, ifp: $o).
279.00/50.34	thf(decl_282, type, theeq: $o).
279.00/50.34	thf(decl_283, type, iftrue: $o).
279.00/50.34	thf(decl_284, type, iffalse: $o).
279.00/50.34	thf(decl_285, type, iftrueorfalse: $o).
279.00/50.34	thf(decl_286, type, binintersectT_lem: $o).
279.00/50.34	thf(decl_287, type, binunionT_lem: $o).
279.00/50.34	thf(decl_288, type, powersetT_lem: $o).
279.00/50.34	thf(decl_289, type, setminusT_lem: $o).
279.00/50.34	thf(decl_290, type, complementT_lem: $o).
279.00/50.34	thf(decl_291, type, setextT: $o).
279.00/50.34	thf(decl_292, type, subsetTI: $o).
279.00/50.34	thf(decl_293, type, powersetTI1: $o).
279.00/50.34	thf(decl_294, type, powersetTE1: $o).
279.00/50.34	thf(decl_295, type, complementTI1: $o).
279.00/50.34	thf(decl_296, type, complementTE1: $o).
279.00/50.34	thf(decl_297, type, binintersectTELcontra: $o).
279.00/50.34	thf(decl_298, type, binintersectTERcontra: $o).
279.00/50.34	thf(decl_299, type, contrasubsetT: $o).
279.00/50.34	thf(decl_300, type, contrasubsetT1: $o).
279.00/50.34	thf(decl_301, type, contrasubsetT2: $o).
279.00/50.34	thf(decl_302, type, contrasubsetT3: $o).
279.00/50.34	thf(decl_303, type, doubleComplementI1: $o).
279.00/50.34	thf(decl_304, type, doubleComplementE1: $o).
279.00/50.34	thf(decl_305, type, doubleComplementSub1: $o).
279.00/50.34	thf(decl_306, type, doubleComplementSub2: $o).
279.00/50.34	thf(decl_307, type, doubleComplementEq: $o).
279.00/50.34	thf(decl_308, type, complementTnotintersectT: $o).
279.00/50.34	thf(decl_309, type, complementImpComplementIntersect: $o).
279.00/50.34	thf(decl_310, type, complementSubsetComplementIntersect: $o).
279.00/50.34	thf(decl_311, type, complementInPowersetComplementIntersect: $o).
279.00/50.34	thf(decl_312, type, contraSubsetComplement: $o).
279.00/50.34	thf(decl_313, type, complementTcontraSubset: $o).
279.00/50.34	thf(decl_314, type, binunionTILcontra: $o).
279.00/50.34	thf(decl_315, type, binunionTIRcontra: $o).
279.00/50.34	thf(decl_316, type, inIntersectImpInUnion: $o).
279.00/50.34	thf(decl_317, type, inIntersectImpInUnion2: $o).
279.00/50.34	thf(decl_318, type, inIntersectImpInIntersectUnions: $o).
279.00/50.34	thf(decl_319, type, intersectInPowersetIntersectUnions: $o).
279.00/50.34	thf(decl_320, type, inComplementUnionImpNotIn1: $o).
279.00/50.34	thf(decl_321, type, inComplementUnionImpInComplement1: $o).
279.00/50.34	thf(decl_322, type, binunionTE: $o).
279.00/50.34	thf(decl_323, type, binunionTEcontra: $o).
279.00/50.34	thf(decl_324, type, demorgan2a1: $o).
279.00/50.34	thf(decl_325, type, complementUnionInPowersetComplement: $o).
279.00/50.34	thf(decl_326, type, demorgan2a2: $o).
279.00/50.34	thf(decl_327, type, demorgan1a: $o).
279.00/50.34	thf(decl_328, type, demorgan1b: $o).
279.00/50.34	thf(decl_329, type, demorgan1: $o).
279.00/50.34	thf(decl_330, type, demorgan2a: $o).
279.00/50.34	thf(decl_331, type, demorgan2b2: $o).
279.00/50.34	thf(decl_332, type, demorgan2b: $o).
279.00/50.34	thf(decl_333, type, demorgan2: $o).
279.00/50.34	thf(decl_334, type, woz13rule0: $o).
279.00/50.34	thf(decl_335, type, woz13rule1: $o).
279.00/50.34	thf(decl_336, type, woz13rule2: $o).
279.00/50.34	thf(decl_337, type, woz13rule3: $o).
279.00/50.34	thf(decl_338, type, woz13rule4: $o).
279.00/50.34	thf(decl_339, type, woz1_1: $o).
279.00/50.34	thf(decl_340, type, woz1_2: $o).
279.00/50.34	thf(decl_341, type, woz1_3: $o).
279.00/50.34	thf(decl_342, type, woz1_4: $o).
279.00/50.34	thf(decl_343, type, woz1_5: $o).
279.00/50.34	thf(decl_344, type, breln1: $i > $i > $o).
279.00/50.34	thf(decl_345, type, breln1all2: $o).
279.00/50.34	thf(decl_346, type, breln1Set: $i > $i).
279.00/50.34	thf(decl_347, type, breln1SetBreln1: $o).
279.00/50.34	thf(decl_354, type, choice2fnsingleton: $o).
279.00/50.34	thf(decl_355, type, setOfPairsIsBReln1: $o).
279.00/50.34	thf(decl_356, type, breln1all1: $o).
279.00/50.34	thf(decl_357, type, subbreln1: $o).
279.00/50.34	thf(decl_358, type, eqbreln1: $o).
279.00/50.34	thf(decl_359, type, breln1invset: $i > $i > $i).
279.00/50.34	thf(decl_360, type, breln1invprop: $o).
279.00/50.34	thf(decl_361, type, breln1invI: $o).
279.00/50.34	thf(decl_362, type, breln1invE: $o).
279.00/50.34	thf(decl_363, type, breln1compset: $i > $i > $i > $i).
279.00/50.34	thf(decl_364, type, breln1compprop: $o).
279.00/50.34	thf(decl_365, type, breln1compI: $o).
279.00/50.34	thf(decl_366, type, breln1compE: $o).
279.00/50.34	thf(decl_367, type, breln1compEex: $o).
279.00/50.34	thf(decl_368, type, breln1unionprop: $o).
279.00/50.34	thf(decl_369, type, breln1unionIL: $o).
279.00/50.34	thf(decl_370, type, breln1unionIR: $o).
279.00/50.34	thf(decl_371, type, breln1unionI: $o).
279.00/50.34	thf(decl_372, type, breln1unionE: $o).
279.00/50.34	thf(decl_373, type, breln1unionEcases: $o).
279.00/50.34	thf(decl_374, type, breln1unionCommutes: $o).
279.00/50.34	thf(decl_375, type, woz2Ex: $o).
279.00/50.34	thf(decl_376, type, woz2W: $o).
279.00/50.34	thf(decl_377, type, woz2A: $o).
279.00/50.34	thf(decl_378, type, woz2B: $o).
279.00/50.34	thf(decl_379, type, image1Ex: $o).
279.00/50.34	thf(decl_380, type, image1Ex1: $o).
279.00/50.34	thf(decl_381, type, image1: $i > ($i > $i) > $i).
279.00/50.34	thf(decl_382, type, image1Equiv: $o).
279.00/50.34	thf(decl_383, type, image1E: $o).
279.00/50.34	thf(decl_384, type, image1I: $o).
279.00/50.34	thf(decl_385, type, injective: $i > $i > $i > $o).
279.00/50.34	thf(decl_386, type, injFuncSet: $i > $i > $i).
279.00/50.34	thf(decl_387, type, injFuncInInjFuncSet: $o).
279.00/50.34	thf(decl_388, type, injFuncSetFuncIn: $o).
279.00/50.34	thf(decl_389, type, injFuncSetFuncInj: $o).
279.00/50.34	thf(decl_390, type, surjective: $i > $i > $i > $o).
279.00/50.34	thf(decl_391, type, surjFuncSet: $i > $i > $i).
279.00/50.34	thf(decl_392, type, surjFuncSetFuncIn: $o).
279.00/50.34	thf(decl_393, type, surjFuncSetFuncSurj: $o).
279.00/50.34	thf(decl_394, type, leftInvIsSurj: $o).
279.00/50.34	thf(decl_395, type, surjCantorThm: $o).
279.00/50.34	thf(decl_396, type, epred1_0: $o).
279.00/50.34	thf(decl_397, type, esk1_2: $i > $i > $i).
279.00/50.34	thf(decl_398, type, esk2_2: $i > $i > $i).
279.00/50.34	thf(decl_399, type, esk3_2: $i > $i > $i).
279.00/50.34	thf(decl_400, type, esk4_1: $i > $i).
279.00/50.34	thf(decl_401, type, esk5_2: ($i > $i > $o) > $i > $i).
279.00/50.34	thf(decl_402, type, esk6_2: ($i > $i > $o) > $i > $i).
279.00/50.34	thf(decl_403, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
279.00/50.34	thf(decl_404, type, esk8_1: $i > $i).
279.00/50.34	thf(decl_405, type, esk9_1: ($i > $o) > $i).
279.00/50.34	thf(decl_406, type, esk10_1: ($i > $o) > $i).
279.00/50.34	thf(decl_407, type, esk11_2: $i > $i > $i).
279.00/50.34	thf(decl_408, type, esk12_2: $i > $i > $i).
279.00/50.34	thf(decl_409, type, esk13_1: $i > $i).
279.00/50.34	thf(decl_410, type, esk14_1: $i > $i).
279.00/50.34	thf(decl_411, type, esk15_1: $i > $i).
279.00/50.34	thf(decl_412, type, esk16_2: $i > $i > $i).
279.00/50.34	thf(decl_413, type, esk17_3: $i > $i > $o > $i).
279.00/50.34	thf(decl_414, type, esk18_1: ($i > $o) > $i).
279.00/50.34	thf(decl_415, type, esk19_1: $i > $i).
279.00/50.34	thf(decl_416, type, esk20_2: $i > ($i > $o) > $i).
279.00/50.34	thf(decl_417, type, esk21_2: $i > ($i > $o) > $i).
279.00/50.34	thf(decl_418, type, esk22_2: $i > ($i > $o) > $i).
279.00/50.34	thf(decl_419, type, esk23_2: $i > ($i > $o) > $i).
279.00/50.34	thf(decl_420, type, esk24_2: $i > ($i > $o) > $i).
279.00/50.34	thf(decl_421, type, esk25_2: $i > ($i > $o) > $i).
279.00/50.34	thf(decl_422, type, esk26_2: ($i > $o) > $i > $i).
279.00/50.34	thf(decl_423, type, esk27_1: ($i > $o) > $i).
279.00/50.34	thf(decl_424, type, esk28_1: ($i > $o) > $i).
279.00/50.34	thf(decl_425, type, esk29_2: ($i > $o) > $i > $i).
279.00/50.34	thf(decl_426, type, esk30_2: ($i > $o) > ($i > $o) > $i).
279.00/50.34	thf(decl_427, type, esk31_2: ($i > $o) > ($i > $o) > $i).
279.00/50.34	thf(decl_428, type, esk32_2: ($i > $o) > ($i > $o) > $i).
279.00/50.34	thf(decl_429, type, esk33_2: ($i > $o) > ($i > $o) > $i).
279.00/50.34	thf(decl_430, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
279.00/50.34	thf(decl_431, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
279.00/50.34	thf(decl_432, type, esk36_2: $i > $i > $i).
279.00/50.34	thf(decl_433, type, esk37_2: $i > $i > $i).
279.00/50.34	thf(decl_434, type, esk38_2: $i > $i > $i).
279.00/50.34	thf(decl_435, type, esk39_3: $i > $i > $i > $i).
279.00/50.34	thf(decl_436, type, esk40_3: $i > $i > $i > $i).
279.00/50.34	thf(decl_437, type, esk41_2: $i > $i > $i).
279.00/50.34	thf(decl_438, type, esk42_2: $i > ($i > $o) > $i).
279.00/50.34	thf(decl_439, type, esk43_2: $i > ($i > $o) > $i).
279.00/50.34	thf(decl_440, type, esk44_2: $i > ($i > $o) > $i).
279.00/50.34	thf(decl_441, type, esk45_3: $i > ($i > $o) > $i > $i).
279.00/50.34	thf(decl_442, type, esk46_2: $i > ($i > $o) > $i).
279.00/50.34	thf(decl_443, type, esk47_2: $i > ($i > $o) > $i).
279.00/50.34	thf(decl_444, type, esk48_3: $i > $i > ($i > $i) > $i).
279.00/50.34	thf(decl_445, type, esk49_3: $i > $i > ($i > $i) > $i).
279.00/50.34	thf(decl_446, type, esk50_3: $i > $i > ($i > $i) > $i).
279.00/50.34	thf(decl_447, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
279.00/50.34	thf(decl_448, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
279.00/50.34	thf(decl_449, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
279.00/50.34	thf(decl_450, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
279.00/50.34	thf(decl_451, type, esk55_4: $i > $i > $i > $i > $i).
279.00/50.34	thf(decl_452, type, esk56_4: $i > $i > $i > $i > $i).
279.00/50.34	thf(decl_453, type, esk57_4: $i > $i > $i > $i > $i).
279.00/50.34	thf(decl_454, type, esk58_4: $i > $i > $i > $i > $i).
279.00/50.34	thf(decl_455, type, esk59_4: $i > $i > $i > $i > $i).
279.00/50.34	thf(decl_456, type, esk60_4: $i > $i > $i > $i > $i).
279.00/50.34	thf(decl_457, type, esk61_4: $i > $i > $i > $i > $i).
279.00/50.34	thf(decl_458, type, esk62_4: $i > $i > $i > $i > $i).
279.00/50.34	thf(decl_459, type, esk63_4: $i > $i > $i > $i > $i).
279.00/50.34	thf(decl_460, type, esk64_3: $i > $i > ($i > $i) > $i).
279.00/50.34	thf(decl_461, type, esk65_3: $i > $i > ($i > $i) > $i).
279.00/50.34	thf(decl_462, type, esk66_3: $i > $i > ($i > $i) > $i).
279.00/50.34	thf(decl_463, type, esk67_3: $i > $i > $i > $i).
279.00/50.34	thf(decl_464, type, esk68_3: $i > $i > $i > $i).
279.00/50.34	thf(decl_465, type, esk69_3: $i > $i > $i > $i).
279.00/50.34	thf(decl_466, type, esk70_3: $i > $i > $i > $i).
279.00/50.34	thf(decl_467, type, esk71_3: $i > $i > ($i > $o) > $i).
279.00/50.34	thf(decl_468, type, esk72_3: $i > $i > ($i > $o) > $i).
279.00/50.34	thf(decl_469, type, esk73_3: $i > $i > ($i > $o) > $i).
279.00/50.34	thf(decl_470, type, esk74_3: $i > $i > ($i > $o) > $i).
279.00/50.34	thf(decl_471, type, esk75_3: $i > $i > $i > $i).
279.00/50.34	thf(decl_472, type, esk76_3: $i > $i > $i > $i).
279.00/50.34	thf(decl_473, type, esk77_3: $i > $i > $i > $i).
279.00/50.34	thf(decl_474, type, esk78_3: $i > $i > $i > $i).
279.00/50.34	thf(decl_475, type, esk79_3: $i > $i > $i > $i).
279.00/50.34	thf(decl_476, type, esk80_3: $i > $i > $i > $i).
279.00/50.34	thf(decl_477, type, esk81_5: $i > $i > $i > $i > $i > $i).
279.00/50.34	thf(decl_478, type, esk82_6: $i > $i > $i > $i > $i > $o > $i).
279.00/50.34	thf(decl_479, type, esk83_2: $i > ($i > $i) > $i).
279.00/50.34	thf(decl_480, type, esk84_3: $i > ($i > $i) > $i > $i).
279.00/50.34	thf(decl_481, type, esk85_3: $i > ($i > $i) > $i > $i).
279.00/50.34	thf(decl_482, type, esk86_3: $i > ($i > $i) > $i > $i).
279.00/50.34	thf(decl_483, type, esk87_3: $i > $i > ($i > $i) > $i).
279.00/50.34	thf(decl_484, type, esk88_4: $i > $i > ($i > $i) > $i > $i).
279.00/50.34	thf(decl_485, type, esk89_0: $i).
279.00/50.34	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', nonempty)).
279.00/50.34	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', nonemptyI)).
279.00/50.34	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', singletonprop)).
279.00/50.34	thf(ex1I, axiom, ((ex1I)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', ex1I)).
279.00/50.34	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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', ex1I2)).
279.00/50.34	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', exuEu)).
279.00/50.34	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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', exu__Cong)).
279.00/50.34	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', exuI3)).
279.00/50.34	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', exuI1)).
279.00/50.34	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', nonemptyImpWitness)).
279.00/50.34	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', exuE2)).
279.00/50.34	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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', dpsetconstrI)).
279.00/50.34	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setoftrueEq)).
279.00/50.34	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', nonemptyE1)).
279.00/50.34	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', dpsetconstrSub)).
279.00/50.34	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setOfPairsIsBReln)).
279.00/50.34	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', dpsetconstrERa)).
279.00/50.34	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', dsetconstrEL)).
279.00/50.34	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', dpsetconstrEL2)).
279.00/50.34	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', descrp)).
279.00/50.34	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', replAx)).
279.00/50.34	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', funcImageSingleton)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', lamProp)).
279.00/50.34	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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', lam2p)).
279.00/50.34	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', ex1E2)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', eta1)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', beta2)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', eta2)).
279.00/50.34	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', iffalseProp2)).
279.00/50.34	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', iftrueProp1)).
279.00/50.34	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', iftrueProp2)).
279.00/50.34	thf(image1Ex1, axiom, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', image1Ex1)).
279.00/50.34	thf(image1Equiv, axiom, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X59 @ X3))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', image1Equiv)).
279.00/50.34	thf(image1E, axiom, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X60 @ X3))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', image1E)).
279.00/50.34	thf(image1I, axiom, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X61 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', image1I)).
279.00/50.34	thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setOfPairsIsBReln1)).
279.00/50.34	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', ifSingleton)).
279.00/50.34	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', iffalseProp1)).
279.00/50.34	thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', lam2lamEq)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', beta1)).
279.00/50.34	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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', lamp)).
279.00/50.34	thf(apProp, axiom, ((apProp)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', apProp)).
279.00/50.34	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:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', dpsetconstrER)).
279.00/50.34	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', dpsetconstrEL1)).
279.00/50.34	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', ksndsingleton)).
279.00/50.34	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', kfstsingleton)).
279.00/50.34	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', ex1E1)).
279.00/50.34	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', sepSubset)).
279.00/50.34	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', sepInPowerset)).
279.00/50.34	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', dsetconstr__Cong)).
279.00/50.34	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', descr__Cong)).
279.00/50.34	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', exuE3u)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', exuI2)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', emptyE1)).
279.00/50.34	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', nonemptyI1)).
279.00/50.34	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setbeta)).
279.00/50.34	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', exuE3e)).
279.00/50.34	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', exuE1)).
279.00/50.34	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', dsetconstrER)).
279.00/50.34	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', dsetconstrI)).
279.00/50.34	thf(foundation2, conjecture, (((emptysetAx)=>(((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>(((foundationAx)=>((wellorderingAx)=>(((dsetconstrI)=>(((dsetconstrER)=>((exuE1)=>((((((exuE3e)=>((setext)=>((((setbeta)=>(((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((((powersetI)=>((emptyinPowerset)=>(((powersetE)=>(((setunionE)=>((subPowSU)=>(((((notinsingleton)=>((((upairsetE)=>((upairsetIL)=>(((emptyE1)=>((((((quantDeMorgan4)=>(((prop2set2propI)=>((((((exuI2)=>(((in__Cong)=>((exuE3u)=>(((((powerset__Cong)=>(((((descr__Cong)=>((dsetconstr__Cong)=>(((eqimpsubset2)=>(((subsetI2)=>(((subsetE)=>((subsetE2)=>((notsubsetI)=>(((notequalI2)=>((((setadjoinSub)=>(((subset2powerset)=>(((subsetemptysetimpeq)=>(((powersetE1)=>((inPowerset)=>(((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((((binunionE)=>((((((((binintersectSubset2)=>((((disjointsetsI1)=>(((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>(((((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((((symdiffE)=>((((symdiffIneg1)=>((symdiffIneg2)=>((((setukpairIR)=>((kpairiskpair)=>(((((singletoninpowunion)=>(((upairsubunion)=>(((ubforcartprodlem1)=>((((((cartprodmempair)=>((setunionE2)=>(((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>(((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((((kfstpairEq)=>((((setukpairinjL)=>((((((((((kpairsurjEq)=>(((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>(((dpsetconstrEL2)=>(((funcImageSingleton)=>((((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>(((lam2p)=>((brelnall1)=>(((ex1E2)=>((((((((eqbreln)=>((funcext)=>((funcext2)=>(((ap2apEq2)=>(((eta1)=>(((beta2)=>((eta2)=>(((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((((theeq)=>(((iffalse)=>((iftrueorfalse)=>((((powersetT_lem)=>((setminusT_lem)=>(((setextT)=>((subsetTI)=>((powersetTI1)=>((((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((((((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((((complementImpComplementIntersect)=>(((((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>(((((((demorgan2a)=>(((((((woz13rule2)=>((woz13rule3)=>(((woz1_1)=>(((((((breln1SetBreln1)=>((choice2fnsingleton)=>((((subbreln1)=>((eqbreln1)=>(((breln1invI)=>((((breln1compI)=>(((breln1compEex)=>(((breln1unionIL)=>((breln1unionIR)=>((((breln1unionEcases)=>((breln1unionCommutes)=>((((woz2A)=>(((image1Ex)=>((image1Ex1)=>((image1Equiv)=>((image1E)=>((((injFuncSetFuncIn)=>(((surjFuncSetFuncIn)=>(((leftInvIsSurj)=>(![X4:$i]:(((nonempty @ X4)=>?[X21:$i]:(((in @ X21 @ X4)&((binintersect @ X21 @ X4)=(emptyset))))))<=(surjCantorThm)))<=(surjFuncSetFuncSurj)))<=(injFuncSetFuncInj)))<=(injFuncInInjFuncSet))<=(image1I))))))<=(woz2B)))<=(woz2W))<=(woz2Ex))))<=(breln1unionE))<=(breln1unionI))))<=(breln1unionprop)))<=(breln1compE)))<=(breln1compprop))<=(breln1invE)))<=(breln1invprop))))<=(breln1all1))<=(setOfPairsIsBReln1))))<=(breln1all2))<=(woz1_5))<=(woz1_4))<=(woz1_3))<=(woz1_2)))<=(woz13rule4))))<=(woz13rule1))<=(woz13rule0))<=(demorgan2))<=(demorgan2b))<=(demorgan2b2)))<=(demorgan1))<=(demorgan1b))<=(demorgan1a))<=(demorgan2a2))<=(complementUnionInPowersetComplement)))))))))<=(inIntersectImpInUnion2))<=(inIntersectImpInUnion)))))<=(contraSubsetComplement))<=(complementInPowersetComplementIntersect))<=(complementSubsetComplementIntersect)))<=(complementTnotintersectT))<=(doubleComplementEq))))))<=(contrasubsetT3))<=(contrasubsetT2))<=(contrasubsetT1))<=(contrasubsetT)))))<=(complementTI1))<=(powersetTE1)))))<=(complementT_lem))))<=(binunionT_lem))<=(binintersectT_lem))))<=(iftrue)))<=(ifp))<=(ifSingleton)))))<=(iffalseProp1))))<=(lam2lamEq)))<=(beta1)))<=(ap2apEq1)))))<=(subbreln))<=(funcGraphProp4))<=(funcextLem))<=(funcGraphProp2))<=(funcGraphProp3))<=(funcGraphProp1)))<=(brelnall2))))<=(lamp))))))<=(app))<=(apProp)))<=(dpsetconstrER)))<=(dpsetconstrEL1))))))))))))<=(cartprodsndin)))<=(ksndpairEq))<=(ksndsingleton))<=(setukpairinjR))<=(setukpairinjR2))<=(upairequniteq))<=(setukpairinjR1))<=(setukpairinjR12))<=(setukpairinjR11)))<=(setukpairinjL2))<=(cartprodfstin)))<=(theprop))<=(kfstsingleton))))))<=(ex1E1)))))<=(setunionsingleton1))))<=(cartprodmempair1))<=(cartprodpairin))<=(ubforcartprodlem3))<=(ubforcartprodlem2)))<=(upairinpowunion)))<=(upairset2E)))<=(singletoninpowerset))<=(singletonsubset))<=(kpairp))))<=(setukpairIL))<=(secondinupair))))<=(symdiffI2))<=(symdiffI1)))<=(setminusSubset1))<=(setminusLsub)))))))<=(setminusER))<=(setminusEL))<=(setminusI)))))<=(binintersectRsub)))<=(binintersectER))<=(binintersectSubset3)))<=(binintersectLsub))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI))<=(binunionRsub))<=(binunionLsub)))<=(binunionEcases))<=(binunionIR))))))<=(powersetsubset))))<=(powersetI1)))<=(setextsub)))<=(setadjoinSub2)))<=(subsetTrans))<=(subsetRefl)))<=(notequalI1)))))<=(emptysetsubset)))<=(eqimpsubset1)))<=(subsetI1))))<=(exuEu))<=(omega__Cong))<=(setunion__Cong)))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong))))<=(inCongP)))<=(exuI3))<=(exuI1))<=(notdallE))<=(notdexE)))<=(prop2setI)))<=(quantDeMorgan3))<=(quantDeMorgan2))<=(quantDeMorgan1))<=(vacuousDall)))<=(upairsetIR))))<=(singletonsswitch))<=(eqinunit)))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))))<=(setunionI)))<=(emptyInPowerset))))<=(setoftrueEq))<=(setadjoinOr))))))))<=(nonemptyE1)))<=(noeltsimpempty))<=(emptyI))))<=(notinemptyset))<=(emptysetimpfalse))<=(emptysetE))<=(prop2setE))))<=(dsetconstrEL)))<=(descrp))))<=(replAx)))))))<=(setadjoinAx)))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', foundation2)).
279.00/50.34	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', omega__Cong)).
279.00/50.34	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setextAx)).
279.00/50.34	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binintersectER)).
279.00/50.34	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', upairsubunion)).
279.00/50.34	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binintersectSubset3)).
279.00/50.34	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binintersectLsub)).
279.00/50.34	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binintersectEL)).
279.00/50.34	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setunionsingleton)).
279.00/50.34	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binintersectSubset5)).
279.00/50.34	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binintersectI)).
279.00/50.34	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binunionRsub)).
279.00/50.34	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binunionLsub)).
279.00/50.34	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binunionEcases)).
279.00/50.34	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binunionIR)).
279.00/50.34	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', powersetsubset)).
279.00/50.34	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', powersetI1)).
279.00/50.34	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setextsub)).
279.00/50.34	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setadjoinSub2)).
279.00/50.34	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', singletonsuniq)).
279.00/50.34	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', subsetTrans)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', ubforcartprodlem1)).
279.00/50.34	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', subsetRefl)).
279.00/50.34	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', notequalI1)).
279.00/50.34	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.OzmfPJvcVc/E---3.1_25410.p', setukpairinjL1)).
279.00/50.34	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', emptysetsubset)).
279.00/50.34	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', eqimpsubset1)).
279.00/50.34	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', subsetI1)).
279.00/50.34	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', kfstpairEq)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', ap2p)).
279.00/50.34	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setunion__Cong)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', setukpairinjL)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', setadjoin__Cong)).
279.00/50.34	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', emptyset__Cong)).
279.00/50.34	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', kpairsurjEq)).
279.00/50.34	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', inCongP)).
279.00/50.34	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', cartprodpairmemEL)).
279.00/50.34	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', notdallE)).
279.00/50.34	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', notdexE)).
279.00/50.34	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', cartprodpairmemER)).
279.00/50.34	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', prop2setI)).
279.00/50.34	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', quantDeMorgan3)).
279.00/50.34	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', cartprodmempaircEq)).
279.00/50.34	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', quantDeMorgan2)).
279.00/50.34	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', quantDeMorgan1)).
279.00/50.34	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', vacuousDall)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', cartprodfstpairEq)).
279.00/50.34	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', upairsetIR)).
279.00/50.34	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', singletonsswitch)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', cartprodsndpairEq)).
279.00/50.34	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', eqinunit)).
279.00/50.34	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', uniqinunit)).
279.00/50.34	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', cartprodpairsurjEq)).
279.00/50.34	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setunionI)).
279.00/50.34	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', cartprodmempair)).
279.00/50.34	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', emptyInPowerset)).
279.00/50.34	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setadjoinOr)).
279.00/50.34	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', noeltsimpempty)).
279.00/50.34	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', emptyI)).
279.00/50.34	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', notinemptyset)).
279.00/50.34	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', emptysetimpfalse)).
279.00/50.34	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', emptysetE)).
279.00/50.34	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', prop2setE)).
279.00/50.34	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setadjoinAx)).
279.00/50.34	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', infuncsetfunc)).
279.00/50.34	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', complementTcontraSubset)).
279.00/50.34	thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binunionTILcontra)).
279.00/50.34	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', funcinfuncset)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', brelnall1)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', eqbreln)).
279.00/50.34	thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', funcext)).
279.00/50.34	thf(funcext2, axiom, ((funcext2)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', funcext2)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', ap2apEq2)).
279.00/50.34	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setunionE2)).
279.00/50.34	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', theeq)).
279.00/50.34	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', iffalse)).
279.00/50.34	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', iftrueorfalse)).
279.00/50.34	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', powersetT_lem)).
279.00/50.34	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', setminusT_lem)).
279.00/50.34	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setextT)).
279.00/50.34	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', subsetTI)).
279.00/50.34	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', powersetTI1)).
279.00/50.34	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', complementTE1)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', binintersectTELcontra)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', binintersectTERcontra)).
279.00/50.34	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', doubleComplementI1)).
279.00/50.34	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', doubleComplementE1)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', doubleComplementSub1)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', doubleComplementSub2)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', complementImpComplementIntersect)).
279.00/50.34	thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', demorgan1a)).
279.00/50.34	thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', demorgan2a2)).
279.00/50.34	thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', complementUnionInPowersetComplement)).
279.00/50.34	thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', inIntersectImpInUnion2)).
279.00/50.34	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', inIntersectImpInUnion)).
279.00/50.34	thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binunionTIRcontra)).
279.00/50.34	thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', inIntersectImpInIntersectUnions)).
279.00/50.34	thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', intersectInPowersetIntersectUnions)).
279.00/50.34	thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', inComplementUnionImpNotIn1)).
279.00/50.34	thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', inComplementUnionImpInComplement1)).
279.00/50.34	thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binunionTE)).
279.00/50.34	thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binunionTEcontra)).
279.00/50.34	thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', demorgan2a1)).
279.00/50.34	thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', demorgan2a)).
279.00/50.34	thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', woz13rule2)).
279.00/50.34	thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', woz13rule3)).
279.00/50.34	thf(woz1_1, axiom, ((woz1_1)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', woz1_1)).
279.00/50.34	thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', breln1SetBreln1)).
279.00/50.34	thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', subbreln1)).
279.00/50.34	thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', eqbreln1)).
279.00/50.34	thf(breln1invI, axiom, ((breln1invI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', breln1invI)).
279.00/50.34	thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', breln1compI)).
279.00/50.34	thf(breln1compEex, axiom, ((breln1compEex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>![X54:$o]:((![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(X54)))))=>(X54))))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', breln1compEex)).
279.00/50.34	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setunionsingleton2)).
279.00/50.34	thf(breln1unionIL, axiom, ((breln1unionIL)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', breln1unionIL)).
279.00/50.34	thf(breln1unionIR, axiom, ((breln1unionIR)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', breln1unionIR)).
279.00/50.34	thf(breln1unionEcases, axiom, ((breln1unionEcases)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>![X55:$o]:((((in @ (kpair @ X2 @ X3) @ X33)=>(X55))=>(((in @ (kpair @ X2 @ X3) @ X35)=>(X55))=>(X55)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', breln1unionEcases)).
279.00/50.34	thf(breln1unionCommutes, axiom, ((breln1unionCommutes)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((binunion @ X33 @ X35)=(binunion @ X35 @ X33))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', breln1unionCommutes)).
279.00/50.34	thf(woz2A, axiom, ((woz2A)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1compset @ X4 @ X33 @ X56) @ (breln1compset @ X4 @ X35 @ X56)))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', woz2A)).
279.00/50.34	thf(image1Ex, axiom, ((image1Ex)<=>![X4:$i, X57:$i > $i]:(?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X57 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', image1Ex)).
279.00/50.34	thf(injFuncSetFuncIn, axiom, ((injFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', injFuncSetFuncIn)).
279.00/50.34	thf(surjFuncSetFuncIn, axiom, ((surjFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', surjFuncSetFuncIn)).
279.00/50.34	thf(leftInvIsSurj, axiom, ((leftInvIsSurj)<=>![X4:$i, X5:$i, X62:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X62 @ X2) @ X5)))=>![X34:$i]:(((in @ X34 @ (funcSet @ X5 @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X5 @ X4 @ X34 @ (X62 @ X2))=(X2))))=>(surjective @ X5 @ X4 @ X34))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', leftInvIsSurj)).
279.00/50.34	thf(surjCantorThm, axiom, ((surjCantorThm)<=>![X4:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ (powerset @ X4)))=>~((surjective @ X4 @ (powerset @ X4) @ X29))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', surjCantorThm)).
279.00/50.34	thf(surjFuncSetFuncSurj, axiom, ((surjFuncSetFuncSurj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X2 @ X3))=>(surjective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', surjFuncSetFuncSurj)).
279.00/50.34	thf(injFuncSetFuncInj, axiom, ((injFuncSetFuncInj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X2 @ X3))=>(injective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', injFuncSetFuncInj)).
279.00/50.34	thf(injFuncInInjFuncSet, axiom, ((injFuncInInjFuncSet)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((injective @ X4 @ X5 @ X29)=>(in @ X29 @ (injFuncSet @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', injFuncInInjFuncSet)).
279.00/50.34	thf(woz2B, axiom, ((woz2B)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X35))) @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X33)))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', woz2B)).
279.00/50.34	thf(woz2W, axiom, ((woz2W)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((breln1invset @ X4 @ (breln1compset @ X4 @ X33 @ X35))=(breln1compset @ X4 @ (breln1invset @ X4 @ X35) @ (breln1invset @ X4 @ X33)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', woz2W)).
279.00/50.34	thf(woz2Ex, axiom, ((woz2Ex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>((X33)=(breln1invset @ X4 @ (breln1invset @ X4 @ X33)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', woz2Ex)).
279.00/50.34	thf(breln1unionE, axiom, ((breln1unionE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', breln1unionE)).
279.00/50.34	thf(breln1unionI, axiom, ((breln1unionI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35))=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', breln1unionI)).
279.00/50.34	thf(breln1unionprop, axiom, ((breln1unionprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', breln1unionprop)).
279.00/50.34	thf(breln1compE, axiom, ((breln1compE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35))))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', breln1compE)).
279.00/50.34	thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', breln1compprop)).
279.00/50.34	thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', breln1invE)).
279.00/50.34	thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', breln1invprop)).
279.00/50.34	thf(breln1all1, axiom, ((breln1all1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', breln1all1)).
279.00/50.34	thf(breln1all2, axiom, ((breln1all2)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', breln1all2)).
279.00/50.34	thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', woz1_5)).
279.00/50.34	thf(woz1_4, axiom, ((woz1_4)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', woz1_4)).
279.00/50.34	thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', woz1_3)).
279.00/50.34	thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', woz1_2)).
279.00/50.34	thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', woz13rule4)).
279.00/50.34	thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', woz13rule1)).
279.00/50.34	thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', woz13rule0)).
279.00/50.34	thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', demorgan2)).
279.00/50.34	thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', demorgan2b)).
279.00/50.34	thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', demorgan2b2)).
279.00/50.34	thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', demorgan1)).
279.00/50.34	thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', demorgan1b)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', contraSubsetComplement)).
279.00/50.34	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', complementInPowersetComplementIntersect)).
279.00/50.34	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', complementSubsetComplementIntersect)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', complementTnotintersectT)).
279.00/50.34	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', doubleComplementEq)).
279.00/50.34	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', contrasubsetT3)).
279.00/50.34	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', contrasubsetT2)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', contrasubsetT1)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', contrasubsetT)).
279.00/50.34	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', complementTI1)).
279.00/50.34	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', powersetTE1)).
279.00/50.34	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', complementT_lem)).
279.00/50.34	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', binunionT_lem)).
279.00/50.34	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binintersectT_lem)).
279.00/50.34	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', iftrue)).
279.00/50.34	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', ifp)).
279.00/50.34	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', ap2apEq1)).
279.00/50.34	thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', subbreln)).
279.00/50.34	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', funcGraphProp4)).
279.00/50.34	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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', funcextLem)).
279.00/50.34	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', funcGraphProp2)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', funcGraphProp3)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', funcGraphProp1)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', brelnall2)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', app)).
279.00/50.34	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', cartprodsndin)).
279.00/50.34	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', ksndpairEq)).
279.00/50.34	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setukpairinjR)).
279.00/50.34	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setukpairinjR2)).
279.00/50.34	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', upairequniteq)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', setukpairinjR1)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', setukpairinjR12)).
279.00/50.34	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setukpairinjR11)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', setukpairinjL2)).
279.00/50.34	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', cartprodfstin)).
279.00/50.34	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', theprop)).
279.00/50.34	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setunionsingleton1)).
279.00/50.34	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', cartprodmempair1)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', cartprodpairin)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', ubforcartprodlem3)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', ubforcartprodlem2)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', upairinpowunion)).
279.00/50.34	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', upairset2E)).
279.00/50.34	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', singletoninpowerset)).
279.00/50.34	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', singletonsubset)).
279.00/50.34	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', kpairp)).
279.00/50.34	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setukpairIL)).
279.00/50.34	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', secondinupair)).
279.00/50.34	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', symdiffI2)).
279.00/50.34	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', symdiffI1)).
279.00/50.34	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setminusSubset1)).
279.00/50.34	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setminusLsub)).
279.00/50.34	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setminusER)).
279.00/50.34	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setminusEL)).
279.00/50.34	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setminusI)).
279.00/50.34	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binintersectRsub)).
279.00/50.34	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', singletoninpowunion)).
279.00/50.34	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', kpairiskpair)).
279.00/50.34	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setukpairIR)).
279.00/50.34	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', symdiffIneg2)).
279.00/50.34	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', symdiffIneg1)).
279.00/50.34	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', symdiffE)).
279.00/50.34	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setminusIRneg)).
279.00/50.34	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setminusILneg)).
279.00/50.34	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setminusELneg)).
279.00/50.34	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setminusERneg)).
279.00/50.34	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setminusSubset2)).
279.00/50.34	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', bs114d)).
279.00/50.34	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binintersectSubset1)).
279.00/50.34	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binintersectSubset4)).
279.00/50.34	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', disjointsetsI1)).
279.00/50.34	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binintersectSubset2)).
279.00/50.34	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binunionE)).
279.00/50.34	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', upairset2IR)).
279.00/50.34	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', binunionIL)).
279.00/50.34	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', inPowerset)).
279.00/50.34	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', powersetE1)).
279.00/50.34	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', subsetemptysetimpeq)).
279.00/50.34	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', subset2powerset)).
279.00/50.34	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setadjoinSub)).
279.00/50.34	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', notequalI2)).
279.00/50.34	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', notsubsetI)).
279.00/50.34	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', subsetE2)).
279.00/50.34	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', subsetE)).
279.00/50.34	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', subsetI2)).
279.00/50.34	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', eqimpsubset2)).
279.00/50.34	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', powerset__Cong)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', in__Cong)).
279.00/50.34	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', quantDeMorgan4)).
279.00/50.34	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', upairsetIL)).
279.00/50.34	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', upairsetE)).
279.00/50.34	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', notinsingleton)).
279.00/50.34	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', subPowSU)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', setunionE)).
279.00/50.34	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', powersetE)).
279.00/50.34	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', emptyinPowerset)).
279.00/50.34	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', powersetI)).
279.00/50.34	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setadjoinE)).
279.00/50.34	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setadjoinIR)).
279.00/50.34	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', emptyinunitempty)).
279.00/50.34	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setadjoinIL)).
279.00/50.34	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.OzmfPJvcVc/E---3.1_25410.p', setext)).
279.00/50.34	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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', wellorderingAx)).
279.00/50.34	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', foundationAx)).
279.00/50.34	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.OzmfPJvcVc/E---3.1_25410.p', omegaIndAx)).
279.00/50.34	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', omegaSAx)).
279.00/50.34	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', omega0Ax)).
279.00/50.34	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', setunionAx)).
279.00/50.34	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', powersetAx)).
279.00/50.34	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.OzmfPJvcVc/E---3.1_25410.p', emptysetAx)).
279.00/50.34	thf(c_0_321, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
279.00/50.34	thf(c_0_322, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
279.00/50.34	thf(c_0_323, plain, ((singletonprop)<=>![X4:$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/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
279.00/50.34	thf(c_0_324, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
279.00/50.34	thf(c_0_325, 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/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
279.00/50.34	thf(c_0_326, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
279.00/50.34	thf(c_0_327, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
279.00/50.34	thf(c_0_328, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
279.00/50.34	thf(c_0_329, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
279.00/50.34	thf(c_0_330, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_321])).
279.00/50.34	thf(c_0_331, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
279.00/50.34	thf(c_0_332, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
279.00/50.34	thf(c_0_333, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
279.00/50.34	thf(c_0_334, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_321])).
279.00/50.34	thf(c_0_335, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
279.00/50.34	thf(c_0_336, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
279.00/50.34	thf(c_0_337, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
279.00/50.34	thf(c_0_338, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
279.00/50.34	thf(c_0_339, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
279.00/50.34	thf(c_0_340, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
279.00/50.34	thf(c_0_341, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
279.00/50.34	thf(c_0_342, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
279.00/50.34	thf(c_0_343, 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/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
279.00/50.34	thf(c_0_344, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
279.00/50.34	thf(c_0_345, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$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])).
279.00/50.34	thf(c_0_346, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
279.00/50.34	thf(c_0_347, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
279.00/50.34	thf(c_0_348, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
279.00/50.34	thf(c_0_349, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
279.00/50.34	thf(c_0_350, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
279.00/50.34	thf(c_0_351, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
279.00/50.34	thf(c_0_352, plain, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[Z0/* 6 */:$i]:(![X2:$i]:(((in @ X2 @ Z0)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3))))))))))), inference(fof_simplification,[status(thm)],[image1Ex1])).
279.00/50.34	thf(c_0_353, plain, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X59 @ Z0))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), inference(fof_simplification,[status(thm)],[image1Equiv])).
279.00/50.34	thf(c_0_354, plain, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X60 @ Z0))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), inference(fof_simplification,[status(thm)],[image1E])).
279.00/50.34	thf(c_0_355, plain, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X61 @ Z0))))))), inference(fof_simplification,[status(thm)],[image1I])).
279.00/50.34	thf(c_0_356, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
279.00/50.34	thf(c_0_357, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
279.00/50.34	thf(c_0_358, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
279.00/50.34	thf(c_0_359, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
279.00/50.34	thf(c_0_360, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
279.00/50.34	thf(c_0_361, 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/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
279.00/50.34	thf(c_0_362, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
279.00/50.34	thf(c_0_363, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
279.00/50.34	thf(c_0_364, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
279.00/50.34	thf(c_0_365, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
279.00/50.34	thf(c_0_366, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
279.00/50.34	thf(c_0_367, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
279.00/50.34	thf(c_0_368, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
279.00/50.34	thf(c_0_369, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
279.00/50.34	thf(c_0_370, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
279.00/50.34	thf(c_0_371, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
279.00/50.34	thf(c_0_372, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
279.00/50.34	thf(c_0_373, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
279.00/50.34	thf(c_0_374, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
279.00/50.34	thf(c_0_375, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_321])).
279.00/50.34	thf(c_0_376, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_322, c_0_321])).
279.00/50.34	thf(c_0_377, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
279.00/50.34	thf(c_0_378, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
279.00/50.34	thf(c_0_379, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
279.00/50.34	thf(c_0_380, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
279.00/50.34	thf(c_0_381, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
279.00/50.34	thf(c_0_382, plain, ((epred1_0)<=>![X1133:$i]:(?[X1134:$i]:((((![X1135:$i]:(((in @ X1135 @ X1134)=>![X1136:$i]:(((in @ X1136 @ X1135)=>(in @ X1136 @ X1133)))))&![X1137:$i, X1138:$i]:((((in @ X1137 @ X1133)&(in @ X1138 @ X1133))=>(![X1139:$i]:(((in @ X1139 @ X1134)=>((in @ X1137 @ X1139)<=>(in @ X1138 @ X1139))))=>((X1137)=(X1138))))))&![X1140:$i, X1141:$i]:((((in @ X1140 @ X1134)&(in @ X1141 @ X1134))=>(![X1142:$i]:(((in @ X1142 @ X1140)=>(in @ X1142 @ X1141)))|![X1143:$i]:(((in @ X1143 @ X1141)=>(in @ X1143 @ X1140)))))))&![X1144:$i]:(((![X1145:$i]:(((in @ X1145 @ X1144)=>(in @ X1145 @ X1133)))&?[X1146:$i]:((in @ X1146 @ X1144)))=>?[X1147:$i, X1148:$i]:(((((in @ X1147 @ X1134)&(in @ X1148 @ X1144))&~(?[X1149:$i]:(((in @ X1149 @ X1147)&(in @ X1149 @ X1144)))))&![X1150:$i]:(((in @ X1150 @ X1134)=>(![X1151:$i]:(((in @ X1151 @ X1150)=>(in @ X1151 @ X1147)))|(in @ X1148 @ X1150)))))))))))), introduced(definition)).
279.00/50.34	thf(c_0_383, negated_conjecture, ~((![X2170:$i, X2171:$i]:((![X2172:$i]:(((in @ X2172 @ X2170)<=>(in @ X2172 @ X2171)))=>((X2170)=(X2171))))=>(![X1118:$i]:(~(in @ X1118 @ emptyset))=>(![X2167:$i, X2168:$i, X2169:$i]:(((in @ X2169 @ (setadjoin @ X2167 @ X2168))<=>(((X2169)=(X2167))|(in @ X2169 @ X2168))))=>(![X1119:$i, X1120:$i]:(((in @ X1120 @ (powerset @ X1119))<=>![X1121:$i]:(((in @ X1121 @ X1120)=>(in @ X1121 @ X1119)))))=>(![X1122:$i, X1123:$i]:(((in @ X1123 @ (setunion @ X1122))<=>?[X1124:$i]:(((in @ X1123 @ X1124)&(in @ X1124 @ X1122)))))=>((in @ emptyset @ omega)=>(![X1125:$i]:(((in @ X1125 @ omega)=>(in @ (setadjoin @ X1125 @ X1125) @ omega)))=>(![X1126:$i]:((((in @ emptyset @ X1126)&![X1127:$i]:((((in @ X1127 @ omega)&(in @ X1127 @ X1126))=>(in @ (setadjoin @ X1127 @ X1127) @ X1126))))=>![X1128:$i]:(((in @ X1128 @ omega)=>(in @ X1128 @ X1126)))))=>(![X2161:$i > $i > $o, X2162:$i]:((![X2163:$i]:(((in @ X2163 @ X2162)=>(exu @ (X2161 @ X2163))))=>?[X2164:$i]:(![X2165:$i]:(((in @ X2165 @ X2164)<=>?[X2166:$i]:(((in @ X2166 @ X2162)&(X2161 @ X2166 @ X2165))))))))=>(![X1129:$i]:((?[X1130:$i]:((in @ X1130 @ X1129))=>?[X1131:$i]:(((in @ X1131 @ X1129)&~(?[X1132:$i]:(((in @ X1132 @ X1131)&(in @ X1132 @ X1129))))))))=>((epred1_0)=>(![X2160:$i > $o]:(((exu @ X2160)=>(X2160 @ (descr @ (^[Z0/* 17 */:$i]:(X2160 @ Z0))))))=>(![X1152:$i, X1153:$i > $o, X1154:$i]:(((in @ X1154 @ X1152)=>((X1153 @ X1154)=>(in @ X1154 @ (dsetconstr @ X1152 @ X1153)))))=>(![X2157:$i, X2158:$i > $o, X2159:$i]:(((in @ X2159 @ (dsetconstr @ X2157 @ X2158))=>(in @ X2159 @ X2157)))=>(![X1155:$i, X1156:$i > $o, X1157:$i]:(((in @ X1157 @ (dsetconstr @ X1155 @ X1156))=>(X1156 @ X1157)))=>(![X1158:$i > $o]:(((exu @ X1158)=>?[X1159:$i]:(((X1158 @ X1159)&![X1160:$i]:(((X1158 @ X1160)=>((X1159)=(X1160))))))))=>(![X2155:$o, X2156:$i]:(((in @ X2156 @ (prop2set @ ((X2155))))=>(X2155)))=>(![X2153:$i]:(((in @ X2153 @ emptyset)=>![X2154:$o]:((X2154))))=>(![X2152:$i]:(((in @ X2152 @ emptyset)=>~($true)))=>(![X2151:$i]:(~(in @ X2151 @ emptyset))=>(![X1161:$i > $o]:(((exu @ X1161)=>?[X1162:$i]:((X1161 @ X1162))))=>(![X1163:$i, X1164:$i]:((![X1165:$i]:(((in @ X1165 @ X1163)=>(in @ X1165 @ X1164)))=>(![X1166:$i]:(((in @ X1166 @ X1164)=>(in @ X1166 @ X1163)))=>((X1163)=(X1164)))))=>(![X2149:$i]:((![X2150:$i]:(~(in @ X2150 @ X2149))=>((X2149)=(emptyset))))=>(![X2147:$i]:((![X2148:$i]:(~(in @ X2148 @ X2147))=>((X2147)=(emptyset))))=>(![X1167:$i, X1168:$i > $o, X1169:$i]:(((in @ X1169 @ X1167)=>((in @ X1169 @ (dsetconstr @ X1167 @ X1168))<=>(X1168 @ X1169))))=>(![X2145:$i]:((((X2145)!=(emptyset))=>?[X2146:$i]:((in @ X2146 @ X2145))))=>(![X1170:$i, X1171:$i > $o, X1172:$i]:(((in @ X1172 @ X1170)=>((X1171 @ X1172)=>((dsetconstr @ X1170 @ X1171)!=(emptyset)))))=>(![X1173:$i]:((?[X1174:$i]:((in @ X1174 @ X1173))=>((X1173)!=(emptyset))))=>(![X1175:$i, X1176:$i]:((in @ X1175 @ (setadjoin @ X1175 @ X1176)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1177:$i, X1178:$i, X1179:$i]:(((in @ X1179 @ X1178)=>(in @ X1179 @ (setadjoin @ X1177 @ X1178))))=>(![X1180:$i, X1181:$i, X1182:$i]:(((in @ X1182 @ (setadjoin @ X1180 @ X1181))=>![X1183:$o]:(((((X1182)=(X1180))=>(X1183))=>(((in @ X1182 @ X1181)=>(X1183))=>(X1183))))))=>(![X2142:$i, X2143:$i, X2144:$i]:(((in @ X2144 @ (setadjoin @ X2142 @ X2143))=>(((X2144)=(X2142))|(in @ X2144 @ X2143))))=>(![X2141:$i]:(((dsetconstr @ X2141 @ (^[Z0/* 1 */:$i]:($true)))=(X2141)))=>(![X1184:$i, X1185:$i]:((![X1186:$i]:(((in @ X1186 @ X1185)=>(in @ X1186 @ X1184)))=>(in @ X1185 @ (powerset @ X1184))))=>(![X1187:$i]:((in @ emptyset @ (powerset @ X1187)))=>(![X2140:$i]:((in @ emptyset @ (powerset @ X2140)))=>(![X1188:$i, X1189:$i, X1190:$i]:(((in @ X1189 @ (powerset @ X1188))=>((in @ X1190 @ X1189)=>(in @ X1190 @ X1188))))=>(![X2137:$i, X2138:$i, X2139:$i]:(((in @ X2138 @ X2139)=>((in @ X2139 @ X2137)=>(in @ X2138 @ (setunion @ X2137)))))=>(![X1191:$i, X1192:$i]:(((in @ X1192 @ (setunion @ X1191))=>![X1193:$o]:((![X1194:$i]:(((in @ X1192 @ X1194)=>((in @ X1194 @ X1191)=>(X1193))))=>(X1193)))))=>(![X1195:$i, X1196:$i]:(((in @ X1196 @ X1195)=>(in @ X1196 @ (powerset @ (setunion @ X1195)))))=>(![X2134:$i > $o]:(((exu @ X2134)=>?[X2135:$i]:(![X2136:$i]:(((X2134 @ X2136)<=>((X2136)=(X2135)))))))=>(![X2132:$i]:((((X2132)!=(emptyset))=>?[X2133:$i]:(((in @ X2133 @ X2132)&$true))))=>(![X2130:$i, X2131:$i]:(((in @ X2130 @ (setadjoin @ X2131 @ emptyset))=>((X2130)=(X2131))))=>(![X1197:$i, X1198:$i]:((((X1197)!=(X1198))=>~(in @ X1198 @ (setadjoin @ X1197 @ emptyset))))=>(![X2128:$i, X2129:$i]:((((X2128)=(X2129))=>(in @ X2128 @ (setadjoin @ X2129 @ emptyset))))=>(![X2126:$i, X2127:$i]:(((in @ X2126 @ (setadjoin @ X2127 @ emptyset))=>(in @ X2127 @ (setadjoin @ X2126 @ emptyset))))=>(![X1199:$i, X1200:$i, X1201:$i]:(((in @ X1201 @ (setadjoin @ X1199 @ (setadjoin @ X1200 @ emptyset)))=>(((X1201)=(X1199))|((X1201)=(X1200)))))=>(![X1202:$i, X1203:$i]:((in @ X1202 @ (setadjoin @ X1202 @ (setadjoin @ X1203 @ emptyset))))=>(![X2124:$i, X2125:$i]:((in @ X2125 @ (setadjoin @ X2124 @ (setadjoin @ X2125 @ emptyset))))=>(![X1204:$i, X1205:$i > $o]:((?[X1206:$i]:(((in @ X1206 @ X1204)&(X1205 @ X1206)))=>(((dsetconstr @ X1204 @ X1205)=(emptyset))=>~($true))))=>(![X2122:$i > $o, X2123:$i]:(((in @ X2123 @ emptyset)=>(X2122 @ X2123)))=>(![X2118:$i, X2119:$i > $o]:((~(![X2120:$i]:(((in @ X2120 @ X2118)=>(X2119 @ X2120))))=>?[X2121:$i]:(((in @ X2121 @ X2118)&~((X2119 @ X2121))))))=>(![X2114:$i, X2115:$i > $o]:((![X2116:$i]:(((in @ X2116 @ X2114)=>~((X2115 @ X2116))))=>~(?[X2117:$i]:(((in @ X2117 @ X2114)&(X2115 @ X2117))))))=>(![X2110:$i, X2111:$i > $o]:((~(?[X2112:$i]:(((in @ X2112 @ X2110)&(X2111 @ X2112))))=>![X2113:$i]:(((in @ X2113 @ X2110)=>~((X2111 @ X2113))))))=>(![X1207:$i, X1208:$i > $o]:((?[X1209:$i]:(((in @ X1209 @ X1207)&~((X1208 @ X1209))))=>~(![X1210:$i]:(((in @ X1210 @ X1207)=>(X1208 @ X1210))))))=>(![X2109:$o]:(((X2109)=>(in @ emptyset @ (prop2set @ ((X2109))))))=>((prop2set2propI)=>(![X2105:$i, X2106:$i > $o]:((~(?[X2107:$i]:(((in @ X2107 @ X2105)&(X2106 @ X2107))))=>![X2108:$i]:(((in @ X2108 @ X2105)=>~((X2106 @ X2108))))))=>(![X2101:$i, X2102:$i > $o]:((~(![X2103:$i]:(((in @ X2103 @ X2101)=>(X2102 @ X2103))))=>?[X2104:$i]:(((in @ X2104 @ X2101)&~((X2102 @ X2104))))))=>(![X2098:$i > $o]:((?[X2099:$i]:(((X2098 @ X2099)&![X2100:$i]:(((X2098 @ X2100)=>((X2099)=(X2100))))))=>(exu @ X2098)))=>(![X2094:$i > $o]:((?[X2095:$i]:((X2094 @ X2095))=>(![X2096:$i, X2097:$i]:(((X2094 @ X2096)=>((X2094 @ X2097)=>((X2096)=(X2097)))))=>(exu @ X2094))))=>(![X1211:$i > $o]:((?[X1212:$i]:(![X1213:$i]:(((X1211 @ X1213)<=>((X1213)=(X1212)))))=>(exu @ X1211)))=>(![X2090:$i, X2091:$i]:((((X2090)=(X2091))=>![X2092:$i, X2093:$i]:((((X2092)=(X2093))=>((in @ X2092 @ X2090)=>(in @ X2093 @ X2091))))))=>(![X1214:$i, X1215:$i]:((((X1214)=(X1215))=>![X1216:$i, X1217:$i]:((((X1216)=(X1217))=>((in @ X1216 @ X1214)<=>(in @ X1217 @ X1215))))))=>(![X1218:$i > $o]:(((exu @ X1218)=>![X1219:$i, X1220:$i]:(((X1218 @ X1219)=>((X1218 @ X1220)=>((X1219)=(X1220)))))))=>(![X2086:$i > $o, X2087:$i > $o]:((![X2088:$i, X2089:$i]:((((X2088)=(X2089))=>((X2086 @ X2088)<=>(X2087 @ X2089))))=>((exu @ X2086)<=>(exu @ X2087))))=>(((emptyset)=(emptyset))=>(![X2082:$i, X2083:$i]:((((X2082)=(X2083))=>![X2084:$i, X2085:$i]:((((X2084)=(X2085))=>((setadjoin @ X2082 @ X2084)=(setadjoin @ X2083 @ X2085))))))=>(![X1221:$i, X1222:$i]:((((X1221)=(X1222))=>((powerset @ X1221)=(powerset @ X1222))))=>(![X2080:$i, X2081:$i]:((((X2080)=(X2081))=>((setunion @ X2080)=(setunion @ X2081))))=>(((omega)=(omega))=>(![X2077:$i > $o]:(((exu @ X2077)=>![X2078:$i, X2079:$i]:(((X2077 @ X2078)=>((X2077 @ X2079)=>((X2078)=(X2079)))))))=>(![X1223:$i > $o, X1224:$i > $o]:((![X1225:$i, X1226:$i]:((((X1225)=(X1226))=>((X1223 @ X1225)<=>(X1224 @ X1226))))=>((exu @ X1223)=>((exu @ X1224)=>((descr @ X1223)=(descr @ X1224))))))=>(![X1227:$i, X1228:$i]:((((X1227)=(X1228))=>![X1229:$i > $o, X1230:$i > $o]:((![X1231:$i]:(((in @ X1231 @ X1227)=>![X1232:$i]:(((in @ X1232 @ X1228)=>(((X1231)=(X1232))=>((X1229 @ X1231)<=>(X1230 @ X1232)))))))=>((dsetconstr @ X1227 @ X1229)=(dsetconstr @ X1228 @ X1230))))))=>(![X2074:$i, X2075:$i]:((![X2076:$i]:(((in @ X2076 @ X2074)=>(in @ X2076 @ X2075)))=>(subset @ X2074 @ X2075)))=>(![X1233:$i, X1234:$i]:((((X1233)=(X1234))=>(subset @ X1234 @ X1233)))=>(![X2072:$i, X2073:$i]:((((X2072)=(X2073))=>(subset @ X2072 @ X2073)))=>(![X1235:$i, X1236:$i]:((![X1237:$i]:(((in @ X1237 @ X1235)=>(in @ X1237 @ X1236)))=>(subset @ X1235 @ X1236)))=>(![X2071:$i]:((subset @ emptyset @ X2071))=>(![X1238:$i, X1239:$i, X1240:$i]:(((subset @ X1238 @ X1239)=>((in @ X1240 @ X1238)=>(in @ X1240 @ X1239))))=>(![X1241:$i, X1242:$i, X1243:$i]:(((subset @ X1241 @ X1242)=>(~(in @ X1243 @ X1242)=>~(in @ X1243 @ X1241))))=>(![X1244:$i, X1245:$i, X1246:$i]:(((in @ X1246 @ X1244)=>(~(in @ X1246 @ X1245)=>~(subset @ X1244 @ X1245))))=>(![X2069:$i, X2070:$i]:((~(subset @ X2069 @ X2070)=>((X2069)!=(X2070))))=>(![X1247:$i, X1248:$i, X1249:$i]:(((in @ X1249 @ X1247)=>(~(in @ X1249 @ X1248)=>((X1247)!=(X1248)))))=>(![X2068:$i]:((subset @ X2068 @ X2068))=>(![X2065:$i, X2066:$i, X2067:$i]:(((subset @ X2065 @ X2066)=>((subset @ X2066 @ X2067)=>(subset @ X2065 @ X2067))))=>(![X1250:$i, X1251:$i]:((subset @ X1251 @ (setadjoin @ X1250 @ X1251)))=>(![X2062:$i, X2063:$i, X2064:$i]:(((subset @ X2062 @ X2064)=>(subset @ X2062 @ (setadjoin @ X2063 @ X2064))))=>(![X1252:$i, X1253:$i]:(((subset @ X1252 @ X1253)=>(in @ X1252 @ (powerset @ X1253))))=>(![X2060:$i, X2061:$i]:(((subset @ X2060 @ X2061)=>((subset @ X2061 @ X2060)=>((X2060)=(X2061)))))=>(![X1254:$i]:(((subset @ X1254 @ emptyset)=>((X1254)=(emptyset))))=>(![X2058:$i, X2059:$i]:(((subset @ X2059 @ X2058)=>(in @ X2059 @ (powerset @ X2058))))=>(![X1255:$i, X1256:$i]:(((in @ X1256 @ (powerset @ X1255))=>(subset @ X1256 @ X1255)))=>(![X1257:$i]:((in @ X1257 @ (powerset @ X1257)))=>(![X2056:$i, X2057:$i]:(((subset @ X2056 @ X2057)=>(subset @ (powerset @ X2056) @ (powerset @ X2057))))=>(![X1258:$i, X1259:$i > $o]:((in @ (dsetconstr @ X1258 @ X1259) @ (powerset @ X1258)))=>(![X1260:$i, X1261:$i > $o]:((subset @ (dsetconstr @ X1260 @ X1261) @ X1260))=>(![X1262:$i, X1263:$i, X1264:$i]:(((in @ X1264 @ X1262)=>(in @ X1264 @ (binunion @ X1262 @ X1263))))=>(![X1265:$i, X1266:$i]:((in @ X1266 @ (setadjoin @ X1265 @ (setadjoin @ X1266 @ emptyset))))=>(![X2053:$i, X2054:$i, X2055:$i]:(((in @ X2055 @ X2054)=>(in @ X2055 @ (binunion @ X2053 @ X2054))))=>(![X2049:$i, X2050:$i, X2051:$i, X2052:$o]:(((in @ X2051 @ (binunion @ X2049 @ X2050))=>(((in @ X2051 @ X2049)=>(X2052))=>(((in @ X2051 @ X2050)=>(X2052))=>(X2052)))))=>(![X1267:$i, X1268:$i, X1269:$i]:(((in @ X1269 @ (binunion @ X1267 @ X1268))=>((in @ X1269 @ X1267)|(in @ X1269 @ X1268))))=>(![X2047:$i, X2048:$i]:((subset @ X2047 @ (binunion @ X2047 @ X2048)))=>(![X2045:$i, X2046:$i]:((subset @ X2046 @ (binunion @ X2045 @ X2046)))=>(![X2042:$i, X2043:$i, X2044:$i]:(((in @ X2044 @ X2042)=>((in @ X2044 @ X2043)=>(in @ X2044 @ (binintersect @ X2042 @ X2043)))))=>(![X2039:$i, X2040:$i, X2041:$i]:(((subset @ X2041 @ X2039)=>((subset @ X2041 @ X2040)=>(subset @ X2041 @ (binintersect @ X2039 @ X2040)))))=>(![X2036:$i, X2037:$i, X2038:$i]:(((in @ X2038 @ (binintersect @ X2036 @ X2037))=>(in @ X2038 @ X2036)))=>(![X2034:$i, X2035:$i]:((subset @ (binintersect @ X2034 @ X2035) @ X2034))=>(![X1270:$i, X1271:$i]:(((subset @ X1270 @ X1271)=>((binintersect @ X1270 @ X1271)=(X1270))))=>(![X2032:$i, X2033:$i]:((((binintersect @ X2032 @ X2033)=(X2033))=>(subset @ X2033 @ X2032)))=>(![X2029:$i, X2030:$i, X2031:$i]:(((in @ X2031 @ (binintersect @ X2029 @ X2030))=>(in @ X2031 @ X2030)))=>(![X1272:$i, X1273:$i]:((~(?[X1274:$i]:(((in @ X1274 @ X1272)&(in @ X1274 @ X1273))))=>((binintersect @ X1272 @ X1273)=(emptyset))))=>(![X2027:$i, X2028:$i]:((subset @ (binintersect @ X2027 @ X2028) @ X2028))=>(![X1275:$i, X1276:$i]:(((subset @ X1276 @ X1275)=>((binintersect @ X1275 @ X1276)=(X1276))))=>(![X1277:$i, X1278:$i]:((((binintersect @ X1277 @ X1278)=(X1277))=>(subset @ X1277 @ X1278)))=>(![X1279:$i, X1280:$i, X1281:$i]:(((binintersect @ X1279 @ (binunion @ X1280 @ X1281))=(binunion @ (binintersect @ X1279 @ X1280) @ (binintersect @ X1279 @ X1281))))=>(![X2024:$i, X2025:$i, X2026:$i]:(((in @ X2026 @ X2024)=>(~(in @ X2026 @ X2025)=>(in @ X2026 @ (setminus @ X2024 @ X2025)))))=>(![X2021:$i, X2022:$i, X2023:$i]:(((in @ X2023 @ (setminus @ X2021 @ X2022))=>(in @ X2023 @ X2021)))=>(![X2018:$i, X2019:$i, X2020:$i]:(((in @ X2020 @ (setminus @ X2018 @ X2019))=>~(in @ X2020 @ X2019)))=>(![X1282:$i, X1283:$i]:(((subset @ X1282 @ X1283)=>((setminus @ X1282 @ X1283)=(emptyset))))=>(![X1284:$i, X1285:$i, X1286:$i]:((~(in @ X1286 @ (setminus @ X1284 @ X1285))=>((in @ X1286 @ X1284)=>(in @ X1286 @ X1285))))=>(![X1287:$i, X1288:$i, X1289:$i]:((~(in @ X1289 @ (setminus @ X1287 @ X1288))=>(~(in @ X1289 @ X1288)=>~(in @ X1289 @ X1287))))=>(![X1290:$i, X1291:$i, X1292:$i]:((~(in @ X1292 @ X1290)=>~(in @ X1292 @ (setminus @ X1290 @ X1291))))=>(![X1293:$i, X1294:$i, X1295:$i]:(((in @ X1295 @ X1294)=>~(in @ X1295 @ (setminus @ X1293 @ X1294))))=>(![X2016:$i, X2017:$i]:((subset @ (setminus @ X2016 @ X2017) @ X2016))=>(![X2014:$i, X2015:$i]:((((setminus @ X2014 @ X2015)=(emptyset))=>(subset @ X2014 @ X2015)))=>(![X1296:$i, X1297:$i, X1298:$i]:(((in @ X1298 @ (symdiff @ X1296 @ X1297))=>![X1299:$o]:((((in @ X1298 @ X1296)=>(~(in @ X1298 @ X1297)=>(X1299)))=>((~(in @ X1298 @ X1296)=>((in @ X1298 @ X1297)=>(X1299)))=>(X1299))))))=>(![X2011:$i, X2012:$i, X2013:$i]:(((in @ X2013 @ X2011)=>(~(in @ X2013 @ X2012)=>(in @ X2013 @ (symdiff @ X2011 @ X2012)))))=>(![X2008:$i, X2009:$i, X2010:$i]:((~(in @ X2010 @ X2008)=>((in @ X2010 @ X2009)=>(in @ X2010 @ (symdiff @ X2008 @ X2009)))))=>(![X1300:$i, X1301:$i, X1302:$i]:(((in @ X1302 @ X1300)=>((in @ X1302 @ X1301)=>~(in @ X1302 @ (symdiff @ X1300 @ X1301)))))=>(![X1303:$i, X1304:$i, X1305:$i]:((~(in @ X1305 @ X1303)=>(~(in @ X1305 @ X1304)=>~(in @ X1305 @ (symdiff @ X1303 @ X1304)))))=>(![X2006:$i, X2007:$i]:((in @ X2007 @ (setadjoin @ X2006 @ (setadjoin @ X2007 @ emptyset))))=>(![X2004:$i, X2005:$i]:((in @ X2004 @ (setunion @ (setadjoin @ (setadjoin @ X2004 @ emptyset) @ (setadjoin @ (setadjoin @ X2004 @ (setadjoin @ X2005 @ emptyset)) @ emptyset)))))=>(![X1306:$i, X1307:$i]:((in @ X1307 @ (setunion @ (setadjoin @ (setadjoin @ X1306 @ emptyset) @ (setadjoin @ (setadjoin @ X1306 @ (setadjoin @ X1307 @ emptyset)) @ emptyset)))))=>(![X1308:$i, X1309:$i]:((iskpair @ (setadjoin @ (setadjoin @ X1308 @ emptyset) @ (setadjoin @ (setadjoin @ X1308 @ (setadjoin @ X1309 @ emptyset)) @ emptyset))))=>(![X2002:$i, X2003:$i]:((iskpair @ (kpair @ X2002 @ X2003)))=>(![X2000:$i, X2001:$i]:(((in @ X2001 @ X2000)=>(subset @ (setadjoin @ X2001 @ emptyset) @ X2000)))=>(![X1998:$i, X1999:$i]:(((in @ X1999 @ 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$o]:((![X1732:$i]:(((in @ X1732 @ X1729)=>![X1733:$i]:(((in @ X1733 @ X1729)=>((in @ (kpair @ X1732 @ X1733) @ X1730)=>(X1731 @ (kpair @ X1732 @ X1733)))))))=>![X1734:$i]:(((in @ X1734 @ X1730)=>(X1731 @ X1734)))))))=>(![X1586:$i, X1587:$i]:(((in @ X1587 @ (breln1Set @ X1586))=>(breln1 @ X1586 @ X1587)))=>((choice2fnsingleton)=>(![X1727:$i, X1728:$i > $i > $o]:((breln1 @ X1727 @ (dpsetconstr @ X1727 @ X1727 @ X1728)))=>(![X1721:$i, X1722:$i]:(((breln1 @ X1721 @ X1722)=>![X1723:$i > $o]:((![X1724:$i]:(((in @ X1724 @ X1721)=>![X1725:$i]:(((in @ X1725 @ X1721)=>((in @ (kpair @ X1724 @ X1725) @ X1722)=>(X1723 @ (kpair @ X1724 @ X1725)))))))=>![X1726:$i]:(((in @ X1726 @ X1722)=>(X1723 @ X1726)))))))=>(![X1588:$i, X1589:$i]:(((breln1 @ X1588 @ X1589)=>![X1590:$i]:(((breln1 @ X1588 @ X1590)=>(![X1591:$i]:(((in @ X1591 @ X1588)=>![X1592:$i]:(((in @ X1592 @ X1588)=>((in @ (kpair @ X1591 @ X1592) @ X1589)=>(in @ (kpair @ X1591 @ X1592) @ X1590))))))=>(subset @ X1589 @ X1590))))))=>(![X1593:$i, 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X1668))=(X1668))))=>(surjective @ X1664 @ X1663 @ X1667))))))=>(![X1669:$i, X1670:$i]:(((in @ X1670 @ (funcSet @ X1669 @ (powerset @ X1669)))=>~(surjective @ X1669 @ (powerset @ X1669) @ X1670)))=>![X4:$i]:((((X4)!=(emptyset))=>?[X21:$i]:(((in @ X21 @ X4)&((binintersect @ X21 @ X4)=(emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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y_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[foundation2]), omega__Cong]), setextAx]), binintersectER]), upairsubunion]), binintersectSubset3]), binintersectLsub]), binintersectEL]), setunionsingleton]), binintersectSubset5]), binintersectI]), c_0_323]), binunionRsub]), binunionLsub]), binunionEcases]), c_0_324]), binunionIR]), powersetsubset]), c_0_325]), powersetI1]), setextsub]), setadjoinSub2]), singletonsuniq]), subsetTrans]), ubforcartprodlem1]), subsetRefl]), notequalI1]), setukpairinjL1]), emptysetsubset]), eqimpsubset1]), subsetI1]), kfstpairEq]), c_0_326]), ap2p]), setunion__Cong]), setukpairinjL]), setadjoin__Cong]), emptyset__Cong]), c_0_327]), kpairsurjEq]), inCongP]), c_0_328]), cartprodpairmemEL]), c_0_329]), notdallE]), notdexE]), cartprodpairmemER]), prop2setI]), quantDeMorgan3]), cartprodmempaircEq]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), cartprodfstpairEq]), upairsetIR]), singletonsswitch]), cartprodsndpairEq]), eqinunit]), uniqinunit]), c_0_330]), cartprodpairsurjEq]), c_0_331]), setunionI]), cartprodmempair]), emptyInPowerset]), c_0_332]), c_0_333]), setadjoinOr]), c_0_334]), c_0_335]), noeltsimpempty]), emptyI]), c_0_336]), notinemptyset]), emptysetimpfalse]), emptysetE]), c_0_337]), prop2setE]), c_0_338]), c_0_339]), c_0_340]), c_0_341]), setadjoinAx]), c_0_342]), infuncsetfunc]), complementTcontraSubset]), binunionTILcontra]), funcinfuncset]), c_0_343]), c_0_344]), brelnall1]), c_0_345]), eqbreln]), funcext]), funcext2]), ap2apEq2]), setunionE2]), c_0_346]), c_0_347]), c_0_348]), c_0_349]), c_0_350]), c_0_351]), theeq]), iffalse]), iftrueorfalse]), powersetT_lem]), setminusT_lem]), setextT]), subsetTI]), powersetTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), complementImpComplementIntersect]), demorgan1a]), demorgan2a2]), complementUnionInPowersetComplement]), inIntersectImpInUnion2]), inIntersectImpInUnion]), binunionTIRcontra]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), demorgan2a]), woz13rule2]), woz13rule3]), woz1_1]), breln1SetBreln1]), subbreln1]), eqbreln1]), breln1invI]), breln1compI]), breln1compEex]), setunionsingleton2]), breln1unionIL]), breln1unionIR]), breln1unionEcases]), breln1unionCommutes]), woz2A]), image1Ex]), c_0_352]), c_0_353]), c_0_354]), injFuncSetFuncIn]), surjFuncSetFuncIn]), leftInvIsSurj]), c_0_321]), surjCantorThm]), surjFuncSetFuncSurj]), injFuncSetFuncInj]), injFuncInInjFuncSet]), c_0_355]), woz2B]), woz2W]), woz2Ex]), breln1unionE]), breln1unionI]), breln1unionprop]), breln1compE]), breln1compprop]), breln1invE]), breln1invprop]), breln1all1]), c_0_356]), breln1all2]), woz1_5]), woz1_4]), woz1_3]), woz1_2]), woz13rule4]), woz13rule1]), woz13rule0]), demorgan2]), demorgan2b]), demorgan2b2]), demorgan1]), demorgan1b]), contraSubsetComplement]), complementInPowersetComplementIntersect]), complementSubsetComplementIntersect]), complementTnotintersectT]), doubleComplementEq]), contrasubsetT3]), contrasubsetT2]), contrasubsetT1]), contrasubsetT]), complementTI1]), powersetTE1]), complementT_lem]), binunionT_lem]), binintersectT_lem]), iftrue]), ifp]), c_0_357]), c_0_358]), c_0_359]), c_0_360]), ap2apEq1]), subbreln]), funcGraphProp4]), funcextLem]), funcGraphProp2]), funcGraphProp3]), funcGraphProp1]), brelnall2]), c_0_361]), app]), c_0_362]), c_0_363]), c_0_364]), cartprodsndin]), ksndpairEq]), c_0_365]), setukpairinjR]), setukpairinjR2]), upairequniteq]), setukpairinjR1]), setukpairinjR12]), setukpairinjR11]), setukpairinjL2]), cartprodfstin]), theprop]), c_0_366]), c_0_367]), setunionsingleton1]), cartprodmempair1]), cartprodpairin]), ubforcartprodlem3]), ubforcartprodlem2]), upairinpowunion]), upairset2E]), singletoninpowerset]), singletonsubset]), kpairp]), setukpairIL]), secondinupair]), symdiffI2]), symdiffI1]), setminusSubset1]), setminusLsub]), setminusER]), setminusEL]), setminusI]), binintersectRsub]), singletoninpowunion]), kpairiskpair]), setukpairIR]), symdiffIneg2]), symdiffIneg1]), symdiffE]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusERneg]), setminusSubset2]), bs114d]), binintersectSubset1]), binintersectSubset4]), disjointsetsI1]), binintersectSubset2]), binunionE]), upairset2IR]), binunionIL]), c_0_368]), c_0_369]), inPowerset]), powersetE1]), subsetemptysetimpeq]), subset2powerset]), setadjoinSub]), notequalI2]), notsubsetI]), subsetE2]), subsetE]), subsetI2]), eqimpsubset2]), c_0_370]), c_0_371]), powerset__Cong]), c_0_372]), in__Cong]), c_0_373]), quantDeMorgan4]), c_0_374]), upairsetIL]), upairsetE]), notinsingleton]), subPowSU]), setunionE]), powersetE]), emptyinPowerset]), powersetI]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_375]), c_0_376]), c_0_377]), setext]), c_0_378]), c_0_379]), c_0_380]), c_0_381]), wellorderingAx]), foundationAx]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), emptysetAx])])]), c_0_382])).
279.00/50.34	thf(c_0_384, negated_conjecture, ![X2173:$i, X2174:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2186:$i, X2187:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2195:$i, X2196:$i > $i > $o, X2197:$i, X2200:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2207:$i, X2208:$i > $o, X2209:$i, X2210:$i > $o, X2211:$i, X2212:$i, X2213:$i > $o, X2214:$i, X2215:$i, X2216:$i > $o, X2217:$i, X2218:$i > $o, X2220:$i, X2221:$o, X2222:$i, X2223:$i, X2224:$o, X2225:$i, X2226:$i, X2227:$i > $o, X2229:$i, X2230:$i, X2233:$i, X2235:$i, X2237:$i, X2238:$i > $o, X2239:$i, X2240:$i, X2242:$i, X2243:$i > $o, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$o, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$o, X2275:$i, X2276:$i, X2277:$i > $o, X2279:$i, X2280:$i, X2281:$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 > $o, X2300:$i, X2301:$i > $o, X2302:$i, X2303:$i, X2304:$i > $o, X2305:$i, X2307:$i, X2308:$i > $o, X2310:$i, X2311:$i, X2312:$i > $o, X2314:$i, X2315:$i, X2316:$i > $o, X2317:$i, X2319:$o, X2320:$i, X2321:$i > $o, X2323:$i, X2324:$i, X2325:$i > $o, X2326:$i, X2328:$i > $o, X2329:$i, X2331:$i > $o, X2332:$i, X2335:$i > $o, X2336:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i > $o, X2347:$i, X2348:$i, X2349:$i > $o, X2350:$i > $o, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i, X2360:$i, X2361:$i > $o, X2362:$i, X2363:$i, X2364:$i > $o, X2365:$i > $o, X2368:$i, X2369:$i, X2370:$i > $o, X2371:$i > $o, X2374:$i, X2375:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2384:$i, X2385:$i, X2386:$i, X2387:$i, X2388:$i, X2389:$i, X2390:$i, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$i, X2404:$i, X2405:$i, X2406:$i, X2407:$i, X2408:$i, X2409:$i, X2410:$i, X2411:$i, X2412:$i, X2413:$i, X2414:$i, X2415:$i, X2416:$i, X2417:$i, X2418:$i, X2419:$i, X2420:$i, X2421:$i > $o, X2422:$i, X2423:$i > $o, X2424:$i, X2425:$i, X2426:$i, X2427:$i, X2428:$i, X2429:$i, X2430:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2435:$o, X2436:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, X2442:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$i, X2455:$i, X2456:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i, X2464:$i, X2465:$i, X2466:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2471:$i, X2472:$i, X2473:$i, X2474:$i, X2475:$i, X2476:$i, X2477:$i, X2478:$i, X2479:$i, X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$i, X2486:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2493:$i, X2494:$i, X2495:$i, X2496:$i, X2497:$i, X2498:$i, X2499:$i, X2500:$i, X2501:$i, X2502:$i, X2503:$o, X2504:$i, X2505:$i, X2506:$i, X2507:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i, X2546:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i, X2551:$i, X2552:$i, X2553:$i, X2554:$i, X2555:$i, X2556:$i, X2557:$i, X2558:$i, X2559:$i, X2560:$i, X2561:$i, X2562:$i, X2565:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i > $o, X2578:$i, X2579:$i, X2580:$i > $o, X2582:$i, X2583:$i > $o, X2584:$i, X2586:$i, X2587:$i > $o, X2590:$i, X2591:$i, X2592:$i, X2593:$i, X2594:$i, X2595:$i, X2596:$i, X2597:$i, X2598:$i, X2599:$i, X2600:$i, X2601:$i, X2602:$i, X2603:$i, X2604:$i, X2605:$i, X2606:$i, X2607:$i, X2608:$i, X2609:$i, X2610:$i, X2611:$i, X2612:$i, X2613:$i, X2614:$i, X2615:$i, X2616:$i, X2617:$i, X2618:$i, X2619:$i, X2620:$i, X2621:$i, X2622:$i, X2623:$i, X2624:$i, X2625:$i, X2626:$i, X2627:$i, X2628:$i, X2629:$i, X2630:$i, X2631:$i, X2632:$i, X2633:$i, X2634:$i, X2635:$i, X2636:$i, X2637:$i, X2638:$i, X2639:$i, X2640:$i, X2641:$i, X2642:$i, X2643:$i, X2644:$i, X2645:$i, X2646:$i, X2647:$i, X2648:$i, X2649:$i, X2650:$i, X2651:$i, X2652:$i, X2653:$i, X2654:$i, X2655:$i, X2656:$i, X2657:$i, X2658:$i, X2659:$i, X2660:$i, X2661:$i, X2662:$i > $i > $o, X2663:$i, X2664:$i, X2665:$i, X2666:$i, X2667:$i > $i > $o, X2668:$i, X2669:$i, X2670:$i > $i > $o, X2671:$i, X2672:$i, X2673:$i > $i > $o, X2674:$i, X2675:$i, X2676:$i, X2677:$i, X2678:$i > $i > $o, X2679:$i, X2680:$i, X2681:$i, X2682:$i, X2683:$i > $i > $o, X2684:$i, X2685:$i, X2686:$i, X2687:$i, X2688:$i > $i > $o, X2689:$i, X2690:$i, X2691:$i, X2692:$i, X2693:$i, X2694:$i, X2695:$i, X2696:$i, X2697:$i, X2698:$i, X2699:$i, X2700:$i, X2701:$i, X2702:$i, X2703:$i, X2704:$i, X2705:$i, X2706:$i, X2707:$i, X2708:$i, X2709:$i, X2710:$i, X2711:$i, X2712:$i, X2713:$i, X2714:$i, X2715:$i > $i, X2717:$i, X2718:$i, X2719:$i > $i, X2721:$i, X2722:$i, X2723:$i > $i, X2725:$i, X2726:$i, X2727:$i, X2728:$i > $o, X2731:$i, X2732:$i, X2733:$i, X2734:$i, X2735:$i > $o, X2738:$i, X2739:$i, X2740:$i > $o, X2741:$i, X2742:$i, X2743:$i, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i, X2749:$i, X2750:$i, X2751:$i, X2752:$i, X2753:$i, X2754:$i, X2755:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2761:$i, X2762:$i, X2763:$i, X2764:$i, X2765:$i, X2766:$i, X2767:$i, X2768:$i, X2769:$i, X2770:$i, X2771:$i, X2774:$i, X2775:$i, X2776:$i, X2777:$i, X2782:$i, X2783:$i, X2784:$i, X2785:$i, X2787:$i, X2788:$i, X2789:$i, X2790:$i, X2792:$i, X2793:$i, X2794:$i, X2795:$i, X2796:$i, X2797:$i, X2798:$i, X2799:$i, X2800:$i, X2801:$i, X2802:$i > $i, X2804:$i, X2805:$i, X2806:$i, X2807:$i, X2808:$i, X2809:$i, X2810:$i > $i, X2812:$i, X2813:$i, X2814:$i > $i, X2816:$i, X2817:$i, X2818:$i, X2819:$i, X2820:$i, X2821:$o, X2822:$i, X2823:$i, X2824:$i, X2825:$o, X2826:$i, X2827:$i, X2828:$i, X2829:$o, X2830:$i, X2831:$i, X2832:$i, X2833:$o, X2834:$i, X2835:$i, X2836:$i, X2837:$o, X2838:$i, X2839:$i, X2840:$i, X2841:$o, X2842:$i, X2843:$i, X2844:$i, X2845:$i, X2846:$i, X2847:$o, X2848:$i, X2849:$i, X2850:$i, X2851:$o, X2852:$i, X2853:$i, X2854:$i, X2855:$o, X2856:$i, X2857:$i, X2858:$i, X2859:$i, X2860:$i, X2861:$i, X2862:$i, X2863:$i, X2864:$i, X2865:$i, X2866:$i, X2867:$i, X2868:$i, X2869:$i, X2870:$i, X2871:$i, X2872:$i, X2873:$i, X2876:$i, X2877:$i, X2878:$i, X2880:$i, X2881:$i, X2882:$i, X2884:$i, X2885:$i, X2886:$i, X2887:$i, X2888:$i, X2889:$i, X2890:$i, X2891:$i, X2892:$i, X2893:$i, X2894:$i, X2895:$i, X2896:$i, X2897:$i, X2898:$i, X2899:$i, X2900:$i, X2901:$i, X2902:$i, X2903:$i, X2904:$i, X2905:$i, X2906:$i, X2907:$i, X2908:$i, X2909:$i, X2910:$i, X2911:$i, X2912:$i, X2913:$i, X2914:$i, X2915:$i, X2916:$i, X2917:$i, X2918:$i, X2919:$i, X2920:$i, X2921:$i, X2922:$i, X2923:$i, X2924:$i, X2925:$i, X2926:$i, X2927:$i, X2928:$i, X2929:$i, X2930:$i, X2931:$i, X2932:$i, X2933:$i, X2934:$i, X2935:$i, X2936:$i, X2937:$i, X2938:$i, X2939:$i, X2940:$i, X2941:$i, X2942:$i, X2943:$i, X2944:$i, X2945:$i, X2946:$i, X2947:$i, X2948:$i, X2949:$i, X2950:$i, X2951:$i, X2952:$i, X2953:$i, X2954:$i, X2955:$i, X2956:$i, X2957:$i, X2958:$i, X2959:$i, X2960:$i, X2961:$i, X2962:$i, X2963:$i, X2964:$i, X2965:$i, X2966:$i, X2967:$i, X2968:$i, X2969:$i, X2970:$i, X2971:$i, X2972:$i, X2973:$i, X2974:$i, X2975:$i, X2976:$i, X2977:$i, X2978:$i, X2979:$i, X2980:$i, X2981:$i, X2982:$i, X2983:$i, X2984:$i, X2985:$i, X2986:$i, X2987:$o, X2988:$i, X2989:$i, X2990:$i, X2991:$i, X2992:$i, X2993:$i, X2994:$i, X2995:$i, X2996:$i, X2997:$i, X2998:$i, X2999:$i, X3000:$i, X3001:$i, X3002:$i, X3003:$i, X3004:$i, X3005:$i, X3006:$i, X3007:$i, X3008:$i, X3009:$i, X3010:$i, X3011:$i, X3012:$i, X3013:$i, X3014:$i, X3015:$i, X3016:$i, X3017:$i, X3018:$i, X3019:$i, X3020:$i, X3021:$i, X3022:$i, X3023:$i, X3024:$i, X3025:$i, X3026:$i, X3027:$i, X3028:$i, X3029:$i, X3030:$i, X3031:$i, X3032:$i, X3033:$i, X3034:$i, X3035:$i, X3036:$i, X3037:$i, X3038:$i, X3039:$i, X3040:$i, X3041:$i, X3042:$i, X3043:$i, X3044:$i, X3045:$i, X3046:$i, X3047:$i, X3048:$i, X3049:$i, X3050:$i, X3051:$i, X3052:$i, X3053:$i, X3054:$i, X3055:$i, X3056:$i, X3057:$i, X3058:$i, X3059:$i, X3060:$i, X3061:$i, X3062:$i, X3063:$i, X3064:$i, X3065:$i, X3066:$i, X3067:$i, X3068:$i, X3069:$i, X3070:$i, X3071:$i > $o, X3074:$i, X3075:$i, X3076:$i, X3077:$i, X3078:$i > $i > $o, X3079:$i, X3080:$i, X3081:$i > $o, X3084:$i, X3085:$i, X3086:$i, X3087:$i, X3090:$i, X3091:$i, X3092:$i, X3097:$i, X3098:$i, X3099:$i, X3100:$i, X3101:$i, X3102:$i, X3103:$i, X3104:$i, X3105:$i, X3106:$i, X3107:$i, X3108:$i, X3109:$i, X3110:$i, X3111:$i, X3112:$i, X3113:$i, X3114:$i, X3115:$i, X3116:$i, X3117:$i, X3118:$i, X3119:$i, X3120:$i, X3122:$i, X3123:$i, X3124:$i, X3125:$i, X3126:$i, X3127:$o, X3129:$i, X3130:$i, X3131:$i, X3132:$i, X3133:$i, X3134:$i, X3135:$i, X3136:$i, X3137:$i, X3138:$i, X3139:$i, X3140:$i, X3141:$i, X3142:$i, X3143:$i, X3144:$i, X3145:$i, X3146:$i, X3147:$i, X3148:$i, X3149:$i, X3150:$i, X3151:$i, X3152:$i, X3153:$i, X3154:$i, X3155:$i, X3156:$i, X3157:$o, X3158:$i, X3159:$i, X3160:$i, X3161:$i, X3162:$i, X3163:$i, X3164:$i, X3165:$i, X3166:$i, X3167:$i, X3168:$i, X3169:$i, X3170:$i, X3171:$i, X3172:$i, X3173:$i, X3174:$i, X3175:$i > $i, X3177:$i, X3179:$i, X3180:$i, X3181:$i, X3182:$i > $i, X3183:$i, X3184:$i > $i, X3185:$i, X3187:$i, X3188:$i > $i, X3189:$i, X3190:$i, X3191:$i, X3192:$i > $i, X3193:$i, X3195:$i, X3196:$i > $i, X3197:$i, X3198:$i, X3199:$i, X3200:$i, X3201:$i, X3202:$i, X3203:$i, X3204:$i, X3205:$i, X3206:$i, X3207:$i, X3208:$i, X3209:$i, X3210:$i, X3211:$i, X3212:$i, X3213:$i, X3214:$i, X3215:$i, X3216:$i > $i, X3218:$i, X3220:$i, X3221:$i, X3223:$i]:((((~(in @ (esk1_2 @ X2173 @ X2174) @ X2173)|~(in @ (esk1_2 @ X2173 @ X2174) @ X2174)|((X2173)=(X2174)))&((in @ (esk1_2 @ X2173 @ X2174) @ X2173)|(in @ (esk1_2 @ X2173 @ X2174) @ X2174)|((X2173)=(X2174))))&(~(in @ X2176 @ emptyset)&(((~(in @ X2179 @ (setadjoin @ X2177 @ X2178))|(((X2179)=(X2177))|(in @ X2179 @ X2178)))&((((X2179)!=(X2177))|(in @ X2179 @ (setadjoin @ X2177 @ X2178)))&(~(in @ X2179 @ X2178)|(in @ X2179 @ (setadjoin @ X2177 @ X2178)))))&(((~(in @ X2181 @ (powerset @ X2180))|(~(in @ X2182 @ X2181)|(in @ X2182 @ X2180)))&(((in @ (esk2_2 @ X2183 @ X2184) @ X2184)|(in @ X2184 @ (powerset @ X2183)))&(~(in @ (esk2_2 @ X2183 @ X2184) @ X2183)|(in @ X2184 @ (powerset @ X2183)))))&(((((in @ X2187 @ (esk3_2 @ X2186 @ X2187))|~(in @ X2187 @ (setunion @ X2186)))&((in @ (esk3_2 @ X2186 @ X2187) @ X2186)|~(in @ X2187 @ (setunion @ X2186))))&(~(in @ X2190 @ X2191)|~(in @ X2191 @ X2189)|(in @ X2190 @ (setunion @ X2189))))&((in @ emptyset @ omega)&((~(in @ X2192 @ omega)|(in @ (setadjoin @ X2192 @ X2192) @ omega))&(((((in @ (esk4_1 @ X2193) @ omega)|~(in @ emptyset @ X2193)|(~(in @ X2195 @ omega)|(in @ X2195 @ X2193)))&((in @ (esk4_1 @ X2193) @ X2193)|~(in @ emptyset @ X2193)|(~(in @ X2195 @ omega)|(in @ X2195 @ X2193))))&(~(in @ (setadjoin @ (esk4_1 @ X2193) @ (esk4_1 @ X2193)) @ X2193)|~(in @ emptyset @ X2193)|(~(in @ X2195 @ omega)|(in @ X2195 @ X2193))))&((((((in @ (esk7_3 @ X2196 @ X2197 @ X2200) @ X2197)|~(in @ X2200 @ (esk6_2 @ X2196 @ X2197))|(in @ (esk5_2 @ X2196 @ X2197) @ X2197))&((X2196 @ (esk7_3 @ X2196 @ X2197 @ X2200) @ X2200)|~(in @ X2200 @ (esk6_2 @ X2196 @ X2197))|(in @ (esk5_2 @ X2196 @ X2197) @ X2197)))&(~(in @ X2203 @ X2197)|~(X2196 @ X2203 @ X2202)|(in @ X2202 @ (esk6_2 @ X2196 @ X2197))|(in @ (esk5_2 @ X2196 @ X2197) @ X2197)))&((((in @ (esk7_3 @ X2196 @ X2197 @ X2200) @ X2197)|~(in @ X2200 @ (esk6_2 @ X2196 @ X2197))|~(exu @ (X2196 @ (esk5_2 @ X2196 @ X2197))))&((X2196 @ (esk7_3 @ X2196 @ X2197 @ X2200) @ X2200)|~(in @ X2200 @ (esk6_2 @ X2196 @ X2197))|~(exu @ (X2196 @ (esk5_2 @ X2196 @ X2197)))))&(~(in @ X2203 @ X2197)|~(X2196 @ X2203 @ X2202)|(in @ X2202 @ (esk6_2 @ X2196 @ X2197))|~(exu @ (X2196 @ (esk5_2 @ X2196 @ X2197))))))&((((in @ (esk8_1 @ X2204) @ X2204)|~(in @ X2205 @ X2204))&(~(in @ X2207 @ (esk8_1 @ X2204))|~(in @ X2207 @ X2204)|~(in @ X2205 @ X2204)))&((epred1_0)&((~(exu @ X2208)|(X2208 @ (descr @ X2208)))&((~(in @ X2211 @ X2209)|(~(X2210 @ X2211)|(in @ X2211 @ (dsetconstr @ X2209 @ X2210))))&((~(in @ X2214 @ (dsetconstr @ X2212 @ X2213))|(in @ X2214 @ X2212))&((~(in @ X2217 @ (dsetconstr @ X2215 @ X2216))|(X2216 @ X2217))&((((X2218 @ (esk9_1 @ X2218))|~(exu @ X2218))&(~(X2218 @ X2220)|((esk9_1 @ X2218)=(X2220))|~(exu @ X2218)))&((~(in @ X2222 @ (prop2set @ ((X2221))))|(X2221))&((~(in @ X2223 @ emptyset)|(X2224))&((~(in @ X2225 @ emptyset)|~($true))&(~(in @ X2226 @ emptyset)&((~(exu @ X2227)|(X2227 @ (esk10_1 @ X2227)))&(((((in @ (esk12_2 @ X2229 @ X2230) @ 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X3181)&((X1647)=(X3182 @ X1648)))))))))&(((((in @ (esk85_3 @ X3183 @ X3184 @ X3185) @ X3183)|~(in @ X3185 @ (image1 @ X3183 @ X3184)))&(((X3185)=(X3184 @ (esk85_3 @ X3183 @ X3184 @ X3185)))|~(in @ X3185 @ (image1 @ X3183 @ X3184))))&(~(in @ X3190 @ X3187)|((X3189)!=(X3188 @ X3190))|(in @ X3189 @ (image1 @ X3187 @ X3188))))&((((in @ (esk86_3 @ X3191 @ X3192 @ X3193) @ X3191)|~(in @ X3193 @ (image1 @ X3191 @ X3192)))&(((X3193)=(X3192 @ (esk86_3 @ X3191 @ X3192 @ X3193)))|~(in @ X3193 @ (image1 @ X3191 @ X3192))))&((~(in @ X3198 @ X3195)|((X3197)!=(X3196 @ X3198))|(in @ X3197 @ (image1 @ X3195 @ X3196)))&((~(in @ X3201 @ (funcSet @ X3199 @ X3200))|(~(injective @ X3199 @ X3200 @ X3201)|(in @ X3201 @ (injFuncSet @ X3199 @ X3200))))&((~(in @ X3204 @ (injFuncSet @ X3202 @ X3203))|(in @ X3204 @ (funcSet @ X3202 @ X3203)))&((~(in @ X3207 @ (injFuncSet @ X3205 @ X3206))|(injective @ X3205 @ X3206 @ X3207))&((~(in @ X3210 @ (surjFuncSet @ X3208 @ X3209))|(in @ X3210 @ (funcSet @ X3208 @ X3209)))&((~(in @ X3213 @ (surjFuncSet @ X3211 @ X3212))|(surjective @ X3211 @ X3212 @ X3213))&(((((in @ (esk88_4 @ X3214 @ X3215 @ X3216 @ X3218) @ X3214)|(surjective @ X3215 @ X3214 @ X3218)|~(in @ X3218 @ (funcSet @ X3215 @ X3214))|(in @ (esk87_3 @ X3214 @ X3215 @ X3216) @ X3214))&(((ap @ X3215 @ X3214 @ X3218 @ (X3216 @ (esk88_4 @ X3214 @ X3215 @ X3216 @ X3218)))!=(esk88_4 @ X3214 @ X3215 @ X3216 @ X3218))|(surjective @ X3215 @ X3214 @ X3218)|~(in @ X3218 @ (funcSet @ X3215 @ X3214))|(in @ (esk87_3 @ X3214 @ X3215 @ X3216) @ X3214)))&(((in @ (esk88_4 @ X3214 @ X3215 @ X3216 @ X3218) @ X3214)|(surjective @ X3215 @ X3214 @ X3218)|~(in @ X3218 @ (funcSet @ X3215 @ X3214))|~(in @ (X3216 @ (esk87_3 @ X3214 @ X3215 @ X3216)) @ X3215))&(((ap @ X3215 @ X3214 @ X3218 @ (X3216 @ (esk88_4 @ X3214 @ X3215 @ X3216 @ X3218)))!=(esk88_4 @ X3214 @ X3215 @ X3216 @ X3218))|(surjective @ X3215 @ X3214 @ X3218)|~(in @ X3218 @ (funcSet @ X3215 @ X3214))|~(in @ (X3216 @ (esk87_3 @ X3214 @ X3215 @ X3216)) @ X3215))))&((~(in @ X3221 @ (funcSet @ X3220 @ (powerset @ X3220)))|~(surjective @ X3220 @ (powerset @ X3220) @ X3221))&(((esk89_0)!=(emptyset))&(~(in @ X3223 @ esk89_0)|((binintersect @ X3223 @ esk89_0)!=(emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_383])])])])])])])).
279.00/50.34	thf(c_0_385, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:((~((in @ X2 @ (esk8_1 @ X3)))|~((in @ X2 @ X3))|~((in @ X4 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_384])).
279.00/50.34	thf(c_0_386, negated_conjecture, ![X2:$i, X3:$i]:((~((in @ X2 @ (esk8_1 @ X3)))|~((in @ X2 @ X3)))), inference(condense,[status(thm)],[c_0_385])).
279.00/50.34	thf(c_0_387, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk38_2 @ X2 @ X3) @ X2)|((binintersect @ X2 @ X3)=(emptyset)))), inference(split_conjunct,[status(thm)],[c_0_384])).
279.00/50.34	thf(c_0_388, negated_conjecture, ![X3:$i, X2:$i]:((((binintersect @ (esk8_1 @ X2) @ X3)=(emptyset))|~((in @ (esk38_2 @ (esk8_1 @ X2) @ X3) @ X2)))), inference(spm,[status(thm)],[c_0_386, c_0_387])).
279.00/50.34	thf(c_0_389, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk38_2 @ X2 @ X3) @ X3)|((binintersect @ X2 @ X3)=(emptyset)))), inference(split_conjunct,[status(thm)],[c_0_384])).
279.00/50.34	thf(c_0_390, negated_conjecture, ![X2:$i]:((~((in @ X2 @ esk89_0))|((binintersect @ X2 @ esk89_0)!=(emptyset)))), inference(split_conjunct,[status(thm)],[c_0_384])).
279.00/50.34	thf(c_0_391, negated_conjecture, ![X2:$i]:(((binintersect @ (esk8_1 @ X2) @ X2)=(emptyset))), inference(spm,[status(thm)],[c_0_388, c_0_389])).
279.00/50.34	thf(c_0_392, negated_conjecture, ![X3:$i, X2:$i]:(((in @ (esk8_1 @ X2) @ X2)|~((in @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_384])).
279.00/50.34	thf(c_0_393, negated_conjecture, ![X2:$i]:(((in @ (esk19_1 @ X2) @ X2)|((X2)=(emptyset)))), inference(split_conjunct,[status(thm)],[c_0_384])).
279.00/50.34	thf(c_0_394, negated_conjecture, ~((in @ (esk8_1 @ esk89_0) @ esk89_0)), inference(spm,[status(thm)],[c_0_390, c_0_391])).
279.00/50.34	thf(c_0_395, negated_conjecture, ![X2:$i]:((((X2)=(emptyset))|(in @ (esk8_1 @ X2) @ X2))), inference(spm,[status(thm)],[c_0_392, c_0_393])).
279.00/50.34	thf(c_0_396, negated_conjecture, ((esk89_0)!=(emptyset)), inference(split_conjunct,[status(thm)],[c_0_384])).
279.00/50.34	thf(c_0_397, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_394, c_0_395]), c_0_396]), ['proof']).
279.00/50.34	# SZS output end CNFRefutation
279.00/50.34	# Parsed axioms                        : 698
279.00/50.34	# Removed by relevancy pruning/SinE    : 377
279.00/50.34	# Initial clauses                      : 530
279.00/50.34	# Removed in clause preprocessing      : 41
279.00/50.34	# Initial clauses in saturation        : 489
279.00/50.34	# Processed clauses                    : 1776
279.00/50.34	# ...of these trivial                  : 24
279.00/50.34	# ...subsumed                          : 437
279.00/50.34	# ...remaining for further processing  : 1315
279.00/50.34	# Other redundant clauses eliminated   : 112
279.00/50.34	# Clauses deleted for lack of memory   : 0
279.00/50.34	# Backward-subsumed                    : 28
279.00/50.34	# Backward-rewritten                   : 27
279.00/50.34	# Generated clauses                    : 31195
279.00/50.34	# ...of the previous two non-redundant : 30425
279.00/50.34	# ...aggressively subsumed             : 0
279.00/50.34	# Contextual simplify-reflections      : 15
279.00/50.34	# Paramodulations                      : 31044
279.00/50.34	# Factorizations                       : 2
279.00/50.34	# NegExts                              : 2
279.00/50.34	# Equation resolutions                 : 119
279.00/50.34	# Disequality decompositions           : 0
279.00/50.34	# Total rewrite steps                  : 1284
279.00/50.34	# ...of those cached                   : 1022
279.00/50.34	# Propositional unsat checks           : 0
279.00/50.34	#    Propositional check models        : 0
279.00/50.34	#    Propositional check unsatisfiable : 0
279.00/50.34	#    Propositional clauses             : 0
279.00/50.34	#    Propositional clauses after purity: 0
279.00/50.34	#    Propositional unsat core size     : 0
279.00/50.34	#    Propositional preprocessing time  : 0.000
279.00/50.34	#    Propositional encoding time       : 0.000
279.00/50.34	#    Propositional solver time         : 0.000
279.00/50.34	#    Success case prop preproc time    : 0.000
279.00/50.34	#    Success case prop encoding time   : 0.000
279.00/50.34	#    Success case prop solver time     : 0.000
279.00/50.34	# Current number of processed clauses  : 814
279.00/50.34	#    Positive orientable unit clauses  : 80
279.00/50.34	#    Positive unorientable unit clauses: 0
279.00/50.34	#    Negative unit clauses             : 17
279.00/50.34	#    Non-unit-clauses                  : 717
279.00/50.34	# Current number of unprocessed clauses: 29281
279.00/50.34	# ...number of literals in the above   : 124158
279.00/50.34	# Current number of archived formulas  : 0
279.00/50.34	# Current number of archived clauses   : 480
279.00/50.34	# Clause-clause subsumption calls (NU) : 169843
279.00/50.34	# Rec. Clause-clause subsumption calls : 75726
279.00/50.34	# Non-unit clause-clause subsumptions  : 285
279.00/50.34	# Unit Clause-clause subsumption calls : 2114
279.00/50.34	# Rewrite failures with RHS unbound    : 0
279.00/50.34	# BW rewrite match attempts            : 65
279.00/50.34	# BW rewrite match successes           : 18
279.00/50.34	# Condensation attempts                : 1776
279.00/50.34	# Condensation successes               : 16
279.00/50.34	# Termbank termtop insertions          : 630350
279.00/50.34	# Search garbage collected termcells   : 34959
279.00/50.34	
279.00/50.34	# -------------------------------------------------
279.00/50.34	# User time                : 32.791 s
279.00/50.34	# System time              : 0.998 s
279.00/50.34	# Total time               : 33.789 s
279.00/50.34	# Maximum resident set size: 10552 pages
279.00/50.34	
279.00/50.34	# -------------------------------------------------
279.00/50.34	# User time                : 32.804 s
279.00/50.34	# System time              : 1.003 s
279.00/50.34	# Total time               : 33.806 s
279.00/50.34	# Maximum resident set size: 2880 pages
279.00/50.34	% E---3.1 exiting
279.00/50.34	% E exiting
279.00/50.35	EOF