0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 240 THM
0.12/0.33	% Computer : n020.cluster.edu
0.12/0.33	% Model    : x86_64 x86_64
0.12/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory   : 8042.1875MB
0.12/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 1920
0.12/0.33	% WCLimit    : 240
0.12/0.33	% DateTime   : Wed Jul 30 06:39:34 EDT 2025
0.12/0.34	% CPUTime    : 
0.20/0.48	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=240 /export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p
7.08/1.45	# Version: 3.0.0-ho
7.08/1.45	# Preprocessing class: HSLMSLSSLLLCHFA.
7.08/1.45	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
7.08/1.45	# Starting ehoh_best5 with 240s (1) cores
7.08/1.45	# Starting almost_fo_3_lam with 240s (1) cores
7.08/1.45	# Starting new_bool_5 with 240s (1) cores
7.08/1.45	# Starting pre_casc_3 with 240s (1) cores
7.08/1.45	# Starting ho_unfolding_8 with 240s (1) cores
7.08/1.45	# Starting new_ho_10_cnf2 with 240s (1) cores
7.08/1.45	# Starting new_bool_3 with 240s (1) cores
7.08/1.45	# Starting new_ho_5 with 240s (1) cores
7.08/1.45	# new_bool_3 with pid 19431 completed with status 0
7.08/1.45	# Result found by new_bool_3
7.08/1.45	# Preprocessing class: HSLMSLSSLLLCHFA.
7.08/1.45	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
7.08/1.45	# Starting ehoh_best5 with 240s (1) cores
7.08/1.45	# Starting almost_fo_3_lam with 240s (1) cores
7.08/1.45	# Starting new_bool_5 with 240s (1) cores
7.08/1.45	# Starting pre_casc_3 with 240s (1) cores
7.08/1.45	# Starting ho_unfolding_8 with 240s (1) cores
7.08/1.45	# Starting new_ho_10_cnf2 with 240s (1) cores
7.08/1.45	# Starting new_bool_3 with 240s (1) cores
7.08/1.45	# SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
7.08/1.45	# Search class: HGHSM-FSLM32-DHFMMSBN
7.08/1.45	# partial match(1): HGHSM-FSLM32-MHFMMSBN
7.08/1.45	# Scheduled 9 strats onto 1 cores with 240 seconds (240 total)
7.08/1.45	# Starting ho_unfolding_8 with 49s (1) cores
7.08/1.45	# ho_unfolding_8 with pid 19439 completed with status 0
7.08/1.45	# Result found by ho_unfolding_8
7.08/1.45	# Preprocessing class: HSLMSLSSLLLCHFA.
7.08/1.45	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
7.08/1.45	# Starting ehoh_best5 with 240s (1) cores
7.08/1.45	# Starting almost_fo_3_lam with 240s (1) cores
7.08/1.45	# Starting new_bool_5 with 240s (1) cores
7.08/1.45	# Starting pre_casc_3 with 240s (1) cores
7.08/1.45	# Starting ho_unfolding_8 with 240s (1) cores
7.08/1.45	# Starting new_ho_10_cnf2 with 240s (1) cores
7.08/1.45	# Starting new_bool_3 with 240s (1) cores
7.08/1.45	# SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
7.08/1.45	# Search class: HGHSM-FSLM32-DHFMMSBN
7.08/1.45	# partial match(1): HGHSM-FSLM32-MHFMMSBN
7.08/1.45	# Scheduled 9 strats onto 1 cores with 240 seconds (240 total)
7.08/1.45	# Starting ho_unfolding_8 with 49s (1) cores
7.08/1.45	# Preprocessing time       : 0.185 s
7.08/1.45	# Presaturation interreduction done
7.08/1.45	
7.08/1.45	# Proof found!
7.08/1.45	# SZS status Theorem
7.08/1.45	# SZS output start CNFRefutation
7.08/1.45	thf(decl_23, type, in: $i > $i > $o).
7.08/1.45	thf(decl_24, type, exu: ($i > $o) > $o).
7.08/1.45	thf(decl_25, type, setextAx: $o).
7.08/1.45	thf(decl_26, type, emptyset: $i).
7.08/1.45	thf(decl_27, type, emptysetAx: $o).
7.08/1.45	thf(decl_28, type, setadjoin: $i > $i > $i).
7.08/1.45	thf(decl_29, type, setadjoinAx: $o).
7.08/1.45	thf(decl_30, type, powerset: $i > $i).
7.08/1.45	thf(decl_31, type, powersetAx: $o).
7.08/1.45	thf(decl_32, type, setunion: $i > $i).
7.08/1.45	thf(decl_33, type, setunionAx: $o).
7.08/1.45	thf(decl_34, type, omega: $i).
7.08/1.45	thf(decl_35, type, omega0Ax: $o).
7.08/1.45	thf(decl_36, type, omegaSAx: $o).
7.08/1.45	thf(decl_37, type, omegaIndAx: $o).
7.08/1.45	thf(decl_38, type, replAx: $o).
7.08/1.45	thf(decl_39, type, foundationAx: $o).
7.08/1.45	thf(decl_40, type, wellorderingAx: $o).
7.08/1.45	thf(decl_41, type, descr: ($i > $o) > $i).
7.08/1.45	thf(decl_42, type, descrp: $o).
7.08/1.45	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
7.08/1.45	thf(decl_44, type, dsetconstrI: $o).
7.08/1.45	thf(decl_45, type, dsetconstrEL: $o).
7.08/1.45	thf(decl_46, type, dsetconstrER: $o).
7.08/1.45	thf(decl_47, type, exuE1: $o).
7.08/1.45	thf(decl_48, type, prop2set: $o > $i).
7.08/1.45	thf(decl_49, type, prop2setE: $o).
7.08/1.45	thf(decl_50, type, emptysetE: $o).
7.08/1.45	thf(decl_51, type, emptysetimpfalse: $o).
7.08/1.45	thf(decl_52, type, notinemptyset: $o).
7.08/1.45	thf(decl_53, type, exuE3e: $o).
7.08/1.45	thf(decl_54, type, setext: $o).
7.08/1.45	thf(decl_55, type, emptyI: $o).
7.08/1.45	thf(decl_56, type, noeltsimpempty: $o).
7.08/1.45	thf(decl_57, type, setbeta: $o).
7.08/1.45	thf(decl_58, type, nonempty: $i > $o).
7.08/1.45	thf(decl_59, type, nonemptyE1: $o).
7.08/1.45	thf(decl_60, type, nonemptyI: $o).
7.08/1.45	thf(decl_61, type, nonemptyI1: $o).
7.08/1.45	thf(decl_62, type, setadjoinIL: $o).
7.08/1.45	thf(decl_63, type, emptyinunitempty: $o).
7.08/1.45	thf(decl_64, type, setadjoinIR: $o).
7.08/1.45	thf(decl_65, type, setadjoinE: $o).
7.08/1.45	thf(decl_66, type, setadjoinOr: $o).
7.08/1.45	thf(decl_67, type, setoftrueEq: $o).
7.08/1.45	thf(decl_68, type, powersetI: $o).
7.08/1.45	thf(decl_69, type, emptyinPowerset: $o).
7.08/1.45	thf(decl_70, type, emptyInPowerset: $o).
7.08/1.45	thf(decl_71, type, powersetE: $o).
7.08/1.45	thf(decl_72, type, setunionI: $o).
7.08/1.45	thf(decl_73, type, setunionE: $o).
7.08/1.45	thf(decl_74, type, subPowSU: $o).
7.08/1.45	thf(decl_75, type, exuE2: $o).
7.08/1.45	thf(decl_76, type, nonemptyImpWitness: $o).
7.08/1.45	thf(decl_77, type, uniqinunit: $o).
7.08/1.45	thf(decl_78, type, notinsingleton: $o).
7.08/1.45	thf(decl_79, type, eqinunit: $o).
7.08/1.45	thf(decl_80, type, singletonsswitch: $o).
7.08/1.45	thf(decl_81, type, upairsetE: $o).
7.08/1.45	thf(decl_82, type, upairsetIL: $o).
7.08/1.45	thf(decl_83, type, upairsetIR: $o).
7.08/1.45	thf(decl_84, type, emptyE1: $o).
7.08/1.45	thf(decl_85, type, vacuousDall: $o).
7.08/1.45	thf(decl_86, type, quantDeMorgan1: $o).
7.08/1.45	thf(decl_87, type, quantDeMorgan2: $o).
7.08/1.45	thf(decl_88, type, quantDeMorgan3: $o).
7.08/1.45	thf(decl_89, type, quantDeMorgan4: $o).
7.08/1.45	thf(decl_90, type, prop2setI: $o).
7.08/1.45	thf(decl_92, type, prop2set2propI: $o).
7.08/1.45	thf(decl_93, type, notdexE: $o).
7.08/1.45	thf(decl_94, type, notdallE: $o).
7.08/1.45	thf(decl_95, type, exuI1: $o).
7.08/1.45	thf(decl_96, type, exuI3: $o).
7.08/1.45	thf(decl_97, type, exuI2: $o).
7.08/1.45	thf(decl_98, type, inCongP: $o).
7.08/1.45	thf(decl_99, type, in__Cong: $o).
7.08/1.45	thf(decl_100, type, exuE3u: $o).
7.08/1.45	thf(decl_101, type, exu__Cong: $o).
7.08/1.45	thf(decl_102, type, emptyset__Cong: $o).
7.08/1.45	thf(decl_103, type, setadjoin__Cong: $o).
7.08/1.45	thf(decl_104, type, powerset__Cong: $o).
7.08/1.45	thf(decl_105, type, setunion__Cong: $o).
7.08/1.45	thf(decl_106, type, omega__Cong: $o).
7.08/1.45	thf(decl_107, type, exuEu: $o).
7.08/1.45	thf(decl_108, type, descr__Cong: $o).
7.08/1.45	thf(decl_109, type, dsetconstr__Cong: $o).
7.08/1.45	thf(decl_110, type, subset: $i > $i > $o).
7.08/1.45	thf(decl_113, type, subsetI1: $o).
7.08/1.45	thf(decl_114, type, eqimpsubset2: $o).
7.08/1.45	thf(decl_115, type, eqimpsubset1: $o).
7.08/1.45	thf(decl_116, type, subsetI2: $o).
7.08/1.45	thf(decl_117, type, emptysetsubset: $o).
7.08/1.45	thf(decl_118, type, subsetE: $o).
7.08/1.45	thf(decl_119, type, subsetE2: $o).
7.08/1.45	thf(decl_120, type, notsubsetI: $o).
7.08/1.45	thf(decl_121, type, notequalI1: $o).
7.08/1.45	thf(decl_122, type, notequalI2: $o).
7.08/1.45	thf(decl_123, type, subsetRefl: $o).
7.08/1.45	thf(decl_124, type, subsetTrans: $o).
7.08/1.45	thf(decl_125, type, setadjoinSub: $o).
7.08/1.45	thf(decl_126, type, setadjoinSub2: $o).
7.08/1.45	thf(decl_127, type, subset2powerset: $o).
7.08/1.45	thf(decl_128, type, setextsub: $o).
7.08/1.45	thf(decl_129, type, subsetemptysetimpeq: $o).
7.08/1.45	thf(decl_130, type, powersetI1: $o).
7.08/1.45	thf(decl_131, type, powersetE1: $o).
7.08/1.45	thf(decl_132, type, inPowerset: $o).
7.08/1.45	thf(decl_133, type, powersetsubset: $o).
7.08/1.45	thf(decl_134, type, sepInPowerset: $o).
7.08/1.45	thf(decl_135, type, sepSubset: $o).
7.08/1.45	thf(decl_136, type, binunion: $i > $i > $i).
7.08/1.45	thf(decl_137, type, binunionIL: $o).
7.08/1.45	thf(decl_138, type, upairset2IR: $o).
7.08/1.45	thf(decl_139, type, binunionIR: $o).
7.08/1.45	thf(decl_140, type, binunionEcases: $o).
7.08/1.45	thf(decl_141, type, binunionE: $o).
7.08/1.45	thf(decl_142, type, binunionLsub: $o).
7.08/1.45	thf(decl_143, type, binunionRsub: $o).
7.08/1.45	thf(decl_144, type, binintersect: $i > $i > $i).
7.08/1.45	thf(decl_145, type, binintersectI: $o).
7.08/1.45	thf(decl_146, type, binintersectSubset5: $o).
7.08/1.45	thf(decl_147, type, binintersectEL: $o).
7.08/1.45	thf(decl_148, type, binintersectLsub: $o).
7.08/1.45	thf(decl_149, type, binintersectSubset2: $o).
7.08/1.45	thf(decl_150, type, binintersectSubset3: $o).
7.08/1.45	thf(decl_151, type, binintersectER: $o).
7.08/1.45	thf(decl_152, type, disjointsetsI1: $o).
7.08/1.45	thf(decl_153, type, binintersectRsub: $o).
7.08/1.45	thf(decl_154, type, binintersectSubset4: $o).
7.08/1.45	thf(decl_155, type, binintersectSubset1: $o).
7.08/1.45	thf(decl_156, type, bs114d: $o).
7.08/1.45	thf(decl_158, type, setminus: $i > $i > $i).
7.08/1.45	thf(decl_159, type, setminusI: $o).
7.08/1.45	thf(decl_160, type, setminusEL: $o).
7.08/1.45	thf(decl_161, type, setminusER: $o).
7.08/1.45	thf(decl_162, type, setminusSubset2: $o).
7.08/1.45	thf(decl_163, type, setminusERneg: $o).
7.08/1.45	thf(decl_164, type, setminusELneg: $o).
7.08/1.45	thf(decl_165, type, setminusILneg: $o).
7.08/1.45	thf(decl_166, type, setminusIRneg: $o).
7.08/1.45	thf(decl_167, type, setminusLsub: $o).
7.08/1.45	thf(decl_168, type, setminusSubset1: $o).
7.08/1.45	thf(decl_169, type, symdiff: $i > $i > $i).
7.08/1.45	thf(decl_170, type, symdiffE: $o).
7.08/1.45	thf(decl_171, type, symdiffI1: $o).
7.08/1.45	thf(decl_172, type, symdiffI2: $o).
7.08/1.45	thf(decl_173, type, symdiffIneg1: $o).
7.08/1.45	thf(decl_174, type, symdiffIneg2: $o).
7.08/1.45	thf(decl_175, type, iskpair: $i > $o).
7.08/1.45	thf(decl_176, type, secondinupair: $o).
7.08/1.45	thf(decl_177, type, setukpairIL: $o).
7.08/1.45	thf(decl_178, type, setukpairIR: $o).
7.08/1.45	thf(decl_179, type, kpairiskpair: $o).
7.08/1.45	thf(decl_180, type, kpair: $i > $i > $i).
7.08/1.45	thf(decl_181, type, kpairp: $o).
7.08/1.45	thf(decl_182, type, cartprod: $i > $i > $i).
7.08/1.45	thf(decl_183, type, singletonsubset: $o).
7.08/1.45	thf(decl_184, type, singletoninpowerset: $o).
7.08/1.45	thf(decl_185, type, singletoninpowunion: $o).
7.08/1.45	thf(decl_186, type, upairset2E: $o).
7.08/1.45	thf(decl_187, type, upairsubunion: $o).
7.08/1.45	thf(decl_188, type, upairinpowunion: $o).
7.08/1.45	thf(decl_189, type, ubforcartprodlem1: $o).
7.08/1.45	thf(decl_190, type, ubforcartprodlem2: $o).
7.08/1.45	thf(decl_191, type, ubforcartprodlem3: $o).
7.08/1.45	thf(decl_192, type, cartprodpairin: $o).
7.08/1.45	thf(decl_193, type, cartprodmempair1: $o).
7.08/1.45	thf(decl_194, type, cartprodmempair: $o).
7.08/1.45	thf(decl_195, type, setunionE2: $o).
7.08/1.45	thf(decl_196, type, setunionsingleton1: $o).
7.08/1.45	thf(decl_197, type, setunionsingleton2: $o).
7.08/1.45	thf(decl_198, type, setunionsingleton: $o).
7.08/1.45	thf(decl_199, type, singleton: $i > $o).
7.08/1.45	thf(decl_200, type, singletonprop: $o).
7.08/1.45	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
7.08/1.45	thf(decl_202, type, ex1E1: $o).
7.08/1.45	thf(decl_203, type, ex1I: $o).
7.08/1.45	thf(decl_204, type, ex1I2: $o).
7.08/1.45	thf(decl_205, type, singletonsuniq: $o).
7.08/1.45	thf(decl_210, type, setukpairinjL1: $o).
7.08/1.45	thf(decl_211, type, kfstsingleton: $o).
7.08/1.45	thf(decl_212, type, theprop: $o).
7.08/1.45	thf(decl_213, type, kfst: $i > $i).
7.08/1.45	thf(decl_214, type, kfstpairEq: $o).
7.08/1.45	thf(decl_215, type, cartprodfstin: $o).
7.08/1.45	thf(decl_216, type, setukpairinjL2: $o).
7.08/1.45	thf(decl_217, type, setukpairinjL: $o).
7.08/1.45	thf(decl_218, type, setukpairinjR11: $o).
7.08/1.45	thf(decl_219, type, setukpairinjR12: $o).
7.08/1.45	thf(decl_220, type, setukpairinjR1: $o).
7.08/1.45	thf(decl_221, type, upairequniteq: $o).
7.08/1.45	thf(decl_222, type, setukpairinjR2: $o).
7.08/1.45	thf(decl_223, type, setukpairinjR: $o).
7.08/1.45	thf(decl_224, type, ksndsingleton: $o).
7.08/1.45	thf(decl_225, type, ksnd: $i > $i).
7.08/1.45	thf(decl_226, type, ksndpairEq: $o).
7.08/1.45	thf(decl_227, type, kpairsurjEq: $o).
7.08/1.45	thf(decl_228, type, cartprodsndin: $o).
7.08/1.45	thf(decl_229, type, cartprodpairmemEL: $o).
7.08/1.45	thf(decl_230, type, cartprodpairmemER: $o).
7.08/1.45	thf(decl_231, type, cartprodmempaircEq: $o).
7.08/1.45	thf(decl_232, type, cartprodfstpairEq: $o).
7.08/1.45	thf(decl_233, type, cartprodsndpairEq: $o).
7.08/1.45	thf(decl_234, type, cartprodpairsurjEq: $o).
7.08/1.45	thf(decl_235, type, breln: $i > $i > $i > $o).
7.08/1.45	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
7.08/1.45	thf(decl_237, type, dpsetconstrI: $o).
7.08/1.45	thf(decl_238, type, dpsetconstrSub: $o).
7.08/1.45	thf(decl_239, type, setOfPairsIsBReln: $o).
7.08/1.45	thf(decl_240, type, dpsetconstrERa: $o).
7.08/1.45	thf(decl_241, type, dpsetconstrEL1: $o).
7.08/1.45	thf(decl_242, type, dpsetconstrEL2: $o).
7.08/1.45	thf(decl_243, type, dpsetconstrER: $o).
7.08/1.45	thf(decl_244, type, func: $i > $i > $i > $o).
7.08/1.45	thf(decl_245, type, funcSet: $i > $i > $i).
7.08/1.45	thf(decl_246, type, funcImageSingleton: $o).
7.08/1.45	thf(decl_247, type, apProp: $o).
7.08/1.45	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
7.08/1.45	thf(decl_249, type, app: $o).
7.08/1.45	thf(decl_250, type, infuncsetfunc: $o).
7.08/1.45	thf(decl_251, type, ap2p: $o).
7.08/1.45	thf(decl_252, type, funcinfuncset: $o).
7.08/1.45	thf(decl_253, type, lamProp: $o).
7.08/1.45	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
7.08/1.45	thf(decl_255, type, lamp: $o).
7.08/1.45	thf(decl_256, type, lam2p: $o).
7.08/1.45	thf(decl_257, type, brelnall1: $o).
7.08/1.45	thf(decl_258, type, brelnall2: $o).
7.08/1.45	thf(decl_259, type, ex1E2: $o).
7.08/1.45	thf(decl_260, type, funcGraphProp1: $o).
7.08/1.45	thf(decl_261, type, funcGraphProp3: $o).
7.08/1.45	thf(decl_262, type, funcGraphProp2: $o).
7.08/1.45	thf(decl_263, type, funcextLem: $o).
7.08/1.45	thf(decl_264, type, funcGraphProp4: $o).
7.08/1.45	thf(decl_265, type, subbreln: $o).
7.08/1.45	thf(decl_266, type, eqbreln: $o).
7.08/1.45	thf(decl_267, type, funcext: $o).
7.08/1.45	thf(decl_268, type, funcext2: $o).
7.08/1.45	thf(decl_269, type, ap2apEq1: $o).
7.08/1.45	thf(decl_270, type, ap2apEq2: $o).
7.08/1.45	thf(decl_271, type, beta1: $o).
7.08/1.45	thf(decl_272, type, eta1: $o).
7.08/1.45	thf(decl_273, type, lam2lamEq: $o).
7.08/1.45	thf(decl_274, type, beta2: $o).
7.08/1.45	thf(decl_275, type, eta2: $o).
7.08/1.45	thf(decl_276, type, iffalseProp1: $o).
7.08/1.45	thf(decl_277, type, iffalseProp2: $o).
7.08/1.45	thf(decl_278, type, iftrueProp1: $o).
7.08/1.45	thf(decl_279, type, iftrueProp2: $o).
7.08/1.45	thf(decl_280, type, ifSingleton: $o).
7.08/1.45	thf(decl_281, type, if: $i > $o > $i > $i > $i).
7.08/1.45	thf(decl_282, type, ifp: $o).
7.08/1.45	thf(decl_283, type, theeq: $o).
7.08/1.45	thf(decl_284, type, iftrue: $o).
7.08/1.45	thf(decl_285, type, iffalse: $o).
7.08/1.45	thf(decl_286, type, iftrueorfalse: $o).
7.08/1.45	thf(decl_287, type, binintersectT_lem: $o).
7.08/1.45	thf(decl_288, type, binunionT_lem: $o).
7.08/1.45	thf(decl_289, type, powersetT_lem: $o).
7.08/1.45	thf(decl_290, type, setminusT_lem: $o).
7.08/1.45	thf(decl_291, type, complementT_lem: $o).
7.08/1.45	thf(decl_292, type, setextT: $o).
7.08/1.45	thf(decl_293, type, subsetTI: $o).
7.08/1.45	thf(decl_294, type, powersetTI1: $o).
7.08/1.45	thf(decl_295, type, powersetTE1: $o).
7.08/1.45	thf(decl_296, type, complementTI1: $o).
7.08/1.45	thf(decl_297, type, complementTE1: $o).
7.08/1.45	thf(decl_298, type, binintersectTELcontra: $o).
7.08/1.45	thf(decl_299, type, binintersectTERcontra: $o).
7.08/1.45	thf(decl_300, type, contrasubsetT: $o).
7.08/1.45	thf(decl_301, type, contrasubsetT1: $o).
7.08/1.45	thf(decl_302, type, contrasubsetT2: $o).
7.08/1.45	thf(decl_303, type, contrasubsetT3: $o).
7.08/1.45	thf(decl_304, type, doubleComplementI1: $o).
7.08/1.45	thf(decl_305, type, doubleComplementE1: $o).
7.08/1.45	thf(decl_306, type, doubleComplementSub1: $o).
7.08/1.45	thf(decl_307, type, doubleComplementSub2: $o).
7.08/1.45	thf(decl_308, type, doubleComplementEq: $o).
7.08/1.45	thf(decl_309, type, complementTnotintersectT: $o).
7.08/1.45	thf(decl_310, type, complementImpComplementIntersect: $o).
7.08/1.45	thf(decl_311, type, complementSubsetComplementIntersect: $o).
7.08/1.45	thf(decl_312, type, complementInPowersetComplementIntersect: $o).
7.08/1.45	thf(decl_313, type, contraSubsetComplement: $o).
7.08/1.45	thf(decl_314, type, complementTcontraSubset: $o).
7.08/1.45	thf(decl_315, type, binunionTILcontra: $o).
7.08/1.45	thf(decl_316, type, binunionTIRcontra: $o).
7.08/1.45	thf(decl_317, type, inIntersectImpInUnion: $o).
7.08/1.45	thf(decl_318, type, inIntersectImpInUnion2: $o).
7.08/1.45	thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
7.08/1.45	thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
7.08/1.45	thf(decl_321, type, inComplementUnionImpNotIn1: $o).
7.08/1.45	thf(decl_322, type, inComplementUnionImpInComplement1: $o).
7.08/1.45	thf(decl_323, type, binunionTE: $o).
7.08/1.45	thf(decl_324, type, binunionTEcontra: $o).
7.08/1.45	thf(decl_325, type, demorgan2a1: $o).
7.08/1.45	thf(decl_326, type, complementUnionInPowersetComplement: $o).
7.08/1.45	thf(decl_327, type, demorgan2a2: $o).
7.08/1.45	thf(decl_328, type, demorgan1a: $o).
7.08/1.45	thf(decl_329, type, demorgan1b: $o).
7.08/1.45	thf(decl_330, type, demorgan1: $o).
7.08/1.45	thf(decl_331, type, demorgan2a: $o).
7.08/1.45	thf(decl_332, type, demorgan2b2: $o).
7.08/1.45	thf(decl_333, type, demorgan2b: $o).
7.08/1.45	thf(decl_334, type, demorgan2: $o).
7.08/1.45	thf(decl_335, type, woz13rule0: $o).
7.08/1.45	thf(decl_336, type, woz13rule1: $o).
7.08/1.45	thf(decl_337, type, woz13rule2: $o).
7.08/1.45	thf(decl_338, type, woz13rule3: $o).
7.08/1.45	thf(decl_339, type, woz13rule4: $o).
7.08/1.45	thf(decl_340, type, woz1_1: $o).
7.08/1.45	thf(decl_341, type, woz1_2: $o).
7.08/1.45	thf(decl_342, type, woz1_3: $o).
7.08/1.45	thf(decl_343, type, woz1_4: $o).
7.08/1.45	thf(decl_344, type, woz1_5: $o).
7.08/1.45	thf(decl_345, type, breln1: $i > $i > $o).
7.08/1.45	thf(decl_346, type, breln1all2: $o).
7.08/1.45	thf(decl_347, type, breln1Set: $i > $i).
7.08/1.45	thf(decl_348, type, breln1SetBreln1: $o).
7.08/1.45	thf(decl_355, type, choice2fnsingleton: $o).
7.08/1.45	thf(decl_356, type, setOfPairsIsBReln1: $o).
7.08/1.45	thf(decl_357, type, breln1all1: $o).
7.08/1.45	thf(decl_358, type, subbreln1: $o).
7.08/1.45	thf(decl_359, type, eqbreln1: $o).
7.08/1.45	thf(decl_360, type, breln1invset: $i > $i > $i).
7.08/1.45	thf(decl_361, type, breln1invprop: $o).
7.08/1.45	thf(decl_362, type, breln1invI: $o).
7.08/1.45	thf(decl_363, type, breln1invE: $o).
7.08/1.45	thf(decl_364, type, breln1compset: $i > $i > $i > $i).
7.08/1.45	thf(decl_365, type, breln1compprop: $o).
7.08/1.45	thf(decl_366, type, epred1_0: $o).
7.08/1.45	thf(decl_367, type, esk1_2: $i > $i > $i).
7.08/1.45	thf(decl_368, type, esk2_2: $i > $i > $i).
7.08/1.45	thf(decl_369, type, esk3_2: $i > $i > $i).
7.08/1.45	thf(decl_370, type, esk4_1: $i > $i).
7.08/1.45	thf(decl_371, type, esk5_2: ($i > $i > $o) > $i > $i).
7.08/1.45	thf(decl_372, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
7.08/1.45	thf(decl_373, type, esk7_2: ($i > $i > $o) > $i > $i).
7.08/1.45	thf(decl_374, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
7.08/1.45	thf(decl_375, type, esk9_1: $i > $i).
7.08/1.45	thf(decl_376, type, esk10_2: ($i > $o) > $i > $i).
7.08/1.45	thf(decl_377, type, esk11_2: ($i > $o) > $i > $i).
7.08/1.45	thf(decl_378, type, esk12_1: ($i > $o) > $i).
7.08/1.45	thf(decl_379, type, esk13_2: ($i > $o) > $i > $i).
7.08/1.45	thf(decl_380, type, esk14_1: ($i > $o) > $i).
7.08/1.45	thf(decl_381, type, esk15_2: $i > $i > $i).
7.08/1.45	thf(decl_382, type, esk16_2: $i > $i > $i).
7.08/1.45	thf(decl_383, type, esk17_1: $i > $i).
7.08/1.45	thf(decl_384, type, esk18_1: $i > $i).
7.08/1.45	thf(decl_385, type, esk19_1: $i > $i).
7.08/1.45	thf(decl_386, type, esk20_2: $i > $i > $i).
7.08/1.45	thf(decl_387, type, esk21_3: $i > $i > $o > $i).
7.08/1.45	thf(decl_388, type, esk22_2: ($i > $o) > $i > $i).
7.08/1.45	thf(decl_389, type, esk23_1: ($i > $o) > $i).
7.08/1.45	thf(decl_390, type, esk24_1: $i > $i).
7.08/1.45	thf(decl_391, type, esk25_2: $i > ($i > $o) > $i).
7.08/1.45	thf(decl_392, type, esk26_2: $i > ($i > $o) > $i).
7.08/1.45	thf(decl_393, type, esk27_2: $i > ($i > $o) > $i).
7.08/1.45	thf(decl_394, type, esk28_2: $i > ($i > $o) > $i).
7.08/1.45	thf(decl_395, type, esk29_2: $i > ($i > $o) > $i).
7.08/1.45	thf(decl_396, type, esk30_2: $i > ($i > $o) > $i).
7.08/1.45	thf(decl_397, type, esk31_2: ($i > $o) > $i > $i).
7.08/1.45	thf(decl_398, type, esk32_1: ($i > $o) > $i).
7.08/1.45	thf(decl_399, type, esk33_1: ($i > $o) > $i).
7.08/1.45	thf(decl_400, type, esk34_1: ($i > $o) > $i).
7.08/1.45	thf(decl_401, type, esk35_1: ($i > $o) > $i).
7.08/1.45	thf(decl_402, type, esk36_2: ($i > $o) > $i > $i).
7.08/1.45	thf(decl_403, type, esk37_1: ($i > $o) > $i).
7.08/1.45	thf(decl_404, type, esk38_2: ($i > $o) > $i > $i).
7.08/1.45	thf(decl_405, type, esk39_2: ($i > $o) > ($i > $o) > $i).
7.08/1.45	thf(decl_406, type, esk40_2: ($i > $o) > ($i > $o) > $i).
7.08/1.45	thf(decl_407, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
7.08/1.45	thf(decl_408, type, esk42_2: ($i > $o) > ($i > $o) > $i).
7.08/1.45	thf(decl_409, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
7.08/1.45	thf(decl_410, type, esk44_2: ($i > $o) > ($i > $o) > $i).
7.08/1.45	thf(decl_411, type, esk45_2: ($i > $o) > $i > $i).
7.08/1.45	thf(decl_412, type, esk46_2: ($i > $o) > ($i > $o) > $i).
7.08/1.45	thf(decl_413, type, esk47_2: ($i > $o) > ($i > $o) > $i).
7.08/1.45	thf(decl_414, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
7.08/1.45	thf(decl_415, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
7.08/1.45	thf(decl_416, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
7.08/1.45	thf(decl_417, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
7.08/1.45	thf(decl_418, type, esk52_2: $i > $i > $i).
7.08/1.45	thf(decl_419, type, esk53_2: $i > $i > $i).
7.08/1.45	thf(decl_420, type, esk54_2: $i > $i > $i).
7.08/1.45	thf(decl_421, type, esk55_3: $i > $i > $i > $i).
7.08/1.45	thf(decl_422, type, esk56_3: $i > $i > $i > $i).
7.08/1.45	thf(decl_423, type, esk57_2: $i > $i > $i).
7.08/1.45	thf(decl_424, type, esk58_2: $i > ($i > $o) > $i).
7.08/1.45	thf(decl_425, type, esk59_2: $i > ($i > $o) > $i).
7.08/1.45	thf(decl_426, type, esk60_2: $i > ($i > $o) > $i).
7.08/1.45	thf(decl_427, type, esk61_3: $i > ($i > $o) > $i > $i).
7.08/1.45	thf(decl_428, type, esk62_2: $i > ($i > $o) > $i).
7.08/1.45	thf(decl_429, type, esk63_2: $i > ($i > $o) > $i).
7.08/1.45	thf(decl_430, type, esk64_3: $i > $i > ($i > $i) > $i).
7.08/1.45	thf(decl_431, type, esk65_3: $i > $i > ($i > $i) > $i).
7.08/1.45	thf(decl_432, type, esk66_3: $i > $i > ($i > $i) > $i).
7.08/1.45	thf(decl_433, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
7.08/1.45	thf(decl_434, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
7.08/1.45	thf(decl_435, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
7.08/1.45	thf(decl_436, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
7.08/1.45	thf(decl_437, type, esk71_4: $i > $i > $i > $i > $i).
7.08/1.45	thf(decl_438, type, esk72_4: $i > $i > $i > $i > $i).
7.08/1.45	thf(decl_439, type, esk73_4: $i > $i > $i > $i > $i).
7.08/1.45	thf(decl_440, type, esk74_4: $i > $i > $i > $i > $i).
7.08/1.45	thf(decl_441, type, esk75_4: $i > $i > $i > $i > $i).
7.08/1.45	thf(decl_442, type, esk76_4: $i > $i > $i > $i > $i).
7.08/1.45	thf(decl_443, type, esk77_4: $i > $i > $i > $i > $i).
7.08/1.45	thf(decl_444, type, esk78_4: $i > $i > $i > $i > $i).
7.08/1.45	thf(decl_445, type, esk79_4: $i > $i > $i > $i > $i).
7.08/1.45	thf(decl_446, type, esk80_3: $i > $i > ($i > $i) > $i).
7.08/1.45	thf(decl_447, type, esk81_3: $i > $i > ($i > $i) > $i).
7.08/1.45	thf(decl_448, type, esk82_3: $i > $i > ($i > $i) > $i).
7.08/1.45	thf(decl_449, type, esk83_3: $i > $i > $i > $i).
7.08/1.45	thf(decl_450, type, esk84_3: $i > $i > $i > $i).
7.08/1.45	thf(decl_451, type, esk85_3: $i > $i > $i > $i).
7.08/1.45	thf(decl_452, type, esk86_3: $i > $i > $i > $i).
7.08/1.45	thf(decl_453, type, esk87_3: $i > $i > ($i > $o) > $i).
7.08/1.45	thf(decl_454, type, esk88_3: $i > $i > ($i > $o) > $i).
7.08/1.45	thf(decl_455, type, esk89_3: $i > $i > ($i > $o) > $i).
7.08/1.45	thf(decl_456, type, esk90_3: $i > $i > ($i > $o) > $i).
7.08/1.45	thf(decl_457, type, esk91_3: $i > $i > $i > $i).
7.08/1.45	thf(decl_458, type, esk92_3: $i > $i > $i > $i).
7.08/1.45	thf(decl_459, type, esk93_3: $i > $i > $i > $i).
7.08/1.45	thf(decl_460, type, esk94_3: $i > $i > $i > $i).
7.08/1.45	thf(decl_461, type, esk95_3: $i > $i > $i > $i).
7.08/1.45	thf(decl_462, type, esk96_3: $i > $i > $i > $i).
7.08/1.45	thf(decl_463, type, esk97_0: $i).
7.08/1.45	thf(decl_464, type, esk98_0: $i).
7.08/1.45	thf(decl_465, type, esk99_0: $i).
7.08/1.45	thf(decl_466, type, esk100_0: $i).
7.08/1.45	thf(decl_467, type, esk101_0: $i).
7.08/1.45	thf(decl_468, type, esk102_0: $i).
7.08/1.45	thf(breln1, axiom, ((breln1)=(^[X4:$i, X33:$i]:((breln @ X4 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', breln1)).
7.08/1.45	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', breln)).
7.08/1.45	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', descr__Cong)).
7.08/1.45	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', exu)).
7.08/1.45	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', exu__Cong)).
7.08/1.45	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', exuI1)).
7.08/1.45	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', nonempty)).
7.08/1.45	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', exuE2)).
7.08/1.45	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', nonemptyI)).
7.08/1.45	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', exuE3e)).
7.08/1.45	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', exuE1)).
7.08/1.45	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setOfPairsIsBReln)).
7.08/1.45	thf(breln1compset, axiom, ((breln1compset)=(^[X4:$i, X33:$i, X35:$i]:(dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:(?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35)))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', breln1compset)).
7.08/1.45	thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setOfPairsIsBReln1)).
7.08/1.45	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', exuEu)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', exuE3u)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', exuI2)).
7.08/1.45	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', exuI3)).
7.08/1.45	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', descrp)).
7.08/1.45	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', replAx)).
7.08/1.45	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', emptyE1)).
7.08/1.45	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', nonemptyImpWitness)).
7.08/1.45	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setoftrueEq)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', ex1I)).
7.08/1.45	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', dsetconstrER)).
7.08/1.45	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', dsetconstrI)).
7.08/1.45	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', ex1I2)).
7.08/1.45	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', kfstsingleton)).
7.08/1.45	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', dpsetconstrI)).
7.08/1.45	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', dpsetconstrEL1)).
7.08/1.45	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', dpsetconstrEL2)).
7.08/1.45	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', dpsetconstrER)).
7.08/1.45	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', funcImageSingleton)).
7.08/1.45	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', apProp)).
7.08/1.45	thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', lamp)).
7.08/1.45	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', lam2p)).
7.08/1.45	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', brelnall1)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', ex1E2)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', subbreln)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', eta2)).
7.08/1.45	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', iffalseProp2)).
7.08/1.45	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', ifSingleton)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', beta1)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', eqbreln)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', brelnall2)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', lamProp)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', breln1all1)).
7.08/1.45	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:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', eqbreln1)).
7.08/1.45	thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', breln1invE)).
7.08/1.45	thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', breln1compprop)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', breln1invI)).
7.08/1.45	thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', breln1invprop)).
7.08/1.45	thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', subbreln1)).
7.08/1.45	thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', breln1SetBreln1)).
7.08/1.45	thf(breln1all2, axiom, ((breln1all2)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', breln1all2)).
7.08/1.45	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', iftrueProp2)).
7.08/1.45	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', iftrueProp1)).
7.08/1.45	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', iffalseProp1)).
7.08/1.45	thf(beta2, axiom, ((beta2)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', beta2)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', lam2lamEq)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', eta1)).
7.08/1.45	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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', dpsetconstrERa)).
7.08/1.45	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', dpsetconstrSub)).
7.08/1.45	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', ksndsingleton)).
7.08/1.45	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', ex1E1)).
7.08/1.45	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', singletonprop)).
7.08/1.45	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', sepSubset)).
7.08/1.45	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', sepInPowerset)).
7.08/1.45	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', dsetconstr__Cong)).
7.08/1.45	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', nonemptyI1)).
7.08/1.45	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', nonemptyE1)).
7.08/1.45	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setbeta)).
7.08/1.45	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', dsetconstrEL)).
7.08/1.45	thf(breln1compI, conjecture, ((setextAx)=>(((setadjoinAx)=>((powersetAx)=>((setunionAx)=>(((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>(((descrp)=>(((dsetconstrEL)=>((((prop2setE)=>(((emptysetimpfalse)=>((notinemptyset)=>((((emptyI)=>(((setbeta)=>((nonemptyE1)=>(((nonemptyI1)=>(((emptyinunitempty)=>(((setadjoinE)=>((((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>(((setunionI)=>((setunionE)=>((((((notinsingleton)=>((((upairsetE)=>((upairsetIL)=>((((vacuousDall)=>(((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>(((prop2set2propI)=>((notdexE)=>((((exuI3)=>((exuI2)=>(((in__Cong)=>((exuE3u)=>(((emptyset__Cong)=>((setadjoin__Cong)=>((((omega__Cong)=>((exuEu)=>(((dsetconstr__Cong)=>((subsetI1)=>((((subsetI2)=>((emptysetsubset)=>((subsetE)=>(((notsubsetI)=>(((notequalI2)=>((((setadjoinSub)=>(((subset2powerset)=>(((subsetemptysetimpeq)=>((powersetI1)=>((((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>(((binunionEcases)=>(((binunionLsub)=>((binunionRsub)=>(((binintersectSubset5)=>((binintersectEL)=>((((binintersectSubset3)=>((((binintersectRsub)=>(((binintersectSubset1)=>((bs114d)=>((((setminusER)=>((setminusSubset2)=>(((((((setminusSubset1)=>((symdiffE)=>(((symdiffI2)=>((symdiffIneg1)=>((((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>(((singletoninpowerset)=>(((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>(((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>(((setunionE2)=>(((setunionsingleton2)=>((setunionsingleton)=>((((ex1I)=>((ex1I2)=>(((setukpairinjL1)=>((kfstsingleton)=>(((kfstpairEq)=>((((setukpairinjL)=>(((setukpairinjR12)=>((setukpairinjR1)=>(((setukpairinjR2)=>((((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((((dpsetconstrI)=>(((setOfPairsIsBReln)=>(((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>(((((funcinfuncset)=>(((lamp)=>((lam2p)=>((brelnall1)=>(((ex1E2)=>((funcGraphProp1)=>(((funcGraphProp2)=>((funcextLem)=>(((subbreln)=>(((((ap2apEq1)=>((ap2apEq2)=>((((((eta2)=>(((iffalseProp2)=>((((ifSingleton)=>(((theeq)=>(((iffalse)=>((((binunionT_lem)=>((powersetT_lem)=>((((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((((((((contrasubsetT3)=>((doubleComplementI1)=>(((((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>(((((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>(((((binunionTEcontra)=>((((demorgan2a2)=>((((demorgan1)=>(((((((((woz13rule3)=>(((((woz1_3)=>((woz1_4)=>(((((((breln1all1)=>(((eqbreln1)=>((((breln1invE)=>(![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 @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35)))<=(in @ (kpair @ X2 @ X14) @ X33))))))))))))<=(breln1compprop)))<=(breln1invI))<=(breln1invprop)))<=(subbreln1)))<=(setOfPairsIsBReln1))<=(choice2fnsingleton))<=(breln1SetBreln1))<=(breln1all2))<=(woz1_5))))<=(woz1_2))<=(woz1_1))<=(woz13rule4)))<=(woz13rule2))<=(woz13rule1))<=(woz13rule0))<=(demorgan2))<=(demorgan2b))<=(demorgan2b2))<=(demorgan2a)))<=(demorgan1b))<=(demorgan1a)))<=(complementUnionInPowersetComplement))<=(demorgan2a1)))<=(binunionTE))<=(inComplementUnionImpInComplement1))<=(inComplementUnionImpNotIn1))))<=(inIntersectImpInUnion2))<=(inIntersectImpInUnion)))))<=(contraSubsetComplement))<=(complementInPowersetComplementIntersect))<=(complementSubsetComplementIntersect)))))<=(doubleComplementSub2))<=(doubleComplementSub1))<=(doubleComplementE1))))<=(contrasubsetT2))<=(contrasubsetT1))<=(contrasubsetT))<=(binintersectTERcontra))<=(binintersectTELcontra))<=(complementTE1)))))))<=(complementT_lem))<=(setminusT_lem))))<=(binintersectT_lem))<=(iftrueorfalse)))<=(iftrue)))<=(ifp)))<=(iftrueProp2))<=(iftrueProp1)))<=(iffalseProp1)))<=(beta2))<=(lam2lamEq))<=(eta1))<=(beta1))))<=(funcext2))<=(funcext))<=(eqbreln)))<=(funcGraphProp4))))<=(funcGraphProp3))))<=(brelnall2)))))<=(lamProp)))<=(ap2p))<=(infuncsetfunc))<=(app)))))))<=(dpsetconstrERa)))<=(dpsetconstrSub)))<=(cartprodpairsurjEq))<=(cartprodsndpairEq)))))))))<=(ksndsingleton))<=(setukpairinjR)))<=(upairequniteq))))<=(setukpairinjR11)))<=(setukpairinjL2))<=(cartprodfstin)))<=(theprop))))<=(singletonsuniq))))<=(ex1E1))<=(singletonprop))))<=(setunionsingleton1)))<=(cartprodmempair))))))<=(ubforcartprodlem1)))))<=(singletoninpowunion)))<=(singletonsubset))))))<=(secondinupair))<=(symdiffIneg2))))<=(symdiffI1))))<=(setminusLsub))<=(setminusIRneg))<=(setminusILneg))<=(setminusELneg))<=(setminusERneg))))<=(setminusEL))<=(setminusI))))<=(binintersectSubset4)))<=(disjointsetsI1))<=(binintersectER)))<=(binintersectSubset2))<=(binintersectLsub))))<=(binintersectI))))<=(binunionE)))<=(binunionIR)))))))<=(inPowerset))<=(powersetE1))))<=(setextsub)))<=(setadjoinSub2)))<=(subsetTrans))<=(subsetRefl)))<=(notequalI1)))<=(subsetE2)))))<=(eqimpsubset1))<=(eqimpsubset2))))<=(descr__Cong))))<=(setunion__Cong))<=(powerset__Cong))))<=(exu__Cong))))<=(inCongP))))<=(exuI1))<=(notdallE))))<=(prop2setI)))))<=(quantDeMorgan1)))<=(emptyE1))<=(upairsetIR))))<=(singletonsswitch))<=(eqinunit)))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU))))<=(powersetE)))))<=(setoftrueEq))<=(setadjoinOr)))<=(setadjoinIR)))<=(setadjoinIL)))<=(nonemptyI))))<=(noeltsimpempty)))<=(setext))<=(exuE3e))))<=(emptysetE)))<=(exuE1))<=(dsetconstrER)))<=(dsetconstrI)))<=(wellorderingAx))))))<=(omega0Ax)))))<=(emptysetAx))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', breln1compI)).
7.08/1.45	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', upairinpowunion)).
7.08/1.45	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', emptysetAx)).
7.08/1.45	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', binintersectSubset2)).
7.08/1.45	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', binintersectLsub)).
7.08/1.45	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', binintersectI)).
7.08/1.45	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setukpairIR)).
7.08/1.45	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', binunionE)).
7.08/1.45	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', binunionIR)).
7.08/1.45	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', inPowerset)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', kpairiskpair)).
7.08/1.45	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', powersetE1)).
7.08/1.45	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setextsub)).
7.08/1.45	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', kpairp)).
7.08/1.45	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setadjoinSub2)).
7.08/1.45	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', subsetTrans)).
7.08/1.45	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', subsetRefl)).
7.08/1.45	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', singletoninpowerset)).
7.08/1.45	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', notequalI1)).
7.08/1.45	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', subsetE2)).
7.08/1.45	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', upairset2E)).
7.08/1.45	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', eqimpsubset1)).
7.08/1.45	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setminusSubset1)).
7.08/1.45	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', eqimpsubset2)).
7.08/1.45	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setunion__Cong)).
7.08/1.45	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', upairsubunion)).
7.08/1.45	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', powerset__Cong)).
7.08/1.45	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setukpairinjR1)).
7.08/1.45	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', inCongP)).
7.08/1.45	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', notdallE)).
7.08/1.45	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', prop2setI)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', ubforcartprodlem2)).
7.08/1.45	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', quantDeMorgan1)).
7.08/1.45	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', symdiffE)).
7.08/1.45	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', upairsetIR)).
7.08/1.45	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', ubforcartprodlem3)).
7.08/1.45	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', singletonsswitch)).
7.08/1.45	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', eqinunit)).
7.08/1.45	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', uniqinunit)).
7.08/1.45	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', cartprodpairin)).
7.08/1.45	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', cartprodmempair1)).
7.08/1.45	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', subPowSU)).
7.08/1.45	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', powersetE)).
7.08/1.45	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setunionE2)).
7.08/1.45	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setadjoinOr)).
7.08/1.45	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setadjoinIR)).
7.08/1.45	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setunionsingleton2)).
7.08/1.45	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setadjoinIL)).
7.08/1.45	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', noeltsimpempty)).
7.08/1.45	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setunionsingleton)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', setext)).
7.08/1.45	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', emptysetE)).
7.08/1.45	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', symdiffI2)).
7.08/1.45	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', wellorderingAx)).
7.08/1.45	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', omega0Ax)).
7.08/1.45	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setukpairinjL1)).
7.08/1.45	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', kfstpairEq)).
7.08/1.45	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setukpairinjL)).
7.08/1.45	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setukpairinjR12)).
7.08/1.45	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', binunionT_lem)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', powersetT_lem)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', setukpairinjR2)).
7.08/1.45	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', ksndpairEq)).
7.08/1.45	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', kpairsurjEq)).
7.08/1.45	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', cartprodsndin)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', cartprodpairmemEL)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', cartprodpairmemER)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', cartprodmempaircEq)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', cartprodfstpairEq)).
7.08/1.45	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', symdiffIneg1)).
7.08/1.45	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', funcinfuncset)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', funcGraphProp1)).
7.08/1.45	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', funcGraphProp2)).
7.08/1.45	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', funcextLem)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', ap2apEq1)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', ap2apEq2)).
7.08/1.45	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', theeq)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', iffalse)).
7.08/1.45	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', funcext2)).
7.08/1.45	thf(funcext, axiom, ((funcext)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', funcext)).
7.08/1.45	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', funcGraphProp4)).
7.08/1.45	thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', funcGraphProp3)).
7.08/1.45	thf(setextT, axiom, ((setextT)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', setextT)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', subsetTI)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', powersetTI1)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', powersetTE1)).
7.08/1.45	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', complementTI1)).
7.08/1.45	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', contrasubsetT3)).
7.08/1.45	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', doubleComplementI1)).
7.08/1.45	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', doubleComplementEq)).
7.08/1.45	thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', complementTnotintersectT)).
7.08/1.45	thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', complementImpComplementIntersect)).
7.08/1.45	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', complementTcontraSubset)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', binunionTILcontra)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', binunionTIRcontra)).
7.08/1.45	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', inIntersectImpInIntersectUnions)).
7.08/1.45	thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', intersectInPowersetIntersectUnions)).
7.08/1.45	thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', binunionTEcontra)).
7.08/1.45	thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', demorgan2a2)).
7.08/1.45	thf(demorgan1, axiom, ((demorgan1)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', demorgan1)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', woz13rule3)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', woz1_3)).
7.08/1.45	thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', woz1_4)).
7.08/1.45	thf(woz1_5, axiom, ((woz1_5)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', woz1_5)).
7.08/1.45	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:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', woz1_2)).
7.08/1.45	thf(woz1_1, axiom, ((woz1_1)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', woz1_1)).
7.08/1.45	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:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', woz13rule4)).
7.08/1.45	thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', woz13rule2)).
7.08/1.45	thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', woz13rule1)).
7.08/1.45	thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', woz13rule0)).
7.08/1.45	thf(demorgan2, axiom, ((demorgan2)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', demorgan2)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', demorgan2b)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', demorgan2b2)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', demorgan2a)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', demorgan1b)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', demorgan1a)).
7.08/1.45	thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', complementUnionInPowersetComplement)).
7.08/1.45	thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', demorgan2a1)).
7.08/1.45	thf(binunionTE, axiom, ((binunionTE)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', binunionTE)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', inComplementUnionImpInComplement1)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', inComplementUnionImpNotIn1)).
7.08/1.45	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', inIntersectImpInUnion2)).
7.08/1.45	thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', inIntersectImpInUnion)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', contraSubsetComplement)).
7.08/1.45	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', complementInPowersetComplementIntersect)).
7.08/1.45	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', complementSubsetComplementIntersect)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', doubleComplementSub2)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', doubleComplementSub1)).
7.08/1.45	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', doubleComplementE1)).
7.08/1.45	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', contrasubsetT2)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', contrasubsetT1)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', contrasubsetT)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', binintersectTERcontra)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', binintersectTELcontra)).
7.08/1.45	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', complementTE1)).
7.08/1.45	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', complementT_lem)).
7.08/1.45	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.zBubz8cEYJ/E---3.1_19346.p', setminusT_lem)).
7.08/1.45	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', binintersectT_lem)).
7.08/1.45	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', iftrueorfalse)).
7.08/1.45	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', iftrue)).
7.08/1.45	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', ifp)).
7.08/1.45	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', ap2p)).
7.08/1.45	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', infuncsetfunc)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', app)).
7.08/1.45	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', cartprodpairsurjEq)).
7.08/1.45	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', cartprodsndpairEq)).
7.08/1.45	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setukpairinjR)).
7.08/1.45	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', upairequniteq)).
7.08/1.45	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setukpairinjR11)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', setukpairinjL2)).
7.08/1.45	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', cartprodfstin)).
7.08/1.45	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', theprop)).
7.08/1.45	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', singletonsuniq)).
7.08/1.45	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setunionsingleton1)).
7.08/1.45	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', cartprodmempair)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', ubforcartprodlem1)).
7.08/1.45	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', singletoninpowunion)).
7.08/1.45	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', singletonsubset)).
7.08/1.45	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', secondinupair)).
7.08/1.45	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', symdiffIneg2)).
7.08/1.45	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', symdiffI1)).
7.08/1.45	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setminusLsub)).
7.08/1.45	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setminusIRneg)).
7.08/1.45	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setminusILneg)).
7.08/1.45	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setminusELneg)).
7.08/1.45	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setminusERneg)).
7.08/1.45	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setminusEL)).
7.08/1.45	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setminusI)).
7.08/1.45	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', binintersectSubset4)).
7.08/1.45	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', disjointsetsI1)).
7.08/1.45	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', binintersectER)).
7.08/1.45	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setukpairIL)).
7.08/1.45	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setminusSubset2)).
7.08/1.45	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setminusER)).
7.08/1.45	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', bs114d)).
7.08/1.45	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', binintersectSubset1)).
7.08/1.45	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', binintersectRsub)).
7.08/1.45	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', binintersectSubset3)).
7.08/1.45	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', binintersectEL)).
7.08/1.45	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', binintersectSubset5)).
7.08/1.45	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', binunionRsub)).
7.08/1.45	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', binunionLsub)).
7.08/1.45	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', binunionEcases)).
7.08/1.45	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', upairset2IR)).
7.08/1.45	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', binunionIL)).
7.08/1.45	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', powersetsubset)).
7.08/1.45	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', powersetI1)).
7.08/1.45	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', subsetemptysetimpeq)).
7.08/1.45	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', subset2powerset)).
7.08/1.45	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setadjoinSub)).
7.08/1.45	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', notequalI2)).
7.08/1.45	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', notsubsetI)).
7.08/1.45	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', subsetE)).
7.08/1.45	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', emptysetsubset)).
7.08/1.45	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', subsetI2)).
7.08/1.45	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', subsetI1)).
7.08/1.45	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', omega__Cong)).
7.08/1.45	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setadjoin__Cong)).
7.08/1.45	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', emptyset__Cong)).
7.08/1.45	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', in__Cong)).
7.08/1.45	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', notdexE)).
7.08/1.45	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', quantDeMorgan4)).
7.08/1.45	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', quantDeMorgan3)).
7.08/1.45	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', quantDeMorgan2)).
7.08/1.45	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', vacuousDall)).
7.08/1.45	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', upairsetIL)).
7.08/1.45	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', upairsetE)).
7.08/1.45	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', notinsingleton)).
7.08/1.45	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setunionE)).
7.08/1.45	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setunionI)).
7.08/1.45	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', emptyInPowerset)).
7.08/1.45	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', emptyinPowerset)).
7.08/1.45	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', powersetI)).
7.08/1.45	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setadjoinE)).
7.08/1.45	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', emptyinunitempty)).
7.08/1.45	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', emptyI)).
7.08/1.45	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', notinemptyset)).
7.08/1.45	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', emptysetimpfalse)).
7.08/1.45	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', prop2setE)).
7.08/1.45	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.zBubz8cEYJ/E---3.1_19346.p', foundationAx)).
7.08/1.45	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', omegaIndAx)).
7.08/1.45	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', omegaSAx)).
7.08/1.45	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setunionAx)).
7.08/1.45	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', powersetAx)).
7.08/1.45	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setadjoinAx)).
7.08/1.45	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.zBubz8cEYJ/E---3.1_19346.p', setextAx)).
7.08/1.45	thf(c_0_299, plain, ((breln1)=(^[Z0/* 19 */:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(fof_simplification,[status(thm)],[breln1])).
7.08/1.45	thf(c_0_300, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
7.08/1.45	thf(c_0_301, plain, ((descr__Cong)<=>![X1:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
7.08/1.45	thf(c_0_302, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
7.08/1.45	thf(c_0_303, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
7.08/1.45	thf(c_0_304, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
7.08/1.45	thf(c_0_305, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
7.08/1.45	thf(c_0_306, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
7.08/1.45	thf(c_0_307, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
7.08/1.45	thf(c_0_308, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
7.08/1.45	thf(c_0_309, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
7.08/1.45	thf(c_0_310, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
7.08/1.45	thf(c_0_311, plain, ((breln1)=(^[Z0/* 19 */:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(apply_def,[status(thm)],[c_0_299, c_0_300])).
7.08/1.45	thf(c_0_312, plain, ((breln1compset)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:(dpsetconstr @ Z0 @ Z0 @ (^[Z3/* 19 */:$i, Z4:$i]:(?[X14:$i]:((((in @ X14 @ Z0)&(in @ (kpair @ Z3 @ X14) @ Z1))&(in @ (kpair @ X14 @ Z4) @ Z2)))))))), inference(fof_simplification,[status(thm)],[breln1compset])).
7.08/1.45	thf(c_0_313, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
7.08/1.45	thf(c_0_314, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
7.08/1.45	thf(c_0_315, 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])).
7.08/1.45	thf(c_0_316, 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])).
7.08/1.45	thf(c_0_317, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
7.08/1.45	thf(c_0_318, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
7.08/1.45	thf(c_0_319, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
7.08/1.45	thf(c_0_320, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1031:$i]:((((X1 @ X1031))&![X1032:$i]:((((X1 @ X1032))=>((X1031)=(X1032)))))))=>((?[X1033:$i]:((((X17 @ X1033))&![X1034:$i]:((((X17 @ X1034))=>((X1033)=(X1034)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_301, c_0_302])).
7.08/1.45	thf(c_0_321, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1025:$i]:((((X1 @ X1025))&![X1026:$i]:((((X1 @ X1026))=>((X1025)=(X1026)))))))<=>(?[X1027:$i]:((((X17 @ X1027))&![X1028:$i]:((((X17 @ X1028))=>((X1027)=(X1028)))))))))))), inference(apply_def,[status(thm)],[c_0_303, c_0_302])).
7.08/1.45	thf(c_0_322, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X1017:$i]:((((X1 @ X1017))&![X1018:$i]:((((X1 @ X1018))=>((X1017)=(X1018))))))))))), inference(apply_def,[status(thm)],[c_0_304, c_0_302])).
7.08/1.45	thf(c_0_323, plain, ((emptyE1)<=>![X4:$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])).
7.08/1.45	thf(c_0_324, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_305])).
7.08/1.45	thf(c_0_325, plain, ((exuE2)=(![X1:$i > $o]:(((?[X1015:$i]:((((X1 @ X1015))&![X1016:$i]:((((X1 @ X1016))=>((X1015)=(X1016)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_306, c_0_302])).
7.08/1.45	thf(c_0_326, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
7.08/1.45	thf(c_0_327, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_307, c_0_305])).
7.08/1.45	thf(c_0_328, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X1013:$i]:((((X1 @ X1013))&![X1014:$i]:((((X1 @ X1014))=>((X1013)=(X1014)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_308, c_0_302])).
7.08/1.45	thf(c_0_329, 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])).
7.08/1.45	thf(c_0_330, plain, ((exuE1)=(![X1:$i > $o]:(((?[X1011:$i]:((((X1 @ X1011))&![X1012:$i]:((((X1 @ X1012))=>((X1011)=(X1012)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_309, c_0_302])).
7.08/1.45	thf(c_0_331, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
7.08/1.45	thf(c_0_332, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
7.08/1.45	thf(c_0_333, plain, ((ex1I2)<=>![X4:$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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
7.08/1.45	thf(c_0_334, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
7.08/1.45	thf(c_0_335, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
7.08/1.45	thf(c_0_336, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_310, c_0_300])).
7.08/1.45	thf(c_0_337, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
7.08/1.45	thf(c_0_338, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
7.08/1.45	thf(c_0_339, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
7.08/1.45	thf(c_0_340, plain, ((funcImageSingleton)<=>![X4:$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])).
7.08/1.45	thf(c_0_341, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
7.08/1.45	thf(c_0_342, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
7.08/1.45	thf(c_0_343, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
7.08/1.45	thf(c_0_344, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_300])).
7.08/1.45	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])).
7.08/1.45	thf(c_0_346, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln, c_0_300])).
7.08/1.45	thf(c_0_347, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 248 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
7.08/1.45	thf(c_0_348, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
7.08/1.45	thf(c_0_349, plain, ((ifSingleton)<=>![X4:$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])).
7.08/1.45	thf(c_0_350, 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])).
7.08/1.45	thf(c_0_351, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_300])).
7.08/1.45	thf(c_0_352, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_300])).
7.08/1.45	thf(c_0_353, 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])).
7.08/1.45	thf(c_0_354, axiom, ((breln1all1)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![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))))))))), inference(apply_def,[status(thm)],[breln1all1, c_0_311])).
7.08/1.45	thf(c_0_355, axiom, ((eqbreln1)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X4)))=>(![X2:$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:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln1, c_0_311])).
7.08/1.45	thf(c_0_356, axiom, ((breln1invE)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33)))))))))), inference(apply_def,[status(thm)],[breln1invE, c_0_311])).
7.08/1.45	thf(c_0_357, axiom, ((breln1compprop)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X4)))=>((subset @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:(?[X1035:$i]:((((in @ X1035 @ X4)&(in @ (kpair @ Z0 @ X1035) @ X33))&(in @ (kpair @ X1035 @ Z1) @ X35)))))) @ (cartprod @ X4 @ X4))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[breln1compprop, c_0_312]), c_0_311])).
7.08/1.45	thf(c_0_358, axiom, ((breln1invI)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))))))))))), inference(apply_def,[status(thm)],[breln1invI, c_0_311])).
7.08/1.45	thf(c_0_359, axiom, ((breln1invprop)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>((subset @ (breln1invset @ X4 @ X33) @ (cartprod @ X4 @ X4))))))), inference(apply_def,[status(thm)],[breln1invprop, c_0_311])).
7.08/1.45	thf(c_0_360, axiom, ((subbreln1)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X4)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln1, c_0_311])).
7.08/1.45	thf(c_0_361, plain, ((setOfPairsIsBReln1)=(![X4:$i, X53:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X4)))))), inference(apply_def,[status(thm)],[c_0_313, c_0_311])).
7.08/1.45	thf(c_0_362, axiom, ((breln1SetBreln1)=(![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>((subset @ X33 @ (cartprod @ X4 @ X4))))))), inference(apply_def,[status(thm)],[breln1SetBreln1, c_0_311])).
7.08/1.45	thf(c_0_363, axiom, ((breln1all2)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X1:$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))))))))), inference(apply_def,[status(thm)],[breln1all2, c_0_311])).
7.08/1.45	thf(c_0_364, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
7.08/1.45	thf(c_0_365, plain, ((iftrueProp1)<=>![X4:$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])).
7.08/1.45	thf(c_0_366, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
7.08/1.45	thf(c_0_367, plain, ((beta2)<=>![X4:$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])).
7.08/1.45	thf(c_0_368, 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])).
7.08/1.45	thf(c_0_369, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 248 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
7.08/1.45	thf(c_0_370, 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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
7.08/1.45	thf(c_0_371, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
7.08/1.45	thf(c_0_372, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
7.08/1.45	thf(c_0_373, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
7.08/1.45	thf(c_0_374, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
7.08/1.45	thf(c_0_375, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
7.08/1.45	thf(c_0_376, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
7.08/1.45	thf(c_0_377, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
7.08/1.45	thf(c_0_378, plain, ((exuEu)=(![X1:$i > $o]:(((?[X1029:$i]:((((X1 @ X1029))&![X1030:$i]:((((X1 @ X1030))=>((X1029)=(X1030)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_314, c_0_302])).
7.08/1.45	thf(c_0_379, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X1023:$i]:((((X1 @ X1023))&![X1024:$i]:((((X1 @ X1024))=>((X1023)=(X1024)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_315, c_0_302])).
7.08/1.45	thf(c_0_380, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X1021:$i]:((((X1 @ X1021))&![X1022:$i]:((((X1 @ X1022))=>((X1021)=(X1022))))))))))), inference(apply_def,[status(thm)],[c_0_316, c_0_302])).
7.08/1.45	thf(c_0_381, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X1019:$i]:((((X1 @ X1019))&![X1020:$i]:((((X1 @ X1020))=>((X1019)=(X1020)))))))))))), inference(apply_def,[status(thm)],[c_0_317, c_0_302])).
7.08/1.45	thf(c_0_382, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_305])).
7.08/1.45	thf(c_0_383, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_305])).
7.08/1.45	thf(c_0_384, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
7.08/1.45	thf(c_0_385, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
7.08/1.45	thf(c_0_386, plain, ((descrp)=(![X1:$i > $o]:(((?[X1009:$i]:((((X1 @ X1009))&![X1010:$i]:((((X1 @ X1010))=>((X1009)=(X1010)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_318, c_0_302])).
7.08/1.45	thf(c_0_387, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X1007:$i]:((((X6 @ X2 @ X1007))&![X1008:$i]:((((X6 @ X2 @ X1008))=>((X1007)=(X1008)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_319, c_0_302])).
7.08/1.45	thf(c_0_388, plain, ((epred1_0)<=>![X1993:$i]:(?[X1994:$i]:((((![X1995:$i]:(((in @ X1995 @ X1994)=>![X1996:$i]:(((in @ X1996 @ X1995)=>(in @ X1996 @ X1993)))))&![X1997:$i, X1998:$i]:((((in @ X1997 @ X1993)&(in @ X1998 @ X1993))=>(![X1999:$i]:(((in @ X1999 @ X1994)=>((in @ X1997 @ X1999)<=>(in @ X1998 @ X1999))))=>((X1997)=(X1998))))))&![X2000:$i, X2001:$i]:((((in @ X2000 @ X1994)&(in @ X2001 @ X1994))=>(![X2002:$i]:(((in @ X2002 @ X2000)=>(in @ X2002 @ X2001)))|![X2003:$i]:(((in @ X2003 @ X2001)=>(in @ X2003 @ X2000)))))))&![X2004:$i]:(((![X2005:$i]:(((in @ X2005 @ X2004)=>(in @ X2005 @ X1993)))&?[X2006:$i]:((in @ X2006 @ X2004)))=>?[X2007:$i, X2008:$i]:(((((in @ X2007 @ X1994)&(in @ X2008 @ X2004))&~(?[X2009:$i]:(((in @ X2009 @ X2007)&(in @ X2009 @ X2004)))))&![X2010:$i]:(((in @ X2010 @ X1994)=>(![X2011:$i]:(((in @ X2011 @ X2010)=>(in @ X2011 @ X2007)))|(in @ X2008 @ X2010)))))))))))), introduced(definition)).
7.08/1.45	thf(c_0_389, negated_conjecture, ~((![X1036:$i, X1037:$i]:((![X1038:$i]:(((in @ X1038 @ X1036)<=>(in @ X1038 @ X1037)))=>((X1036)=(X1037))))=>(![X2012:$i]:(~(in @ X2012 @ emptyset))=>(![X1039:$i, X1040:$i, X1041:$i]:(((in @ X1041 @ (setadjoin @ X1039 @ X1040))<=>(((X1041)=(X1039))|(in @ X1041 @ X1040))))=>(![X1042:$i, X1043:$i]:(((in @ X1043 @ (powerset @ X1042))<=>![X1044:$i]:(((in @ X1044 @ X1043)=>(in @ X1044 @ X1042)))))=>(![X1045:$i, X1046:$i]:(((in @ X1046 @ (setunion @ X1045))<=>?[X1047:$i]:(((in @ X1046 @ X1047)&(in @ X1047 @ X1045)))))=>((in @ emptyset @ omega)=>(![X1048:$i]:(((in @ X1048 @ omega)=>(in @ (setadjoin @ X1048 @ X1048) @ omega)))=>(![X1049:$i]:((((in @ emptyset @ X1049)&![X1050:$i]:((((in @ X1050 @ omega)&(in @ X1050 @ X1049))=>(in @ (setadjoin @ X1050 @ X1050) @ X1049))))=>![X1051:$i]:(((in @ X1051 @ omega)=>(in @ X1051 @ X1049)))))=>(![X1052:$i > $i > $o, X1053:$i]:((![X1054:$i]:(((in @ X1054 @ X1053)=>?[X1055:$i]:(((X1052 @ X1054 @ X1055)&![X1056:$i]:(((X1052 @ X1054 @ X1056)=>((X1055)=(X1056))))))))=>?[X1057:$i]:(![X1058:$i]:(((in @ X1058 @ X1057)<=>?[X1059:$i]:(((in @ X1059 @ X1053)&(X1052 @ X1059 @ X1058))))))))=>(![X1060:$i]:((?[X1061:$i]:((in @ X1061 @ X1060))=>?[X1062:$i]:(((in @ X1062 @ X1060)&~(?[X1063:$i]:(((in @ X1063 @ X1062)&(in @ X1063 @ X1060))))))))=>((epred1_0)=>(![X1064:$i > $o]:((?[X1065:$i]:(((X1064 @ X1065)&![X1066:$i]:(((X1064 @ X1066)=>((X1065)=(X1066))))))=>(X1064 @ (descr @ (^[Z0/* 17 */:$i]:(X1064 @ Z0))))))=>(![X1990:$i, X1991:$i > $o, X1992:$i]:(((in @ X1992 @ X1990)=>((X1991 @ X1992)=>(in @ X1992 @ (dsetconstr @ X1990 @ X1991)))))=>(![X1067:$i, X1068:$i > $o, X1069:$i]:(((in @ X1069 @ (dsetconstr @ X1067 @ X1068))=>(in @ X1069 @ X1067)))=>(![X1987:$i, X1988:$i > $o, X1989:$i]:(((in @ X1989 @ (dsetconstr @ X1987 @ X1988))=>(X1988 @ X1989)))=>(![X1982:$i > $o]:((?[X1983:$i]:(((X1982 @ X1983)&![X1984:$i]:(((X1982 @ X1984)=>((X1983)=(X1984))))))=>?[X1985:$i]:(((X1982 @ X1985)&![X1986:$i]:(((X1982 @ X1986)=>((X1985)=(X1986))))))))=>(![X1070:$o, X1071:$i]:(((in @ X1071 @ (prop2set @ ((X1070))))=>(X1070)))=>(![X1980:$i]:(((in @ X1980 @ emptyset)=>![X1981:$o]:((X1981))))=>(![X1072:$i]:(((in @ X1072 @ emptyset)=>~($true)))=>(![X1073:$i]:(~(in @ X1073 @ emptyset))=>(![X1976:$i > $o]:((?[X1977:$i]:(((X1976 @ X1977)&![X1978:$i]:(((X1976 @ X1978)=>((X1977)=(X1978))))))=>?[X1979:$i]:((X1976 @ X1979))))=>(![X1972:$i, X1973:$i]:((![X1974:$i]:(((in @ X1974 @ X1972)=>(in @ X1974 @ X1973)))=>(![X1975:$i]:(((in @ X1975 @ X1973)=>(in @ X1975 @ X1972)))=>((X1972)=(X1973)))))=>(![X1074:$i]:((![X1075:$i]:(~(in @ X1075 @ X1074))=>((X1074)=(emptyset))))=>(![X1970:$i]:((![X1971:$i]:(~(in @ X1971 @ X1970))=>((X1970)=(emptyset))))=>(![X1076:$i, X1077:$i > $o, X1078:$i]:(((in @ X1078 @ X1076)=>((in @ X1078 @ (dsetconstr @ X1076 @ X1077))<=>(X1077 @ X1078))))=>(![X1079:$i]:((((X1079)!=(emptyset))=>?[X1080:$i]:((in @ X1080 @ X1079))))=>(![X1967:$i, X1968:$i > $o, X1969:$i]:(((in @ X1969 @ X1967)=>((X1968 @ X1969)=>((dsetconstr @ X1967 @ X1968)!=(emptyset)))))=>(![X1081:$i]:((?[X1082:$i]:((in @ X1082 @ X1081))=>((X1081)!=(emptyset))))=>(![X1965:$i, X1966:$i]:((in @ X1965 @ (setadjoin @ X1965 @ X1966)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1962:$i, X1963:$i, X1964:$i]:(((in @ X1964 @ X1963)=>(in @ X1964 @ (setadjoin @ X1962 @ X1963))))=>(![X1083:$i, X1084:$i, X1085:$i]:(((in @ X1085 @ (setadjoin @ X1083 @ X1084))=>![X1086:$o]:(((((X1085)=(X1083))=>(X1086))=>(((in @ X1085 @ X1084)=>(X1086))=>(X1086))))))=>(![X1959:$i, X1960:$i, X1961:$i]:(((in @ X1961 @ (setadjoin @ X1959 @ X1960))=>(((X1961)=(X1959))|(in @ X1961 @ X1960))))=>(![X1958:$i]:(((dsetconstr @ X1958 @ (^[Z0/* 1 */:$i]:($true)))=(X1958)))=>(![X1087:$i, X1088:$i]:((![X1089:$i]:(((in @ X1089 @ X1088)=>(in @ X1089 @ X1087)))=>(in @ X1088 @ (powerset @ X1087))))=>(![X1090:$i]:((in @ emptyset @ (powerset @ X1090)))=>(![X1091:$i]:((in @ emptyset @ (powerset @ X1091)))=>(![X1955:$i, X1956:$i, X1957:$i]:(((in @ X1956 @ (powerset @ X1955))=>((in @ X1957 @ X1956)=>(in @ X1957 @ X1955))))=>(![X1092:$i, X1093:$i, X1094:$i]:(((in @ X1093 @ X1094)=>((in @ X1094 @ X1092)=>(in @ X1093 @ (setunion @ X1092)))))=>(![X1095:$i, X1096:$i]:(((in @ X1096 @ (setunion @ X1095))=>![X1097:$o]:((![X1098:$i]:(((in @ X1096 @ X1098)=>((in @ X1098 @ X1095)=>(X1097))))=>(X1097)))))=>(![X1953:$i, X1954:$i]:(((in @ X1954 @ X1953)=>(in @ X1954 @ (powerset @ (setunion @ X1953)))))=>(![X1948:$i > $o]:((?[X1949:$i]:(((X1948 @ X1949)&![X1950:$i]:(((X1948 @ X1950)=>((X1949)=(X1950))))))=>?[X1951:$i]:(![X1952:$i]:(((X1948 @ X1952)<=>((X1952)=(X1951)))))))=>(![X1946:$i]:((((X1946)!=(emptyset))=>?[X1947:$i]:(((in @ X1947 @ X1946)&$true))))=>(![X1944:$i, X1945:$i]:(((in @ X1944 @ (setadjoin @ X1945 @ emptyset))=>((X1944)=(X1945))))=>(![X1099:$i, X1100:$i]:((((X1099)!=(X1100))=>~(in @ X1100 @ (setadjoin @ X1099 @ emptyset))))=>(![X1942:$i, X1943:$i]:((((X1942)=(X1943))=>(in @ X1942 @ (setadjoin @ X1943 @ emptyset))))=>(![X1940:$i, X1941:$i]:(((in @ X1940 @ (setadjoin @ X1941 @ emptyset))=>(in @ X1941 @ (setadjoin @ X1940 @ emptyset))))=>(![X1101:$i, X1102:$i, X1103:$i]:(((in @ X1103 @ (setadjoin @ X1101 @ (setadjoin @ X1102 @ emptyset)))=>(((X1103)=(X1101))|((X1103)=(X1102)))))=>(![X1104:$i, X1105:$i]:((in @ X1104 @ (setadjoin @ X1104 @ (setadjoin @ X1105 @ emptyset))))=>(![X1938:$i, X1939:$i]:((in @ X1939 @ (setadjoin @ X1938 @ (setadjoin @ X1939 @ emptyset))))=>(![X1935:$i, X1936:$i > $o]:((?[X1937:$i]:(((in @ X1937 @ X1935)&(X1936 @ X1937)))=>(((dsetconstr @ X1935 @ X1936)=(emptyset))=>~($true))))=>(![X1106:$i > $o, X1107:$i]:(((in @ X1107 @ emptyset)=>(X1106 @ X1107)))=>(![X1931:$i, X1932:$i > $o]:((~(![X1933:$i]:(((in @ X1933 @ X1931)=>(X1932 @ X1933))))=>?[X1934:$i]:(((in @ X1934 @ X1931)&~((X1932 @ X1934))))))=>(![X1108:$i, X1109:$i > $o]:((![X1110:$i]:(((in @ X1110 @ X1108)=>~((X1109 @ X1110))))=>~(?[X1111:$i]:(((in @ X1111 @ X1108)&(X1109 @ X1111))))))=>(![X1112:$i, X1113:$i > $o]:((~(?[X1114:$i]:(((in @ X1114 @ X1112)&(X1113 @ X1114))))=>![X1115:$i]:(((in @ X1115 @ X1112)=>~((X1113 @ X1115))))))=>(![X1116:$i, X1117:$i > $o]:((?[X1118:$i]:(((in @ X1118 @ X1116)&~((X1117 @ X1118))))=>~(![X1119:$i]:(((in @ X1119 @ X1116)=>(X1117 @ X1119))))))=>(![X1930:$o]:(((X1930)=>(in @ emptyset @ (prop2set @ ((X1930))))))=>((prop2set2propI)=>(![X1120:$i, X1121:$i > $o]:((~(?[X1122:$i]:(((in @ X1122 @ X1120)&(X1121 @ X1122))))=>![X1123:$i]:(((in @ X1123 @ X1120)=>~((X1121 @ X1123))))))=>(![X1926:$i, X1927:$i > $o]:((~(![X1928:$i]:(((in @ X1928 @ X1926)=>(X1927 @ X1928))))=>?[X1929:$i]:(((in @ X1929 @ X1926)&~((X1927 @ X1929))))))=>(![X1921:$i > $o]:((?[X1922:$i]:(((X1921 @ X1922)&![X1923:$i]:(((X1921 @ X1923)=>((X1922)=(X1923))))))=>?[X1924:$i]:(((X1921 @ X1924)&![X1925:$i]:(((X1921 @ X1925)=>((X1924)=(X1925))))))))=>(![X1124:$i > $o]:((?[X1125:$i]:((X1124 @ X1125))=>(![X1126:$i, X1127:$i]:(((X1124 @ X1126)=>((X1124 @ X1127)=>((X1126)=(X1127)))))=>?[X1128:$i]:(((X1124 @ X1128)&![X1129:$i]:(((X1124 @ X1129)=>((X1128)=(X1129)))))))))=>(![X1130:$i > $o]:((?[X1131:$i]:(![X1132:$i]:(((X1130 @ X1132)<=>((X1132)=(X1131)))))=>?[X1133:$i]:(((X1130 @ X1133)&![X1134:$i]:(((X1130 @ X1134)=>((X1133)=(X1134))))))))=>(![X1917:$i, X1918:$i]:((((X1917)=(X1918))=>![X1919:$i, X1920:$i]:((((X1919)=(X1920))=>((in @ X1919 @ X1917)=>(in @ X1920 @ X1918))))))=>(![X1135:$i, X1136:$i]:((((X1135)=(X1136))=>![X1137:$i, X1138:$i]:((((X1137)=(X1138))=>((in @ X1137 @ X1135)<=>(in @ X1138 @ X1136))))))=>(![X1139:$i > $o]:((?[X1140:$i]:(((X1139 @ X1140)&![X1141:$i]:(((X1139 @ X1141)=>((X1140)=(X1141))))))=>![X1142:$i, X1143:$i]:(((X1139 @ X1142)=>((X1139 @ X1143)=>((X1142)=(X1143)))))))=>(![X1909:$i > $o, X1910:$i > $o]:((![X1911:$i, X1912:$i]:((((X1911)=(X1912))=>((X1909 @ X1911)<=>(X1910 @ X1912))))=>(?[X1913:$i]:(((X1909 @ X1913)&![X1914:$i]:(((X1909 @ X1914)=>((X1913)=(X1914))))))<=>?[X1915:$i]:(((X1910 @ X1915)&![X1916:$i]:(((X1910 @ X1916)=>((X1915)=(X1916)))))))))=>(((emptyset)=(emptyset))=>(![X1144:$i, X1145:$i]:((((X1144)=(X1145))=>![X1146:$i, X1147:$i]:((((X1146)=(X1147))=>((setadjoin @ X1144 @ X1146)=(setadjoin @ X1145 @ X1147))))))=>(![X1907:$i, X1908:$i]:((((X1907)=(X1908))=>((powerset @ X1907)=(powerset @ X1908))))=>(![X1905:$i, X1906:$i]:((((X1905)=(X1906))=>((setunion @ X1905)=(setunion @ X1906))))=>(((omega)=(omega))=>(![X1148:$i > $o]:((?[X1149:$i]:(((X1148 @ X1149)&![X1150:$i]:(((X1148 @ X1150)=>((X1149)=(X1150))))))=>![X1151:$i, X1152:$i]:(((X1148 @ X1151)=>((X1148 @ X1152)=>((X1151)=(X1152)))))))=>(![X1897:$i > $o, X1898:$i > $o]:((![X1899:$i, X1900:$i]:((((X1899)=(X1900))=>((X1897 @ X1899)<=>(X1898 @ X1900))))=>(?[X1901:$i]:(((X1897 @ X1901)&![X1902:$i]:(((X1897 @ X1902)=>((X1901)=(X1902))))))=>(?[X1903:$i]:(((X1898 @ X1903)&![X1904:$i]:(((X1898 @ X1904)=>((X1903)=(X1904))))))=>((descr @ X1897)=(descr @ X1898))))))=>(![X1153:$i, X1154:$i]:((((X1153)=(X1154))=>![X1155:$i > $o, X1156:$i > $o]:((![X1157:$i]:(((in @ X1157 @ X1153)=>![X1158:$i]:(((in @ X1158 @ X1154)=>(((X1157)=(X1158))=>((X1155 @ X1157)<=>(X1156 @ X1158)))))))=>((dsetconstr @ X1153 @ X1155)=(dsetconstr @ X1154 @ X1156))))))=>(![X1159:$i, X1160:$i]:((![X1161:$i]:(((in @ X1161 @ X1159)=>(in @ X1161 @ X1160)))=>(subset @ X1159 @ X1160)))=>(![X1895:$i, X1896:$i]:((((X1895)=(X1896))=>(subset @ X1896 @ X1895)))=>(![X1893:$i, X1894:$i]:((((X1893)=(X1894))=>(subset @ X1893 @ X1894)))=>(![X1162:$i, X1163:$i]:((![X1164:$i]:(((in @ X1164 @ X1162)=>(in @ X1164 @ X1163)))=>(subset @ X1162 @ X1163)))=>(![X1165:$i]:((subset @ emptyset @ X1165))=>(![X1166:$i, X1167:$i, X1168:$i]:(((subset @ X1166 @ X1167)=>((in @ X1168 @ X1166)=>(in @ X1168 @ X1167))))=>(![X1890:$i, X1891:$i, X1892:$i]:(((subset @ X1890 @ X1891)=>(~(in @ X1892 @ X1891)=>~(in @ X1892 @ X1890))))=>(![X1169:$i, X1170:$i, X1171:$i]:(((in @ X1171 @ X1169)=>(~(in @ X1171 @ X1170)=>~(subset @ X1169 @ X1170))))=>(![X1888:$i, X1889:$i]:((~(subset @ X1888 @ X1889)=>((X1888)!=(X1889))))=>(![X1172:$i, X1173:$i, X1174:$i]:(((in @ X1174 @ X1172)=>(~(in @ X1174 @ X1173)=>((X1172)!=(X1173)))))=>(![X1887:$i]:((subset @ X1887 @ X1887))=>(![X1884:$i, X1885:$i, X1886:$i]:(((subset @ X1884 @ X1885)=>((subset @ X1885 @ X1886)=>(subset @ X1884 @ X1886))))=>(![X1175:$i, X1176:$i]:((subset @ X1176 @ (setadjoin @ X1175 @ X1176)))=>(![X1881:$i, X1882:$i, X1883:$i]:(((subset @ X1881 @ X1883)=>(subset @ X1881 @ (setadjoin @ X1882 @ X1883))))=>(![X1177:$i, X1178:$i]:(((subset @ X1177 @ X1178)=>(in @ X1177 @ (powerset @ X1178))))=>(![X1879:$i, X1880:$i]:(((subset @ X1879 @ X1880)=>((subset @ X1880 @ X1879)=>((X1879)=(X1880)))))=>(![X1179:$i]:(((subset @ X1179 @ emptyset)=>((X1179)=(emptyset))))=>(![X1180:$i, X1181:$i]:(((subset @ X1181 @ X1180)=>(in @ X1181 @ (powerset @ X1180))))=>(![X1877:$i, X1878:$i]:(((in @ X1878 @ (powerset @ X1877))=>(subset @ X1878 @ X1877)))=>(![X1876:$i]:((in @ X1876 @ (powerset @ X1876)))=>(![X1182:$i, X1183:$i]:(((subset @ X1182 @ X1183)=>(subset @ (powerset @ X1182) @ (powerset @ X1183))))=>(![X1184:$i, X1185:$i > $o]:((in @ (dsetconstr @ X1184 @ X1185) @ (powerset @ X1184)))=>(![X1186:$i, X1187:$i > $o]:((subset @ (dsetconstr @ X1186 @ X1187) @ X1186))=>(![X1188:$i, X1189:$i, X1190:$i]:(((in @ X1190 @ X1188)=>(in @ X1190 @ (binunion @ X1188 @ X1189))))=>(![X1191:$i, X1192:$i]:((in @ X1192 @ (setadjoin @ X1191 @ (setadjoin @ X1192 @ emptyset))))=>(![X1873:$i, X1874:$i, X1875:$i]:(((in @ X1875 @ X1874)=>(in @ X1875 @ (binunion @ X1873 @ X1874))))=>(![X1193:$i, X1194:$i, X1195:$i, X1196:$o]:(((in @ X1195 @ (binunion @ X1193 @ X1194))=>(((in @ X1195 @ X1193)=>(X1196))=>(((in @ X1195 @ X1194)=>(X1196))=>(X1196)))))=>(![X1870:$i, X1871:$i, X1872:$i]:(((in @ X1872 @ (binunion @ X1870 @ X1871))=>((in @ X1872 @ X1870)|(in @ X1872 @ X1871))))=>(![X1197:$i, X1198:$i]:((subset @ X1197 @ (binunion @ X1197 @ X1198)))=>(![X1199:$i, X1200:$i]:((subset @ X1200 @ (binunion @ X1199 @ X1200)))=>(![X1867:$i, X1868:$i, X1869:$i]:(((in @ X1869 @ X1867)=>((in @ X1869 @ X1868)=>(in @ X1869 @ (binintersect @ X1867 @ X1868)))))=>(![X1201:$i, X1202:$i, X1203:$i]:(((subset @ X1203 @ X1201)=>((subset @ X1203 @ X1202)=>(subset @ X1203 @ (binintersect @ X1201 @ X1202)))))=>(![X1204:$i, X1205:$i, X1206:$i]:(((in @ X1206 @ (binintersect @ X1204 @ X1205))=>(in @ X1206 @ X1204)))=>(![X1865:$i, X1866:$i]:((subset @ (binintersect @ X1865 @ X1866) @ X1865))=>(![X1863:$i, X1864:$i]:(((subset @ X1863 @ X1864)=>((binintersect @ X1863 @ X1864)=(X1863))))=>(![X1207:$i, X1208:$i]:((((binintersect @ X1207 @ X1208)=(X1208))=>(subset @ X1208 @ X1207)))=>(![X1860:$i, X1861:$i, X1862:$i]:(((in @ X1862 @ (binintersect @ X1860 @ X1861))=>(in @ X1862 @ X1861)))=>(![X1857:$i, X1858:$i]:((~(?[X1859:$i]:(((in @ X1859 @ X1857)&(in @ X1859 @ X1858))))=>((binintersect @ X1857 @ X1858)=(emptyset))))=>(![X1209:$i, X1210:$i]:((subset @ (binintersect @ X1209 @ X1210) @ X1210))=>(![X1855:$i, X1856:$i]:(((subset @ X1856 @ X1855)=>((binintersect @ X1855 @ X1856)=(X1856))))=>(![X1211:$i, X1212:$i]:((((binintersect @ X1211 @ X1212)=(X1211))=>(subset @ X1211 @ X1212)))=>(![X1213:$i, X1214:$i, X1215:$i]:(((binintersect @ X1213 @ (binunion @ X1214 @ X1215))=(binunion @ (binintersect @ X1213 @ X1214) @ (binintersect @ X1213 @ X1215))))=>(![X1852:$i, X1853:$i, X1854:$i]:(((in @ X1854 @ X1852)=>(~(in @ X1854 @ X1853)=>(in @ X1854 @ (setminus @ X1852 @ X1853)))))=>(![X1849:$i, X1850:$i, X1851:$i]:(((in @ X1851 @ (setminus @ X1849 @ X1850))=>(in @ X1851 @ X1849)))=>(![X1216:$i, X1217:$i, X1218:$i]:(((in @ X1218 @ (setminus @ X1216 @ X1217))=>~(in @ X1218 @ X1217)))=>(![X1219:$i, X1220:$i]:(((subset @ X1219 @ X1220)=>((setminus @ X1219 @ X1220)=(emptyset))))=>(![X1846:$i, X1847:$i, X1848:$i]:((~(in @ X1848 @ (setminus @ X1846 @ X1847))=>((in @ X1848 @ X1846)=>(in @ X1848 @ X1847))))=>(![X1843:$i, X1844:$i, X1845:$i]:((~(in @ X1845 @ (setminus @ X1843 @ X1844))=>(~(in @ X1845 @ X1844)=>~(in @ X1845 @ X1843))))=>(![X1840:$i, X1841:$i, X1842:$i]:((~(in @ X1842 @ X1840)=>~(in @ X1842 @ (setminus @ X1840 @ X1841))))=>(![X1837:$i, X1838:$i, X1839:$i]:(((in @ X1839 @ X1838)=>~(in @ X1839 @ (setminus @ X1837 @ X1838))))=>(![X1835:$i, X1836:$i]:((subset @ (setminus @ X1835 @ X1836) @ X1835))=>(![X1221:$i, X1222:$i]:((((setminus @ X1221 @ X1222)=(emptyset))=>(subset @ X1221 @ X1222)))=>(![X1223:$i, X1224:$i, X1225:$i]:(((in @ X1225 @ (symdiff @ X1223 @ X1224))=>![X1226:$o]:((((in @ X1225 @ X1223)=>(~(in @ X1225 @ X1224)=>(X1226)))=>((~(in @ X1225 @ X1223)=>((in @ X1225 @ X1224)=>(X1226)))=>(X1226))))))=>(![X1832:$i, X1833:$i, X1834:$i]:(((in @ X1834 @ X1832)=>(~(in @ X1834 @ X1833)=>(in @ X1834 @ (symdiff @ X1832 @ X1833)))))=>(![X1227:$i, X1228:$i, X1229:$i]:((~(in @ X1229 @ X1227)=>((in @ X1229 @ X1228)=>(in @ X1229 @ (symdiff @ X1227 @ X1228)))))=>(![X1230:$i, X1231:$i, X1232:$i]:(((in @ X1232 @ X1230)=>((in @ X1232 @ X1231)=>~(in @ X1232 @ (symdiff @ X1230 @ 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omega0Ax]), setukpairinjL1]), c_0_334]), kfstpairEq]), setukpairinjL]), setukpairinjR12]), binunionT_lem]), powersetT_lem]), setukpairinjR2]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), c_0_335]), symdiffIneg1]), c_0_336]), c_0_337]), c_0_338]), c_0_339]), c_0_340]), c_0_341]), funcinfuncset]), c_0_342]), c_0_343]), c_0_344]), c_0_345]), funcGraphProp1]), funcGraphProp2]), funcextLem]), c_0_346]), ap2apEq1]), ap2apEq2]), c_0_347]), c_0_348]), c_0_349]), theeq]), iffalse]), c_0_350]), funcext2]), funcext]), c_0_351]), funcGraphProp4]), funcGraphProp3]), c_0_352]), c_0_353]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), contrasubsetT3]), doubleComplementI1]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), binunionTEcontra]), demorgan2a2]), demorgan1]), woz13rule3]), woz1_3]), woz1_4]), c_0_354]), c_0_355]), c_0_356]), c_0_312]), c_0_357]), c_0_358]), c_0_359]), c_0_360]), c_0_361]), c_0_362]), c_0_363]), woz1_5]), woz1_2]), woz1_1]), woz13rule4]), woz13rule2]), woz13rule1]), woz13rule0]), demorgan2]), demorgan2b]), demorgan2b2]), demorgan2a]), demorgan1b]), demorgan1a]), complementUnionInPowersetComplement]), demorgan2a1]), binunionTE]), inComplementUnionImpInComplement1]), inComplementUnionImpNotIn1]), inIntersectImpInUnion2]), inIntersectImpInUnion]), contraSubsetComplement]), complementInPowersetComplementIntersect]), complementSubsetComplementIntersect]), doubleComplementSub2]), doubleComplementSub1]), doubleComplementE1]), contrasubsetT2]), contrasubsetT1]), contrasubsetT]), binintersectTERcontra]), binintersectTELcontra]), complementTE1]), complementT_lem]), setminusT_lem]), binintersectT_lem]), iftrueorfalse]), iftrue]), ifp]), c_0_364]), c_0_365]), c_0_366]), c_0_367]), c_0_368]), c_0_369]), ap2p]), infuncsetfunc]), app]), c_0_370]), c_0_371]), cartprodpairsurjEq]), cartprodsndpairEq]), c_0_372]), setukpairinjR]), upairequniteq]), setukpairinjR11]), setukpairinjL2]), cartprodfstin]), theprop]), singletonsuniq]), c_0_373]), c_0_374]), setunionsingleton1]), cartprodmempair]), ubforcartprodlem1]), singletoninpowunion]), singletonsubset]), secondinupair]), symdiffIneg2]), symdiffI1]), setminusLsub]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusERneg]), setminusEL]), setminusI]), binintersectSubset4]), disjointsetsI1]), binintersectER]), setukpairIL]), setminusSubset2]), setminusER]), bs114d]), binintersectSubset1]), binintersectRsub]), binintersectSubset3]), binintersectEL]), binintersectSubset5]), binunionRsub]), binunionLsub]), binunionEcases]), upairset2IR]), binunionIL]), c_0_375]), c_0_376]), powersetsubset]), powersetI1]), subsetemptysetimpeq]), subset2powerset]), setadjoinSub]), notequalI2]), notsubsetI]), subsetE]), emptysetsubset]), subsetI2]), subsetI1]), c_0_377]), c_0_378]), omega__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_379]), in__Cong]), c_0_380]), c_0_381]), notdexE]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), vacuousDall]), upairsetIL]), upairsetE]), notinsingleton]), setunionE]), setunionI]), emptyInPowerset]), emptyinPowerset]), powersetI]), setadjoinE]), emptyinunitempty]), c_0_382]), c_0_383]), c_0_384]), emptyI]), notinemptyset]), emptysetimpfalse]), prop2setE]), c_0_385]), c_0_386]), foundationAx]), c_0_387]), omegaIndAx]), omegaSAx]), setunionAx]), powersetAx]), setadjoinAx]), setextAx]), c_0_311])])]), c_0_388])).
7.08/1.45	thf(c_0_390, negated_conjecture, ![X2013:$i, X2014:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2026:$i, X2027:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2035:$i, X2036:$i > $i > $o, X2037:$i, X2039:$i, X2042:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2049:$i, X2050:$i > $o, X2051:$i, X2053:$i, X2054:$i > $o, X2055:$i, X2056:$i, X2057:$i > $o, X2058:$i, X2059:$i, X2060:$i > $o, X2061:$i, X2062:$i > $o, X2063:$i, X2066:$i, X2067:$o, X2068:$i, X2069:$i, X2070:$o, X2071:$i, X2072:$i, X2073:$i > $o, X2074:$i, X2077:$i, X2078:$i, X2081:$i, X2083:$i, X2085:$i, X2086:$i > $o, X2087:$i, X2088:$i, X2090:$i, X2091:$i > $o, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$o, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$o, X2123:$i, X2124:$i, X2125:$i > $o, X2126:$i, X2129:$i, X2130:$i, X2131:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i > $o, X2150:$i, X2151:$i > $o, X2152:$i, X2153:$i, X2154:$i > $o, X2155:$i, X2157:$i, X2158:$i > $o, X2160:$i, X2161:$i, X2162:$i > $o, X2164:$i, X2165:$i, X2166:$i > $o, X2167:$i, X2169:$o, X2170:$i, X2171:$i > $o, X2173:$i, X2174:$i, X2175:$i > $o, X2176:$i, X2178:$i > $o, X2179:$i, X2182:$i, X2183:$i > $o, X2184:$i, X2188:$i, X2189:$i > $o, X2190:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i > $o, X2203:$i, X2205:$i, X2206:$i, X2207:$i > $o, X2208:$i > $o, X2211:$i, X2214:$i, X2215:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i > $o, X2228:$i, X2230:$i, X2231:$i, X2232:$i > $o, X2233:$i > $o, X2236:$i, X2238:$i, X2240:$i, X2241:$i, X2242:$i > $o, X2243:$i > $o, X2246:$i, X2247:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i, X2292:$i, X2293:$i > $o, X2294:$i, X2295:$i > $o, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$o, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2327:$i, X2328:$i, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$i, X2364:$i, X2365:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$i, X2372:$i, X2373:$i, X2374:$i, X2375:$o, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2383:$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, X2422:$i, X2423:$i, X2424:$i, X2425:$i, X2426:$i, X2427:$i, X2428:$i, X2429:$i, X2430:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i, X2447:$i > $o, X2450:$i, X2451:$i, X2452:$i > $o, X2454:$i, X2455:$i > $o, X2456:$i, X2458:$i, X2459:$i > $o, X2462:$i, X2463:$i, X2464:$i, X2465:$i, X2466:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2471:$i, X2472:$i, X2473:$i, X2474:$i, X2475:$i, X2476:$i, X2477:$i, X2478:$i, X2479:$i, X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$i, X2486:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2493:$i, X2494:$i, X2495:$i, X2496:$i, X2497:$i, X2498:$i, X2499:$i, X2500:$i, X2501:$i, X2502:$i, X2503:$i, X2504:$i, X2505:$i, X2506:$i, X2507:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i > $i > $o, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i > $i > $o, X2540:$i, X2541:$i, X2542:$i > $i > $o, X2543:$i, X2544:$i, X2545:$i > $i > $o, X2546:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i > $i > $o, X2551:$i, X2552:$i, X2553:$i, X2554:$i, X2555:$i > $i > $o, X2556:$i, X2557:$i, X2558:$i, X2559:$i, X2560:$i > $i > $o, X2561:$i, X2562:$i, X2563:$i, X2564:$i, X2565:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2570:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i, X2576:$i, X2577:$i, X2578:$i, X2579:$i, X2580:$i, X2581:$i, X2582:$i, X2583:$i, X2584:$i, X2585:$i, X2586:$i, X2587:$i > $i, X2589:$i, X2590:$i, X2591:$i > $i, X2593:$i, X2594:$i, X2595:$i > $i, X2597:$i, X2598:$i, X2599:$i, X2600:$i > $o, X2603:$i, X2604:$i, X2605:$i, X2606:$i, X2607:$i > $o, X2610:$i, X2611:$i, X2612:$i > $o, X2613:$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, X2633:$i, X2634:$i, X2635:$i, X2636:$i, X2637:$i, X2638:$i, X2639:$i, X2640:$i, X2641:$i, X2642:$i, X2643:$i, X2646:$i, X2647:$i, X2648:$i, X2649:$i, X2654:$i, X2655:$i, X2656:$i, X2657:$i, X2659:$i, X2660:$i, X2661:$i, X2662:$i, X2664:$i, X2665:$i, X2666:$i, X2667:$i, X2668:$i, X2669:$i, X2670:$i, X2671:$i, X2672:$i, X2673:$i, X2674:$i > $i, X2676:$i, X2677:$i, X2678:$i, X2679:$i, X2680:$i, X2681:$i, X2682:$i > $i, X2684:$i, X2685:$i, X2686:$i > $i, X2688:$i, X2689:$i, X2690:$i, X2691:$i, X2692:$i, X2693:$o, X2694:$i, X2695:$i, X2696:$i, X2697:$o, X2698:$i, X2699:$i, X2700:$i, X2701:$o, X2702:$i, X2703:$i, X2704:$i, X2705:$o, X2706:$i, X2707:$i, X2708:$i, X2709:$o, X2710:$i, X2711:$i, X2712:$i, X2713:$o, X2714:$i, X2715:$i, X2716:$i, X2717:$i, X2718:$i, X2719:$o, X2720:$i, X2721:$i, X2722:$i, X2723:$o, X2724:$i, X2725:$i, X2726:$i, X2727:$o, X2728:$i, X2729:$i, X2730:$i, X2731:$i, X2732:$i, X2733:$i, X2734:$i, X2735:$i, X2736:$i, X2737:$i, X2738:$i, X2739:$i, X2740:$i, X2741:$i, X2742:$i, X2743:$i, X2744:$i, X2745:$i, X2748:$i, X2749:$i, X2750:$i, X2752:$i, X2753:$i, X2754:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2760:$i, X2761:$i, X2762:$i, X2763:$i, X2764:$i, X2765:$i, X2766:$i, X2767:$i, X2768:$i, X2769:$i, X2770:$i, X2771:$i, X2772:$i, X2773:$i, X2774:$i, X2775:$i, X2776:$i, X2777:$i, X2778:$i, X2779:$i, X2780:$i, X2781:$i, X2782:$i, X2783:$i, X2784:$i, X2785:$i, X2786:$i, X2787:$i, X2788:$i, X2789:$i, X2790:$i, X2791:$i, X2792:$i, X2793:$i, X2794:$i, X2795:$i, X2796:$i, X2797:$i, X2798:$i, X2799:$i, X2800:$i, X2801:$i, X2802:$i, X2803:$i, X2804:$i, X2805:$i, X2806:$i, X2807:$i, X2808:$i, X2809:$i, X2810:$i, X2811:$i, X2812:$i, X2813:$i, X2814:$i, X2815:$i, X2816:$i, X2817:$i, X2818:$i, X2819:$i, X2820:$i, X2821:$i, X2822:$i, X2823:$i, X2824:$i, X2825:$i, X2826:$i, X2827:$i, X2828:$i, X2829:$i, X2830:$i, X2831:$i, X2832:$i, X2833:$i, X2834:$i, X2835:$i, X2836:$i, X2837:$i, X2838:$i, X2839:$i, X2840:$i, X2841:$i, X2842:$i, X2843:$i, X2844:$i, X2845:$i, X2846:$i, X2847:$i, X2848:$i, X2849:$i, X2850:$i, X2851:$i, X2852:$i, X2853:$i, X2854:$i, X2855:$i, X2856:$i, X2857:$i, X2858:$i, X2859:$o, X2860:$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:$i, X2874:$i, X2875:$i, X2876:$i, X2877:$i, X2878:$i, X2879:$i, X2880:$i, X2881:$i, X2882:$i, X2883:$i, X2884:$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 > $o, X2946:$i, X2947:$i, X2948:$i, X2949:$i, X2950:$i > $i > $o, X2951:$i, X2952:$i, X2953:$i > $o, X2956:$i, X2957:$i, X2958:$i, X2959:$i, X2962:$i, X2963:$i, X2964:$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]:((((~(in @ (esk1_2 @ X2013 @ X2014) @ X2013)|~(in @ (esk1_2 @ X2013 @ X2014) @ X2014)|((X2013)=(X2014)))&((in @ (esk1_2 @ X2013 @ X2014) @ X2013)|(in @ (esk1_2 @ X2013 @ X2014) @ X2014)|((X2013)=(X2014))))&(~(in @ X2016 @ emptyset)&(((~(in @ X2019 @ (setadjoin @ X2017 @ X2018))|(((X2019)=(X2017))|(in @ X2019 @ X2018)))&((((X2019)!=(X2017))|(in @ X2019 @ (setadjoin @ X2017 @ X2018)))&(~(in @ X2019 @ X2018)|(in @ X2019 @ (setadjoin @ X2017 @ X2018)))))&(((~(in @ X2021 @ (powerset @ X2020))|(~(in @ X2022 @ X2021)|(in @ X2022 @ X2020)))&(((in @ (esk2_2 @ X2023 @ X2024) @ X2024)|(in @ X2024 @ (powerset @ X2023)))&(~(in @ (esk2_2 @ X2023 @ X2024) @ X2023)|(in @ X2024 @ (powerset @ X2023)))))&(((((in @ X2027 @ (esk3_2 @ X2026 @ X2027))|~(in @ X2027 @ (setunion @ X2026)))&((in @ (esk3_2 @ X2026 @ X2027) @ X2026)|~(in @ X2027 @ (setunion @ X2026))))&(~(in @ X2030 @ X2031)|~(in @ X2031 @ X2029)|(in @ X2030 @ (setunion @ X2029))))&((in @ emptyset @ omega)&((~(in @ X2032 @ omega)|(in @ (setadjoin @ X2032 @ X2032) @ omega))&(((((in @ (esk4_1 @ X2033) @ omega)|~(in @ emptyset @ X2033)|(~(in @ X2035 @ omega)|(in @ X2035 @ X2033)))&((in @ (esk4_1 @ X2033) @ X2033)|~(in @ emptyset @ X2033)|(~(in @ X2035 @ omega)|(in @ X2035 @ X2033))))&(~(in @ (setadjoin @ (esk4_1 @ X2033) @ (esk4_1 @ X2033)) @ X2033)|~(in @ emptyset @ X2033)|(~(in @ X2035 @ omega)|(in @ X2035 @ X2033))))&((((((in @ (esk8_3 @ X2036 @ X2037 @ X2042) @ X2037)|~(in @ X2042 @ (esk7_2 @ X2036 @ X2037))|(in @ (esk5_2 @ X2036 @ X2037) @ X2037))&((X2036 @ (esk8_3 @ X2036 @ X2037 @ X2042) @ X2042)|~(in @ X2042 @ (esk7_2 @ X2036 @ X2037))|(in @ (esk5_2 @ X2036 @ X2037) @ X2037)))&(~(in @ X2045 @ X2037)|~(X2036 @ X2045 @ X2044)|(in @ X2044 @ (esk7_2 @ X2036 @ X2037))|(in @ (esk5_2 @ X2036 @ X2037) @ X2037)))&(((((in @ (esk8_3 @ X2036 @ X2037 @ X2042) @ X2037)|~(in @ X2042 @ (esk7_2 @ X2036 @ X2037))|((X2036 @ (esk5_2 @ 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(binintersect @ X2903 @ X2904))|(in @ X2905 @ X2902))))&((~(in @ X2907 @ (powerset @ X2906))|(~(in @ X2908 @ (powerset @ X2906))|(~(in @ X2909 @ (powerset @ X2906))|(~(subset @ X2907 @ X2909)|(subset @ (binintersect @ X2907 @ X2908) @ X2909)))))&((~(in @ X2911 @ (powerset @ X2910))|(~(in @ X2912 @ (powerset @ X2910))|(~(in @ X2913 @ (powerset @ X2910))|(~(subset @ X2912 @ X2913)|(subset @ (binintersect @ X2911 @ X2912) @ X2913)))))&((~(in @ X2915 @ (powerset @ X2914))|(~(in @ X2916 @ (powerset @ X2914))|(~(in @ X2917 @ (powerset @ X2914))|(~(subset @ X2915 @ X2916)|(~(subset @ X2915 @ X2917)|(subset @ X2915 @ (binintersect @ X2916 @ X2917)))))))&((~(in @ X2919 @ (powerset @ X2918))|(~(in @ X2920 @ (powerset @ X2918))|(~(in @ X2921 @ (powerset @ X2918))|(~(in @ X2922 @ (powerset @ X2918))|(~(subset @ X2919 @ X2921)|(~(subset @ X2920 @ X2922)|(subset @ (binintersect @ X2919 @ X2920) @ (binintersect @ X2921 @ X2922))))))))&((~(in @ X2924 @ (powerset @ X2923))|(~(in @ X2925 @ (powerset @ X2923))|(in @ (setminus @ X2923 @ X2924) @ (powerset @ (setminus @ X2923 @ (binintersect @ X2924 @ X2925))))))&((~(in @ X2927 @ (powerset @ X2926))|(~(in @ X2928 @ (powerset @ X2926))|(~(in @ X2929 @ (powerset @ X2926))|(~(in @ X2930 @ (powerset @ X2926))|((setminus @ X2926 @ (binintersect @ (binunion @ X2927 @ X2928) @ (binunion @ X2929 @ X2930)))=(binunion @ (binintersect @ (setminus @ X2926 @ X2927) @ (setminus @ X2926 @ X2928)) @ (binintersect @ (setminus @ X2926 @ X2929) @ (setminus @ X2926 @ X2930))))))))&((~(in @ X2932 @ (powerset @ X2931))|(~(in @ X2933 @ (powerset @ X2931))|(~(in @ X2934 @ (powerset @ X2931))|(in @ (binintersect @ X2932 @ X2933) @ (powerset @ (binintersect @ (binunion @ X2932 @ X2934) @ (binunion @ X2933 @ X2934)))))))&((~(in @ X2936 @ (powerset @ X2935))|(~(in @ X2937 @ (powerset @ X2935))|(~(subset @ X2936 @ (setminus @ X2935 @ X2937))|(subset @ X2937 @ (setminus @ X2935 @ X2936)))))&((~(in @ X2939 @ (powerset @ X2938))|(~(in @ X2940 @ (powerset @ X2938))|(in @ (setminus @ X2938 @ (binunion @ X2939 @ X2940)) @ (powerset @ (setminus @ X2938 @ X2939)))))&((((in @ (esk87_3 @ X2941 @ X2942 @ X2943) @ X2941)|(~(in @ X2946 @ X2942)|(X2943 @ X2946))|~(subset @ X2942 @ (cartprod @ X2941 @ X2941)))&(((in @ (esk88_3 @ X2941 @ X2942 @ X2943) @ X2941)|(~(in @ X2946 @ X2942)|(X2943 @ X2946))|~(subset @ X2942 @ (cartprod @ X2941 @ X2941)))&(((in @ (kpair @ (esk87_3 @ X2941 @ X2942 @ X2943) @ (esk88_3 @ X2941 @ X2942 @ X2943)) @ X2942)|(~(in @ X2946 @ X2942)|(X2943 @ X2946))|~(subset @ X2942 @ (cartprod @ X2941 @ X2941)))&(~(X2943 @ (kpair @ (esk87_3 @ X2941 @ X2942 @ X2943) @ (esk88_3 @ X2941 @ X2942 @ X2943)))|(~(in @ X2946 @ X2942)|(X2943 @ X2946))|~(subset @ X2942 @ (cartprod @ X2941 @ X2941))))))&((~(in @ X2948 @ (breln1Set @ X2947))|(subset @ X2948 @ (cartprod @ X2947 @ X2947)))&((choice2fnsingleton)&((subset @ (dpsetconstr @ X2949 @ X2949 @ X2950) @ (cartprod @ X2949 @ X2949))&((((in @ (esk89_3 @ X2951 @ X2952 @ X2953) @ X2951)|(~(in @ X2956 @ X2952)|(X2953 @ X2956))|~(subset @ X2952 @ (cartprod @ X2951 @ X2951)))&(((in @ (esk90_3 @ X2951 @ X2952 @ X2953) @ X2951)|(~(in @ X2956 @ X2952)|(X2953 @ X2956))|~(subset @ X2952 @ (cartprod @ X2951 @ X2951)))&(((in @ (kpair @ (esk89_3 @ X2951 @ X2952 @ X2953) @ (esk90_3 @ X2951 @ X2952 @ X2953)) @ X2952)|(~(in @ X2956 @ X2952)|(X2953 @ X2956))|~(subset @ X2952 @ (cartprod @ X2951 @ X2951)))&(~(X2953 @ (kpair @ (esk89_3 @ X2951 @ X2952 @ X2953) @ (esk90_3 @ X2951 @ X2952 @ X2953)))|(~(in @ X2956 @ X2952)|(X2953 @ X2956))|~(subset @ X2952 @ (cartprod @ X2951 @ X2951))))))&((((in @ (esk91_3 @ X2957 @ X2958 @ X2959) @ X2957)|(subset @ X2958 @ X2959)|~(subset @ X2959 @ (cartprod @ X2957 @ X2957))|~(subset @ X2958 @ (cartprod @ X2957 @ X2957)))&(((in @ (esk92_3 @ X2957 @ X2958 @ X2959) @ X2957)|(subset @ X2958 @ X2959)|~(subset @ X2959 @ (cartprod @ X2957 @ X2957))|~(subset @ X2958 @ (cartprod @ X2957 @ X2957)))&(((in @ (kpair @ (esk91_3 @ X2957 @ X2958 @ X2959) @ (esk92_3 @ X2957 @ X2958 @ X2959)) @ X2958)|(subset @ X2958 @ X2959)|~(subset @ X2959 @ (cartprod @ X2957 @ X2957))|~(subset @ X2958 @ (cartprod @ X2957 @ X2957)))&(~(in @ (kpair @ (esk91_3 @ X2957 @ X2958 @ X2959) @ (esk92_3 @ X2957 @ X2958 @ X2959)) @ X2959)|(subset @ X2958 @ X2959)|~(subset @ X2959 @ (cartprod @ X2957 @ X2957))|~(subset @ X2958 @ (cartprod @ X2957 @ X2957))))))&(((((in @ (esk95_3 @ X2962 @ X2963 @ X2964) @ X2962)|((X2963)=(X2964))|(in @ (esk93_3 @ X2962 @ X2963 @ X2964) @ X2962)|~(subset @ X2964 @ (cartprod @ X2962 @ X2962))|~(subset @ X2963 @ (cartprod @ X2962 @ X2962)))&(((in @ (esk96_3 @ X2962 @ X2963 @ X2964) @ X2962)|((X2963)=(X2964))|(in @ (esk93_3 @ X2962 @ X2963 @ X2964) @ X2962)|~(subset @ X2964 @ (cartprod @ X2962 @ X2962))|~(subset @ X2963 @ (cartprod @ X2962 @ X2962)))&(((in @ (kpair @ (esk95_3 @ X2962 @ X2963 @ X2964) @ (esk96_3 @ X2962 @ X2963 @ X2964)) @ X2964)|((X2963)=(X2964))|(in @ (esk93_3 @ X2962 @ X2963 @ X2964) @ X2962)|~(subset @ X2964 @ (cartprod @ X2962 @ X2962))|~(subset @ X2963 @ (cartprod @ X2962 @ X2962)))&(~(in @ (kpair @ (esk95_3 @ X2962 @ X2963 @ X2964) @ (esk96_3 @ X2962 @ X2963 @ X2964)) @ X2963)|((X2963)=(X2964))|(in @ (esk93_3 @ X2962 @ X2963 @ X2964) @ X2962)|~(subset @ X2964 @ (cartprod @ X2962 @ X2962))|~(subset @ X2963 @ (cartprod @ X2962 @ X2962))))))&((((in @ (esk95_3 @ X2962 @ X2963 @ X2964) @ X2962)|((X2963)=(X2964))|(in @ (esk94_3 @ X2962 @ X2963 @ X2964) @ X2962)|~(subset @ X2964 @ (cartprod @ X2962 @ X2962))|~(subset @ X2963 @ (cartprod @ X2962 @ X2962)))&(((in @ (esk96_3 @ X2962 @ X2963 @ X2964) @ X2962)|((X2963)=(X2964))|(in @ (esk94_3 @ X2962 @ X2963 @ X2964) @ X2962)|~(subset @ X2964 @ (cartprod @ X2962 @ X2962))|~(subset @ X2963 @ (cartprod @ X2962 @ X2962)))&(((in @ (kpair @ (esk95_3 @ X2962 @ X2963 @ X2964) @ (esk96_3 @ X2962 @ X2963 @ X2964)) @ X2964)|((X2963)=(X2964))|(in @ (esk94_3 @ X2962 @ X2963 @ X2964) @ X2962)|~(subset @ X2964 @ (cartprod @ X2962 @ X2962))|~(subset @ X2963 @ (cartprod @ X2962 @ X2962)))&(~(in @ (kpair @ (esk95_3 @ X2962 @ X2963 @ X2964) @ (esk96_3 @ X2962 @ X2963 @ X2964)) @ X2963)|((X2963)=(X2964))|(in @ (esk94_3 @ X2962 @ X2963 @ X2964) @ X2962)|~(subset @ X2964 @ (cartprod @ X2962 @ X2962))|~(subset @ X2963 @ (cartprod @ X2962 @ X2962))))))&((((in @ (esk95_3 @ X2962 @ X2963 @ X2964) @ X2962)|((X2963)=(X2964))|(in @ (kpair @ (esk93_3 @ X2962 @ X2963 @ X2964) @ (esk94_3 @ X2962 @ X2963 @ X2964)) @ X2963)|~(subset @ X2964 @ (cartprod @ X2962 @ X2962))|~(subset @ X2963 @ (cartprod @ X2962 @ X2962)))&(((in @ (esk96_3 @ X2962 @ X2963 @ X2964) @ X2962)|((X2963)=(X2964))|(in @ (kpair @ (esk93_3 @ X2962 @ X2963 @ X2964) @ (esk94_3 @ X2962 @ X2963 @ X2964)) @ X2963)|~(subset @ X2964 @ (cartprod @ X2962 @ X2962))|~(subset @ X2963 @ (cartprod @ X2962 @ X2962)))&(((in @ (kpair @ (esk95_3 @ X2962 @ X2963 @ X2964) @ (esk96_3 @ X2962 @ X2963 @ X2964)) @ X2964)|((X2963)=(X2964))|(in @ (kpair @ (esk93_3 @ X2962 @ X2963 @ X2964) @ (esk94_3 @ X2962 @ X2963 @ X2964)) @ X2963)|~(subset @ X2964 @ (cartprod @ X2962 @ X2962))|~(subset @ X2963 @ (cartprod @ X2962 @ X2962)))&(~(in @ (kpair @ (esk95_3 @ X2962 @ X2963 @ X2964) @ (esk96_3 @ X2962 @ X2963 @ X2964)) @ X2963)|((X2963)=(X2964))|(in @ (kpair @ (esk93_3 @ X2962 @ X2963 @ X2964) @ (esk94_3 @ X2962 @ X2963 @ X2964)) @ X2963)|~(subset @ X2964 @ (cartprod @ X2962 @ X2962))|~(subset @ X2963 @ (cartprod @ X2962 @ X2962))))))&(((in @ (esk95_3 @ X2962 @ X2963 @ X2964) @ X2962)|((X2963)=(X2964))|~(in @ (kpair @ (esk93_3 @ X2962 @ X2963 @ X2964) @ (esk94_3 @ X2962 @ X2963 @ X2964)) @ X2964)|~(subset @ X2964 @ (cartprod @ X2962 @ X2962))|~(subset @ X2963 @ (cartprod @ X2962 @ X2962)))&(((in @ (esk96_3 @ X2962 @ X2963 @ X2964) @ X2962)|((X2963)=(X2964))|~(in @ (kpair @ (esk93_3 @ X2962 @ X2963 @ X2964) @ (esk94_3 @ X2962 @ X2963 @ X2964)) @ X2964)|~(subset @ X2964 @ (cartprod @ X2962 @ X2962))|~(subset @ X2963 @ (cartprod @ X2962 @ X2962)))&(((in @ (kpair @ (esk95_3 @ X2962 @ X2963 @ X2964) @ (esk96_3 @ X2962 @ X2963 @ X2964)) @ X2964)|((X2963)=(X2964))|~(in @ (kpair @ (esk93_3 @ X2962 @ X2963 @ X2964) @ (esk94_3 @ X2962 @ X2963 @ X2964)) @ X2964)|~(subset @ X2964 @ (cartprod @ X2962 @ X2962))|~(subset @ X2963 @ (cartprod @ X2962 @ X2962)))&(~(in @ (kpair @ (esk95_3 @ X2962 @ X2963 @ X2964) @ (esk96_3 @ X2962 @ X2963 @ X2964)) @ X2963)|((X2963)=(X2964))|~(in @ (kpair @ (esk93_3 @ X2962 @ X2963 @ X2964) @ (esk94_3 @ X2962 @ X2963 @ X2964)) @ X2964)|~(subset @ X2964 @ (cartprod @ X2962 @ X2962))|~(subset @ X2963 @ (cartprod @ X2962 @ X2962)))))))))&((~(subset @ X2970 @ (cartprod @ X2969 @ X2969))|(subset @ (breln1invset @ X2969 @ X2970) @ (cartprod @ X2969 @ X2969)))&((~(subset @ X2972 @ (cartprod @ X2971 @ X2971))|(~(in @ X2973 @ X2971)|(~(in @ X2974 @ X2971)|(~(in @ (kpair @ X2973 @ X2974) @ X2972)|(in @ (kpair @ X2974 @ X2973) @ (breln1invset @ X2971 @ X2972))))))&((~(subset @ X2976 @ (cartprod @ X2975 @ X2975))|(~(in @ X2977 @ X2975)|(~(in @ X2978 @ X2975)|(~(in @ (kpair @ X2978 @ X2977) @ (breln1invset @ X2975 @ X2976))|(in @ (kpair @ X2977 @ X2978) @ X2976)))))&((~(subset @ X2980 @ (cartprod @ X2979 @ X2979))|(~(subset @ X2981 @ (cartprod @ X2979 @ X2979))|(subset @ (dpsetconstr @ X2979 @ X2979 @ (^[Z0/* 19 */:$i, Z1:$i]:(?[X1531:$i]:((((in @ X1531 @ X2979)&(in @ (kpair @ Z0 @ X1531) @ X2980))&(in @ (kpair @ X1531 @ Z1) @ X2981)))))) @ (cartprod @ X2979 @ X2979))))&((subset @ esk98_0 @ (cartprod @ esk97_0 @ esk97_0))&((subset @ esk99_0 @ (cartprod @ esk97_0 @ esk97_0))&((in @ esk100_0 @ esk97_0)&((in @ esk101_0 @ esk97_0)&((in @ esk102_0 @ esk97_0)&((in @ (kpair @ esk100_0 @ esk102_0) @ esk98_0)&((in @ (kpair @ esk102_0 @ esk101_0) @ esk99_0)&~(in @ (kpair @ esk100_0 @ esk101_0) @ (dpsetconstr @ esk97_0 @ esk97_0 @ (^[Z0/* 19 */:$i, Z1:$i]:(?[X1527:$i]:((((in @ X1527 @ esk97_0)&(in @ (kpair @ Z0 @ X1527) @ esk98_0))&(in @ (kpair @ X1527 @ Z1) @ esk99_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_389])])])])])])])).
7.08/1.45	thf(c_0_391, negated_conjecture, ~((in @ (kpair @ esk100_0 @ esk101_0) @ (dpsetconstr @ esk97_0 @ esk97_0 @ (^[Z0/* 19 */:$i, Z1:$i]:(?[X3009:$i]:((((in @ X3009 @ esk97_0)&(in @ (kpair @ Z0 @ X3009) @ esk98_0))&(in @ (kpair @ X3009 @ Z1) @ esk99_0)))))))), inference(split_conjunct,[status(thm)],[c_0_390])).
7.08/1.45	thf(c_0_392, negated_conjecture, ![X3:$i, X2:$i, X6:$i > $i > $o, X5:$i, X4:$i]:(((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X5 @ X6))|~((in @ X2 @ X3))|~((in @ X4 @ X5))|~((X6 @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_390])).
7.08/1.45	thf(c_0_393, negated_conjecture, (in @ esk101_0 @ esk97_0), inference(split_conjunct,[status(thm)],[c_0_390])).
7.08/1.45	thf(c_0_394, negated_conjecture, (in @ esk100_0 @ esk97_0), inference(split_conjunct,[status(thm)],[c_0_390])).
7.08/1.45	thf(c_0_395, negated_conjecture, ~(?[X3010:$i]:((((in @ X3010 @ esk97_0)&(in @ (kpair @ esk100_0 @ X3010) @ esk98_0))&(in @ (kpair @ X3010 @ esk101_0) @ esk99_0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_391, c_0_392]), c_0_393]), c_0_394])])).
7.08/1.45	thf(c_0_396, negated_conjecture, ![X2:$i]:((~((in @ (kpair @ esk100_0 @ X2) @ esk98_0))|~((in @ (kpair @ X2 @ esk101_0) @ esk99_0))|~((in @ X2 @ esk97_0)))), inference(dynamic_cnf,[status(thm)],[c_0_395])).
7.08/1.45	thf(c_0_397, negated_conjecture, (in @ (kpair @ esk100_0 @ esk102_0) @ esk98_0), inference(split_conjunct,[status(thm)],[c_0_390])).
7.08/1.45	thf(c_0_398, negated_conjecture, (in @ (kpair @ esk102_0 @ esk101_0) @ esk99_0), inference(split_conjunct,[status(thm)],[c_0_390])).
7.08/1.45	thf(c_0_399, negated_conjecture, (in @ esk102_0 @ esk97_0), inference(split_conjunct,[status(thm)],[c_0_390])).
7.08/1.45	thf(c_0_400, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_396, c_0_397]), c_0_398]), c_0_399])]), ['proof']).
7.08/1.45	# SZS output end CNFRefutation
7.08/1.45	# Parsed axioms                        : 644
7.08/1.45	# Removed by relevancy pruning/SinE    : 345
7.08/1.45	# Initial clauses                      : 511
7.08/1.45	# Removed in clause preprocessing      : 32
7.08/1.45	# Initial clauses in saturation        : 479
7.08/1.45	# Processed clauses                    : 1216
7.08/1.45	# ...of these trivial                  : 15
7.08/1.45	# ...subsumed                          : 154
7.08/1.45	# ...remaining for further processing  : 1047
7.08/1.45	# Other redundant clauses eliminated   : 43
7.08/1.45	# Clauses deleted for lack of memory   : 0
7.08/1.45	# Backward-subsumed                    : 3
7.08/1.45	# Backward-rewritten                   : 3
7.08/1.45	# Generated clauses                    : 21058
7.08/1.45	# ...of the previous two non-redundant : 20751
7.08/1.45	# ...aggressively subsumed             : 0
7.08/1.45	# Contextual simplify-reflections      : 18
7.08/1.45	# Paramodulations                      : 20989
7.08/1.45	# Factorizations                       : 2
7.08/1.45	# NegExts                              : 0
7.08/1.45	# Equation resolutions                 : 50
7.08/1.45	# Disequality decompositions           : 0
7.08/1.45	# Total rewrite steps                  : 366
7.08/1.45	# ...of those cached                   : 252
7.08/1.45	# Propositional unsat checks           : 0
7.08/1.45	#    Propositional check models        : 0
7.08/1.45	#    Propositional check unsatisfiable : 0
7.08/1.45	#    Propositional clauses             : 0
7.08/1.45	#    Propositional clauses after purity: 0
7.08/1.45	#    Propositional unsat core size     : 0
7.08/1.45	#    Propositional preprocessing time  : 0.000
7.08/1.45	#    Propositional encoding time       : 0.000
7.08/1.45	#    Propositional solver time         : 0.000
7.08/1.45	#    Success case prop preproc time    : 0.000
7.08/1.45	#    Success case prop encoding time   : 0.000
7.08/1.45	#    Success case prop solver time     : 0.000
7.08/1.45	# Current number of processed clauses  : 608
7.08/1.45	#    Positive orientable unit clauses  : 48
7.08/1.45	#    Positive unorientable unit clauses: 0
7.08/1.45	#    Negative unit clauses             : 26
7.08/1.45	#    Non-unit-clauses                  : 534
7.08/1.45	# Current number of unprocessed clauses: 20387
7.08/1.45	# ...number of literals in the above   : 92880
7.08/1.45	# Current number of archived formulas  : 0
7.08/1.45	# Current number of archived clauses   : 424
7.08/1.45	# Clause-clause subsumption calls (NU) : 95486
7.08/1.45	# Rec. Clause-clause subsumption calls : 31245
7.08/1.45	# Non-unit clause-clause subsumptions  : 148
7.08/1.45	# Unit Clause-clause subsumption calls : 1003
7.08/1.45	# Rewrite failures with RHS unbound    : 0
7.08/1.45	# BW rewrite match attempts            : 25
7.08/1.45	# BW rewrite match successes           : 3
7.08/1.45	# Condensation attempts                : 0
7.08/1.45	# Condensation successes               : 0
7.08/1.45	# Termbank termtop insertions          : 535305
7.08/1.45	# Search garbage collected termcells   : 32347
7.08/1.45	
7.08/1.45	# -------------------------------------------------
7.08/1.45	# User time                : 0.770 s
7.08/1.45	# System time              : 0.039 s
7.08/1.45	# Total time               : 0.809 s
7.08/1.45	# Maximum resident set size: 10056 pages
7.08/1.45	
7.08/1.45	# -------------------------------------------------
7.08/1.45	# User time                : 0.788 s
7.08/1.45	# System time              : 0.044 s
7.08/1.45	# Total time               : 0.833 s
7.08/1.45	# Maximum resident set size: 2764 pages
7.08/1.45	% E exiting
7.08/1.45	% E exiting
7.08/1.45	EOF