0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command    : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM
0.12/0.33	% Computer : n021.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 04:40:49 EDT 2025
0.12/0.33	% CPUTime    : 
0.20/0.47	Running higher-order theorem proving
0.38/0.54	Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=240 /export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p
2.70/240.03	# Version: 3.0.0-ho
2.70/240.03	# Preprocessing class: HSLMSLSSLLLCHFA.
2.70/240.03	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
2.70/240.03	# Starting ehoh_best5 with 240s (1) cores
2.70/240.03	# Starting almost_fo_3_lam with 240s (1) cores
2.70/240.03	# Starting new_bool_5 with 240s (1) cores
2.70/240.03	# Starting pre_casc_3 with 240s (1) cores
2.70/240.03	# Starting ho_unfolding_8 with 240s (1) cores
2.70/240.03	# Starting new_ho_10_cnf2 with 240s (1) cores
2.70/240.03	# Starting new_bool_3 with 240s (1) cores
2.70/240.03	# Starting new_ho_5 with 240s (1) cores
2.70/240.03	# new_ho_5 with pid 6075 completed with status 0
2.70/240.03	# Result found by new_ho_5
2.70/240.03	# Preprocessing class: HSLMSLSSLLLCHFA.
2.70/240.03	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
2.70/240.03	# Starting ehoh_best5 with 240s (1) cores
2.70/240.03	# Starting almost_fo_3_lam with 240s (1) cores
2.70/240.03	# Starting new_bool_5 with 240s (1) cores
2.70/240.03	# Starting pre_casc_3 with 240s (1) cores
2.70/240.03	# Starting ho_unfolding_8 with 240s (1) cores
2.70/240.03	# Starting new_ho_10_cnf2 with 240s (1) cores
2.70/240.03	# Starting new_bool_3 with 240s (1) cores
2.70/240.03	# Starting new_ho_5 with 240s (1) cores
2.70/240.03	# SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
2.70/240.03	# Search class: HGHSM-FSLM32-MHFMMSBN
2.70/240.03	# Scheduled 9 strats onto 1 cores with 240 seconds (240 total)
2.70/240.03	# Starting ho_unfolding_8 with 49s (1) cores
2.70/240.03	# ho_unfolding_8 with pid 6078 completed with status 0
2.70/240.03	# Result found by ho_unfolding_8
2.70/240.03	# Preprocessing class: HSLMSLSSLLLCHFA.
2.70/240.03	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
2.70/240.03	# Starting ehoh_best5 with 240s (1) cores
2.70/240.03	# Starting almost_fo_3_lam with 240s (1) cores
2.70/240.03	# Starting new_bool_5 with 240s (1) cores
2.70/240.03	# Starting pre_casc_3 with 240s (1) cores
2.70/240.03	# Starting ho_unfolding_8 with 240s (1) cores
2.70/240.03	# Starting new_ho_10_cnf2 with 240s (1) cores
2.70/240.03	# Starting new_bool_3 with 240s (1) cores
2.70/240.03	# Starting new_ho_5 with 240s (1) cores
2.70/240.03	# SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
2.70/240.03	# Search class: HGHSM-FSLM32-MHFMMSBN
2.70/240.03	# Scheduled 9 strats onto 1 cores with 240 seconds (240 total)
2.70/240.03	# Starting ho_unfolding_8 with 49s (1) cores
2.70/240.03	# Preprocessing time       : 0.059 s
2.70/240.03	# Presaturation interreduction done
2.70/240.03	
2.70/240.03	# Proof found!
2.70/240.03	# SZS status Theorem
2.70/240.03	# SZS output start CNFRefutation
2.70/240.03	thf(decl_23, type, in: $i > $i > $o).
2.70/240.03	thf(decl_24, type, exu: ($i > $o) > $o).
2.70/240.03	thf(decl_25, type, setextAx: $o).
2.70/240.03	thf(decl_26, type, emptyset: $i).
2.70/240.03	thf(decl_27, type, emptysetAx: $o).
2.70/240.03	thf(decl_28, type, setadjoin: $i > $i > $i).
2.70/240.03	thf(decl_29, type, setadjoinAx: $o).
2.70/240.03	thf(decl_30, type, powerset: $i > $i).
2.70/240.03	thf(decl_31, type, powersetAx: $o).
2.70/240.03	thf(decl_32, type, setunion: $i > $i).
2.70/240.03	thf(decl_33, type, setunionAx: $o).
2.70/240.03	thf(decl_34, type, omega: $i).
2.70/240.03	thf(decl_35, type, omega0Ax: $o).
2.70/240.03	thf(decl_36, type, omegaSAx: $o).
2.70/240.03	thf(decl_37, type, omegaIndAx: $o).
2.70/240.03	thf(decl_38, type, replAx: $o).
2.70/240.03	thf(decl_39, type, foundationAx: $o).
2.70/240.03	thf(decl_40, type, wellorderingAx: $o).
2.70/240.03	thf(decl_41, type, descr: ($i > $o) > $i).
2.70/240.03	thf(decl_42, type, descrp: $o).
2.70/240.03	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
2.70/240.03	thf(decl_44, type, dsetconstrI: $o).
2.70/240.03	thf(decl_45, type, dsetconstrEL: $o).
2.70/240.03	thf(decl_46, type, dsetconstrER: $o).
2.70/240.03	thf(decl_47, type, exuE1: $o).
2.70/240.03	thf(decl_48, type, prop2set: $o > $i).
2.70/240.03	thf(decl_49, type, prop2setE: $o).
2.70/240.03	thf(decl_50, type, emptysetE: $o).
2.70/240.03	thf(decl_51, type, emptysetimpfalse: $o).
2.70/240.03	thf(decl_52, type, notinemptyset: $o).
2.70/240.03	thf(decl_53, type, exuE3e: $o).
2.70/240.03	thf(decl_54, type, setext: $o).
2.70/240.03	thf(decl_55, type, emptyI: $o).
2.70/240.03	thf(decl_56, type, noeltsimpempty: $o).
2.70/240.03	thf(decl_57, type, setbeta: $o).
2.70/240.03	thf(decl_58, type, nonempty: $i > $o).
2.70/240.03	thf(decl_59, type, nonemptyE1: $o).
2.70/240.03	thf(decl_60, type, nonemptyI: $o).
2.70/240.03	thf(decl_61, type, nonemptyI1: $o).
2.70/240.03	thf(decl_62, type, setadjoinIL: $o).
2.70/240.03	thf(decl_63, type, emptyinunitempty: $o).
2.70/240.03	thf(decl_64, type, setadjoinIR: $o).
2.70/240.03	thf(decl_65, type, setadjoinE: $o).
2.70/240.03	thf(decl_66, type, setadjoinOr: $o).
2.70/240.03	thf(decl_67, type, setoftrueEq: $o).
2.70/240.03	thf(decl_68, type, powersetI: $o).
2.70/240.03	thf(decl_69, type, emptyinPowerset: $o).
2.70/240.03	thf(decl_70, type, emptyInPowerset: $o).
2.70/240.03	thf(decl_71, type, powersetE: $o).
2.70/240.03	thf(decl_72, type, setunionI: $o).
2.70/240.03	thf(decl_73, type, setunionE: $o).
2.70/240.03	thf(decl_74, type, subPowSU: $o).
2.70/240.03	thf(decl_75, type, exuE2: $o).
2.70/240.03	thf(decl_76, type, nonemptyImpWitness: $o).
2.70/240.03	thf(decl_77, type, uniqinunit: $o).
2.70/240.03	thf(decl_78, type, notinsingleton: $o).
2.70/240.03	thf(decl_79, type, eqinunit: $o).
2.70/240.03	thf(decl_80, type, singletonsswitch: $o).
2.70/240.03	thf(decl_81, type, upairsetE: $o).
2.70/240.03	thf(decl_82, type, upairsetIL: $o).
2.70/240.03	thf(decl_83, type, upairsetIR: $o).
2.70/240.03	thf(decl_84, type, emptyE1: $o).
2.70/240.03	thf(decl_85, type, vacuousDall: $o).
2.70/240.03	thf(decl_86, type, quantDeMorgan1: $o).
2.70/240.03	thf(decl_87, type, quantDeMorgan2: $o).
2.70/240.03	thf(decl_88, type, quantDeMorgan3: $o).
2.70/240.03	thf(decl_89, type, quantDeMorgan4: $o).
2.70/240.03	thf(decl_90, type, prop2setI: $o).
2.70/240.03	thf(decl_91, type, set2prop: $i > $o).
2.70/240.03	thf(decl_92, type, prop2set2propI: $o).
2.70/240.03	thf(decl_93, type, notdexE: $o).
2.70/240.03	thf(decl_94, type, notdallE: $o).
2.70/240.03	thf(decl_95, type, exuI1: $o).
2.70/240.03	thf(decl_96, type, exuI3: $o).
2.70/240.03	thf(decl_97, type, exuI2: $o).
2.70/240.03	thf(decl_98, type, inCongP: $o).
2.70/240.03	thf(decl_99, type, in__Cong: $o).
2.70/240.03	thf(decl_100, type, exuE3u: $o).
2.70/240.03	thf(decl_101, type, exu__Cong: $o).
2.70/240.03	thf(decl_102, type, emptyset__Cong: $o).
2.70/240.03	thf(decl_103, type, setadjoin__Cong: $o).
2.70/240.03	thf(decl_104, type, powerset__Cong: $o).
2.70/240.03	thf(decl_105, type, setunion__Cong: $o).
2.70/240.03	thf(decl_106, type, omega__Cong: $o).
2.70/240.03	thf(decl_107, type, exuEu: $o).
2.70/240.03	thf(decl_108, type, descr__Cong: $o).
2.70/240.03	thf(decl_109, type, dsetconstr__Cong: $o).
2.70/240.03	thf(decl_110, type, subset: $i > $i > $o).
2.70/240.03	thf(decl_113, type, subsetI1: $o).
2.70/240.03	thf(decl_114, type, eqimpsubset2: $o).
2.70/240.03	thf(decl_115, type, eqimpsubset1: $o).
2.70/240.03	thf(decl_116, type, subsetI2: $o).
2.70/240.03	thf(decl_117, type, emptysetsubset: $o).
2.70/240.03	thf(decl_118, type, subsetE: $o).
2.70/240.03	thf(decl_119, type, subsetE2: $o).
2.70/240.03	thf(decl_120, type, notsubsetI: $o).
2.70/240.03	thf(decl_121, type, notequalI1: $o).
2.70/240.03	thf(decl_122, type, notequalI2: $o).
2.70/240.03	thf(decl_123, type, subsetRefl: $o).
2.70/240.03	thf(decl_124, type, subsetTrans: $o).
2.70/240.03	thf(decl_125, type, setadjoinSub: $o).
2.70/240.03	thf(decl_126, type, setadjoinSub2: $o).
2.70/240.03	thf(decl_127, type, subset2powerset: $o).
2.70/240.03	thf(decl_128, type, setextsub: $o).
2.70/240.03	thf(decl_129, type, subsetemptysetimpeq: $o).
2.70/240.03	thf(decl_130, type, powersetI1: $o).
2.70/240.03	thf(decl_131, type, powersetE1: $o).
2.70/240.03	thf(decl_132, type, inPowerset: $o).
2.70/240.03	thf(decl_133, type, powersetsubset: $o).
2.70/240.03	thf(decl_134, type, sepInPowerset: $o).
2.70/240.03	thf(decl_135, type, sepSubset: $o).
2.70/240.03	thf(decl_136, type, binunion: $i > $i > $i).
2.70/240.03	thf(decl_137, type, binunionIL: $o).
2.70/240.03	thf(decl_138, type, upairset2IR: $o).
2.70/240.03	thf(decl_139, type, binunionIR: $o).
2.70/240.03	thf(decl_140, type, binunionEcases: $o).
2.70/240.03	thf(decl_141, type, binunionE: $o).
2.70/240.03	thf(decl_142, type, binunionLsub: $o).
2.70/240.03	thf(decl_143, type, binunionRsub: $o).
2.70/240.03	thf(decl_144, type, binintersect: $i > $i > $i).
2.70/240.03	thf(decl_145, type, binintersectI: $o).
2.70/240.03	thf(decl_146, type, binintersectSubset5: $o).
2.70/240.03	thf(decl_147, type, binintersectEL: $o).
2.70/240.03	thf(decl_148, type, binintersectLsub: $o).
2.70/240.03	thf(decl_149, type, binintersectSubset2: $o).
2.70/240.03	thf(decl_150, type, binintersectSubset3: $o).
2.70/240.03	thf(decl_151, type, binintersectER: $o).
2.70/240.03	thf(decl_152, type, disjointsetsI1: $o).
2.70/240.03	thf(decl_153, type, binintersectRsub: $o).
2.70/240.03	thf(decl_154, type, binintersectSubset4: $o).
2.70/240.03	thf(decl_155, type, binintersectSubset1: $o).
2.70/240.03	thf(decl_156, type, bs114d: $o).
2.70/240.03	thf(decl_158, type, setminus: $i > $i > $i).
2.70/240.03	thf(decl_159, type, setminusI: $o).
2.70/240.03	thf(decl_160, type, setminusEL: $o).
2.70/240.03	thf(decl_161, type, setminusER: $o).
2.70/240.03	thf(decl_162, type, setminusSubset2: $o).
2.70/240.03	thf(decl_163, type, setminusERneg: $o).
2.70/240.03	thf(decl_164, type, setminusELneg: $o).
2.70/240.03	thf(decl_165, type, setminusILneg: $o).
2.70/240.03	thf(decl_166, type, setminusIRneg: $o).
2.70/240.03	thf(decl_167, type, setminusLsub: $o).
2.70/240.03	thf(decl_168, type, setminusSubset1: $o).
2.70/240.03	thf(decl_169, type, symdiff: $i > $i > $i).
2.70/240.03	thf(decl_170, type, symdiffE: $o).
2.70/240.03	thf(decl_171, type, symdiffI1: $o).
2.70/240.03	thf(decl_172, type, symdiffI2: $o).
2.70/240.03	thf(decl_173, type, symdiffIneg1: $o).
2.70/240.03	thf(decl_174, type, symdiffIneg2: $o).
2.70/240.03	thf(decl_175, type, iskpair: $i > $o).
2.70/240.03	thf(decl_176, type, secondinupair: $o).
2.70/240.03	thf(decl_177, type, setukpairIL: $o).
2.70/240.03	thf(decl_178, type, setukpairIR: $o).
2.70/240.03	thf(decl_179, type, kpairiskpair: $o).
2.70/240.03	thf(decl_180, type, kpair: $i > $i > $i).
2.70/240.03	thf(decl_181, type, kpairp: $o).
2.70/240.03	thf(decl_182, type, cartprod: $i > $i > $i).
2.70/240.03	thf(decl_183, type, singletonsubset: $o).
2.70/240.03	thf(decl_184, type, singletoninpowerset: $o).
2.70/240.03	thf(decl_185, type, singletoninpowunion: $o).
2.70/240.03	thf(decl_186, type, upairset2E: $o).
2.70/240.03	thf(decl_187, type, upairsubunion: $o).
2.70/240.03	thf(decl_188, type, upairinpowunion: $o).
2.70/240.03	thf(decl_189, type, ubforcartprodlem1: $o).
2.70/240.03	thf(decl_190, type, ubforcartprodlem2: $o).
2.70/240.03	thf(decl_191, type, ubforcartprodlem3: $o).
2.70/240.03	thf(decl_192, type, cartprodpairin: $o).
2.70/240.03	thf(decl_193, type, cartprodmempair1: $o).
2.70/240.03	thf(decl_194, type, cartprodmempair: $o).
2.70/240.03	thf(decl_195, type, setunionE2: $o).
2.70/240.03	thf(decl_196, type, setunionsingleton1: $o).
2.70/240.03	thf(decl_197, type, setunionsingleton2: $o).
2.70/240.03	thf(decl_198, type, setunionsingleton: $o).
2.70/240.03	thf(decl_199, type, singleton: $i > $o).
2.70/240.03	thf(decl_200, type, singletonprop: $o).
2.70/240.03	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
2.70/240.03	thf(decl_202, type, ex1E1: $o).
2.70/240.03	thf(decl_203, type, ex1I: $o).
2.70/240.03	thf(decl_204, type, ex1I2: $o).
2.70/240.03	thf(decl_205, type, singletonsuniq: $o).
2.70/240.03	thf(decl_210, type, setukpairinjL1: $o).
2.70/240.03	thf(decl_211, type, kfstsingleton: $o).
2.70/240.03	thf(decl_212, type, theprop: $o).
2.70/240.03	thf(decl_213, type, kfst: $i > $i).
2.70/240.03	thf(decl_214, type, kfstpairEq: $o).
2.70/240.03	thf(decl_215, type, cartprodfstin: $o).
2.70/240.03	thf(decl_216, type, setukpairinjL2: $o).
2.70/240.03	thf(decl_217, type, setukpairinjL: $o).
2.70/240.03	thf(decl_218, type, setukpairinjR11: $o).
2.70/240.03	thf(decl_219, type, setukpairinjR12: $o).
2.70/240.03	thf(decl_220, type, setukpairinjR1: $o).
2.70/240.03	thf(decl_221, type, upairequniteq: $o).
2.70/240.03	thf(decl_222, type, setukpairinjR2: $o).
2.70/240.03	thf(decl_223, type, setukpairinjR: $o).
2.70/240.03	thf(decl_224, type, ksndsingleton: $o).
2.70/240.03	thf(decl_225, type, ksnd: $i > $i).
2.70/240.03	thf(decl_226, type, ksndpairEq: $o).
2.70/240.03	thf(decl_227, type, kpairsurjEq: $o).
2.70/240.03	thf(decl_228, type, cartprodsndin: $o).
2.70/240.03	thf(decl_229, type, cartprodpairmemEL: $o).
2.70/240.03	thf(decl_230, type, cartprodpairmemER: $o).
2.70/240.03	thf(decl_231, type, cartprodmempaircEq: $o).
2.70/240.03	thf(decl_232, type, cartprodfstpairEq: $o).
2.70/240.03	thf(decl_233, type, cartprodsndpairEq: $o).
2.70/240.03	thf(decl_234, type, cartprodpairsurjEq: $o).
2.70/240.03	thf(decl_235, type, breln: $i > $i > $i > $o).
2.70/240.03	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
2.70/240.03	thf(decl_237, type, dpsetconstrI: $o).
2.70/240.03	thf(decl_238, type, dpsetconstrSub: $o).
2.70/240.03	thf(decl_239, type, setOfPairsIsBReln: $o).
2.70/240.03	thf(decl_240, type, dpsetconstrERa: $o).
2.70/240.03	thf(decl_241, type, dpsetconstrEL1: $o).
2.70/240.03	thf(decl_242, type, dpsetconstrEL2: $o).
2.70/240.03	thf(decl_243, type, dpsetconstrER: $o).
2.70/240.03	thf(decl_244, type, func: $i > $i > $i > $o).
2.70/240.03	thf(decl_245, type, funcSet: $i > $i > $i).
2.70/240.03	thf(decl_246, type, funcImageSingleton: $o).
2.70/240.03	thf(decl_247, type, apProp: $o).
2.70/240.03	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
2.70/240.03	thf(decl_249, type, app: $o).
2.70/240.03	thf(decl_250, type, infuncsetfunc: $o).
2.70/240.03	thf(decl_251, type, ap2p: $o).
2.70/240.03	thf(decl_252, type, funcinfuncset: $o).
2.70/240.03	thf(decl_253, type, lamProp: $o).
2.70/240.03	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
2.70/240.03	thf(decl_255, type, lamp: $o).
2.70/240.03	thf(decl_256, type, lam2p: $o).
2.70/240.03	thf(decl_257, type, brelnall1: $o).
2.70/240.03	thf(decl_258, type, brelnall2: $o).
2.70/240.03	thf(decl_259, type, ex1E2: $o).
2.70/240.03	thf(decl_260, type, funcGraphProp1: $o).
2.70/240.03	thf(decl_261, type, funcGraphProp3: $o).
2.70/240.03	thf(decl_262, type, funcGraphProp2: $o).
2.70/240.03	thf(decl_263, type, funcextLem: $o).
2.70/240.03	thf(decl_264, type, funcGraphProp4: $o).
2.70/240.03	thf(decl_265, type, subbreln: $o).
2.70/240.03	thf(decl_266, type, eqbreln: $o).
2.70/240.03	thf(decl_267, type, funcext: $o).
2.70/240.03	thf(decl_268, type, funcext2: $o).
2.70/240.03	thf(decl_269, type, ap2apEq1: $o).
2.70/240.03	thf(decl_270, type, ap2apEq2: $o).
2.70/240.03	thf(decl_271, type, beta1: $o).
2.70/240.03	thf(decl_272, type, eta1: $o).
2.70/240.03	thf(decl_273, type, lam2lamEq: $o).
2.70/240.03	thf(decl_274, type, beta2: $o).
2.70/240.03	thf(decl_275, type, eta2: $o).
2.70/240.03	thf(decl_276, type, iffalseProp1: $o).
2.70/240.03	thf(decl_277, type, iffalseProp2: $o).
2.70/240.03	thf(decl_278, type, iftrueProp1: $o).
2.70/240.03	thf(decl_279, type, iftrueProp2: $o).
2.70/240.03	thf(decl_280, type, ifSingleton: $o).
2.70/240.03	thf(decl_281, type, if: $i > $o > $i > $i > $i).
2.70/240.03	thf(decl_282, type, ifp: $o).
2.70/240.03	thf(decl_283, type, theeq: $o).
2.70/240.03	thf(decl_284, type, iftrue: $o).
2.70/240.03	thf(decl_285, type, iffalse: $o).
2.70/240.03	thf(decl_286, type, iftrueorfalse: $o).
2.70/240.03	thf(decl_287, type, binintersectT_lem: $o).
2.70/240.03	thf(decl_288, type, binunionT_lem: $o).
2.70/240.03	thf(decl_289, type, powersetT_lem: $o).
2.70/240.03	thf(decl_290, type, setminusT_lem: $o).
2.70/240.03	thf(decl_291, type, complementT_lem: $o).
2.70/240.03	thf(decl_292, type, setextT: $o).
2.70/240.03	thf(decl_293, type, subsetTI: $o).
2.70/240.03	thf(decl_294, type, powersetTI1: $o).
2.70/240.03	thf(decl_295, type, powersetTE1: $o).
2.70/240.03	thf(decl_296, type, complementTI1: $o).
2.70/240.03	thf(decl_297, type, complementTE1: $o).
2.70/240.03	thf(decl_298, type, binintersectTELcontra: $o).
2.70/240.03	thf(decl_299, type, binintersectTERcontra: $o).
2.70/240.03	thf(decl_300, type, contrasubsetT: $o).
2.70/240.03	thf(decl_301, type, contrasubsetT1: $o).
2.70/240.03	thf(decl_302, type, contrasubsetT2: $o).
2.70/240.03	thf(decl_303, type, contrasubsetT3: $o).
2.70/240.03	thf(decl_304, type, doubleComplementI1: $o).
2.70/240.03	thf(decl_305, type, doubleComplementE1: $o).
2.70/240.03	thf(decl_306, type, doubleComplementSub1: $o).
2.70/240.03	thf(decl_307, type, doubleComplementSub2: $o).
2.70/240.03	thf(decl_308, type, doubleComplementEq: $o).
2.70/240.03	thf(decl_309, type, complementTnotintersectT: $o).
2.70/240.03	thf(decl_310, type, complementImpComplementIntersect: $o).
2.70/240.03	thf(decl_311, type, complementSubsetComplementIntersect: $o).
2.70/240.03	thf(decl_312, type, complementInPowersetComplementIntersect: $o).
2.70/240.03	thf(decl_313, type, contraSubsetComplement: $o).
2.70/240.03	thf(decl_314, type, complementTcontraSubset: $o).
2.70/240.03	thf(decl_315, type, binunionTILcontra: $o).
2.70/240.03	thf(decl_316, type, binunionTIRcontra: $o).
2.70/240.03	thf(decl_317, type, inIntersectImpInUnion: $o).
2.70/240.03	thf(decl_318, type, inIntersectImpInUnion2: $o).
2.70/240.03	thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
2.70/240.03	thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
2.70/240.03	thf(decl_321, type, inComplementUnionImpNotIn1: $o).
2.70/240.03	thf(decl_322, type, inComplementUnionImpInComplement1: $o).
2.70/240.03	thf(decl_323, type, binunionTE: $o).
2.70/240.03	thf(decl_324, type, binunionTEcontra: $o).
2.70/240.03	thf(decl_325, type, demorgan2a1: $o).
2.70/240.03	thf(decl_326, type, complementUnionInPowersetComplement: $o).
2.70/240.03	thf(decl_327, type, demorgan2a2: $o).
2.70/240.03	thf(decl_328, type, demorgan1a: $o).
2.70/240.03	thf(decl_329, type, demorgan1b: $o).
2.70/240.03	thf(decl_330, type, demorgan1: $o).
2.70/240.03	thf(decl_331, type, demorgan2a: $o).
2.70/240.03	thf(decl_332, type, demorgan2b2: $o).
2.70/240.03	thf(decl_333, type, demorgan2b: $o).
2.70/240.03	thf(decl_334, type, demorgan2: $o).
2.70/240.03	thf(decl_335, type, woz13rule0: $o).
2.70/240.03	thf(decl_336, type, woz13rule1: $o).
2.70/240.03	thf(decl_337, type, woz13rule2: $o).
2.70/240.03	thf(decl_338, type, woz13rule3: $o).
2.70/240.03	thf(decl_339, type, woz13rule4: $o).
2.70/240.03	thf(decl_340, type, woz1_1: $o).
2.70/240.03	thf(decl_341, type, woz1_2: $o).
2.70/240.03	thf(decl_342, type, woz1_3: $o).
2.70/240.03	thf(decl_343, type, woz1_4: $o).
2.70/240.03	thf(decl_344, type, woz1_5: $o).
2.70/240.03	thf(decl_345, type, breln1: $i > $i > $o).
2.70/240.03	thf(decl_346, type, breln1all2: $o).
2.70/240.03	thf(decl_347, type, breln1Set: $i > $i).
2.70/240.03	thf(decl_348, type, breln1SetBreln1: $o).
2.70/240.03	thf(decl_354, type, reflwellordering: $i > $i > $o).
2.70/240.03	thf(decl_355, type, choice2fnsingleton: $o).
2.70/240.03	thf(decl_356, type, setOfPairsIsBReln1: $o).
2.70/240.03	thf(decl_357, type, breln1all1: $o).
2.70/240.03	thf(decl_358, type, subbreln1: $o).
2.70/240.03	thf(decl_359, type, eqbreln1: $o).
2.70/240.03	thf(decl_360, type, breln1invset: $i > $i > $i).
2.70/240.03	thf(decl_361, type, breln1invprop: $o).
2.70/240.03	thf(decl_362, type, breln1invI: $o).
2.70/240.03	thf(decl_363, type, breln1invE: $o).
2.70/240.03	thf(decl_364, type, breln1compset: $i > $i > $i > $i).
2.70/240.03	thf(decl_365, type, breln1compprop: $o).
2.70/240.03	thf(decl_366, type, breln1compI: $o).
2.70/240.03	thf(decl_367, type, breln1compE: $o).
2.70/240.03	thf(decl_368, type, breln1compEex: $o).
2.70/240.03	thf(decl_369, type, breln1unionprop: $o).
2.70/240.03	thf(decl_370, type, breln1unionIL: $o).
2.70/240.03	thf(decl_371, type, breln1unionIR: $o).
2.70/240.03	thf(decl_372, type, breln1unionI: $o).
2.70/240.03	thf(decl_373, type, epred1_0: $o).
2.70/240.03	thf(decl_374, type, esk1_2: $i > $i > $i).
2.70/240.03	thf(decl_375, type, esk2_2: $i > $i > $i).
2.70/240.03	thf(decl_376, type, esk3_2: $i > $i > $i).
2.70/240.03	thf(decl_377, type, esk4_1: $i > $i).
2.70/240.03	thf(decl_378, type, esk5_2: ($i > $i > $o) > $i > $i).
2.70/240.03	thf(decl_379, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
2.70/240.03	thf(decl_380, type, esk7_2: ($i > $i > $o) > $i > $i).
2.70/240.03	thf(decl_381, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
2.70/240.03	thf(decl_382, type, esk9_1: $i > $i).
2.70/240.03	thf(decl_383, type, esk10_2: ($i > $o) > $i > $i).
2.70/240.03	thf(decl_384, type, esk11_2: ($i > $o) > $i > $i).
2.70/240.03	thf(decl_385, type, esk12_1: ($i > $o) > $i).
2.70/240.03	thf(decl_386, type, esk13_2: ($i > $o) > $i > $i).
2.70/240.03	thf(decl_387, type, esk14_1: ($i > $o) > $i).
2.70/240.03	thf(decl_388, type, esk15_2: $i > $i > $i).
2.70/240.03	thf(decl_389, type, esk16_2: $i > $i > $i).
2.70/240.03	thf(decl_390, type, esk17_1: $i > $i).
2.70/240.03	thf(decl_391, type, esk18_1: $i > $i).
2.70/240.03	thf(decl_392, type, esk19_1: $i > $i).
2.70/240.03	thf(decl_393, type, esk20_2: $i > $i > $i).
2.70/240.03	thf(decl_394, type, esk21_3: $i > $i > $o > $i).
2.70/240.03	thf(decl_395, type, esk22_2: ($i > $o) > $i > $i).
2.70/240.03	thf(decl_396, type, esk23_1: ($i > $o) > $i).
2.70/240.03	thf(decl_397, type, esk24_1: $i > $i).
2.70/240.03	thf(decl_398, type, esk25_2: $i > ($i > $o) > $i).
2.70/240.03	thf(decl_399, type, esk26_2: $i > ($i > $o) > $i).
2.70/240.03	thf(decl_400, type, esk27_2: $i > ($i > $o) > $i).
2.70/240.03	thf(decl_401, type, esk28_2: $i > ($i > $o) > $i).
2.70/240.03	thf(decl_402, type, esk29_2: $i > ($i > $o) > $i).
2.70/240.03	thf(decl_403, type, esk30_2: $i > ($i > $o) > $i).
2.70/240.03	thf(decl_404, type, esk31_2: ($i > $o) > $i > $i).
2.70/240.03	thf(decl_405, type, esk32_1: ($i > $o) > $i).
2.70/240.03	thf(decl_406, type, esk33_1: ($i > $o) > $i).
2.70/240.03	thf(decl_407, type, esk34_1: ($i > $o) > $i).
2.70/240.03	thf(decl_408, type, esk35_1: ($i > $o) > $i).
2.70/240.03	thf(decl_409, type, esk36_2: ($i > $o) > $i > $i).
2.70/240.03	thf(decl_410, type, esk37_1: ($i > $o) > $i).
2.70/240.03	thf(decl_411, type, esk38_2: ($i > $o) > $i > $i).
2.70/240.03	thf(decl_412, type, esk39_2: ($i > $o) > ($i > $o) > $i).
2.70/240.03	thf(decl_413, type, esk40_2: ($i > $o) > ($i > $o) > $i).
2.70/240.03	thf(decl_414, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
2.70/240.03	thf(decl_415, type, esk42_2: ($i > $o) > ($i > $o) > $i).
2.70/240.03	thf(decl_416, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
2.70/240.03	thf(decl_417, type, esk44_2: ($i > $o) > ($i > $o) > $i).
2.70/240.03	thf(decl_418, type, esk45_2: ($i > $o) > $i > $i).
2.70/240.03	thf(decl_419, type, esk46_2: ($i > $o) > ($i > $o) > $i).
2.70/240.03	thf(decl_420, type, esk47_2: ($i > $o) > ($i > $o) > $i).
2.70/240.03	thf(decl_421, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
2.70/240.03	thf(decl_422, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
2.70/240.03	thf(decl_423, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
2.70/240.03	thf(decl_424, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
2.70/240.03	thf(decl_425, type, esk52_2: $i > $i > $i).
2.70/240.03	thf(decl_426, type, esk53_2: $i > $i > $i).
2.70/240.03	thf(decl_427, type, esk54_2: $i > $i > $i).
2.70/240.03	thf(decl_428, type, esk55_3: $i > $i > $i > $i).
2.70/240.03	thf(decl_429, type, esk56_3: $i > $i > $i > $i).
2.70/240.03	thf(decl_430, type, esk57_2: $i > $i > $i).
2.70/240.03	thf(decl_431, type, esk58_2: $i > ($i > $o) > $i).
2.70/240.03	thf(decl_432, type, esk59_2: $i > ($i > $o) > $i).
2.70/240.03	thf(decl_433, type, esk60_2: $i > ($i > $o) > $i).
2.70/240.03	thf(decl_434, type, esk61_3: $i > ($i > $o) > $i > $i).
2.70/240.03	thf(decl_435, type, esk62_2: $i > ($i > $o) > $i).
2.70/240.03	thf(decl_436, type, esk63_2: $i > ($i > $o) > $i).
2.70/240.03	thf(decl_437, type, esk64_3: $i > $i > ($i > $i) > $i).
2.70/240.03	thf(decl_438, type, esk65_3: $i > $i > ($i > $i) > $i).
2.70/240.03	thf(decl_439, type, esk66_3: $i > $i > ($i > $i) > $i).
2.70/240.03	thf(decl_440, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
2.70/240.03	thf(decl_441, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
2.70/240.03	thf(decl_442, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
2.70/240.03	thf(decl_443, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
2.70/240.03	thf(decl_444, type, esk71_4: $i > $i > $i > $i > $i).
2.70/240.03	thf(decl_445, type, esk72_4: $i > $i > $i > $i > $i).
2.70/240.03	thf(decl_446, type, esk73_4: $i > $i > $i > $i > $i).
2.70/240.03	thf(decl_447, type, esk74_4: $i > $i > $i > $i > $i).
2.70/240.03	thf(decl_448, type, esk75_4: $i > $i > $i > $i > $i).
2.70/240.03	thf(decl_449, type, esk76_4: $i > $i > $i > $i > $i).
2.70/240.03	thf(decl_450, type, esk77_4: $i > $i > $i > $i > $i).
2.70/240.03	thf(decl_451, type, esk78_4: $i > $i > $i > $i > $i).
2.70/240.03	thf(decl_452, type, esk79_4: $i > $i > $i > $i > $i).
2.70/240.03	thf(decl_453, type, esk80_3: $i > $i > ($i > $i) > $i).
2.70/240.03	thf(decl_454, type, esk81_3: $i > $i > ($i > $i) > $i).
2.70/240.03	thf(decl_455, type, esk82_3: $i > $i > ($i > $i) > $i).
2.70/240.03	thf(decl_456, type, esk83_3: $i > $i > $i > $i).
2.70/240.03	thf(decl_457, type, esk84_3: $i > $i > $i > $i).
2.70/240.03	thf(decl_458, type, esk85_3: $i > $i > $i > $i).
2.70/240.03	thf(decl_459, type, esk86_3: $i > $i > $i > $i).
2.70/240.03	thf(decl_460, type, esk87_3: $i > $i > ($i > $o) > $i).
2.70/240.03	thf(decl_461, type, esk88_3: $i > $i > ($i > $o) > $i).
2.70/240.03	thf(decl_462, type, esk89_3: $i > $i > ($i > $i > $o) > $i).
2.70/240.03	thf(decl_463, type, esk90_3: $i > $i > ($i > $o) > $i).
2.70/240.03	thf(decl_464, type, esk91_3: $i > $i > ($i > $o) > $i).
2.70/240.03	thf(decl_465, type, esk92_3: $i > $i > $i > $i).
2.70/240.03	thf(decl_466, type, esk93_3: $i > $i > $i > $i).
2.70/240.03	thf(decl_467, type, esk94_3: $i > $i > $i > $i).
2.70/240.03	thf(decl_468, type, esk95_3: $i > $i > $i > $i).
2.70/240.03	thf(decl_469, type, esk96_3: $i > $i > $i > $i).
2.70/240.03	thf(decl_470, type, esk97_3: $i > $i > $i > $i).
2.70/240.03	thf(decl_471, type, esk98_5: $i > $i > $i > $i > $i > $i).
2.70/240.03	thf(decl_472, type, esk99_6: $i > $i > $i > $i > $i > $o > $i).
2.70/240.03	thf(decl_473, type, esk100_0: $i).
2.70/240.03	thf(decl_474, type, esk101_0: $i).
2.70/240.03	thf(decl_475, type, esk102_0: $i).
2.70/240.03	thf(decl_476, type, esk103_0: $i).
2.70/240.03	thf(decl_477, type, esk104_0: $i).
2.70/240.03	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', descr__Cong)).
2.70/240.03	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', exu)).
2.70/240.03	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', exu__Cong)).
2.70/240.03	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', exuE2)).
2.70/240.03	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', nonempty)).
2.70/240.03	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', nonemptyI)).
2.70/240.03	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', exuE3e)).
2.70/240.03	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', exuE1)).
2.70/240.03	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', descrp)).
2.70/240.03	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', exuEu)).
2.70/240.03	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', exuE3u)).
2.70/240.03	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', exuI2)).
2.70/240.03	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', exuI3)).
2.70/240.03	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', exuI1)).
2.70/240.03	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', replAx)).
2.70/240.03	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', sepSubset)).
2.70/240.03	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', nonemptyI1)).
2.70/240.03	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setbeta)).
2.70/240.03	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', singletonprop)).
2.70/240.03	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', ex1E1)).
2.70/240.03	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', dsetconstrER)).
2.70/240.03	thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', ex1I)).
2.70/240.03	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', dsetconstrEL)).
2.70/240.03	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', ex1I2)).
2.70/240.03	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', kfstsingleton)).
2.70/240.03	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', ksndsingleton)).
2.70/240.03	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', dpsetconstrI)).
2.70/240.03	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', dpsetconstrERa)).
2.70/240.03	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', dpsetconstrEL2)).
2.70/240.03	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', dpsetconstrER)).
2.70/240.03	thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', lamProp)).
2.70/240.03	thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', lamp)).
2.70/240.03	thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', beta1)).
2.70/240.03	thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', eta1)).
2.70/240.03	thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', lam2lamEq)).
2.70/240.03	thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', eta2)).
2.70/240.03	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', iftrueProp2)).
2.70/240.03	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', ifSingleton)).
2.70/240.03	thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', beta2)).
2.70/240.03	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', ex1E2)).
2.70/240.03	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', lam2p)).
2.70/240.03	thf(choice2fnsingleton, axiom, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:(((X52 @ X2 @ X3)&![X14:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ X3 @ X14) @ X33))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', choice2fnsingleton)).
2.70/240.03	thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setOfPairsIsBReln1)).
2.70/240.03	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', iftrueProp1)).
2.70/240.03	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', iffalseProp2)).
2.70/240.03	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', iffalseProp1)).
2.70/240.03	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', apProp)).
2.70/240.03	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', funcImageSingleton)).
2.70/240.03	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', dpsetconstrEL1)).
2.70/240.03	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setOfPairsIsBReln)).
2.70/240.03	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', dpsetconstrSub)).
2.70/240.03	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', sepInPowerset)).
2.70/240.03	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', dsetconstr__Cong)).
2.70/240.03	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', emptyE1)).
2.70/240.03	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', nonemptyImpWitness)).
2.70/240.03	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setoftrueEq)).
2.70/240.03	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', nonemptyE1)).
2.70/240.03	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', dsetconstrI)).
2.70/240.03	thf(breln1unionE, conjecture, (((((powersetAx)=>(((omega0Ax)=>(((omegaIndAx)=>((replAx)=>(((((dsetconstrI)=>(((((prop2setE)=>((emptysetE)=>(((notinemptyset)=>((((emptyI)=>((((nonemptyE1)=>(((((emptyinunitempty)=>((((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>(((emptyInPowerset)=>((powersetE)=>((((((nonemptyImpWitness)=>((uniqinunit)=>(((eqinunit)=>((singletonsswitch)=>((upairsetE)=>(((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>(((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>(((in__Cong)=>((exuE3u)=>(((((powerset__Cong)=>(((omega__Cong)=>((exuEu)=>(((dsetconstr__Cong)=>((((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>(((((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>(((powersetI1)=>((powersetE1)=>(((powersetsubset)=>((sepInPowerset)=>(((binunionIL)=>(((((binunionE)=>(((binunionRsub)=>((binintersectI)=>((((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((((binintersectSubset4)=>((binintersectSubset1)=>((((setminusEL)=>((setminusER)=>((((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>(((symdiffI1)=>((((symdiffIneg2)=>((((setukpairIR)=>(((kpairp)=>((((singletoninpowunion)=>(((((ubforcartprodlem1)=>((((cartprodpairin)=>(((cartprodmempair)=>(((setunionsingleton1)=>((((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>(((setukpairinjL1)=>((kfstsingleton)=>(((((setukpairinjL2)=>((((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>(((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((((cartprodfstpairEq)=>((cartprodsndpairEq)=>(((dpsetconstrI)=>((((dpsetconstrERa)=>(((dpsetconstrEL2)=>((dpsetconstrER)=>((((app)=>(((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>(((brelnall1)=>((brelnall2)=>(((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>(((((eqbreln)=>((funcext)=>(((ap2apEq1)=>(((beta1)=>((eta1)=>((lam2lamEq)=>(((eta2)=>(((((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>(((setminusT_lem)=>((((subsetTI)=>((powersetTI1)=>((((complementTE1)=>((binintersectTELcontra)=>(((((contrasubsetT2)=>(((doubleComplementI1)=>(((doubleComplementSub1)=>((doubleComplementSub2)=>(((complementTnotintersectT)=>(((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>(((binunionTIRcontra)=>(((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((((binunionTE)=>(((demorgan2a1)=>(((((demorgan1b)=>(((((((woz13rule0)=>((woz13rule1)=>(((((woz1_1)=>(((woz1_3)=>((((((choice2fnsingleton)=>((((((breln1invprop)=>((breln1invI)=>(((breln1compprop)=>(((breln1compE)=>((breln1compEex)=>(((((breln1unionI)=>![X4:$i, X33:$i]:((![X35:$i]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(((in @ (kpair @ X2 @ X3) @ X35)|(in @ (kpair @ X2 @ X3) @ X33))<=(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))<=(breln1 @ X4 @ X35)))<=(breln1 @ X4 @ X33))))<=(breln1unionIR))<=(breln1unionIL))<=(breln1unionprop))))<=(breln1compI)))<=(breln1invE))))<=(eqbreln1))<=(subbreln1))<=(breln1all1))<=(setOfPairsIsBReln1)))<=(breln1SetBreln1))<=(breln1all2))<=(woz1_5))<=(woz1_4)))<=(woz1_2)))<=(woz13rule4))<=(woz13rule3))<=(woz13rule2))))<=(demorgan2))<=(demorgan2b))<=(demorgan2b2))<=(demorgan2a))<=(demorgan1)))<=(demorgan1a))<=(demorgan2a2))<=(complementUnionInPowersetComplement)))<=(binunionTEcontra)))<=(inComplementUnionImpInComplement1))<=(inComplementUnionImpNotIn1)))))<=(inIntersectImpInUnion)))<=(binunionTILcontra))))))<=(complementImpComplementIntersect)))<=(doubleComplementEq))))<=(doubleComplementE1)))<=(contrasubsetT3)))<=(contrasubsetT1))<=(contrasubsetT))<=(binintersectTERcontra))))<=(complementTI1))<=(powersetTE1))))<=(setextT))<=(complementT_lem)))<=(powersetT_lem)))))))))))<=(iftrueProp1))<=(iffalseProp2))<=(iffalseProp1)))<=(beta2)))))<=(ap2apEq2)))<=(funcext2))))<=(subbreln))<=(funcGraphProp4))<=(funcextLem)))))<=(ex1E2))))<=(lam2p))))))<=(infuncsetfunc)))<=(apProp))<=(funcImageSingleton))))<=(dpsetconstrEL1)))<=(setOfPairsIsBReln))<=(dpsetconstrSub)))<=(cartprodpairsurjEq))))<=(cartprodmempaircEq))<=(cartprodpairmemER)))))<=(ksndpairEq))))))))<=(setukpairinjR11))<=(setukpairinjL)))<=(cartprodfstin))<=(kfstpairEq))<=(theprop))))<=(singletonsuniq))))))<=(setunionsingleton))<=(setunionsingleton2)))<=(setunionE2)))<=(cartprodmempair1)))<=(ubforcartprodlem3))<=(ubforcartprodlem2)))<=(upairinpowunion))<=(upairsubunion))<=(upairset2E)))<=(singletoninpowerset))<=(singletonsubset)))<=(kpairiskpair)))<=(setukpairIL))<=(secondinupair)))<=(symdiffIneg1))<=(symdiffI2)))<=(symdiffE)))))))<=(setminusERneg))<=(setminusSubset2))))<=(setminusI))<=(bs114d))))<=(binintersectRsub))<=(disjointsetsI1))))))<=(binintersectEL))<=(binintersectSubset5))))<=(binunionLsub)))<=(binunionEcases))<=(binunionIR))<=(upairset2IR)))<=(sepSubset))))<=(inPowerset))))<=(subsetemptysetimpeq))))))<=(subsetTrans))<=(subsetRefl))<=(notequalI2)))))))))<=(eqimpsubset2))<=(subsetI1)))<=(descr__Cong))))<=(setunion__Cong)))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong))))<=(inCongP))))))))<=(prop2setI)))))))))<=(upairsetIL)))))<=(notinsingleton))))<=(exuE2))<=(subPowSU))<=(setunionE))<=(setunionI))))<=(emptyinPowerset)))))<=(setadjoinE))<=(setadjoinIR)))<=(setadjoinIL))<=(nonemptyI1))<=(nonemptyI)))<=(setbeta))<=(noeltsimpempty)))<=(setext))<=(exuE3e)))<=(emptysetimpfalse))))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL)))<=(descrp))<=(wellorderingAx))<=(foundationAx))))<=(omegaSAx)))<=(setunionAx)))<=(setadjoinAx))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', breln1unionE)).
2.70/240.03	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setextAx)).
2.70/240.03	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binunionLsub)).
2.70/240.03	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setminusER)).
2.70/240.03	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binunionEcases)).
2.70/240.03	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setminusLsub)).
2.70/240.03	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binunionIR)).
2.70/240.03	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', upairset2IR)).
2.70/240.03	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setminusSubset1)).
2.70/240.03	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', inPowerset)).
2.70/240.03	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', subsetemptysetimpeq)).
2.70/240.03	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', symdiffI1)).
2.70/240.03	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', subsetTrans)).
2.70/240.03	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', subsetRefl)).
2.70/240.03	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', notequalI2)).
2.70/240.03	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', symdiffIneg2)).
2.70/240.03	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', eqimpsubset2)).
2.70/240.03	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', subsetI1)).
2.70/240.03	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setukpairIR)).
2.70/240.03	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setunion__Cong)).
2.70/240.03	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setadjoin__Cong)).
2.70/240.03	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', emptyset__Cong)).
2.70/240.03	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', kpairp)).
2.70/240.03	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', inCongP)).
2.70/240.03	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', singletoninpowunion)).
2.70/240.03	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', prop2setI)).
2.70/240.03	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setukpairinjR2)).
2.70/240.03	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', upairsetIL)).
2.70/240.03	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', notinsingleton)).
2.70/240.03	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setminusELneg)).
2.70/240.03	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', ubforcartprodlem1)).
2.70/240.03	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', subPowSU)).
2.70/240.03	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setunionE)).
2.70/240.03	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', cartprodpairin)).
2.70/240.03	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setunionI)).
2.70/240.03	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', emptyinPowerset)).
2.70/240.03	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setadjoinE)).
2.70/240.03	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setadjoinIR)).
2.70/240.03	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', cartprodmempair)).
2.70/240.03	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setadjoinIL)).
2.70/240.03	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setunionsingleton1)).
2.70/240.03	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', noeltsimpempty)).
2.70/240.03	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setext)).
2.70/240.03	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', emptysetimpfalse)).
2.70/240.03	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', wellorderingAx)).
2.70/240.03	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', foundationAx)).
2.70/240.03	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setminusILneg)).
2.70/240.03	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', omegaSAx)).
2.70/240.03	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setunionAx)).
2.70/240.03	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setukpairinjL1)).
2.70/240.03	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setadjoinAx)).
2.70/240.03	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', emptysetAx)).
2.70/240.03	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setukpairinjL2)).
2.70/240.03	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setukpairinjR12)).
2.70/240.03	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setukpairinjR1)).
2.70/240.03	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', upairequniteq)).
2.70/240.03	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', theeq)).
2.70/240.03	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', iftrue)).
2.70/240.03	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setukpairinjR)).
2.70/240.03	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', kpairsurjEq)).
2.70/240.03	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', cartprodsndin)).
2.70/240.03	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', cartprodpairmemEL)).
2.70/240.03	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', cartprodfstpairEq)).
2.70/240.03	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', cartprodsndpairEq)).
2.70/240.03	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setminusIRneg)).
2.70/240.03	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', app)).
2.70/240.03	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', ap2p)).
2.70/240.03	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', funcinfuncset)).
2.70/240.03	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', brelnall1)).
2.70/240.03	thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', brelnall2)).
2.70/240.03	thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', funcGraphProp1)).
2.70/240.03	thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', funcGraphProp3)).
2.70/240.03	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', funcGraphProp2)).
2.70/240.03	thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', eqbreln)).
2.70/240.03	thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', funcext)).
2.70/240.03	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', ap2apEq1)).
2.70/240.03	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', ifp)).
2.70/240.03	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', ap2apEq2)).
2.70/240.03	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', funcext2)).
2.70/240.03	thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', subbreln)).
2.70/240.03	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', funcGraphProp4)).
2.70/240.03	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', funcextLem)).
2.70/240.03	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', iffalse)).
2.70/240.03	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', iftrueorfalse)).
2.70/240.03	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binintersectT_lem)).
2.70/240.03	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binunionT_lem)).
2.70/240.03	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setminusT_lem)).
2.70/240.03	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', subsetTI)).
2.70/240.03	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', powersetTI1)).
2.70/240.03	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', complementTE1)).
2.70/240.03	thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binintersectTELcontra)).
2.70/240.03	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', contrasubsetT2)).
2.70/240.03	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', doubleComplementI1)).
2.70/240.03	thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', doubleComplementSub1)).
2.70/240.03	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', doubleComplementSub2)).
2.70/240.03	thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', complementTnotintersectT)).
2.70/240.03	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', complementSubsetComplementIntersect)).
2.70/240.03	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', complementInPowersetComplementIntersect)).
2.70/240.03	thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', contraSubsetComplement)).
2.70/240.03	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', complementTcontraSubset)).
2.70/240.03	thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binunionTIRcontra)).
2.70/240.03	thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', inIntersectImpInUnion2)).
2.70/240.03	thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$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/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', inIntersectImpInIntersectUnions)).
2.70/240.03	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/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', intersectInPowersetIntersectUnions)).
2.70/240.03	thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binunionTE)).
2.70/240.03	thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', demorgan2a1)).
2.70/240.03	thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', demorgan1b)).
2.70/240.03	thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', woz13rule0)).
2.70/240.03	thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', woz13rule1)).
2.70/240.03	thf(woz1_1, axiom, ((woz1_1)<=>![X4:$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/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', woz1_1)).
2.70/240.03	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/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', woz1_3)).
2.70/240.03	thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', breln1invprop)).
2.70/240.03	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/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', breln1invI)).
2.70/240.03	thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', breln1compprop)).
2.70/240.03	thf(breln1compE, axiom, ((breln1compE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', breln1compE)).
2.70/240.03	thf(breln1compEex, axiom, ((breln1compEex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>![X54:$o]:((![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(X54)))))=>(X54))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', breln1compEex)).
2.70/240.03	thf(breln1unionI, axiom, ((breln1unionI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35))=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', breln1unionI)).
2.70/240.03	thf(breln1unionIR, axiom, ((breln1unionIR)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', breln1unionIR)).
2.70/240.03	thf(breln1unionIL, axiom, ((breln1unionIL)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', breln1unionIL)).
2.70/240.03	thf(breln1unionprop, axiom, ((breln1unionprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', breln1unionprop)).
2.70/240.03	thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', breln1compI)).
2.70/240.03	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/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', breln1invE)).
2.70/240.03	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:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', eqbreln1)).
2.70/240.03	thf(subbreln1, axiom, ((subbreln1)<=>![X4:$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/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', subbreln1)).
2.70/240.03	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/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', breln1all1)).
2.70/240.03	thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', breln1SetBreln1)).
2.70/240.03	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/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', breln1all2)).
2.70/240.03	thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', woz1_5)).
2.70/240.03	thf(woz1_4, axiom, ((woz1_4)<=>![X4:$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/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', woz1_4)).
2.70/240.03	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:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', woz1_2)).
2.70/240.03	thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$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/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', woz13rule4)).
2.70/240.03	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/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', woz13rule3)).
2.70/240.03	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/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', woz13rule2)).
2.70/240.03	thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', demorgan2)).
2.70/240.03	thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', demorgan2b)).
2.70/240.03	thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', demorgan2b2)).
2.70/240.03	thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', demorgan2a)).
2.70/240.03	thf(demorgan1, axiom, ((demorgan1)<=>![X4:$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/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', demorgan1)).
2.70/240.03	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/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', demorgan1a)).
2.70/240.03	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/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', demorgan2a2)).
2.70/240.03	thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', complementUnionInPowersetComplement)).
2.70/240.03	thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binunionTEcontra)).
2.70/240.03	thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', inComplementUnionImpInComplement1)).
2.70/240.03	thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', inComplementUnionImpNotIn1)).
2.70/240.03	thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', inIntersectImpInUnion)).
2.70/240.03	thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binunionTILcontra)).
2.70/240.03	thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', complementImpComplementIntersect)).
2.70/240.03	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', doubleComplementEq)).
2.70/240.03	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', doubleComplementE1)).
2.70/240.03	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', contrasubsetT3)).
2.70/240.03	thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', contrasubsetT1)).
2.70/240.03	thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', contrasubsetT)).
2.70/240.03	thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binintersectTERcontra)).
2.70/240.03	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', complementTI1)).
2.70/240.03	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', powersetTE1)).
2.70/240.03	thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setextT)).
2.70/240.03	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', complementT_lem)).
2.70/240.03	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', powersetT_lem)).
2.70/240.03	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', infuncsetfunc)).
2.70/240.03	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', cartprodpairsurjEq)).
2.70/240.03	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', cartprodmempaircEq)).
2.70/240.03	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', cartprodpairmemER)).
2.70/240.03	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', ksndpairEq)).
2.70/240.03	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setukpairinjR11)).
2.70/240.03	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setukpairinjL)).
2.70/240.03	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', cartprodfstin)).
2.70/240.03	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', kfstpairEq)).
2.70/240.03	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', theprop)).
2.70/240.03	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', singletonsuniq)).
2.70/240.03	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setunionsingleton)).
2.70/240.03	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setunionsingleton2)).
2.70/240.03	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setunionE2)).
2.70/240.03	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', cartprodmempair1)).
2.70/240.03	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', ubforcartprodlem3)).
2.70/240.03	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', ubforcartprodlem2)).
2.70/240.03	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', upairinpowunion)).
2.70/240.03	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', upairsubunion)).
2.70/240.03	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', upairset2E)).
2.70/240.03	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', singletoninpowerset)).
2.70/240.03	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', singletonsubset)).
2.70/240.03	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', kpairiskpair)).
2.70/240.03	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setukpairIL)).
2.70/240.03	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', secondinupair)).
2.70/240.03	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', symdiffIneg1)).
2.70/240.03	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', symdiffI2)).
2.70/240.03	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', symdiffE)).
2.70/240.03	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setminusERneg)).
2.70/240.03	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setminusSubset2)).
2.70/240.03	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setminusI)).
2.70/240.03	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', bs114d)).
2.70/240.03	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binintersectRsub)).
2.70/240.03	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', disjointsetsI1)).
2.70/240.03	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binintersectEL)).
2.70/240.03	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binintersectSubset5)).
2.70/240.03	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setminusEL)).
2.70/240.03	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binintersectSubset1)).
2.70/240.03	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binintersectSubset4)).
2.70/240.03	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binintersectER)).
2.70/240.03	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binintersectSubset3)).
2.70/240.03	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binintersectSubset2)).
2.70/240.03	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binintersectLsub)).
2.70/240.03	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binintersectI)).
2.70/240.03	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binunionRsub)).
2.70/240.03	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binunionE)).
2.70/240.03	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', binunionIL)).
2.70/240.03	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', powersetsubset)).
2.70/240.03	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', powersetE1)).
2.70/240.03	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', powersetI1)).
2.70/240.03	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setextsub)).
2.70/240.03	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', subset2powerset)).
2.70/240.03	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setadjoinSub2)).
2.70/240.03	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setadjoinSub)).
2.70/240.03	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', notequalI1)).
2.70/240.03	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', notsubsetI)).
2.70/240.03	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', subsetE2)).
2.70/240.03	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', subsetE)).
2.70/240.03	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', emptysetsubset)).
2.70/240.03	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', subsetI2)).
2.70/240.03	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', eqimpsubset1)).
2.70/240.03	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', omega__Cong)).
2.70/240.03	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', powerset__Cong)).
2.70/240.03	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', in__Cong)).
2.70/240.03	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', notdallE)).
2.70/240.03	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', notdexE)).
2.70/240.03	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', prop2set2propI)).
2.70/240.03	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', quantDeMorgan4)).
2.70/240.03	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', quantDeMorgan3)).
2.70/240.03	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', quantDeMorgan2)).
2.70/240.03	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', quantDeMorgan1)).
2.70/240.03	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', vacuousDall)).
2.70/240.03	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', upairsetIR)).
2.70/240.03	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', upairsetE)).
2.70/240.03	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', singletonsswitch)).
2.70/240.03	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', eqinunit)).
2.70/240.03	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', uniqinunit)).
2.70/240.03	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', powersetE)).
2.70/240.03	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', emptyInPowerset)).
2.70/240.03	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', powersetI)).
2.70/240.03	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', setadjoinOr)).
2.70/240.03	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', emptyinunitempty)).
2.70/240.03	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', emptyI)).
2.70/240.03	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', notinemptyset)).
2.70/240.03	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', emptysetE)).
2.70/240.03	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', prop2setE)).
2.70/240.03	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', omegaIndAx)).
2.70/240.03	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', omega0Ax)).
2.70/240.03	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.i1Mz9x1csh/E---3.1_5990.p', powersetAx)).
2.70/240.03	thf(c_0_305, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
2.70/240.03	thf(c_0_306, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
2.70/240.03	thf(c_0_307, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
2.70/240.03	thf(c_0_308, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
2.70/240.03	thf(c_0_309, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
2.70/240.03	thf(c_0_310, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
2.70/240.03	thf(c_0_311, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
2.70/240.03	thf(c_0_312, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
2.70/240.03	thf(c_0_313, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
2.70/240.03	thf(c_0_314, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
2.70/240.03	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])).
2.70/240.03	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])).
2.70/240.03	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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
2.70/240.03	thf(c_0_318, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
2.70/240.03	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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
2.70/240.03	thf(c_0_320, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
2.70/240.03	thf(c_0_321, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1076:$i]:((((X1 @ X1076))&![X1077:$i]:((((X1 @ X1077))=>((X1076)=(X1077)))))))=>((?[X1078:$i]:((((X17 @ X1078))&![X1079:$i]:((((X17 @ X1079))=>((X1078)=(X1079)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_305, c_0_306])).
2.70/240.03	thf(c_0_322, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1070:$i]:((((X1 @ X1070))&![X1071:$i]:((((X1 @ X1071))=>((X1070)=(X1071)))))))<=>(?[X1072:$i]:((((X17 @ X1072))&![X1073:$i]:((((X17 @ X1073))=>((X1072)=(X1073)))))))))))), inference(apply_def,[status(thm)],[c_0_307, c_0_306])).
2.70/240.03	thf(c_0_323, plain, ((exuE2)=(![X1:$i > $o]:(((?[X1060:$i]:((((X1 @ X1060))&![X1061:$i]:((((X1 @ X1061))=>((X1060)=(X1061)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_308, c_0_306])).
2.70/240.03	thf(c_0_324, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_309])).
2.70/240.03	thf(c_0_325, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_310, c_0_309])).
2.70/240.03	thf(c_0_326, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
2.70/240.03	thf(c_0_327, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
2.70/240.03	thf(c_0_328, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X1058:$i]:((((X1 @ X1058))&![X1059:$i]:((((X1 @ X1059))=>((X1058)=(X1059)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_311, c_0_306])).
2.70/240.03	thf(c_0_329, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
2.70/240.03	thf(c_0_330, plain, ((exuE1)=(![X1:$i > $o]:(((?[X1056:$i]:((((X1 @ X1056))&![X1057:$i]:((((X1 @ X1057))=>((X1056)=(X1057)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_312, c_0_306])).
2.70/240.03	thf(c_0_331, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
2.70/240.03	thf(c_0_332, plain, ((ex1I)<=>![X4:$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])).
2.70/240.03	thf(c_0_333, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
2.70/240.03	thf(c_0_334, plain, ((descrp)=(![X1:$i > $o]:(((?[X1054:$i]:((((X1 @ X1054))&![X1055:$i]:((((X1 @ X1055))=>((X1054)=(X1055)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_313, c_0_306])).
2.70/240.03	thf(c_0_335, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
2.70/240.03	thf(c_0_336, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
2.70/240.03	thf(c_0_337, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
2.70/240.03	thf(c_0_338, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
2.70/240.03	thf(c_0_339, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
2.70/240.03	thf(c_0_340, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
2.70/240.03	thf(c_0_341, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
2.70/240.03	thf(c_0_342, plain, ((lamProp)<=>![X4:$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])).
2.70/240.03	thf(c_0_343, 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 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
2.70/240.03	thf(c_0_344, plain, ((beta1)<=>![X4:$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])).
2.70/240.03	thf(c_0_345, 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])).
2.70/240.03	thf(c_0_346, 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])).
2.70/240.03	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])).
2.70/240.03	thf(c_0_348, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
2.70/240.03	thf(c_0_349, plain, ((ifSingleton)<=>![X4:$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])).
2.70/240.03	thf(c_0_350, 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])).
2.70/240.03	thf(c_0_351, 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])).
2.70/240.03	thf(c_0_352, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
2.70/240.03	thf(c_0_353, plain, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 8 */:$i]:(((X52 @ X2 @ Z0)&![X14:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ Z0 @ X14) @ X33))))))))))))))))), inference(fof_simplification,[status(thm)],[choice2fnsingleton])).
2.70/240.03	thf(c_0_354, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
2.70/240.03	thf(c_0_355, plain, ((iftrueProp1)<=>![X4:$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])).
2.70/240.03	thf(c_0_356, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
2.70/240.03	thf(c_0_357, plain, ((iffalseProp1)<=>![X4:$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])).
2.70/240.03	thf(c_0_358, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
2.70/240.03	thf(c_0_359, plain, ((funcImageSingleton)<=>![X4:$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])).
2.70/240.03	thf(c_0_360, 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:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
2.70/240.03	thf(c_0_361, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
2.70/240.03	thf(c_0_362, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
2.70/240.03	thf(c_0_363, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
2.70/240.03	thf(c_0_364, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
2.70/240.03	thf(c_0_365, plain, ((exuEu)=(![X1:$i > $o]:(((?[X1074:$i]:((((X1 @ X1074))&![X1075:$i]:((((X1 @ X1075))=>((X1074)=(X1075)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_314, c_0_306])).
2.70/240.03	thf(c_0_366, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X1068:$i]:((((X1 @ X1068))&![X1069:$i]:((((X1 @ X1069))=>((X1068)=(X1069)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_315, c_0_306])).
2.70/240.03	thf(c_0_367, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X1066:$i]:((((X1 @ X1066))&![X1067:$i]:((((X1 @ X1067))=>((X1066)=(X1067))))))))))), inference(apply_def,[status(thm)],[c_0_316, c_0_306])).
2.70/240.03	thf(c_0_368, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X1064:$i]:((((X1 @ X1064))&![X1065:$i]:((((X1 @ X1065))=>((X1064)=(X1065)))))))))))), inference(apply_def,[status(thm)],[c_0_317, c_0_306])).
2.70/240.03	thf(c_0_369, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X1062:$i]:((((X1 @ X1062))&![X1063:$i]:((((X1 @ X1063))=>((X1062)=(X1063))))))))))), inference(apply_def,[status(thm)],[c_0_318, c_0_306])).
2.70/240.03	thf(c_0_370, plain, ((emptyE1)<=>![X4:$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])).
2.70/240.03	thf(c_0_371, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_309])).
2.70/240.03	thf(c_0_372, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
2.70/240.03	thf(c_0_373, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_309])).
2.70/240.03	thf(c_0_374, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
2.70/240.03	thf(c_0_375, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X1052:$i]:((((X6 @ X2 @ X1052))&![X1053:$i]:((((X6 @ X2 @ X1053))=>((X1052)=(X1053)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_319, c_0_306])).
2.70/240.03	thf(c_0_376, plain, ((epred1_0)<=>![X2067:$i]:(?[X2068:$i]:((((![X2069:$i]:(((in @ X2069 @ X2068)=>![X2070:$i]:(((in @ X2070 @ X2069)=>(in @ X2070 @ X2067)))))&![X2071:$i, X2072:$i]:((((in @ X2071 @ X2067)&(in @ X2072 @ X2067))=>(![X2073:$i]:(((in @ X2073 @ X2068)=>((in @ X2071 @ X2073)<=>(in @ X2072 @ X2073))))=>((X2071)=(X2072))))))&![X2074:$i, X2075:$i]:((((in @ X2074 @ X2068)&(in @ X2075 @ X2068))=>(![X2076:$i]:(((in @ X2076 @ X2074)=>(in @ X2076 @ X2075)))|![X2077:$i]:(((in @ X2077 @ X2075)=>(in @ X2077 @ X2074)))))))&![X2078:$i]:(((![X2079:$i]:(((in @ X2079 @ X2078)=>(in @ X2079 @ X2067)))&?[X2080:$i]:((in @ X2080 @ X2078)))=>?[X2081:$i, X2082:$i]:(((((in @ X2081 @ X2068)&(in @ X2082 @ X2078))&~(?[X2083:$i]:(((in @ X2083 @ X2081)&(in @ X2083 @ X2078)))))&![X2084:$i]:(((in @ X2084 @ X2068)=>(![X2085:$i]:(((in @ X2085 @ X2084)=>(in @ X2085 @ X2081)))|(in @ X2082 @ X2084)))))))))))), introduced(definition)).
2.70/240.03	thf(c_0_377, negated_conjecture, ~((![X2098:$i, X2099:$i]:((![X2100:$i]:(((in @ X2100 @ X2098)<=>(in @ X2100 @ X2099)))=>((X2098)=(X2099))))=>(![X2097:$i]:(~(in @ X2097 @ emptyset))=>(![X2094:$i, X2095:$i, X2096:$i]:(((in @ X2096 @ (setadjoin @ X2094 @ X2095))<=>(((X2096)=(X2094))|(in @ X2096 @ X2095))))=>(![X1080:$i, X1081:$i]:(((in @ X1081 @ (powerset @ X1080))<=>![X1082:$i]:(((in @ X1082 @ X1081)=>(in @ X1082 @ X1080)))))=>(![X2091:$i, X2092:$i]:(((in @ X2092 @ (setunion @ X2091))<=>?[X2093:$i]:(((in @ X2092 @ X2093)&(in @ X2093 @ X2091)))))=>((in @ emptyset @ omega)=>(![X2090:$i]:(((in @ X2090 @ omega)=>(in @ (setadjoin @ X2090 @ X2090) @ omega)))=>(![X1083:$i]:((((in @ emptyset @ X1083)&![X1084:$i]:((((in @ X1084 @ omega)&(in @ X1084 @ X1083))=>(in @ (setadjoin @ X1084 @ X1084) @ X1083))))=>![X1085:$i]:(((in @ X1085 @ omega)=>(in @ X1085 @ X1083)))))=>(![X1086:$i > $i > $o, X1087:$i]:((![X1088:$i]:(((in @ X1088 @ X1087)=>?[X1089:$i]:(((X1086 @ X1088 @ X1089)&![X1090:$i]:(((X1086 @ X1088 @ X1090)=>((X1089)=(X1090))))))))=>?[X1091:$i]:(![X1092:$i]:(((in @ X1092 @ X1091)<=>?[X1093:$i]:(((in @ X1093 @ X1087)&(X1086 @ X1093 @ X1092))))))))=>(![X2086:$i]:((?[X2087:$i]:((in @ X2087 @ X2086))=>?[X2088:$i]:(((in @ X2088 @ X2086)&~(?[X2089:$i]:(((in @ X2089 @ X2088)&(in @ X2089 @ X2086))))))))=>((epred1_0)=>(![X2064:$i > $o]:((?[X2065:$i]:(((X2064 @ X2065)&![X2066:$i]:(((X2064 @ X2066)=>((X2065)=(X2066))))))=>(X2064 @ (descr @ (^[Z0/* 17 */:$i]:(X2064 @ Z0))))))=>(![X1094:$i, X1095:$i > $o, X1096:$i]:(((in @ X1096 @ X1094)=>((X1095 @ X1096)=>(in @ X1096 @ (dsetconstr @ X1094 @ X1095)))))=>(![X2061:$i, X2062:$i > $o, X2063:$i]:(((in @ X2063 @ (dsetconstr @ X2061 @ X2062))=>(in @ X2063 @ X2061)))=>(![X2058:$i, X2059:$i > $o, X2060:$i]:(((in @ X2060 @ (dsetconstr @ X2058 @ X2059))=>(X2059 @ X2060)))=>(![X2053:$i > $o]:((?[X2054:$i]:(((X2053 @ X2054)&![X2055:$i]:(((X2053 @ X2055)=>((X2054)=(X2055))))))=>?[X2056:$i]:(((X2053 @ X2056)&![X2057:$i]:(((X2053 @ X2057)=>((X2056)=(X2057))))))))=>(![X1097:$o, X1098:$i]:(((in @ X1098 @ (prop2set @ ((X1097))))=>(X1097)))=>(![X1099:$i]:(((in @ X1099 @ emptyset)=>![X1100:$o]:((X1100))))=>(![X2052:$i]:(((in @ X2052 @ emptyset)=>~($true)))=>(![X1101:$i]:(~(in @ X1101 @ emptyset))=>(![X2048:$i > $o]:((?[X2049:$i]:(((X2048 @ X2049)&![X2050:$i]:(((X2048 @ X2050)=>((X2049)=(X2050))))))=>?[X2051:$i]:((X2048 @ X2051))))=>(![X2044:$i, X2045:$i]:((![X2046:$i]:(((in @ X2046 @ X2044)=>(in @ X2046 @ X2045)))=>(![X2047:$i]:(((in @ X2047 @ X2045)=>(in @ X2047 @ X2044)))=>((X2044)=(X2045)))))=>(![X1102:$i]:((![X1103:$i]:(~(in @ X1103 @ X1102))=>((X1102)=(emptyset))))=>(![X2042:$i]:((![X2043:$i]:(~(in @ X2043 @ X2042))=>((X2042)=(emptyset))))=>(![X2039:$i, X2040:$i > $o, X2041:$i]:(((in @ X2041 @ X2039)=>((in @ X2041 @ (dsetconstr @ X2039 @ X2040))<=>(X2040 @ X2041))))=>(![X1104:$i]:((((X1104)!=(emptyset))=>?[X1105:$i]:((in @ X1105 @ X1104))))=>(![X2036:$i, X2037:$i > $o, X2038:$i]:(((in @ X2038 @ X2036)=>((X2037 @ X2038)=>((dsetconstr @ X2036 @ X2037)!=(emptyset)))))=>(![X2034:$i]:((?[X2035:$i]:((in @ X2035 @ X2034))=>((X2034)!=(emptyset))))=>(![X2032:$i, X2033:$i]:((in @ X2032 @ (setadjoin @ X2032 @ X2033)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X2029:$i, X2030:$i, X2031:$i]:(((in @ X2031 @ X2030)=>(in @ X2031 @ (setadjoin @ X2029 @ X2030))))=>(![X2025:$i, X2026:$i, X2027:$i]:(((in @ X2027 @ (setadjoin @ X2025 @ X2026))=>![X2028:$o]:(((((X2027)=(X2025))=>(X2028))=>(((in @ X2027 @ X2026)=>(X2028))=>(X2028))))))=>(![X1106:$i, X1107:$i, X1108:$i]:(((in @ X1108 @ (setadjoin @ X1106 @ X1107))=>(((X1108)=(X1106))|(in @ X1108 @ X1107))))=>(![X1109:$i]:(((dsetconstr @ X1109 @ (^[Z0/* 1 */:$i]:($true)))=(X1109)))=>(![X1110:$i, X1111:$i]:((![X1112:$i]:(((in @ X1112 @ X1111)=>(in @ X1112 @ X1110)))=>(in @ X1111 @ (powerset @ X1110))))=>(![X2024:$i]:((in @ emptyset @ (powerset @ X2024)))=>(![X1113:$i]:((in @ emptyset @ (powerset @ X1113)))=>(![X1114:$i, X1115:$i, X1116:$i]:(((in @ X1115 @ (powerset @ X1114))=>((in @ X1116 @ X1115)=>(in @ X1116 @ X1114))))=>(![X2021:$i, X2022:$i, X2023:$i]:(((in @ X2022 @ X2023)=>((in @ X2023 @ X2021)=>(in @ X2022 @ (setunion @ X2021)))))=>(![X2017:$i, X2018:$i]:(((in @ X2018 @ (setunion @ X2017))=>![X2019:$o]:((![X2020:$i]:(((in @ X2018 @ X2020)=>((in @ X2020 @ X2017)=>(X2019))))=>(X2019)))))=>(![X2015:$i, X2016:$i]:(((in @ X2016 @ X2015)=>(in @ X2016 @ (powerset @ (setunion @ X2015)))))=>(![X2010:$i > $o]:((?[X2011:$i]:(((X2010 @ X2011)&![X2012:$i]:(((X2010 @ X2012)=>((X2011)=(X2012))))))=>?[X2013:$i]:(![X2014:$i]:(((X2010 @ X2014)<=>((X2014)=(X2013)))))))=>(![X1117:$i]:((((X1117)!=(emptyset))=>?[X1118:$i]:(((in @ X1118 @ X1117)&$true))))=>(![X1119:$i, X1120:$i]:(((in @ X1119 @ (setadjoin @ X1120 @ emptyset))=>((X1119)=(X1120))))=>(![X2008:$i, X2009:$i]:((((X2008)!=(X2009))=>~(in @ X2009 @ (setadjoin @ X2008 @ emptyset))))=>(![X1121:$i, X1122:$i]:((((X1121)=(X1122))=>(in @ X1121 @ (setadjoin @ X1122 @ emptyset))))=>(![X1123:$i, X1124:$i]:(((in @ X1123 @ (setadjoin @ X1124 @ emptyset))=>(in @ X1124 @ (setadjoin @ X1123 @ emptyset))))=>(![X1125:$i, X1126:$i, X1127:$i]:(((in @ X1127 @ (setadjoin @ X1125 @ (setadjoin @ X1126 @ emptyset)))=>(((X1127)=(X1125))|((X1127)=(X1126)))))=>(![X2006:$i, X2007:$i]:((in @ X2006 @ (setadjoin @ X2006 @ (setadjoin @ X2007 @ emptyset))))=>(![X1128:$i, X1129:$i]:((in @ X1129 @ (setadjoin @ X1128 @ (setadjoin @ X1129 @ emptyset))))=>(![X1130:$i, X1131:$i > $o]:((?[X1132:$i]:(((in @ X1132 @ X1130)&(X1131 @ X1132)))=>(((dsetconstr @ X1130 @ X1131)=(emptyset))=>~($true))))=>(![X1133:$i > $o, X1134:$i]:(((in @ X1134 @ emptyset)=>(X1133 @ X1134)))=>(![X1135:$i, X1136:$i > $o]:((~(![X1137:$i]:(((in @ X1137 @ X1135)=>(X1136 @ X1137))))=>?[X1138:$i]:(((in @ X1138 @ X1135)&~((X1136 @ X1138))))))=>(![X1139:$i, X1140:$i > $o]:((![X1141:$i]:(((in @ X1141 @ X1139)=>~((X1140 @ X1141))))=>~(?[X1142:$i]:(((in @ X1142 @ X1139)&(X1140 @ X1142))))))=>(![X1143:$i, X1144:$i > $o]:((~(?[X1145:$i]:(((in @ X1145 @ X1143)&(X1144 @ X1145))))=>![X1146:$i]:(((in @ X1146 @ X1143)=>~((X1144 @ X1146))))))=>(![X1147:$i, X1148:$i > $o]:((?[X1149:$i]:(((in @ X1149 @ X1147)&~((X1148 @ X1149))))=>~(![X1150:$i]:(((in @ X1150 @ X1147)=>(X1148 @ X1150))))))=>(![X2005:$o]:(((X2005)=>(in @ emptyset @ (prop2set @ ((X2005))))))=>(![X1151:$o]:(((X1151)=>(set2prop @ (prop2set @ ((X1151))))))=>(![X1152:$i, X1153:$i > $o]:((~(?[X1154:$i]:(((in @ X1154 @ X1152)&(X1153 @ X1154))))=>![X1155:$i]:(((in @ X1155 @ X1152)=>~((X1153 @ X1155))))))=>(![X1156:$i, X1157:$i > $o]:((~(![X1158:$i]:(((in @ X1158 @ X1156)=>(X1157 @ X1158))))=>?[X1159:$i]:(((in @ X1159 @ X1156)&~((X1157 @ X1159))))))=>(![X1160:$i > $o]:((?[X1161:$i]:(((X1160 @ X1161)&![X1162:$i]:(((X1160 @ X1162)=>((X1161)=(X1162))))))=>?[X1163:$i]:(((X1160 @ X1163)&![X1164:$i]:(((X1160 @ X1164)=>((X1163)=(X1164))))))))=>(![X1165:$i > $o]:((?[X1166:$i]:((X1165 @ X1166))=>(![X1167:$i, X1168:$i]:(((X1165 @ X1167)=>((X1165 @ X1168)=>((X1167)=(X1168)))))=>?[X1169:$i]:(((X1165 @ X1169)&![X1170:$i]:(((X1165 @ X1170)=>((X1169)=(X1170)))))))))=>(![X1171:$i > $o]:((?[X1172:$i]:(![X1173:$i]:(((X1171 @ X1173)<=>((X1173)=(X1172)))))=>?[X1174:$i]:(((X1171 @ X1174)&![X1175:$i]:(((X1171 @ X1175)=>((X1174)=(X1175))))))))=>(![X2001:$i, X2002:$i]:((((X2001)=(X2002))=>![X2003:$i, X2004:$i]:((((X2003)=(X2004))=>((in @ X2003 @ X2001)=>(in @ X2004 @ X2002))))))=>(![X1176:$i, X1177:$i]:((((X1176)=(X1177))=>![X1178:$i, X1179:$i]:((((X1178)=(X1179))=>((in @ X1178 @ X1176)<=>(in @ X1179 @ X1177))))))=>(![X1180:$i > $o]:((?[X1181:$i]:(((X1180 @ X1181)&![X1182:$i]:(((X1180 @ X1182)=>((X1181)=(X1182))))))=>![X1183:$i, X1184:$i]:(((X1180 @ X1183)=>((X1180 @ X1184)=>((X1183)=(X1184)))))))=>(![X1993:$i > $o, X1994:$i > $o]:((![X1995:$i, X1996:$i]:((((X1995)=(X1996))=>((X1993 @ X1995)<=>(X1994 @ X1996))))=>(?[X1997:$i]:(((X1993 @ X1997)&![X1998:$i]:(((X1993 @ X1998)=>((X1997)=(X1998))))))<=>?[X1999:$i]:(((X1994 @ X1999)&![X2000:$i]:(((X1994 @ X2000)=>((X1999)=(X2000)))))))))=>(((emptyset)=(emptyset))=>(![X1989:$i, X1990:$i]:((((X1989)=(X1990))=>![X1991:$i, X1992:$i]:((((X1991)=(X1992))=>((setadjoin @ X1989 @ X1991)=(setadjoin @ X1990 @ X1992))))))=>(![X1185:$i, X1186:$i]:((((X1185)=(X1186))=>((powerset @ X1185)=(powerset @ X1186))))=>(![X1987:$i, X1988:$i]:((((X1987)=(X1988))=>((setunion @ X1987)=(setunion @ X1988))))=>(((omega)=(omega))=>(![X1187:$i > $o]:((?[X1188:$i]:(((X1187 @ X1188)&![X1189:$i]:(((X1187 @ X1189)=>((X1188)=(X1189))))))=>![X1190:$i, X1191:$i]:(((X1187 @ X1190)=>((X1187 @ X1191)=>((X1190)=(X1191)))))))=>(![X1979:$i > $o, X1980:$i > $o]:((![X1981:$i, X1982:$i]:((((X1981)=(X1982))=>((X1979 @ X1981)<=>(X1980 @ X1982))))=>(?[X1983:$i]:(((X1979 @ X1983)&![X1984:$i]:(((X1979 @ X1984)=>((X1983)=(X1984))))))=>(?[X1985:$i]:(((X1980 @ X1985)&![X1986:$i]:(((X1980 @ X1986)=>((X1985)=(X1986))))))=>((descr @ X1979)=(descr @ X1980))))))=>(![X1192:$i, X1193:$i]:((((X1192)=(X1193))=>![X1194:$i > $o, X1195:$i > $o]:((![X1196:$i]:(((in @ X1196 @ X1192)=>![X1197:$i]:(((in @ X1197 @ X1193)=>(((X1196)=(X1197))=>((X1194 @ X1196)<=>(X1195 @ X1197)))))))=>((dsetconstr @ X1192 @ X1194)=(dsetconstr @ X1193 @ X1195))))))=>(![X1976:$i, X1977:$i]:((![X1978:$i]:(((in @ X1978 @ X1976)=>(in @ X1978 @ X1977)))=>(subset @ X1976 @ X1977)))=>(![X1974:$i, X1975:$i]:((((X1974)=(X1975))=>(subset @ X1975 @ X1974)))=>(![X1198:$i, X1199:$i]:((((X1198)=(X1199))=>(subset @ X1198 @ X1199)))=>(![X1200:$i, X1201:$i]:((![X1202:$i]:(((in @ X1202 @ X1200)=>(in @ X1202 @ X1201)))=>(subset @ X1200 @ X1201)))=>(![X1203:$i]:((subset @ emptyset @ X1203))=>(![X1204:$i, X1205:$i, X1206:$i]:(((subset @ X1204 @ X1205)=>((in @ X1206 @ X1204)=>(in @ X1206 @ X1205))))=>(![X1207:$i, X1208:$i, X1209:$i]:(((subset @ X1207 @ X1208)=>(~(in @ X1209 @ X1208)=>~(in @ X1209 @ X1207))))=>(![X1210:$i, X1211:$i, X1212:$i]:(((in @ X1212 @ X1210)=>(~(in @ X1212 @ X1211)=>~(subset @ X1210 @ X1211))))=>(![X1213:$i, X1214:$i]:((~(subset @ X1213 @ X1214)=>((X1213)!=(X1214))))=>(![X1971:$i, X1972:$i, X1973:$i]:(((in @ X1973 @ X1971)=>(~(in @ X1973 @ X1972)=>((X1971)!=(X1972)))))=>(![X1970:$i]:((subset @ X1970 @ X1970))=>(![X1967:$i, X1968:$i, X1969:$i]:(((subset @ X1967 @ X1968)=>((subset @ X1968 @ X1969)=>(subset @ X1967 @ X1969))))=>(![X1215:$i, X1216:$i]:((subset @ X1216 @ (setadjoin @ X1215 @ X1216)))=>(![X1217:$i, X1218:$i, X1219:$i]:(((subset @ X1217 @ X1219)=>(subset @ X1217 @ (setadjoin @ X1218 @ X1219))))=>(![X1220:$i, X1221:$i]:(((subset @ X1220 @ X1221)=>(in @ X1220 @ (powerset @ X1221))))=>(![X1222:$i, X1223:$i]:(((subset @ X1222 @ X1223)=>((subset @ X1223 @ X1222)=>((X1222)=(X1223)))))=>(![X1966:$i]:(((subset @ X1966 @ emptyset)=>((X1966)=(emptyset))))=>(![X1224:$i, X1225:$i]:(((subset @ X1225 @ X1224)=>(in @ X1225 @ (powerset @ X1224))))=>(![X1226:$i, X1227:$i]:(((in @ X1227 @ (powerset @ X1226))=>(subset @ X1227 @ X1226)))=>(![X1965:$i]:((in @ X1965 @ (powerset @ X1965)))=>(![X1228:$i, X1229:$i]:(((subset @ X1228 @ X1229)=>(subset @ (powerset @ X1228) @ (powerset @ X1229))))=>(![X1230:$i, X1231:$i > $o]:((in @ (dsetconstr @ X1230 @ X1231) @ (powerset @ X1230)))=>(![X1963:$i, X1964:$i > $o]:((subset @ (dsetconstr @ X1963 @ X1964) @ X1963))=>(![X1232:$i, X1233:$i, X1234:$i]:(((in @ X1234 @ X1232)=>(in @ X1234 @ (binunion @ X1232 @ X1233))))=>(![X1961:$i, X1962:$i]:((in @ X1962 @ (setadjoin @ X1961 @ (setadjoin @ X1962 @ emptyset))))=>(![X1958:$i, X1959:$i, X1960:$i]:(((in @ X1960 @ X1959)=>(in @ X1960 @ (binunion @ X1958 @ X1959))))=>(![X1954:$i, X1955:$i, X1956:$i, X1957:$o]:(((in @ X1956 @ (binunion @ X1954 @ X1955))=>(((in @ X1956 @ X1954)=>(X1957))=>(((in @ X1956 @ X1955)=>(X1957))=>(X1957)))))=>(![X1235:$i, X1236:$i, X1237:$i]:(((in @ X1237 @ (binunion @ X1235 @ X1236))=>((in @ X1237 @ X1235)|(in @ X1237 @ X1236))))=>(![X1952:$i, X1953:$i]:((subset @ X1952 @ (binunion @ X1952 @ X1953)))=>(![X1238:$i, X1239:$i]:((subset @ X1239 @ (binunion @ X1238 @ X1239)))=>(![X1240:$i, X1241:$i, X1242:$i]:(((in @ X1242 @ X1240)=>((in @ X1242 @ X1241)=>(in @ X1242 @ (binintersect @ X1240 @ X1241)))))=>(![X1949:$i, X1950:$i, X1951:$i]:(((subset @ X1951 @ X1949)=>((subset @ X1951 @ X1950)=>(subset @ X1951 @ (binintersect @ X1949 @ X1950)))))=>(![X1946:$i, X1947:$i, X1948:$i]:(((in @ X1948 @ (binintersect @ X1946 @ X1947))=>(in @ X1948 @ X1946)))=>(![X1243:$i, X1244:$i]:((subset @ (binintersect @ X1243 @ X1244) @ X1243))=>(![X1245:$i, X1246:$i]:(((subset @ X1245 @ X1246)=>((binintersect @ X1245 @ X1246)=(X1245))))=>(![X1247:$i, X1248:$i]:((((binintersect @ X1247 @ X1248)=(X1248))=>(subset @ X1248 @ X1247)))=>(![X1249:$i, X1250:$i, X1251:$i]:(((in @ X1251 @ (binintersect @ X1249 @ X1250))=>(in @ X1251 @ X1250)))=>(![X1943:$i, X1944:$i]:((~(?[X1945:$i]:(((in @ X1945 @ X1943)&(in @ X1945 @ X1944))))=>((binintersect @ X1943 @ X1944)=(emptyset))))=>(![X1941:$i, X1942:$i]:((subset @ 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(powerset @ X1682))=>![X1685:$i]:(((in @ X1685 @ (powerset @ X1682))=>((subset @ X1683 @ X1684)=>((subset @ X1683 @ X1685)=>(subset @ X1683 @ (binintersect @ X1684 @ X1685))))))))))=>(![X1677:$i, X1678:$i]:(((in @ X1678 @ (powerset @ X1677))=>![X1679:$i]:(((in @ X1679 @ (powerset @ X1677))=>![X1680:$i]:(((in @ X1680 @ (powerset @ X1677))=>![X1681:$i]:(((in @ X1681 @ (powerset @ X1677))=>((subset @ X1678 @ X1680)=>((subset @ X1679 @ X1681)=>(subset @ (binintersect @ X1678 @ X1679) @ (binintersect @ X1680 @ X1681))))))))))))=>(![X1573:$i, X1574:$i]:(((in @ X1574 @ (powerset @ X1573))=>![X1575:$i]:(((in @ X1575 @ (powerset @ X1573))=>(in @ (setminus @ X1573 @ X1574) @ (powerset @ (setminus @ X1573 @ (binintersect @ X1574 @ X1575))))))))=>(![X1672:$i, X1673:$i]:(((in @ X1673 @ (powerset @ X1672))=>![X1674:$i]:(((in @ X1674 @ (powerset @ X1672))=>![X1675:$i]:(((in @ X1675 @ (powerset @ X1672))=>![X1676:$i]:(((in @ X1676 @ (powerset @ X1672))=>((setminus @ X1672 @ (binintersect @ (binunion @ 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X33)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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y_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[breln1unionE]), setextAx]), binunionLsub]), setminusER]), binunionEcases]), setminusLsub]), binunionIR]), upairset2IR]), c_0_320]), setminusSubset1]), inPowerset]), subsetemptysetimpeq]), symdiffI1]), subsetTrans]), subsetRefl]), notequalI2]), symdiffIneg2]), eqimpsubset2]), subsetI1]), setukpairIR]), c_0_321]), setunion__Cong]), setadjoin__Cong]), emptyset__Cong]), kpairp]), c_0_322]), inCongP]), singletoninpowunion]), prop2setI]), setukpairinjR2]), upairsetIL]), notinsingleton]), setminusELneg]), c_0_323]), ubforcartprodlem1]), subPowSU]), setunionE]), cartprodpairin]), setunionI]), emptyinPowerset]), setadjoinE]), setadjoinIR]), cartprodmempair]), setadjoinIL]), c_0_324]), setunionsingleton1]), c_0_325]), c_0_326]), noeltsimpempty]), c_0_327]), setext]), c_0_328]), c_0_329]), emptysetimpfalse]), c_0_330]), c_0_331]), c_0_332]), c_0_333]), c_0_334]), c_0_335]), wellorderingAx]), foundationAx]), setminusILneg]), omegaSAx]), setunionAx]), setukpairinjL1]), setadjoinAx]), emptysetAx]), c_0_336]), setukpairinjL2]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), theeq]), iftrue]), setukpairinjR]), c_0_337]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodfstpairEq]), cartprodsndpairEq]), c_0_338]), setminusIRneg]), c_0_339]), c_0_340]), c_0_341]), app]), ap2p]), funcinfuncset]), c_0_342]), c_0_343]), brelnall1]), brelnall2]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), eqbreln]), funcext]), ap2apEq1]), c_0_344]), c_0_345]), c_0_346]), c_0_347]), c_0_348]), c_0_349]), ifp]), c_0_350]), ap2apEq2]), funcext2]), subbreln]), funcGraphProp4]), funcextLem]), c_0_351]), c_0_352]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), setminusT_lem]), subsetTI]), powersetTI1]), complementTE1]), binintersectTELcontra]), contrasubsetT2]), doubleComplementI1]), doubleComplementSub1]), doubleComplementSub2]), complementTnotintersectT]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTIRcontra]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), binunionTE]), demorgan2a1]), demorgan1b]), woz13rule0]), woz13rule1]), woz1_1]), woz1_3]), c_0_353]), breln1invprop]), breln1invI]), breln1compprop]), breln1compE]), breln1compEex]), breln1unionI]), breln1unionIR]), breln1unionIL]), breln1unionprop]), breln1compI]), breln1invE]), eqbreln1]), subbreln1]), breln1all1]), c_0_354]), breln1SetBreln1]), breln1all2]), woz1_5]), woz1_4]), woz1_2]), woz13rule4]), woz13rule3]), woz13rule2]), demorgan2]), demorgan2b]), demorgan2b2]), demorgan2a]), demorgan1]), demorgan1a]), demorgan2a2]), complementUnionInPowersetComplement]), binunionTEcontra]), inComplementUnionImpInComplement1]), inComplementUnionImpNotIn1]), inIntersectImpInUnion]), binunionTILcontra]), complementImpComplementIntersect]), doubleComplementEq]), doubleComplementE1]), contrasubsetT3]), contrasubsetT1]), contrasubsetT]), binintersectTERcontra]), complementTI1]), powersetTE1]), setextT]), complementT_lem]), powersetT_lem]), c_0_355]), c_0_356]), c_0_357]), infuncsetfunc]), c_0_358]), c_0_359]), c_0_360]), c_0_361]), c_0_362]), cartprodpairsurjEq]), cartprodmempaircEq]), cartprodpairmemER]), ksndpairEq]), setukpairinjR11]), setukpairinjL]), cartprodfstin]), kfstpairEq]), theprop]), singletonsuniq]), setunionsingleton]), setunionsingleton2]), setunionE2]), cartprodmempair1]), ubforcartprodlem3]), ubforcartprodlem2]), upairinpowunion]), upairsubunion]), upairset2E]), singletoninpowerset]), singletonsubset]), kpairiskpair]), setukpairIL]), secondinupair]), symdiffIneg1]), symdiffI2]), symdiffE]), setminusERneg]), setminusSubset2]), setminusI]), bs114d]), binintersectRsub]), disjointsetsI1]), binintersectEL]), binintersectSubset5]), setminusEL]), binintersectSubset1]), binintersectSubset4]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectI]), binunionRsub]), binunionE]), binunionIL]), c_0_363]), powersetsubset]), powersetE1]), powersetI1]), setextsub]), subset2powerset]), setadjoinSub2]), setadjoinSub]), notequalI1]), notsubsetI]), subsetE2]), subsetE]), emptysetsubset]), subsetI2]), eqimpsubset1]), c_0_364]), c_0_365]), omega__Cong]), powerset__Cong]), c_0_366]), in__Cong]), c_0_367]), c_0_368]), c_0_369]), notdallE]), notdexE]), prop2set2propI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_370]), upairsetIR]), upairsetE]), singletonsswitch]), eqinunit]), uniqinunit]), c_0_371]), powersetE]), emptyInPowerset]), powersetI]), c_0_372]), setadjoinOr]), emptyinunitempty]), c_0_373]), emptyI]), notinemptyset]), emptysetE]), prop2setE]), c_0_374]), c_0_375]), omegaIndAx]), omega0Ax]), powersetAx])])]), c_0_376])).
2.70/240.03	thf(c_0_378, negated_conjecture, ![X2101:$i, X2102:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2114:$i, X2115:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2123:$i, X2124:$i > $i > $o, X2125:$i, X2127:$i, X2130:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2137:$i, X2138:$i > $o, X2139:$i, X2141:$i, X2142:$i > $o, X2143:$i, X2144:$i, X2145:$i > $o, X2146:$i, X2147:$i, X2148:$i > $o, X2149:$i, X2150:$i > $o, X2151:$i, X2154:$i, X2155:$o, X2156:$i, X2157:$i, X2158:$o, X2159:$i, X2160:$i, X2161:$i > $o, X2162:$i, X2165:$i, X2166:$i, X2169:$i, X2171:$i, X2173:$i, X2174:$i > $o, X2175:$i, X2176:$i, X2178:$i, X2179:$i > $o, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$o, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$o, X2211:$i, X2212:$i, X2213:$i > $o, X2214:$i, X2217:$i, X2218:$i, X2219:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i > $o, X2238:$i, X2239:$i > $o, X2240:$i, X2241:$i, X2242:$i > $o, X2243:$i, X2245:$i, X2246:$i > $o, X2248:$i, X2249:$i, X2250:$i > $o, X2252:$i, X2253:$i, X2254:$i > $o, X2255:$i, X2257:$o, X2258:$o, X2259:$i, X2260:$i > $o, X2262:$i, X2263:$i, X2264:$i > $o, X2265:$i, X2267:$i > $o, X2268:$i, X2271:$i, X2272:$i > $o, X2273:$i, X2277:$i, X2278:$i > $o, X2279:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i > $o, X2292:$i, X2294:$i, X2295:$i, X2296:$i > $o, X2297:$i > $o, X2300:$i, X2303:$i, X2304:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i > $o, X2317:$i, X2319:$i, X2320:$i, X2321:$i > $o, X2322:$i > $o, X2325:$i, X2327:$i, X2329:$i, X2330:$i, X2331:$i > $o, X2332:$i > $o, X2335:$i, X2336:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2345:$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:$i, X2375:$i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i > $o, X2383:$i, X2384:$i > $o, X2385:$i, X2386:$i, X2387:$i, X2388:$i, X2389:$i, X2390:$i, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2395:$i, X2396:$o, X2397:$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, X2425:$i, X2426:$i, X2427:$i, X2428:$i, X2429:$i, X2430:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2435:$i, X2436:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, X2442:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$i, X2455:$i, X2456:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i, X2463:$i, X2464:$o, 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:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i > $o, X2539:$i, X2540:$i, X2541:$i > $o, X2543:$i, X2544:$i > $o, X2545:$i, X2547:$i, X2548:$i > $o, X2551:$i, X2552:$i, X2553:$i, X2554:$i, X2555:$i, X2556:$i, X2557:$i, X2558:$i, X2559:$i, X2560:$i, X2561:$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, X2588:$i, X2589:$i, X2590:$i, X2591:$i, X2592:$i, X2593:$i, X2594:$i, X2595:$i, X2596:$i, X2597:$i, X2598:$i, X2599:$i, X2600:$i, X2601:$i, X2602:$i, X2603:$i, X2604:$i, X2605:$i, X2606:$i, X2607:$i, X2608:$i, X2609:$i, X2610:$i, X2611:$i, X2612:$i, X2613:$i, X2614:$i, X2615:$i, X2616:$i, X2617:$i, X2618:$i, X2619:$i, X2620:$i, X2621:$i, X2622:$i, X2623:$i > $i > $o, X2624:$i, X2625:$i, X2626:$i, X2627:$i, X2628:$i > $i > $o, X2629:$i, X2630:$i, X2631:$i > $i > $o, X2632:$i, X2633:$i, X2634:$i > $i > $o, X2635:$i, X2636:$i, X2637:$i, X2638:$i, X2639:$i > $i > $o, X2640:$i, X2641:$i, X2642:$i, X2643:$i, X2644:$i > $i > $o, X2645:$i, X2646:$i, X2647:$i, X2648:$i, X2649:$i > $i > $o, X2650:$i, X2651:$i, X2652:$i, X2653:$i, X2654:$i, X2655:$i, X2656:$i, X2657:$i, X2658:$i, X2659:$i, X2660:$i, X2661:$i, X2662:$i, X2663:$i, X2664:$i, X2665:$i, X2666:$i, X2667:$i, X2668:$i, X2669:$i, X2670:$i, X2671:$i, X2672:$i, X2673:$i, X2674:$i, X2675:$i, X2676:$i > $i, X2678:$i, X2679:$i, X2680:$i > $i, X2682:$i, X2683:$i, X2684:$i > $i, X2686:$i, X2687:$i, X2688:$i, X2689:$i > $o, X2692:$i, X2693:$i, X2694:$i, X2695:$i, X2696:$i > $o, X2699:$i, X2700:$i, X2701:$i > $o, X2702:$i, X2703:$i, X2704:$i, X2705:$i, X2706:$i, X2707:$i, X2708:$i, X2709:$i, X2710:$i, X2711:$i, X2712:$i, X2713:$i, X2714:$i, X2715:$i, X2716:$i, X2717:$i, X2718:$i, X2719:$i, X2720:$i, X2722:$i, X2723:$i, X2724:$i, X2725:$i, X2726:$i, X2727:$i, X2728:$i, X2729:$i, X2730:$i, X2731:$i, X2732:$i, X2735:$i, X2736:$i, X2737:$i, X2738:$i, X2743:$i, X2744:$i, X2745:$i, X2746:$i, X2748:$i, X2749:$i, X2750:$i, X2751:$i, X2753:$i, X2754:$i, X2755:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2760:$i, X2761:$i, X2762:$i, X2763:$i > $i, X2765:$i, X2766:$i, X2767:$i, X2768:$i, X2769:$i, X2770:$i, X2771:$i > $i, X2773:$i, X2774:$i, X2775:$i > $i, X2777:$i, X2778:$i, X2779:$i, X2780:$i, X2781:$i, X2782:$o, X2783:$i, X2784:$i, X2785:$i, X2786:$o, X2787:$i, X2788:$i, X2789:$i, X2790:$o, X2791:$i, X2792:$i, X2793:$i, X2794:$o, X2795:$i, X2796:$i, X2797:$i, X2798:$o, X2799:$i, X2800:$i, X2801:$i, X2802:$o, X2803:$i, X2804:$i, X2805:$i, X2806:$i, X2807:$i, X2808:$o, X2809:$i, X2810:$i, X2811:$i, X2812:$o, X2813:$i, X2814:$i, X2815:$i, X2816:$o, X2817:$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:$i, X2837:$i, X2838:$i, X2839:$i, X2841:$i, X2842:$i, X2843:$i, X2845:$i, X2846:$i, X2847:$i, X2848:$i, X2849:$i, X2850:$i, X2851:$i, 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X2952:$i, X2953:$i, X2954:$i, X2955:$i, X2956:$i, X2957:$i, X2958:$i, X2959:$i, X2960:$i, X2961:$i, X2962:$i, X2963:$i, X2964:$i, X2965:$i, X2966:$i, X2967:$i, X2968:$i, X2969:$i, X2970:$i, X2971:$i, X2972:$i, X2973:$i, X2974:$i, X2975:$i, X2976:$i, X2977:$i, X2978:$i, X2979:$i, X2980:$i, X2981:$i, X2982:$i, X2983:$i, X2984:$i, X2985:$i, X2986:$i, X2987:$i, X2988:$i, X2989:$i, X2990:$i, X2991:$i, X2992:$i, X2993:$i, X2994:$i, X2995:$i, X2996:$i, X2997:$i, X2998:$i, X2999:$i, X3000:$i, X3001:$i, X3002:$i, X3003:$i, X3004:$i, X3005:$i, X3006:$i, X3007:$i, X3008:$i, X3009:$i, X3010:$i, X3011:$i, X3012:$i, X3013:$i, X3014:$i, X3015:$i, X3016:$i, X3017:$i, X3018:$i, X3019:$i, X3020:$i, X3021:$i, X3022:$i, X3023:$i, X3024:$i, X3025:$i, X3026:$i, X3027:$i, X3028:$i, X3029:$i, X3030:$i, X3031:$i, X3032:$i > $o, X3035:$i, X3036:$i, X3037:$i, X3038:$i, X3039:$i, X3040:$i > $i > $o, X3042:$i, X3043:$i, X3044:$i, X3045:$i, X3046:$i > $i > $o, X3047:$i, X3048:$i, X3049:$i > $o, X3052:$i, X3053:$i, 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X3066)))&((~(breln1 @ X3067 @ X3068)|(~(in @ X3069 @ X3067)|(~(in @ X3070 @ X3067)|(~(in @ (kpair @ X3069 @ X3070) @ X3068)|(in @ (kpair @ X3070 @ X3069) @ (breln1invset @ X3067 @ X3068))))))&((~(breln1 @ X3071 @ X3072)|(~(in @ X3073 @ X3071)|(~(in @ X3074 @ X3071)|(~(in @ (kpair @ X3074 @ X3073) @ (breln1invset @ X3071 @ X3072))|(in @ (kpair @ X3073 @ X3074) @ X3072)))))&((~(breln1 @ X3075 @ X3076)|(~(breln1 @ X3075 @ X3077)|(breln1 @ X3075 @ (breln1compset @ X3075 @ X3076 @ X3077))))&((~(breln1 @ X3078 @ X3079)|(~(breln1 @ X3078 @ X3080)|(~(in @ X3081 @ X3078)|(~(in @ X3082 @ X3078)|(~(in @ X3083 @ X3078)|(~(in @ (kpair @ X3081 @ X3083) @ X3079)|(~(in @ (kpair @ X3083 @ X3082) @ X3080)|(in @ (kpair @ X3081 @ X3082) @ (breln1compset @ X3078 @ X3079 @ X3080)))))))))&(((((in @ (esk98_5 @ X3084 @ X3085 @ X3086 @ X3087 @ X3088) @ X3084)|~(in @ (kpair @ X3087 @ X3088) @ (breln1compset @ X3084 @ X3085 @ X3086))|~(in @ X3088 @ X3084)|~(in @ X3087 @ X3084)|~(breln1 @ X3084 @ X3086)|~(breln1 @ X3084 @ X3085))&((in @ (kpair @ X3087 @ (esk98_5 @ X3084 @ X3085 @ X3086 @ X3087 @ X3088)) @ X3085)|~(in @ (kpair @ X3087 @ X3088) @ (breln1compset @ X3084 @ X3085 @ X3086))|~(in @ X3088 @ X3084)|~(in @ X3087 @ X3084)|~(breln1 @ X3084 @ X3086)|~(breln1 @ X3084 @ X3085)))&((in @ (kpair @ (esk98_5 @ X3084 @ X3085 @ X3086 @ X3087 @ X3088) @ X3088) @ X3086)|~(in @ (kpair @ X3087 @ X3088) @ (breln1compset @ X3084 @ X3085 @ X3086))|~(in @ X3088 @ X3084)|~(in @ X3087 @ X3084)|~(breln1 @ X3084 @ X3086)|~(breln1 @ X3084 @ X3085)))&((((in @ (esk99_6 @ X3090 @ X3091 @ X3092 @ X3093 @ X3094 @ X3095) @ X3090)|(X3095)|~(in @ (kpair @ X3093 @ X3094) @ (breln1compset @ X3090 @ X3091 @ X3092))|~(in @ X3094 @ X3090)|~(in @ X3093 @ X3090)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091))&(((in @ (kpair @ X3093 @ (esk99_6 @ X3090 @ X3091 @ X3092 @ X3093 @ X3094 @ X3095)) @ X3091)|(X3095)|~(in @ (kpair @ X3093 @ X3094) @ (breln1compset @ X3090 @ X3091 @ X3092))|~(in @ X3094 @ X3090)|~(in @ X3093 @ X3090)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091))&(((in @ (kpair @ (esk99_6 @ X3090 @ X3091 @ X3092 @ X3093 @ X3094 @ X3095) @ X3094) @ X3092)|(X3095)|~(in @ (kpair @ X3093 @ X3094) @ (breln1compset @ X3090 @ X3091 @ X3092))|~(in @ X3094 @ X3090)|~(in @ X3093 @ X3090)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091))&(~(X3095)|(X3095)|~(in @ (kpair @ X3093 @ X3094) @ (breln1compset @ X3090 @ X3091 @ X3092))|~(in @ X3094 @ X3090)|~(in @ X3093 @ X3090)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091)))))&((~(breln1 @ X3097 @ X3098)|(~(breln1 @ X3097 @ X3099)|(breln1 @ X3097 @ (binunion @ X3098 @ X3099))))&((~(breln1 @ X3100 @ X3101)|(~(breln1 @ X3100 @ X3102)|(~(in @ X3103 @ X3100)|(~(in @ X3104 @ X3100)|(~(in @ (kpair @ X3103 @ X3104) @ X3101)|(in @ (kpair @ X3103 @ X3104) @ (binunion @ X3101 @ X3102)))))))&((~(breln1 @ X3105 @ X3106)|(~(breln1 @ X3105 @ X3107)|(~(in @ X3108 @ X3105)|(~(in @ X3109 @ X3105)|(~(in @ (kpair @ X3108 @ X3109) @ X3107)|(in @ (kpair @ X3108 @ X3109) @ (binunion @ X3106 @ X3107)))))))&(((~(in @ (kpair @ X3113 @ X3114) @ X3111)|(in @ (kpair @ X3113 @ X3114) @ (binunion @ X3111 @ X3112))|~(in @ X3114 @ X3110)|~(in @ X3113 @ X3110)|~(breln1 @ X3110 @ X3112)|~(breln1 @ X3110 @ X3111))&(~(in @ (kpair @ X3113 @ X3114) @ X3112)|(in @ (kpair @ X3113 @ X3114) @ (binunion @ X3111 @ X3112))|~(in @ X3114 @ X3110)|~(in @ X3113 @ X3110)|~(breln1 @ X3110 @ X3112)|~(breln1 @ X3110 @ X3111)))&((breln1 @ esk100_0 @ esk101_0)&((breln1 @ esk100_0 @ esk102_0)&((in @ esk103_0 @ esk100_0)&((in @ esk104_0 @ esk100_0)&((in @ (kpair @ esk103_0 @ esk104_0) @ (binunion @ esk101_0 @ esk102_0))&(~(in @ (kpair @ esk103_0 @ esk104_0) @ esk102_0)&~(in @ (kpair @ esk103_0 @ esk104_0) @ esk101_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_377])])])])])])])).
2.70/240.03	thf(c_0_379, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ X3)|(in @ X2 @ X4)|~((in @ X2 @ (binunion @ X4 @ X3))))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_378])])])).
2.70/240.03	thf(c_0_380, negated_conjecture, (in @ (kpair @ esk103_0 @ esk104_0) @ (binunion @ esk101_0 @ esk102_0)), inference(split_conjunct,[status(thm)],[c_0_378])).
2.70/240.03	thf(c_0_381, negated_conjecture, ~((in @ (kpair @ esk103_0 @ esk104_0) @ esk101_0)), inference(split_conjunct,[status(thm)],[c_0_378])).
2.70/240.03	thf(c_0_382, negated_conjecture, ~((in @ (kpair @ esk103_0 @ esk104_0) @ esk102_0)), inference(split_conjunct,[status(thm)],[c_0_378])).
2.70/240.03	thf(c_0_383, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_379, c_0_380]), c_0_381]), c_0_382]), ['proof']).
2.70/240.03	# SZS output end CNFRefutation
2.70/240.03	# Parsed axioms                        : 655
2.70/240.03	# Removed by relevancy pruning/SinE    : 350
2.70/240.03	# Initial clauses                      : 550
2.70/240.03	# Removed in clause preprocessing      : 38
2.70/240.03	# Initial clauses in saturation        : 512
2.70/240.03	# Processed clauses                    : 690
2.70/240.03	# ...of these trivial                  : 9
2.70/240.03	# ...subsumed                          : 48
2.70/240.03	# ...remaining for further processing  : 633
2.70/240.03	# Other redundant clauses eliminated   : 31
2.70/240.03	# Clauses deleted for lack of memory   : 0
2.70/240.03	# Backward-subsumed                    : 0
2.70/240.03	# Backward-rewritten                   : 1
2.70/240.03	# Generated clauses                    : 1120
2.70/240.03	# ...of the previous two non-redundant : 1019
2.70/240.03	# ...aggressively subsumed             : 0
2.70/240.03	# Contextual simplify-reflections      : 14
2.70/240.03	# Paramodulations                      : 1080
2.70/240.03	# Factorizations                       : 0
2.70/240.03	# NegExts                              : 0
2.70/240.03	# Equation resolutions                 : 36
2.70/240.03	# Disequality decompositions           : 0
2.70/240.03	# Total rewrite steps                  : 113
2.70/240.03	# ...of those cached                   : 80
2.70/240.03	# Propositional unsat checks           : 0
2.70/240.03	#    Propositional check models        : 0
2.70/240.03	#    Propositional check unsatisfiable : 0
2.70/240.03	#    Propositional clauses             : 0
2.70/240.03	#    Propositional clauses after purity: 0
2.70/240.03	#    Propositional unsat core size     : 0
2.70/240.03	#    Propositional preprocessing time  : 0.000
2.70/240.03	#    Propositional encoding time       : 0.000
2.70/240.03	#    Propositional solver time         : 0.000
2.70/240.03	#    Success case prop preproc time    : 0.000
2.70/240.03	#    Success case prop encoding time   : 0.000
2.70/240.03	#    Success case prop solver time     : 0.000
2.70/240.03	# Current number of processed clauses  : 165
2.70/240.03	#    Positive orientable unit clauses  : 41
2.70/240.03	#    Positive unorientable unit clauses: 0
2.70/240.03	#    Negative unit clauses             : 4
2.70/240.03	#    Non-unit-clauses                  : 120
2.70/240.03	# Current number of unprocessed clauses: 1277
2.70/240.03	# ...number of literals in the above   : 3876
2.70/240.03	# Current number of archived formulas  : 0
2.70/240.03	# Current number of archived clauses   : 450
2.70/240.03	# Clause-clause subsumption calls (NU) : 44877
2.70/240.03	# Rec. Clause-clause subsumption calls : 13169
2.70/240.03	# Non-unit clause-clause subsumptions  : 57
2.70/240.03	# Unit Clause-clause subsumption calls : 337
2.70/240.03	# Rewrite failures with RHS unbound    : 0
2.70/240.03	# BW rewrite match attempts            : 27
2.70/240.03	# BW rewrite match successes           : 1
2.70/240.03	# Condensation attempts                : 0
2.70/240.03	# Condensation successes               : 0
2.70/240.03	# Termbank termtop insertions          : 116272
2.70/240.03	# Search garbage collected termcells   : 34216
2.70/240.03	
2.70/240.03	# -------------------------------------------------
2.70/240.03	# User time                : 0.256 s
2.70/240.03	# System time              : 0.020 s
2.70/240.03	# Total time               : 0.276 s
2.70/240.03	# Maximum resident set size: 10416 pages
2.70/240.03	
2.70/240.03	# -------------------------------------------------
2.70/240.03	# User time                : 0.274 s
2.70/240.03	# System time              : 0.025 s
2.70/240.03	# Total time               : 0.299 s
2.70/240.03	# Maximum resident set size: 3076 pages
2.70/240.03	% E exiting
2.70/240.03	% E exiting
2.70/240.03	EOF