0.11/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.12	% Command    : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM
0.11/0.33	% Computer : n018.cluster.edu
0.11/0.33	% Model    : x86_64 x86_64
0.11/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.33	% Memory   : 8042.1875MB
0.11/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.33	% CPULimit   : 1920
0.11/0.33	% WCLimit    : 240
0.11/0.33	% DateTime   : Wed Jul 30 02:05:49 EDT 2025
0.11/0.33	% CPUTime    : 
0.20/0.47	Running higher-order theorem proving
0.20/0.53	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.YEvJ2f8LwU/E---3.1_29452.p
1.27/0.99	# Version: 3.0.0-ho
1.27/0.99	# Preprocessing class: HSLMSLSSLLLCHFA.
1.27/0.99	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
1.27/0.99	# Starting ehoh_best5 with 240s (1) cores
1.27/0.99	# Starting almost_fo_3_lam with 240s (1) cores
1.27/0.99	# Starting new_bool_5 with 240s (1) cores
1.27/0.99	# Starting pre_casc_3 with 240s (1) cores
1.27/0.99	# Starting ho_unfolding_8 with 240s (1) cores
1.27/0.99	# Starting new_ho_10_cnf2 with 240s (1) cores
1.27/0.99	# Starting new_bool_3 with 240s (1) cores
1.27/0.99	# Starting new_ho_5 with 240s (1) cores
1.27/0.99	# new_bool_5 with pid 29552 completed with status 0
1.27/0.99	# Result found by new_bool_5
1.27/0.99	# Preprocessing class: HSLMSLSSLLLCHFA.
1.27/0.99	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
1.27/0.99	# Starting ehoh_best5 with 240s (1) cores
1.27/0.99	# Starting almost_fo_3_lam with 240s (1) cores
1.27/0.99	# Starting new_bool_5 with 240s (1) cores
1.27/0.99	# SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
1.27/0.99	# Search class: HGHSM-FSLM32-MHFMMSBN
1.27/0.99	# Scheduled 10 strats onto 1 cores with 240 seconds (240 total)
1.27/0.99	# Starting ho_unfolding_8 with 44s (1) cores
1.27/0.99	# ho_unfolding_8 with pid 29623 completed with status 0
1.27/0.99	# Result found by ho_unfolding_8
1.27/0.99	# Preprocessing class: HSLMSLSSLLLCHFA.
1.27/0.99	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
1.27/0.99	# Starting ehoh_best5 with 240s (1) cores
1.27/0.99	# Starting almost_fo_3_lam with 240s (1) cores
1.27/0.99	# Starting new_bool_5 with 240s (1) cores
1.27/0.99	# SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
1.27/0.99	# Search class: HGHSM-FSLM32-MHFMMSBN
1.27/0.99	# Scheduled 10 strats onto 1 cores with 240 seconds (240 total)
1.27/0.99	# Starting ho_unfolding_8 with 44s (1) cores
1.27/0.99	# Preprocessing time       : 0.054 s
1.27/0.99	# Presaturation interreduction done
1.27/0.99	
1.27/0.99	# Proof found!
1.27/0.99	# SZS status Theorem
1.27/0.99	# SZS output start CNFRefutation
1.27/0.99	thf(decl_23, type, in: $i > $i > $o).
1.27/0.99	thf(decl_24, type, exu: ($i > $o) > $o).
1.27/0.99	thf(decl_25, type, setextAx: $o).
1.27/0.99	thf(decl_26, type, emptyset: $i).
1.27/0.99	thf(decl_27, type, emptysetAx: $o).
1.27/0.99	thf(decl_28, type, setadjoin: $i > $i > $i).
1.27/0.99	thf(decl_29, type, setadjoinAx: $o).
1.27/0.99	thf(decl_30, type, powerset: $i > $i).
1.27/0.99	thf(decl_31, type, powersetAx: $o).
1.27/0.99	thf(decl_32, type, setunion: $i > $i).
1.27/0.99	thf(decl_33, type, setunionAx: $o).
1.27/0.99	thf(decl_34, type, omega: $i).
1.27/0.99	thf(decl_35, type, omega0Ax: $o).
1.27/0.99	thf(decl_36, type, omegaSAx: $o).
1.27/0.99	thf(decl_37, type, omegaIndAx: $o).
1.27/0.99	thf(decl_38, type, replAx: $o).
1.27/0.99	thf(decl_39, type, foundationAx: $o).
1.27/0.99	thf(decl_40, type, wellorderingAx: $o).
1.27/0.99	thf(decl_41, type, descr: ($i > $o) > $i).
1.27/0.99	thf(decl_42, type, descrp: $o).
1.27/0.99	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
1.27/0.99	thf(decl_44, type, dsetconstrI: $o).
1.27/0.99	thf(decl_45, type, dsetconstrEL: $o).
1.27/0.99	thf(decl_46, type, dsetconstrER: $o).
1.27/0.99	thf(decl_47, type, exuE1: $o).
1.27/0.99	thf(decl_48, type, prop2set: $o > $i).
1.27/0.99	thf(decl_49, type, prop2setE: $o).
1.27/0.99	thf(decl_50, type, emptysetE: $o).
1.27/0.99	thf(decl_51, type, emptysetimpfalse: $o).
1.27/0.99	thf(decl_52, type, notinemptyset: $o).
1.27/0.99	thf(decl_53, type, exuE3e: $o).
1.27/0.99	thf(decl_54, type, setext: $o).
1.27/0.99	thf(decl_55, type, emptyI: $o).
1.27/0.99	thf(decl_56, type, noeltsimpempty: $o).
1.27/0.99	thf(decl_57, type, setbeta: $o).
1.27/0.99	thf(decl_58, type, nonempty: $i > $o).
1.27/0.99	thf(decl_59, type, nonemptyE1: $o).
1.27/0.99	thf(decl_60, type, nonemptyI: $o).
1.27/0.99	thf(decl_61, type, nonemptyI1: $o).
1.27/0.99	thf(decl_62, type, setadjoinIL: $o).
1.27/0.99	thf(decl_63, type, emptyinunitempty: $o).
1.27/0.99	thf(decl_64, type, setadjoinIR: $o).
1.27/0.99	thf(decl_65, type, setadjoinE: $o).
1.27/0.99	thf(decl_66, type, setadjoinOr: $o).
1.27/0.99	thf(decl_67, type, setoftrueEq: $o).
1.27/0.99	thf(decl_68, type, powersetI: $o).
1.27/0.99	thf(decl_69, type, emptyinPowerset: $o).
1.27/0.99	thf(decl_70, type, emptyInPowerset: $o).
1.27/0.99	thf(decl_71, type, powersetE: $o).
1.27/0.99	thf(decl_72, type, setunionI: $o).
1.27/0.99	thf(decl_73, type, setunionE: $o).
1.27/0.99	thf(decl_74, type, subPowSU: $o).
1.27/0.99	thf(decl_75, type, exuE2: $o).
1.27/0.99	thf(decl_76, type, nonemptyImpWitness: $o).
1.27/0.99	thf(decl_77, type, uniqinunit: $o).
1.27/0.99	thf(decl_78, type, notinsingleton: $o).
1.27/0.99	thf(decl_79, type, eqinunit: $o).
1.27/0.99	thf(decl_80, type, singletonsswitch: $o).
1.27/0.99	thf(decl_81, type, upairsetE: $o).
1.27/0.99	thf(decl_82, type, upairsetIL: $o).
1.27/0.99	thf(decl_83, type, upairsetIR: $o).
1.27/0.99	thf(decl_84, type, emptyE1: $o).
1.27/0.99	thf(decl_85, type, vacuousDall: $o).
1.27/0.99	thf(decl_86, type, quantDeMorgan1: $o).
1.27/0.99	thf(decl_87, type, quantDeMorgan2: $o).
1.27/0.99	thf(decl_88, type, quantDeMorgan3: $o).
1.27/0.99	thf(decl_89, type, quantDeMorgan4: $o).
1.27/0.99	thf(decl_90, type, prop2setI: $o).
1.27/0.99	thf(decl_92, type, prop2set2propI: $o).
1.27/0.99	thf(decl_93, type, notdexE: $o).
1.27/0.99	thf(decl_94, type, notdallE: $o).
1.27/0.99	thf(decl_95, type, exuI1: $o).
1.27/0.99	thf(decl_96, type, exuI3: $o).
1.27/0.99	thf(decl_97, type, exuI2: $o).
1.27/0.99	thf(decl_98, type, inCongP: $o).
1.27/0.99	thf(decl_99, type, in__Cong: $o).
1.27/0.99	thf(decl_100, type, exuE3u: $o).
1.27/0.99	thf(decl_101, type, exu__Cong: $o).
1.27/0.99	thf(decl_102, type, emptyset__Cong: $o).
1.27/0.99	thf(decl_103, type, setadjoin__Cong: $o).
1.27/0.99	thf(decl_104, type, powerset__Cong: $o).
1.27/0.99	thf(decl_105, type, setunion__Cong: $o).
1.27/0.99	thf(decl_106, type, omega__Cong: $o).
1.27/0.99	thf(decl_107, type, exuEu: $o).
1.27/0.99	thf(decl_108, type, descr__Cong: $o).
1.27/0.99	thf(decl_109, type, dsetconstr__Cong: $o).
1.27/0.99	thf(decl_110, type, subset: $i > $i > $o).
1.27/0.99	thf(decl_113, type, subsetI1: $o).
1.27/0.99	thf(decl_114, type, eqimpsubset2: $o).
1.27/0.99	thf(decl_115, type, eqimpsubset1: $o).
1.27/0.99	thf(decl_116, type, subsetI2: $o).
1.27/0.99	thf(decl_117, type, emptysetsubset: $o).
1.27/0.99	thf(decl_118, type, subsetE: $o).
1.27/0.99	thf(decl_119, type, subsetE2: $o).
1.27/0.99	thf(decl_120, type, notsubsetI: $o).
1.27/0.99	thf(decl_121, type, notequalI1: $o).
1.27/0.99	thf(decl_122, type, notequalI2: $o).
1.27/0.99	thf(decl_123, type, subsetRefl: $o).
1.27/0.99	thf(decl_124, type, subsetTrans: $o).
1.27/0.99	thf(decl_125, type, setadjoinSub: $o).
1.27/0.99	thf(decl_126, type, setadjoinSub2: $o).
1.27/0.99	thf(decl_127, type, subset2powerset: $o).
1.27/0.99	thf(decl_128, type, setextsub: $o).
1.27/0.99	thf(decl_129, type, subsetemptysetimpeq: $o).
1.27/0.99	thf(decl_130, type, powersetI1: $o).
1.27/0.99	thf(decl_131, type, powersetE1: $o).
1.27/0.99	thf(decl_132, type, inPowerset: $o).
1.27/0.99	thf(decl_133, type, powersetsubset: $o).
1.27/0.99	thf(decl_134, type, sepInPowerset: $o).
1.27/0.99	thf(decl_135, type, sepSubset: $o).
1.27/0.99	thf(decl_136, type, binunion: $i > $i > $i).
1.27/0.99	thf(decl_137, type, binunionIL: $o).
1.27/0.99	thf(decl_138, type, upairset2IR: $o).
1.27/0.99	thf(decl_139, type, binunionIR: $o).
1.27/0.99	thf(decl_140, type, binunionEcases: $o).
1.27/0.99	thf(decl_141, type, binunionE: $o).
1.27/0.99	thf(decl_142, type, binunionLsub: $o).
1.27/0.99	thf(decl_143, type, binunionRsub: $o).
1.27/0.99	thf(decl_144, type, binintersect: $i > $i > $i).
1.27/0.99	thf(decl_145, type, binintersectI: $o).
1.27/0.99	thf(decl_146, type, binintersectSubset5: $o).
1.27/0.99	thf(decl_147, type, binintersectEL: $o).
1.27/0.99	thf(decl_148, type, binintersectLsub: $o).
1.27/0.99	thf(decl_149, type, binintersectSubset2: $o).
1.27/0.99	thf(decl_150, type, binintersectSubset3: $o).
1.27/0.99	thf(decl_151, type, binintersectER: $o).
1.27/0.99	thf(decl_152, type, disjointsetsI1: $o).
1.27/0.99	thf(decl_153, type, binintersectRsub: $o).
1.27/0.99	thf(decl_154, type, binintersectSubset4: $o).
1.27/0.99	thf(decl_155, type, binintersectSubset1: $o).
1.27/0.99	thf(decl_156, type, bs114d: $o).
1.27/0.99	thf(decl_158, type, setminus: $i > $i > $i).
1.27/0.99	thf(decl_159, type, setminusI: $o).
1.27/0.99	thf(decl_160, type, setminusEL: $o).
1.27/0.99	thf(decl_161, type, setminusER: $o).
1.27/0.99	thf(decl_162, type, setminusSubset2: $o).
1.27/0.99	thf(decl_163, type, setminusERneg: $o).
1.27/0.99	thf(decl_164, type, setminusELneg: $o).
1.27/0.99	thf(decl_165, type, setminusILneg: $o).
1.27/0.99	thf(decl_166, type, setminusIRneg: $o).
1.27/0.99	thf(decl_167, type, setminusLsub: $o).
1.27/0.99	thf(decl_168, type, setminusSubset1: $o).
1.27/0.99	thf(decl_169, type, symdiff: $i > $i > $i).
1.27/0.99	thf(decl_170, type, symdiffE: $o).
1.27/0.99	thf(decl_171, type, symdiffI1: $o).
1.27/0.99	thf(decl_172, type, symdiffI2: $o).
1.27/0.99	thf(decl_173, type, symdiffIneg1: $o).
1.27/0.99	thf(decl_174, type, symdiffIneg2: $o).
1.27/0.99	thf(decl_175, type, iskpair: $i > $o).
1.27/0.99	thf(decl_176, type, secondinupair: $o).
1.27/0.99	thf(decl_177, type, setukpairIL: $o).
1.27/0.99	thf(decl_178, type, setukpairIR: $o).
1.27/0.99	thf(decl_179, type, kpairiskpair: $o).
1.27/0.99	thf(decl_180, type, kpair: $i > $i > $i).
1.27/0.99	thf(decl_181, type, kpairp: $o).
1.27/0.99	thf(decl_182, type, cartprod: $i > $i > $i).
1.27/0.99	thf(decl_183, type, singletonsubset: $o).
1.27/0.99	thf(decl_184, type, singletoninpowerset: $o).
1.27/0.99	thf(decl_185, type, singletoninpowunion: $o).
1.27/0.99	thf(decl_186, type, upairset2E: $o).
1.27/0.99	thf(decl_187, type, upairsubunion: $o).
1.27/0.99	thf(decl_188, type, upairinpowunion: $o).
1.27/0.99	thf(decl_189, type, ubforcartprodlem1: $o).
1.27/0.99	thf(decl_190, type, ubforcartprodlem2: $o).
1.27/0.99	thf(decl_191, type, ubforcartprodlem3: $o).
1.27/0.99	thf(decl_192, type, cartprodpairin: $o).
1.27/0.99	thf(decl_193, type, cartprodmempair1: $o).
1.27/0.99	thf(decl_194, type, cartprodmempair: $o).
1.27/0.99	thf(decl_195, type, setunionE2: $o).
1.27/0.99	thf(decl_196, type, setunionsingleton1: $o).
1.27/0.99	thf(decl_197, type, setunionsingleton2: $o).
1.27/0.99	thf(decl_198, type, setunionsingleton: $o).
1.27/0.99	thf(decl_199, type, singleton: $i > $o).
1.27/0.99	thf(decl_200, type, singletonprop: $o).
1.27/0.99	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
1.27/0.99	thf(decl_202, type, ex1E1: $o).
1.27/0.99	thf(decl_203, type, ex1I: $o).
1.27/0.99	thf(decl_204, type, ex1I2: $o).
1.27/0.99	thf(decl_205, type, singletonsuniq: $o).
1.27/0.99	thf(decl_210, type, setukpairinjL1: $o).
1.27/0.99	thf(decl_211, type, kfstsingleton: $o).
1.27/0.99	thf(decl_212, type, theprop: $o).
1.27/0.99	thf(decl_213, type, kfst: $i > $i).
1.27/0.99	thf(decl_214, type, kfstpairEq: $o).
1.27/0.99	thf(decl_215, type, cartprodfstin: $o).
1.27/0.99	thf(decl_216, type, setukpairinjL2: $o).
1.27/0.99	thf(decl_217, type, setukpairinjL: $o).
1.27/0.99	thf(decl_218, type, setukpairinjR11: $o).
1.27/0.99	thf(decl_219, type, setukpairinjR12: $o).
1.27/0.99	thf(decl_220, type, setukpairinjR1: $o).
1.27/0.99	thf(decl_221, type, upairequniteq: $o).
1.27/0.99	thf(decl_222, type, setukpairinjR2: $o).
1.27/0.99	thf(decl_223, type, setukpairinjR: $o).
1.27/0.99	thf(decl_224, type, ksndsingleton: $o).
1.27/0.99	thf(decl_225, type, ksnd: $i > $i).
1.27/0.99	thf(decl_226, type, ksndpairEq: $o).
1.27/0.99	thf(decl_227, type, kpairsurjEq: $o).
1.27/0.99	thf(decl_228, type, cartprodsndin: $o).
1.27/0.99	thf(decl_229, type, cartprodpairmemEL: $o).
1.27/0.99	thf(decl_230, type, cartprodpairmemER: $o).
1.27/0.99	thf(decl_231, type, cartprodmempaircEq: $o).
1.27/0.99	thf(decl_232, type, cartprodfstpairEq: $o).
1.27/0.99	thf(decl_233, type, cartprodsndpairEq: $o).
1.27/0.99	thf(decl_234, type, cartprodpairsurjEq: $o).
1.27/0.99	thf(decl_235, type, breln: $i > $i > $i > $o).
1.27/0.99	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
1.27/0.99	thf(decl_237, type, dpsetconstrI: $o).
1.27/0.99	thf(decl_238, type, dpsetconstrSub: $o).
1.27/0.99	thf(decl_239, type, setOfPairsIsBReln: $o).
1.27/0.99	thf(decl_240, type, dpsetconstrERa: $o).
1.27/0.99	thf(decl_241, type, dpsetconstrEL1: $o).
1.27/0.99	thf(decl_242, type, dpsetconstrEL2: $o).
1.27/0.99	thf(decl_243, type, dpsetconstrER: $o).
1.27/0.99	thf(decl_244, type, func: $i > $i > $i > $o).
1.27/0.99	thf(decl_245, type, funcSet: $i > $i > $i).
1.27/0.99	thf(decl_246, type, funcImageSingleton: $o).
1.27/0.99	thf(decl_247, type, apProp: $o).
1.27/0.99	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
1.27/0.99	thf(decl_249, type, app: $o).
1.27/0.99	thf(decl_250, type, infuncsetfunc: $o).
1.27/0.99	thf(decl_251, type, ap2p: $o).
1.27/0.99	thf(decl_252, type, funcinfuncset: $o).
1.27/0.99	thf(decl_253, type, lamProp: $o).
1.27/0.99	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
1.27/0.99	thf(decl_255, type, lamp: $o).
1.27/0.99	thf(decl_256, type, lam2p: $o).
1.27/0.99	thf(decl_257, type, brelnall1: $o).
1.27/0.99	thf(decl_258, type, brelnall2: $o).
1.27/0.99	thf(decl_259, type, ex1E2: $o).
1.27/0.99	thf(decl_260, type, funcGraphProp1: $o).
1.27/0.99	thf(decl_261, type, funcGraphProp3: $o).
1.27/0.99	thf(decl_262, type, funcGraphProp2: $o).
1.27/0.99	thf(decl_263, type, funcextLem: $o).
1.27/0.99	thf(decl_264, type, funcGraphProp4: $o).
1.27/0.99	thf(decl_265, type, subbreln: $o).
1.27/0.99	thf(decl_266, type, eqbreln: $o).
1.27/0.99	thf(decl_267, type, funcext: $o).
1.27/0.99	thf(decl_268, type, funcext2: $o).
1.27/0.99	thf(decl_269, type, ap2apEq1: $o).
1.27/0.99	thf(decl_270, type, ap2apEq2: $o).
1.27/0.99	thf(decl_271, type, beta1: $o).
1.27/0.99	thf(decl_272, type, eta1: $o).
1.27/0.99	thf(decl_273, type, lam2lamEq: $o).
1.27/0.99	thf(decl_274, type, beta2: $o).
1.27/0.99	thf(decl_275, type, eta2: $o).
1.27/0.99	thf(decl_276, type, iffalseProp1: $o).
1.27/0.99	thf(decl_277, type, iffalseProp2: $o).
1.27/0.99	thf(decl_278, type, iftrueProp1: $o).
1.27/0.99	thf(decl_279, type, iftrueProp2: $o).
1.27/0.99	thf(decl_280, type, ifSingleton: $o).
1.27/0.99	thf(decl_281, type, if: $i > $o > $i > $i > $i).
1.27/0.99	thf(decl_282, type, ifp: $o).
1.27/0.99	thf(decl_283, type, theeq: $o).
1.27/0.99	thf(decl_284, type, iftrue: $o).
1.27/0.99	thf(decl_285, type, iffalse: $o).
1.27/0.99	thf(decl_286, type, iftrueorfalse: $o).
1.27/0.99	thf(decl_287, type, binintersectT_lem: $o).
1.27/0.99	thf(decl_288, type, binunionT_lem: $o).
1.27/0.99	thf(decl_289, type, powersetT_lem: $o).
1.27/0.99	thf(decl_290, type, setminusT_lem: $o).
1.27/0.99	thf(decl_291, type, complementT_lem: $o).
1.27/0.99	thf(decl_292, type, setextT: $o).
1.27/0.99	thf(decl_293, type, subsetTI: $o).
1.27/0.99	thf(decl_294, type, powersetTI1: $o).
1.27/0.99	thf(decl_295, type, powersetTE1: $o).
1.27/0.99	thf(decl_296, type, complementTI1: $o).
1.27/0.99	thf(decl_297, type, complementTE1: $o).
1.27/0.99	thf(decl_298, type, binintersectTELcontra: $o).
1.27/0.99	thf(decl_299, type, binintersectTERcontra: $o).
1.27/0.99	thf(decl_300, type, contrasubsetT: $o).
1.27/0.99	thf(decl_301, type, contrasubsetT1: $o).
1.27/0.99	thf(decl_302, type, contrasubsetT2: $o).
1.27/0.99	thf(decl_303, type, contrasubsetT3: $o).
1.27/0.99	thf(decl_304, type, doubleComplementI1: $o).
1.27/0.99	thf(decl_305, type, doubleComplementE1: $o).
1.27/0.99	thf(decl_306, type, doubleComplementSub1: $o).
1.27/0.99	thf(decl_307, type, doubleComplementSub2: $o).
1.27/0.99	thf(decl_308, type, doubleComplementEq: $o).
1.27/0.99	thf(decl_309, type, complementTnotintersectT: $o).
1.27/0.99	thf(decl_310, type, complementImpComplementIntersect: $o).
1.27/0.99	thf(decl_311, type, complementSubsetComplementIntersect: $o).
1.27/0.99	thf(decl_312, type, complementInPowersetComplementIntersect: $o).
1.27/0.99	thf(decl_313, type, contraSubsetComplement: $o).
1.27/0.99	thf(decl_314, type, complementTcontraSubset: $o).
1.27/0.99	thf(decl_315, type, binunionTILcontra: $o).
1.27/0.99	thf(decl_316, type, binunionTIRcontra: $o).
1.27/0.99	thf(decl_317, type, inIntersectImpInUnion: $o).
1.27/0.99	thf(decl_318, type, inIntersectImpInUnion2: $o).
1.27/0.99	thf(decl_319, type, epred1_0: $o).
1.27/0.99	thf(decl_320, type, esk1_2: $i > $i > $i).
1.27/0.99	thf(decl_321, type, esk2_2: $i > $i > $i).
1.27/0.99	thf(decl_322, type, esk3_2: $i > $i > $i).
1.27/0.99	thf(decl_323, type, esk4_1: $i > $i).
1.27/0.99	thf(decl_324, type, esk5_2: ($i > $i > $o) > $i > $i).
1.27/0.99	thf(decl_325, type, esk6_2: ($i > $i > $o) > $i > $i).
1.27/0.99	thf(decl_326, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
1.27/0.99	thf(decl_327, type, esk8_1: $i > $i).
1.27/0.99	thf(decl_328, type, esk9_1: ($i > $o) > $i).
1.27/0.99	thf(decl_329, type, esk10_1: ($i > $o) > $i).
1.27/0.99	thf(decl_330, type, esk11_2: $i > $i > $i).
1.27/0.99	thf(decl_331, type, esk12_2: $i > $i > $i).
1.27/0.99	thf(decl_332, type, esk13_1: $i > $i).
1.27/0.99	thf(decl_333, type, esk14_1: $i > $i).
1.27/0.99	thf(decl_334, type, esk15_1: $i > $i).
1.27/0.99	thf(decl_335, type, esk16_2: $i > $i > $i).
1.27/0.99	thf(decl_336, type, esk17_3: $i > $i > $o > $i).
1.27/0.99	thf(decl_337, type, esk18_1: ($i > $o) > $i).
1.27/0.99	thf(decl_338, type, esk19_1: $i > $i).
1.27/0.99	thf(decl_339, type, esk20_2: $i > ($i > $o) > $i).
1.27/0.99	thf(decl_340, type, esk21_2: $i > ($i > $o) > $i).
1.27/0.99	thf(decl_341, type, esk22_2: $i > ($i > $o) > $i).
1.27/0.99	thf(decl_342, type, esk23_2: $i > ($i > $o) > $i).
1.27/0.99	thf(decl_343, type, esk24_2: $i > ($i > $o) > $i).
1.27/0.99	thf(decl_344, type, esk25_2: $i > ($i > $o) > $i).
1.27/0.99	thf(decl_345, type, esk26_2: ($i > $o) > $i > $i).
1.27/0.99	thf(decl_346, type, esk27_1: ($i > $o) > $i).
1.27/0.99	thf(decl_347, type, esk28_1: ($i > $o) > $i).
1.27/0.99	thf(decl_348, type, esk29_2: ($i > $o) > $i > $i).
1.27/0.99	thf(decl_349, type, esk30_2: ($i > $o) > ($i > $o) > $i).
1.27/0.99	thf(decl_350, type, esk31_2: ($i > $o) > ($i > $o) > $i).
1.27/0.99	thf(decl_351, type, esk32_2: ($i > $o) > ($i > $o) > $i).
1.27/0.99	thf(decl_352, type, esk33_2: ($i > $o) > ($i > $o) > $i).
1.27/0.99	thf(decl_353, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
1.27/0.99	thf(decl_354, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
1.27/0.99	thf(decl_355, type, esk36_2: $i > $i > $i).
1.27/0.99	thf(decl_356, type, esk37_2: $i > $i > $i).
1.27/0.99	thf(decl_357, type, esk38_2: $i > $i > $i).
1.27/0.99	thf(decl_358, type, esk39_3: $i > $i > $i > $i).
1.27/0.99	thf(decl_359, type, esk40_3: $i > $i > $i > $i).
1.27/0.99	thf(decl_360, type, esk41_2: $i > $i > $i).
1.27/0.99	thf(decl_361, type, esk42_2: $i > ($i > $o) > $i).
1.27/0.99	thf(decl_362, type, esk43_2: $i > ($i > $o) > $i).
1.27/0.99	thf(decl_363, type, esk44_2: $i > ($i > $o) > $i).
1.27/0.99	thf(decl_364, type, esk45_3: $i > ($i > $o) > $i > $i).
1.27/0.99	thf(decl_365, type, esk46_2: $i > ($i > $o) > $i).
1.27/0.99	thf(decl_366, type, esk47_2: $i > ($i > $o) > $i).
1.27/0.99	thf(decl_367, type, esk48_3: $i > $i > ($i > $i) > $i).
1.27/0.99	thf(decl_368, type, esk49_3: $i > $i > ($i > $i) > $i).
1.27/0.99	thf(decl_369, type, esk50_3: $i > $i > ($i > $i) > $i).
1.27/0.99	thf(decl_370, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
1.27/0.99	thf(decl_371, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
1.27/0.99	thf(decl_372, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
1.27/0.99	thf(decl_373, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
1.27/0.99	thf(decl_374, type, esk55_4: $i > $i > $i > $i > $i).
1.27/0.99	thf(decl_375, type, esk56_4: $i > $i > $i > $i > $i).
1.27/0.99	thf(decl_376, type, esk57_4: $i > $i > $i > $i > $i).
1.27/0.99	thf(decl_377, type, esk58_4: $i > $i > $i > $i > $i).
1.27/0.99	thf(decl_378, type, esk59_4: $i > $i > $i > $i > $i).
1.27/0.99	thf(decl_379, type, esk60_4: $i > $i > $i > $i > $i).
1.27/0.99	thf(decl_380, type, esk61_4: $i > $i > $i > $i > $i).
1.27/0.99	thf(decl_381, type, esk62_4: $i > $i > $i > $i > $i).
1.27/0.99	thf(decl_382, type, esk63_4: $i > $i > $i > $i > $i).
1.27/0.99	thf(decl_383, type, esk64_3: $i > $i > ($i > $i) > $i).
1.27/0.99	thf(decl_384, type, esk65_3: $i > $i > ($i > $i) > $i).
1.27/0.99	thf(decl_385, type, esk66_3: $i > $i > ($i > $i) > $i).
1.27/0.99	thf(decl_386, type, esk67_3: $i > $i > $i > $i).
1.27/0.99	thf(decl_387, type, esk68_3: $i > $i > $i > $i).
1.27/0.99	thf(decl_388, type, esk69_3: $i > $i > $i > $i).
1.27/0.99	thf(decl_389, type, esk70_3: $i > $i > $i > $i).
1.27/0.99	thf(decl_390, type, esk71_0: $i).
1.27/0.99	thf(decl_391, type, esk72_0: $i).
1.27/0.99	thf(decl_392, type, esk73_0: $i).
1.27/0.99	thf(decl_393, type, esk74_0: $i).
1.27/0.99	thf(decl_394, type, esk75_0: $i).
1.27/0.99	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', sepSubset)).
1.27/0.99	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', sepInPowerset)).
1.27/0.99	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', dsetconstr__Cong)).
1.27/0.99	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', descr__Cong)).
1.27/0.99	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', exuI3)).
1.27/0.99	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setoftrueEq)).
1.27/0.99	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', exuE3e)).
1.27/0.99	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', exuE1)).
1.27/0.99	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', dsetconstrEL)).
1.27/0.99	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', descrp)).
1.27/0.99	thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', eta2)).
1.27/0.99	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', ifSingleton)).
1.27/0.99	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', ex1E1)).
1.27/0.99	thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', ex1I)).
1.27/0.99	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', dpsetconstrSub)).
1.27/0.99	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setOfPairsIsBReln)).
1.27/0.99	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', dpsetconstrERa)).
1.27/0.99	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', dpsetconstrER)).
1.27/0.99	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', funcImageSingleton)).
1.27/0.99	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', apProp)).
1.27/0.99	thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', lamp)).
1.27/0.99	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', lam2p)).
1.27/0.99	thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', beta1)).
1.27/0.99	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', iftrueProp2)).
1.27/0.99	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', iftrueProp1)).
1.27/0.99	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', iffalseProp2)).
1.27/0.99	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', iffalseProp1)).
1.27/0.99	thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', beta2)).
1.27/0.99	thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', lam2lamEq)).
1.27/0.99	thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', eta1)).
1.27/0.99	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', ex1E2)).
1.27/0.99	thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', lamProp)).
1.27/0.99	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', dpsetconstrEL2)).
1.27/0.99	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', dpsetconstrEL1)).
1.27/0.99	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', dpsetconstrI)).
1.27/0.99	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', ksndsingleton)).
1.27/0.99	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', kfstsingleton)).
1.27/0.99	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', ex1I2)).
1.27/0.99	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', singletonprop)).
1.27/0.99	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', exuEu)).
1.27/0.99	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', exu__Cong)).
1.27/0.99	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', exuE3u)).
1.27/0.99	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', exuI2)).
1.27/0.99	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', exuI1)).
1.27/0.99	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', emptyE1)).
1.27/0.99	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', exuE2)).
1.27/0.99	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', nonemptyI)).
1.27/0.99	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setbeta)).
1.27/0.99	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', dsetconstrER)).
1.27/0.99	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', dsetconstrI)).
1.27/0.99	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', replAx)).
1.27/0.99	thf(inIntersectImpInIntersectUnions, conjecture, (((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>(((omegaIndAx)=>((replAx)=>((foundationAx)=>((((dsetconstrI)=>(((dsetconstrER)=>(((prop2setE)=>((((notinemptyset)=>(((setext)=>((((setbeta)=>(((nonemptyI)=>((nonemptyI1)=>(((emptyinunitempty)=>((setadjoinIR)=>(((setadjoinOr)=>(((((emptyInPowerset)=>(((((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>(((((singletonsswitch)=>((upairsetE)=>(((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>(((quantDeMorgan4)=>((prop2setI)=>((((notdallE)=>((exuI1)=>(((exuI2)=>((inCongP)=>(((exuE3u)=>((exu__Cong)=>(((((setunion__Cong)=>((omega__Cong)=>((exuEu)=>(((((eqimpsubset2)=>(((((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>(((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((((((upairset2IR)=>((binunionIR)=>((((((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>(((((((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>(((setminusI)=>((setminusEL)=>(((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>(((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((((((secondinupair)=>((((kpairiskpair)=>((kpairp)=>((singletonsubset)=>(((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>(((((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>(((setunionE2)=>(((setunionsingleton2)=>((((ex1E1)=>((ex1I)=>(((((((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>(((setukpairinjR1)=>((upairequniteq)=>(((setukpairinjR)=>(((((cartprodsndin)=>(((cartprodpairmemER)=>((cartprodmempaircEq)=>((((((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((((ap2p)=>((funcinfuncset)=>(((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>(((funcGraphProp1)=>(((funcGraphProp2)=>((((subbreln)=>((eqbreln)=>((((((beta1)=>(((((eta2)=>((((((ifSingleton)=>(((theeq)=>((iftrue)=>((iffalse)=>(((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((((setextT)=>((subsetTI)=>((powersetTI1)=>(((complementTI1)=>((complementTE1)=>(((((contrasubsetT1)=>((contrasubsetT2)=>((((doubleComplementE1)=>((doubleComplementSub1)=>(((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>(((complementInPowersetComplementIntersect)=>((((binunionTILcontra)=>(((![X4:$i, X21:$i]:((![X48:$i]:((![X49:$i]:((![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49)))<=(in @ X2 @ (binintersect @ X21 @ X48)))))<=(in @ X49 @ (powerset @ X4))))<=(in @ X48 @ (powerset @ X4))))<=(in @ X21 @ (powerset @ X4))))<=(inIntersectImpInUnion2))<=(inIntersectImpInUnion))<=(binunionTIRcontra)))<=(complementTcontraSubset))<=(contraSubsetComplement)))<=(complementSubsetComplementIntersect)))))<=(doubleComplementSub2))))<=(doubleComplementI1))<=(contrasubsetT3))))<=(contrasubsetT))<=(binintersectTERcontra))<=(binintersectTELcontra))))<=(powersetTE1)))))<=(complementT_lem))<=(setminusT_lem)))))<=(iftrueorfalse)))))<=(ifp)))<=(iftrueProp2))<=(iftrueProp1))<=(iffalseProp2))<=(iffalseProp1)))<=(beta2))<=(lam2lamEq))<=(eta1)))<=(ap2apEq2))<=(ap2apEq1))<=(funcext2))<=(funcext))))<=(funcGraphProp4))<=(funcextLem)))<=(funcGraphProp3)))<=(ex1E2))))))<=(lamProp))))<=(infuncsetfunc))<=(app)))))<=(dpsetconstrEL2))<=(dpsetconstrEL1)))))<=(dpsetconstrI))<=(cartprodpairsurjEq))<=(cartprodsndpairEq))<=(cartprodfstpairEq))))<=(cartprodpairmemEL)))<=(kpairsurjEq))<=(ksndpairEq))<=(ksndsingleton)))<=(setukpairinjR2))))<=(setukpairinjR12)))))))<=(theprop))<=(kfstsingleton))<=(setukpairinjL1))<=(singletonsuniq))<=(ex1I2))))<=(singletonprop))<=(setunionsingleton)))<=(setunionsingleton1)))<=(cartprodmempair)))))<=(ubforcartprodlem2))<=(ubforcartprodlem1))<=(upairinpowunion)))))<=(singletoninpowerset)))))<=(setukpairIR))<=(setukpairIL)))<=(symdiffIneg2))<=(symdiffIneg1))<=(symdiffI2))<=(symdiffI1)))))<=(setminusIRneg))))))<=(setminusER))))<=(bs114d)))))<=(disjointsetsI1))<=(binintersectER))<=(binintersectSubset3))<=(binintersectSubset2))<=(binintersectLsub)))))<=(binunionRsub))<=(binunionLsub))<=(binunionE))<=(binunionEcases))))<=(binunionIL))<=(sepSubset))<=(sepInPowerset))<=(powersetsubset))))))))<=(setadjoinSub2))))))))))<=(emptysetsubset))<=(subsetI2))<=(eqimpsubset1)))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong)))))<=(powerset__Cong))<=(setadjoin__Cong))<=(emptyset__Cong))))<=(in__Cong))))<=(exuI3))))<=(notdexE))<=(prop2set2propI))))<=(quantDeMorgan3)))))))<=(upairsetIL))))<=(eqinunit))<=(notinsingleton))<=(uniqinunit)))))<=(setunionE))<=(setunionI))<=(powersetE)))<=(emptyinPowerset))<=(powersetI))<=(setoftrueEq)))<=(setadjoinE))))<=(setadjoinIL))))<=(nonemptyE1)))<=(noeltsimpempty))<=(emptyI)))<=(exuE3e)))<=(emptysetimpfalse))<=(emptysetE)))<=(exuE1)))<=(dsetconstrEL)))<=(descrp))<=(wellorderingAx)))))<=(omegaSAx)))))))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', inIntersectImpInIntersectUnions)).
1.27/0.99	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setminusELneg)).
1.27/0.99	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setextAx)).
1.27/0.99	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binunionLsub)).
1.27/0.99	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binunionIR)).
1.27/0.99	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binunionE)).
1.27/0.99	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binunionEcases)).
1.27/0.99	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binunionIL)).
1.27/0.99	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binintersectSubset4)).
1.27/0.99	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binintersectSubset1)).
1.27/0.99	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', powersetsubset)).
1.27/0.99	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setadjoinSub2)).
1.27/0.99	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', emptysetsubset)).
1.27/0.99	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setminusI)).
1.27/0.99	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', subsetI2)).
1.27/0.99	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', eqimpsubset1)).
1.27/0.99	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setminusEL)).
1.27/0.99	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', subsetI1)).
1.27/0.99	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setminusSubset2)).
1.27/0.99	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', powerset__Cong)).
1.27/0.99	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binintersectI)).
1.27/0.99	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setadjoin__Cong)).
1.27/0.99	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', emptyset__Cong)).
1.27/0.99	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setminusERneg)).
1.27/0.99	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', in__Cong)).
1.27/0.99	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', notdexE)).
1.27/0.99	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', quantDeMorgan3)).
1.27/0.99	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', upairsetIL)).
1.27/0.99	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', eqinunit)).
1.27/0.99	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setminusILneg)).
1.27/0.99	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', notinsingleton)).
1.27/0.99	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', uniqinunit)).
1.27/0.99	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setunionE)).
1.27/0.99	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binintersectSubset5)).
1.27/0.99	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setunionI)).
1.27/0.99	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setminusLsub)).
1.27/0.99	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', powersetE)).
1.27/0.99	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', emptyinPowerset)).
1.27/0.99	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setminusSubset1)).
1.27/0.99	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', powersetI)).
1.27/0.99	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setadjoinE)).
1.27/0.99	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', symdiffE)).
1.27/0.99	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setadjoinIL)).
1.27/0.99	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', nonemptyE1)).
1.27/0.99	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', secondinupair)).
1.27/0.99	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', noeltsimpempty)).
1.27/0.99	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', emptyI)).
1.27/0.99	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', kpairiskpair)).
1.27/0.99	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', emptysetimpfalse)).
1.27/0.99	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', emptysetE)).
1.27/0.99	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', kpairp)).
1.27/0.99	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', singletonsubset)).
1.27/0.99	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', wellorderingAx)).
1.27/0.99	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', omegaSAx)).
1.27/0.99	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', singletoninpowunion)).
1.27/0.99	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', upairset2E)).
1.27/0.99	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', upairsubunion)).
1.27/0.99	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', ubforcartprodlem3)).
1.27/0.99	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', cartprodpairin)).
1.27/0.99	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', cartprodmempair1)).
1.27/0.99	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setunionE2)).
1.27/0.99	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', theeq)).
1.27/0.99	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setunionsingleton2)).
1.27/0.99	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', kfstpairEq)).
1.27/0.99	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', cartprodfstin)).
1.27/0.99	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setukpairinjL2)).
1.27/0.99	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setukpairinjL)).
1.27/0.99	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setukpairinjR11)).
1.27/0.99	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setukpairinjR1)).
1.27/0.99	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binintersectEL)).
1.27/0.99	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', upairequniteq)).
1.27/0.99	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binintersectRsub)).
1.27/0.99	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setukpairinjR)).
1.27/0.99	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', cartprodsndin)).
1.27/0.99	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', cartprodpairmemER)).
1.27/0.99	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', cartprodmempaircEq)).
1.27/0.99	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', ap2p)).
1.27/0.99	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', funcinfuncset)).
1.27/0.99	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', brelnall1)).
1.27/0.99	thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', brelnall2)).
1.27/0.99	thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', funcGraphProp1)).
1.27/0.99	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', funcGraphProp2)).
1.27/0.99	thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', subbreln)).
1.27/0.99	thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', eqbreln)).
1.27/0.99	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', iftrue)).
1.27/0.99	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', iffalse)).
1.27/0.99	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binintersectT_lem)).
1.27/0.99	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binunionT_lem)).
1.27/0.99	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', powersetT_lem)).
1.27/0.99	thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setextT)).
1.27/0.99	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.YEvJ2f8LwU/E---3.1_29452.p', subsetTI)).
1.27/0.99	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.YEvJ2f8LwU/E---3.1_29452.p', powersetTI1)).
1.27/0.99	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', complementTI1)).
1.27/0.99	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$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.YEvJ2f8LwU/E---3.1_29452.p', complementTE1)).
1.27/0.99	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.YEvJ2f8LwU/E---3.1_29452.p', contrasubsetT1)).
1.27/0.99	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', contrasubsetT2)).
1.27/0.99	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$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.YEvJ2f8LwU/E---3.1_29452.p', doubleComplementE1)).
1.27/0.99	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.YEvJ2f8LwU/E---3.1_29452.p', doubleComplementSub1)).
1.27/0.99	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', doubleComplementEq)).
1.27/0.99	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.YEvJ2f8LwU/E---3.1_29452.p', complementTnotintersectT)).
1.27/0.99	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.YEvJ2f8LwU/E---3.1_29452.p', complementImpComplementIntersect)).
1.27/0.99	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', complementInPowersetComplementIntersect)).
1.27/0.99	thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binunionTILcontra)).
1.27/0.99	thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$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.YEvJ2f8LwU/E---3.1_29452.p', inIntersectImpInUnion2)).
1.27/0.99	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', inIntersectImpInUnion)).
1.27/0.99	thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binunionTIRcontra)).
1.27/0.99	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$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.YEvJ2f8LwU/E---3.1_29452.p', complementTcontraSubset)).
1.27/0.99	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.YEvJ2f8LwU/E---3.1_29452.p', contraSubsetComplement)).
1.27/0.99	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', complementSubsetComplementIntersect)).
1.27/0.99	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', doubleComplementSub2)).
1.27/0.99	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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.YEvJ2f8LwU/E---3.1_29452.p', doubleComplementI1)).
1.27/0.99	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', contrasubsetT3)).
1.27/0.99	thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', contrasubsetT)).
1.27/0.99	thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binintersectTERcontra)).
1.27/0.99	thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binintersectTELcontra)).
1.27/0.99	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', powersetTE1)).
1.27/0.99	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', complementT_lem)).
1.27/0.99	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setminusT_lem)).
1.27/0.99	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', iftrueorfalse)).
1.27/0.99	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', ifp)).
1.27/0.99	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', ap2apEq2)).
1.27/0.99	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', ap2apEq1)).
1.27/0.99	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', funcext2)).
1.27/0.99	thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', funcext)).
1.27/0.99	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', funcGraphProp4)).
1.27/0.99	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', funcextLem)).
1.27/0.99	thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', funcGraphProp3)).
1.27/0.99	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', infuncsetfunc)).
1.27/0.99	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', app)).
1.27/0.99	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', cartprodpairsurjEq)).
1.27/0.99	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', cartprodsndpairEq)).
1.27/0.99	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', cartprodfstpairEq)).
1.27/0.99	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', cartprodpairmemEL)).
1.27/0.99	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', kpairsurjEq)).
1.27/0.99	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', ksndpairEq)).
1.27/0.99	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setukpairinjR2)).
1.27/0.99	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setukpairinjR12)).
1.27/0.99	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', theprop)).
1.27/0.99	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setukpairinjL1)).
1.27/0.99	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', singletonsuniq)).
1.27/0.99	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setunionsingleton)).
1.27/0.99	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setunionsingleton1)).
1.27/0.99	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', cartprodmempair)).
1.27/0.99	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', ubforcartprodlem2)).
1.27/0.99	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', ubforcartprodlem1)).
1.27/0.99	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', upairinpowunion)).
1.27/0.99	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', singletoninpowerset)).
1.27/0.99	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setukpairIR)).
1.27/0.99	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setukpairIL)).
1.27/0.99	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', symdiffIneg2)).
1.27/0.99	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', symdiffIneg1)).
1.27/0.99	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', symdiffI2)).
1.27/0.99	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', symdiffI1)).
1.27/0.99	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setminusIRneg)).
1.27/0.99	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setminusER)).
1.27/0.99	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', bs114d)).
1.27/0.99	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', disjointsetsI1)).
1.27/0.99	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binintersectER)).
1.27/0.99	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binintersectSubset3)).
1.27/0.99	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binintersectSubset2)).
1.27/0.99	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binintersectLsub)).
1.27/0.99	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', binunionRsub)).
1.27/0.99	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', upairset2IR)).
1.27/0.99	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', inPowerset)).
1.27/0.99	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', powersetE1)).
1.27/0.99	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', powersetI1)).
1.27/0.99	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', subsetemptysetimpeq)).
1.27/0.99	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setextsub)).
1.27/0.99	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', subset2powerset)).
1.27/0.99	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setadjoinSub)).
1.27/0.99	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', subsetTrans)).
1.27/0.99	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', subsetRefl)).
1.27/0.99	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', notequalI2)).
1.27/0.99	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', notequalI1)).
1.27/0.99	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', notsubsetI)).
1.27/0.99	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', subsetE2)).
1.27/0.99	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', subsetE)).
1.27/0.99	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', eqimpsubset2)).
1.27/0.99	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', omega__Cong)).
1.27/0.99	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setunion__Cong)).
1.27/0.99	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', inCongP)).
1.27/0.99	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', notdallE)).
1.27/0.99	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', prop2setI)).
1.27/0.99	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', quantDeMorgan4)).
1.27/0.99	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', quantDeMorgan2)).
1.27/0.99	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', quantDeMorgan1)).
1.27/0.99	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', vacuousDall)).
1.27/0.99	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', upairsetIR)).
1.27/0.99	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', upairsetE)).
1.27/0.99	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', singletonsswitch)).
1.27/0.99	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', nonemptyImpWitness)).
1.27/0.99	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', subPowSU)).
1.27/0.99	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', emptyInPowerset)).
1.27/0.99	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setadjoinOr)).
1.27/0.99	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setadjoinIR)).
1.27/0.99	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', emptyinunitempty)).
1.27/0.99	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', nonemptyI1)).
1.27/0.99	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setext)).
1.27/0.99	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', notinemptyset)).
1.27/0.99	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', prop2setE)).
1.27/0.99	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', foundationAx)).
1.27/0.99	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', omegaIndAx)).
1.27/0.99	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', omega0Ax)).
1.27/0.99	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setunionAx)).
1.27/0.99	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', powersetAx)).
1.27/0.99	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', setadjoinAx)).
1.27/0.99	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.YEvJ2f8LwU/E---3.1_29452.p', emptysetAx)).
1.27/0.99	thf(c_0_258, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
1.27/0.99	thf(c_0_259, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
1.27/0.99	thf(c_0_260, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
1.27/0.99	thf(c_0_261, plain, ((descr__Cong)<=>![X1:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
1.27/0.99	thf(c_0_262, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
1.27/0.99	thf(c_0_263, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
1.27/0.99	thf(c_0_264, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
1.27/0.99	thf(c_0_265, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
1.27/0.99	thf(c_0_266, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
1.27/0.99	thf(c_0_267, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
1.27/0.99	thf(c_0_268, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 248 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
1.27/0.99	thf(c_0_269, plain, ((ifSingleton)<=>![X4:$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])).
1.27/0.99	thf(c_0_270, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
1.27/0.99	thf(c_0_271, plain, ((ex1I)<=>![X4:$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])).
1.27/0.99	thf(c_0_272, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
1.27/0.99	thf(c_0_273, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
1.27/0.99	thf(c_0_274, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
1.27/0.99	thf(c_0_275, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
1.27/0.99	thf(c_0_276, plain, ((funcImageSingleton)<=>![X4:$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])).
1.27/0.99	thf(c_0_277, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
1.27/0.99	thf(c_0_278, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
1.27/0.99	thf(c_0_279, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
1.27/0.99	thf(c_0_280, plain, ((beta1)<=>![X4:$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])).
1.27/0.99	thf(c_0_281, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
1.27/0.99	thf(c_0_282, plain, ((iftrueProp1)<=>![X4:$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])).
1.27/0.99	thf(c_0_283, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
1.27/0.99	thf(c_0_284, plain, ((iffalseProp1)<=>![X4:$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])).
1.27/0.99	thf(c_0_285, 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])).
1.27/0.99	thf(c_0_286, 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])).
1.27/0.99	thf(c_0_287, 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])).
1.27/0.99	thf(c_0_288, 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])).
1.27/0.99	thf(c_0_289, 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])).
1.27/0.99	thf(c_0_290, 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:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
1.27/0.99	thf(c_0_291, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
1.27/0.99	thf(c_0_292, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
1.27/0.99	thf(c_0_293, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
1.27/0.99	thf(c_0_294, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
1.27/0.99	thf(c_0_295, plain, ((ex1I2)<=>![X4:$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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
1.27/0.99	thf(c_0_296, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
1.27/0.99	thf(c_0_297, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
1.27/0.99	thf(c_0_298, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
1.27/0.99	thf(c_0_299, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
1.27/0.99	thf(c_0_300, 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])).
1.27/0.99	thf(c_0_301, 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])).
1.27/0.99	thf(c_0_302, 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])).
1.27/0.99	thf(c_0_303, 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])).
1.27/0.99	thf(c_0_304, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
1.27/0.99	thf(c_0_305, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
1.27/0.99	thf(c_0_306, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
1.27/0.99	thf(c_0_307, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
1.27/0.99	thf(c_0_308, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
1.27/0.99	thf(c_0_309, plain, ((epred1_0)<=>![X1640:$i]:(?[X1641:$i]:((((![X1642:$i]:(((in @ X1642 @ X1641)=>![X1643:$i]:(((in @ X1643 @ X1642)=>(in @ X1643 @ X1640)))))&![X1644:$i, X1645:$i]:((((in @ X1644 @ X1640)&(in @ X1645 @ X1640))=>(![X1646:$i]:(((in @ X1646 @ X1641)=>((in @ X1644 @ X1646)<=>(in @ X1645 @ X1646))))=>((X1644)=(X1645))))))&![X1647:$i, X1648:$i]:((((in @ X1647 @ X1641)&(in @ X1648 @ X1641))=>(![X1649:$i]:(((in @ X1649 @ X1647)=>(in @ X1649 @ X1648)))|![X1650:$i]:(((in @ X1650 @ X1648)=>(in @ X1650 @ X1647)))))))&![X1651:$i]:(((![X1652:$i]:(((in @ X1652 @ X1651)=>(in @ X1652 @ X1640)))&?[X1653:$i]:((in @ X1653 @ X1651)))=>?[X1654:$i, X1655:$i]:(((((in @ X1654 @ X1641)&(in @ X1655 @ X1651))&~(?[X1656:$i]:(((in @ X1656 @ X1654)&(in @ X1656 @ X1651)))))&![X1657:$i]:(((in @ X1657 @ X1641)=>(![X1658:$i]:(((in @ X1658 @ X1657)=>(in @ X1658 @ X1654)))|(in @ X1655 @ X1657)))))))))))), introduced(definition)).
1.27/0.99	thf(c_0_310, negated_conjecture, ~((![X1660:$i, X1661:$i]:((![X1662:$i]:(((in @ X1662 @ X1660)<=>(in @ X1662 @ X1661)))=>((X1660)=(X1661))))=>(![X859:$i]:(~(in @ X859 @ emptyset))=>(![X860:$i, X861:$i, X862:$i]:(((in @ X862 @ (setadjoin @ X860 @ X861))<=>(((X862)=(X860))|(in @ X862 @ X861))))=>(![X863:$i, X864:$i]:(((in @ X864 @ (powerset @ X863))<=>![X865:$i]:(((in @ X865 @ X864)=>(in @ X865 @ X863)))))=>(![X866:$i, X867:$i]:(((in @ X867 @ (setunion @ X866))<=>?[X868:$i]:(((in @ X867 @ X868)&(in @ X868 @ X866)))))=>((in @ emptyset @ omega)=>(![X1659:$i]:(((in @ X1659 @ omega)=>(in @ (setadjoin @ X1659 @ X1659) @ omega)))=>(![X869:$i]:((((in @ emptyset @ X869)&![X870:$i]:((((in @ X870 @ omega)&(in @ X870 @ X869))=>(in @ (setadjoin @ X870 @ X870) @ X869))))=>![X871:$i]:(((in @ X871 @ omega)=>(in @ X871 @ X869)))))=>(![X872:$i > $i > $o, X873:$i]:((![X874:$i]:(((in @ X874 @ X873)=>(exu @ (X872 @ X874))))=>?[X875:$i]:(![X876:$i]:(((in @ X876 @ X875)<=>?[X877:$i]:(((in @ X877 @ X873)&(X872 @ X877 @ X876))))))))=>(![X878:$i]:((?[X879:$i]:((in @ X879 @ X878))=>?[X880:$i]:(((in @ X880 @ X878)&~(?[X881:$i]:(((in @ X881 @ X880)&(in @ X881 @ X878))))))))=>((epred1_0)=>(![X1639:$i > $o]:(((exu @ X1639)=>(X1639 @ (descr @ (^[Z0/* 17 */:$i]:(X1639 @ Z0))))))=>(![X882:$i, X883:$i > $o, X884:$i]:(((in @ X884 @ X882)=>((X883 @ X884)=>(in @ X884 @ (dsetconstr @ X882 @ X883)))))=>(![X1636:$i, X1637:$i > $o, X1638:$i]:(((in @ X1638 @ (dsetconstr @ X1636 @ X1637))=>(in @ X1638 @ X1636)))=>(![X885:$i, X886:$i > $o, X887:$i]:(((in @ X887 @ (dsetconstr @ X885 @ X886))=>(X886 @ X887)))=>(![X1633:$i > $o]:(((exu @ X1633)=>?[X1634:$i]:(((X1633 @ X1634)&![X1635:$i]:(((X1633 @ X1635)=>((X1634)=(X1635))))))))=>(![X888:$o, X889:$i]:(((in @ X889 @ (prop2set @ ((X888))))=>(X888)))=>(![X1631:$i]:(((in @ X1631 @ emptyset)=>![X1632:$o]:((X1632))))=>(![X1630:$i]:(((in @ X1630 @ emptyset)=>~($true)))=>(![X890:$i]:(~(in @ X890 @ emptyset))=>(![X1628:$i > $o]:(((exu @ X1628)=>?[X1629:$i]:((X1628 @ X1629))))=>(![X891:$i, X892:$i]:((![X893:$i]:(((in @ X893 @ X891)=>(in @ X893 @ X892)))=>(![X894:$i]:(((in @ X894 @ X892)=>(in @ X894 @ X891)))=>((X891)=(X892)))))=>(![X1626:$i]:((![X1627:$i]:(~(in @ X1627 @ X1626))=>((X1626)=(emptyset))))=>(![X1624:$i]:((![X1625:$i]:(~(in @ X1625 @ X1624))=>((X1624)=(emptyset))))=>(![X895:$i, X896:$i > $o, X897:$i]:(((in @ X897 @ X895)=>((in @ X897 @ (dsetconstr @ X895 @ X896))<=>(X896 @ X897))))=>(![X1622:$i]:(((nonempty @ X1622)=>?[X1623:$i]:((in @ X1623 @ X1622))))=>(![X898:$i, X899:$i > $o, X900:$i]:(((in @ X900 @ X898)=>((X899 @ X900)=>(nonempty @ (dsetconstr @ X898 @ X899)))))=>(![X901:$i]:((?[X902:$i]:((in @ X902 @ X901))=>(nonempty @ X901)))=>(![X1620:$i, X1621:$i]:((in @ X1620 @ (setadjoin @ X1620 @ X1621)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X903:$i, X904:$i, X905:$i]:(((in @ X905 @ X904)=>(in @ X905 @ (setadjoin @ X903 @ X904))))=>(![X1616:$i, X1617:$i, X1618:$i]:(((in @ X1618 @ (setadjoin @ X1616 @ X1617))=>![X1619:$o]:(((((X1618)=(X1616))=>(X1619))=>(((in @ X1618 @ X1617)=>(X1619))=>(X1619))))))=>(![X906:$i, X907:$i, X908:$i]:(((in @ X908 @ (setadjoin @ X906 @ X907))=>(((X908)=(X906))|(in @ X908 @ X907))))=>(![X1615:$i]:(((dsetconstr @ X1615 @ (^[Z0/* 1 */:$i]:($true)))=(X1615)))=>(![X1612:$i, X1613:$i]:((![X1614:$i]:(((in @ X1614 @ X1613)=>(in @ X1614 @ X1612)))=>(in @ X1613 @ (powerset @ X1612))))=>(![X1611:$i]:((in @ emptyset @ (powerset @ X1611)))=>(![X909:$i]:((in @ emptyset @ (powerset @ X909)))=>(![X1608:$i, X1609:$i, X1610:$i]:(((in @ X1609 @ (powerset @ X1608))=>((in @ X1610 @ X1609)=>(in @ X1610 @ X1608))))=>(![X1605:$i, X1606:$i, X1607:$i]:(((in @ X1606 @ X1607)=>((in @ X1607 @ X1605)=>(in @ X1606 @ (setunion @ X1605)))))=>(![X1601:$i, X1602:$i]:(((in @ X1602 @ (setunion @ X1601))=>![X1603:$o]:((![X1604:$i]:(((in @ X1602 @ X1604)=>((in @ X1604 @ X1601)=>(X1603))))=>(X1603)))))=>(![X910:$i, X911:$i]:(((in @ X911 @ X910)=>(in @ X911 @ (powerset @ (setunion @ X910)))))=>(![X912:$i > $o]:(((exu @ X912)=>?[X913:$i]:(![X914:$i]:(((X912 @ X914)<=>((X914)=(X913)))))))=>(![X915:$i]:(((nonempty @ X915)=>?[X916:$i]:(((in @ X916 @ X915)&$true))))=>(![X1599:$i, X1600:$i]:(((in @ X1599 @ (setadjoin @ X1600 @ emptyset))=>((X1599)=(X1600))))=>(![X1597:$i, X1598:$i]:((((X1597)!=(X1598))=>~(in @ X1598 @ (setadjoin @ X1597 @ emptyset))))=>(![X1595:$i, X1596:$i]:((((X1595)=(X1596))=>(in @ X1595 @ (setadjoin @ X1596 @ emptyset))))=>(![X917:$i, X918:$i]:(((in @ X917 @ (setadjoin @ X918 @ emptyset))=>(in @ X918 @ (setadjoin @ X917 @ emptyset))))=>(![X919:$i, X920:$i, X921:$i]:(((in @ X921 @ (setadjoin @ X919 @ (setadjoin @ X920 @ emptyset)))=>(((X921)=(X919))|((X921)=(X920)))))=>(![X1593:$i, X1594:$i]:((in @ X1593 @ (setadjoin @ X1593 @ (setadjoin @ X1594 @ emptyset))))=>(![X922:$i, X923:$i]:((in @ X923 @ (setadjoin @ X922 @ (setadjoin @ X923 @ emptyset))))=>(![X924:$i, X925:$i > $o]:((?[X926:$i]:(((in @ X926 @ X924)&(X925 @ X926)))=>(((dsetconstr @ X924 @ X925)=(emptyset))=>~($true))))=>(![X927:$i > $o, X928:$i]:(((in @ X928 @ emptyset)=>(X927 @ X928)))=>(![X929:$i, X930:$i > $o]:((~(![X931:$i]:(((in @ X931 @ X929)=>(X930 @ X931))))=>?[X932:$i]:(((in @ X932 @ X929)&~((X930 @ X932))))))=>(![X933:$i, X934:$i > $o]:((![X935:$i]:(((in @ X935 @ X933)=>~((X934 @ X935))))=>~(?[X936:$i]:(((in @ X936 @ X933)&(X934 @ X936))))))=>(![X1589:$i, X1590:$i > $o]:((~(?[X1591:$i]:(((in @ X1591 @ X1589)&(X1590 @ X1591))))=>![X1592:$i]:(((in @ X1592 @ X1589)=>~((X1590 @ X1592))))))=>(![X937:$i, X938:$i > $o]:((?[X939:$i]:(((in @ X939 @ X937)&~((X938 @ X939))))=>~(![X940:$i]:(((in @ X940 @ X937)=>(X938 @ X940))))))=>(![X941:$o]:(((X941)=>(in @ emptyset @ (prop2set @ ((X941))))))=>((prop2set2propI)=>(![X1585:$i, X1586:$i > $o]:((~(?[X1587:$i]:(((in @ X1587 @ X1585)&(X1586 @ X1587))))=>![X1588:$i]:(((in @ X1588 @ X1585)=>~((X1586 @ X1588))))))=>(![X942:$i, X943:$i > $o]:((~(![X944:$i]:(((in @ X944 @ X942)=>(X943 @ X944))))=>?[X945:$i]:(((in @ X945 @ X942)&~((X943 @ X945))))))=>(![X946:$i > $o]:((?[X947:$i]:(((X946 @ X947)&![X948:$i]:(((X946 @ X948)=>((X947)=(X948))))))=>(exu @ X946)))=>(![X1581:$i > $o]:((?[X1582:$i]:((X1581 @ X1582))=>(![X1583:$i, X1584:$i]:(((X1581 @ X1583)=>((X1581 @ X1584)=>((X1583)=(X1584)))))=>(exu @ X1581))))=>(![X949:$i > $o]:((?[X950:$i]:(![X951:$i]:(((X949 @ X951)<=>((X951)=(X950)))))=>(exu @ X949)))=>(![X952:$i, X953:$i]:((((X952)=(X953))=>![X954:$i, X955:$i]:((((X954)=(X955))=>((in @ X954 @ X952)=>(in @ X955 @ X953))))))=>(![X1577:$i, X1578:$i]:((((X1577)=(X1578))=>![X1579:$i, X1580:$i]:((((X1579)=(X1580))=>((in @ X1579 @ X1577)<=>(in @ X1580 @ X1578))))))=>(![X956:$i > $o]:(((exu @ X956)=>![X957:$i, X958:$i]:(((X956 @ X957)=>((X956 @ X958)=>((X957)=(X958)))))))=>(![X959:$i > $o, X960:$i > $o]:((![X961:$i, X962:$i]:((((X961)=(X962))=>((X959 @ X961)<=>(X960 @ X962))))=>((exu @ X959)<=>(exu @ X960))))=>(((emptyset)=(emptyset))=>(![X1573:$i, X1574:$i]:((((X1573)=(X1574))=>![X1575:$i, X1576:$i]:((((X1575)=(X1576))=>((setadjoin @ X1573 @ X1575)=(setadjoin @ X1574 @ X1576))))))=>(![X1571:$i, X1572:$i]:((((X1571)=(X1572))=>((powerset @ X1571)=(powerset @ X1572))))=>(![X963:$i, X964:$i]:((((X963)=(X964))=>((setunion @ X963)=(setunion @ X964))))=>(((omega)=(omega))=>(![X965:$i > $o]:(((exu @ X965)=>![X966:$i, X967:$i]:(((X965 @ X966)=>((X965 @ X967)=>((X966)=(X967)))))))=>(![X1567:$i > $o, X1568:$i > $o]:((![X1569:$i, X1570:$i]:((((X1569)=(X1570))=>((X1567 @ X1569)<=>(X1568 @ X1570))))=>((exu @ X1567)=>((exu @ X1568)=>((descr @ X1567)=(descr @ X1568))))))=>(![X1561:$i, X1562:$i]:((((X1561)=(X1562))=>![X1563:$i > $o, X1564:$i > $o]:((![X1565:$i]:(((in @ X1565 @ X1561)=>![X1566:$i]:(((in @ X1566 @ X1562)=>(((X1565)=(X1566))=>((X1563 @ X1565)<=>(X1564 @ X1566)))))))=>((dsetconstr @ X1561 @ X1563)=(dsetconstr @ X1562 @ X1564))))))=>(![X1558:$i, X1559:$i]:((![X1560:$i]:(((in @ X1560 @ X1558)=>(in @ X1560 @ X1559)))=>(subset @ X1558 @ X1559)))=>(![X968:$i, X969:$i]:((((X968)=(X969))=>(subset @ X969 @ X968)))=>(![X1556:$i, X1557:$i]:((((X1556)=(X1557))=>(subset @ X1556 @ X1557)))=>(![X1553:$i, X1554:$i]:((![X1555:$i]:(((in @ X1555 @ X1553)=>(in @ X1555 @ X1554)))=>(subset @ X1553 @ X1554)))=>(![X1552:$i]:((subset @ emptyset @ X1552))=>(![X970:$i, X971:$i, X972:$i]:(((subset @ X970 @ X971)=>((in @ X972 @ X970)=>(in @ X972 @ X971))))=>(![X973:$i, X974:$i, X975:$i]:(((subset @ X973 @ X974)=>(~(in @ X975 @ X974)=>~(in @ X975 @ X973))))=>(![X976:$i, X977:$i, X978:$i]:(((in @ X978 @ X976)=>(~(in @ X978 @ X977)=>~(subset @ X976 @ X977))))=>(![X979:$i, X980:$i]:((~(subset @ X979 @ X980)=>((X979)!=(X980))))=>(![X981:$i, X982:$i, X983:$i]:(((in @ X983 @ X981)=>(~(in @ X983 @ X982)=>((X981)!=(X982)))))=>(![X984:$i]:((subset @ X984 @ X984))=>(![X985:$i, X986:$i, X987:$i]:(((subset @ X985 @ X986)=>((subset @ X986 @ X987)=>(subset @ X985 @ X987))))=>(![X988:$i, X989:$i]:((subset @ X989 @ (setadjoin @ X988 @ X989)))=>(![X1549:$i, X1550:$i, X1551:$i]:(((subset @ X1549 @ X1551)=>(subset @ X1549 @ (setadjoin @ X1550 @ X1551))))=>(![X990:$i, X991:$i]:(((subset @ X990 @ X991)=>(in @ X990 @ (powerset @ X991))))=>(![X992:$i, X993:$i]:(((subset @ X992 @ X993)=>((subset @ X993 @ X992)=>((X992)=(X993)))))=>(![X994:$i]:(((subset @ X994 @ emptyset)=>((X994)=(emptyset))))=>(![X995:$i, X996:$i]:(((subset @ X996 @ X995)=>(in @ X996 @ (powerset @ X995))))=>(![X997:$i, X998:$i]:(((in @ X998 @ (powerset @ X997))=>(subset @ X998 @ X997)))=>(![X999:$i]:((in @ X999 @ (powerset @ X999)))=>(![X1547:$i, X1548:$i]:(((subset @ X1547 @ X1548)=>(subset @ (powerset @ X1547) @ (powerset @ X1548))))=>(![X1545:$i, X1546:$i > $o]:((in @ (dsetconstr @ X1545 @ X1546) @ (powerset @ X1545)))=>(![X1543:$i, X1544:$i > $o]:((subset @ (dsetconstr @ X1543 @ X1544) @ X1543))=>(![X1540:$i, X1541:$i, X1542:$i]:(((in @ X1542 @ X1540)=>(in @ X1542 @ (binunion @ X1540 @ X1541))))=>(![X1000:$i, X1001:$i]:((in @ X1001 @ (setadjoin @ X1000 @ (setadjoin @ X1001 @ emptyset))))=>(![X1002:$i, X1003:$i, X1004:$i]:(((in @ X1004 @ X1003)=>(in @ X1004 @ (binunion @ X1002 @ X1003))))=>(![X1536:$i, X1537:$i, X1538:$i, X1539:$o]:(((in @ X1538 @ (binunion @ X1536 @ X1537))=>(((in @ X1538 @ X1536)=>(X1539))=>(((in @ X1538 @ X1537)=>(X1539))=>(X1539)))))=>(![X1533:$i, X1534:$i, X1535:$i]:(((in @ X1535 @ (binunion @ X1533 @ X1534))=>((in @ X1535 @ X1533)|(in @ X1535 @ X1534))))=>(![X1531:$i, X1532:$i]:((subset @ X1531 @ (binunion @ X1531 @ X1532)))=>(![X1529:$i, X1530:$i]:((subset @ X1530 @ (binunion @ X1529 @ X1530)))=>(![X1005:$i, X1006:$i, X1007:$i]:(((in @ X1007 @ X1005)=>((in @ X1007 @ X1006)=>(in @ X1007 @ (binintersect @ X1005 @ X1006)))))=>(![X1008:$i, X1009:$i, X1010:$i]:(((subset @ X1010 @ X1008)=>((subset @ X1010 @ X1009)=>(subset @ X1010 @ (binintersect @ X1008 @ X1009)))))=>(![X1011:$i, X1012:$i, X1013:$i]:(((in @ X1013 @ (binintersect @ X1011 @ X1012))=>(in @ X1013 @ X1011)))=>(![X1527:$i, X1528:$i]:((subset @ (binintersect @ X1527 @ X1528) @ X1527))=>(![X1525:$i, X1526:$i]:(((subset @ X1525 @ X1526)=>((binintersect @ X1525 @ X1526)=(X1525))))=>(![X1523:$i, X1524:$i]:((((binintersect @ X1523 @ X1524)=(X1524))=>(subset @ X1524 @ X1523)))=>(![X1520:$i, X1521:$i, X1522:$i]:(((in @ X1522 @ (binintersect @ X1520 @ X1521))=>(in @ X1522 @ X1521)))=>(![X1517:$i, X1518:$i]:((~(?[X1519:$i]:(((in @ X1519 @ X1517)&(in @ X1519 @ X1518))))=>((binintersect @ X1517 @ X1518)=(emptyset))))=>(![X1014:$i, X1015:$i]:((subset @ (binintersect @ X1014 @ X1015) @ X1015))=>(![X1016:$i, X1017:$i]:(((subset @ X1017 @ X1016)=>((binintersect @ X1016 @ X1017)=(X1017))))=>(![X1018:$i, X1019:$i]:((((binintersect @ X1018 @ X1019)=(X1018))=>(subset @ X1018 @ X1019)))=>(![X1514:$i, X1515:$i, X1516:$i]:(((binintersect @ X1514 @ (binunion @ X1515 @ X1516))=(binunion @ (binintersect @ X1514 @ X1515) @ (binintersect @ X1514 @ X1516))))=>(![X1020:$i, X1021:$i, X1022:$i]:(((in @ X1022 @ X1020)=>(~(in @ X1022 @ X1021)=>(in @ X1022 @ (setminus @ X1020 @ 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setminusELneg]), setextAx]), binunionLsub]), binunionIR]), binunionE]), binunionEcases]), binunionIL]), binintersectSubset4]), c_0_258]), c_0_259]), binintersectSubset1]), powersetsubset]), setadjoinSub2]), emptysetsubset]), setminusI]), subsetI2]), eqimpsubset1]), setminusEL]), subsetI1]), c_0_260]), c_0_261]), setminusSubset2]), powerset__Cong]), binintersectI]), setadjoin__Cong]), emptyset__Cong]), setminusERneg]), in__Cong]), c_0_262]), notdexE]), quantDeMorgan3]), upairsetIL]), eqinunit]), setminusILneg]), notinsingleton]), uniqinunit]), setunionE]), binintersectSubset5]), setunionI]), setminusLsub]), powersetE]), emptyinPowerset]), setminusSubset1]), powersetI]), c_0_263]), setadjoinE]), symdiffE]), setadjoinIL]), nonemptyE1]), secondinupair]), noeltsimpempty]), emptyI]), c_0_264]), kpairiskpair]), emptysetimpfalse]), emptysetE]), kpairp]), c_0_265]), c_0_266]), c_0_267]), singletonsubset]), wellorderingAx]), omegaSAx]), singletoninpowunion]), upairset2E]), upairsubunion]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), setunionE2]), c_0_268]), c_0_269]), theeq]), setunionsingleton2]), c_0_270]), c_0_271]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR1]), binintersectEL]), upairequniteq]), binintersectRsub]), setukpairinjR]), cartprodsndin]), cartprodpairmemER]), cartprodmempaircEq]), c_0_272]), c_0_273]), c_0_274]), c_0_275]), c_0_276]), c_0_277]), ap2p]), funcinfuncset]), c_0_278]), c_0_279]), brelnall1]), brelnall2]), funcGraphProp1]), funcGraphProp2]), subbreln]), eqbreln]), c_0_280]), iftrue]), iffalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setextT]), subsetTI]), powersetTI1]), complementTI1]), complementTE1]), contrasubsetT1]), contrasubsetT2]), doubleComplementE1]), doubleComplementSub1]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementInPowersetComplementIntersect]), binunionTILcontra]), inIntersectImpInUnion2]), inIntersectImpInUnion]), binunionTIRcontra]), complementTcontraSubset]), contraSubsetComplement]), complementSubsetComplementIntersect]), doubleComplementSub2]), doubleComplementI1]), contrasubsetT3]), contrasubsetT]), binintersectTERcontra]), binintersectTELcontra]), powersetTE1]), complementT_lem]), setminusT_lem]), iftrueorfalse]), ifp]), c_0_281]), c_0_282]), c_0_283]), c_0_284]), c_0_285]), c_0_286]), c_0_287]), ap2apEq2]), ap2apEq1]), funcext2]), funcext]), funcGraphProp4]), funcextLem]), funcGraphProp3]), c_0_288]), c_0_289]), infuncsetfunc]), app]), c_0_290]), c_0_291]), c_0_292]), cartprodpairsurjEq]), cartprodsndpairEq]), cartprodfstpairEq]), cartprodpairmemEL]), kpairsurjEq]), ksndpairEq]), c_0_293]), setukpairinjR2]), setukpairinjR12]), theprop]), c_0_294]), setukpairinjL1]), singletonsuniq]), c_0_295]), c_0_296]), setunionsingleton]), setunionsingleton1]), cartprodmempair]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), singletoninpowerset]), setukpairIR]), setukpairIL]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), symdiffI1]), setminusIRneg]), setminusER]), bs114d]), disjointsetsI1]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binunionRsub]), upairset2IR]), inPowerset]), powersetE1]), powersetI1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), setadjoinSub]), subsetTrans]), subsetRefl]), notequalI2]), notequalI1]), notsubsetI]), subsetE2]), subsetE]), eqimpsubset2]), c_0_297]), omega__Cong]), setunion__Cong]), c_0_298]), c_0_299]), inCongP]), c_0_300]), c_0_301]), notdallE]), prop2setI]), quantDeMorgan4]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_302]), upairsetIR]), upairsetE]), singletonsswitch]), nonemptyImpWitness]), c_0_303]), subPowSU]), emptyInPowerset]), setadjoinOr]), setadjoinIR]), emptyinunitempty]), nonemptyI1]), c_0_304]), c_0_305]), setext]), notinemptyset]), prop2setE]), c_0_306]), c_0_307]), foundationAx]), c_0_308]), omegaIndAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx])])]), c_0_309])).
1.27/0.99	thf(c_0_311, negated_conjecture, ![X1663:$i, X1664:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1676:$i, X1677:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1685:$i, X1686:$i > $i > $o, X1687:$i, X1690:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1697:$i, X1698:$i > $o, X1699:$i, X1700:$i > $o, X1701:$i, X1702:$i, X1703:$i > $o, X1704:$i, X1705:$i, X1706:$i > $o, X1707:$i, X1708:$i > $o, X1710:$i, X1711:$o, X1712:$i, X1713:$i, X1714:$o, X1715:$i, X1716:$i, X1717:$i > $o, X1719:$i, X1720:$i, X1723:$i, X1725:$i, X1727:$i, X1728:$i > $o, X1729:$i, X1730:$i, X1732:$i, X1733:$i > $o, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$o, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$o, X1765:$i, X1766:$i, X1767:$i > $o, X1769:$i, X1770:$i, X1771:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i > $o, X1790:$i, X1791:$i > $o, X1792:$i, X1793:$i, X1794:$i > $o, X1795:$i, X1797:$i, X1798:$i > $o, X1800:$i, X1801:$i, X1802:$i > $o, X1804:$i, X1805:$i, X1806:$i > $o, X1807:$i, X1809:$o, X1810:$i, X1811:$i > $o, X1813:$i, X1814:$i, X1815:$i > $o, X1816:$i, X1818:$i > $o, X1819:$i, X1821:$i > $o, X1822:$i, X1825:$i > $o, X1826:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i > $o, X1837:$i, X1838:$i, X1839:$i > $o, X1840:$i > $o, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i > $o, X1852:$i, X1853:$i, X1854:$i > $o, X1855:$i > $o, X1858:$i, X1859:$i, X1860:$i > $o, X1861:$i > $o, X1864:$i, X1865:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i > $o, X1912:$i, X1913:$i > $o, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$o, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$o, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i > $o, X2068:$i, X2069:$i, X2070:$i > $o, X2072:$i, X2073:$i > $o, X2074:$i, X2076:$i, X2077:$i > $o, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i > $i > $o, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i > $i > $o, X2158:$i, X2159:$i, X2160:$i > $i > $o, X2161:$i, X2162:$i, X2163:$i > $i > $o, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i > $i > $o, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i > $i > $o, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i > $i > $o, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i > $i, X2207:$i, X2208:$i, X2209:$i > $i, X2211:$i, X2212:$i, X2213:$i > $i, X2215:$i, X2216:$i, X2217:$i, X2218:$i > $o, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i > $o, X2228:$i, X2229:$i, X2230:$i > $o, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i, X2292:$i > 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(powerset @ X2361))|~(in @ X2362 @ (powerset @ X2361)))&(~(in @ (esk68_3 @ X2361 @ X2362 @ X2363) @ X2362)|((X2362)=(X2363))|(in @ (esk67_3 @ X2361 @ X2362 @ X2363) @ X2362)|~(in @ X2363 @ (powerset @ X2361))|~(in @ X2362 @ (powerset @ X2361)))))&(((in @ (esk68_3 @ X2361 @ X2362 @ X2363) @ X2361)|((X2362)=(X2363))|~(in @ (esk67_3 @ X2361 @ X2362 @ X2363) @ X2363)|~(in @ X2363 @ (powerset @ X2361))|~(in @ X2362 @ (powerset @ X2361)))&(((in @ (esk68_3 @ X2361 @ X2362 @ X2363) @ X2363)|((X2362)=(X2363))|~(in @ (esk67_3 @ X2361 @ X2362 @ X2363) @ X2363)|~(in @ X2363 @ (powerset @ X2361))|~(in @ X2362 @ (powerset @ X2361)))&(~(in @ (esk68_3 @ X2361 @ X2362 @ X2363) @ X2362)|((X2362)=(X2363))|~(in @ (esk67_3 @ X2361 @ X2362 @ X2363) @ X2363)|~(in @ X2363 @ (powerset @ X2361))|~(in @ X2362 @ (powerset @ X2361)))))))&((((in @ (esk69_3 @ X2366 @ X2367 @ X2368) @ X2366)|(subset @ X2367 @ X2368)|~(in @ X2368 @ (powerset @ X2366))|~(in @ X2367 @ (powerset @ X2366)))&(((in @ (esk69_3 @ X2366 @ X2367 @ X2368) @ X2367)|(subset @ X2367 @ X2368)|~(in @ X2368 @ (powerset @ X2366))|~(in @ X2367 @ (powerset @ X2366)))&(~(in @ (esk69_3 @ X2366 @ X2367 @ X2368) @ X2368)|(subset @ X2367 @ X2368)|~(in @ X2368 @ (powerset @ X2366))|~(in @ X2367 @ (powerset @ X2366)))))&((((in @ (esk70_3 @ X2370 @ X2371 @ X2372) @ X2370)|(in @ X2371 @ (powerset @ X2372))|~(in @ X2372 @ (powerset @ X2370))|~(in @ X2371 @ (powerset @ X2370)))&(((in @ (esk70_3 @ X2370 @ X2371 @ X2372) @ X2371)|(in @ X2371 @ (powerset @ X2372))|~(in @ X2372 @ (powerset @ X2370))|~(in @ X2371 @ (powerset @ X2370)))&(~(in @ (esk70_3 @ X2370 @ X2371 @ X2372) @ X2372)|(in @ X2371 @ (powerset @ X2372))|~(in @ X2372 @ (powerset @ X2370))|~(in @ X2371 @ (powerset @ X2370)))))&((~(in @ X2375 @ (powerset @ X2374))|(~(in @ X2376 @ (powerset @ X2374))|(~(in @ X2377 @ X2374)|(~(in @ X2375 @ (powerset @ X2376))|(~(in @ X2377 @ X2375)|(in @ X2377 @ X2376))))))&((~(in @ X2379 @ (powerset @ X2378))|(~(in @ X2380 @ X2378)|(~(in @ X2380 @ X2379)|~(in @ X2380 @ (setminus @ X2378 @ X2379)))))&((~(in @ X2382 @ (powerset @ X2381))|(~(in @ X2383 @ X2381)|((in @ X2383 @ (setminus @ X2381 @ X2382))|(in @ X2383 @ X2382))))&((~(in @ X2385 @ (powerset @ X2384))|(~(in @ X2386 @ (powerset @ X2384))|(~(in @ X2387 @ X2384)|((in @ X2387 @ X2385)|~(in @ X2387 @ (binintersect @ X2385 @ X2386))))))&((~(in @ X2389 @ (powerset @ X2388))|(~(in @ X2390 @ (powerset @ X2388))|(~(in @ X2391 @ X2388)|((in @ X2391 @ X2390)|~(in @ X2391 @ (binintersect @ X2389 @ X2390))))))&((~(in @ X2393 @ (powerset @ X2392))|(~(in @ X2394 @ (powerset @ X2392))|(~(in @ X2395 @ X2392)|(~(subset @ X2393 @ (setminus @ X2392 @ X2394))|(~(in @ X2395 @ X2394)|~(in @ X2395 @ X2393))))))&((~(in @ X2397 @ (powerset @ X2396))|(~(in @ X2398 @ (powerset @ X2396))|(~(in @ X2399 @ X2396)|(~(subset @ X2397 @ X2398)|((in @ X2399 @ X2398)|~(in @ X2399 @ X2397))))))&((~(in @ X2401 @ (powerset @ X2400))|(~(in @ X2402 @ (powerset @ X2400))|(~(subset @ X2401 @ X2402)|(subset @ (setminus @ X2400 @ X2402) @ (setminus @ X2400 @ X2401)))))&((~(in @ X2404 @ (powerset @ X2403))|(~(in @ X2405 @ (powerset @ X2403))|(~(subset @ (setminus @ X2403 @ X2405) @ (setminus @ X2403 @ X2404))|(subset @ X2404 @ X2405))))&((~(in @ X2407 @ (powerset @ X2406))|(~(in @ X2408 @ X2406)|(~(in @ X2408 @ X2407)|(in @ X2408 @ (setminus @ X2406 @ (setminus @ X2406 @ X2407))))))&((~(in @ X2410 @ (powerset @ X2409))|(~(in @ X2411 @ X2409)|(~(in @ X2411 @ (setminus @ X2409 @ (setminus @ X2409 @ X2410)))|(in @ X2411 @ X2410))))&((~(in @ X2413 @ (powerset @ X2412))|(subset @ X2413 @ (setminus @ X2412 @ (setminus @ X2412 @ X2413))))&((~(in @ X2415 @ (powerset @ X2414))|(subset @ (setminus @ X2414 @ (setminus @ X2414 @ X2415)) @ X2415))&((~(in @ X2417 @ (powerset @ X2416))|((X2417)=(setminus @ X2416 @ (setminus @ X2416 @ X2417))))&((~(in @ X2419 @ (powerset @ X2418))|(~(in @ X2420 @ (powerset @ X2418))|(~(in @ X2421 @ X2418)|(~(in @ X2421 @ (setminus @ X2418 @ X2419))|~(in @ X2421 @ (binintersect @ X2419 @ X2420))))))&((~(in @ X2423 @ (powerset @ X2422))|(~(in @ X2424 @ (powerset @ X2422))|(~(in @ X2425 @ X2422)|(~(in @ X2425 @ (setminus @ X2422 @ X2423))|(in @ X2425 @ (setminus @ X2422 @ (binintersect @ X2423 @ X2424)))))))&((~(in @ X2427 @ (powerset @ X2426))|(~(in @ X2428 @ (powerset @ X2426))|(subset @ (setminus @ X2426 @ X2427) @ (setminus @ X2426 @ (binintersect @ X2427 @ X2428)))))&((~(in @ X2430 @ (powerset @ X2429))|(~(in @ X2431 @ (powerset @ X2429))|(in @ (setminus @ X2429 @ X2430) @ (powerset @ (setminus @ X2429 @ (binintersect @ X2430 @ X2431))))))&((~(in @ X2433 @ (powerset @ X2432))|(~(in @ X2434 @ (powerset @ X2432))|(~(subset @ X2433 @ (setminus @ X2432 @ X2434))|(~(in @ X2435 @ X2432)|(~(in @ X2435 @ X2434)|(in @ X2435 @ (setminus @ X2432 @ X2433)))))))&((~(in @ X2437 @ (powerset @ X2436))|(~(in @ X2438 @ (powerset @ X2436))|(~(subset @ X2437 @ (setminus @ X2436 @ X2438))|(subset @ X2438 @ (setminus @ X2436 @ X2437)))))&((~(in @ X2440 @ (powerset @ X2439))|(~(in @ X2441 @ (powerset @ X2439))|(~(in @ X2442 @ X2439)|((in @ X2442 @ (binunion @ X2440 @ X2441))|~(in @ X2442 @ X2440)))))&((~(in @ X2444 @ (powerset @ X2443))|(~(in @ X2445 @ (powerset @ X2443))|(~(in @ X2446 @ X2443)|((in @ X2446 @ (binunion @ X2444 @ X2445))|~(in @ X2446 @ X2445)))))&((~(in @ X2448 @ (powerset @ X2447))|(~(in @ X2449 @ (powerset @ X2447))|(~(in @ X2450 @ (powerset @ X2447))|(~(in @ X2451 @ X2447)|(~(in @ X2451 @ (binintersect @ X2448 @ X2449))|(in @ X2451 @ (binunion @ X2448 @ X2450)))))))&((~(in @ X2453 @ (powerset @ X2452))|(~(in @ X2454 @ (powerset @ X2452))|(~(in @ X2455 @ (powerset @ X2452))|(~(in @ X2456 @ X2452)|(~(in @ X2456 @ (binintersect @ X2453 @ X2454))|(in @ X2456 @ (binunion @ X2454 @ X2455)))))))&((in @ esk72_0 @ (powerset @ esk71_0))&((in @ esk73_0 @ (powerset @ esk71_0))&((in @ esk74_0 @ (powerset @ esk71_0))&((in @ esk75_0 @ esk71_0)&((in @ esk75_0 @ (binintersect @ esk72_0 @ esk73_0))&~(in @ esk75_0 @ (binintersect @ (binunion @ esk72_0 @ esk74_0) @ (binunion @ esk73_0 @ esk74_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_310])])])])])])])).
1.27/0.99	thf(c_0_312, negated_conjecture, ~((in @ esk75_0 @ (binintersect @ (binunion @ esk72_0 @ esk74_0) @ (binunion @ esk73_0 @ esk74_0)))), inference(split_conjunct,[status(thm)],[c_0_311])).
1.27/0.99	thf(c_0_313, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ (binintersect @ X3 @ X4))|~((in @ X2 @ X3))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_311])).
1.27/0.99	thf(c_0_314, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X4)|~((in @ X2 @ (binintersect @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_311])).
1.27/0.99	thf(c_0_315, negated_conjecture, (in @ esk75_0 @ (binintersect @ esk72_0 @ esk73_0)), inference(split_conjunct,[status(thm)],[c_0_311])).
1.27/0.99	thf(c_0_316, negated_conjecture, (~((in @ esk75_0 @ (binunion @ esk73_0 @ esk74_0)))|~((in @ esk75_0 @ (binunion @ esk72_0 @ esk74_0)))), inference(spm,[status(thm)],[c_0_312, c_0_313])).
1.27/0.99	thf(c_0_317, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X3 @ X4))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_311])).
1.27/0.99	thf(c_0_318, negated_conjecture, (in @ esk75_0 @ esk73_0), inference(spm,[status(thm)],[c_0_314, c_0_315])).
1.27/0.99	thf(c_0_319, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X3)|~((in @ X2 @ (binintersect @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_311])).
1.27/0.99	thf(c_0_320, negated_conjecture, ~((in @ esk75_0 @ (binunion @ esk72_0 @ esk74_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_316, c_0_317]), c_0_318])])).
1.27/0.99	thf(c_0_321, negated_conjecture, (in @ esk75_0 @ esk72_0), inference(spm,[status(thm)],[c_0_319, c_0_315])).
1.27/0.99	thf(c_0_322, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_320, c_0_317]), c_0_321])]), ['proof']).
1.27/0.99	# SZS output end CNFRefutation
1.27/0.99	# Parsed axioms                        : 559
1.27/0.99	# Removed by relevancy pruning/SinE    : 301
1.27/0.99	# Initial clauses                      : 421
1.27/0.99	# Removed in clause preprocessing      : 34
1.27/0.99	# Initial clauses in saturation        : 387
1.27/0.99	# Processed clauses                    : 764
1.27/0.99	# ...of these trivial                  : 12
1.27/0.99	# ...subsumed                          : 41
1.27/0.99	# ...remaining for further processing  : 711
1.27/0.99	# Other redundant clauses eliminated   : 54
1.27/0.99	# Clauses deleted for lack of memory   : 0
1.27/0.99	# Backward-subsumed                    : 1
1.27/0.99	# Backward-rewritten                   : 3
1.27/0.99	# Generated clauses                    : 7837
1.27/0.99	# ...of the previous two non-redundant : 7598
1.27/0.99	# ...aggressively subsumed             : 0
1.27/0.99	# Contextual simplify-reflections      : 6
1.27/0.99	# Paramodulations                      : 7748
1.27/0.99	# Factorizations                       : 2
1.27/0.99	# NegExts                              : 0
1.27/0.99	# Equation resolutions                 : 61
1.27/0.99	# Disequality decompositions           : 0
1.27/0.99	# Total rewrite steps                  : 204
1.27/0.99	# ...of those cached                   : 136
1.27/0.99	# Propositional unsat checks           : 0
1.27/0.99	#    Propositional check models        : 0
1.27/0.99	#    Propositional check unsatisfiable : 0
1.27/0.99	#    Propositional clauses             : 0
1.27/0.99	#    Propositional clauses after purity: 0
1.27/0.99	#    Propositional unsat core size     : 0
1.27/0.99	#    Propositional preprocessing time  : 0.000
1.27/0.99	#    Propositional encoding time       : 0.000
1.27/0.99	#    Propositional solver time         : 0.000
1.27/0.99	#    Success case prop preproc time    : 0.000
1.27/0.99	#    Success case prop encoding time   : 0.000
1.27/0.99	#    Success case prop solver time     : 0.000
1.27/0.99	# Current number of processed clauses  : 353
1.27/0.99	#    Positive orientable unit clauses  : 50
1.27/0.99	#    Positive unorientable unit clauses: 0
1.27/0.99	#    Negative unit clauses             : 5
1.27/0.99	#    Non-unit-clauses                  : 298
1.27/0.99	# Current number of unprocessed clauses: 7556
1.27/0.99	# ...number of literals in the above   : 31642
1.27/0.99	# Current number of archived formulas  : 0
1.27/0.99	# Current number of archived clauses   : 342
1.27/0.99	# Clause-clause subsumption calls (NU) : 60043
1.27/0.99	# Rec. Clause-clause subsumption calls : 25327
1.27/0.99	# Non-unit clause-clause subsumptions  : 39
1.27/0.99	# Unit Clause-clause subsumption calls : 1532
1.27/0.99	# Rewrite failures with RHS unbound    : 0
1.27/0.99	# BW rewrite match attempts            : 34
1.27/0.99	# BW rewrite match successes           : 2
1.27/0.99	# Condensation attempts                : 0
1.27/0.99	# Condensation successes               : 0
1.27/0.99	# Termbank termtop insertions          : 209351
1.27/0.99	# Search garbage collected termcells   : 25904
1.27/0.99	
1.27/0.99	# -------------------------------------------------
1.27/0.99	# User time                : 0.361 s
1.27/0.99	# System time              : 0.031 s
1.27/0.99	# Total time               : 0.392 s
1.27/0.99	# Maximum resident set size: 8524 pages
1.27/0.99	
1.27/0.99	# -------------------------------------------------
1.27/0.99	# User time                : 0.377 s
1.27/0.99	# System time              : 0.035 s
1.27/0.99	# Total time               : 0.412 s
1.27/0.99	# Maximum resident set size: 2488 pages
1.27/0.99	% E exiting
1.27/0.99	% E exiting
1.27/0.99	EOF