0.06/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.11	% Command    : run_E %s %d THM
0.11/0.32	% Computer : n007.cluster.edu
0.11/0.32	% Model    : x86_64 x86_64
0.11/0.32	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.32	% Memory   : 8042.1875MB
0.11/0.32	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.32	% CPULimit   : 1440
0.11/0.32	% WCLimit    : 180
0.11/0.32	% DateTime   : Thu Jul  4 08:06:24 EDT 2024
0.11/0.32	% CPUTime    : 
0.18/0.47	Running higher-order theorem proving
0.18/0.53	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=180 /export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p
2.72/180.05	# Version: 3.2.0-ho
2.72/180.05	# Preprocessing class: HSLMSLSSLLLCHFA.
2.72/180.05	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
2.72/180.05	# Starting ehoh_best5 with 180s (1) cores
2.72/180.05	# Starting almost_fo_3_lam with 180s (1) cores
2.72/180.05	# Starting new_bool_5 with 180s (1) cores
2.72/180.05	# Starting pre_casc_3 with 180s (1) cores
2.72/180.05	# Starting ho_unfolding_8 with 180s (1) cores
2.72/180.05	# Starting new_ho_10_cnf2 with 180s (1) cores
2.72/180.05	# Starting new_bool_3 with 180s (1) cores
2.72/180.05	# Starting new_ho_5 with 180s (1) cores
2.72/180.05	# new_bool_5 with pid 14986 completed with status 0
2.72/180.05	# Result found by new_bool_5
2.72/180.05	# Preprocessing class: HSLMSLSSLLLCHFA.
2.72/180.05	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
2.72/180.05	# Starting ehoh_best5 with 180s (1) cores
2.72/180.05	# Starting almost_fo_3_lam with 180s (1) cores
2.72/180.05	# Starting new_bool_5 with 180s (1) cores
2.72/180.05	# SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
2.72/180.05	# Search class: HGHSM-FSLM32-MHFMMSBN
2.72/180.05	# Scheduled 10 strats onto 1 cores with 180 seconds (180 total)
2.72/180.05	# Starting ho_unfolding_8 with 33s (1) cores
2.72/180.05	# ho_unfolding_8 with pid 15001 completed with status 0
2.72/180.05	# Result found by ho_unfolding_8
2.72/180.05	# Preprocessing class: HSLMSLSSLLLCHFA.
2.72/180.05	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
2.72/180.05	# Starting ehoh_best5 with 180s (1) cores
2.72/180.05	# Starting almost_fo_3_lam with 180s (1) cores
2.72/180.05	# Starting new_bool_5 with 180s (1) cores
2.72/180.05	# SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
2.72/180.05	# Search class: HGHSM-FSLM32-MHFMMSBN
2.72/180.05	# Scheduled 10 strats onto 1 cores with 180 seconds (180 total)
2.72/180.05	# Starting ho_unfolding_8 with 33s (1) cores
2.72/180.05	# Preprocessing time       : 0.048 s
2.72/180.05	# Presaturation interreduction done
2.72/180.05	
2.72/180.05	# Proof found!
2.72/180.05	# SZS status Theorem
2.72/180.05	# SZS output start CNFRefutation
2.72/180.05	thf(decl_22, type, in: $i > $i > $o).
2.72/180.05	thf(decl_23, type, exu: ($i > $o) > $o).
2.72/180.05	thf(decl_24, type, setextAx: $o).
2.72/180.05	thf(decl_25, type, emptyset: $i).
2.72/180.05	thf(decl_26, type, emptysetAx: $o).
2.72/180.05	thf(decl_27, type, setadjoin: $i > $i > $i).
2.72/180.05	thf(decl_28, type, setadjoinAx: $o).
2.72/180.05	thf(decl_29, type, powerset: $i > $i).
2.72/180.05	thf(decl_30, type, powersetAx: $o).
2.72/180.05	thf(decl_31, type, setunion: $i > $i).
2.72/180.05	thf(decl_32, type, setunionAx: $o).
2.72/180.05	thf(decl_33, type, omega: $i).
2.72/180.05	thf(decl_34, type, omega0Ax: $o).
2.72/180.05	thf(decl_35, type, omegaSAx: $o).
2.72/180.05	thf(decl_36, type, omegaIndAx: $o).
2.72/180.05	thf(decl_37, type, replAx: $o).
2.72/180.05	thf(decl_38, type, foundationAx: $o).
2.72/180.05	thf(decl_39, type, wellorderingAx: $o).
2.72/180.05	thf(decl_40, type, descr: ($i > $o) > $i).
2.72/180.05	thf(decl_41, type, descrp: $o).
2.72/180.05	thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
2.72/180.05	thf(decl_43, type, dsetconstrI: $o).
2.72/180.05	thf(decl_44, type, dsetconstrEL: $o).
2.72/180.05	thf(decl_45, type, dsetconstrER: $o).
2.72/180.05	thf(decl_46, type, exuE1: $o).
2.72/180.05	thf(decl_47, type, prop2set: $o > $i).
2.72/180.05	thf(decl_48, type, prop2setE: $o).
2.72/180.05	thf(decl_49, type, emptysetE: $o).
2.72/180.05	thf(decl_50, type, emptysetimpfalse: $o).
2.72/180.05	thf(decl_51, type, notinemptyset: $o).
2.72/180.05	thf(decl_52, type, exuE3e: $o).
2.72/180.05	thf(decl_53, type, setext: $o).
2.72/180.05	thf(decl_54, type, emptyI: $o).
2.72/180.05	thf(decl_55, type, noeltsimpempty: $o).
2.72/180.05	thf(decl_56, type, setbeta: $o).
2.72/180.05	thf(decl_57, type, nonempty: $i > $o).
2.72/180.05	thf(decl_58, type, nonemptyE1: $o).
2.72/180.05	thf(decl_59, type, nonemptyI: $o).
2.72/180.05	thf(decl_60, type, nonemptyI1: $o).
2.72/180.05	thf(decl_61, type, setadjoinIL: $o).
2.72/180.05	thf(decl_62, type, emptyinunitempty: $o).
2.72/180.05	thf(decl_63, type, setadjoinIR: $o).
2.72/180.05	thf(decl_64, type, setadjoinE: $o).
2.72/180.05	thf(decl_65, type, setadjoinOr: $o).
2.72/180.05	thf(decl_66, type, setoftrueEq: $o).
2.72/180.05	thf(decl_67, type, powersetI: $o).
2.72/180.05	thf(decl_68, type, emptyinPowerset: $o).
2.72/180.05	thf(decl_69, type, emptyInPowerset: $o).
2.72/180.05	thf(decl_70, type, powersetE: $o).
2.72/180.05	thf(decl_71, type, setunionI: $o).
2.72/180.05	thf(decl_72, type, setunionE: $o).
2.72/180.05	thf(decl_73, type, subPowSU: $o).
2.72/180.05	thf(decl_74, type, exuE2: $o).
2.72/180.05	thf(decl_75, type, nonemptyImpWitness: $o).
2.72/180.05	thf(decl_76, type, uniqinunit: $o).
2.72/180.05	thf(decl_77, type, notinsingleton: $o).
2.72/180.05	thf(decl_78, type, eqinunit: $o).
2.72/180.05	thf(decl_79, type, singletonsswitch: $o).
2.72/180.05	thf(decl_80, type, upairsetE: $o).
2.72/180.05	thf(decl_81, type, upairsetIL: $o).
2.72/180.05	thf(decl_82, type, upairsetIR: $o).
2.72/180.05	thf(decl_83, type, emptyE1: $o).
2.72/180.05	thf(decl_84, type, vacuousDall: $o).
2.72/180.05	thf(decl_85, type, quantDeMorgan1: $o).
2.72/180.05	thf(decl_86, type, quantDeMorgan2: $o).
2.72/180.05	thf(decl_87, type, quantDeMorgan3: $o).
2.72/180.05	thf(decl_88, type, quantDeMorgan4: $o).
2.72/180.05	thf(decl_89, type, prop2setI: $o).
2.72/180.05	thf(decl_91, type, prop2set2propI: $o).
2.72/180.05	thf(decl_92, type, notdexE: $o).
2.72/180.05	thf(decl_93, type, notdallE: $o).
2.72/180.05	thf(decl_94, type, exuI1: $o).
2.72/180.05	thf(decl_95, type, exuI3: $o).
2.72/180.05	thf(decl_96, type, exuI2: $o).
2.72/180.05	thf(decl_97, type, inCongP: $o).
2.72/180.05	thf(decl_98, type, in__Cong: $o).
2.72/180.05	thf(decl_99, type, exuE3u: $o).
2.72/180.05	thf(decl_100, type, exu__Cong: $o).
2.72/180.05	thf(decl_101, type, emptyset__Cong: $o).
2.72/180.05	thf(decl_102, type, setadjoin__Cong: $o).
2.72/180.05	thf(decl_103, type, powerset__Cong: $o).
2.72/180.05	thf(decl_104, type, setunion__Cong: $o).
2.72/180.05	thf(decl_105, type, omega__Cong: $o).
2.72/180.05	thf(decl_106, type, exuEu: $o).
2.72/180.05	thf(decl_107, type, descr__Cong: $o).
2.72/180.05	thf(decl_108, type, dsetconstr__Cong: $o).
2.72/180.05	thf(decl_109, type, subset: $i > $i > $o).
2.72/180.05	thf(decl_112, type, subsetI1: $o).
2.72/180.05	thf(decl_113, type, eqimpsubset2: $o).
2.72/180.05	thf(decl_114, type, eqimpsubset1: $o).
2.72/180.05	thf(decl_115, type, subsetI2: $o).
2.72/180.05	thf(decl_116, type, emptysetsubset: $o).
2.72/180.05	thf(decl_117, type, subsetE: $o).
2.72/180.05	thf(decl_118, type, subsetE2: $o).
2.72/180.05	thf(decl_119, type, notsubsetI: $o).
2.72/180.05	thf(decl_120, type, notequalI1: $o).
2.72/180.05	thf(decl_121, type, notequalI2: $o).
2.72/180.05	thf(decl_122, type, subsetRefl: $o).
2.72/180.05	thf(decl_123, type, subsetTrans: $o).
2.72/180.05	thf(decl_124, type, setadjoinSub: $o).
2.72/180.05	thf(decl_125, type, setadjoinSub2: $o).
2.72/180.05	thf(decl_126, type, subset2powerset: $o).
2.72/180.05	thf(decl_127, type, setextsub: $o).
2.72/180.05	thf(decl_128, type, subsetemptysetimpeq: $o).
2.72/180.05	thf(decl_129, type, powersetI1: $o).
2.72/180.05	thf(decl_130, type, powersetE1: $o).
2.72/180.05	thf(decl_131, type, inPowerset: $o).
2.72/180.05	thf(decl_132, type, powersetsubset: $o).
2.72/180.05	thf(decl_133, type, sepInPowerset: $o).
2.72/180.05	thf(decl_134, type, sepSubset: $o).
2.72/180.05	thf(decl_135, type, binunion: $i > $i > $i).
2.72/180.05	thf(decl_136, type, binunionIL: $o).
2.72/180.05	thf(decl_137, type, upairset2IR: $o).
2.72/180.05	thf(decl_138, type, binunionIR: $o).
2.72/180.05	thf(decl_139, type, binunionEcases: $o).
2.72/180.05	thf(decl_140, type, binunionE: $o).
2.72/180.05	thf(decl_141, type, binunionLsub: $o).
2.72/180.05	thf(decl_142, type, binunionRsub: $o).
2.72/180.05	thf(decl_143, type, binintersect: $i > $i > $i).
2.72/180.05	thf(decl_144, type, binintersectI: $o).
2.72/180.05	thf(decl_145, type, binintersectSubset5: $o).
2.72/180.05	thf(decl_146, type, binintersectEL: $o).
2.72/180.05	thf(decl_147, type, binintersectLsub: $o).
2.72/180.05	thf(decl_148, type, binintersectSubset2: $o).
2.72/180.05	thf(decl_149, type, binintersectSubset3: $o).
2.72/180.05	thf(decl_150, type, binintersectER: $o).
2.72/180.05	thf(decl_151, type, disjointsetsI1: $o).
2.72/180.05	thf(decl_152, type, binintersectRsub: $o).
2.72/180.05	thf(decl_153, type, binintersectSubset4: $o).
2.72/180.05	thf(decl_154, type, binintersectSubset1: $o).
2.72/180.05	thf(decl_155, type, bs114d: $o).
2.72/180.05	thf(decl_157, type, setminus: $i > $i > $i).
2.72/180.05	thf(decl_158, type, setminusI: $o).
2.72/180.05	thf(decl_159, type, setminusEL: $o).
2.72/180.05	thf(decl_160, type, setminusER: $o).
2.72/180.05	thf(decl_161, type, setminusSubset2: $o).
2.72/180.05	thf(decl_162, type, setminusERneg: $o).
2.72/180.05	thf(decl_163, type, setminusELneg: $o).
2.72/180.05	thf(decl_164, type, setminusILneg: $o).
2.72/180.05	thf(decl_165, type, setminusIRneg: $o).
2.72/180.05	thf(decl_166, type, setminusLsub: $o).
2.72/180.05	thf(decl_167, type, setminusSubset1: $o).
2.72/180.05	thf(decl_168, type, symdiff: $i > $i > $i).
2.72/180.05	thf(decl_169, type, symdiffE: $o).
2.72/180.05	thf(decl_170, type, symdiffI1: $o).
2.72/180.05	thf(decl_171, type, symdiffI2: $o).
2.72/180.05	thf(decl_172, type, symdiffIneg1: $o).
2.72/180.05	thf(decl_173, type, symdiffIneg2: $o).
2.72/180.05	thf(decl_174, type, iskpair: $i > $o).
2.72/180.05	thf(decl_175, type, secondinupair: $o).
2.72/180.05	thf(decl_176, type, setukpairIL: $o).
2.72/180.05	thf(decl_177, type, setukpairIR: $o).
2.72/180.05	thf(decl_178, type, kpairiskpair: $o).
2.72/180.05	thf(decl_179, type, kpair: $i > $i > $i).
2.72/180.05	thf(decl_180, type, kpairp: $o).
2.72/180.05	thf(decl_181, type, cartprod: $i > $i > $i).
2.72/180.05	thf(decl_182, type, singletonsubset: $o).
2.72/180.05	thf(decl_183, type, singletoninpowerset: $o).
2.72/180.05	thf(decl_184, type, singletoninpowunion: $o).
2.72/180.05	thf(decl_185, type, upairset2E: $o).
2.72/180.05	thf(decl_186, type, upairsubunion: $o).
2.72/180.05	thf(decl_187, type, upairinpowunion: $o).
2.72/180.05	thf(decl_188, type, ubforcartprodlem1: $o).
2.72/180.05	thf(decl_189, type, ubforcartprodlem2: $o).
2.72/180.05	thf(decl_190, type, ubforcartprodlem3: $o).
2.72/180.05	thf(decl_191, type, cartprodpairin: $o).
2.72/180.05	thf(decl_192, type, cartprodmempair1: $o).
2.72/180.05	thf(decl_193, type, cartprodmempair: $o).
2.72/180.05	thf(decl_194, type, setunionE2: $o).
2.72/180.05	thf(decl_195, type, setunionsingleton1: $o).
2.72/180.05	thf(decl_196, type, setunionsingleton2: $o).
2.72/180.05	thf(decl_197, type, setunionsingleton: $o).
2.72/180.05	thf(decl_198, type, singleton: $i > $o).
2.72/180.05	thf(decl_199, type, singletonprop: $o).
2.72/180.05	thf(decl_200, type, ex1: $i > ($i > $o) > $o).
2.72/180.05	thf(decl_201, type, ex1E1: $o).
2.72/180.05	thf(decl_202, type, ex1I: $o).
2.72/180.05	thf(decl_203, type, ex1I2: $o).
2.72/180.05	thf(decl_204, type, singletonsuniq: $o).
2.72/180.05	thf(decl_209, type, setukpairinjL1: $o).
2.72/180.05	thf(decl_210, type, kfstsingleton: $o).
2.72/180.05	thf(decl_211, type, theprop: $o).
2.72/180.05	thf(decl_212, type, kfst: $i > $i).
2.72/180.05	thf(decl_213, type, kfstpairEq: $o).
2.72/180.05	thf(decl_214, type, cartprodfstin: $o).
2.72/180.05	thf(decl_215, type, setukpairinjL2: $o).
2.72/180.05	thf(decl_216, type, setukpairinjL: $o).
2.72/180.05	thf(decl_217, type, setukpairinjR11: $o).
2.72/180.05	thf(decl_218, type, setukpairinjR12: $o).
2.72/180.05	thf(decl_219, type, setukpairinjR1: $o).
2.72/180.05	thf(decl_220, type, upairequniteq: $o).
2.72/180.05	thf(decl_221, type, setukpairinjR2: $o).
2.72/180.05	thf(decl_222, type, setukpairinjR: $o).
2.72/180.05	thf(decl_223, type, ksndsingleton: $o).
2.72/180.05	thf(decl_224, type, ksnd: $i > $i).
2.72/180.05	thf(decl_225, type, ksndpairEq: $o).
2.72/180.05	thf(decl_226, type, kpairsurjEq: $o).
2.72/180.05	thf(decl_227, type, cartprodsndin: $o).
2.72/180.05	thf(decl_228, type, cartprodpairmemEL: $o).
2.72/180.05	thf(decl_229, type, cartprodpairmemER: $o).
2.72/180.05	thf(decl_230, type, cartprodmempaircEq: $o).
2.72/180.05	thf(decl_231, type, cartprodfstpairEq: $o).
2.72/180.05	thf(decl_232, type, cartprodsndpairEq: $o).
2.72/180.05	thf(decl_233, type, cartprodpairsurjEq: $o).
2.72/180.05	thf(decl_234, type, breln: $i > $i > $i > $o).
2.72/180.05	thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
2.72/180.05	thf(decl_236, type, dpsetconstrI: $o).
2.72/180.05	thf(decl_237, type, dpsetconstrSub: $o).
2.72/180.05	thf(decl_238, type, setOfPairsIsBReln: $o).
2.72/180.05	thf(decl_239, type, dpsetconstrERa: $o).
2.72/180.05	thf(decl_240, type, dpsetconstrEL1: $o).
2.72/180.05	thf(decl_241, type, dpsetconstrEL2: $o).
2.72/180.05	thf(decl_242, type, dpsetconstrER: $o).
2.72/180.05	thf(decl_243, type, func: $i > $i > $i > $o).
2.72/180.05	thf(decl_244, type, funcSet: $i > $i > $i).
2.72/180.05	thf(decl_245, type, funcImageSingleton: $o).
2.72/180.05	thf(decl_246, type, apProp: $o).
2.72/180.05	thf(decl_247, type, ap: $i > $i > $i > $i > $i).
2.72/180.05	thf(decl_248, type, app: $o).
2.72/180.05	thf(decl_249, type, infuncsetfunc: $o).
2.72/180.05	thf(decl_250, type, ap2p: $o).
2.72/180.05	thf(decl_251, type, funcinfuncset: $o).
2.72/180.05	thf(decl_252, type, lamProp: $o).
2.72/180.05	thf(decl_253, type, lam: $i > $i > ($i > $i) > $i).
2.72/180.05	thf(decl_254, type, lamp: $o).
2.72/180.05	thf(decl_255, type, lam2p: $o).
2.72/180.05	thf(decl_256, type, brelnall1: $o).
2.72/180.05	thf(decl_257, type, brelnall2: $o).
2.72/180.05	thf(decl_258, type, ex1E2: $o).
2.72/180.05	thf(decl_259, type, funcGraphProp1: $o).
2.72/180.05	thf(decl_260, type, funcGraphProp3: $o).
2.72/180.05	thf(decl_261, type, funcGraphProp2: $o).
2.72/180.05	thf(decl_262, type, funcextLem: $o).
2.72/180.05	thf(decl_263, type, funcGraphProp4: $o).
2.72/180.05	thf(decl_264, type, subbreln: $o).
2.72/180.05	thf(decl_265, type, eqbreln: $o).
2.72/180.05	thf(decl_266, type, funcext: $o).
2.72/180.05	thf(decl_267, type, funcext2: $o).
2.72/180.05	thf(decl_268, type, ap2apEq1: $o).
2.72/180.05	thf(decl_269, type, ap2apEq2: $o).
2.72/180.05	thf(decl_270, type, beta1: $o).
2.72/180.05	thf(decl_271, type, eta1: $o).
2.72/180.05	thf(decl_272, type, lam2lamEq: $o).
2.72/180.05	thf(decl_273, type, beta2: $o).
2.72/180.05	thf(decl_274, type, eta2: $o).
2.72/180.05	thf(decl_275, type, iffalseProp1: $o).
2.72/180.05	thf(decl_276, type, iffalseProp2: $o).
2.72/180.05	thf(decl_277, type, iftrueProp1: $o).
2.72/180.05	thf(decl_278, type, iftrueProp2: $o).
2.72/180.05	thf(decl_279, type, ifSingleton: $o).
2.72/180.05	thf(decl_280, type, if: $i > $o > $i > $i > $i).
2.72/180.05	thf(decl_281, type, ifp: $o).
2.72/180.05	thf(decl_282, type, theeq: $o).
2.72/180.05	thf(decl_283, type, iftrue: $o).
2.72/180.05	thf(decl_284, type, iffalse: $o).
2.72/180.05	thf(decl_285, type, iftrueorfalse: $o).
2.72/180.05	thf(decl_286, type, binintersectT_lem: $o).
2.72/180.05	thf(decl_287, type, binunionT_lem: $o).
2.72/180.05	thf(decl_288, type, powersetT_lem: $o).
2.72/180.05	thf(decl_289, type, setminusT_lem: $o).
2.72/180.05	thf(decl_290, type, complementT_lem: $o).
2.72/180.05	thf(decl_291, type, setextT: $o).
2.72/180.05	thf(decl_292, type, subsetTI: $o).
2.72/180.05	thf(decl_293, type, powersetTI1: $o).
2.72/180.05	thf(decl_294, type, powersetTE1: $o).
2.72/180.05	thf(decl_295, type, complementTI1: $o).
2.72/180.05	thf(decl_296, type, complementTE1: $o).
2.72/180.05	thf(decl_297, type, binintersectTELcontra: $o).
2.72/180.05	thf(decl_298, type, binintersectTERcontra: $o).
2.72/180.05	thf(decl_299, type, contrasubsetT: $o).
2.72/180.05	thf(decl_300, type, contrasubsetT1: $o).
2.72/180.05	thf(decl_301, type, contrasubsetT2: $o).
2.72/180.05	thf(decl_302, type, contrasubsetT3: $o).
2.72/180.05	thf(decl_303, type, doubleComplementI1: $o).
2.72/180.05	thf(decl_304, type, doubleComplementE1: $o).
2.72/180.05	thf(decl_305, type, doubleComplementSub1: $o).
2.72/180.05	thf(decl_306, type, doubleComplementSub2: $o).
2.72/180.05	thf(decl_307, type, doubleComplementEq: $o).
2.72/180.05	thf(decl_308, type, complementTnotintersectT: $o).
2.72/180.05	thf(decl_309, type, complementImpComplementIntersect: $o).
2.72/180.05	thf(decl_310, type, complementSubsetComplementIntersect: $o).
2.72/180.05	thf(decl_311, type, complementInPowersetComplementIntersect: $o).
2.72/180.05	thf(decl_312, type, contraSubsetComplement: $o).
2.72/180.05	thf(decl_313, type, complementTcontraSubset: $o).
2.72/180.05	thf(decl_314, type, binunionTILcontra: $o).
2.72/180.05	thf(decl_315, type, binunionTIRcontra: $o).
2.72/180.05	thf(decl_316, type, inIntersectImpInUnion: $o).
2.72/180.05	thf(decl_317, type, inIntersectImpInUnion2: $o).
2.72/180.05	thf(decl_318, type, inIntersectImpInIntersectUnions: $o).
2.72/180.05	thf(decl_319, type, intersectInPowersetIntersectUnions: $o).
2.72/180.05	thf(decl_320, type, inComplementUnionImpNotIn1: $o).
2.72/180.05	thf(decl_321, type, inComplementUnionImpInComplement1: $o).
2.72/180.05	thf(decl_322, type, binunionTE: $o).
2.72/180.05	thf(decl_323, type, binunionTEcontra: $o).
2.72/180.05	thf(decl_324, type, demorgan2a1: $o).
2.72/180.05	thf(decl_325, type, complementUnionInPowersetComplement: $o).
2.72/180.05	thf(decl_326, type, demorgan2a2: $o).
2.72/180.05	thf(decl_327, type, demorgan1a: $o).
2.72/180.05	thf(decl_328, type, demorgan1b: $o).
2.72/180.05	thf(decl_329, type, demorgan1: $o).
2.72/180.05	thf(decl_330, type, demorgan2a: $o).
2.72/180.05	thf(decl_331, type, demorgan2b2: $o).
2.72/180.05	thf(decl_332, type, demorgan2b: $o).
2.72/180.05	thf(decl_333, type, demorgan2: $o).
2.72/180.05	thf(decl_334, type, woz13rule0: $o).
2.72/180.05	thf(decl_335, type, woz13rule1: $o).
2.72/180.05	thf(decl_336, type, woz13rule2: $o).
2.72/180.05	thf(decl_337, type, woz13rule3: $o).
2.72/180.05	thf(decl_338, type, woz13rule4: $o).
2.72/180.05	thf(decl_339, type, woz1_1: $o).
2.72/180.05	thf(decl_340, type, woz1_2: $o).
2.72/180.05	thf(decl_341, type, woz1_3: $o).
2.72/180.05	thf(decl_342, type, epred1_0: $o).
2.72/180.05	thf(decl_343, type, esk1_2: $i > $i > $i).
2.72/180.05	thf(decl_344, type, esk2_2: $i > $i > $i).
2.72/180.05	thf(decl_345, type, esk3_2: $i > $i > $i).
2.72/180.05	thf(decl_346, type, esk4_1: $i > $i).
2.72/180.05	thf(decl_347, type, esk5_2: ($i > $i > $o) > $i > $i).
2.72/180.05	thf(decl_348, type, esk6_2: ($i > $i > $o) > $i > $i).
2.72/180.05	thf(decl_349, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
2.72/180.05	thf(decl_350, type, esk8_1: $i > $i).
2.72/180.05	thf(decl_351, type, esk9_1: ($i > $o) > $i).
2.72/180.05	thf(decl_352, type, esk10_1: ($i > $o) > $i).
2.72/180.05	thf(decl_353, type, esk11_2: $i > $i > $i).
2.72/180.05	thf(decl_354, type, esk12_2: $i > $i > $i).
2.72/180.05	thf(decl_355, type, esk13_1: $i > $i).
2.72/180.05	thf(decl_356, type, esk14_1: $i > $i).
2.72/180.05	thf(decl_357, type, esk15_1: $i > $i).
2.72/180.05	thf(decl_358, type, esk16_2: $i > $i > $i).
2.72/180.05	thf(decl_359, type, esk17_3: $i > $i > $o > $i).
2.72/180.05	thf(decl_360, type, esk18_1: ($i > $o) > $i).
2.72/180.05	thf(decl_361, type, esk19_1: $i > $i).
2.72/180.05	thf(decl_362, type, esk20_2: $i > ($i > $o) > $i).
2.72/180.05	thf(decl_363, type, esk21_2: $i > ($i > $o) > $i).
2.72/180.05	thf(decl_364, type, esk22_2: $i > ($i > $o) > $i).
2.72/180.05	thf(decl_365, type, esk23_2: $i > ($i > $o) > $i).
2.72/180.05	thf(decl_366, type, esk24_2: $i > ($i > $o) > $i).
2.72/180.05	thf(decl_367, type, esk25_2: $i > ($i > $o) > $i).
2.72/180.05	thf(decl_368, type, esk26_2: ($i > $o) > $i > $i).
2.72/180.05	thf(decl_369, type, esk27_1: ($i > $o) > $i).
2.72/180.05	thf(decl_370, type, esk28_1: ($i > $o) > $i).
2.72/180.05	thf(decl_371, type, esk29_2: ($i > $o) > $i > $i).
2.72/180.05	thf(decl_372, type, esk30_2: ($i > $o) > ($i > $o) > $i).
2.72/180.05	thf(decl_373, type, esk31_2: ($i > $o) > ($i > $o) > $i).
2.72/180.05	thf(decl_374, type, esk32_2: ($i > $o) > ($i > $o) > $i).
2.72/180.05	thf(decl_375, type, esk33_2: ($i > $o) > ($i > $o) > $i).
2.72/180.05	thf(decl_376, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
2.72/180.05	thf(decl_377, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
2.72/180.05	thf(decl_378, type, esk36_2: $i > $i > $i).
2.72/180.05	thf(decl_379, type, esk37_2: $i > $i > $i).
2.72/180.05	thf(decl_380, type, esk38_2: $i > $i > $i).
2.72/180.05	thf(decl_381, type, esk39_3: $i > $i > $i > $i).
2.72/180.05	thf(decl_382, type, esk40_3: $i > $i > $i > $i).
2.72/180.05	thf(decl_383, type, esk41_2: $i > $i > $i).
2.72/180.05	thf(decl_384, type, esk42_2: $i > ($i > $o) > $i).
2.72/180.05	thf(decl_385, type, esk43_2: $i > ($i > $o) > $i).
2.72/180.05	thf(decl_386, type, esk44_2: $i > ($i > $o) > $i).
2.72/180.05	thf(decl_387, type, esk45_3: $i > ($i > $o) > $i > $i).
2.72/180.05	thf(decl_388, type, esk46_2: $i > ($i > $o) > $i).
2.72/180.05	thf(decl_389, type, esk47_2: $i > ($i > $o) > $i).
2.72/180.05	thf(decl_390, type, esk48_3: $i > $i > ($i > $i) > $i).
2.72/180.05	thf(decl_391, type, esk49_3: $i > $i > ($i > $i) > $i).
2.72/180.05	thf(decl_392, type, esk50_3: $i > $i > ($i > $i) > $i).
2.72/180.05	thf(decl_393, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
2.72/180.05	thf(decl_394, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
2.72/180.05	thf(decl_395, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
2.72/180.05	thf(decl_396, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
2.72/180.05	thf(decl_397, type, esk55_4: $i > $i > $i > $i > $i).
2.72/180.05	thf(decl_398, type, esk56_4: $i > $i > $i > $i > $i).
2.72/180.05	thf(decl_399, type, esk57_4: $i > $i > $i > $i > $i).
2.72/180.05	thf(decl_400, type, esk58_4: $i > $i > $i > $i > $i).
2.72/180.05	thf(decl_401, type, esk59_4: $i > $i > $i > $i > $i).
2.72/180.05	thf(decl_402, type, esk60_4: $i > $i > $i > $i > $i).
2.72/180.05	thf(decl_403, type, esk61_4: $i > $i > $i > $i > $i).
2.72/180.05	thf(decl_404, type, esk62_4: $i > $i > $i > $i > $i).
2.72/180.05	thf(decl_405, type, esk63_4: $i > $i > $i > $i > $i).
2.72/180.05	thf(decl_406, type, esk64_3: $i > $i > ($i > $i) > $i).
2.72/180.05	thf(decl_407, type, esk65_3: $i > $i > ($i > $i) > $i).
2.72/180.05	thf(decl_408, type, esk66_3: $i > $i > ($i > $i) > $i).
2.72/180.05	thf(decl_409, type, esk67_3: $i > $i > $i > $i).
2.72/180.05	thf(decl_410, type, esk68_3: $i > $i > $i > $i).
2.72/180.05	thf(decl_411, type, esk69_3: $i > $i > $i > $i).
2.72/180.05	thf(decl_412, type, esk70_3: $i > $i > $i > $i).
2.72/180.05	thf(decl_413, type, esk71_0: $i).
2.72/180.05	thf(decl_414, type, esk72_0: $i).
2.72/180.05	thf(decl_415, type, esk73_0: $i).
2.72/180.05	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', sepSubset)).
2.72/180.05	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', descr__Cong)).
2.72/180.05	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', exuEu)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', exuE3u)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', exuI2)).
2.72/180.05	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', exuI3)).
2.72/180.05	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', exuI1)).
2.72/180.05	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', nonemptyI)).
2.72/180.05	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setbeta)).
2.72/180.05	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', exuE3e)).
2.72/180.05	thf(ex1I, axiom, ((ex1I)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', ex1I)).
2.72/180.05	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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', ex1I2)).
2.72/180.05	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', exuE1)).
2.72/180.05	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', descrp)).
2.72/180.05	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', replAx)).
2.72/180.05	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', ksndsingleton)).
2.72/180.05	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', dpsetconstrI)).
2.72/180.05	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', dpsetconstrEL1)).
2.72/180.05	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', funcImageSingleton)).
2.72/180.05	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', apProp)).
2.72/180.05	thf(beta1, axiom, ((beta1)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', beta1)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', lam2lamEq)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', beta2)).
2.72/180.05	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', iffalseProp1)).
2.72/180.05	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', iftrueProp1)).
2.72/180.05	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', iftrueProp2)).
2.72/180.05	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', ifSingleton)).
2.72/180.05	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', iffalseProp2)).
2.72/180.05	thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', eta2)).
2.72/180.05	thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', eta1)).
2.72/180.05	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', ex1E2)).
2.72/180.05	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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', lam2p)).
2.72/180.05	thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', lamp)).
2.72/180.05	thf(lamProp, axiom, ((lamProp)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', lamProp)).
2.72/180.05	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:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', dpsetconstrER)).
2.72/180.05	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', dpsetconstrEL2)).
2.72/180.05	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', dpsetconstrERa)).
2.72/180.05	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setOfPairsIsBReln)).
2.72/180.05	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', dpsetconstrSub)).
2.72/180.05	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', kfstsingleton)).
2.72/180.05	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', ex1E1)).
2.72/180.05	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', singletonprop)).
2.72/180.05	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', sepInPowerset)).
2.72/180.05	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', dsetconstr__Cong)).
2.72/180.05	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', exu__Cong)).
2.72/180.05	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', emptyE1)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', exuE2)).
2.72/180.05	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setoftrueEq)).
2.72/180.05	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', dsetconstrER)).
2.72/180.05	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', dsetconstrEL)).
2.72/180.05	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', dsetconstrI)).
2.72/180.05	thf(woz1_4, conjecture, (((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>(((omegaSAx)=>(((((wellorderingAx)=>(((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>(((prop2setE)=>((((notinemptyset)=>(((setext)=>((emptyI)=>((((nonemptyE1)=>((((((setadjoinIR)=>(((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>(((emptyInPowerset)=>((((setunionE)=>((subPowSU)=>((exuE2)=>((((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((((quantDeMorgan3)=>(((((((((((in__Cong)=>(((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>(((setunion__Cong)=>(((((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>(((subsetE2)=>(((notequalI1)=>((notequalI2)=>(((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>(((powersetE1)=>(((powersetsubset)=>((sepInPowerset)=>(((((((((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((((binintersectSubset3)=>(((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>(((setminusI)=>((setminusEL)=>((((((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>(((((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>(((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((((singletoninpowerset)=>((singletoninpowunion)=>(((upairsubunion)=>(((ubforcartprodlem1)=>(((ubforcartprodlem3)=>((cartprodpairin)=>((((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>(((((ex1I)=>((ex1I2)=>(((((((cartprodfstin)=>(((((setukpairinjR12)=>(((upairequniteq)=>((setukpairinjR2)=>(((ksndsingleton)=>((ksndpairEq)=>(((cartprodsndin)=>((cartprodpairmemEL)=>(((((cartprodsndpairEq)=>(((dpsetconstrI)=>(((((dpsetconstrEL1)=>((((funcImageSingleton)=>((apProp)=>(((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>(((((brelnall1)=>((brelnall2)=>((((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>(((eqbreln)=>((funcext)=>((funcext2)=>((((beta1)=>(((lam2lamEq)=>((beta2)=>(((iffalseProp1)=>(((iftrueProp1)=>((iftrueProp2)=>(((ifp)=>(((((((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((((subsetTI)=>(((powersetTE1)=>(((complementTE1)=>((((contrasubsetT)=>((((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((((doubleComplementEq)=>(((complementImpComplementIntersect)=>(((complementInPowersetComplementIntersect)=>(((complementTcontraSubset)=>((binunionTILcontra)=>(((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>(((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>(((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>(((((((((((woz1_2)=>(![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X48 @ (setminus @ X4 @ X21))<=(subset @ X21 @ (setminus @ X4 @ X48)))))))<=(woz1_3)))<=(woz1_1))<=(woz13rule4))<=(woz13rule3))<=(woz13rule2))<=(woz13rule1))<=(woz13rule0))<=(demorgan2))<=(demorgan2b))<=(demorgan2b2))))))))))<=(binunionTE))))<=(intersectInPowersetIntersectUnions)))))<=(binunionTIRcontra))))<=(contraSubsetComplement)))<=(complementSubsetComplementIntersect)))<=(complementTnotintersectT)))<=(doubleComplementSub2))<=(doubleComplementSub1)))))<=(contrasubsetT2))<=(contrasubsetT1)))<=(binintersectTERcontra))<=(binintersectTELcontra)))<=(complementTI1)))<=(powersetTI1)))<=(setextT))<=(complementT_lem)))))<=(binintersectT_lem))<=(iftrueorfalse))<=(iffalse))<=(iftrue))<=(theeq)))<=(ifSingleton))))<=(iffalseProp2)))<=(eta2))))<=(eta1)))<=(ap2apEq2))<=(ap2apEq1)))))<=(subbreln))))))<=(funcGraphProp1))<=(ex1E2))))<=(lam2p))<=(lamp))<=(lamProp)))))<=(app))))<=(dpsetconstrER))<=(dpsetconstrEL2)))<=(dpsetconstrERa))<=(setOfPairsIsBReln))<=(dpsetconstrSub)))<=(cartprodpairsurjEq)))<=(cartprodfstpairEq))<=(cartprodmempaircEq))<=(cartprodpairmemER))))<=(kpairsurjEq))))<=(setukpairinjR))))<=(setukpairinjR1)))<=(setukpairinjR11))<=(setukpairinjL))<=(setukpairinjL2)))<=(kfstpairEq))<=(theprop))<=(kfstsingleton))<=(setukpairinjL1))<=(singletonsuniq))))<=(ex1E1))<=(singletonprop))<=(setunionsingleton)))))<=(cartprodmempair))<=(cartprodmempair1))))<=(ubforcartprodlem2)))<=(upairinpowunion)))<=(upairset2E))))<=(singletonsubset))<=(kpairp)))))<=(secondinupair)))))<=(symdiffI1))<=(symdiffE))<=(setminusSubset1)))))<=(setminusELneg))<=(setminusERneg))<=(setminusSubset2))<=(setminusER))))<=(bs114d))))))<=(binintersectER)))<=(binintersectSubset2))<=(binintersectLsub))))))<=(binunionLsub))<=(binunionE))<=(binunionEcases))<=(binunionIR))<=(upairset2IR))<=(binunionIL))<=(sepSubset))))<=(inPowerset)))<=(powersetI1))))))))<=(subsetRefl))))<=(notsubsetI)))<=(subsetE))))))))<=(descr__Cong))<=(exuEu))<=(omega__Cong)))<=(powerset__Cong)))))<=(exuE3u)))<=(inCongP))<=(exuI2))<=(exuI3))<=(exuI1))<=(notdallE))<=(notdexE))<=(prop2set2propI))<=(prop2setI))<=(quantDeMorgan4)))<=(quantDeMorgan2))<=(quantDeMorgan1))))))))))<=(uniqinunit))<=(nonemptyImpWitness)))))<=(setunionI))<=(powersetE)))<=(emptyinPowerset)))))<=(setadjoinE)))<=(emptyinunitempty))<=(setadjoinIL))<=(nonemptyI1))<=(nonemptyI)))<=(setbeta))<=(noeltsimpempty))))<=(exuE3e)))<=(emptysetimpfalse))<=(emptysetE)))<=(exuE1)))))<=(descrp)))<=(foundationAx))<=(replAx))<=(omegaIndAx)))<=(omega0Ax))))))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', woz1_4)).
2.72/180.05	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', symdiffI2)).
2.72/180.05	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', quantDeMorgan2)).
2.72/180.05	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setextAx)).
2.72/180.05	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', upairset2IR)).
2.72/180.05	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setminusLsub)).
2.72/180.05	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binunionIL)).
2.72/180.05	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', inPowerset)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', setukpairIL)).
2.72/180.05	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', powersetI1)).
2.72/180.05	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', subsetRefl)).
2.72/180.05	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setukpairIR)).
2.72/180.05	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', notsubsetI)).
2.72/180.05	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', subsetE)).
2.72/180.05	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', kpairiskpair)).
2.72/180.05	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', omega__Cong)).
2.72/180.05	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', singletoninpowerset)).
2.72/180.05	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', powerset__Cong)).
2.72/180.05	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', inCongP)).
2.72/180.05	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', singletoninpowunion)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', upairsubunion)).
2.72/180.05	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', notdallE)).
2.72/180.05	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', notdexE)).
2.72/180.05	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', prop2setI)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', ubforcartprodlem1)).
2.72/180.05	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', quantDeMorgan4)).
2.72/180.05	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', cartprodsndpairEq)).
2.72/180.05	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', quantDeMorgan1)).
2.72/180.05	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', ubforcartprodlem3)).
2.72/180.05	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', uniqinunit)).
2.72/180.05	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', nonemptyImpWitness)).
2.72/180.05	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setunionI)).
2.72/180.05	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', cartprodpairin)).
2.72/180.05	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', powersetE)).
2.72/180.05	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', emptyinPowerset)).
2.72/180.05	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setunionE2)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', setadjoinE)).
2.72/180.05	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', emptyinunitempty)).
2.72/180.05	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setadjoinIL)).
2.72/180.05	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setunionsingleton1)).
2.72/180.05	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', nonemptyI1)).
2.72/180.05	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setunionsingleton2)).
2.72/180.05	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', noeltsimpempty)).
2.72/180.05	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', emptysetimpfalse)).
2.72/180.05	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', emptysetE)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', foundationAx)).
2.72/180.05	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', cartprodfstin)).
2.72/180.05	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', omegaIndAx)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', setukpairinjR12)).
2.72/180.05	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', omega0Ax)).
2.72/180.05	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', upairequniteq)).
2.72/180.05	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setukpairinjR2)).
2.72/180.05	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', ksndpairEq)).
2.72/180.05	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', cartprodsndin)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', cartprodpairmemEL)).
2.72/180.05	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', doubleComplementI1)).
2.72/180.05	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', doubleComplementE1)).
2.72/180.05	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', infuncsetfunc)).
2.72/180.05	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', ap2p)).
2.72/180.05	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', funcinfuncset)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', brelnall1)).
2.72/180.05	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', symdiffIneg1)).
2.72/180.05	thf(brelnall2, axiom, ((brelnall2)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', brelnall2)).
2.72/180.05	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', symdiffIneg2)).
2.72/180.05	thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', funcGraphProp3)).
2.72/180.05	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', funcGraphProp2)).
2.72/180.05	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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', funcextLem)).
2.72/180.05	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', funcGraphProp4)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', eqbreln)).
2.72/180.05	thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', funcext)).
2.72/180.05	thf(funcext2, axiom, ((funcext2)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', funcext2)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', ifp)).
2.72/180.05	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binunionT_lem)).
2.72/180.05	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', powersetT_lem)).
2.72/180.05	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', setminusT_lem)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', subsetTI)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', powersetTE1)).
2.72/180.05	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', complementTE1)).
2.72/180.05	thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', contrasubsetT)).
2.72/180.05	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', contrasubsetT3)).
2.72/180.05	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', upairset2E)).
2.72/180.05	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', singletonsubset)).
2.72/180.05	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', kpairp)).
2.72/180.05	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', secondinupair)).
2.72/180.05	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', symdiffI1)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', symdiffE)).
2.72/180.05	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setminusSubset1)).
2.72/180.05	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', doubleComplementEq)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', complementImpComplementIntersect)).
2.72/180.05	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', complementInPowersetComplementIntersect)).
2.72/180.05	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', complementTcontraSubset)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', binunionTILcontra)).
2.72/180.05	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', inIntersectImpInUnion)).
2.72/180.05	thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', inIntersectImpInUnion2)).
2.72/180.05	thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', inIntersectImpInIntersectUnions)).
2.72/180.05	thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', inComplementUnionImpNotIn1)).
2.72/180.05	thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', inComplementUnionImpInComplement1)).
2.72/180.05	thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binunionTEcontra)).
2.72/180.05	thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', demorgan2a1)).
2.72/180.05	thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', complementUnionInPowersetComplement)).
2.72/180.05	thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', demorgan2a2)).
2.72/180.05	thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', demorgan1a)).
2.72/180.05	thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', demorgan1b)).
2.72/180.05	thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', demorgan1)).
2.72/180.05	thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', demorgan2a)).
2.72/180.05	thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', woz1_2)).
2.72/180.05	thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', woz1_3)).
2.72/180.05	thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', woz1_1)).
2.72/180.05	thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', woz13rule4)).
2.72/180.05	thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', woz13rule3)).
2.72/180.05	thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', woz13rule2)).
2.72/180.05	thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', woz13rule1)).
2.72/180.05	thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', woz13rule0)).
2.72/180.05	thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', demorgan2)).
2.72/180.05	thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', demorgan2b)).
2.72/180.05	thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', demorgan2b2)).
2.72/180.05	thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binunionTE)).
2.72/180.05	thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', intersectInPowersetIntersectUnions)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', binunionTIRcontra)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', contraSubsetComplement)).
2.72/180.05	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', complementSubsetComplementIntersect)).
2.72/180.05	thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', complementTnotintersectT)).
2.72/180.05	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', doubleComplementSub2)).
2.72/180.05	thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', doubleComplementSub1)).
2.72/180.05	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', contrasubsetT2)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', contrasubsetT1)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', binintersectTERcontra)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', binintersectTELcontra)).
2.72/180.05	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', complementTI1)).
2.72/180.05	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', powersetTI1)).
2.72/180.05	thf(setextT, axiom, ((setextT)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', setextT)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', complementT_lem)).
2.72/180.05	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binintersectT_lem)).
2.72/180.05	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', iftrueorfalse)).
2.72/180.05	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', iffalse)).
2.72/180.05	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', iftrue)).
2.72/180.05	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', theeq)).
2.72/180.05	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', ap2apEq2)).
2.72/180.05	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', ap2apEq1)).
2.72/180.05	thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', subbreln)).
2.72/180.05	thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', funcGraphProp1)).
2.72/180.05	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', app)).
2.72/180.05	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', cartprodpairsurjEq)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', cartprodfstpairEq)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', cartprodmempaircEq)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', cartprodpairmemER)).
2.72/180.05	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', kpairsurjEq)).
2.72/180.05	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setukpairinjR)).
2.72/180.05	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setukpairinjR1)).
2.72/180.05	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setukpairinjR11)).
2.72/180.05	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setukpairinjL)).
2.72/180.05	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setukpairinjL2)).
2.72/180.05	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', kfstpairEq)).
2.72/180.05	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', theprop)).
2.72/180.05	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setukpairinjL1)).
2.72/180.05	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', singletonsuniq)).
2.72/180.05	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setunionsingleton)).
2.72/180.05	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', cartprodmempair)).
2.72/180.05	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.HNmXg0U3A1/E---3.1_14865.p', cartprodmempair1)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', ubforcartprodlem2)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', upairinpowunion)).
2.72/180.05	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setminusELneg)).
2.72/180.05	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setminusERneg)).
2.72/180.05	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setminusSubset2)).
2.72/180.05	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setminusER)).
2.72/180.05	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', bs114d)).
2.72/180.05	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binintersectER)).
2.72/180.05	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binintersectSubset2)).
2.72/180.05	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binintersectLsub)).
2.72/180.05	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binunionLsub)).
2.72/180.05	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binunionE)).
2.72/180.05	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.HNmXg0U3A1/E---3.1_14865.p', binunionEcases)).
2.72/180.05	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binunionIR)).
2.72/180.05	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setminusIRneg)).
2.72/180.05	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setminusILneg)).
2.72/180.05	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setminusEL)).
2.72/180.05	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setminusI)).
2.72/180.05	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binintersectSubset1)).
2.72/180.05	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binintersectSubset4)).
2.72/180.05	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binintersectRsub)).
2.72/180.05	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', disjointsetsI1)).
2.72/180.05	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binintersectSubset3)).
2.72/180.05	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binintersectEL)).
2.72/180.05	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binintersectSubset5)).
2.72/180.05	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binintersectI)).
2.72/180.05	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', binunionRsub)).
2.72/180.05	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', powersetsubset)).
2.72/180.05	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', powersetE1)).
2.72/180.05	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', subsetemptysetimpeq)).
2.72/180.05	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setextsub)).
2.72/180.05	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', subset2powerset)).
2.72/180.05	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setadjoinSub2)).
2.72/180.05	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setadjoinSub)).
2.72/180.05	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', subsetTrans)).
2.72/180.05	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', notequalI2)).
2.72/180.05	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', notequalI1)).
2.72/180.05	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', subsetE2)).
2.72/180.05	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', emptysetsubset)).
2.72/180.05	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', subsetI2)).
2.72/180.05	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', eqimpsubset1)).
2.72/180.05	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', eqimpsubset2)).
2.72/180.05	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', subsetI1)).
2.72/180.05	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setunion__Cong)).
2.72/180.05	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setadjoin__Cong)).
2.72/180.05	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', emptyset__Cong)).
2.72/180.05	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', in__Cong)).
2.72/180.05	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', quantDeMorgan3)).
2.72/180.05	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', vacuousDall)).
2.72/180.05	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', upairsetIR)).
2.72/180.05	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', upairsetIL)).
2.72/180.05	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', upairsetE)).
2.72/180.05	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', singletonsswitch)).
2.72/180.05	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', eqinunit)).
2.72/180.05	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', notinsingleton)).
2.72/180.05	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', subPowSU)).
2.72/180.05	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setunionE)).
2.72/180.05	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', emptyInPowerset)).
2.72/180.05	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', powersetI)).
2.72/180.05	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setadjoinOr)).
2.72/180.05	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setadjoinIR)).
2.72/180.05	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', nonemptyE1)).
2.72/180.05	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', emptyI)).
2.72/180.05	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setext)).
2.72/180.05	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', notinemptyset)).
2.72/180.05	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', prop2setE)).
2.72/180.05	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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', wellorderingAx)).
2.72/180.05	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', omegaSAx)).
2.72/180.05	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setunionAx)).
2.72/180.05	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', powersetAx)).
2.72/180.05	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', setadjoinAx)).
2.72/180.05	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.HNmXg0U3A1/E---3.1_14865.p', emptysetAx)).
2.72/180.05	thf(c_0_282, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
2.72/180.05	thf(c_0_283, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
2.72/180.05	thf(c_0_284, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
2.72/180.05	thf(c_0_285, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
2.72/180.05	thf(c_0_286, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
2.72/180.05	thf(c_0_287, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
2.72/180.05	thf(c_0_288, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
2.72/180.05	thf(c_0_289, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
2.72/180.05	thf(c_0_290, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
2.72/180.05	thf(c_0_291, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
2.72/180.05	thf(c_0_292, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
2.72/180.05	thf(c_0_293, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
2.72/180.05	thf(c_0_294, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
2.72/180.05	thf(c_0_295, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
2.72/180.05	thf(c_0_296, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
2.72/180.05	thf(c_0_297, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
2.72/180.05	thf(c_0_298, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
2.72/180.05	thf(c_0_299, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
2.72/180.05	thf(c_0_300, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
2.72/180.05	thf(c_0_301, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
2.72/180.05	thf(c_0_302, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
2.72/180.05	thf(c_0_303, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
2.72/180.05	thf(c_0_304, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
2.72/180.05	thf(c_0_305, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
2.72/180.05	thf(c_0_306, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
2.72/180.05	thf(c_0_307, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
2.72/180.05	thf(c_0_308, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
2.72/180.05	thf(c_0_309, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
2.72/180.05	thf(c_0_310, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
2.72/180.05	thf(c_0_311, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
2.72/180.05	thf(c_0_312, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
2.72/180.05	thf(c_0_313, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
2.72/180.05	thf(c_0_314, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
2.72/180.05	thf(c_0_315, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
2.72/180.05	thf(c_0_316, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
2.72/180.05	thf(c_0_317, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
2.72/180.05	thf(c_0_318, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
2.72/180.05	thf(c_0_319, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
2.72/180.05	thf(c_0_320, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
2.72/180.05	thf(c_0_321, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
2.72/180.05	thf(c_0_322, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
2.72/180.05	thf(c_0_323, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
2.72/180.05	thf(c_0_324, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
2.72/180.05	thf(c_0_325, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
2.72/180.05	thf(c_0_326, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
2.72/180.05	thf(c_0_327, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
2.72/180.05	thf(c_0_328, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
2.72/180.05	thf(c_0_329, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
2.72/180.05	thf(c_0_330, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
2.72/180.05	thf(c_0_331, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
2.72/180.05	thf(c_0_332, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
2.72/180.05	thf(c_0_333, plain, ((epred1_0)<=>![X966:$i]:(?[X967:$i]:((((![X968:$i]:(((in @ X968 @ X967)=>![X969:$i]:(((in @ X969 @ X968)=>(in @ X969 @ X966)))))&![X970:$i, X971:$i]:((((in @ X970 @ X966)&(in @ X971 @ X966))=>(![X972:$i]:(((in @ X972 @ X967)=>((in @ X970 @ X972)<=>(in @ X971 @ X972))))=>((X970)=(X971))))))&![X973:$i, X974:$i]:((((in @ X973 @ X967)&(in @ X974 @ X967))=>(![X975:$i]:(((in @ X975 @ X973)=>(in @ X975 @ X974)))|![X976:$i]:(((in @ X976 @ X974)=>(in @ X976 @ X973)))))))&![X977:$i]:(((![X978:$i]:(((in @ X978 @ X977)=>(in @ X978 @ X966)))&?[X979:$i]:((in @ X979 @ X977)))=>?[X980:$i, X981:$i]:(((((in @ X980 @ X967)&(in @ X981 @ X977))&~(?[X982:$i]:(((in @ X982 @ X980)&(in @ X982 @ X977)))))&![X983:$i]:(((in @ X983 @ X967)=>(![X984:$i]:(((in @ X984 @ X983)=>(in @ X984 @ X980)))|(in @ X981 @ X983)))))))))))), introduced(definition)).
2.72/180.05	thf(c_0_334, negated_conjecture, ~((![X1852:$i, X1853:$i]:((![X1854:$i]:(((in @ X1854 @ X1852)<=>(in @ X1854 @ X1853)))=>((X1852)=(X1853))))=>(![X955:$i]:(~(in @ X955 @ emptyset))=>(![X956:$i, X957:$i, X958:$i]:(((in @ X958 @ (setadjoin @ X956 @ X957))<=>(((X958)=(X956))|(in @ X958 @ X957))))=>(![X959:$i, X960:$i]:(((in @ X960 @ (powerset @ X959))<=>![X961:$i]:(((in @ X961 @ X960)=>(in @ X961 @ X959)))))=>(![X962:$i, X963:$i]:(((in @ X963 @ (setunion @ X962))<=>?[X964:$i]:(((in @ X963 @ X964)&(in @ X964 @ X962)))))=>((in @ emptyset @ omega)=>(![X965:$i]:(((in @ X965 @ omega)=>(in @ (setadjoin @ X965 @ X965) @ omega)))=>(![X1849:$i]:((((in @ emptyset @ X1849)&![X1850:$i]:((((in @ X1850 @ omega)&(in @ X1850 @ X1849))=>(in @ (setadjoin @ X1850 @ X1850) @ X1849))))=>![X1851:$i]:(((in @ X1851 @ omega)=>(in @ X1851 @ X1849)))))=>(![X1843:$i > $i > $o, X1844:$i]:((![X1845:$i]:(((in @ X1845 @ X1844)=>(exu @ (X1843 @ X1845))))=>?[X1846:$i]:(![X1847:$i]:(((in @ X1847 @ X1846)<=>?[X1848:$i]:(((in @ X1848 @ X1844)&(X1843 @ X1848 @ X1847))))))))=>(![X1839:$i]:((?[X1840:$i]:((in @ X1840 @ X1839))=>?[X1841:$i]:(((in @ X1841 @ X1839)&~(?[X1842:$i]:(((in @ X1842 @ X1841)&(in @ X1842 @ X1839))))))))=>((epred1_0)=>(![X1838:$i > $o]:(((exu @ X1838)=>(X1838 @ (descr @ (^[Z0/* 17 */:$i]:(X1838 @ Z0))))))=>(![X985:$i, X986:$i > $o, X987:$i]:(((in @ X987 @ X985)=>((X986 @ X987)=>(in @ X987 @ (dsetconstr @ X985 @ X986)))))=>(![X988:$i, X989:$i > $o, X990:$i]:(((in @ X990 @ (dsetconstr @ X988 @ X989))=>(in @ X990 @ X988)))=>(![X991:$i, X992:$i > $o, X993:$i]:(((in @ X993 @ (dsetconstr @ X991 @ X992))=>(X992 @ X993)))=>(![X1835:$i > $o]:(((exu @ X1835)=>?[X1836:$i]:(((X1835 @ X1836)&![X1837:$i]:(((X1835 @ X1837)=>((X1836)=(X1837))))))))=>(![X994:$o, X995:$i]:(((in @ X995 @ (prop2set @ ((X994))))=>(X994)))=>(![X1833:$i]:(((in @ X1833 @ emptyset)=>![X1834:$o]:((X1834))))=>(![X1832:$i]:(((in @ X1832 @ emptyset)=>~($true)))=>(![X996:$i]:(~(in @ X996 @ emptyset))=>(![X1830:$i > $o]:(((exu @ X1830)=>?[X1831:$i]:((X1830 @ X1831))))=>(![X997:$i, X998:$i]:((![X999:$i]:(((in @ X999 @ X997)=>(in @ X999 @ X998)))=>(![X1000:$i]:(((in @ X1000 @ X998)=>(in @ X1000 @ X997)))=>((X997)=(X998)))))=>(![X1001:$i]:((![X1002:$i]:(~(in @ X1002 @ X1001))=>((X1001)=(emptyset))))=>(![X1828:$i]:((![X1829:$i]:(~(in @ X1829 @ X1828))=>((X1828)=(emptyset))))=>(![X1825:$i, X1826:$i > $o, X1827:$i]:(((in @ X1827 @ X1825)=>((in @ X1827 @ (dsetconstr @ X1825 @ X1826))<=>(X1826 @ X1827))))=>(![X1003:$i]:(((nonempty @ X1003)=>?[X1004:$i]:((in @ X1004 @ X1003))))=>(![X1822:$i, X1823:$i > $o, X1824:$i]:(((in @ X1824 @ X1822)=>((X1823 @ X1824)=>(nonempty @ (dsetconstr @ X1822 @ X1823)))))=>(![X1820:$i]:((?[X1821:$i]:((in @ X1821 @ X1820))=>(nonempty @ X1820)))=>(![X1818:$i, X1819:$i]:((in @ X1818 @ (setadjoin @ X1818 @ X1819)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1005:$i, X1006:$i, X1007:$i]:(((in @ X1007 @ X1006)=>(in @ X1007 @ (setadjoin @ 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, symdiffI2]), quantDeMorgan2]), setextAx]), upairset2IR]), setminusLsub]), binunionIL]), c_0_282]), inPowerset]), setukpairIL]), powersetI1]), subsetRefl]), setukpairIR]), notsubsetI]), subsetE]), c_0_283]), kpairiskpair]), c_0_284]), omega__Cong]), singletoninpowerset]), powerset__Cong]), c_0_285]), inCongP]), singletoninpowunion]), c_0_286]), c_0_287]), c_0_288]), upairsubunion]), notdallE]), notdexE]), prop2setI]), ubforcartprodlem1]), quantDeMorgan4]), cartprodsndpairEq]), quantDeMorgan1]), ubforcartprodlem3]), uniqinunit]), nonemptyImpWitness]), setunionI]), cartprodpairin]), powersetE]), emptyinPowerset]), setunionE2]), setadjoinE]), emptyinunitempty]), setadjoinIL]), setunionsingleton1]), nonemptyI1]), c_0_289]), setunionsingleton2]), c_0_290]), noeltsimpempty]), c_0_291]), c_0_292]), emptysetimpfalse]), emptysetE]), c_0_293]), c_0_294]), c_0_295]), foundationAx]), cartprodfstin]), c_0_296]), omegaIndAx]), setukpairinjR12]), omega0Ax]), upairequniteq]), setukpairinjR2]), c_0_297]), ksndpairEq]), cartprodsndin]), cartprodpairmemEL]), doubleComplementI1]), doubleComplementE1]), c_0_298]), c_0_299]), c_0_300]), c_0_301]), infuncsetfunc]), ap2p]), funcinfuncset]), brelnall1]), symdiffIneg1]), brelnall2]), symdiffIneg2]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), eqbreln]), funcext]), funcext2]), c_0_302]), c_0_303]), c_0_304]), c_0_305]), c_0_306]), c_0_307]), ifp]), binunionT_lem]), powersetT_lem]), setminusT_lem]), subsetTI]), powersetTE1]), complementTE1]), contrasubsetT]), contrasubsetT3]), upairset2E]), singletonsubset]), kpairp]), secondinupair]), symdiffI1]), symdiffE]), setminusSubset1]), doubleComplementEq]), complementImpComplementIntersect]), complementInPowersetComplementIntersect]), complementTcontraSubset]), binunionTILcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan1]), demorgan2a]), woz1_2]), woz1_3]), woz1_1]), woz13rule4]), woz13rule3]), woz13rule2]), woz13rule1]), woz13rule0]), demorgan2]), demorgan2b]), demorgan2b2]), binunionTE]), intersectInPowersetIntersectUnions]), binunionTIRcontra]), contraSubsetComplement]), complementSubsetComplementIntersect]), complementTnotintersectT]), doubleComplementSub2]), doubleComplementSub1]), contrasubsetT2]), contrasubsetT1]), binintersectTERcontra]), binintersectTELcontra]), complementTI1]), powersetTI1]), setextT]), complementT_lem]), binintersectT_lem]), iftrueorfalse]), iffalse]), iftrue]), theeq]), c_0_308]), c_0_309]), c_0_310]), c_0_311]), ap2apEq2]), ap2apEq1]), subbreln]), funcGraphProp1]), c_0_312]), c_0_313]), c_0_314]), c_0_315]), app]), c_0_316]), c_0_317]), c_0_318]), c_0_319]), c_0_320]), cartprodpairsurjEq]), cartprodfstpairEq]), cartprodmempaircEq]), cartprodpairmemER]), kpairsurjEq]), setukpairinjR]), setukpairinjR1]), setukpairinjR11]), setukpairinjL]), setukpairinjL2]), kfstpairEq]), theprop]), c_0_321]), setukpairinjL1]), singletonsuniq]), c_0_322]), c_0_323]), setunionsingleton]), cartprodmempair]), cartprodmempair1]), ubforcartprodlem2]), upairinpowunion]), setminusELneg]), setminusERneg]), setminusSubset2]), setminusER]), bs114d]), binintersectER]), binintersectSubset2]), binintersectLsub]), binunionLsub]), binunionE]), binunionEcases]), binunionIR]), setminusIRneg]), setminusILneg]), setminusEL]), setminusI]), binintersectSubset1]), binintersectSubset4]), binintersectRsub]), disjointsetsI1]), binintersectSubset3]), binintersectEL]), binintersectSubset5]), binintersectI]), binunionRsub]), c_0_324]), powersetsubset]), powersetE1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), setadjoinSub2]), setadjoinSub]), subsetTrans]), notequalI2]), notequalI1]), subsetE2]), emptysetsubset]), subsetI2]), eqimpsubset1]), eqimpsubset2]), subsetI1]), c_0_325]), setunion__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_326]), in__Cong]), quantDeMorgan3]), vacuousDall]), c_0_327]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), c_0_328]), subPowSU]), setunionE]), emptyInPowerset]), powersetI]), c_0_329]), setadjoinOr]), setadjoinIR]), nonemptyE1]), emptyI]), setext]), notinemptyset]), prop2setE]), c_0_330]), c_0_331]), c_0_332]), wellorderingAx]), omegaSAx]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx])])]), c_0_333])).
2.72/180.05	thf(c_0_335, negated_conjecture, ![X1855:$i, X1856:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1868:$i, X1869:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1877:$i, X1878:$i > $i > $o, X1879:$i, X1882:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1889:$i, X1890:$i > $o, X1891:$i, X1892:$i > $o, X1893:$i, X1894:$i, X1895:$i > $o, X1896:$i, X1897:$i, X1898:$i > $o, X1899:$i, X1900:$i > $o, X1902:$i, X1903:$o, X1904:$i, X1905:$i, X1906:$o, X1907:$i, X1908:$i, X1909:$i > $o, X1911:$i, X1912:$i, X1915:$i, X1917:$i, X1919:$i, X1920:$i > $o, X1921:$i, X1922:$i, X1924:$i, X1925:$i > $o, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$o, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$o, X1957:$i, X1958:$i, X1959:$i > $o, X1961:$i, X1962:$i, X1963:$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 > $o, X1982:$i, X1983:$i > $o, X1984:$i, X1985:$i, X1986:$i > $o, X1987:$i, X1989:$i, X1990:$i > $o, X1992:$i, X1993:$i, X1994:$i > $o, X1996:$i, X1997:$i, X1998:$i > $o, X1999:$i, X2001:$o, X2002:$i, X2003:$i > $o, X2005:$i, X2006:$i, X2007:$i > $o, X2008:$i, X2010:$i > $o, X2011:$i, X2013:$i > $o, X2014:$i, X2017:$i > $o, X2018:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i > $o, X2029:$i, X2030:$i, X2031:$i > $o, X2032:$i > $o, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i > $o, X2044:$i, X2045:$i, X2046:$i > $o, X2047:$i > $o, X2050:$i, X2051:$i, X2052:$i > $o, X2053:$i > $o, X2056:$i, X2057:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, 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(powerset @ X2553))|~(in @ X2554 @ (powerset @ X2553)))&(~(in @ (esk68_3 @ X2553 @ X2554 @ X2555) @ X2554)|((X2554)=(X2555))|(in @ (esk67_3 @ X2553 @ X2554 @ X2555) @ X2554)|~(in @ X2555 @ (powerset @ X2553))|~(in @ X2554 @ (powerset @ X2553)))))&(((in @ (esk68_3 @ X2553 @ X2554 @ X2555) @ X2553)|((X2554)=(X2555))|~(in @ (esk67_3 @ X2553 @ X2554 @ X2555) @ X2555)|~(in @ X2555 @ (powerset @ X2553))|~(in @ X2554 @ (powerset @ X2553)))&(((in @ (esk68_3 @ X2553 @ X2554 @ X2555) @ X2555)|((X2554)=(X2555))|~(in @ (esk67_3 @ X2553 @ X2554 @ X2555) @ X2555)|~(in @ X2555 @ (powerset @ X2553))|~(in @ X2554 @ (powerset @ X2553)))&(~(in @ (esk68_3 @ X2553 @ X2554 @ X2555) @ X2554)|((X2554)=(X2555))|~(in @ (esk67_3 @ X2553 @ X2554 @ X2555) @ X2555)|~(in @ X2555 @ (powerset @ X2553))|~(in @ X2554 @ (powerset @ X2553)))))))&((((in @ (esk69_3 @ X2558 @ X2559 @ X2560) @ X2558)|(subset @ X2559 @ X2560)|~(in @ X2560 @ (powerset @ X2558))|~(in @ X2559 @ (powerset @ X2558)))&(((in @ (esk69_3 @ X2558 @ X2559 @ X2560) @ X2559)|(subset @ X2559 @ X2560)|~(in @ X2560 @ (powerset @ X2558))|~(in @ X2559 @ (powerset @ X2558)))&(~(in @ (esk69_3 @ X2558 @ X2559 @ X2560) @ X2560)|(subset @ X2559 @ X2560)|~(in @ X2560 @ (powerset @ X2558))|~(in @ X2559 @ (powerset @ X2558)))))&((((in @ (esk70_3 @ X2562 @ X2563 @ X2564) @ X2562)|(in @ X2563 @ (powerset @ X2564))|~(in @ X2564 @ (powerset @ X2562))|~(in @ X2563 @ (powerset @ X2562)))&(((in @ (esk70_3 @ X2562 @ X2563 @ X2564) @ X2563)|(in @ X2563 @ (powerset @ X2564))|~(in @ X2564 @ (powerset @ X2562))|~(in @ X2563 @ (powerset @ X2562)))&(~(in @ (esk70_3 @ X2562 @ X2563 @ X2564) @ X2564)|(in @ X2563 @ (powerset @ X2564))|~(in @ X2564 @ (powerset @ X2562))|~(in @ X2563 @ (powerset @ X2562)))))&((~(in @ X2567 @ (powerset @ X2566))|(~(in @ X2568 @ (powerset @ X2566))|(~(in @ X2569 @ X2566)|(~(in @ X2567 @ (powerset @ X2568))|(~(in @ X2569 @ X2567)|(in @ X2569 @ X2568))))))&((~(in @ X2571 @ (powerset @ X2570))|(~(in @ X2572 @ X2570)|(~(in @ X2572 @ X2571)|~(in @ X2572 @ (setminus @ X2570 @ X2571)))))&((~(in @ X2574 @ (powerset @ X2573))|(~(in @ X2575 @ X2573)|((in @ X2575 @ (setminus @ X2573 @ X2574))|(in @ X2575 @ X2574))))&((~(in @ X2577 @ (powerset @ X2576))|(~(in @ X2578 @ (powerset @ X2576))|(~(in @ X2579 @ X2576)|((in @ X2579 @ X2577)|~(in @ X2579 @ (binintersect @ X2577 @ X2578))))))&((~(in @ X2581 @ (powerset @ X2580))|(~(in @ X2582 @ (powerset @ X2580))|(~(in @ X2583 @ X2580)|((in @ X2583 @ X2582)|~(in @ X2583 @ (binintersect @ X2581 @ X2582))))))&((~(in @ X2585 @ (powerset @ X2584))|(~(in @ X2586 @ (powerset @ X2584))|(~(in @ X2587 @ X2584)|(~(subset @ X2585 @ (setminus @ X2584 @ X2586))|(~(in @ X2587 @ X2586)|~(in @ X2587 @ X2585))))))&((~(in @ X2589 @ (powerset @ X2588))|(~(in @ X2590 @ (powerset @ X2588))|(~(in @ X2591 @ X2588)|(~(subset @ X2589 @ X2590)|((in @ X2591 @ X2590)|~(in @ X2591 @ X2589))))))&((~(in @ X2593 @ (powerset @ X2592))|(~(in @ X2594 @ (powerset @ X2592))|(~(subset @ X2593 @ X2594)|(subset @ (setminus @ X2592 @ X2594) @ (setminus @ X2592 @ X2593)))))&((~(in @ X2596 @ (powerset @ X2595))|(~(in @ X2597 @ (powerset @ X2595))|(~(subset @ (setminus @ X2595 @ X2597) @ (setminus @ X2595 @ X2596))|(subset @ X2596 @ X2597))))&((~(in @ X2599 @ (powerset @ X2598))|(~(in @ X2600 @ X2598)|(~(in @ X2600 @ X2599)|(in @ X2600 @ (setminus @ X2598 @ (setminus @ X2598 @ X2599))))))&((~(in @ X2602 @ (powerset @ X2601))|(~(in @ X2603 @ X2601)|(~(in @ X2603 @ (setminus @ X2601 @ (setminus @ X2601 @ X2602)))|(in @ X2603 @ X2602))))&((~(in @ X2605 @ (powerset @ X2604))|(subset @ X2605 @ (setminus @ X2604 @ (setminus @ X2604 @ X2605))))&((~(in @ X2607 @ (powerset @ X2606))|(subset @ (setminus @ X2606 @ (setminus @ X2606 @ X2607)) @ X2607))&((~(in @ X2609 @ (powerset @ X2608))|((X2609)=(setminus @ X2608 @ (setminus @ X2608 @ X2609))))&((~(in @ X2611 @ (powerset @ X2610))|(~(in @ X2612 @ (powerset @ X2610))|(~(in @ X2613 @ X2610)|(~(in @ X2613 @ (setminus @ X2610 @ X2611))|~(in @ X2613 @ (binintersect @ X2611 @ X2612))))))&((~(in @ X2615 @ (powerset @ X2614))|(~(in @ X2616 @ (powerset @ X2614))|(~(in @ X2617 @ X2614)|(~(in @ X2617 @ (setminus @ X2614 @ X2615))|(in @ X2617 @ (setminus @ X2614 @ (binintersect @ X2615 @ X2616)))))))&((~(in @ X2619 @ (powerset @ X2618))|(~(in @ X2620 @ (powerset @ X2618))|(subset @ (setminus @ X2618 @ X2619) @ (setminus @ X2618 @ (binintersect @ X2619 @ X2620)))))&((~(in @ X2622 @ (powerset @ X2621))|(~(in @ X2623 @ (powerset @ X2621))|(in @ (setminus @ X2621 @ X2622) @ (powerset @ (setminus @ X2621 @ (binintersect @ X2622 @ X2623))))))&((~(in @ X2625 @ (powerset @ X2624))|(~(in @ X2626 @ (powerset @ X2624))|(~(subset @ X2625 @ (setminus @ X2624 @ X2626))|(~(in @ X2627 @ X2624)|(~(in @ X2627 @ X2626)|(in @ X2627 @ (setminus @ X2624 @ X2625)))))))&((~(in @ X2629 @ (powerset @ X2628))|(~(in @ X2630 @ (powerset @ X2628))|(~(subset @ X2629 @ (setminus @ X2628 @ X2630))|(subset @ X2630 @ (setminus @ X2628 @ X2629)))))&((~(in @ X2632 @ (powerset @ X2631))|(~(in @ X2633 @ (powerset @ X2631))|(~(in @ X2634 @ X2631)|((in @ X2634 @ (binunion @ X2632 @ X2633))|~(in @ X2634 @ X2632)))))&((~(in @ X2636 @ (powerset @ X2635))|(~(in @ X2637 @ (powerset @ X2635))|(~(in @ X2638 @ X2635)|((in @ X2638 @ (binunion @ X2636 @ X2637))|~(in @ X2638 @ X2637)))))&((~(in @ X2640 @ (powerset @ X2639))|(~(in @ X2641 @ (powerset @ X2639))|(~(in @ X2642 @ (powerset @ X2639))|(~(in @ X2643 @ X2639)|(~(in @ X2643 @ (binintersect @ X2640 @ X2641))|(in @ X2643 @ (binunion @ X2640 @ X2642)))))))&((~(in @ X2645 @ (powerset @ X2644))|(~(in @ X2646 @ (powerset @ X2644))|(~(in @ X2647 @ (powerset @ X2644))|(~(in @ X2648 @ X2644)|(~(in @ X2648 @ (binintersect @ X2645 @ X2646))|(in @ X2648 @ (binunion @ X2646 @ X2647)))))))&((~(in @ X2650 @ (powerset @ X2649))|(~(in @ X2651 @ (powerset @ X2649))|(~(in @ X2652 @ (powerset @ X2649))|(~(in @ X2653 @ X2649)|(~(in @ X2653 @ (binintersect @ X2650 @ X2651))|(in @ X2653 @ (binintersect @ (binunion @ X2650 @ X2652) @ (binunion @ X2651 @ X2652))))))))&((~(in @ X2655 @ (powerset @ X2654))|(~(in @ X2656 @ (powerset @ X2654))|(~(in @ X2657 @ (powerset @ X2654))|(in @ (binintersect @ X2655 @ X2656) @ (powerset @ (binintersect @ (binunion @ X2655 @ X2657) @ (binunion @ X2656 @ X2657)))))))&((~(in @ X2659 @ (powerset @ X2658))|(~(in @ X2660 @ (powerset @ X2658))|(~(in @ X2661 @ X2658)|(~(in @ X2661 @ (setminus @ X2658 @ (binunion @ X2659 @ X2660)))|~(in @ X2661 @ X2659)))))&((~(in @ X2663 @ (powerset @ X2662))|(~(in @ X2664 @ (powerset @ X2662))|(~(in @ X2665 @ X2662)|(~(in @ X2665 @ (setminus @ X2662 @ (binunion @ X2663 @ X2664)))|(in @ X2665 @ (setminus @ X2662 @ X2663))))))&(((((in @ X2670 @ X2668)|(X2669)|(in @ X2670 @ X2667)|~(in @ X2670 @ (binunion @ X2667 @ X2668))|~(in @ X2670 @ X2666)|~(in @ X2668 @ (powerset @ X2666))|~(in @ X2667 @ (powerset @ X2666)))&(~(X2669)|(X2669)|(in @ X2670 @ X2667)|~(in @ X2670 @ (binunion @ X2667 @ X2668))|~(in @ X2670 @ X2666)|~(in @ X2668 @ (powerset @ X2666))|~(in @ X2667 @ (powerset @ X2666))))&(((in @ X2670 @ X2668)|(X2669)|~(X2669)|~(in @ X2670 @ (binunion @ X2667 @ X2668))|~(in @ X2670 @ X2666)|~(in @ X2668 @ (powerset @ X2666))|~(in @ X2667 @ (powerset @ X2666)))&(~(X2669)|(X2669)|~(X2669)|~(in @ X2670 @ (binunion @ X2667 @ X2668))|~(in @ X2670 @ X2666)|~(in @ X2668 @ (powerset @ X2666))|~(in @ X2667 @ (powerset @ X2666)))))&((~(in @ X2672 @ (powerset @ X2671))|(~(in @ X2673 @ (powerset @ X2671))|(~(in @ X2674 @ X2671)|((in @ X2674 @ X2672)|((in @ X2674 @ X2673)|~(in @ X2674 @ (binunion @ X2672 @ X2673)))))))&((~(in @ X2676 @ (powerset @ X2675))|(~(in @ X2677 @ (powerset @ X2675))|(~(in @ X2678 @ X2675)|(~(in @ X2678 @ (setminus @ X2675 @ (binunion @ X2676 @ X2677)))|(in @ X2678 @ (setminus @ X2675 @ X2676))))))&((~(in @ X2680 @ (powerset @ X2679))|(~(in @ X2681 @ (powerset @ X2679))|(in @ (setminus @ X2679 @ (binunion @ X2680 @ X2681)) @ (powerset @ (setminus @ X2679 @ X2680)))))&((~(in @ X2683 @ (powerset @ X2682))|(~(in @ X2684 @ (powerset @ X2682))|(~(in @ X2685 @ X2682)|(~(in @ X2685 @ (setminus @ X2682 @ (binunion @ X2683 @ X2684)))|(in @ X2685 @ (setminus @ X2682 @ X2684))))))&((~(in @ X2687 @ (powerset @ X2686))|(~(in @ X2688 @ (powerset @ X2686))|(~(in @ X2689 @ X2686)|(~(in @ X2689 @ (setminus @ X2686 @ (binintersect @ X2687 @ X2688)))|(in @ X2689 @ (binunion @ (setminus @ X2686 @ X2687) @ (setminus @ X2686 @ X2688)))))))&((~(in @ X2691 @ (powerset @ X2690))|(~(in @ X2692 @ (powerset @ X2690))|(~(in @ X2693 @ X2690)|(~(in @ X2693 @ (binunion @ (setminus @ X2690 @ X2691) @ (setminus @ X2690 @ X2692)))|(in @ X2693 @ (setminus @ X2690 @ (binintersect @ X2691 @ X2692)))))))&((~(in @ X2695 @ (powerset @ X2694))|(~(in @ X2696 @ (powerset @ X2694))|((setminus @ X2694 @ (binintersect @ X2695 @ X2696))=(binunion @ (setminus @ X2694 @ X2695) @ (setminus @ X2694 @ X2696)))))&((~(in @ X2698 @ (powerset @ X2697))|(~(in @ X2699 @ (powerset @ X2697))|(~(in @ X2700 @ X2697)|(~(in @ X2700 @ (setminus @ X2697 @ (binunion @ X2698 @ X2699)))|(in @ X2700 @ (binintersect @ (setminus @ X2697 @ X2698) @ (setminus @ X2697 @ X2699)))))))&((~(in @ X2702 @ (powerset @ X2701))|(~(in @ X2703 @ (powerset @ X2701))|(~(in @ X2704 @ X2701)|(~(in @ X2704 @ (setminus @ X2701 @ X2702))|(~(in @ X2704 @ (setminus @ X2701 @ X2703))|(in @ X2704 @ (setminus @ X2701 @ (binunion @ X2702 @ X2703))))))))&((~(in @ X2706 @ (powerset @ X2705))|(~(in @ X2707 @ (powerset @ X2705))|(~(in @ X2708 @ X2705)|(~(in @ X2708 @ (binintersect @ (setminus @ X2705 @ X2706) @ (setminus @ X2705 @ X2707)))|(in @ X2708 @ (setminus @ X2705 @ (binunion @ X2706 @ X2707)))))))&((~(in @ X2710 @ (powerset @ X2709))|(~(in @ X2711 @ (powerset @ X2709))|((setminus @ X2709 @ (binunion @ X2710 @ X2711))=(binintersect @ (setminus @ X2709 @ X2710) @ (setminus @ X2709 @ X2711)))))&((~(in @ X2713 @ (powerset @ X2712))|(~(in @ X2714 @ (powerset @ X2712))|(~(in @ X2715 @ (binintersect @ X2713 @ X2714))|(in @ X2715 @ X2712))))&((~(in @ X2717 @ (powerset @ X2716))|(~(in @ X2718 @ (powerset @ X2716))|(~(in @ X2719 @ (powerset @ X2716))|(~(subset @ X2717 @ X2719)|(subset @ (binintersect @ X2717 @ X2718) @ X2719)))))&((~(in @ X2721 @ (powerset @ X2720))|(~(in @ X2722 @ (powerset @ X2720))|(~(in @ X2723 @ (powerset @ X2720))|(~(subset @ X2722 @ X2723)|(subset @ (binintersect @ X2721 @ X2722) @ X2723)))))&((~(in @ X2725 @ (powerset @ X2724))|(~(in @ X2726 @ (powerset @ X2724))|(~(in @ X2727 @ (powerset @ X2724))|(~(subset @ X2725 @ X2726)|(~(subset @ X2725 @ X2727)|(subset @ X2725 @ (binintersect @ X2726 @ X2727)))))))&((~(in @ X2729 @ (powerset @ X2728))|(~(in @ X2730 @ (powerset @ X2728))|(~(in @ X2731 @ (powerset @ X2728))|(~(in @ X2732 @ (powerset @ X2728))|(~(subset @ X2729 @ X2731)|(~(subset @ X2730 @ X2732)|(subset @ (binintersect @ X2729 @ X2730) @ (binintersect @ X2731 @ X2732))))))))&((~(in @ X2734 @ (powerset @ X2733))|(~(in @ X2735 @ (powerset @ X2733))|(in @ (setminus @ X2733 @ X2734) @ (powerset @ (setminus @ X2733 @ (binintersect @ X2734 @ X2735))))))&((~(in @ X2737 @ (powerset @ X2736))|(~(in @ X2738 @ (powerset @ X2736))|(~(in @ X2739 @ (powerset @ X2736))|(~(in @ X2740 @ (powerset @ X2736))|((setminus @ X2736 @ (binintersect @ (binunion @ X2737 @ X2738) @ (binunion @ X2739 @ X2740)))=(binunion @ (binintersect @ (setminus @ X2736 @ X2737) @ (setminus @ X2736 @ X2738)) @ (binintersect @ (setminus @ X2736 @ X2739) @ (setminus @ X2736 @ X2740))))))))&((~(in @ X2742 @ (powerset @ X2741))|(~(in @ X2743 @ (powerset @ X2741))|(~(in @ X2744 @ (powerset @ X2741))|(in @ (binintersect @ X2742 @ X2743) @ (powerset @ (binintersect @ (binunion @ X2742 @ X2744) @ (binunion @ X2743 @ X2744)))))))&((in @ esk72_0 @ (powerset @ esk71_0))&((in @ esk73_0 @ (powerset @ esk71_0))&((subset @ esk72_0 @ (setminus @ esk71_0 @ esk73_0))&~(subset @ esk73_0 @ (setminus @ esk71_0 @ esk72_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_334])])])])])])])).
2.72/180.05	thf(c_0_336, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((subset @ X4 @ (setminus @ X3 @ X2))|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3)))|~((subset @ X2 @ (setminus @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_335])).
2.72/180.05	thf(c_0_337, negated_conjecture, (subset @ esk72_0 @ (setminus @ esk71_0 @ esk73_0)), inference(split_conjunct,[status(thm)],[c_0_335])).
2.72/180.05	thf(c_0_338, negated_conjecture, (in @ esk73_0 @ (powerset @ esk71_0)), inference(split_conjunct,[status(thm)],[c_0_335])).
2.72/180.05	thf(c_0_339, negated_conjecture, (in @ esk72_0 @ (powerset @ esk71_0)), inference(split_conjunct,[status(thm)],[c_0_335])).
2.72/180.05	thf(c_0_340, negated_conjecture, ~((subset @ esk73_0 @ (setminus @ esk71_0 @ esk72_0))), inference(split_conjunct,[status(thm)],[c_0_335])).
2.72/180.05	thf(c_0_341, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_336, c_0_337]), c_0_338]), c_0_339])]), c_0_340]), ['proof']).
2.72/180.05	# SZS output end CNFRefutation
2.72/180.05	# Parsed axioms                        : 607
2.72/180.05	# Removed by relevancy pruning/SinE    : 325
2.72/180.05	# Initial clauses                      : 446
2.72/180.05	# Removed in clause preprocessing      : 37
2.72/180.05	# Initial clauses in saturation        : 409
2.72/180.05	# Processed clauses                    : 668
2.72/180.05	# ...of these trivial                  : 9
2.72/180.05	# ...subsumed                          : 41
2.72/180.05	# ...remaining for further processing  : 618
2.72/180.05	# Other redundant clauses eliminated   : 45
2.72/180.05	# Clauses deleted for lack of memory   : 0
2.72/180.05	# Backward-subsumed                    : 0
2.72/180.05	# Backward-rewritten                   : 1
2.72/180.05	# Generated clauses                    : 3575
2.72/180.05	# ...of the previous two non-redundant : 3388
2.72/180.05	# ...aggressively subsumed             : 0
2.72/180.05	# Contextual simplify-reflections      : 14
2.72/180.05	# Paramodulations                      : 3501
2.72/180.05	# Factorizations                       : 2
2.72/180.05	# NegExts                              : 0
2.72/180.05	# Equation resolutions                 : 51
2.72/180.05	# Disequality decompositions           : 0
2.72/180.05	# Total rewrite steps                  : 127
2.72/180.05	# ...of those cached                   : 88
2.72/180.05	# Propositional unsat checks           : 0
2.72/180.05	#    Propositional check models        : 0
2.72/180.05	#    Propositional check unsatisfiable : 0
2.72/180.05	#    Propositional clauses             : 0
2.72/180.05	#    Propositional clauses after purity: 0
2.72/180.05	#    Propositional unsat core size     : 0
2.72/180.05	#    Propositional preprocessing time  : 0.000
2.72/180.05	#    Propositional encoding time       : 0.000
2.72/180.05	#    Propositional solver time         : 0.000
2.72/180.05	#    Success case prop preproc time    : 0.000
2.72/180.05	#    Success case prop encoding time   : 0.000
2.72/180.05	#    Success case prop solver time     : 0.000
2.72/180.05	# Current number of processed clauses  : 248
2.72/180.05	#    Positive orientable unit clauses  : 38
2.72/180.05	#    Positive unorientable unit clauses: 0
2.72/180.05	#    Negative unit clauses             : 3
2.72/180.05	#    Non-unit-clauses                  : 207
2.72/180.05	# Current number of unprocessed clauses: 3481
2.72/180.05	# ...number of literals in the above   : 11398
2.72/180.05	# Current number of archived formulas  : 0
2.72/180.05	# Current number of archived clauses   : 354
2.72/180.05	# Clause-clause subsumption calls (NU) : 44297
2.72/180.05	# Rec. Clause-clause subsumption calls : 21135
2.72/180.05	# Non-unit clause-clause subsumptions  : 51
2.72/180.05	# Unit Clause-clause subsumption calls : 756
2.72/180.05	# Rewrite failures with RHS unbound    : 0
2.72/180.05	# BW rewrite match attempts            : 34
2.72/180.05	# BW rewrite match successes           : 1
2.72/180.05	# Condensation attempts                : 0
2.72/180.05	# Condensation successes               : 0
2.72/180.05	# Termbank termtop insertions          : 131699
2.72/180.05	# Search garbage collected termcells   : 29045
2.72/180.05	
2.72/180.05	# -------------------------------------------------
2.72/180.05	# User time                : 0.270 s
2.72/180.05	# System time              : 0.023 s
2.72/180.05	# Total time               : 0.293 s
2.72/180.05	# Maximum resident set size: 9232 pages
2.72/180.05	
2.72/180.05	# -------------------------------------------------
2.72/180.05	# User time                : 0.287 s
2.72/180.05	# System time              : 0.028 s
2.72/180.05	# Total time               : 0.315 s
2.72/180.05	# Maximum resident set size: 2744 pages
2.72/180.05	% E---3.1 exiting
2.72/180.05	% E exiting
2.72/180.05	EOF