0.04/0.14	% Problem    : Vampire---4.8_10653 : TPTP v0.0.0. Released v0.0.0.
0.14/0.15	% Command    : run_E %s %d THM
0.14/0.35	% Computer : n009.cluster.edu
0.14/0.35	% Model    : x86_64 x86_64
0.14/0.35	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.35	% Memory   : 8042.1875MB
0.14/0.35	% OS       : Linux 3.10.0-693.el7.x86_64
0.14/0.35	% CPULimit   : 1440
0.14/0.35	% WCLimit    : 180
0.14/0.35	% DateTime   : Mon Jul  3 12:52:56 EDT 2023
0.14/0.35	% CPUTime    : 
0.20/0.50	Running higher-order theorem provingRunning: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653
0.20/0.50	# Version: 3.1pre001-ho
0.82/1.03	# Preprocessing class: HSLMSLSSLLLCHFA.
0.82/1.03	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
0.82/1.03	# Starting ehoh_best5 with 180s (1) cores
0.82/1.03	# Starting almost_fo_3_lam with 180s (1) cores
0.82/1.03	# Starting new_bool_5 with 180s (1) cores
0.82/1.03	# Starting pre_casc_3 with 180s (1) cores
0.82/1.03	# Starting ho_unfolding_8 with 180s (1) cores
0.82/1.03	# Starting new_ho_10_cnf2 with 180s (1) cores
0.82/1.03	# Starting new_bool_3 with 180s (1) cores
0.82/1.03	# Starting new_ho_5 with 180s (1) cores
0.82/1.03	# new_bool_5 with pid 10834 completed with status 0
0.82/1.03	# Result found by new_bool_5
0.82/1.03	# Preprocessing class: HSLMSLSSLLLCHFA.
0.82/1.03	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
0.82/1.03	# Starting ehoh_best5 with 180s (1) cores
0.82/1.03	# Starting almost_fo_3_lam with 180s (1) cores
0.82/1.03	# Starting new_bool_5 with 180s (1) cores
0.82/1.03	# SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
0.82/1.03	# Search class: HGHSM-FSLM32-MHFMMSBN
0.82/1.03	# Scheduled 10 strats onto 1 cores with 180 seconds (180 total)
0.82/1.03	# Starting ho_unfolding_8 with 33s (1) cores
0.82/1.03	# ho_unfolding_8 with pid 10841 completed with status 0
0.82/1.03	# Result found by ho_unfolding_8
0.82/1.03	# Preprocessing class: HSLMSLSSLLLCHFA.
0.82/1.03	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
0.82/1.03	# Starting ehoh_best5 with 180s (1) cores
0.82/1.03	# Starting almost_fo_3_lam with 180s (1) cores
0.82/1.03	# Starting new_bool_5 with 180s (1) cores
0.82/1.03	# SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
0.82/1.03	# Search class: HGHSM-FSLM32-MHFMMSBN
0.82/1.03	# Scheduled 10 strats onto 1 cores with 180 seconds (180 total)
0.82/1.03	# Starting ho_unfolding_8 with 33s (1) cores
0.82/1.03	# Preprocessing time       : 0.074 s
0.82/1.03	# Presaturation interreduction done
0.82/1.03	
0.82/1.03	# Proof found!
0.82/1.03	# SZS status Theorem
0.82/1.03	# SZS output start CNFRefutation
0.82/1.03	thf(decl_22, type, in: $i > $i > $o).
0.82/1.03	thf(decl_23, type, exu: ($i > $o) > $o).
0.82/1.03	thf(decl_24, type, setextAx: $o).
0.82/1.03	thf(decl_25, type, emptyset: $i).
0.82/1.03	thf(decl_26, type, emptysetAx: $o).
0.82/1.03	thf(decl_27, type, setadjoin: $i > $i > $i).
0.82/1.03	thf(decl_28, type, setadjoinAx: $o).
0.82/1.03	thf(decl_29, type, powerset: $i > $i).
0.82/1.03	thf(decl_30, type, powersetAx: $o).
0.82/1.03	thf(decl_31, type, setunion: $i > $i).
0.82/1.03	thf(decl_32, type, setunionAx: $o).
0.82/1.03	thf(decl_33, type, omega: $i).
0.82/1.03	thf(decl_34, type, omega0Ax: $o).
0.82/1.03	thf(decl_35, type, omegaSAx: $o).
0.82/1.03	thf(decl_36, type, omegaIndAx: $o).
0.82/1.03	thf(decl_37, type, replAx: $o).
0.82/1.03	thf(decl_38, type, foundationAx: $o).
0.82/1.03	thf(decl_39, type, wellorderingAx: $o).
0.82/1.03	thf(decl_40, type, descr: ($i > $o) > $i).
0.82/1.03	thf(decl_41, type, descrp: $o).
0.82/1.03	thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
0.82/1.03	thf(decl_43, type, dsetconstrI: $o).
0.82/1.03	thf(decl_44, type, dsetconstrEL: $o).
0.82/1.03	thf(decl_45, type, dsetconstrER: $o).
0.82/1.03	thf(decl_46, type, exuE1: $o).
0.82/1.03	thf(decl_47, type, prop2set: $o > $i).
0.82/1.03	thf(decl_48, type, prop2setE: $o).
0.82/1.03	thf(decl_49, type, emptysetE: $o).
0.82/1.03	thf(decl_50, type, emptysetimpfalse: $o).
0.82/1.03	thf(decl_51, type, notinemptyset: $o).
0.82/1.03	thf(decl_52, type, exuE3e: $o).
0.82/1.03	thf(decl_53, type, setext: $o).
0.82/1.03	thf(decl_54, type, emptyI: $o).
0.82/1.03	thf(decl_55, type, noeltsimpempty: $o).
0.82/1.03	thf(decl_56, type, setbeta: $o).
0.82/1.03	thf(decl_57, type, nonempty: $i > $o).
0.82/1.03	thf(decl_58, type, nonemptyE1: $o).
0.82/1.03	thf(decl_59, type, nonemptyI: $o).
0.82/1.03	thf(decl_60, type, nonemptyI1: $o).
0.82/1.03	thf(decl_61, type, setadjoinIL: $o).
0.82/1.03	thf(decl_62, type, emptyinunitempty: $o).
0.82/1.03	thf(decl_63, type, setadjoinIR: $o).
0.82/1.03	thf(decl_64, type, setadjoinE: $o).
0.82/1.03	thf(decl_65, type, setadjoinOr: $o).
0.82/1.03	thf(decl_66, type, setoftrueEq: $o).
0.82/1.03	thf(decl_67, type, powersetI: $o).
0.82/1.03	thf(decl_68, type, emptyinPowerset: $o).
0.82/1.03	thf(decl_69, type, emptyInPowerset: $o).
0.82/1.03	thf(decl_70, type, powersetE: $o).
0.82/1.03	thf(decl_71, type, setunionI: $o).
0.82/1.03	thf(decl_72, type, setunionE: $o).
0.82/1.03	thf(decl_73, type, subPowSU: $o).
0.82/1.03	thf(decl_74, type, exuE2: $o).
0.82/1.03	thf(decl_75, type, nonemptyImpWitness: $o).
0.82/1.03	thf(decl_76, type, uniqinunit: $o).
0.82/1.03	thf(decl_77, type, notinsingleton: $o).
0.82/1.03	thf(decl_78, type, eqinunit: $o).
0.82/1.03	thf(decl_79, type, singletonsswitch: $o).
0.82/1.03	thf(decl_80, type, upairsetE: $o).
0.82/1.03	thf(decl_81, type, upairsetIL: $o).
0.82/1.03	thf(decl_82, type, upairsetIR: $o).
0.82/1.03	thf(decl_83, type, emptyE1: $o).
0.82/1.03	thf(decl_84, type, vacuousDall: $o).
0.82/1.03	thf(decl_85, type, quantDeMorgan1: $o).
0.82/1.03	thf(decl_86, type, quantDeMorgan2: $o).
0.82/1.03	thf(decl_87, type, quantDeMorgan3: $o).
0.82/1.03	thf(decl_88, type, quantDeMorgan4: $o).
0.82/1.03	thf(decl_89, type, prop2setI: $o).
0.82/1.03	thf(decl_91, type, prop2set2propI: $o).
0.82/1.03	thf(decl_92, type, notdexE: $o).
0.82/1.03	thf(decl_93, type, notdallE: $o).
0.82/1.03	thf(decl_94, type, exuI1: $o).
0.82/1.03	thf(decl_95, type, exuI3: $o).
0.82/1.03	thf(decl_96, type, exuI2: $o).
0.82/1.03	thf(decl_97, type, inCongP: $o).
0.82/1.03	thf(decl_98, type, in__Cong: $o).
0.82/1.03	thf(decl_99, type, exuE3u: $o).
0.82/1.03	thf(decl_100, type, exu__Cong: $o).
0.82/1.03	thf(decl_101, type, emptyset__Cong: $o).
0.82/1.03	thf(decl_102, type, setadjoin__Cong: $o).
0.82/1.03	thf(decl_103, type, powerset__Cong: $o).
0.82/1.03	thf(decl_104, type, setunion__Cong: $o).
0.82/1.03	thf(decl_105, type, omega__Cong: $o).
0.82/1.03	thf(decl_106, type, exuEu: $o).
0.82/1.03	thf(decl_107, type, descr__Cong: $o).
0.82/1.03	thf(decl_108, type, dsetconstr__Cong: $o).
0.82/1.03	thf(decl_109, type, subset: $i > $i > $o).
0.82/1.03	thf(decl_112, type, subsetI1: $o).
0.82/1.03	thf(decl_113, type, eqimpsubset2: $o).
0.82/1.03	thf(decl_114, type, eqimpsubset1: $o).
0.82/1.03	thf(decl_115, type, subsetI2: $o).
0.82/1.03	thf(decl_116, type, emptysetsubset: $o).
0.82/1.03	thf(decl_117, type, subsetE: $o).
0.82/1.03	thf(decl_118, type, subsetE2: $o).
0.82/1.03	thf(decl_119, type, notsubsetI: $o).
0.82/1.03	thf(decl_120, type, notequalI1: $o).
0.82/1.03	thf(decl_121, type, notequalI2: $o).
0.82/1.03	thf(decl_122, type, subsetRefl: $o).
0.82/1.03	thf(decl_123, type, subsetTrans: $o).
0.82/1.03	thf(decl_124, type, setadjoinSub: $o).
0.82/1.03	thf(decl_125, type, setadjoinSub2: $o).
0.82/1.03	thf(decl_126, type, subset2powerset: $o).
0.82/1.03	thf(decl_127, type, setextsub: $o).
0.82/1.03	thf(decl_128, type, subsetemptysetimpeq: $o).
0.82/1.03	thf(decl_129, type, powersetI1: $o).
0.82/1.03	thf(decl_130, type, powersetE1: $o).
0.82/1.03	thf(decl_131, type, inPowerset: $o).
0.82/1.03	thf(decl_132, type, powersetsubset: $o).
0.82/1.03	thf(decl_133, type, sepInPowerset: $o).
0.82/1.03	thf(decl_134, type, sepSubset: $o).
0.82/1.03	thf(decl_135, type, binunion: $i > $i > $i).
0.82/1.03	thf(decl_136, type, binunionIL: $o).
0.82/1.03	thf(decl_137, type, upairset2IR: $o).
0.82/1.03	thf(decl_138, type, binunionIR: $o).
0.82/1.03	thf(decl_139, type, binunionEcases: $o).
0.82/1.03	thf(decl_140, type, binunionE: $o).
0.82/1.03	thf(decl_141, type, binunionLsub: $o).
0.82/1.03	thf(decl_142, type, binunionRsub: $o).
0.82/1.03	thf(decl_143, type, binintersect: $i > $i > $i).
0.82/1.03	thf(decl_144, type, binintersectI: $o).
0.82/1.03	thf(decl_145, type, binintersectSubset5: $o).
0.82/1.03	thf(decl_146, type, binintersectEL: $o).
0.82/1.03	thf(decl_147, type, binintersectLsub: $o).
0.82/1.03	thf(decl_148, type, binintersectSubset2: $o).
0.82/1.03	thf(decl_149, type, binintersectSubset3: $o).
0.82/1.03	thf(decl_150, type, binintersectER: $o).
0.82/1.03	thf(decl_151, type, disjointsetsI1: $o).
0.82/1.03	thf(decl_152, type, binintersectRsub: $o).
0.82/1.03	thf(decl_153, type, binintersectSubset4: $o).
0.82/1.03	thf(decl_154, type, binintersectSubset1: $o).
0.82/1.03	thf(decl_155, type, bs114d: $o).
0.82/1.03	thf(decl_157, type, setminus: $i > $i > $i).
0.82/1.03	thf(decl_158, type, setminusI: $o).
0.82/1.03	thf(decl_159, type, setminusEL: $o).
0.82/1.03	thf(decl_160, type, setminusER: $o).
0.82/1.03	thf(decl_161, type, setminusSubset2: $o).
0.82/1.03	thf(decl_162, type, setminusERneg: $o).
0.82/1.03	thf(decl_163, type, setminusELneg: $o).
0.82/1.03	thf(decl_164, type, setminusILneg: $o).
0.82/1.03	thf(decl_165, type, setminusIRneg: $o).
0.82/1.03	thf(decl_166, type, setminusLsub: $o).
0.82/1.03	thf(decl_167, type, setminusSubset1: $o).
0.82/1.03	thf(decl_168, type, symdiff: $i > $i > $i).
0.82/1.03	thf(decl_169, type, symdiffE: $o).
0.82/1.03	thf(decl_170, type, symdiffI1: $o).
0.82/1.03	thf(decl_171, type, symdiffI2: $o).
0.82/1.03	thf(decl_172, type, symdiffIneg1: $o).
0.82/1.03	thf(decl_173, type, symdiffIneg2: $o).
0.82/1.03	thf(decl_174, type, iskpair: $i > $o).
0.82/1.03	thf(decl_175, type, secondinupair: $o).
0.82/1.03	thf(decl_176, type, setukpairIL: $o).
0.82/1.03	thf(decl_177, type, setukpairIR: $o).
0.82/1.03	thf(decl_178, type, kpairiskpair: $o).
0.82/1.03	thf(decl_179, type, kpair: $i > $i > $i).
0.82/1.03	thf(decl_180, type, kpairp: $o).
0.82/1.03	thf(decl_181, type, cartprod: $i > $i > $i).
0.82/1.03	thf(decl_182, type, singletonsubset: $o).
0.82/1.03	thf(decl_183, type, singletoninpowerset: $o).
0.82/1.03	thf(decl_184, type, singletoninpowunion: $o).
0.82/1.03	thf(decl_185, type, upairset2E: $o).
0.82/1.03	thf(decl_186, type, upairsubunion: $o).
0.82/1.03	thf(decl_187, type, upairinpowunion: $o).
0.82/1.03	thf(decl_188, type, ubforcartprodlem1: $o).
0.82/1.03	thf(decl_189, type, ubforcartprodlem2: $o).
0.82/1.03	thf(decl_190, type, ubforcartprodlem3: $o).
0.82/1.03	thf(decl_191, type, cartprodpairin: $o).
0.82/1.03	thf(decl_192, type, cartprodmempair1: $o).
0.82/1.03	thf(decl_193, type, cartprodmempair: $o).
0.82/1.03	thf(decl_194, type, setunionE2: $o).
0.82/1.03	thf(decl_195, type, setunionsingleton1: $o).
0.82/1.03	thf(decl_196, type, setunionsingleton2: $o).
0.82/1.03	thf(decl_197, type, setunionsingleton: $o).
0.82/1.03	thf(decl_198, type, singleton: $i > $o).
0.82/1.03	thf(decl_199, type, singletonprop: $o).
0.82/1.03	thf(decl_200, type, ex1: $i > ($i > $o) > $o).
0.82/1.03	thf(decl_201, type, ex1E1: $o).
0.82/1.03	thf(decl_202, type, ex1I: $o).
0.82/1.03	thf(decl_203, type, ex1I2: $o).
0.82/1.03	thf(decl_204, type, singletonsuniq: $o).
0.82/1.03	thf(decl_209, type, setukpairinjL1: $o).
0.82/1.03	thf(decl_210, type, kfstsingleton: $o).
0.82/1.03	thf(decl_211, type, theprop: $o).
0.82/1.03	thf(decl_212, type, kfst: $i > $i).
0.82/1.03	thf(decl_213, type, kfstpairEq: $o).
0.82/1.03	thf(decl_214, type, cartprodfstin: $o).
0.82/1.03	thf(decl_215, type, setukpairinjL2: $o).
0.82/1.03	thf(decl_216, type, setukpairinjL: $o).
0.82/1.03	thf(decl_217, type, setukpairinjR11: $o).
0.82/1.03	thf(decl_218, type, setukpairinjR12: $o).
0.82/1.03	thf(decl_219, type, setukpairinjR1: $o).
0.82/1.03	thf(decl_220, type, upairequniteq: $o).
0.82/1.03	thf(decl_221, type, setukpairinjR2: $o).
0.82/1.03	thf(decl_222, type, setukpairinjR: $o).
0.82/1.03	thf(decl_223, type, ksndsingleton: $o).
0.82/1.03	thf(decl_224, type, ksnd: $i > $i).
0.82/1.03	thf(decl_225, type, ksndpairEq: $o).
0.82/1.03	thf(decl_226, type, kpairsurjEq: $o).
0.82/1.03	thf(decl_227, type, cartprodsndin: $o).
0.82/1.03	thf(decl_228, type, cartprodpairmemEL: $o).
0.82/1.03	thf(decl_229, type, cartprodpairmemER: $o).
0.82/1.03	thf(decl_230, type, cartprodmempaircEq: $o).
0.82/1.03	thf(decl_231, type, cartprodfstpairEq: $o).
0.82/1.03	thf(decl_232, type, cartprodsndpairEq: $o).
0.82/1.03	thf(decl_233, type, cartprodpairsurjEq: $o).
0.82/1.03	thf(decl_234, type, breln: $i > $i > $i > $o).
0.82/1.03	thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
0.82/1.03	thf(decl_236, type, dpsetconstrI: $o).
0.82/1.03	thf(decl_237, type, dpsetconstrSub: $o).
0.82/1.03	thf(decl_238, type, setOfPairsIsBReln: $o).
0.82/1.03	thf(decl_239, type, dpsetconstrERa: $o).
0.82/1.03	thf(decl_240, type, dpsetconstrEL1: $o).
0.82/1.03	thf(decl_241, type, dpsetconstrEL2: $o).
0.82/1.03	thf(decl_242, type, dpsetconstrER: $o).
0.82/1.03	thf(decl_243, type, func: $i > $i > $i > $o).
0.82/1.03	thf(decl_244, type, funcSet: $i > $i > $i).
0.82/1.03	thf(decl_245, type, funcImageSingleton: $o).
0.82/1.03	thf(decl_246, type, apProp: $o).
0.82/1.03	thf(decl_247, type, ap: $i > $i > $i > $i > $i).
0.82/1.03	thf(decl_248, type, app: $o).
0.82/1.03	thf(decl_249, type, infuncsetfunc: $o).
0.82/1.03	thf(decl_250, type, ap2p: $o).
0.82/1.03	thf(decl_251, type, funcinfuncset: $o).
0.82/1.03	thf(decl_252, type, lamProp: $o).
0.82/1.03	thf(decl_253, type, lam: $i > $i > ($i > $i) > $i).
0.82/1.03	thf(decl_254, type, lamp: $o).
0.82/1.03	thf(decl_255, type, lam2p: $o).
0.82/1.03	thf(decl_256, type, brelnall1: $o).
0.82/1.03	thf(decl_257, type, brelnall2: $o).
0.82/1.03	thf(decl_258, type, ex1E2: $o).
0.82/1.03	thf(decl_259, type, funcGraphProp1: $o).
0.82/1.03	thf(decl_260, type, funcGraphProp3: $o).
0.82/1.03	thf(decl_261, type, funcGraphProp2: $o).
0.82/1.03	thf(decl_262, type, funcextLem: $o).
0.82/1.03	thf(decl_263, type, funcGraphProp4: $o).
0.82/1.03	thf(decl_264, type, subbreln: $o).
0.82/1.03	thf(decl_265, type, eqbreln: $o).
0.82/1.03	thf(decl_266, type, funcext: $o).
0.82/1.03	thf(decl_267, type, funcext2: $o).
0.82/1.03	thf(decl_268, type, ap2apEq1: $o).
0.82/1.03	thf(decl_269, type, ap2apEq2: $o).
0.82/1.03	thf(decl_270, type, beta1: $o).
0.82/1.03	thf(decl_271, type, eta1: $o).
0.82/1.03	thf(decl_272, type, lam2lamEq: $o).
0.82/1.03	thf(decl_273, type, beta2: $o).
0.82/1.03	thf(decl_274, type, eta2: $o).
0.82/1.03	thf(decl_275, type, iffalseProp1: $o).
0.82/1.03	thf(decl_276, type, iffalseProp2: $o).
0.82/1.03	thf(decl_277, type, iftrueProp1: $o).
0.82/1.03	thf(decl_278, type, iftrueProp2: $o).
0.82/1.03	thf(decl_279, type, ifSingleton: $o).
0.82/1.03	thf(decl_280, type, if: $i > $o > $i > $i > $i).
0.82/1.03	thf(decl_281, type, ifp: $o).
0.82/1.03	thf(decl_282, type, theeq: $o).
0.82/1.03	thf(decl_283, type, iftrue: $o).
0.82/1.03	thf(decl_284, type, iffalse: $o).
0.82/1.03	thf(decl_285, type, iftrueorfalse: $o).
0.82/1.03	thf(decl_286, type, binintersectT_lem: $o).
0.82/1.03	thf(decl_287, type, binunionT_lem: $o).
0.82/1.03	thf(decl_288, type, powersetT_lem: $o).
0.82/1.03	thf(decl_289, type, setminusT_lem: $o).
0.82/1.03	thf(decl_290, type, complementT_lem: $o).
0.82/1.03	thf(decl_291, type, setextT: $o).
0.82/1.03	thf(decl_292, type, subsetTI: $o).
0.82/1.03	thf(decl_293, type, powersetTI1: $o).
0.82/1.03	thf(decl_294, type, powersetTE1: $o).
0.82/1.03	thf(decl_295, type, complementTI1: $o).
0.82/1.03	thf(decl_296, type, complementTE1: $o).
0.82/1.03	thf(decl_297, type, binintersectTELcontra: $o).
0.82/1.03	thf(decl_298, type, binintersectTERcontra: $o).
0.82/1.03	thf(decl_299, type, contrasubsetT: $o).
0.82/1.03	thf(decl_300, type, contrasubsetT1: $o).
0.82/1.03	thf(decl_301, type, contrasubsetT2: $o).
0.82/1.03	thf(decl_302, type, contrasubsetT3: $o).
0.82/1.03	thf(decl_303, type, doubleComplementI1: $o).
0.82/1.03	thf(decl_304, type, doubleComplementE1: $o).
0.82/1.03	thf(decl_305, type, doubleComplementSub1: $o).
0.82/1.03	thf(decl_306, type, doubleComplementSub2: $o).
0.82/1.03	thf(decl_307, type, doubleComplementEq: $o).
0.82/1.03	thf(decl_308, type, complementTnotintersectT: $o).
0.82/1.03	thf(decl_309, type, complementImpComplementIntersect: $o).
0.82/1.03	thf(decl_310, type, complementSubsetComplementIntersect: $o).
0.82/1.03	thf(decl_311, type, complementInPowersetComplementIntersect: $o).
0.82/1.03	thf(decl_312, type, contraSubsetComplement: $o).
0.82/1.03	thf(decl_313, type, complementTcontraSubset: $o).
0.82/1.03	thf(decl_314, type, binunionTILcontra: $o).
0.82/1.03	thf(decl_315, type, binunionTIRcontra: $o).
0.82/1.03	thf(decl_316, type, inIntersectImpInUnion: $o).
0.82/1.03	thf(decl_317, type, inIntersectImpInUnion2: $o).
0.82/1.03	thf(decl_318, type, inIntersectImpInIntersectUnions: $o).
0.82/1.03	thf(decl_319, type, intersectInPowersetIntersectUnions: $o).
0.82/1.03	thf(decl_320, type, inComplementUnionImpNotIn1: $o).
0.82/1.03	thf(decl_321, type, inComplementUnionImpInComplement1: $o).
0.82/1.03	thf(decl_322, type, binunionTE: $o).
0.82/1.03	thf(decl_323, type, binunionTEcontra: $o).
0.82/1.03	thf(decl_324, type, demorgan2a1: $o).
0.82/1.03	thf(decl_325, type, complementUnionInPowersetComplement: $o).
0.82/1.03	thf(decl_326, type, demorgan2a2: $o).
0.82/1.03	thf(decl_327, type, demorgan1a: $o).
0.82/1.03	thf(decl_328, type, demorgan1b: $o).
0.82/1.03	thf(decl_329, type, demorgan1: $o).
0.82/1.03	thf(decl_330, type, demorgan2a: $o).
0.82/1.03	thf(decl_331, type, demorgan2b2: $o).
0.82/1.03	thf(decl_332, type, epred1_0: $o).
0.82/1.03	thf(decl_333, type, esk1_2: $i > $i > $i).
0.82/1.03	thf(decl_334, type, esk2_2: $i > $i > $i).
0.82/1.03	thf(decl_335, type, esk3_2: $i > $i > $i).
0.82/1.03	thf(decl_336, type, esk4_1: $i > $i).
0.82/1.03	thf(decl_337, type, esk5_2: ($i > $i > $o) > $i > $i).
0.82/1.03	thf(decl_338, type, esk6_2: ($i > $i > $o) > $i > $i).
0.82/1.03	thf(decl_339, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
0.82/1.03	thf(decl_340, type, esk8_1: $i > $i).
0.82/1.03	thf(decl_341, type, esk9_1: ($i > $o) > $i).
0.82/1.03	thf(decl_342, type, esk10_1: ($i > $o) > $i).
0.82/1.03	thf(decl_343, type, esk11_2: $i > $i > $i).
0.82/1.03	thf(decl_344, type, esk12_2: $i > $i > $i).
0.82/1.03	thf(decl_345, type, esk13_1: $i > $i).
0.82/1.03	thf(decl_346, type, esk14_1: $i > $i).
0.82/1.03	thf(decl_347, type, esk15_1: $i > $i).
0.82/1.03	thf(decl_348, type, esk16_2: $i > $i > $i).
0.82/1.03	thf(decl_349, type, esk17_3: $i > $i > $o > $i).
0.82/1.03	thf(decl_350, type, esk18_1: ($i > $o) > $i).
0.82/1.03	thf(decl_351, type, esk19_1: $i > $i).
0.82/1.03	thf(decl_352, type, esk20_2: $i > ($i > $o) > $i).
0.82/1.03	thf(decl_353, type, esk21_2: $i > ($i > $o) > $i).
0.82/1.03	thf(decl_354, type, esk22_2: $i > ($i > $o) > $i).
0.82/1.03	thf(decl_355, type, esk23_2: $i > ($i > $o) > $i).
0.82/1.03	thf(decl_356, type, esk24_2: $i > ($i > $o) > $i).
0.82/1.03	thf(decl_357, type, esk25_2: $i > ($i > $o) > $i).
0.82/1.03	thf(decl_358, type, esk26_2: ($i > $o) > $i > $i).
0.82/1.03	thf(decl_359, type, esk27_1: ($i > $o) > $i).
0.82/1.03	thf(decl_360, type, esk28_1: ($i > $o) > $i).
0.82/1.03	thf(decl_361, type, esk29_2: ($i > $o) > $i > $i).
0.82/1.03	thf(decl_362, type, esk30_2: ($i > $o) > ($i > $o) > $i).
0.82/1.03	thf(decl_363, type, esk31_2: ($i > $o) > ($i > $o) > $i).
0.82/1.03	thf(decl_364, type, esk32_2: ($i > $o) > ($i > $o) > $i).
0.82/1.03	thf(decl_365, type, esk33_2: ($i > $o) > ($i > $o) > $i).
0.82/1.03	thf(decl_366, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
0.82/1.03	thf(decl_367, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
0.82/1.03	thf(decl_368, type, esk36_2: $i > $i > $i).
0.82/1.03	thf(decl_369, type, esk37_2: $i > $i > $i).
0.82/1.03	thf(decl_370, type, esk38_2: $i > $i > $i).
0.82/1.03	thf(decl_371, type, esk39_3: $i > $i > $i > $i).
0.82/1.03	thf(decl_372, type, esk40_3: $i > $i > $i > $i).
0.82/1.03	thf(decl_373, type, esk41_2: $i > $i > $i).
0.82/1.03	thf(decl_374, type, esk42_2: $i > ($i > $o) > $i).
0.82/1.03	thf(decl_375, type, esk43_2: $i > ($i > $o) > $i).
0.82/1.03	thf(decl_376, type, esk44_2: $i > ($i > $o) > $i).
0.82/1.03	thf(decl_377, type, esk45_3: $i > ($i > $o) > $i > $i).
0.82/1.03	thf(decl_378, type, esk46_2: $i > ($i > $o) > $i).
0.82/1.03	thf(decl_379, type, esk47_2: $i > ($i > $o) > $i).
0.82/1.03	thf(decl_380, type, esk48_3: $i > $i > ($i > $i) > $i).
0.82/1.03	thf(decl_381, type, esk49_3: $i > $i > ($i > $i) > $i).
0.82/1.03	thf(decl_382, type, esk50_3: $i > $i > ($i > $i) > $i).
0.82/1.03	thf(decl_383, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
0.82/1.03	thf(decl_384, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
0.82/1.03	thf(decl_385, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
0.82/1.03	thf(decl_386, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
0.82/1.03	thf(decl_387, type, esk55_4: $i > $i > $i > $i > $i).
0.82/1.03	thf(decl_388, type, esk56_4: $i > $i > $i > $i > $i).
0.82/1.03	thf(decl_389, type, esk57_4: $i > $i > $i > $i > $i).
0.82/1.03	thf(decl_390, type, esk58_4: $i > $i > $i > $i > $i).
0.82/1.03	thf(decl_391, type, esk59_4: $i > $i > $i > $i > $i).
0.82/1.03	thf(decl_392, type, esk60_4: $i > $i > $i > $i > $i).
0.82/1.03	thf(decl_393, type, esk61_4: $i > $i > $i > $i > $i).
0.82/1.03	thf(decl_394, type, esk62_4: $i > $i > $i > $i > $i).
0.82/1.03	thf(decl_395, type, esk63_4: $i > $i > $i > $i > $i).
0.82/1.03	thf(decl_396, type, esk64_3: $i > $i > ($i > $i) > $i).
0.82/1.03	thf(decl_397, type, esk65_3: $i > $i > ($i > $i) > $i).
0.82/1.03	thf(decl_398, type, esk66_3: $i > $i > ($i > $i) > $i).
0.82/1.03	thf(decl_399, type, esk67_3: $i > $i > $i > $i).
0.82/1.03	thf(decl_400, type, esk68_3: $i > $i > $i > $i).
0.82/1.03	thf(decl_401, type, esk69_3: $i > $i > $i > $i).
0.82/1.03	thf(decl_402, type, esk70_3: $i > $i > $i > $i).
0.82/1.03	thf(decl_403, type, esk71_0: $i).
0.82/1.03	thf(decl_404, type, esk72_0: $i).
0.82/1.03	thf(decl_405, type, esk73_0: $i).
0.82/1.03	thf(decl_406, type, esk74_0: $i).
0.82/1.03	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', dsetconstr__Cong)).
0.82/1.03	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', exuEu)).
0.82/1.03	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', exu__Cong)).
0.82/1.03	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', exuI2)).
0.82/1.03	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', exuI3)).
0.82/1.03	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', singletonprop)).
0.82/1.03	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', emptyE1)).
0.82/1.03	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', ex1I2)).
0.82/1.03	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', dpsetconstrSub)).
0.82/1.03	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setoftrueEq)).
0.82/1.03	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', kfstsingleton)).
0.82/1.03	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setbeta)).
0.82/1.03	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', exuE1)).
0.82/1.03	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', dsetconstrEL)).
0.82/1.03	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', dpsetconstrEL1)).
0.82/1.03	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', dpsetconstrER)).
0.82/1.03	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', apProp)).
0.82/1.03	thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', lamProp)).
0.82/1.03	thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', lamp)).
0.82/1.03	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', lam2p)).
0.82/1.03	thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', beta1)).
0.82/1.03	thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', lam2lamEq)).
0.82/1.03	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', ifSingleton)).
0.82/1.03	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', sepSubset)).
0.82/1.03	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', iftrueProp2)).
0.82/1.03	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', iftrueProp1)).
0.82/1.03	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', iffalseProp2)).
0.82/1.03	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', iffalseProp1)).
0.82/1.03	thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', eta2)).
0.82/1.03	thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', beta2)).
0.82/1.03	thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', eta1)).
0.82/1.03	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', ex1E2)).
0.82/1.03	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', funcImageSingleton)).
0.82/1.03	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', dpsetconstrEL2)).
0.82/1.03	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', dpsetconstrERa)).
0.82/1.03	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setOfPairsIsBReln)).
0.82/1.03	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', dpsetconstrI)).
0.82/1.03	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', ksndsingleton)).
0.82/1.03	thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', ex1I)).
0.82/1.03	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', ex1E1)).
0.82/1.03	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', sepInPowerset)).
0.82/1.03	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', descr__Cong)).
0.82/1.03	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', exuE3u)).
0.82/1.03	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', exuI1)).
0.82/1.03	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', exuE2)).
0.82/1.03	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', nonemptyI)).
0.82/1.03	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', exuE3e)).
0.82/1.03	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', dsetconstrER)).
0.82/1.03	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', dsetconstrI)).
0.82/1.03	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', descrp)).
0.82/1.03	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', replAx)).
0.82/1.03	thf(demorgan2b, conjecture, (((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((((((replAx)=>((((descrp)=>((dsetconstrI)=>(((dsetconstrER)=>(((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>(((exuE3e)=>((((((nonemptyE1)=>((nonemptyI)=>(((setadjoinIL)=>(((((setadjoinOr)=>(((powersetI)=>((emptyinPowerset)=>(((powersetE)=>(((((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>(((eqinunit)=>((((upairsetIL)=>(((((((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>(((notdexE)=>((notdallE)=>((exuI1)=>((((inCongP)=>((in__Cong)=>((exuE3u)=>(((((((omega__Cong)=>(((descr__Cong)=>((((eqimpsubset2)=>(((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((((((subsetTrans)=>((((subset2powerset)=>(((subsetemptysetimpeq)=>((((((sepInPowerset)=>(((binunionIL)=>(((binunionIR)=>(((((binunionRsub)=>((binintersectI)=>(((((binintersectSubset2)=>((((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>(((setminusERneg)=>(((setminusILneg)=>((setminusIRneg)=>((((((symdiffI2)=>((symdiffIneg1)=>(((((setukpairIR)=>((kpairiskpair)=>((kpairp)=>(((singletoninpowerset)=>((singletoninpowunion)=>((((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>(((cartprodmempair)=>(((((setunionsingleton)=>((singletonprop)=>((((ex1I2)=>((singletonsuniq)=>(((kfstsingleton)=>((((((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>(((((dpsetconstrSub)=>((((dpsetconstrEL1)=>(((dpsetconstrER)=>(((apProp)=>(((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((((funcGraphProp3)=>((funcGraphProp2)=>(((funcGraphProp4)=>((subbreln)=>((eqbreln)=>(((((ap2apEq2)=>((beta1)=>(((lam2lamEq)=>((((((((ifSingleton)=>((ifp)=>(((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>(((((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>(((doubleComplementI1)=>(((doubleComplementSub1)=>((((((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((((binunionTIRcontra)=>(((inIntersectImpInUnion2)=>((((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>(((((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((![X4:$i, X21:$i]:((![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:((((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))<=(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))<=(in @ X2 @ X4)))))<=(in @ X21 @ (powerset @ X4))))<=(demorgan2b2))<=(demorgan2a)))))))<=(demorgan2a1))<=(binunionTEcontra))<=(binunionTE))))<=(intersectInPowersetIntersectUnions))<=(inIntersectImpInIntersectUnions)))<=(inIntersectImpInUnion)))<=(binunionTILcontra))<=(complementTcontraSubset)))))<=(complementImpComplementIntersect))<=(complementTnotintersectT))<=(doubleComplementEq))<=(doubleComplementSub2)))<=(doubleComplementE1)))<=(contrasubsetT3)))))))<=(complementTE1))<=(complementTI1))<=(powersetTE1)))))))<=(powersetT_lem))<=(binunionT_lem))))))<=(theeq))))<=(iftrueProp2))<=(iftrueProp1))<=(iffalseProp2))<=(iffalseProp1))<=(eta2))<=(beta2)))<=(eta1))))<=(ap2apEq1))<=(funcext2))<=(funcext)))))<=(funcextLem))))<=(funcGraphProp1))<=(ex1E2))))))))))<=(app)))<=(funcImageSingleton)))<=(dpsetconstrEL2)))<=(dpsetconstrERa))<=(setOfPairsIsBReln)))<=(dpsetconstrI))<=(cartprodpairsurjEq))<=(cartprodsndpairEq))))))))<=(ksndpairEq))<=(ksndsingleton)))))))))<=(setukpairinjL2))<=(cartprodfstin))<=(kfstpairEq))<=(theprop)))<=(setukpairinjL1))))<=(ex1I))<=(ex1E1))))<=(setunionsingleton2))<=(setunionsingleton1))<=(setunionE2)))<=(cartprodmempair1)))))))<=(upairsubunion))<=(upairset2E))))<=(singletonsubset)))))<=(setukpairIL))<=(secondinupair))<=(symdiffIneg2))))<=(symdiffI1))<=(symdiffE))<=(setminusSubset1))<=(setminusLsub))))<=(setminusELneg)))<=(setminusSubset2))))))))))<=(binintersectER))<=(binintersectSubset3)))<=(binintersectLsub))<=(binintersectEL))<=(binintersectSubset5))))<=(binunionLsub))<=(binunionE))<=(binunionEcases)))<=(upairset2IR)))<=(sepSubset)))<=(powersetsubset))<=(inPowerset))<=(powersetE1))<=(powersetI1)))<=(setextsub)))<=(setadjoinSub2))<=(setadjoinSub)))<=(subsetRefl))<=(notequalI2))<=(notequalI1))<=(notsubsetI))))))<=(eqimpsubset1)))<=(subsetI1))<=(dsetconstr__Cong)))<=(exuEu)))<=(setunion__Cong))<=(powerset__Cong))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong)))))<=(exuI2))<=(exuI3)))))<=(prop2set2propI)))))<=(quantDeMorgan2))<=(quantDeMorgan1))<=(vacuousDall))<=(emptyE1))<=(upairsetIR)))<=(upairsetE))<=(singletonsswitch)))<=(notinsingleton)))))<=(subPowSU))<=(setunionE))<=(setunionI)))<=(emptyInPowerset))))<=(setoftrueEq)))<=(setadjoinE))<=(setadjoinIR))<=(emptyinunitempty)))<=(nonemptyI1))))<=(setbeta))<=(noeltsimpempty))<=(emptyI))<=(setext)))<=(notinemptyset)))))<=(exuE1)))<=(dsetconstrEL))))<=(wellorderingAx))<=(foundationAx)))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax))<=(setunionAx)))))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', demorgan2b)).
0.82/1.03	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', kpairp)).
0.82/1.03	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', notinsingleton)).
0.82/1.03	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setextAx)).
0.82/1.03	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', notequalI2)).
0.82/1.03	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', kpairiskpair)).
0.82/1.03	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', notequalI1)).
0.82/1.03	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', notsubsetI)).
0.82/1.03	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', eqimpsubset1)).
0.82/1.03	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', ubforcartprodlem2)).
0.82/1.03	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', subsetI1)).
0.82/1.03	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', ubforcartprodlem3)).
0.82/1.03	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setunion__Cong)).
0.82/1.03	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', powerset__Cong)).
0.82/1.03	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', cartprodpairin)).
0.82/1.03	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setadjoin__Cong)).
0.82/1.03	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', emptyset__Cong)).
0.82/1.03	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', cartprodmempair)).
0.82/1.03	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setunionsingleton)).
0.82/1.03	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', quantDeMorgan2)).
0.82/1.03	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', quantDeMorgan1)).
0.82/1.03	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', vacuousDall)).
0.82/1.03	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', upairsetIR)).
0.82/1.03	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', upairsetE)).
0.82/1.03	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', singletonsswitch)).
0.82/1.03	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', singletoninpowerset)).
0.82/1.03	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', subPowSU)).
0.82/1.03	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setunionE)).
0.82/1.03	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', singletonsuniq)).
0.82/1.03	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setunionI)).
0.82/1.03	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', emptyInPowerset)).
0.82/1.03	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setadjoinE)).
0.82/1.03	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setadjoinIR)).
0.82/1.03	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setukpairinjL)).
0.82/1.03	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', emptyinunitempty)).
0.82/1.03	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', nonemptyI1)).
0.82/1.03	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setukpairinjR11)).
0.82/1.03	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', noeltsimpempty)).
0.82/1.03	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', emptyI)).
0.82/1.03	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setukpairinjR12)).
0.82/1.03	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setext)).
0.82/1.03	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', notinemptyset)).
0.82/1.03	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setukpairinjR1)).
0.82/1.03	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', wellorderingAx)).
0.82/1.03	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', upairequniteq)).
0.82/1.03	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', foundationAx)).
0.82/1.03	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', omegaIndAx)).
0.82/1.03	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', omegaSAx)).
0.82/1.03	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setukpairinjR2)).
0.82/1.03	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', omega0Ax)).
0.82/1.03	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setunionAx)).
0.82/1.03	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setukpairinjR)).
0.82/1.03	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', kpairsurjEq)).
0.82/1.03	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', cartprodsndin)).
0.82/1.03	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', cartprodpairmemEL)).
0.82/1.03	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', cartprodpairmemER)).
0.82/1.03	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', cartprodmempaircEq)).
0.82/1.03	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', cartprodfstpairEq)).
0.82/1.03	thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binintersectTELcontra)).
0.82/1.03	thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binintersectTERcontra)).
0.82/1.03	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', infuncsetfunc)).
0.82/1.03	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', ap2p)).
0.82/1.03	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', funcinfuncset)).
0.82/1.03	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', singletoninpowunion)).
0.82/1.03	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', brelnall1)).
0.82/1.03	thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', brelnall2)).
0.82/1.03	thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', funcGraphProp3)).
0.82/1.03	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', funcGraphProp2)).
0.82/1.03	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', funcGraphProp4)).
0.82/1.03	thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', subbreln)).
0.82/1.03	thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', eqbreln)).
0.82/1.03	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', ap2apEq2)).
0.82/1.03	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', upairinpowunion)).
0.82/1.03	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', ifp)).
0.82/1.03	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', iftrue)).
0.82/1.03	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', iffalse)).
0.82/1.03	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', iftrueorfalse)).
0.82/1.03	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binintersectT_lem)).
0.82/1.03	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setminusT_lem)).
0.82/1.03	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', complementT_lem)).
0.82/1.03	thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setextT)).
0.82/1.03	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', subsetTI)).
0.82/1.03	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', powersetTI1)).
0.82/1.03	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', upairset2IR)).
0.82/1.03	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', powersetsubset)).
0.82/1.03	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', inPowerset)).
0.82/1.03	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', powersetE1)).
0.82/1.03	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', powersetI1)).
0.82/1.03	thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', contrasubsetT)).
0.82/1.03	thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', contrasubsetT1)).
0.82/1.03	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', contrasubsetT2)).
0.82/1.03	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', doubleComplementI1)).
0.82/1.03	thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', doubleComplementSub1)).
0.82/1.03	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', complementSubsetComplementIntersect)).
0.82/1.03	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', complementInPowersetComplementIntersect)).
0.82/1.03	thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', contraSubsetComplement)).
0.82/1.03	thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binunionTIRcontra)).
0.82/1.03	thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', inIntersectImpInUnion2)).
0.82/1.03	thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', inComplementUnionImpNotIn1)).
0.82/1.03	thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', inComplementUnionImpInComplement1)).
0.82/1.03	thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', complementUnionInPowersetComplement)).
0.82/1.03	thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', demorgan2a2)).
0.82/1.03	thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', demorgan1a)).
0.82/1.03	thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', demorgan1b)).
0.82/1.03	thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', demorgan1)).
0.82/1.03	thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', demorgan2b2)).
0.82/1.03	thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', demorgan2a)).
0.82/1.03	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', ubforcartprodlem1)).
0.82/1.03	thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', demorgan2a1)).
0.82/1.03	thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binunionTEcontra)).
0.82/1.03	thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binunionTE)).
0.82/1.03	thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', intersectInPowersetIntersectUnions)).
0.82/1.03	thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', inIntersectImpInIntersectUnions)).
0.82/1.03	thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', inIntersectImpInUnion)).
0.82/1.03	thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binunionTILcontra)).
0.82/1.03	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', complementTcontraSubset)).
0.82/1.03	thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', complementImpComplementIntersect)).
0.82/1.03	thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', complementTnotintersectT)).
0.82/1.03	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', doubleComplementEq)).
0.82/1.03	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', doubleComplementSub2)).
0.82/1.03	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', doubleComplementE1)).
0.82/1.03	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', contrasubsetT3)).
0.82/1.03	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', complementTE1)).
0.82/1.03	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', complementTI1)).
0.82/1.03	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', powersetTE1)).
0.82/1.03	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', powersetT_lem)).
0.82/1.03	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binunionT_lem)).
0.82/1.03	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', theeq)).
0.82/1.03	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', ap2apEq1)).
0.82/1.03	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', funcext2)).
0.82/1.03	thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', funcext)).
0.82/1.03	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', funcextLem)).
0.82/1.03	thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', funcGraphProp1)).
0.82/1.03	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', app)).
0.82/1.03	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', cartprodpairsurjEq)).
0.82/1.03	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', cartprodsndpairEq)).
0.82/1.03	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', ksndpairEq)).
0.82/1.03	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setukpairinjL2)).
0.82/1.03	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', cartprodfstin)).
0.82/1.03	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', kfstpairEq)).
0.82/1.03	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', theprop)).
0.82/1.03	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setukpairinjL1)).
0.82/1.03	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setunionsingleton2)).
0.82/1.03	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setunionsingleton1)).
0.82/1.03	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setunionE2)).
0.82/1.03	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', cartprodmempair1)).
0.82/1.03	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', upairsubunion)).
0.82/1.03	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', upairset2E)).
0.82/1.03	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', singletonsubset)).
0.82/1.03	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setukpairIL)).
0.82/1.03	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', secondinupair)).
0.82/1.03	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', symdiffIneg2)).
0.82/1.03	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', symdiffI1)).
0.82/1.03	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', symdiffE)).
0.82/1.03	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setminusSubset1)).
0.82/1.03	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setminusLsub)).
0.82/1.03	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setminusELneg)).
0.82/1.03	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setminusSubset2)).
0.82/1.03	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binintersectER)).
0.82/1.03	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binintersectSubset3)).
0.82/1.03	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binintersectLsub)).
0.82/1.03	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binintersectEL)).
0.82/1.03	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binintersectSubset5)).
0.82/1.03	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binunionLsub)).
0.82/1.03	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binunionE)).
0.82/1.03	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binunionEcases)).
0.82/1.03	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setextsub)).
0.82/1.03	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setadjoinSub2)).
0.82/1.03	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setadjoinSub)).
0.82/1.03	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', subsetRefl)).
0.82/1.03	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setukpairIR)).
0.82/1.03	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', symdiffIneg1)).
0.82/1.03	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', symdiffI2)).
0.82/1.03	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setminusIRneg)).
0.82/1.03	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setminusILneg)).
0.82/1.03	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setminusERneg)).
0.82/1.03	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setminusER)).
0.82/1.03	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setminusEL)).
0.82/1.03	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setminusI)).
0.82/1.03	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', bs114d)).
0.82/1.03	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binintersectSubset1)).
0.82/1.03	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binintersectSubset4)).
0.82/1.03	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binintersectRsub)).
0.82/1.03	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', disjointsetsI1)).
0.82/1.03	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binintersectSubset2)).
0.82/1.03	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binintersectI)).
0.82/1.03	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binunionRsub)).
0.82/1.03	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binunionIR)).
0.82/1.03	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', binunionIL)).
0.82/1.03	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', subsetemptysetimpeq)).
0.82/1.03	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', subset2powerset)).
0.82/1.03	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', subsetTrans)).
0.82/1.03	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', subsetE2)).
0.82/1.03	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', subsetE)).
0.82/1.03	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', emptysetsubset)).
0.82/1.03	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', subsetI2)).
0.82/1.03	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', eqimpsubset2)).
0.82/1.03	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', omega__Cong)).
0.82/1.03	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', in__Cong)).
0.82/1.03	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', inCongP)).
0.82/1.03	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', notdallE)).
0.82/1.03	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', notdexE)).
0.82/1.03	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', prop2setI)).
0.82/1.03	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', quantDeMorgan4)).
0.82/1.03	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', quantDeMorgan3)).
0.82/1.03	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', upairsetIL)).
0.82/1.03	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', eqinunit)).
0.82/1.03	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', uniqinunit)).
0.82/1.03	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', nonemptyImpWitness)).
0.82/1.03	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', powersetE)).
0.82/1.03	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', emptyinPowerset)).
0.82/1.03	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', powersetI)).
0.82/1.03	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setadjoinOr)).
0.82/1.03	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setadjoinIL)).
0.82/1.03	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', nonemptyE1)).
0.82/1.03	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', emptysetimpfalse)).
0.82/1.03	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', emptysetE)).
0.82/1.03	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', prop2setE)).
0.82/1.03	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', powersetAx)).
0.82/1.03	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', setadjoinAx)).
0.82/1.03	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.sAG6mKxnLG/Vampire---4.8_10653', emptysetAx)).
0.82/1.03	thf(c_0_272, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
0.82/1.03	thf(c_0_273, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
0.82/1.03	thf(c_0_274, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
0.82/1.03	thf(c_0_275, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
0.82/1.03	thf(c_0_276, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
0.82/1.03	thf(c_0_277, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
0.82/1.03	thf(c_0_278, plain, ((emptyE1)<=>![X4:$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])).
0.82/1.03	thf(c_0_279, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
0.82/1.03	thf(c_0_280, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
0.82/1.03	thf(c_0_281, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
0.82/1.03	thf(c_0_282, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
0.82/1.03	thf(c_0_283, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
0.82/1.03	thf(c_0_284, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
0.82/1.03	thf(c_0_285, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
0.82/1.03	thf(c_0_286, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
0.82/1.03	thf(c_0_287, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
0.82/1.03	thf(c_0_288, plain, ((apProp)<=>![X4:$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])).
0.82/1.03	thf(c_0_289, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
0.82/1.03	thf(c_0_290, 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 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
0.82/1.03	thf(c_0_291, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
0.82/1.03	thf(c_0_292, plain, ((beta1)<=>![X4:$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])).
0.82/1.03	thf(c_0_293, 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])).
0.82/1.03	thf(c_0_294, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
0.82/1.03	thf(c_0_295, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
0.82/1.03	thf(c_0_296, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
0.82/1.03	thf(c_0_297, plain, ((iftrueProp1)<=>![X4:$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])).
0.82/1.03	thf(c_0_298, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
0.82/1.03	thf(c_0_299, plain, ((iffalseProp1)<=>![X4:$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])).
0.82/1.03	thf(c_0_300, 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])).
0.82/1.03	thf(c_0_301, 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])).
0.82/1.03	thf(c_0_302, 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])).
0.82/1.03	thf(c_0_303, 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])).
0.82/1.03	thf(c_0_304, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
0.82/1.03	thf(c_0_305, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
0.82/1.03	thf(c_0_306, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
0.82/1.03	thf(c_0_307, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
0.82/1.03	thf(c_0_308, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
0.82/1.03	thf(c_0_309, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
0.82/1.03	thf(c_0_310, plain, ((ex1I)<=>![X4:$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])).
0.82/1.03	thf(c_0_311, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
0.82/1.03	thf(c_0_312, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
0.82/1.03	thf(c_0_313, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
0.82/1.03	thf(c_0_314, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
0.82/1.03	thf(c_0_315, 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])).
0.82/1.03	thf(c_0_316, 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])).
0.82/1.03	thf(c_0_317, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
0.82/1.03	thf(c_0_318, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
0.82/1.03	thf(c_0_319, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
0.82/1.03	thf(c_0_320, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
0.82/1.03	thf(c_0_321, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
0.82/1.03	thf(c_0_322, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
0.82/1.03	thf(c_0_323, plain, ((epred1_0)<=>![X1742:$i]:(?[X1743:$i]:((((![X1744:$i]:(((in @ X1744 @ X1743)=>![X1745:$i]:(((in @ X1745 @ X1744)=>(in @ X1745 @ X1742)))))&![X1746:$i, X1747:$i]:((((in @ X1746 @ X1742)&(in @ X1747 @ X1742))=>(![X1748:$i]:(((in @ X1748 @ X1743)=>((in @ X1746 @ X1748)<=>(in @ X1747 @ X1748))))=>((X1746)=(X1747))))))&![X1749:$i, X1750:$i]:((((in @ X1749 @ X1743)&(in @ X1750 @ X1743))=>(![X1751:$i]:(((in @ X1751 @ X1749)=>(in @ X1751 @ X1750)))|![X1752:$i]:(((in @ X1752 @ X1750)=>(in @ X1752 @ X1749)))))))&![X1753:$i]:(((![X1754:$i]:(((in @ X1754 @ X1753)=>(in @ X1754 @ X1742)))&?[X1755:$i]:((in @ X1755 @ X1753)))=>?[X1756:$i, X1757:$i]:(((((in @ X1756 @ X1743)&(in @ X1757 @ X1753))&~(?[X1758:$i]:(((in @ X1758 @ X1756)&(in @ X1758 @ X1753)))))&![X1759:$i]:(((in @ X1759 @ X1743)=>(![X1760:$i]:(((in @ X1760 @ X1759)=>(in @ X1760 @ X1756)))|(in @ X1757 @ X1759)))))))))))), introduced(definition)).
0.82/1.03	thf(c_0_324, negated_conjecture, ~((![X1772:$i, X1773:$i]:((![X1774:$i]:(((in @ X1774 @ X1772)<=>(in @ X1774 @ X1773)))=>((X1772)=(X1773))))=>(![X915:$i]:(~(in @ X915 @ emptyset))=>(![X916:$i, X917:$i, X918:$i]:(((in @ X918 @ (setadjoin @ X916 @ X917))<=>(((X918)=(X916))|(in @ X918 @ X917))))=>(![X919:$i, X920:$i]:(((in @ X920 @ (powerset @ X919))<=>![X921:$i]:(((in @ X921 @ X920)=>(in @ X921 @ X919)))))=>(![X1769:$i, X1770:$i]:(((in @ X1770 @ (setunion @ X1769))<=>?[X1771:$i]:(((in @ X1770 @ X1771)&(in @ X1771 @ X1769)))))=>((in @ emptyset @ omega)=>(![X1768:$i]:(((in @ X1768 @ omega)=>(in @ (setadjoin @ X1768 @ X1768) @ omega)))=>(![X1765:$i]:((((in @ emptyset @ X1765)&![X1766:$i]:((((in @ X1766 @ omega)&(in @ X1766 @ X1765))=>(in @ (setadjoin @ X1766 @ X1766) @ X1765))))=>![X1767:$i]:(((in @ X1767 @ omega)=>(in @ X1767 @ X1765)))))=>(![X922:$i > $i > $o, X923:$i]:((![X924:$i]:(((in @ X924 @ X923)=>(exu @ (^[Z0/* 3 */:$i]:((X922 @ X924 @ Z0))))))=>?[X925:$i]:(![X926:$i]:(((in @ X926 @ X925)<=>?[X927:$i]:(((in @ X927 @ X923)&(X922 @ X927 @ X926))))))))=>(![X1761:$i]:((?[X1762:$i]:((in @ X1762 @ X1761))=>?[X1763:$i]:(((in @ X1763 @ X1761)&~(?[X1764:$i]:(((in @ X1764 @ X1763)&(in @ X1764 @ X1761))))))))=>((epred1_0)=>(![X928:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X928 @ Z0))))=>(X928 @ (descr @ (^[Z0/* 3 */:$i]:((X928 @ Z0)))))))=>(![X929:$i, X930:$i > $o, X931:$i]:(((in @ X931 @ X929)=>((X930 @ X931)=>(in @ X931 @ (dsetconstr @ X929 @ (^[Z0/* 3 */:$i]:((X930 @ Z0))))))))=>(![X1739:$i, X1740:$i > $o, X1741:$i]:(((in @ X1741 @ (dsetconstr @ X1739 @ (^[Z0/* 3 */:$i]:((X1740 @ Z0)))))=>(in @ X1741 @ X1739)))=>(![X932:$i, X933:$i > $o, X934:$i]:(((in @ X934 @ (dsetconstr @ X932 @ (^[Z0/* 3 */:$i]:((X933 @ Z0)))))=>(X933 @ X934)))=>(![X1736:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1736 @ Z0))))=>?[X1737:$i]:(((X1736 @ X1737)&![X1738:$i]:(((X1736 @ X1738)=>((X1737)=(X1738))))))))=>(![X935:$o, X936:$i]:(((in @ X936 @ (prop2set @ ((X935))))=>(X935)))=>(![X937:$i]:(((in @ X937 @ emptyset)=>![X938:$o]:((X938))))=>(![X939:$i]:(~(in @ X939 @ emptyset))=>(![X1735:$i]:(~(in @ X1735 @ emptyset))=>(![X940:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X940 @ Z0))))=>?[X941:$i]:((X940 @ X941))))=>(![X1731:$i, X1732:$i]:((![X1733:$i]:(((in @ X1733 @ X1731)=>(in @ X1733 @ X1732)))=>(![X1734:$i]:(((in @ X1734 @ X1732)=>(in @ X1734 @ X1731)))=>((X1731)=(X1732)))))=>(![X1729:$i]:((![X1730:$i]:(~(in @ X1730 @ X1729))=>((X1729)=(emptyset))))=>(![X1727:$i]:((![X1728:$i]:(~(in @ X1728 @ X1727))=>((X1727)=(emptyset))))=>(![X1724:$i, X1725:$i > $o, X1726:$i]:(((in @ X1726 @ X1724)=>((in @ X1726 @ (dsetconstr @ X1724 @ (^[Z0/* 3 */:$i]:((X1725 @ Z0)))))<=>(X1725 @ X1726))))=>(![X942:$i]:(((nonempty @ X942)=>?[X943:$i]:((in @ X943 @ X942))))=>(![X944:$i, X945:$i > $o, X946:$i]:(((in @ X946 @ X944)=>((X945 @ X946)=>(nonempty @ (dsetconstr @ X944 @ (^[Z0/* 3 */:$i]:((X945 @ Z0))))))))=>(![X1722:$i]:((?[X1723:$i]:((in @ X1723 @ X1722))=>(nonempty @ X1722)))=>(![X947:$i, X948:$i]:((in @ X947 @ (setadjoin @ X947 @ X948)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1719:$i, X1720:$i, X1721:$i]:(((in @ X1721 @ X1720)=>(in @ X1721 @ (setadjoin @ X1719 @ X1720))))=>(![X1715:$i, X1716:$i, X1717:$i]:(((in @ X1717 @ (setadjoin @ X1715 @ X1716))=>![X1718:$o]:(((((X1717)=(X1715))=>(X1718))=>(((in @ X1717 @ X1716)=>(X1718))=>(X1718))))))=>(![X949:$i, X950:$i, X951:$i]:(((in @ X951 @ (setadjoin @ X949 @ X950))=>(((X951)=(X949))|(in @ X951 @ X950))))=>(![X1714:$i]:(((dsetconstr @ X1714 @ (^[Z0/* 3 */:$i]:(($true))))=(X1714)))=>(![X952:$i, X953:$i]:((![X954:$i]:(((in @ X954 @ X953)=>(in @ X954 @ X952)))=>(in @ X953 @ (powerset @ X952))))=>(![X955:$i]:((in @ emptyset @ (powerset @ X955)))=>(![X1713:$i]:((in @ emptyset @ (powerset @ X1713)))=>(![X956:$i, X957:$i, X958:$i]:(((in @ X957 @ (powerset @ X956))=>((in @ X958 @ X957)=>(in @ X958 @ X956))))=>(![X1710:$i, X1711:$i, X1712:$i]:(((in @ X1711 @ X1712)=>((in @ X1712 @ X1710)=>(in @ X1711 @ (setunion @ X1710)))))=>(![X1706:$i, X1707:$i]:(((in @ X1707 @ (setunion @ X1706))=>![X1708:$o]:((![X1709:$i]:(((in @ X1707 @ X1709)=>((in @ X1709 @ X1706)=>(X1708))))=>(X1708)))))=>(![X1704:$i, X1705:$i]:(((in @ X1705 @ X1704)=>(in @ X1705 @ (powerset @ (setunion @ X1704)))))=>(![X959:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X959 @ Z0))))=>?[X960:$i]:(![X961:$i]:(((X959 @ X961)<=>((X961)=(X960)))))))=>(![X962:$i]:(((nonempty @ X962)=>?[X963:$i]:((in @ X963 @ X962))))=>(![X964:$i, X965:$i]:(((in @ X964 @ (setadjoin @ X965 @ emptyset))=>((X964)=(X965))))=>(![X1702:$i, X1703:$i]:((((X1702)!=(X1703))=>~(in @ X1703 @ (setadjoin @ X1702 @ emptyset))))=>(![X966:$i, X967:$i]:((((X966)=(X967))=>(in @ X966 @ (setadjoin @ X967 @ emptyset))))=>(![X1700:$i, X1701:$i]:(((in @ X1700 @ (setadjoin @ X1701 @ emptyset))=>(in @ X1701 @ (setadjoin @ X1700 @ emptyset))))=>(![X1697:$i, X1698:$i, X1699:$i]:(((in @ X1699 @ (setadjoin @ X1697 @ (setadjoin @ X1698 @ emptyset)))=>(((X1699)=(X1697))|((X1699)=(X1698)))))=>(![X968:$i, X969:$i]:((in @ X968 @ (setadjoin @ X968 @ (setadjoin @ X969 @ emptyset))))=>(![X1695:$i, X1696:$i]:((in @ X1696 @ (setadjoin @ X1695 @ (setadjoin @ X1696 @ emptyset))))=>(![X1692:$i, X1693:$i > $o]:((?[X1694:$i]:(((in @ X1694 @ X1692)&(X1693 @ X1694)))=>((dsetconstr @ X1692 @ (^[Z0/* 3 */:$i]:((X1693 @ Z0))))!=(emptyset))))=>(![X1690:$i > $o, X1691:$i]:(((in @ X1691 @ emptyset)=>(X1690 @ X1691)))=>(![X1686:$i, X1687:$i > $o]:((~(![X1688:$i]:(((in @ X1688 @ X1686)=>(X1687 @ X1688))))=>?[X1689:$i]:(((in @ X1689 @ X1686)&~(X1687 @ X1689)))))=>(![X1682:$i, X1683:$i > $o]:((![X1684:$i]:(((in @ X1684 @ X1682)=>~(X1683 @ X1684)))=>~(?[X1685:$i]:(((in @ X1685 @ X1682)&(X1683 @ X1685))))))=>(![X970:$i, X971:$i > $o]:((~(?[X972:$i]:(((in @ X972 @ X970)&(X971 @ X972))))=>![X973:$i]:(((in @ X973 @ X970)=>~(X971 @ X973)))))=>(![X974:$i, X975:$i > $o]:((?[X976:$i]:(((in @ X976 @ X974)&~(X975 @ X976)))=>~(![X977:$i]:(((in @ X977 @ X974)=>(X975 @ X977))))))=>(![X978:$o]:(((X978)=>(in @ emptyset @ (prop2set @ ((X978))))))=>((prop2set2propI)=>(![X979:$i, X980:$i > $o]:((~(?[X981:$i]:(((in @ X981 @ X979)&(X980 @ X981))))=>![X982:$i]:(((in @ X982 @ X979)=>~(X980 @ X982)))))=>(![X983:$i, X984:$i > $o]:((~(![X985:$i]:(((in @ X985 @ X983)=>(X984 @ X985))))=>?[X986:$i]:(((in @ X986 @ X983)&~(X984 @ X986)))))=>(![X987:$i > $o]:((?[X988:$i]:(((X987 @ X988)&![X989:$i]:(((X987 @ X989)=>((X988)=(X989))))))=>(exu @ (^[Z0/* 3 */:$i]:((X987 @ Z0))))))=>(![X1678:$i > $o]:((?[X1679:$i]:((X1678 @ X1679))=>(![X1680:$i, X1681:$i]:(((X1678 @ X1680)=>((X1678 @ X1681)=>((X1680)=(X1681)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1678 @ Z0)))))))=>(![X1675:$i > $o]:((?[X1676:$i]:(![X1677:$i]:(((X1675 @ X1677)<=>((X1677)=(X1676)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1675 @ Z0))))))=>(![X990:$i, X991:$i]:((((X990)=(X991))=>![X992:$i, X993:$i]:((((X992)=(X993))=>((in @ X992 @ X990)=>(in @ X993 @ X991))))))=>(![X994:$i, X995:$i]:((((X994)=(X995))=>![X996:$i, X997:$i]:((((X996)=(X997))=>((in @ X996 @ X994)<=>(in @ X997 @ X995))))))=>(![X998:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X998 @ Z0))))=>![X999:$i, X1000:$i]:(((X998 @ X999)=>((X998 @ X1000)=>((X999)=(X1000)))))))=>(![X1671:$i > $o, X1672:$i > $o]:((![X1673:$i, X1674:$i]:((((X1673)=(X1674))=>((X1671 @ X1673)<=>(X1672 @ X1674))))=>((exu @ (^[Z0/* 3 */:$i]:((X1671 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X1672 @ Z0)))))))=>(((emptyset)=(emptyset))=>(![X1667:$i, X1668:$i]:((((X1667)=(X1668))=>![X1669:$i, X1670:$i]:((((X1669)=(X1670))=>((setadjoin @ X1667 @ X1669)=(setadjoin @ X1668 @ X1670))))))=>(![X1665:$i, X1666:$i]:((((X1665)=(X1666))=>((powerset @ X1665)=(powerset @ X1666))))=>(![X1663:$i, X1664:$i]:((((X1663)=(X1664))=>((setunion @ X1663)=(setunion @ X1664))))=>(((omega)=(omega))=>(![X1660:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1660 @ Z0))))=>![X1661:$i, X1662:$i]:(((X1660 @ X1661)=>((X1660 @ X1662)=>((X1661)=(X1662)))))))=>(![X1001:$i > $o, X1002:$i > $o]:((![X1003:$i, X1004:$i]:((((X1003)=(X1004))=>((X1001 @ X1003)<=>(X1002 @ X1004))))=>((exu @ (^[Z0/* 3 */:$i]:((X1001 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X1002 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1001 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X1002 @ Z0)))))))))=>(![X1654:$i, X1655:$i]:((((X1654)=(X1655))=>![X1656:$i > $o, X1657:$i > $o]:((![X1658:$i]:(((in @ X1658 @ X1654)=>![X1659:$i]:(((in @ X1659 @ X1655)=>(((X1658)=(X1659))=>((X1656 @ X1658)<=>(X1657 @ X1659)))))))=>((dsetconstr @ X1654 @ (^[Z0/* 3 */:$i]:((X1656 @ Z0))))=(dsetconstr @ X1655 @ (^[Z0/* 3 */:$i]:((X1657 @ Z0)))))))))=>(![X1651:$i, X1652:$i]:((![X1653:$i]:(((in @ X1653 @ X1651)=>(in @ X1653 @ X1652)))=>(subset @ X1651 @ X1652)))=>(![X1005:$i, X1006:$i]:((((X1005)=(X1006))=>(subset @ X1006 @ X1005)))=>(![X1649:$i, X1650:$i]:((((X1649)=(X1650))=>(subset @ X1649 @ X1650)))=>(![X1007:$i, X1008:$i]:((![X1009:$i]:(((in @ X1009 @ X1007)=>(in @ X1009 @ X1008)))=>(subset @ X1007 @ X1008)))=>(![X1010:$i]:((subset @ emptyset @ 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kpairp]), notinsingleton]), setextAx]), notequalI2]), kpairiskpair]), notequalI1]), notsubsetI]), eqimpsubset1]), ubforcartprodlem2]), subsetI1]), c_0_272]), ubforcartprodlem3]), c_0_273]), setunion__Cong]), powerset__Cong]), cartprodpairin]), setadjoin__Cong]), emptyset__Cong]), cartprodmempair]), c_0_274]), c_0_275]), c_0_276]), setunionsingleton]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_277]), c_0_278]), upairsetIR]), upairsetE]), c_0_279]), singletonsswitch]), c_0_280]), singletoninpowerset]), subPowSU]), setunionE]), singletonsuniq]), setunionI]), emptyInPowerset]), c_0_281]), c_0_282]), setadjoinE]), setadjoinIR]), setukpairinjL]), emptyinunitempty]), nonemptyI1]), c_0_283]), setukpairinjR11]), noeltsimpempty]), emptyI]), setukpairinjR12]), setext]), notinemptyset]), c_0_284]), setukpairinjR1]), c_0_285]), wellorderingAx]), upairequniteq]), foundationAx]), omegaIndAx]), omegaSAx]), setukpairinjR2]), omega0Ax]), setunionAx]), setukpairinjR]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), binintersectTELcontra]), binintersectTERcontra]), c_0_286]), c_0_287]), c_0_288]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_289]), c_0_290]), singletoninpowunion]), c_0_291]), brelnall1]), brelnall2]), funcGraphProp3]), funcGraphProp2]), funcGraphProp4]), subbreln]), eqbreln]), ap2apEq2]), c_0_292]), upairinpowunion]), c_0_293]), c_0_294]), ifp]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), upairset2IR]), c_0_295]), powersetsubset]), inPowerset]), powersetE1]), powersetI1]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), doubleComplementI1]), doubleComplementSub1]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), binunionTIRcontra]), inIntersectImpInUnion2]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan1]), demorgan2b2]), demorgan2a]), ubforcartprodlem1]), demorgan2a1]), binunionTEcontra]), binunionTE]), intersectInPowersetIntersectUnions]), inIntersectImpInIntersectUnions]), inIntersectImpInUnion]), binunionTILcontra]), complementTcontraSubset]), complementImpComplementIntersect]), complementTnotintersectT]), doubleComplementEq]), doubleComplementSub2]), doubleComplementE1]), contrasubsetT3]), complementTE1]), complementTI1]), powersetTE1]), powersetT_lem]), binunionT_lem]), theeq]), c_0_296]), c_0_297]), c_0_298]), c_0_299]), c_0_300]), c_0_301]), c_0_302]), ap2apEq1]), funcext2]), funcext]), funcextLem]), funcGraphProp1]), c_0_303]), app]), c_0_304]), c_0_305]), c_0_306]), c_0_307]), c_0_308]), cartprodpairsurjEq]), cartprodsndpairEq]), ksndpairEq]), c_0_309]), setukpairinjL2]), cartprodfstin]), kfstpairEq]), theprop]), setukpairinjL1]), c_0_310]), c_0_311]), setunionsingleton2]), setunionsingleton1]), setunionE2]), cartprodmempair1]), upairsubunion]), upairset2E]), singletonsubset]), setukpairIL]), secondinupair]), symdiffIneg2]), symdiffI1]), symdiffE]), setminusSubset1]), setminusLsub]), setminusELneg]), setminusSubset2]), binintersectER]), binintersectSubset3]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binunionLsub]), binunionE]), binunionEcases]), setextsub]), setadjoinSub2]), setadjoinSub]), subsetRefl]), setukpairIR]), symdiffIneg1]), symdiffI2]), setminusIRneg]), setminusILneg]), setminusERneg]), setminusER]), setminusEL]), setminusI]), bs114d]), binintersectSubset1]), binintersectSubset4]), binintersectRsub]), disjointsetsI1]), binintersectSubset2]), binintersectI]), binunionRsub]), binunionIR]), binunionIL]), c_0_312]), subsetemptysetimpeq]), subset2powerset]), subsetTrans]), subsetE2]), subsetE]), emptysetsubset]), subsetI2]), eqimpsubset2]), c_0_313]), omega__Cong]), c_0_314]), in__Cong]), inCongP]), c_0_315]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), upairsetIL]), eqinunit]), uniqinunit]), nonemptyImpWitness]), c_0_316]), powersetE]), emptyinPowerset]), powersetI]), setadjoinOr]), setadjoinIL]), c_0_317]), nonemptyE1]), c_0_318]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_319]), c_0_320]), c_0_321]), c_0_322]), powersetAx]), setadjoinAx]), emptysetAx])])]), c_0_323])).
0.82/1.03	thf(c_0_325, negated_conjecture, ![X1775:$i, X1776:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1788:$i, X1789:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1797:$i, X1798:$i > $i > $o, X1799:$i, X1802:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1809:$i, X1810:$i > $o, X1811:$i, X1812:$i > $o, X1813:$i, X1814:$i, X1815:$i > $o, X1816:$i, X1817:$i, X1818:$i > $o, X1819:$i, X1820:$i > $o, X1822:$i, X1823:$o, X1824:$i, X1825:$i, X1826:$o, X1827:$i, X1828:$i, X1829:$i > $o, X1831:$i, X1832:$i, X1835:$i, X1837:$i, X1839:$i, X1840:$i > $o, X1841:$i, X1842:$i, X1844:$i, X1845:$i > $o, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$o, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$o, X1877:$i, X1878:$i, X1879:$i > $o, X1881:$i, X1882:$i, X1883:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i > $o, X1902:$i, X1903:$i > $o, X1904:$i, X1905:$i, X1906:$i > $o, X1907:$i, X1909:$i, X1910:$i > $o, X1912:$i, X1913:$i, X1914:$i > $o, X1916:$i, X1917:$i, X1918:$i > $o, X1919:$i, X1921:$o, X1922:$i, X1923:$i > $o, X1925:$i, X1926:$i, X1927:$i > $o, X1928:$i, X1930:$i > $o, X1931:$i, X1933:$i > $o, X1934:$i, X1937:$i > $o, X1938:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i > $o, X1949:$i, X1950:$i, X1951:$i > $o, X1952:$i > $o, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i > $o, X1964:$i, X1965:$i, X1966:$i > $o, X1967:$i > $o, X1970:$i, X1971:$i, X1972:$i > $o, X1973:$i > $o, X1976:$i, X1977:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i > $o, X2024:$i, X2025:$i > $o, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$o, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$o, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i > $o, X2180:$i, X2181:$i, X2182:$i > $o, X2184:$i, X2185:$i > $o, X2186:$i, X2188:$i, X2189:$i > $o, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i > $i > $o, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i > $i > $o, X2270:$i, X2271:$i, X2272:$i > $i > $o, X2273:$i, X2274:$i, X2275:$i > $i > $o, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i > $i > $o, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i > $i > $o, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i > $i > $o, X2291:$i, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i > $i, X2319:$i, X2320:$i, X2321:$i > $i, X2323:$i, X2324:$i, X2325:$i > $i, X2327:$i, X2328:$i, X2329:$i, X2330:$i > $o, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i > $o, X2340:$i, X2341:$i, X2342:$i > $o, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i, X2360:$i, X2361:$i, X2363:$i, X2364:$i, X2365:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$i, X2372:$i, X2373:$i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2384:$i, X2385:$i, X2386:$i, X2387:$i, X2389:$i, X2390:$i, X2391:$i, X2392:$i, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$i, X2404:$i > $i, X2406:$i, X2407:$i, X2408:$i, X2409:$i, X2410:$i, X2411:$i, X2412:$i > $i, X2414:$i, X2415:$i, X2416:$i > $i, X2418:$i, X2419:$i, X2420:$i, X2421:$i, X2422:$i, X2423:$o, X2424:$i, X2425:$i, X2426:$i, X2427:$o, X2428:$i, X2429:$i, X2430:$i, X2431:$o, X2432:$i, X2433:$i, X2434:$i, X2435:$o, X2436:$i, X2437:$i, X2438:$i, X2439:$o, X2440:$i, X2441:$i, X2442:$i, X2443:$o, X2444:$i, X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$o, X2450:$i, X2451:$i, X2452:$i, X2453:$o, X2454:$i, X2455:$i, X2456:$i, X2457:$o, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i, X2463:$i, X2464:$i, X2465:$i, X2466:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2471:$i, X2472:$i, X2473:$i, X2474:$i, X2475:$i, X2478:$i, X2479:$i, X2480:$i, X2482:$i, X2483:$i, X2484:$i, X2486:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2493:$i, X2494:$i, X2495:$i, X2496:$i, X2497:$i, X2498:$i, X2499:$i, X2500:$i, X2501:$i, X2502:$i, X2503:$i, X2504:$i, X2505:$i, X2506:$i, X2507:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i, X2546:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i, X2551:$i, X2552:$i, X2553:$i, X2554:$i, X2555:$i, X2556:$i, X2557:$i, X2558:$i, X2559:$i, X2560:$i, X2561:$i, X2562:$i, X2563:$i, X2564:$i, X2565:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2570:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i, X2576:$i, X2577:$i, X2578:$i, X2579:$i, X2580:$i, X2581:$i, X2582:$i, X2583:$i, X2584:$i, X2585:$i, X2586:$i, X2587:$i, X2588:$i, X2589:$o, X2590:$i, X2591:$i, X2592:$i, X2593:$i, X2594:$i, X2595:$i, X2596:$i, X2597:$i, X2598:$i, X2599:$i, X2600:$i, X2601:$i, X2602:$i, X2603:$i, X2604:$i, X2605:$i, X2606:$i, X2607:$i, X2608:$i, X2609:$i, X2610:$i, X2611:$i, X2612:$i, X2613:$i, X2614:$i, X2615:$i, X2616:$i, X2617:$i, X2618:$i, X2619:$i, X2620:$i, X2621:$i, X2622:$i, X2623:$i, X2624:$i]:((((~(in @ (esk1_2 @ X1775 @ X1776) @ X1775)|~(in @ (esk1_2 @ X1775 @ X1776) @ X1776)|((X1775)=(X1776)))&((in @ (esk1_2 @ X1775 @ X1776) @ X1775)|(in @ (esk1_2 @ X1775 @ X1776) @ X1776)|((X1775)=(X1776))))&(~(in @ X1778 @ emptyset)&(((~(in @ X1781 @ (setadjoin @ X1779 @ X1780))|(((X1781)=(X1779))|(in @ X1781 @ X1780)))&((((X1781)!=(X1779))|(in @ X1781 @ (setadjoin @ X1779 @ X1780)))&(~(in @ X1781 @ X1780)|(in @ X1781 @ (setadjoin @ X1779 @ X1780)))))&(((~(in @ X1783 @ (powerset @ X1782))|(~(in @ X1784 @ X1783)|(in @ X1784 @ X1782)))&(((in @ (esk2_2 @ X1785 @ X1786) @ X1786)|(in @ X1786 @ (powerset @ X1785)))&(~(in @ (esk2_2 @ X1785 @ X1786) @ X1785)|(in @ X1786 @ (powerset @ X1785)))))&(((((in @ X1789 @ (esk3_2 @ X1788 @ X1789))|~(in @ X1789 @ (setunion @ X1788)))&((in @ (esk3_2 @ X1788 @ X1789) @ X1788)|~(in @ X1789 @ (setunion @ X1788))))&(~(in @ X1792 @ X1793)|~(in @ X1793 @ X1791)|(in @ X1792 @ (setunion @ X1791))))&((in @ emptyset @ omega)&((~(in @ X1794 @ omega)|(in @ (setadjoin @ X1794 @ X1794) @ omega))&(((((in @ (esk4_1 @ X1795) @ omega)|~(in @ emptyset @ X1795)|(~(in @ X1797 @ omega)|(in @ X1797 @ X1795)))&((in @ (esk4_1 @ X1795) @ X1795)|~(in @ emptyset @ X1795)|(~(in @ X1797 @ omega)|(in @ X1797 @ X1795))))&(~(in @ (setadjoin @ (esk4_1 @ X1795) @ (esk4_1 @ X1795)) @ X1795)|~(in @ emptyset @ X1795)|(~(in @ X1797 @ omega)|(in @ X1797 @ X1795))))&((((((in @ (esk7_3 @ X1798 @ X1799 @ X1802) @ X1799)|~(in @ X1802 @ (esk6_2 @ X1798 @ X1799))|(in @ (esk5_2 @ X1798 @ X1799) @ X1799))&((X1798 @ (esk7_3 @ X1798 @ X1799 @ X1802) @ X1802)|~(in @ X1802 @ (esk6_2 @ X1798 @ X1799))|(in @ (esk5_2 @ X1798 @ X1799) @ X1799)))&(~(in @ X1805 @ X1799)|~(X1798 @ X1805 @ X1804)|(in @ X1804 @ (esk6_2 @ X1798 @ X1799))|(in @ (esk5_2 @ X1798 @ X1799) @ X1799)))&((((in @ (esk7_3 @ X1798 @ X1799 @ X1802) @ X1799)|~(in @ X1802 @ (esk6_2 @ X1798 @ X1799))|~(exu @ (^[Z0/* 3 */:$i]:((X1798 @ (esk5_2 @ X1798 @ X1799) @ Z0)))))&((X1798 @ (esk7_3 @ X1798 @ X1799 @ X1802) @ X1802)|~(in @ X1802 @ (esk6_2 @ X1798 @ X1799))|~(exu @ (^[Z0/* 3 */:$i]:((X1798 @ (esk5_2 @ X1798 @ X1799) @ Z0))))))&(~(in @ X1805 @ X1799)|~(X1798 @ X1805 @ X1804)|(in @ X1804 @ (esk6_2 @ X1798 @ X1799))|~(exu @ (^[Z0/* 3 */:$i]:((X1798 @ (esk5_2 @ X1798 @ X1799) @ Z0)))))))&((((in @ (esk8_1 @ X1806) @ X1806)|~(in @ X1807 @ X1806))&(~(in @ X1809 @ (esk8_1 @ X1806))|~(in @ X1809 @ X1806)|~(in @ X1807 @ X1806)))&((epred1_0)&((~(exu @ (^[Z0/* 3 */:$i]:((X1810 @ Z0))))|(X1810 @ (descr @ (^[Z0/* 3 */:$i]:((X1810 @ Z0))))))&((~(in @ X1813 @ X1811)|(~(X1812 @ X1813)|(in @ X1813 @ (dsetconstr @ X1811 @ (^[Z0/* 3 */:$i]:((X1812 @ Z0)))))))&((~(in @ X1816 @ (dsetconstr @ X1814 @ (^[Z0/* 3 */:$i]:((X1815 @ Z0)))))|(in @ X1816 @ X1814))&((~(in @ X1819 @ (dsetconstr @ X1817 @ (^[Z0/* 3 */:$i]:((X1818 @ Z0)))))|(X1818 @ X1819))&((((X1820 @ (esk9_1 @ X1820))|~(exu @ (^[Z0/* 3 */:$i]:((X1820 @ Z0)))))&(~(X1820 @ X1822)|((esk9_1 @ X1820)=(X1822))|~(exu @ (^[Z0/* 3 */:$i]:((X1820 @ Z0))))))&((~(in @ X1824 @ (prop2set @ ((X1823))))|(X1823))&((~(in @ X1825 @ emptyset)|(X1826))&(~(in @ X1827 @ emptyset)&(~(in @ X1828 @ emptyset)&((~(exu @ (^[Z0/* 3 */:$i]:((X1829 @ Z0))))|(X1829 @ (esk10_1 @ X1829)))&(((((in @ (esk12_2 @ X1831 @ X1832) @ X1832)|((X1831)=(X1832))|(in @ (esk11_2 @ X1831 @ X1832) @ X1831))&(~(in @ (esk12_2 @ X1831 @ X1832) @ X1831)|((X1831)=(X1832))|(in @ (esk11_2 @ X1831 @ X1832) @ X1831)))&(((in @ (esk12_2 @ X1831 @ X1832) @ X1832)|((X1831)=(X1832))|~(in @ (esk11_2 @ X1831 @ X1832) @ X1832))&(~(in @ (esk12_2 @ X1831 @ X1832) @ X1831)|((X1831)=(X1832))|~(in @ (esk11_2 @ X1831 @ X1832) @ X1832))))&(((in @ (esk13_1 @ X1835) @ X1835)|((X1835)=(emptyset)))&(((in @ (esk14_1 @ X1837) @ X1837)|((X1837)=(emptyset)))&(((~(in @ X1841 @ (dsetconstr @ X1839 @ (^[Z0/* 3 */:$i]:((X1840 @ Z0)))))|(X1840 @ X1841)|~(in @ X1841 @ 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X2588)|(X2589)|~(X2589)|~(in @ X2590 @ (binunion @ X2587 @ X2588))|~(in @ X2590 @ X2586)|~(in @ X2588 @ (powerset @ X2586))|~(in @ X2587 @ (powerset @ X2586)))&(~(X2589)|(X2589)|~(X2589)|~(in @ X2590 @ (binunion @ X2587 @ X2588))|~(in @ X2590 @ X2586)|~(in @ X2588 @ (powerset @ X2586))|~(in @ X2587 @ (powerset @ X2586)))))&((~(in @ X2592 @ (powerset @ X2591))|(~(in @ X2593 @ (powerset @ X2591))|(~(in @ X2594 @ X2591)|((in @ X2594 @ X2592)|((in @ X2594 @ X2593)|~(in @ X2594 @ (binunion @ X2592 @ X2593)))))))&((~(in @ X2596 @ (powerset @ X2595))|(~(in @ X2597 @ (powerset @ X2595))|(~(in @ X2598 @ X2595)|(~(in @ X2598 @ (setminus @ X2595 @ (binunion @ X2596 @ X2597)))|(in @ X2598 @ (setminus @ X2595 @ X2596))))))&((~(in @ X2600 @ (powerset @ X2599))|(~(in @ X2601 @ (powerset @ X2599))|(in @ (setminus @ X2599 @ (binunion @ X2600 @ X2601)) @ (powerset @ (setminus @ X2599 @ X2600)))))&((~(in @ X2603 @ (powerset @ X2602))|(~(in @ X2604 @ (powerset @ X2602))|(~(in @ X2605 @ X2602)|(~(in @ X2605 @ (setminus @ X2602 @ (binunion @ X2603 @ X2604)))|(in @ X2605 @ (setminus @ X2602 @ X2604))))))&((~(in @ X2607 @ (powerset @ X2606))|(~(in @ X2608 @ (powerset @ X2606))|(~(in @ X2609 @ X2606)|(~(in @ X2609 @ (setminus @ X2606 @ (binintersect @ X2607 @ X2608)))|(in @ X2609 @ (binunion @ (setminus @ X2606 @ X2607) @ (setminus @ X2606 @ X2608)))))))&((~(in @ X2611 @ (powerset @ X2610))|(~(in @ X2612 @ (powerset @ X2610))|(~(in @ X2613 @ X2610)|(~(in @ X2613 @ (binunion @ (setminus @ X2610 @ X2611) @ (setminus @ X2610 @ X2612)))|(in @ X2613 @ (setminus @ X2610 @ (binintersect @ X2611 @ X2612)))))))&((~(in @ X2615 @ (powerset @ X2614))|(~(in @ X2616 @ (powerset @ X2614))|((setminus @ X2614 @ (binintersect @ X2615 @ X2616))=(binunion @ (setminus @ X2614 @ X2615) @ (setminus @ X2614 @ X2616)))))&((~(in @ X2618 @ (powerset @ X2617))|(~(in @ X2619 @ (powerset @ X2617))|(~(in @ X2620 @ X2617)|(~(in @ X2620 @ (setminus @ X2617 @ (binunion @ X2618 @ X2619)))|(in @ X2620 @ (binintersect @ (setminus @ X2617 @ X2618) @ (setminus @ X2617 @ X2619)))))))&((~(in @ X2622 @ (powerset @ X2621))|(~(in @ X2623 @ (powerset @ X2621))|(~(in @ X2624 @ X2621)|(~(in @ X2624 @ (setminus @ X2621 @ X2622))|(~(in @ X2624 @ (setminus @ X2621 @ X2623))|(in @ X2624 @ (setminus @ X2621 @ (binunion @ X2622 @ X2623))))))))&((in @ esk72_0 @ (powerset @ esk71_0))&((in @ esk73_0 @ (powerset @ esk71_0))&((in @ esk74_0 @ esk71_0)&((in @ esk74_0 @ (binintersect @ (setminus @ esk71_0 @ esk72_0) @ (setminus @ esk71_0 @ esk73_0)))&~(in @ esk74_0 @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[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_324])])])])])])).
0.82/1.03	thf(c_0_326, negated_conjecture, ![X2:$i, X3:$i, X5:$i, X4:$i]:(((in @ X5 @ (setminus @ X3 @ (binunion @ X2 @ X4)))|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3)))|~((in @ X5 @ X3))|~((in @ X5 @ (setminus @ X3 @ X2)))|~((in @ X5 @ (setminus @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_325])).
0.82/1.03	thf(c_0_327, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X3)|~((in @ X2 @ (setminus @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_325])).
0.82/1.03	thf(c_0_328, negated_conjecture, ~((in @ esk74_0 @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0)))), inference(split_conjunct,[status(thm)],[c_0_325])).
0.82/1.03	thf(c_0_329, negated_conjecture, ![X2:$i, X5:$i, X4:$i, X3:$i]:(((in @ X2 @ (setminus @ X3 @ (binunion @ X4 @ X5)))|~((in @ X2 @ (setminus @ X3 @ X5)))|~((in @ X2 @ (setminus @ X3 @ X4)))|~((in @ X5 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3))))), inference(csr,[status(thm)],[c_0_326, c_0_327])).
0.82/1.03	thf(c_0_330, negated_conjecture, (in @ esk73_0 @ (powerset @ esk71_0)), inference(split_conjunct,[status(thm)],[c_0_325])).
0.82/1.03	thf(c_0_331, negated_conjecture, (in @ esk72_0 @ (powerset @ esk71_0)), inference(split_conjunct,[status(thm)],[c_0_325])).
0.82/1.03	thf(c_0_332, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X4)|~((in @ X2 @ (binintersect @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_325])).
0.82/1.03	thf(c_0_333, negated_conjecture, (in @ esk74_0 @ (binintersect @ (setminus @ esk71_0 @ esk72_0) @ (setminus @ esk71_0 @ esk73_0))), inference(split_conjunct,[status(thm)],[c_0_325])).
0.82/1.03	thf(c_0_334, negated_conjecture, (~((in @ esk74_0 @ (setminus @ esk71_0 @ esk73_0)))|~((in @ esk74_0 @ (setminus @ esk71_0 @ esk72_0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_328, c_0_329]), c_0_330]), c_0_331])])).
0.82/1.03	thf(c_0_335, negated_conjecture, (in @ esk74_0 @ (setminus @ esk71_0 @ esk73_0)), inference(spm,[status(thm)],[c_0_332, c_0_333])).
0.82/1.03	thf(c_0_336, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X3)|~((in @ X2 @ (binintersect @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_325])).
0.82/1.03	thf(c_0_337, negated_conjecture, ~((in @ esk74_0 @ (setminus @ esk71_0 @ esk72_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_334, c_0_335])])).
0.82/1.03	thf(c_0_338, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_336, c_0_333]), c_0_337]), ['proof']).
0.82/1.03	# SZS output end CNFRefutation
0.82/1.03	# Parsed axioms                        : 587
0.82/1.03	# Removed by relevancy pruning/SinE    : 315
0.82/1.03	# Initial clauses                      : 431
0.82/1.03	# Removed in clause preprocessing      : 32
0.82/1.03	# Initial clauses in saturation        : 399
0.82/1.03	# Processed clauses                    : 890
0.82/1.03	# ...of these trivial                  : 13
0.82/1.03	# ...subsumed                          : 73
0.82/1.03	# ...remaining for further processing  : 803
0.82/1.03	# Other redundant clauses eliminated   : 54
0.82/1.03	# Clauses deleted for lack of memory   : 0
0.82/1.03	# Backward-subsumed                    : 1
0.82/1.03	# Backward-rewritten                   : 8
0.82/1.03	# Generated clauses                    : 9872
0.82/1.03	# ...of the previous two non-redundant : 9611
0.82/1.03	# ...aggressively subsumed             : 0
0.82/1.03	# Contextual simplify-reflections      : 11
0.82/1.03	# Paramodulations                      : 9782
0.82/1.03	# Factorizations                       : 2
0.82/1.03	# NegExts                              : 0
0.82/1.03	# Equation resolutions                 : 61
0.82/1.03	# Total rewrite steps                  : 233
0.82/1.03	# Propositional unsat checks           : 0
0.82/1.03	#    Propositional check models        : 0
0.82/1.03	#    Propositional check unsatisfiable : 0
0.82/1.03	#    Propositional clauses             : 0
0.82/1.03	#    Propositional clauses after purity: 0
0.82/1.03	#    Propositional unsat core size     : 0
0.82/1.03	#    Propositional preprocessing time  : 0.000
0.82/1.03	#    Propositional encoding time       : 0.000
0.82/1.03	#    Propositional solver time         : 0.000
0.82/1.03	#    Success case prop preproc time    : 0.000
0.82/1.03	#    Success case prop encoding time   : 0.000
0.82/1.03	#    Success case prop solver time     : 0.000
0.82/1.03	# Current number of processed clauses  : 429
0.82/1.03	#    Positive orientable unit clauses  : 54
0.82/1.03	#    Positive unorientable unit clauses: 0
0.82/1.03	#    Negative unit clauses             : 15
0.82/1.03	#    Non-unit-clauses                  : 360
0.82/1.03	# Current number of unprocessed clauses: 9450
0.82/1.03	# ...number of literals in the above   : 39519
0.82/1.03	# Current number of archived formulas  : 0
0.82/1.03	# Current number of archived clauses   : 358
0.82/1.03	# Clause-clause subsumption calls (NU) : 76692
0.82/1.03	# Rec. Clause-clause subsumption calls : 31723
0.82/1.03	# Non-unit clause-clause subsumptions  : 68
0.82/1.03	# Unit Clause-clause subsumption calls : 2179
0.82/1.03	# Rewrite failures with RHS unbound    : 0
0.82/1.03	# BW rewrite match attempts            : 36
0.82/1.03	# BW rewrite match successes           : 6
0.82/1.03	# Condensation attempts                : 0
0.82/1.03	# Condensation successes               : 0
0.82/1.03	# Termbank termtop insertions          : 247026
0.82/1.03	
0.82/1.03	# -------------------------------------------------
0.82/1.03	# User time                : 0.488 s
0.82/1.03	# System time              : 0.023 s
0.82/1.03	# Total time               : 0.511 s
0.82/1.03	# Maximum resident set size: 8596 pages
0.82/1.06	
0.82/1.06	# -------------------------------------------------
0.82/1.06	# User time                : 0.504 s
0.82/1.06	# System time              : 0.026 s
0.82/1.06	# Total time               : 0.530 s
0.82/1.06	# Maximum resident set size: 2748 pages
0.82/1.06	% E---3.1 exiting
0.82/1.07	EOF