0.04/0.10	% Problem    : Vampire---4.8_3435 : TPTP v0.0.0. Released v0.0.0.
0.04/0.11	% Command    : run_E %s %d THM
0.11/0.29	% Computer : n007.cluster.edu
0.11/0.29	% Model    : x86_64 x86_64
0.11/0.29	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.29	% Memory   : 8042.1875MB
0.11/0.29	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.29	% CPULimit   : 1440
0.11/0.29	% WCLimit    : 180
0.11/0.29	% DateTime   : Mon Jul  3 12:58:28 EDT 2023
0.11/0.29	% CPUTime    : 
0.15/0.40	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.g9DFcvTYTG/Vampire---4.8_3435
0.15/0.40	# Version: 3.1pre001-ho
2.01/0.65	# Preprocessing class: HSLMSLSSLLLCHFA.
2.01/0.65	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
2.01/0.65	# Starting ehoh_best5 with 180s (1) cores
2.01/0.65	# Starting almost_fo_3_lam with 180s (1) cores
2.01/0.65	# Starting new_bool_5 with 180s (1) cores
2.01/0.65	# Starting pre_casc_3 with 180s (1) cores
2.01/0.65	# Starting ho_unfolding_8 with 180s (1) cores
2.01/0.65	# Starting new_ho_10_cnf2 with 180s (1) cores
2.01/0.65	# Starting new_bool_3 with 180s (1) cores
2.01/0.65	# Starting new_ho_5 with 180s (1) cores
2.01/0.65	# new_bool_3 with pid 3619 completed with status 0
2.01/0.65	# Result found by new_bool_3
2.01/0.65	# Preprocessing class: HSLMSLSSLLLCHFA.
2.01/0.65	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
2.01/0.65	# Starting ehoh_best5 with 180s (1) cores
2.01/0.65	# Starting almost_fo_3_lam with 180s (1) cores
2.01/0.65	# Starting new_bool_5 with 180s (1) cores
2.01/0.65	# Starting pre_casc_3 with 180s (1) cores
2.01/0.65	# Starting ho_unfolding_8 with 180s (1) cores
2.01/0.65	# Starting new_ho_10_cnf2 with 180s (1) cores
2.01/0.65	# Starting new_bool_3 with 180s (1) cores
2.01/0.65	# SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
2.01/0.65	# Search class: HGHSM-FSLM32-MHFMMSBN
2.01/0.65	# Scheduled 9 strats onto 1 cores with 180 seconds (180 total)
2.01/0.65	# Starting ho_unfolding_8 with 37s (1) cores
2.01/0.65	# ho_unfolding_8 with pid 3623 completed with status 0
2.01/0.65	# Result found by ho_unfolding_8
2.01/0.65	# Preprocessing class: HSLMSLSSLLLCHFA.
2.01/0.65	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
2.01/0.65	# Starting ehoh_best5 with 180s (1) cores
2.01/0.65	# Starting almost_fo_3_lam with 180s (1) cores
2.01/0.65	# Starting new_bool_5 with 180s (1) cores
2.01/0.65	# Starting pre_casc_3 with 180s (1) cores
2.01/0.65	# Starting ho_unfolding_8 with 180s (1) cores
2.01/0.65	# Starting new_ho_10_cnf2 with 180s (1) cores
2.01/0.65	# Starting new_bool_3 with 180s (1) cores
2.01/0.65	# SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
2.01/0.65	# Search class: HGHSM-FSLM32-MHFMMSBN
2.01/0.65	# Scheduled 9 strats onto 1 cores with 180 seconds (180 total)
2.01/0.65	# Starting ho_unfolding_8 with 37s (1) cores
2.01/0.65	# Preprocessing time       : 0.108 s
2.01/0.65	# Presaturation interreduction done
2.01/0.65	
2.01/0.65	# Proof found!
2.01/0.65	# SZS status Theorem
2.01/0.65	# SZS output start CNFRefutation
2.01/0.65	thf(decl_22, type, in: $i > $i > $o).
2.01/0.65	thf(decl_23, type, exu: ($i > $o) > $o).
2.01/0.65	thf(decl_24, type, setextAx: $o).
2.01/0.65	thf(decl_25, type, emptyset: $i).
2.01/0.65	thf(decl_26, type, emptysetAx: $o).
2.01/0.65	thf(decl_27, type, setadjoin: $i > $i > $i).
2.01/0.65	thf(decl_28, type, setadjoinAx: $o).
2.01/0.65	thf(decl_29, type, powerset: $i > $i).
2.01/0.65	thf(decl_30, type, powersetAx: $o).
2.01/0.65	thf(decl_31, type, setunion: $i > $i).
2.01/0.65	thf(decl_32, type, setunionAx: $o).
2.01/0.65	thf(decl_33, type, omega: $i).
2.01/0.65	thf(decl_34, type, omega0Ax: $o).
2.01/0.65	thf(decl_35, type, omegaSAx: $o).
2.01/0.65	thf(decl_36, type, omegaIndAx: $o).
2.01/0.65	thf(decl_37, type, replAx: $o).
2.01/0.65	thf(decl_38, type, foundationAx: $o).
2.01/0.65	thf(decl_39, type, wellorderingAx: $o).
2.01/0.65	thf(decl_40, type, descr: ($i > $o) > $i).
2.01/0.65	thf(decl_41, type, descrp: $o).
2.01/0.65	thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
2.01/0.65	thf(decl_43, type, dsetconstrI: $o).
2.01/0.65	thf(decl_44, type, dsetconstrEL: $o).
2.01/0.65	thf(decl_45, type, dsetconstrER: $o).
2.01/0.65	thf(decl_46, type, exuE1: $o).
2.01/0.65	thf(decl_47, type, prop2set: $o > $i).
2.01/0.65	thf(decl_48, type, prop2setE: $o).
2.01/0.65	thf(decl_49, type, emptysetE: $o).
2.01/0.65	thf(decl_50, type, emptysetimpfalse: $o).
2.01/0.65	thf(decl_51, type, notinemptyset: $o).
2.01/0.65	thf(decl_52, type, exuE3e: $o).
2.01/0.65	thf(decl_53, type, setext: $o).
2.01/0.65	thf(decl_54, type, emptyI: $o).
2.01/0.65	thf(decl_55, type, noeltsimpempty: $o).
2.01/0.65	thf(decl_56, type, setbeta: $o).
2.01/0.65	thf(decl_57, type, nonempty: $i > $o).
2.01/0.65	thf(decl_58, type, nonemptyE1: $o).
2.01/0.65	thf(decl_59, type, nonemptyI: $o).
2.01/0.65	thf(decl_60, type, nonemptyI1: $o).
2.01/0.65	thf(decl_61, type, setadjoinIL: $o).
2.01/0.65	thf(decl_62, type, emptyinunitempty: $o).
2.01/0.65	thf(decl_63, type, setadjoinIR: $o).
2.01/0.65	thf(decl_64, type, setadjoinE: $o).
2.01/0.65	thf(decl_65, type, setadjoinOr: $o).
2.01/0.65	thf(decl_66, type, setoftrueEq: $o).
2.01/0.65	thf(decl_67, type, powersetI: $o).
2.01/0.65	thf(decl_68, type, emptyinPowerset: $o).
2.01/0.65	thf(decl_69, type, emptyInPowerset: $o).
2.01/0.65	thf(decl_70, type, powersetE: $o).
2.01/0.65	thf(decl_71, type, setunionI: $o).
2.01/0.65	thf(decl_72, type, setunionE: $o).
2.01/0.65	thf(decl_73, type, subPowSU: $o).
2.01/0.65	thf(decl_74, type, exuE2: $o).
2.01/0.65	thf(decl_75, type, nonemptyImpWitness: $o).
2.01/0.65	thf(decl_76, type, uniqinunit: $o).
2.01/0.65	thf(decl_77, type, notinsingleton: $o).
2.01/0.65	thf(decl_78, type, eqinunit: $o).
2.01/0.65	thf(decl_79, type, singletonsswitch: $o).
2.01/0.65	thf(decl_80, type, upairsetE: $o).
2.01/0.65	thf(decl_81, type, upairsetIL: $o).
2.01/0.65	thf(decl_82, type, upairsetIR: $o).
2.01/0.65	thf(decl_83, type, emptyE1: $o).
2.01/0.65	thf(decl_84, type, vacuousDall: $o).
2.01/0.65	thf(decl_85, type, quantDeMorgan1: $o).
2.01/0.65	thf(decl_86, type, quantDeMorgan2: $o).
2.01/0.65	thf(decl_87, type, quantDeMorgan3: $o).
2.01/0.65	thf(decl_88, type, quantDeMorgan4: $o).
2.01/0.65	thf(decl_89, type, prop2setI: $o).
2.01/0.65	thf(decl_91, type, prop2set2propI: $o).
2.01/0.65	thf(decl_92, type, notdexE: $o).
2.01/0.65	thf(decl_93, type, notdallE: $o).
2.01/0.65	thf(decl_94, type, exuI1: $o).
2.01/0.65	thf(decl_95, type, exuI3: $o).
2.01/0.65	thf(decl_96, type, exuI2: $o).
2.01/0.65	thf(decl_97, type, inCongP: $o).
2.01/0.65	thf(decl_98, type, in__Cong: $o).
2.01/0.65	thf(decl_99, type, exuE3u: $o).
2.01/0.65	thf(decl_100, type, exu__Cong: $o).
2.01/0.65	thf(decl_101, type, emptyset__Cong: $o).
2.01/0.65	thf(decl_102, type, setadjoin__Cong: $o).
2.01/0.65	thf(decl_103, type, powerset__Cong: $o).
2.01/0.65	thf(decl_104, type, setunion__Cong: $o).
2.01/0.65	thf(decl_105, type, omega__Cong: $o).
2.01/0.65	thf(decl_106, type, exuEu: $o).
2.01/0.65	thf(decl_107, type, descr__Cong: $o).
2.01/0.65	thf(decl_108, type, dsetconstr__Cong: $o).
2.01/0.65	thf(decl_109, type, subset: $i > $i > $o).
2.01/0.65	thf(decl_112, type, subsetI1: $o).
2.01/0.65	thf(decl_113, type, eqimpsubset2: $o).
2.01/0.65	thf(decl_114, type, eqimpsubset1: $o).
2.01/0.65	thf(decl_115, type, subsetI2: $o).
2.01/0.65	thf(decl_116, type, emptysetsubset: $o).
2.01/0.65	thf(decl_117, type, subsetE: $o).
2.01/0.65	thf(decl_118, type, subsetE2: $o).
2.01/0.65	thf(decl_119, type, notsubsetI: $o).
2.01/0.65	thf(decl_120, type, notequalI1: $o).
2.01/0.65	thf(decl_121, type, notequalI2: $o).
2.01/0.65	thf(decl_122, type, subsetRefl: $o).
2.01/0.65	thf(decl_123, type, subsetTrans: $o).
2.01/0.65	thf(decl_124, type, setadjoinSub: $o).
2.01/0.65	thf(decl_125, type, setadjoinSub2: $o).
2.01/0.65	thf(decl_126, type, subset2powerset: $o).
2.01/0.65	thf(decl_127, type, setextsub: $o).
2.01/0.65	thf(decl_128, type, subsetemptysetimpeq: $o).
2.01/0.65	thf(decl_129, type, powersetI1: $o).
2.01/0.65	thf(decl_130, type, powersetE1: $o).
2.01/0.65	thf(decl_131, type, inPowerset: $o).
2.01/0.65	thf(decl_132, type, powersetsubset: $o).
2.01/0.65	thf(decl_133, type, sepInPowerset: $o).
2.01/0.65	thf(decl_134, type, sepSubset: $o).
2.01/0.65	thf(decl_135, type, binunion: $i > $i > $i).
2.01/0.65	thf(decl_136, type, binunionIL: $o).
2.01/0.65	thf(decl_137, type, upairset2IR: $o).
2.01/0.65	thf(decl_138, type, binunionIR: $o).
2.01/0.65	thf(decl_139, type, binunionEcases: $o).
2.01/0.65	thf(decl_140, type, binunionE: $o).
2.01/0.65	thf(decl_141, type, binunionLsub: $o).
2.01/0.65	thf(decl_142, type, binunionRsub: $o).
2.01/0.65	thf(decl_143, type, binintersect: $i > $i > $i).
2.01/0.65	thf(decl_144, type, binintersectI: $o).
2.01/0.65	thf(decl_145, type, binintersectSubset5: $o).
2.01/0.65	thf(decl_146, type, binintersectEL: $o).
2.01/0.65	thf(decl_147, type, binintersectLsub: $o).
2.01/0.65	thf(decl_148, type, binintersectSubset2: $o).
2.01/0.65	thf(decl_149, type, binintersectSubset3: $o).
2.01/0.65	thf(decl_150, type, binintersectER: $o).
2.01/0.65	thf(decl_151, type, disjointsetsI1: $o).
2.01/0.65	thf(decl_152, type, binintersectRsub: $o).
2.01/0.65	thf(decl_153, type, binintersectSubset4: $o).
2.01/0.65	thf(decl_154, type, binintersectSubset1: $o).
2.01/0.65	thf(decl_155, type, bs114d: $o).
2.01/0.65	thf(decl_157, type, setminus: $i > $i > $i).
2.01/0.65	thf(decl_158, type, setminusI: $o).
2.01/0.65	thf(decl_159, type, setminusEL: $o).
2.01/0.65	thf(decl_160, type, setminusER: $o).
2.01/0.65	thf(decl_161, type, setminusSubset2: $o).
2.01/0.65	thf(decl_162, type, setminusERneg: $o).
2.01/0.65	thf(decl_163, type, setminusELneg: $o).
2.01/0.65	thf(decl_164, type, setminusILneg: $o).
2.01/0.65	thf(decl_165, type, setminusIRneg: $o).
2.01/0.65	thf(decl_166, type, setminusLsub: $o).
2.01/0.65	thf(decl_167, type, setminusSubset1: $o).
2.01/0.65	thf(decl_168, type, symdiff: $i > $i > $i).
2.01/0.65	thf(decl_169, type, symdiffE: $o).
2.01/0.65	thf(decl_170, type, symdiffI1: $o).
2.01/0.65	thf(decl_171, type, symdiffI2: $o).
2.01/0.65	thf(decl_172, type, symdiffIneg1: $o).
2.01/0.65	thf(decl_173, type, symdiffIneg2: $o).
2.01/0.65	thf(decl_174, type, iskpair: $i > $o).
2.01/0.65	thf(decl_175, type, secondinupair: $o).
2.01/0.65	thf(decl_176, type, setukpairIL: $o).
2.01/0.65	thf(decl_177, type, setukpairIR: $o).
2.01/0.65	thf(decl_178, type, kpairiskpair: $o).
2.01/0.65	thf(decl_179, type, kpair: $i > $i > $i).
2.01/0.65	thf(decl_180, type, kpairp: $o).
2.01/0.65	thf(decl_181, type, cartprod: $i > $i > $i).
2.01/0.65	thf(decl_182, type, singletonsubset: $o).
2.01/0.65	thf(decl_183, type, singletoninpowerset: $o).
2.01/0.65	thf(decl_184, type, singletoninpowunion: $o).
2.01/0.65	thf(decl_185, type, upairset2E: $o).
2.01/0.65	thf(decl_186, type, upairsubunion: $o).
2.01/0.65	thf(decl_187, type, upairinpowunion: $o).
2.01/0.65	thf(decl_188, type, ubforcartprodlem1: $o).
2.01/0.65	thf(decl_189, type, ubforcartprodlem2: $o).
2.01/0.65	thf(decl_190, type, ubforcartprodlem3: $o).
2.01/0.65	thf(decl_191, type, cartprodpairin: $o).
2.01/0.65	thf(decl_192, type, cartprodmempair1: $o).
2.01/0.65	thf(decl_193, type, cartprodmempair: $o).
2.01/0.65	thf(decl_194, type, setunionE2: $o).
2.01/0.65	thf(decl_195, type, setunionsingleton1: $o).
2.01/0.65	thf(decl_196, type, setunionsingleton2: $o).
2.01/0.65	thf(decl_197, type, setunionsingleton: $o).
2.01/0.65	thf(decl_198, type, singleton: $i > $o).
2.01/0.65	thf(decl_199, type, singletonprop: $o).
2.01/0.65	thf(decl_200, type, ex1: $i > ($i > $o) > $o).
2.01/0.65	thf(decl_201, type, ex1E1: $o).
2.01/0.65	thf(decl_202, type, ex1I: $o).
2.01/0.65	thf(decl_203, type, ex1I2: $o).
2.01/0.65	thf(decl_204, type, singletonsuniq: $o).
2.01/0.65	thf(decl_209, type, setukpairinjL1: $o).
2.01/0.65	thf(decl_210, type, kfstsingleton: $o).
2.01/0.65	thf(decl_211, type, theprop: $o).
2.01/0.65	thf(decl_212, type, kfst: $i > $i).
2.01/0.65	thf(decl_213, type, kfstpairEq: $o).
2.01/0.65	thf(decl_214, type, cartprodfstin: $o).
2.01/0.65	thf(decl_215, type, setukpairinjL2: $o).
2.01/0.65	thf(decl_216, type, setukpairinjL: $o).
2.01/0.65	thf(decl_217, type, setukpairinjR11: $o).
2.01/0.65	thf(decl_218, type, setukpairinjR12: $o).
2.01/0.65	thf(decl_219, type, setukpairinjR1: $o).
2.01/0.65	thf(decl_220, type, upairequniteq: $o).
2.01/0.65	thf(decl_221, type, setukpairinjR2: $o).
2.01/0.65	thf(decl_222, type, setukpairinjR: $o).
2.01/0.65	thf(decl_223, type, ksndsingleton: $o).
2.01/0.65	thf(decl_224, type, ksnd: $i > $i).
2.01/0.65	thf(decl_225, type, ksndpairEq: $o).
2.01/0.65	thf(decl_226, type, kpairsurjEq: $o).
2.01/0.65	thf(decl_227, type, cartprodsndin: $o).
2.01/0.65	thf(decl_228, type, cartprodpairmemEL: $o).
2.01/0.65	thf(decl_229, type, cartprodpairmemER: $o).
2.01/0.65	thf(decl_230, type, cartprodmempaircEq: $o).
2.01/0.65	thf(decl_231, type, cartprodfstpairEq: $o).
2.01/0.65	thf(decl_232, type, cartprodsndpairEq: $o).
2.01/0.65	thf(decl_233, type, cartprodpairsurjEq: $o).
2.01/0.65	thf(decl_234, type, breln: $i > $i > $i > $o).
2.01/0.65	thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
2.01/0.65	thf(decl_236, type, dpsetconstrI: $o).
2.01/0.65	thf(decl_237, type, dpsetconstrSub: $o).
2.01/0.65	thf(decl_238, type, setOfPairsIsBReln: $o).
2.01/0.65	thf(decl_239, type, dpsetconstrERa: $o).
2.01/0.65	thf(decl_240, type, dpsetconstrEL1: $o).
2.01/0.65	thf(decl_241, type, dpsetconstrEL2: $o).
2.01/0.65	thf(decl_242, type, dpsetconstrER: $o).
2.01/0.65	thf(decl_243, type, func: $i > $i > $i > $o).
2.01/0.65	thf(decl_244, type, funcSet: $i > $i > $i).
2.01/0.65	thf(decl_245, type, funcImageSingleton: $o).
2.01/0.65	thf(decl_246, type, apProp: $o).
2.01/0.65	thf(decl_247, type, ap: $i > $i > $i > $i > $i).
2.01/0.65	thf(decl_248, type, app: $o).
2.01/0.65	thf(decl_249, type, infuncsetfunc: $o).
2.01/0.65	thf(decl_250, type, ap2p: $o).
2.01/0.65	thf(decl_251, type, funcinfuncset: $o).
2.01/0.65	thf(decl_252, type, lamProp: $o).
2.01/0.65	thf(decl_253, type, lam: $i > $i > ($i > $i) > $i).
2.01/0.65	thf(decl_254, type, lamp: $o).
2.01/0.65	thf(decl_255, type, lam2p: $o).
2.01/0.65	thf(decl_256, type, brelnall1: $o).
2.01/0.65	thf(decl_257, type, brelnall2: $o).
2.01/0.65	thf(decl_258, type, ex1E2: $o).
2.01/0.65	thf(decl_259, type, funcGraphProp1: $o).
2.01/0.65	thf(decl_260, type, funcGraphProp3: $o).
2.01/0.65	thf(decl_261, type, funcGraphProp2: $o).
2.01/0.65	thf(decl_262, type, funcextLem: $o).
2.01/0.65	thf(decl_263, type, funcGraphProp4: $o).
2.01/0.65	thf(decl_264, type, subbreln: $o).
2.01/0.65	thf(decl_265, type, eqbreln: $o).
2.01/0.65	thf(decl_266, type, funcext: $o).
2.01/0.65	thf(decl_267, type, funcext2: $o).
2.01/0.65	thf(decl_268, type, ap2apEq1: $o).
2.01/0.65	thf(decl_269, type, ap2apEq2: $o).
2.01/0.65	thf(decl_270, type, beta1: $o).
2.01/0.65	thf(decl_271, type, eta1: $o).
2.01/0.65	thf(decl_272, type, lam2lamEq: $o).
2.01/0.65	thf(decl_273, type, beta2: $o).
2.01/0.65	thf(decl_274, type, eta2: $o).
2.01/0.65	thf(decl_275, type, iffalseProp1: $o).
2.01/0.65	thf(decl_276, type, iffalseProp2: $o).
2.01/0.65	thf(decl_277, type, iftrueProp1: $o).
2.01/0.65	thf(decl_278, type, iftrueProp2: $o).
2.01/0.65	thf(decl_279, type, ifSingleton: $o).
2.01/0.65	thf(decl_280, type, if: $i > $o > $i > $i > $i).
2.01/0.65	thf(decl_281, type, ifp: $o).
2.01/0.65	thf(decl_282, type, theeq: $o).
2.01/0.65	thf(decl_283, type, iftrue: $o).
2.01/0.65	thf(decl_284, type, iffalse: $o).
2.01/0.65	thf(decl_285, type, iftrueorfalse: $o).
2.01/0.65	thf(decl_286, type, binintersectT_lem: $o).
2.01/0.65	thf(decl_287, type, binunionT_lem: $o).
2.01/0.65	thf(decl_288, type, powersetT_lem: $o).
2.01/0.65	thf(decl_289, type, setminusT_lem: $o).
2.01/0.65	thf(decl_290, type, complementT_lem: $o).
2.01/0.65	thf(decl_291, type, setextT: $o).
2.01/0.65	thf(decl_292, type, subsetTI: $o).
2.01/0.65	thf(decl_293, type, powersetTI1: $o).
2.01/0.65	thf(decl_294, type, powersetTE1: $o).
2.01/0.65	thf(decl_295, type, complementTI1: $o).
2.01/0.65	thf(decl_296, type, complementTE1: $o).
2.01/0.65	thf(decl_297, type, binintersectTELcontra: $o).
2.01/0.65	thf(decl_298, type, binintersectTERcontra: $o).
2.01/0.65	thf(decl_299, type, contrasubsetT: $o).
2.01/0.65	thf(decl_300, type, contrasubsetT1: $o).
2.01/0.65	thf(decl_301, type, contrasubsetT2: $o).
2.01/0.65	thf(decl_302, type, contrasubsetT3: $o).
2.01/0.65	thf(decl_303, type, doubleComplementI1: $o).
2.01/0.65	thf(decl_304, type, doubleComplementE1: $o).
2.01/0.65	thf(decl_305, type, doubleComplementSub1: $o).
2.01/0.65	thf(decl_306, type, doubleComplementSub2: $o).
2.01/0.65	thf(decl_307, type, doubleComplementEq: $o).
2.01/0.65	thf(decl_308, type, complementTnotintersectT: $o).
2.01/0.65	thf(decl_309, type, complementImpComplementIntersect: $o).
2.01/0.65	thf(decl_310, type, complementSubsetComplementIntersect: $o).
2.01/0.65	thf(decl_311, type, complementInPowersetComplementIntersect: $o).
2.01/0.65	thf(decl_312, type, contraSubsetComplement: $o).
2.01/0.65	thf(decl_313, type, complementTcontraSubset: $o).
2.01/0.65	thf(decl_314, type, binunionTILcontra: $o).
2.01/0.65	thf(decl_315, type, binunionTIRcontra: $o).
2.01/0.65	thf(decl_316, type, inIntersectImpInUnion: $o).
2.01/0.65	thf(decl_317, type, inIntersectImpInUnion2: $o).
2.01/0.65	thf(decl_318, type, inIntersectImpInIntersectUnions: $o).
2.01/0.65	thf(decl_319, type, intersectInPowersetIntersectUnions: $o).
2.01/0.65	thf(decl_320, type, inComplementUnionImpNotIn1: $o).
2.01/0.65	thf(decl_321, type, inComplementUnionImpInComplement1: $o).
2.01/0.65	thf(decl_322, type, binunionTE: $o).
2.01/0.65	thf(decl_323, type, binunionTEcontra: $o).
2.01/0.65	thf(decl_324, type, demorgan2a1: $o).
2.01/0.65	thf(decl_325, type, complementUnionInPowersetComplement: $o).
2.01/0.65	thf(decl_326, type, demorgan2a2: $o).
2.01/0.65	thf(decl_327, type, demorgan1a: $o).
2.01/0.65	thf(decl_328, type, demorgan1b: $o).
2.01/0.65	thf(decl_329, type, demorgan1: $o).
2.01/0.65	thf(decl_330, type, demorgan2a: $o).
2.01/0.65	thf(decl_331, type, demorgan2b2: $o).
2.01/0.65	thf(decl_332, type, demorgan2b: $o).
2.01/0.65	thf(decl_333, type, demorgan2: $o).
2.01/0.65	thf(decl_334, type, woz13rule0: $o).
2.01/0.65	thf(decl_335, type, woz13rule1: $o).
2.01/0.65	thf(decl_336, type, woz13rule2: $o).
2.01/0.65	thf(decl_337, type, woz13rule3: $o).
2.01/0.65	thf(decl_338, type, woz13rule4: $o).
2.01/0.65	thf(decl_339, type, woz1_1: $o).
2.01/0.65	thf(decl_340, type, woz1_2: $o).
2.01/0.65	thf(decl_341, type, woz1_3: $o).
2.01/0.65	thf(decl_342, type, woz1_4: $o).
2.01/0.65	thf(decl_343, type, woz1_5: $o).
2.01/0.65	thf(decl_344, type, breln1: $i > $i > $o).
2.01/0.65	thf(decl_345, type, breln1all2: $o).
2.01/0.65	thf(decl_346, type, breln1Set: $i > $i).
2.01/0.65	thf(decl_347, type, breln1SetBreln1: $o).
2.01/0.65	thf(decl_354, type, choice2fnsingleton: $o).
2.01/0.65	thf(decl_355, type, setOfPairsIsBReln1: $o).
2.01/0.65	thf(decl_356, type, breln1all1: $o).
2.01/0.65	thf(decl_357, type, subbreln1: $o).
2.01/0.65	thf(decl_358, type, eqbreln1: $o).
2.01/0.65	thf(decl_359, type, breln1invset: $i > $i > $i).
2.01/0.65	thf(decl_360, type, breln1invprop: $o).
2.01/0.65	thf(decl_361, type, breln1invI: $o).
2.01/0.65	thf(decl_362, type, breln1invE: $o).
2.01/0.65	thf(decl_363, type, breln1compset: $i > $i > $i > $i).
2.01/0.65	thf(decl_364, type, breln1compprop: $o).
2.01/0.65	thf(decl_365, type, breln1compI: $o).
2.01/0.65	thf(decl_366, type, breln1compE: $o).
2.01/0.65	thf(decl_367, type, breln1compEex: $o).
2.01/0.65	thf(decl_368, type, breln1unionprop: $o).
2.01/0.65	thf(decl_369, type, breln1unionIL: $o).
2.01/0.65	thf(decl_370, type, breln1unionIR: $o).
2.01/0.65	thf(decl_371, type, breln1unionI: $o).
2.01/0.65	thf(decl_372, type, breln1unionE: $o).
2.01/0.65	thf(decl_373, type, breln1unionEcases: $o).
2.01/0.65	thf(decl_374, type, breln1unionCommutes: $o).
2.01/0.65	thf(decl_375, type, woz2Ex: $o).
2.01/0.65	thf(decl_376, type, woz2W: $o).
2.01/0.65	thf(decl_377, type, woz2A: $o).
2.01/0.65	thf(decl_378, type, woz2B: $o).
2.01/0.65	thf(decl_379, type, image1Ex: $o).
2.01/0.65	thf(decl_380, type, image1Ex1: $o).
2.01/0.65	thf(decl_381, type, image1: $i > ($i > $i) > $i).
2.01/0.65	thf(decl_382, type, image1Equiv: $o).
2.01/0.65	thf(decl_383, type, image1E: $o).
2.01/0.65	thf(decl_384, type, image1I: $o).
2.01/0.65	thf(decl_385, type, injective: $i > $i > $i > $o).
2.01/0.65	thf(decl_386, type, injFuncSet: $i > $i > $i).
2.01/0.65	thf(decl_387, type, injFuncInInjFuncSet: $o).
2.01/0.65	thf(decl_388, type, injFuncSetFuncIn: $o).
2.01/0.65	thf(decl_389, type, epred1_0: $o).
2.01/0.65	thf(decl_390, type, esk1_2: $i > $i > $i).
2.01/0.65	thf(decl_391, type, esk2_2: $i > $i > $i).
2.01/0.65	thf(decl_392, type, esk3_2: $i > $i > $i).
2.01/0.65	thf(decl_393, type, esk4_1: $i > $i).
2.01/0.65	thf(decl_394, type, esk5_2: ($i > $i > $o) > $i > $i).
2.01/0.65	thf(decl_395, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
2.01/0.65	thf(decl_396, type, esk7_2: ($i > $i > $o) > $i > $i).
2.01/0.65	thf(decl_397, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
2.01/0.65	thf(decl_398, type, esk9_1: $i > $i).
2.01/0.65	thf(decl_399, type, esk10_2: ($i > $o) > $i > $i).
2.01/0.65	thf(decl_400, type, esk11_2: ($i > $o) > $i > $i).
2.01/0.65	thf(decl_401, type, esk12_1: ($i > $o) > $i).
2.01/0.65	thf(decl_402, type, esk13_2: ($i > $o) > $i > $i).
2.01/0.65	thf(decl_403, type, esk14_1: ($i > $o) > $i).
2.01/0.65	thf(decl_404, type, esk15_2: $i > $i > $i).
2.01/0.65	thf(decl_405, type, esk16_2: $i > $i > $i).
2.01/0.65	thf(decl_406, type, esk17_1: $i > $i).
2.01/0.65	thf(decl_407, type, esk18_1: $i > $i).
2.01/0.65	thf(decl_408, type, esk19_1: $i > $i).
2.01/0.65	thf(decl_409, type, esk20_2: $i > $i > $i).
2.01/0.65	thf(decl_410, type, esk21_3: $i > $i > $o > $i).
2.01/0.65	thf(decl_411, type, esk22_2: ($i > $o) > $i > $i).
2.01/0.65	thf(decl_412, type, esk23_1: ($i > $o) > $i).
2.01/0.65	thf(decl_413, type, esk24_1: $i > $i).
2.01/0.65	thf(decl_414, type, esk25_2: $i > ($i > $o) > $i).
2.01/0.65	thf(decl_415, type, esk26_2: $i > ($i > $o) > $i).
2.01/0.65	thf(decl_416, type, esk27_2: $i > ($i > $o) > $i).
2.01/0.65	thf(decl_417, type, esk28_2: $i > ($i > $o) > $i).
2.01/0.65	thf(decl_418, type, esk29_2: $i > ($i > $o) > $i).
2.01/0.65	thf(decl_419, type, esk30_2: $i > ($i > $o) > $i).
2.01/0.65	thf(decl_420, type, esk31_2: ($i > $o) > $i > $i).
2.01/0.65	thf(decl_421, type, esk32_1: ($i > $o) > $i).
2.01/0.65	thf(decl_422, type, esk33_1: ($i > $o) > $i).
2.01/0.65	thf(decl_423, type, esk34_1: ($i > $o) > $i).
2.01/0.65	thf(decl_424, type, esk35_1: ($i > $o) > $i).
2.01/0.65	thf(decl_425, type, esk36_2: ($i > $o) > $i > $i).
2.01/0.65	thf(decl_426, type, esk37_1: ($i > $o) > $i).
2.01/0.65	thf(decl_427, type, esk38_2: ($i > $o) > $i > $i).
2.01/0.65	thf(decl_428, type, esk39_2: ($i > $o) > ($i > $o) > $i).
2.01/0.65	thf(decl_429, type, esk40_2: ($i > $o) > ($i > $o) > $i).
2.01/0.65	thf(decl_430, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
2.01/0.65	thf(decl_431, type, esk42_2: ($i > $o) > ($i > $o) > $i).
2.01/0.65	thf(decl_432, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
2.01/0.65	thf(decl_433, type, esk44_2: ($i > $o) > ($i > $o) > $i).
2.01/0.65	thf(decl_434, type, esk45_2: ($i > $o) > $i > $i).
2.01/0.65	thf(decl_435, type, esk46_2: ($i > $o) > ($i > $o) > $i).
2.01/0.65	thf(decl_436, type, esk47_2: ($i > $o) > ($i > $o) > $i).
2.01/0.65	thf(decl_437, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
2.01/0.65	thf(decl_438, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
2.01/0.65	thf(decl_439, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
2.01/0.65	thf(decl_440, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
2.01/0.65	thf(decl_441, type, esk52_2: $i > $i > $i).
2.01/0.65	thf(decl_442, type, esk53_2: $i > $i > $i).
2.01/0.65	thf(decl_443, type, esk54_2: $i > $i > $i).
2.01/0.65	thf(decl_444, type, esk55_3: $i > $i > $i > $i).
2.01/0.65	thf(decl_445, type, esk56_3: $i > $i > $i > $i).
2.01/0.65	thf(decl_446, type, esk57_2: $i > $i > $i).
2.01/0.65	thf(decl_447, type, esk58_2: $i > ($i > $o) > $i).
2.01/0.65	thf(decl_448, type, esk59_2: $i > ($i > $o) > $i).
2.01/0.65	thf(decl_449, type, esk60_2: $i > ($i > $o) > $i).
2.01/0.65	thf(decl_450, type, esk61_3: $i > ($i > $o) > $i > $i).
2.01/0.65	thf(decl_451, type, esk62_2: $i > ($i > $o) > $i).
2.01/0.65	thf(decl_452, type, esk63_2: $i > ($i > $o) > $i).
2.01/0.65	thf(decl_453, type, esk64_3: $i > $i > ($i > $i) > $i).
2.01/0.65	thf(decl_454, type, esk65_3: $i > $i > ($i > $i) > $i).
2.01/0.65	thf(decl_455, type, esk66_3: $i > $i > ($i > $i) > $i).
2.01/0.65	thf(decl_456, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
2.01/0.65	thf(decl_457, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
2.01/0.65	thf(decl_458, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
2.01/0.65	thf(decl_459, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
2.01/0.65	thf(decl_460, type, esk71_4: $i > $i > $i > $i > $i).
2.01/0.65	thf(decl_461, type, esk72_4: $i > $i > $i > $i > $i).
2.01/0.65	thf(decl_462, type, esk73_4: $i > $i > $i > $i > $i).
2.01/0.65	thf(decl_463, type, esk74_4: $i > $i > $i > $i > $i).
2.01/0.65	thf(decl_464, type, esk75_4: $i > $i > $i > $i > $i).
2.01/0.65	thf(decl_465, type, esk76_4: $i > $i > $i > $i > $i).
2.01/0.65	thf(decl_466, type, esk77_4: $i > $i > $i > $i > $i).
2.01/0.65	thf(decl_467, type, esk78_4: $i > $i > $i > $i > $i).
2.01/0.65	thf(decl_468, type, esk79_4: $i > $i > $i > $i > $i).
2.01/0.65	thf(decl_469, type, esk80_3: $i > $i > ($i > $i) > $i).
2.01/0.65	thf(decl_470, type, esk81_3: $i > $i > ($i > $i) > $i).
2.01/0.65	thf(decl_471, type, esk82_3: $i > $i > ($i > $i) > $i).
2.01/0.65	thf(decl_472, type, esk83_3: $i > $i > $i > $i).
2.01/0.65	thf(decl_473, type, esk84_3: $i > $i > $i > $i).
2.01/0.65	thf(decl_474, type, esk85_3: $i > $i > $i > $i).
2.01/0.65	thf(decl_475, type, esk86_3: $i > $i > $i > $i).
2.01/0.65	thf(decl_476, type, esk87_3: $i > $i > ($i > $o) > $i).
2.01/0.65	thf(decl_477, type, esk88_3: $i > $i > ($i > $o) > $i).
2.01/0.65	thf(decl_478, type, esk89_3: $i > $i > ($i > $o) > $i).
2.01/0.65	thf(decl_479, type, esk90_3: $i > $i > ($i > $o) > $i).
2.01/0.65	thf(decl_480, type, esk91_3: $i > $i > $i > $i).
2.01/0.65	thf(decl_481, type, esk92_3: $i > $i > $i > $i).
2.01/0.65	thf(decl_482, type, esk93_3: $i > $i > $i > $i).
2.01/0.65	thf(decl_483, type, esk94_3: $i > $i > $i > $i).
2.01/0.65	thf(decl_484, type, esk95_3: $i > $i > $i > $i).
2.01/0.65	thf(decl_485, type, esk96_3: $i > $i > $i > $i).
2.01/0.65	thf(decl_486, type, esk97_5: $i > $i > $i > $i > $i > $i).
2.01/0.65	thf(decl_487, type, esk98_6: $i > $i > $i > $i > $i > $o > $i).
2.01/0.65	thf(decl_488, type, esk99_2: $i > ($i > $i) > $i).
2.01/0.65	thf(decl_489, type, esk100_3: $i > ($i > $i) > $i > $i).
2.01/0.65	thf(decl_490, type, esk101_2: $i > ($i > $i) > $i).
2.01/0.65	thf(decl_491, type, esk102_3: $i > ($i > $i) > $i > $i).
2.01/0.65	thf(decl_492, type, esk103_3: $i > ($i > $i) > $i > $i).
2.01/0.65	thf(decl_493, type, esk104_3: $i > ($i > $i) > $i > $i).
2.01/0.65	thf(decl_494, type, esk105_3: $i > ($i > $i) > $i > $i).
2.01/0.65	thf(decl_495, type, esk106_3: $i > ($i > $i) > $i > $i).
2.01/0.65	thf(decl_496, type, esk107_0: $i).
2.01/0.65	thf(decl_497, type, esk108_0: $i).
2.01/0.65	thf(decl_498, type, esk109_0: $i).
2.01/0.65	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', exu__Cong)).
2.01/0.65	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', exu)).
2.01/0.65	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', exuI2)).
2.01/0.65	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', exuI3)).
2.01/0.65	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', exuI1)).
2.01/0.65	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', nonempty)).
2.01/0.65	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', nonemptyI)).
2.01/0.65	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', exuE1)).
2.01/0.65	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', descrp)).
2.01/0.65	thf(image1Ex1, axiom, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', image1Ex1)).
2.01/0.65	thf(injFuncSet, axiom, ((injFuncSet)=(^[X4:$i, X5:$i]:(dsetconstr @ (funcSet @ X4 @ X5) @ (^[X29:$i]:((injective @ X4 @ X5 @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', injFuncSet)).
2.01/0.65	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', descr__Cong)).
2.01/0.65	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', exuEu)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', exuE3u)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', exuE2)).
2.01/0.65	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', exuE3e)).
2.01/0.65	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', replAx)).
2.01/0.65	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', sepInPowerset)).
2.01/0.65	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', ex1E1)).
2.01/0.65	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', kfstsingleton)).
2.01/0.65	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', dsetconstr__Cong)).
2.01/0.65	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', ksndsingleton)).
2.01/0.65	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setoftrueEq)).
2.01/0.65	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', nonemptyI1)).
2.01/0.65	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', nonemptyE1)).
2.01/0.65	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setbeta)).
2.01/0.65	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', dsetconstrEL)).
2.01/0.65	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', dpsetconstrSub)).
2.01/0.65	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', dsetconstrI)).
2.01/0.65	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', dpsetconstrERa)).
2.01/0.65	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', dpsetconstrEL1)).
2.01/0.65	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', funcImageSingleton)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', lamProp)).
2.01/0.65	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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', lamp)).
2.01/0.65	thf(beta2, axiom, ((beta2)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', beta2)).
2.01/0.65	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', iffalseProp1)).
2.01/0.65	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', iftrueProp1)).
2.01/0.65	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', iftrueProp2)).
2.01/0.65	thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setOfPairsIsBReln1)).
2.01/0.65	thf(image1E, axiom, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X60 @ X3))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', image1E)).
2.01/0.65	thf(image1I, axiom, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X61 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', image1I)).
2.01/0.65	thf(injFuncInInjFuncSet, axiom, ((injFuncInInjFuncSet)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((injective @ X4 @ X5 @ X29)=>(in @ X29 @ (injFuncSet @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', injFuncInInjFuncSet)).
2.01/0.65	thf(injFuncSetFuncIn, axiom, ((injFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', injFuncSetFuncIn)).
2.01/0.65	thf(image1Equiv, axiom, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X59 @ X3))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', image1Equiv)).
2.01/0.65	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', ifSingleton)).
2.01/0.65	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', iffalseProp2)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', eta2)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', lam2lamEq)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', eta1)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', beta1)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', ex1E2)).
2.01/0.65	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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', lam2p)).
2.01/0.65	thf(apProp, axiom, ((apProp)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', apProp)).
2.01/0.65	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:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', dpsetconstrER)).
2.01/0.65	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', dpsetconstrEL2)).
2.01/0.65	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setOfPairsIsBReln)).
2.01/0.65	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', dpsetconstrI)).
2.01/0.65	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', ex1I2)).
2.01/0.65	thf(ex1I, axiom, ((ex1I)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', ex1I)).
2.01/0.65	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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', singletonprop)).
2.01/0.65	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', sepSubset)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', emptyE1)).
2.01/0.65	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', nonemptyImpWitness)).
2.01/0.65	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', dsetconstrER)).
2.01/0.65	thf(injFuncSetFuncInj, conjecture, ((setextAx)=>((((powersetAx)=>(((omega0Ax)=>((omegaSAx)=>(((replAx)=>(((((((dsetconstrER)=>(((prop2setE)=>((emptysetE)=>((((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((((((((setadjoinIR)=>(((setadjoinOr)=>(((powersetI)=>(((emptyInPowerset)=>((powersetE)=>((setunionI)=>(((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((((upairsetIL)=>(((emptyE1)=>((vacuousDall)=>(((((quantDeMorgan4)=>((prop2setI)=>(((notdexE)=>(((((((in__Cong)=>((exuE3u)=>((((setadjoin__Cong)=>(((setunion__Cong)=>(((exuEu)=>((descr__Cong)=>((((eqimpsubset2)=>((eqimpsubset1)=>(((emptysetsubset)=>(((((((((setadjoinSub)=>((setadjoinSub2)=>(((setextsub)=>((subsetemptysetimpeq)=>(((((((sepSubset)=>(((((binunionEcases)=>((binunionE)=>((((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>(((binintersectSubset2)=>(((binintersectER)=>((((binintersectSubset4)=>((((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>(((setminusELneg)=>((setminusILneg)=>((((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>(((setukpairIL)=>(((((singletonsubset)=>((((upairset2E)=>(((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>(((ex1E1)=>(((((setukpairinjL1)=>((kfstsingleton)=>(((kfstpairEq)=>(((setukpairinjL2)=>((setukpairinjL)=>((((setukpairinjR1)=>(((setukpairinjR2)=>(((ksndsingleton)=>(((kpairsurjEq)=>(((cartprodpairmemEL)=>(((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>(((dpsetconstrSub)=>(((dpsetconstrERa)=>((dpsetconstrEL1)=>((((funcImageSingleton)=>(((app)=>(((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>(((((((funcGraphProp3)=>((funcGraphProp2)=>((((((funcext)=>((funcext2)=>(((ap2apEq2)=>(((((beta2)=>(((iffalseProp1)=>(((iftrueProp1)=>((iftrueProp2)=>(((ifp)=>(((iftrue)=>((((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((((setextT)=>(((((((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((((doubleComplementI1)=>(((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>(((((complementTcontraSubset)=>((((inIntersectImpInUnion)=>((((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>(((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((((demorgan1a)=>(((((demorgan2b2)=>((demorgan2b)=>(((((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((((woz1_4)=>((woz1_5)=>(((breln1SetBreln1)=>((choice2fnsingleton)=>((setOfPairsIsBReln1)=>((((eqbreln1)=>((breln1invprop)=>(((((breln1compI)=>((breln1compE)=>((breln1compEex)=>(((((breln1unionI)=>((((breln1unionCommutes)=>(((woz2W)=>((woz2A)=>((woz2B)=>(((image1Ex1)=>(((image1E)=>((image1I)=>((injFuncInInjFuncSet)=>(![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X2 @ X3))=>(injective @ X2 @ X3 @ X29)))<=(injFuncSetFuncIn)))))<=(image1Equiv)))<=(image1Ex)))))<=(woz2Ex)))<=(breln1unionEcases))<=(breln1unionE)))<=(breln1unionIR))<=(breln1unionIL))<=(breln1unionprop)))))<=(breln1compprop))<=(breln1invE))<=(breln1invI))))<=(subbreln1))<=(breln1all1)))))<=(breln1all2))))<=(woz1_3))<=(woz1_2))))))<=(woz13rule1))<=(woz13rule0))<=(demorgan2))))<=(demorgan2a))<=(demorgan1))<=(demorgan1b)))<=(demorgan2a2))<=(complementUnionInPowersetComplement)))))<=(inComplementUnionImpInComplement1))))<=(inIntersectImpInIntersectUnions))<=(inIntersectImpInUnion2)))<=(binunionTIRcontra))<=(binunionTILcontra)))<=(contraSubsetComplement))<=(complementInPowersetComplementIntersect))<=(complementSubsetComplementIntersect)))))))<=(doubleComplementE1)))<=(contrasubsetT3))<=(contrasubsetT2))))))<=(complementTE1))<=(complementTI1))<=(powersetTE1))<=(powersetTI1))<=(subsetTI)))<=(complementT_lem))<=(setminusT_lem)))))<=(iftrueorfalse))<=(iffalse)))<=(theeq)))<=(ifSingleton))))<=(iffalseProp2)))<=(eta2)))<=(lam2lamEq))<=(eta1))<=(beta1)))<=(ap2apEq1))))<=(eqbreln))<=(subbreln))<=(funcGraphProp4))<=(funcextLem))))<=(funcGraphProp1))<=(ex1E2))<=(brelnall2))<=(brelnall1))<=(lam2p))))))<=(infuncsetfunc)))<=(apProp)))<=(dpsetconstrER))<=(dpsetconstrEL2))))<=(setOfPairsIsBReln)))<=(dpsetconstrI))))))<=(cartprodpairmemER)))<=(cartprodsndin)))<=(ksndpairEq)))<=(setukpairinjR)))<=(upairequniteq)))<=(setukpairinjR12))<=(setukpairinjR11))))<=(cartprodfstin)))<=(theprop))))<=(singletonsuniq))<=(ex1I2))<=(ex1I)))<=(singletonprop))))))))<=(cartprodpairin))<=(ubforcartprodlem3)))))<=(upairsubunion)))<=(singletoninpowunion))<=(singletoninpowerset)))<=(kpairp))<=(kpairiskpair))<=(setukpairIR)))<=(secondinupair))))))))<=(setminusLsub))<=(setminusIRneg))))<=(setminusERneg))))))<=(bs114d))<=(binintersectSubset1)))<=(binintersectRsub))<=(disjointsetsI1)))<=(binintersectSubset3)))<=(binintersectLsub)))))<=(binunionRsub))<=(binunionLsub))))<=(binunionIR))<=(upairset2IR))<=(binunionIL)))<=(sepInPowerset))<=(powersetsubset))<=(inPowerset))<=(powersetE1))<=(powersetI1))))<=(subset2powerset))))<=(subsetTrans))<=(subsetRefl))<=(notequalI2))<=(notequalI1))<=(notsubsetI))<=(subsetE2))<=(subsetE)))<=(subsetI2))))<=(subsetI1))<=(dsetconstr__Cong))))<=(omega__Cong)))<=(powerset__Cong)))<=(emptyset__Cong))<=(exu__Cong))))<=(inCongP))<=(exuI2))<=(exuI3))<=(exuI1))<=(notdallE)))<=(prop2set2propI))))<=(quantDeMorgan3))<=(quantDeMorgan2))<=(quantDeMorgan1))))<=(upairsetIR)))<=(upairsetE))<=(singletonsswitch))))))))<=(setunionE)))))<=(emptyinPowerset)))<=(setoftrueEq)))<=(setadjoinE)))<=(emptyinunitempty))<=(setadjoinIL))<=(nonemptyI1))<=(nonemptyI))<=(nonemptyE1))<=(setbeta))))))<=(notinemptyset))<=(emptysetimpfalse))))<=(exuE1)))<=(dsetconstrEL))<=(dsetconstrI))<=(descrp))<=(wellorderingAx))<=(foundationAx)))<=(omegaIndAx))))<=(setunionAx)))<=(setadjoinAx))<=(emptysetAx))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', injFuncSetFuncInj)).
2.01/0.65	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', cartprodmempair)).
2.01/0.65	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', inCongP)).
2.01/0.65	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', emptysetAx)).
2.01/0.65	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', powersetsubset)).
2.01/0.65	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', inPowerset)).
2.01/0.65	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', powersetE1)).
2.01/0.65	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', powersetI1)).
2.01/0.65	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', subset2powerset)).
2.01/0.65	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.g9DFcvTYTG/Vampire---4.8_3435', setukpairinjL1)).
2.01/0.65	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', subsetTrans)).
2.01/0.65	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', subsetRefl)).
2.01/0.65	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', notequalI2)).
2.01/0.65	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', notequalI1)).
2.01/0.65	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', notsubsetI)).
2.01/0.65	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', kfstpairEq)).
2.01/0.65	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', subsetE2)).
2.01/0.65	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', subsetE)).
2.01/0.65	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', subsetI2)).
2.01/0.65	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', cartprodmempair1)).
2.01/0.65	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', subsetI1)).
2.01/0.65	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setukpairinjL2)).
2.01/0.65	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', omega__Cong)).
2.01/0.65	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setukpairinjL)).
2.01/0.65	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', powerset__Cong)).
2.01/0.65	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', emptyset__Cong)).
2.01/0.65	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', funcinfuncset)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', setukpairinjR1)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', setukpairinjR2)).
2.01/0.65	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', notdallE)).
2.01/0.65	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', quantDeMorgan3)).
2.01/0.65	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', quantDeMorgan2)).
2.01/0.65	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', quantDeMorgan1)).
2.01/0.65	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', upairsetIR)).
2.01/0.65	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', kpairsurjEq)).
2.01/0.65	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', upairsetE)).
2.01/0.65	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', singletonsswitch)).
2.01/0.65	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setunionE)).
2.01/0.65	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', cartprodpairmemEL)).
2.01/0.65	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', emptyinPowerset)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', cartprodmempaircEq)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', setadjoinE)).
2.01/0.65	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', emptyinunitempty)).
2.01/0.65	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setadjoinIL)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', cartprodfstpairEq)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', cartprodsndpairEq)).
2.01/0.65	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', notinemptyset)).
2.01/0.65	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setunionE2)).
2.01/0.65	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', emptysetimpfalse)).
2.01/0.65	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', cartprodpairsurjEq)).
2.01/0.65	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', wellorderingAx)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', foundationAx)).
2.01/0.65	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', omegaIndAx)).
2.01/0.65	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setunionAx)).
2.01/0.65	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setadjoinAx)).
2.01/0.65	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', app)).
2.01/0.65	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', ap2p)).
2.01/0.65	thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', inComplementUnionImpNotIn1)).
2.01/0.65	thf(binunionTE, axiom, ((binunionTE)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', binunionTE)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', funcGraphProp3)).
2.01/0.65	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', funcGraphProp2)).
2.01/0.65	thf(funcext, axiom, ((funcext)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', funcext)).
2.01/0.65	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', funcext2)).
2.01/0.65	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', ap2apEq2)).
2.01/0.65	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setunionsingleton1)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', ifp)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', iftrue)).
2.01/0.65	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', binintersectT_lem)).
2.01/0.65	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', binunionT_lem)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', powersetT_lem)).
2.01/0.65	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setextT)).
2.01/0.65	thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', binintersectTELcontra)).
2.01/0.65	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setunionsingleton2)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', binintersectTERcontra)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', contrasubsetT)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', contrasubsetT1)).
2.01/0.65	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', doubleComplementI1)).
2.01/0.65	thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', doubleComplementSub1)).
2.01/0.65	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', doubleComplementSub2)).
2.01/0.65	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', doubleComplementEq)).
2.01/0.65	thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', complementTnotintersectT)).
2.01/0.65	thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', complementImpComplementIntersect)).
2.01/0.65	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', complementTcontraSubset)).
2.01/0.65	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', inIntersectImpInUnion)).
2.01/0.65	thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', intersectInPowersetIntersectUnions)).
2.01/0.65	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', powersetTE1)).
2.01/0.65	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', powersetTI1)).
2.01/0.65	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', subsetTI)).
2.01/0.65	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', complementT_lem)).
2.01/0.65	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', setminusT_lem)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', iftrueorfalse)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', binunionTEcontra)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', demorgan2a1)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', demorgan1a)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', demorgan2b2)).
2.01/0.65	thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', demorgan2b)).
2.01/0.65	thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', woz13rule2)).
2.01/0.65	thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', woz13rule3)).
2.01/0.65	thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', woz13rule4)).
2.01/0.65	thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', woz1_1)).
2.01/0.65	thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', woz1_4)).
2.01/0.65	thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', woz1_5)).
2.01/0.65	thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', breln1SetBreln1)).
2.01/0.65	thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', eqbreln1)).
2.01/0.65	thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', breln1invprop)).
2.01/0.65	thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', breln1compI)).
2.01/0.65	thf(breln1compE, axiom, ((breln1compE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35))))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', breln1compE)).
2.01/0.65	thf(breln1compEex, axiom, ((breln1compEex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>![X54:$o]:((![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(X54)))))=>(X54))))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', breln1compEex)).
2.01/0.65	thf(breln1unionI, axiom, ((breln1unionI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35))=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', breln1unionI)).
2.01/0.65	thf(breln1unionCommutes, axiom, ((breln1unionCommutes)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((binunion @ X33 @ X35)=(binunion @ X35 @ X33))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', breln1unionCommutes)).
2.01/0.65	thf(woz2W, axiom, ((woz2W)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((breln1invset @ X4 @ (breln1compset @ X4 @ X33 @ X35))=(breln1compset @ X4 @ (breln1invset @ X4 @ X35) @ (breln1invset @ X4 @ X33)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', woz2W)).
2.01/0.65	thf(woz2A, axiom, ((woz2A)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1compset @ X4 @ X33 @ X56) @ (breln1compset @ X4 @ X35 @ X56)))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', woz2A)).
2.01/0.65	thf(woz2B, axiom, ((woz2B)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X35))) @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X33)))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', woz2B)).
2.01/0.65	thf(image1Ex, axiom, ((image1Ex)<=>![X4:$i, X57:$i > $i]:(?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X57 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', image1Ex)).
2.01/0.65	thf(woz2Ex, axiom, ((woz2Ex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>((X33)=(breln1invset @ X4 @ (breln1invset @ X4 @ X33)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', woz2Ex)).
2.01/0.65	thf(breln1unionEcases, axiom, ((breln1unionEcases)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>![X55:$o]:((((in @ (kpair @ X2 @ X3) @ X33)=>(X55))=>(((in @ (kpair @ X2 @ X3) @ X35)=>(X55))=>(X55)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', breln1unionEcases)).
2.01/0.65	thf(breln1unionE, axiom, ((breln1unionE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', breln1unionE)).
2.01/0.65	thf(breln1unionIR, axiom, ((breln1unionIR)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', breln1unionIR)).
2.01/0.65	thf(breln1unionIL, axiom, ((breln1unionIL)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', breln1unionIL)).
2.01/0.65	thf(breln1unionprop, axiom, ((breln1unionprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', breln1unionprop)).
2.01/0.65	thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', breln1compprop)).
2.01/0.65	thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', breln1invE)).
2.01/0.65	thf(breln1invI, axiom, ((breln1invI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', breln1invI)).
2.01/0.65	thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', subbreln1)).
2.01/0.65	thf(breln1all1, axiom, ((breln1all1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', breln1all1)).
2.01/0.65	thf(breln1all2, axiom, ((breln1all2)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', breln1all2)).
2.01/0.65	thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', woz1_3)).
2.01/0.65	thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', woz1_2)).
2.01/0.65	thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', woz13rule1)).
2.01/0.65	thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', woz13rule0)).
2.01/0.65	thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', demorgan2)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', demorgan2a)).
2.01/0.65	thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', demorgan1)).
2.01/0.65	thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', demorgan1b)).
2.01/0.65	thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', demorgan2a2)).
2.01/0.65	thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', complementUnionInPowersetComplement)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', inComplementUnionImpInComplement1)).
2.01/0.65	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', inIntersectImpInIntersectUnions)).
2.01/0.65	thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', inIntersectImpInUnion2)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', binunionTIRcontra)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', binunionTILcontra)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', contraSubsetComplement)).
2.01/0.65	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', complementInPowersetComplementIntersect)).
2.01/0.65	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', complementSubsetComplementIntersect)).
2.01/0.65	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', doubleComplementE1)).
2.01/0.65	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', contrasubsetT3)).
2.01/0.65	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', contrasubsetT2)).
2.01/0.65	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', complementTE1)).
2.01/0.65	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', complementTI1)).
2.01/0.65	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', iffalse)).
2.01/0.65	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', theeq)).
2.01/0.65	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', ap2apEq1)).
2.01/0.65	thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', eqbreln)).
2.01/0.65	thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', subbreln)).
2.01/0.65	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', funcGraphProp4)).
2.01/0.65	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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', funcextLem)).
2.01/0.65	thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', funcGraphProp1)).
2.01/0.65	thf(brelnall2, axiom, ((brelnall2)<=>![X4:$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.g9DFcvTYTG/Vampire---4.8_3435', brelnall2)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', brelnall1)).
2.01/0.65	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', infuncsetfunc)).
2.01/0.65	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', cartprodpairmemER)).
2.01/0.65	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', cartprodsndin)).
2.01/0.65	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', ksndpairEq)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', setukpairinjR)).
2.01/0.65	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', upairequniteq)).
2.01/0.65	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setukpairinjR12)).
2.01/0.65	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setukpairinjR11)).
2.01/0.65	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', cartprodfstin)).
2.01/0.65	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', theprop)).
2.01/0.65	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', singletonsuniq)).
2.01/0.65	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', cartprodpairin)).
2.01/0.65	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', ubforcartprodlem3)).
2.01/0.65	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', upairsubunion)).
2.01/0.65	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', singletoninpowunion)).
2.01/0.65	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', singletoninpowerset)).
2.01/0.65	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', kpairp)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', kpairiskpair)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', setukpairIR)).
2.01/0.65	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', secondinupair)).
2.01/0.65	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setminusLsub)).
2.01/0.65	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setminusIRneg)).
2.01/0.65	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setminusERneg)).
2.01/0.65	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', bs114d)).
2.01/0.65	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', binintersectSubset1)).
2.01/0.65	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', binintersectRsub)).
2.01/0.65	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', disjointsetsI1)).
2.01/0.65	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', binintersectSubset3)).
2.01/0.65	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', binintersectLsub)).
2.01/0.65	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', binunionRsub)).
2.01/0.65	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', binunionLsub)).
2.01/0.65	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', binunionIR)).
2.01/0.65	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', upairset2IR)).
2.01/0.65	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', binunionIL)).
2.01/0.65	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setunionsingleton)).
2.01/0.65	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', ubforcartprodlem2)).
2.01/0.65	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', ubforcartprodlem1)).
2.01/0.65	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', upairinpowunion)).
2.01/0.65	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', upairset2E)).
2.01/0.65	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', singletonsubset)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', setukpairIL)).
2.01/0.65	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', symdiffIneg2)).
2.01/0.65	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', symdiffIneg1)).
2.01/0.65	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', symdiffI2)).
2.01/0.65	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', symdiffI1)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', symdiffE)).
2.01/0.65	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setminusSubset1)).
2.01/0.65	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setminusILneg)).
2.01/0.65	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setminusELneg)).
2.01/0.65	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setminusSubset2)).
2.01/0.65	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setminusER)).
2.01/0.65	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setminusEL)).
2.01/0.65	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setminusI)).
2.01/0.65	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', binintersectSubset4)).
2.01/0.65	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', binintersectER)).
2.01/0.65	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', binintersectSubset2)).
2.01/0.65	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', binintersectEL)).
2.01/0.65	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', binintersectSubset5)).
2.01/0.65	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', binintersectI)).
2.01/0.65	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', binunionE)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', binunionEcases)).
2.01/0.65	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', subsetemptysetimpeq)).
2.01/0.65	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setextsub)).
2.01/0.65	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setadjoinSub2)).
2.01/0.65	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setadjoinSub)).
2.01/0.65	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', emptysetsubset)).
2.01/0.65	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', eqimpsubset1)).
2.01/0.65	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', eqimpsubset2)).
2.01/0.65	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setunion__Cong)).
2.01/0.65	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setadjoin__Cong)).
2.01/0.65	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', in__Cong)).
2.01/0.65	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', notdexE)).
2.01/0.65	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', prop2setI)).
2.01/0.65	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', quantDeMorgan4)).
2.01/0.65	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', vacuousDall)).
2.01/0.65	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', upairsetIL)).
2.01/0.65	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', eqinunit)).
2.01/0.65	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', notinsingleton)).
2.01/0.65	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', uniqinunit)).
2.01/0.65	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', subPowSU)).
2.01/0.65	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setunionI)).
2.01/0.65	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', powersetE)).
2.01/0.65	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', emptyInPowerset)).
2.01/0.65	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', powersetI)).
2.01/0.65	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setadjoinOr)).
2.01/0.65	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setadjoinIR)).
2.01/0.65	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', noeltsimpempty)).
2.01/0.65	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', emptyI)).
2.01/0.65	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.g9DFcvTYTG/Vampire---4.8_3435', setext)).
2.01/0.65	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', emptysetE)).
2.01/0.65	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', prop2setE)).
2.01/0.65	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', omegaSAx)).
2.01/0.65	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', omega0Ax)).
2.01/0.65	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', powersetAx)).
2.01/0.65	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.g9DFcvTYTG/Vampire---4.8_3435', setextAx)).
2.01/0.65	thf(c_0_318, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
2.01/0.65	thf(c_0_319, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
2.01/0.65	thf(c_0_320, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
2.01/0.65	thf(c_0_321, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
2.01/0.65	thf(c_0_322, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
2.01/0.65	thf(c_0_323, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
2.01/0.65	thf(c_0_324, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
2.01/0.65	thf(c_0_325, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
2.01/0.65	thf(c_0_326, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
2.01/0.65	thf(c_0_327, plain, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[Z0/* 6 */:$i]:(![X2:$i]:(((in @ X2 @ Z0)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3))))))))))), inference(fof_simplification,[status(thm)],[image1Ex1])).
2.01/0.65	thf(c_0_328, plain, ((injFuncSet)=(^[Z0/* 19 */:$i, Z1:$i]:(dsetconstr @ (funcSet @ Z0 @ Z1) @ (^[Z2/* 3 */:$i]:((injective @ Z0 @ Z1 @ Z2)))))), inference(fof_simplification,[status(thm)],[injFuncSet])).
2.01/0.65	thf(c_0_329, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
2.01/0.65	thf(c_0_330, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
2.01/0.65	thf(c_0_331, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
2.01/0.65	thf(c_0_332, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
2.01/0.65	thf(c_0_333, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
2.01/0.65	thf(c_0_334, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
2.01/0.65	thf(c_0_335, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
2.01/0.65	thf(c_0_336, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
2.01/0.65	thf(c_0_337, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
2.01/0.65	thf(c_0_338, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
2.01/0.65	thf(c_0_339, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1119:$i]:((((X1 @ X1119))&![X1120:$i]:((((X1 @ X1120))=>((X1119)=(X1120)))))))<=>(?[X1121:$i]:((((X17 @ X1121))&![X1122:$i]:((((X17 @ X1122))=>((X1121)=(X1122)))))))))))), inference(apply_def,[status(thm)],[c_0_318, c_0_319])).
2.01/0.65	thf(c_0_340, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X1115:$i]:((((X1 @ X1115))&![X1116:$i]:((((X1 @ X1116))=>((X1115)=(X1116))))))))))), inference(apply_def,[status(thm)],[c_0_320, c_0_319])).
2.01/0.65	thf(c_0_341, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X1113:$i]:((((X1 @ X1113))&![X1114:$i]:((((X1 @ X1114))=>((X1113)=(X1114)))))))))))), inference(apply_def,[status(thm)],[c_0_321, c_0_319])).
2.01/0.65	thf(c_0_342, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X1111:$i]:((((X1 @ X1111))&![X1112:$i]:((((X1 @ X1112))=>((X1111)=(X1112))))))))))), inference(apply_def,[status(thm)],[c_0_322, c_0_319])).
2.01/0.65	thf(c_0_343, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
2.01/0.65	thf(c_0_344, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
2.01/0.65	thf(c_0_345, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_323])).
2.01/0.65	thf(c_0_346, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_324, c_0_323])).
2.01/0.65	thf(c_0_347, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_323])).
2.01/0.65	thf(c_0_348, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
2.01/0.65	thf(c_0_349, plain, ((exuE1)=(![X1:$i > $o]:(((?[X1105:$i]:((((X1 @ X1105))&![X1106:$i]:((((X1 @ X1106))=>((X1105)=(X1106)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_325, c_0_319])).
2.01/0.65	thf(c_0_350, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
2.01/0.65	thf(c_0_351, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
2.01/0.65	thf(c_0_352, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
2.01/0.65	thf(c_0_353, plain, ((descrp)=(![X1:$i > $o]:(((?[X1103:$i]:((((X1 @ X1103))&![X1104:$i]:((((X1 @ X1104))=>((X1103)=(X1104)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_326, c_0_319])).
2.01/0.65	thf(c_0_354, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
2.01/0.65	thf(c_0_355, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
2.01/0.65	thf(c_0_356, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
2.01/0.65	thf(c_0_357, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
2.01/0.65	thf(c_0_358, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
2.01/0.65	thf(c_0_359, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
2.01/0.65	thf(c_0_360, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
2.01/0.65	thf(c_0_361, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
2.01/0.65	thf(c_0_362, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
2.01/0.65	thf(c_0_363, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
2.01/0.65	thf(c_0_364, plain, ((image1Ex1)=(![X4:$i, X58:$i > $i]:((?[X1129:$i]:(((![X2:$i]:(((in @ X2 @ X1129)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3)))))))&![X1130:$i]:(((![X2:$i]:(((in @ X2 @ X1130)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3)))))))=>((X1129)=(X1130)))))))))), inference(apply_def,[status(thm)],[c_0_327, c_0_319])).
2.01/0.65	thf(c_0_365, plain, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X60 @ Z0))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), inference(fof_simplification,[status(thm)],[image1E])).
2.01/0.65	thf(c_0_366, plain, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X61 @ Z0))))))), inference(fof_simplification,[status(thm)],[image1I])).
2.01/0.65	thf(c_0_367, axiom, ((injFuncInInjFuncSet)=(![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((injective @ X4 @ X5 @ X29)=>(in @ X29 @ (dsetconstr @ (funcSet @ X4 @ X5) @ (^[Z0/* 3 */:$i]:((injective @ X4 @ X5 @ Z0)))))))))), inference(apply_def,[status(thm)],[injFuncInInjFuncSet, c_0_328])).
2.01/0.65	thf(c_0_368, axiom, ((injFuncSetFuncIn)=(![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (dsetconstr @ (funcSet @ X4 @ X5) @ (^[Z0/* 3 */:$i]:((injective @ X4 @ X5 @ Z0)))))=>(in @ X29 @ (funcSet @ X4 @ X5)))))), inference(apply_def,[status(thm)],[injFuncSetFuncIn, c_0_328])).
2.01/0.65	thf(c_0_369, plain, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X59 @ Z0))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), inference(fof_simplification,[status(thm)],[image1Equiv])).
2.01/0.65	thf(c_0_370, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
2.01/0.65	thf(c_0_371, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
2.01/0.65	thf(c_0_372, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
2.01/0.65	thf(c_0_373, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
2.01/0.65	thf(c_0_374, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
2.01/0.65	thf(c_0_375, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
2.01/0.65	thf(c_0_376, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
2.01/0.65	thf(c_0_377, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
2.01/0.65	thf(c_0_378, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
2.01/0.65	thf(c_0_379, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
2.01/0.65	thf(c_0_380, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
2.01/0.65	thf(c_0_381, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
2.01/0.65	thf(c_0_382, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
2.01/0.65	thf(c_0_383, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
2.01/0.65	thf(c_0_384, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
2.01/0.65	thf(c_0_385, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
2.01/0.65	thf(c_0_386, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
2.01/0.65	thf(c_0_387, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1125:$i]:((((X1 @ X1125))&![X1126:$i]:((((X1 @ X1126))=>((X1125)=(X1126)))))))=>((?[X1127:$i]:((((X17 @ X1127))&![X1128:$i]:((((X17 @ X1128))=>((X1127)=(X1128)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_329, c_0_319])).
2.01/0.65	thf(c_0_388, plain, ((exuEu)=(![X1:$i > $o]:(((?[X1123:$i]:((((X1 @ X1123))&![X1124:$i]:((((X1 @ X1124))=>((X1123)=(X1124)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_330, c_0_319])).
2.01/0.65	thf(c_0_389, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X1117:$i]:((((X1 @ X1117))&![X1118:$i]:((((X1 @ X1118))=>((X1117)=(X1118)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_331, c_0_319])).
2.01/0.65	thf(c_0_390, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
2.01/0.65	thf(c_0_391, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_323])).
2.01/0.65	thf(c_0_392, plain, ((exuE2)=(![X1:$i > $o]:(((?[X1109:$i]:((((X1 @ X1109))&![X1110:$i]:((((X1 @ X1110))=>((X1109)=(X1110)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_332, c_0_319])).
2.01/0.65	thf(c_0_393, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X1107:$i]:((((X1 @ X1107))&![X1108:$i]:((((X1 @ X1108))=>((X1107)=(X1108)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_333, c_0_319])).
2.01/0.65	thf(c_0_394, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
2.01/0.65	thf(c_0_395, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X1101:$i]:((((X6 @ X2 @ X1101))&![X1102:$i]:((((X6 @ X2 @ X1102))=>((X1101)=(X1102)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_334, c_0_319])).
2.01/0.65	thf(c_0_396, plain, ((epred1_0)<=>![X2168:$i]:(?[X2169:$i]:((((![X2170:$i]:(((in @ X2170 @ X2169)=>![X2171:$i]:(((in @ X2171 @ X2170)=>(in @ X2171 @ X2168)))))&![X2172:$i, X2173:$i]:((((in @ X2172 @ X2168)&(in @ X2173 @ X2168))=>(![X2174:$i]:(((in @ X2174 @ X2169)=>((in @ X2172 @ X2174)<=>(in @ X2173 @ X2174))))=>((X2172)=(X2173))))))&![X2175:$i, X2176:$i]:((((in @ X2175 @ X2169)&(in @ X2176 @ X2169))=>(![X2177:$i]:(((in @ X2177 @ X2175)=>(in @ X2177 @ X2176)))|![X2178:$i]:(((in @ X2178 @ X2176)=>(in @ X2178 @ X2175)))))))&![X2179:$i]:(((![X2180:$i]:(((in @ X2180 @ X2179)=>(in @ X2180 @ X2168)))&?[X2181:$i]:((in @ X2181 @ X2179)))=>?[X2182:$i, X2183:$i]:(((((in @ X2182 @ X2169)&(in @ X2183 @ X2179))&~(?[X2184:$i]:(((in @ X2184 @ X2182)&(in @ X2184 @ X2179)))))&![X2185:$i]:(((in @ X2185 @ X2169)=>(![X2186:$i]:(((in @ X2186 @ X2185)=>(in @ X2186 @ X2182)))|(in @ X2183 @ X2185)))))))))))), introduced(definition)).
2.01/0.65	thf(c_0_397, negated_conjecture, ~((![X1131:$i, X1132:$i]:((![X1133:$i]:(((in @ X1133 @ X1131)<=>(in @ X1133 @ X1132)))=>((X1131)=(X1132))))=>(![X2200:$i]:(~(in @ X2200 @ emptyset))=>(![X2197:$i, X2198:$i, X2199:$i]:(((in @ X2199 @ (setadjoin @ X2197 @ X2198))<=>(((X2199)=(X2197))|(in @ X2199 @ X2198))))=>(![X1134:$i, X1135:$i]:(((in @ X1135 @ (powerset @ X1134))<=>![X1136:$i]:(((in @ X1136 @ X1135)=>(in @ X1136 @ X1134)))))=>(![X2194:$i, X2195:$i]:(((in @ X2195 @ (setunion @ X2194))<=>?[X2196:$i]:(((in @ X2195 @ X2196)&(in @ X2196 @ X2194)))))=>((in @ emptyset @ omega)=>(![X1137:$i]:(((in @ X1137 @ omega)=>(in @ (setadjoin @ X1137 @ X1137) @ omega)))=>(![X2191:$i]:((((in @ emptyset @ X2191)&![X2192:$i]:((((in @ X2192 @ omega)&(in @ X2192 @ X2191))=>(in @ (setadjoin @ X2192 @ X2192) @ X2191))))=>![X2193:$i]:(((in @ X2193 @ omega)=>(in @ X2193 @ X2191)))))=>(![X1138:$i > $i > $o, X1139:$i]:((![X1140:$i]:(((in @ X1140 @ X1139)=>?[X1141:$i]:(((X1138 @ X1140 @ X1141)&![X1142:$i]:(((X1138 @ X1140 @ X1142)=>((X1141)=(X1142))))))))=>?[X1143:$i]:(![X1144:$i]:(((in @ X1144 @ X1143)<=>?[X1145:$i]:(((in @ X1145 @ X1139)&(X1138 @ X1145 @ X1144))))))))=>(![X2187:$i]:((?[X2188:$i]:((in @ X2188 @ X2187))=>?[X2189:$i]:(((in @ X2189 @ X2187)&~(?[X2190:$i]:(((in @ X2190 @ X2189)&(in @ X2190 @ X2187))))))))=>((epred1_0)=>(![X2165:$i > $o]:((?[X2166:$i]:(((X2165 @ X2166)&![X2167:$i]:(((X2165 @ X2167)=>((X2166)=(X2167))))))=>(X2165 @ (descr @ (^[Z0/* 3 */:$i]:((X2165 @ Z0)))))))=>(![X2162:$i, X2163:$i > $o, X2164:$i]:(((in @ X2164 @ X2162)=>((X2163 @ X2164)=>(in @ X2164 @ (dsetconstr @ X2162 @ (^[Z0/* 3 */:$i]:((X2163 @ Z0))))))))=>(![X2159:$i, X2160:$i > $o, X2161:$i]:(((in @ X2161 @ (dsetconstr @ X2159 @ (^[Z0/* 3 */:$i]:((X2160 @ Z0)))))=>(in @ X2161 @ X2159)))=>(![X1146:$i, X1147:$i > $o, X1148:$i]:(((in @ X1148 @ (dsetconstr @ X1146 @ (^[Z0/* 3 */:$i]:((X1147 @ Z0)))))=>(X1147 @ X1148)))=>(![X2154:$i > $o]:((?[X2155:$i]:(((X2154 @ X2155)&![X2156:$i]:(((X2154 @ X2156)=>((X2155)=(X2156))))))=>?[X2157:$i]:(((X2154 @ X2157)&![X2158:$i]:(((X2154 @ X2158)=>((X2157)=(X2158))))))))=>(![X1149:$o, X1150:$i]:(((in @ X1150 @ (prop2set @ ((X1149))))=>(X1149)))=>(![X1151:$i]:(((in @ X1151 @ emptyset)=>![X1152:$o]:((X1152))))=>(![X2153:$i]:(~(in @ X2153 @ emptyset))=>(![X2152:$i]:(~(in @ X2152 @ emptyset))=>(![X1153:$i > $o]:((?[X1154:$i]:(((X1153 @ X1154)&![X1155:$i]:(((X1153 @ X1155)=>((X1154)=(X1155))))))=>?[X1156:$i]:((X1153 @ X1156))))=>(![X1157:$i, X1158:$i]:((![X1159:$i]:(((in @ X1159 @ X1157)=>(in @ X1159 @ X1158)))=>(![X1160:$i]:(((in @ X1160 @ X1158)=>(in @ X1160 @ X1157)))=>((X1157)=(X1158)))))=>(![X1161:$i]:((![X1162:$i]:(~(in @ X1162 @ X1161))=>((X1161)=(emptyset))))=>(![X1163:$i]:((![X1164:$i]:(~(in @ X1164 @ X1163))=>((X1163)=(emptyset))))=>(![X2149:$i, X2150:$i > $o, X2151:$i]:(((in @ X2151 @ X2149)=>((in @ X2151 @ (dsetconstr @ X2149 @ (^[Z0/* 3 */:$i]:((X2150 @ Z0)))))<=>(X2150 @ X2151))))=>(![X2147:$i]:((((X2147)!=(emptyset))=>?[X2148:$i]:((in @ X2148 @ X2147))))=>(![X2144:$i, X2145:$i > $o, X2146:$i]:(((in @ X2146 @ X2144)=>((X2145 @ X2146)=>((dsetconstr @ X2144 @ (^[Z0/* 3 */:$i]:((X2145 @ Z0))))!=(emptyset)))))=>(![X2142:$i]:((?[X2143:$i]:((in @ X2143 @ X2142))=>((X2142)!=(emptyset))))=>(![X2140:$i, X2141:$i]:((in @ X2140 @ (setadjoin @ X2140 @ X2141)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1165:$i, X1166:$i, X1167:$i]:(((in @ X1167 @ X1166)=>(in @ X1167 @ (setadjoin @ X1165 @ X1166))))=>(![X2136:$i, X2137:$i, X2138:$i]:(((in @ X2138 @ (setadjoin @ X2136 @ X2137))=>![X2139:$o]:(((((X2138)=(X2136))=>(X2139))=>(((in @ X2138 @ X2137)=>(X2139))=>(X2139))))))=>(![X1168:$i, X1169:$i, X1170:$i]:(((in @ X1170 @ (setadjoin @ X1168 @ X1169))=>(((X1170)=(X1168))|(in @ X1170 @ X1169))))=>(![X2135:$i]:(((dsetconstr @ X2135 @ (^[Z0/* 3 */:$i]:(($true))))=(X2135)))=>(![X1171:$i, X1172:$i]:((![X1173:$i]:(((in @ X1173 @ X1172)=>(in @ X1173 @ X1171)))=>(in @ X1172 @ (powerset @ X1171))))=>(![X2134:$i]:((in @ emptyset @ (powerset @ X2134)))=>(![X1174:$i]:((in @ emptyset @ (powerset @ X1174)))=>(![X1175:$i, X1176:$i, X1177:$i]:(((in @ X1176 @ (powerset @ X1175))=>((in @ X1177 @ X1176)=>(in @ X1177 @ X1175))))=>(![X1178:$i, X1179:$i, X1180:$i]:(((in @ X1179 @ X1180)=>((in @ X1180 @ X1178)=>(in @ X1179 @ (setunion @ X1178)))))=>(![X2130:$i, X2131:$i]:(((in @ X2131 @ (setunion @ X2130))=>![X2132:$o]:((![X2133:$i]:(((in @ X2131 @ X2133)=>((in @ X2133 @ X2130)=>(X2132))))=>(X2132)))))=>(![X1181:$i, X1182:$i]:(((in @ X1182 @ X1181)=>(in @ X1182 @ (powerset @ (setunion @ X1181)))))=>(![X1183:$i > $o]:((?[X1184:$i]:(((X1183 @ X1184)&![X1185:$i]:(((X1183 @ X1185)=>((X1184)=(X1185))))))=>?[X1186:$i]:(![X1187:$i]:(((X1183 @ X1187)<=>((X1187)=(X1186)))))))=>(![X1188:$i]:((((X1188)!=(emptyset))=>?[X1189:$i]:((in @ X1189 @ X1188))))=>(![X1190:$i, X1191:$i]:(((in @ X1190 @ (setadjoin @ X1191 @ emptyset))=>((X1190)=(X1191))))=>(![X1192:$i, X1193:$i]:((((X1192)!=(X1193))=>~(in @ X1193 @ (setadjoin @ X1192 @ emptyset))))=>(![X1194:$i, X1195:$i]:((((X1194)=(X1195))=>(in @ X1194 @ (setadjoin @ X1195 @ emptyset))))=>(![X2128:$i, X2129:$i]:(((in @ X2128 @ (setadjoin @ X2129 @ emptyset))=>(in @ X2129 @ (setadjoin @ X2128 @ emptyset))))=>(![X2125:$i, X2126:$i, X2127:$i]:(((in @ X2127 @ (setadjoin @ X2125 @ (setadjoin @ X2126 @ emptyset)))=>(((X2127)=(X2125))|((X2127)=(X2126)))))=>(![X1196:$i, X1197:$i]:((in @ X1196 @ (setadjoin @ X1196 @ (setadjoin @ X1197 @ emptyset))))=>(![X2123:$i, X2124:$i]:((in @ X2124 @ (setadjoin @ X2123 @ (setadjoin @ X2124 @ emptyset))))=>(![X1198:$i, X1199:$i > $o]:((?[X1200:$i]:(((in @ X1200 @ X1198)&(X1199 @ X1200)))=>((dsetconstr @ X1198 @ (^[Z0/* 3 */:$i]:((X1199 @ Z0))))!=(emptyset))))=>(![X1201:$i > $o, X1202:$i]:(((in @ X1202 @ emptyset)=>(X1201 @ X1202)))=>(![X2119:$i, X2120:$i > $o]:((~(![X2121:$i]:(((in @ X2121 @ X2119)=>(X2120 @ X2121))))=>?[X2122:$i]:(((in @ X2122 @ X2119)&~(X2120 @ X2122)))))=>(![X2115:$i, X2116:$i > $o]:((![X2117:$i]:(((in @ X2117 @ X2115)=>~(X2116 @ X2117)))=>~(?[X2118:$i]:(((in @ X2118 @ X2115)&(X2116 @ X2118))))))=>(![X2111:$i, X2112:$i > $o]:((~(?[X2113:$i]:(((in @ X2113 @ X2111)&(X2112 @ X2113))))=>![X2114:$i]:(((in @ X2114 @ X2111)=>~(X2112 @ X2114)))))=>(![X1203:$i, X1204:$i > $o]:((?[X1205:$i]:(((in @ X1205 @ X1203)&~(X1204 @ X1205)))=>~(![X1206:$i]:(((in @ X1206 @ X1203)=>(X1204 @ X1206))))))=>(![X1207:$o]:(((X1207)=>(in @ emptyset @ (prop2set @ ((X1207))))))=>((prop2set2propI)=>(![X1208:$i, X1209:$i > $o]:((~(?[X1210:$i]:(((in @ X1210 @ X1208)&(X1209 @ X1210))))=>![X1211:$i]:(((in @ X1211 @ X1208)=>~(X1209 @ X1211)))))=>(![X2107:$i, X2108:$i > $o]:((~(![X2109:$i]:(((in @ X2109 @ X2107)=>(X2108 @ X2109))))=>?[X2110:$i]:(((in @ X2110 @ X2107)&~(X2108 @ X2110)))))=>(![X2102:$i > $o]:((?[X2103:$i]:(((X2102 @ X2103)&![X2104:$i]:(((X2102 @ X2104)=>((X2103)=(X2104))))))=>?[X2105:$i]:(((X2102 @ X2105)&![X2106:$i]:(((X2102 @ X2106)=>((X2105)=(X2106))))))))=>(![X2096:$i > $o]:((?[X2097:$i]:((X2096 @ X2097))=>(![X2098:$i, X2099:$i]:(((X2096 @ X2098)=>((X2096 @ X2099)=>((X2098)=(X2099)))))=>?[X2100:$i]:(((X2096 @ X2100)&![X2101:$i]:(((X2096 @ X2101)=>((X2100)=(X2101)))))))))=>(![X2091:$i > $o]:((?[X2092:$i]:(![X2093:$i]:(((X2091 @ X2093)<=>((X2093)=(X2092)))))=>?[X2094:$i]:(((X2091 @ X2094)&![X2095:$i]:(((X2091 @ X2095)=>((X2094)=(X2095))))))))=>(![X2087:$i, X2088:$i]:((((X2087)=(X2088))=>![X2089:$i, X2090:$i]:((((X2089)=(X2090))=>((in @ X2089 @ X2087)=>(in @ X2090 @ X2088))))))=>(![X1212:$i, X1213:$i]:((((X1212)=(X1213))=>![X1214:$i, X1215:$i]:((((X1214)=(X1215))=>((in @ X1214 @ X1212)<=>(in @ X1215 @ X1213))))))=>(![X1216:$i > $o]:((?[X1217:$i]:(((X1216 @ X1217)&![X1218:$i]:(((X1216 @ X1218)=>((X1217)=(X1218))))))=>![X1219:$i, X1220:$i]:(((X1216 @ X1219)=>((X1216 @ X1220)=>((X1219)=(X1220)))))))=>(![X2079:$i > $o, X2080:$i > $o]:((![X2081:$i, X2082:$i]:((((X2081)=(X2082))=>((X2079 @ X2081)<=>(X2080 @ X2082))))=>(?[X2083:$i]:(((X2079 @ X2083)&![X2084:$i]:(((X2079 @ X2084)=>((X2083)=(X2084))))))<=>?[X2085:$i]:(((X2080 @ X2085)&![X2086:$i]:(((X2080 @ X2086)=>((X2085)=(X2086)))))))))=>(((emptyset)=(emptyset))=>(![X1221:$i, X1222:$i]:((((X1221)=(X1222))=>![X1223:$i, X1224:$i]:((((X1223)=(X1224))=>((setadjoin @ X1221 @ X1223)=(setadjoin @ X1222 @ X1224))))))=>(![X2077:$i, X2078:$i]:((((X2077)=(X2078))=>((powerset @ X2077)=(powerset @ X2078))))=>(![X1225:$i, X1226:$i]:((((X1225)=(X1226))=>((setunion @ X1225)=(setunion @ X1226))))=>(((omega)=(omega))=>(![X1227:$i > $o]:((?[X1228:$i]:(((X1227 @ X1228)&![X1229:$i]:(((X1227 @ X1229)=>((X1228)=(X1229))))))=>![X1230:$i, X1231:$i]:(((X1227 @ X1230)=>((X1227 @ X1231)=>((X1230)=(X1231)))))))=>(![X1232:$i > $o, X1233:$i > $o]:((![X1234:$i, X1235:$i]:((((X1234)=(X1235))=>((X1232 @ X1234)<=>(X1233 @ X1235))))=>(?[X1236:$i]:(((X1232 @ X1236)&![X1237:$i]:(((X1232 @ X1237)=>((X1236)=(X1237))))))=>(?[X1238:$i]:(((X1233 @ X1238)&![X1239:$i]:(((X1233 @ X1239)=>((X1238)=(X1239))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1232 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X1233 @ Z0)))))))))=>(![X2071:$i, X2072:$i]:((((X2071)=(X2072))=>![X2073:$i > $o, X2074:$i > $o]:((![X2075:$i]:(((in @ X2075 @ X2071)=>![X2076:$i]:(((in @ X2076 @ X2072)=>(((X2075)=(X2076))=>((X2073 @ X2075)<=>(X2074 @ X2076)))))))=>((dsetconstr @ X2071 @ (^[Z0/* 3 */:$i]:((X2073 @ Z0))))=(dsetconstr @ X2072 @ (^[Z0/* 3 */:$i]:((X2074 @ Z0)))))))))=>(![X2068:$i, X2069:$i]:((![X2070:$i]:(((in @ X2070 @ X2068)=>(in @ X2070 @ X2069)))=>(subset @ X2068 @ X2069)))=>(![X1240:$i, X1241:$i]:((((X1240)=(X1241))=>(subset @ X1241 @ X1240)))=>(![X1242:$i, X1243:$i]:((((X1242)=(X1243))=>(subset @ X1242 @ X1243)))=>(![X2065:$i, X2066:$i]:((![X2067:$i]:(((in @ X2067 @ X2065)=>(in @ X2067 @ X2066)))=>(subset @ X2065 @ X2066)))=>(![X1244:$i]:((subset @ emptyset @ X1244))=>(![X2062:$i, X2063:$i, X2064:$i]:(((subset @ X2062 @ X2063)=>((in @ X2064 @ X2062)=>(in @ X2064 @ X2063))))=>(![X2059:$i, X2060:$i, X2061:$i]:(((subset @ X2059 @ X2060)=>(~(in @ X2061 @ X2060)=>~(in @ X2061 @ X2059))))=>(![X2056:$i, X2057:$i, X2058:$i]:(((in @ X2058 @ X2056)=>(~(in @ X2058 @ X2057)=>~(subset @ X2056 @ X2057))))=>(![X2054:$i, X2055:$i]:((~(subset @ X2054 @ X2055)=>((X2054)!=(X2055))))=>(![X2051:$i, X2052:$i, X2053:$i]:(((in @ X2053 @ X2051)=>(~(in @ X2053 @ X2052)=>((X2051)!=(X2052)))))=>(![X2050:$i]:((subset @ X2050 @ X2050))=>(![X2047:$i, X2048:$i, X2049:$i]:(((subset @ X2047 @ X2048)=>((subset @ X2048 @ X2049)=>(subset @ X2047 @ X2049))))=>(![X1245:$i, X1246:$i]:((subset @ X1246 @ (setadjoin @ X1245 @ X1246)))=>(![X1247:$i, X1248:$i, X1249:$i]:(((subset @ X1247 @ X1249)=>(subset @ X1247 @ (setadjoin @ X1248 @ X1249))))=>(![X2045:$i, X2046:$i]:(((subset @ X2045 @ X2046)=>(in @ X2045 @ (powerset @ X2046))))=>(![X1250:$i, X1251:$i]:(((subset @ X1250 @ X1251)=>((subset @ X1251 @ X1250)=>((X1250)=(X1251)))))=>(![X1252:$i]:(((subset @ X1252 @ emptyset)=>((X1252)=(emptyset))))=>(![X2043:$i, 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cartprodmempair]), inCongP]), emptysetAx]), c_0_335]), powersetsubset]), inPowerset]), powersetE1]), c_0_336]), powersetI1]), subset2powerset]), setukpairinjL1]), subsetTrans]), subsetRefl]), notequalI2]), c_0_337]), notequalI1]), notsubsetI]), kfstpairEq]), subsetE2]), subsetE]), subsetI2]), cartprodmempair1]), subsetI1]), setukpairinjL2]), c_0_338]), omega__Cong]), setukpairinjL]), powerset__Cong]), emptyset__Cong]), c_0_339]), funcinfuncset]), c_0_340]), setukpairinjR1]), c_0_341]), c_0_342]), setukpairinjR2]), notdallE]), quantDeMorgan3]), quantDeMorgan2]), c_0_343]), quantDeMorgan1]), upairsetIR]), kpairsurjEq]), upairsetE]), singletonsswitch]), setunionE]), cartprodpairmemEL]), emptyinPowerset]), c_0_344]), cartprodmempaircEq]), setadjoinE]), emptyinunitempty]), setadjoinIL]), cartprodfstpairEq]), c_0_345]), c_0_346]), cartprodsndpairEq]), c_0_347]), c_0_348]), notinemptyset]), setunionE2]), emptysetimpfalse]), cartprodpairsurjEq]), c_0_349]), c_0_350]), c_0_351]), c_0_352]), c_0_353]), wellorderingAx]), c_0_354]), foundationAx]), omegaIndAx]), c_0_355]), setunionAx]), setadjoinAx]), c_0_356]), app]), ap2p]), inComplementUnionImpNotIn1]), binunionTE]), c_0_357]), c_0_358]), funcGraphProp3]), funcGraphProp2]), funcext]), funcext2]), ap2apEq2]), c_0_359]), c_0_360]), setunionsingleton1]), c_0_361]), c_0_362]), ifp]), iftrue]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setextT]), binintersectTELcontra]), setunionsingleton2]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), doubleComplementI1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementTcontraSubset]), inIntersectImpInUnion]), intersectInPowersetIntersectUnions]), powersetTE1]), powersetTI1]), subsetTI]), complementT_lem]), setminusT_lem]), iftrueorfalse]), binunionTEcontra]), demorgan2a1]), demorgan1a]), demorgan2b2]), demorgan2b]), woz13rule2]), woz13rule3]), woz13rule4]), woz1_1]), woz1_4]), woz1_5]), breln1SetBreln1]), c_0_363]), eqbreln1]), breln1invprop]), breln1compI]), breln1compE]), breln1compEex]), breln1unionI]), breln1unionCommutes]), woz2W]), woz2A]), woz2B]), c_0_364]), c_0_365]), c_0_366]), c_0_367]), c_0_328]), c_0_368]), c_0_369]), image1Ex]), woz2Ex]), breln1unionEcases]), breln1unionE]), breln1unionIR]), breln1unionIL]), breln1unionprop]), breln1compprop]), breln1invE]), breln1invI]), subbreln1]), breln1all1]), breln1all2]), woz1_3]), woz1_2]), woz13rule1]), woz13rule0]), demorgan2]), demorgan2a]), demorgan1]), demorgan1b]), demorgan2a2]), complementUnionInPowersetComplement]), inComplementUnionImpInComplement1]), inIntersectImpInIntersectUnions]), inIntersectImpInUnion2]), binunionTIRcontra]), binunionTILcontra]), contraSubsetComplement]), complementInPowersetComplementIntersect]), complementSubsetComplementIntersect]), doubleComplementE1]), contrasubsetT3]), contrasubsetT2]), complementTE1]), complementTI1]), iffalse]), theeq]), c_0_370]), c_0_371]), c_0_372]), c_0_373]), c_0_374]), c_0_375]), ap2apEq1]), eqbreln]), subbreln]), funcGraphProp4]), funcextLem]), funcGraphProp1]), c_0_376]), brelnall2]), brelnall1]), c_0_377]), infuncsetfunc]), c_0_378]), c_0_379]), c_0_380]), c_0_381]), c_0_382]), cartprodpairmemER]), cartprodsndin]), ksndpairEq]), setukpairinjR]), upairequniteq]), setukpairinjR12]), setukpairinjR11]), cartprodfstin]), theprop]), singletonsuniq]), c_0_383]), c_0_384]), c_0_385]), cartprodpairin]), ubforcartprodlem3]), upairsubunion]), singletoninpowunion]), singletoninpowerset]), kpairp]), kpairiskpair]), setukpairIR]), secondinupair]), setminusLsub]), setminusIRneg]), setminusERneg]), bs114d]), binintersectSubset1]), binintersectRsub]), disjointsetsI1]), binintersectSubset3]), binintersectLsub]), binunionRsub]), binunionLsub]), binunionIR]), upairset2IR]), binunionIL]), setunionsingleton]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), upairset2E]), singletonsubset]), setukpairIL]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), symdiffI1]), symdiffE]), setminusSubset1]), setminusILneg]), setminusELneg]), setminusSubset2]), setminusER]), setminusEL]), setminusI]), binintersectSubset4]), binintersectER]), binintersectSubset2]), binintersectEL]), binintersectSubset5]), binintersectI]), binunionE]), binunionEcases]), c_0_386]), subsetemptysetimpeq]), setextsub]), setadjoinSub2]), setadjoinSub]), emptysetsubset]), eqimpsubset1]), eqimpsubset2]), c_0_387]), c_0_388]), setunion__Cong]), setadjoin__Cong]), c_0_389]), in__Cong]), notdexE]), prop2setI]), quantDeMorgan4]), vacuousDall]), c_0_390]), upairsetIL]), eqinunit]), notinsingleton]), uniqinunit]), c_0_391]), c_0_392]), subPowSU]), setunionI]), powersetE]), emptyInPowerset]), powersetI]), setadjoinOr]), setadjoinIR]), noeltsimpempty]), emptyI]), setext]), c_0_393]), emptysetE]), prop2setE]), c_0_394]), c_0_395]), omegaSAx]), omega0Ax]), powersetAx]), setextAx])])]), c_0_396])).
2.01/0.65	thf(c_0_398, negated_conjecture, ![X2201:$i, X2202:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2214:$i, X2215:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2223:$i, X2224:$i > $i > $o, X2225:$i, X2227:$i, X2230:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2237:$i, X2238:$i > $o, X2239:$i, X2241:$i, X2242:$i > $o, X2243:$i, X2244:$i, X2245:$i > $o, X2246:$i, X2247:$i, X2248:$i > $o, X2249:$i, X2250:$i > $o, X2251:$i, X2254:$i, X2255:$o, X2256:$i, X2257:$i, X2258:$o, X2259:$i, X2260:$i, X2261:$i > $o, X2262:$i, X2265:$i, X2266:$i, X2269:$i, X2271:$i, X2273:$i, X2274:$i > $o, X2275:$i, X2276:$i, X2278:$i, X2279:$i > $o, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$o, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2308:$i, X2309:$o, X2311:$i, X2312:$i, X2313:$i > $o, X2314:$i, X2317:$i, X2318:$i, X2319:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2327:$i, X2328:$i, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i > $o, X2338:$i, X2339:$i > $o, X2340:$i, X2341:$i, X2342:$i > $o, X2343:$i, X2345:$i, X2346:$i > $o, X2348:$i, X2349:$i, X2350:$i > $o, X2352:$i, X2353:$i, X2354:$i > $o, X2355:$i, X2357:$o, X2358:$i, X2359:$i > $o, X2361:$i, X2362:$i, X2363:$i > $o, X2364:$i, X2366:$i > $o, X2367:$i, X2370:$i, X2371:$i > $o, X2372:$i, X2376:$i, X2377:$i > $o, X2378:$i, X2381:$i, X2382:$i, X2383:$i, X2384:$i, X2385:$i, X2386:$i, X2387:$i, X2388:$i, X2389:$i, X2390:$i > $o, X2391:$i, X2393:$i, X2394:$i, X2395:$i > $o, X2396:$i > $o, X2399:$i, X2402:$i, X2403:$i, X2406:$i, X2407:$i, X2408:$i, X2409:$i, X2410:$i, X2411:$i, X2412:$i, X2413:$i, X2414:$i, X2415:$i > $o, X2416:$i, X2418:$i, X2419:$i, X2420:$i > $o, X2421:$i > $o, X2424:$i, X2426:$i, X2428:$i, X2429:$i, X2430:$i > $o, X2431:$i > $o, X2434:$i, X2435:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, X2442:$i, X2444:$i, X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$i, X2455:$i, X2456:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i, X2463:$i, X2464:$i, X2465:$i, X2466:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2471:$i, X2472:$i, X2473:$i, X2474:$i, X2475:$i, X2476:$i, X2477:$i, X2478:$i, X2479:$i, X2480:$i, X2481:$i > $o, X2482:$i, X2483:$i > $o, X2484:$i, X2485:$i, X2486:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2493:$i, X2494:$i, X2495:$o, X2496:$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, 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:$i, X2563:$o, X2564:$i, X2565:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2570:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i, X2576:$i, X2577:$i, X2578:$i, X2579:$i, X2580:$i, X2581:$i, X2582:$i, X2583:$i, X2584:$i, X2585:$i, X2586:$i, X2587:$i, X2588:$i, X2589:$i, X2590:$i, X2591:$i, X2592:$i, X2593:$i, X2594:$i, X2595:$i, X2596:$i, X2597:$i, X2598:$i, X2599:$i, X2600:$i, X2601:$i, X2602:$i, X2603:$i, X2604:$i, X2605:$i, X2606:$i, X2607:$i, X2608:$i, X2609:$i, X2610:$i, X2611:$i, X2612:$i, X2613:$i, X2614:$i, X2615:$i, X2616:$i, X2617:$i, X2618:$i, X2619:$i, X2620:$i, X2621:$i, X2622:$i, X2625:$i, X2626:$i, X2627:$i, X2628:$i, X2629:$i, X2631:$i, X2632:$i, X2633:$i, X2634:$i, X2635:$i > $o, X2638:$i, X2639:$i, X2640:$i > $o, X2642:$i, X2643:$i > $o, X2644:$i, X2646:$i, X2647:$i > $o, X2650:$i, X2651:$i, X2652:$i, X2653:$i, X2654:$i, X2655:$i, X2656:$i, X2657:$i, X2658:$i, X2659:$i, X2660:$i, X2661:$i, X2662:$i, X2663:$i, X2664:$i, X2665:$i, X2666:$i, X2667:$i, X2668:$i, X2669:$i, X2670:$i, X2671:$i, X2672:$i, X2673:$i, X2674:$i, X2675:$i, X2676:$i, X2677:$i, X2678:$i, X2679:$i, X2680:$i, X2681:$i, X2682:$i, X2683:$i, X2684:$i, X2685:$i, X2686:$i, X2687:$i, X2688:$i, X2689:$i, X2690:$i, X2691:$i, X2692:$i, X2693:$i, X2694:$i, X2695:$i, X2696:$i, X2697:$i, X2698:$i, X2699:$i, X2700:$i, X2701:$i, X2702:$i, X2703:$i, X2704:$i, X2705:$i, X2706:$i, X2707:$i, X2708:$i, X2709:$i, X2710:$i, X2711:$i, X2712:$i, X2713:$i, X2714:$i, X2715:$i, X2716:$i, X2717:$i, X2718:$i, X2719:$i, X2720:$i, X2721:$i, X2722:$i > $i > $o, X2723:$i, X2724:$i, X2725:$i, X2726:$i, X2727:$i > $i > $o, X2728:$i, X2729:$i, X2730:$i > $i > $o, X2731:$i, X2732:$i, X2733:$i > $i > $o, X2734:$i, X2735:$i, X2736:$i, X2737:$i, X2738:$i > $i > $o, X2739:$i, X2740:$i, X2741:$i, X2742:$i, X2743:$i > $i > $o, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i > $i > $o, X2749:$i, X2750:$i, X2751:$i, X2752:$i, X2753:$i, X2754:$i, X2755:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2760:$i, X2761:$i, X2762:$i, X2763:$i, X2764:$i, X2765:$i, X2766:$i, X2767:$i, X2768:$i, X2769:$i, X2770:$i, X2771:$i, X2772:$i, X2773:$i, X2774:$i, X2775:$i > $i, X2777:$i, X2778:$i, X2779:$i > $i, X2781:$i, X2782:$i, X2783:$i > $i, X2785:$i, X2786:$i, X2787:$i, X2788:$i > $o, X2791:$i, X2792:$i, X2793:$i, X2794:$i, X2795:$i > $o, X2798:$i, X2799:$i, X2800:$i > $o, X2801:$i, X2802:$i, X2803:$i, X2804:$i, X2805:$i, X2806:$i, X2807:$i, X2808:$i, X2809:$i, X2810:$i, X2811:$i, X2812:$i, X2813:$i, X2814:$i, X2815:$i, X2816:$i, X2817:$i, X2818:$i, X2819:$i, X2821:$i, X2822:$i, X2823:$i, X2824:$i, X2825:$i, X2826:$i, X2827:$i, X2828:$i, X2829:$i, X2830:$i, X2831:$i, X2834:$i, X2835:$i, X2836:$i, X2837:$i, X2842:$i, X2843:$i, X2844:$i, X2845:$i, X2847:$i, X2848:$i, X2849:$i, X2850:$i, X2852:$i, X2853:$i, X2854:$i, X2855:$i, X2856:$i, X2857:$i, X2858:$i, X2859:$i, X2860:$i, X2861:$i, X2862:$i > $i, X2864:$i, X2865:$i, X2866:$i, X2867:$i, X2868:$i, X2869:$i, X2870:$i > $i, X2872:$i, X2873:$i, X2874:$i > $i, X2876:$i, X2877:$i, X2878:$i, X2879:$i, X2880:$i, X2881:$o, X2882:$i, X2883:$i, X2884:$i, X2885:$o, X2886:$i, X2887:$i, X2888:$i, X2889:$o, X2890:$i, X2891:$i, X2892:$i, X2893:$o, X2894:$i, X2895:$i, X2896:$i, X2897:$o, X2898:$i, X2899:$i, X2900:$i, X2901:$o, X2902:$i, X2903:$i, X2904:$i, X2905:$i, X2906:$i, X2907:$o, X2908:$i, X2909:$i, X2910:$i, X2911:$o, X2912:$i, X2913:$i, X2914:$i, X2915:$o, X2916:$i, X2917:$i, X2918:$i, X2919:$i, X2920:$i, X2921:$i, X2922:$i, X2923:$i, X2924:$i, X2925:$i, X2926:$i, X2927:$i, X2928:$i, X2929:$i, X2930:$i, X2931:$i, X2932:$i, X2933:$i, X2936:$i, X2937:$i, X2938:$i, X2940:$i, X2941:$i, X2942:$i, X2944:$i, X2945:$i, X2946:$i, X2947:$i, X2948:$i, X2949:$i, X2950:$i, X2951:$i, X2952:$i, X2953:$i, X2954:$i, X2955:$i, X2956:$i, X2957:$i, X2958:$i, X2959:$i, X2960:$i, X2961:$i, X2962:$i, X2963:$i, X2964:$i, X2965:$i, X2966:$i, X2967:$i, X2968:$i, X2969:$i, X2970:$i, X2971:$i, X2972:$i, X2973:$i, X2974:$i, X2975:$i, X2976:$i, X2977:$i, X2978:$i, X2979:$i, X2980:$i, X2981:$i, X2982:$i, X2983:$i, X2984:$i, X2985:$i, X2986:$i, X2987:$i, X2988:$i, X2989:$i, X2990:$i, X2991:$i, X2992:$i, X2993:$i, X2994:$i, X2995:$i, X2996:$i, X2997:$i, X2998:$i, X2999:$i, X3000:$i, X3001:$i, X3002:$i, X3003:$i, X3004:$i, X3005:$i, X3006:$i, X3007:$i, X3008:$i, X3009:$i, X3010:$i, X3011:$i, X3012:$i, X3013:$i, X3014:$i, X3015:$i, X3016:$i, X3017:$i, X3018:$i, X3019:$i, X3020:$i, X3021:$i, X3022:$i, X3023:$i, X3024:$i, X3025:$i, X3026:$i, X3027:$i, X3028:$i, X3029:$i, X3030:$i, X3031:$i, X3032:$i, X3033:$i, X3034:$i, X3035:$i, X3036:$i, X3037:$i, X3038:$i, X3039:$i, X3040:$i, X3041:$i, X3042:$i, X3043:$i, X3044:$i, X3045:$i, X3046:$i, X3047:$o, X3048:$i, X3049:$i, X3050:$i, X3051:$i, X3052:$i, X3053:$i, X3054:$i, X3055:$i, X3056:$i, X3057:$i, X3058:$i, X3059:$i, X3060:$i, X3061:$i, X3062:$i, X3063:$i, X3064:$i, X3065:$i, X3066:$i, X3067:$i, X3068:$i, X3069:$i, X3070:$i, X3071:$i, X3072:$i, X3073:$i, X3074:$i, X3075:$i, X3076:$i, X3077:$i, X3078:$i, X3079:$i, X3080:$i, X3081:$i, X3082:$i, X3083:$i, X3084:$i, X3085:$i, X3086:$i, X3087:$i, X3088:$i, X3089:$i, X3090:$i, X3091:$i, X3092:$i, X3093:$i, X3094:$i, X3095:$i, X3096:$i, X3097:$i, X3098:$i, X3099:$i, X3100:$i, X3101:$i, X3102:$i, X3103:$i, X3104:$i, X3105:$i, X3106:$i, X3107:$i, X3108:$i, X3109:$i, X3110:$i, X3111:$i, X3112:$i, X3113:$i, X3114:$i, X3115:$i, X3116:$i, X3117:$i, X3118:$i, X3119:$i, X3120:$i, X3121:$i, X3122:$i, X3123:$i, X3124:$i, X3125:$i, X3126:$i, X3127:$i, X3128:$i, X3129:$i, X3130:$i, X3131:$i > $o, X3134:$i, X3135:$i, X3136:$i, X3137:$i, X3138:$i > $i > $o, X3139:$i, X3140:$i, X3141:$i > $o, X3144:$i, X3145:$i, X3146:$i, X3147:$i, X3150:$i, X3151:$i, X3152:$i, X3157:$i, X3158:$i, X3159:$i, X3160:$i, X3161:$i, X3162:$i, X3163:$i, X3164:$i, X3165:$i, X3166:$i, X3167:$i, X3168:$i, X3169:$i, X3170:$i, X3171:$i, X3172:$i, X3173:$i, X3174:$i, X3175:$i, X3176:$i, X3177:$i, X3178:$i, X3179:$i, X3180:$i, X3182:$i, X3183:$i, X3184:$i, X3185:$i, X3186:$i, X3187:$o, X3189:$i, X3190:$i, X3191:$i, X3192:$i, X3193:$i, X3194:$i, X3195:$i, X3196:$i, X3197:$i, X3198:$i, X3199:$i, X3200:$i, X3201:$i, X3202:$i, X3203:$i, X3204:$i, X3205:$i, X3206:$i, X3207:$i, X3208:$i, X3209:$i, X3210:$i, X3211:$i, X3212:$i, X3213:$i, X3214:$i, X3215:$i, X3216:$i, X3217:$o, X3218:$i, X3219:$i, X3220:$i, X3221:$i, X3222:$i, X3223:$i, X3224:$i, X3225:$i, X3226:$i, X3227:$i, X3228:$i, X3229:$i, X3230:$i, X3231:$i, X3232:$i, X3233:$i, X3234:$i, X3235:$i > $i, X3237:$i, X3239:$i, X3240:$i, X3241:$i, X3242:$i > $i, X3244:$i, X3246:$i, X3247:$i, X3248:$i, X3250:$i, X3252:$i, X3253:$i > $i, X3254:$i, X3256:$i, X3257:$i > $i, X3258:$i, X3259:$i, X3260:$i, X3261:$i > $i, X3262:$i, X3264:$i, X3265:$i > $i, X3266:$i, X3267:$i, X3268:$i, X3269:$i, X3270:$i, X3271:$i, X3272:$i, X3273:$i]:((((~(in @ (esk1_2 @ X2201 @ X2202) @ X2201)|~(in @ (esk1_2 @ X2201 @ X2202) @ X2202)|((X2201)=(X2202)))&((in @ (esk1_2 @ X2201 @ X2202) @ X2201)|(in @ (esk1_2 @ X2201 @ X2202) @ X2202)|((X2201)=(X2202))))&(~(in @ X2204 @ emptyset)&(((~(in @ X2207 @ (setadjoin @ X2205 @ X2206))|(((X2207)=(X2205))|(in @ X2207 @ X2206)))&((((X2207)!=(X2205))|(in @ X2207 @ (setadjoin @ X2205 @ X2206)))&(~(in @ X2207 @ X2206)|(in @ X2207 @ (setadjoin @ X2205 @ X2206)))))&(((~(in @ X2209 @ (powerset @ X2208))|(~(in @ X2210 @ X2209)|(in @ X2210 @ X2208)))&(((in @ (esk2_2 @ X2211 @ X2212) @ X2212)|(in @ X2212 @ (powerset @ X2211)))&(~(in @ (esk2_2 @ X2211 @ X2212) @ X2211)|(in @ X2212 @ (powerset @ X2211)))))&(((((in @ X2215 @ (esk3_2 @ X2214 @ X2215))|~(in @ X2215 @ (setunion @ X2214)))&((in @ (esk3_2 @ X2214 @ X2215) @ X2214)|~(in @ X2215 @ (setunion @ X2214))))&(~(in @ X2218 @ X2219)|~(in @ X2219 @ X2217)|(in @ X2218 @ (setunion @ X2217))))&((in @ emptyset @ omega)&((~(in @ X2220 @ omega)|(in @ (setadjoin @ X2220 @ X2220) @ omega))&(((((in @ (esk4_1 @ X2221) @ omega)|~(in @ emptyset @ X2221)|(~(in @ X2223 @ omega)|(in @ X2223 @ X2221)))&((in @ (esk4_1 @ X2221) @ X2221)|~(in @ emptyset @ X2221)|(~(in @ X2223 @ omega)|(in @ X2223 @ X2221))))&(~(in @ (setadjoin @ (esk4_1 @ X2221) @ (esk4_1 @ X2221)) @ X2221)|~(in @ emptyset @ X2221)|(~(in @ X2223 @ omega)|(in @ X2223 @ X2221))))&((((((in @ (esk8_3 @ X2224 @ X2225 @ X2230) @ X2225)|~(in @ X2230 @ (esk7_2 @ X2224 @ X2225))|(in @ (esk5_2 @ X2224 @ X2225) @ X2225))&((X2224 @ (esk8_3 @ X2224 @ X2225 @ X2230) @ X2230)|~(in @ X2230 @ (esk7_2 @ X2224 @ X2225))|(in @ (esk5_2 @ X2224 @ X2225) @ X2225)))&(~(in @ X2233 @ X2225)|~(X2224 @ X2233 @ X2232)|(in @ X2232 @ (esk7_2 @ X2224 @ X2225))|(in @ (esk5_2 @ X2224 @ X2225) @ X2225)))&(((((in @ (esk8_3 @ X2224 @ X2225 @ X2230) @ X2225)|~(in @ X2230 @ (esk7_2 @ X2224 @ X2225))|((X2224 @ (esk5_2 @ X2224 @ X2225) @ (esk6_3 @ X2224 @ X2225 @ X2227))|~(X2224 @ (esk5_2 @ X2224 @ X2225) @ X2227)))&((X2224 @ (esk8_3 @ X2224 @ X2225 @ X2230) @ X2230)|~(in @ X2230 @ (esk7_2 @ X2224 @ X2225))|((X2224 @ (esk5_2 @ X2224 @ X2225) @ (esk6_3 @ X2224 @ X2225 @ X2227))|~(X2224 @ (esk5_2 @ X2224 @ X2225) @ X2227))))&(~(in @ X2233 @ X2225)|~(X2224 @ X2233 @ X2232)|(in @ X2232 @ (esk7_2 @ X2224 @ X2225))|((X2224 @ (esk5_2 @ X2224 @ X2225) @ (esk6_3 @ X2224 @ X2225 @ X2227))|~(X2224 @ (esk5_2 @ X2224 @ X2225) @ X2227))))&((((in @ (esk8_3 @ X2224 @ X2225 @ X2230) @ X2225)|~(in @ X2230 @ (esk7_2 @ X2224 @ X2225))|(((X2227)!=(esk6_3 @ X2224 @ X2225 @ X2227))|~(X2224 @ (esk5_2 @ X2224 @ X2225) @ X2227)))&((X2224 @ (esk8_3 @ X2224 @ X2225 @ X2230) @ X2230)|~(in @ X2230 @ (esk7_2 @ X2224 @ X2225))|(((X2227)!=(esk6_3 @ X2224 @ X2225 @ X2227))|~(X2224 @ (esk5_2 @ X2224 @ X2225) @ X2227))))&(~(in @ X2233 @ X2225)|~(X2224 @ X2233 @ X2232)|(in @ X2232 @ (esk7_2 @ X2224 @ X2225))|(((X2227)!=(esk6_3 @ X2224 @ X2225 @ X2227))|~(X2224 @ (esk5_2 @ X2224 @ X2225) @ X2227))))))&((((in @ (esk9_1 @ X2234) @ X2234)|~(in @ X2235 @ X2234))&(~(in @ X2237 @ (esk9_1 @ X2234))|~(in @ X2237 @ X2234)|~(in @ X2235 @ X2234)))&((epred1_0)&((((X2238 @ (esk10_2 @ X2238 @ X2239))|~(X2238 @ X2239)|(X2238 @ (descr @ (^[Z0/* 3 */:$i]:((X2238 @ Z0))))))&(((X2239)!=(esk10_2 @ X2238 @ X2239))|~(X2238 @ X2239)|(X2238 @ (descr @ (^[Z0/* 3 */:$i]:((X2238 @ Z0)))))))&((~(in @ X2243 @ X2241)|(~(X2242 @ X2243)|(in @ X2243 @ (dsetconstr @ X2241 @ (^[Z0/* 3 */:$i]:((X2242 @ Z0)))))))&((~(in @ X2246 @ (dsetconstr @ X2244 @ (^[Z0/* 3 */:$i]:((X2245 @ Z0)))))|(in @ X2246 @ X2244))&((~(in @ X2249 @ (dsetconstr @ X2247 @ (^[Z0/* 3 */:$i]:((X2248 @ Z0)))))|(X2248 @ X2249))&(((((X2250 @ (esk12_1 @ X2250))|((X2250 @ (esk11_2 @ X2250 @ X2251))|~(X2250 @ X2251)))&(~(X2250 @ X2254)|((esk12_1 @ X2250)=(X2254))|((X2250 @ (esk11_2 @ X2250 @ X2251))|~(X2250 @ X2251))))&(((X2250 @ (esk12_1 @ X2250))|(((X2251)!=(esk11_2 @ X2250 @ X2251))|~(X2250 @ 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(dpsetconstr @ X3137 @ X3137 @ (^[Z0/* 19 */:$i, Z1:$i]:((X3138 @ Z0 @ Z1)))))&((((in @ (esk89_3 @ X3139 @ X3140 @ X3141) @ X3139)|(~(in @ X3144 @ X3140)|(X3141 @ X3144))|~(breln1 @ X3139 @ X3140))&(((in @ (esk90_3 @ X3139 @ X3140 @ X3141) @ X3139)|(~(in @ X3144 @ X3140)|(X3141 @ X3144))|~(breln1 @ X3139 @ X3140))&(((in @ (kpair @ (esk89_3 @ X3139 @ X3140 @ X3141) @ (esk90_3 @ X3139 @ X3140 @ X3141)) @ X3140)|(~(in @ X3144 @ X3140)|(X3141 @ X3144))|~(breln1 @ X3139 @ X3140))&(~(X3141 @ (kpair @ (esk89_3 @ X3139 @ X3140 @ X3141) @ (esk90_3 @ X3139 @ X3140 @ X3141)))|(~(in @ X3144 @ X3140)|(X3141 @ X3144))|~(breln1 @ X3139 @ X3140)))))&((((in @ (esk91_3 @ X3145 @ X3146 @ X3147) @ X3145)|(subset @ X3146 @ X3147)|~(breln1 @ X3145 @ X3147)|~(breln1 @ X3145 @ X3146))&(((in @ (esk92_3 @ X3145 @ X3146 @ X3147) @ X3145)|(subset @ X3146 @ X3147)|~(breln1 @ X3145 @ X3147)|~(breln1 @ X3145 @ X3146))&(((in @ (kpair @ (esk91_3 @ X3145 @ X3146 @ X3147) @ (esk92_3 @ X3145 @ X3146 @ X3147)) @ X3146)|(subset @ X3146 @ X3147)|~(breln1 @ X3145 @ X3147)|~(breln1 @ X3145 @ X3146))&(~(in @ (kpair @ (esk91_3 @ X3145 @ X3146 @ X3147) @ (esk92_3 @ X3145 @ X3146 @ X3147)) @ X3147)|(subset @ X3146 @ X3147)|~(breln1 @ X3145 @ X3147)|~(breln1 @ X3145 @ X3146)))))&(((((in @ (esk95_3 @ X3150 @ X3151 @ X3152) @ X3150)|((X3151)=(X3152))|(in @ (esk93_3 @ X3150 @ X3151 @ X3152) @ X3150)|~(breln1 @ X3150 @ X3152)|~(breln1 @ X3150 @ X3151))&(((in @ (esk96_3 @ X3150 @ X3151 @ X3152) @ X3150)|((X3151)=(X3152))|(in @ (esk93_3 @ X3150 @ X3151 @ X3152) @ X3150)|~(breln1 @ X3150 @ X3152)|~(breln1 @ X3150 @ X3151))&(((in @ (kpair @ (esk95_3 @ X3150 @ X3151 @ X3152) @ (esk96_3 @ X3150 @ X3151 @ X3152)) @ X3152)|((X3151)=(X3152))|(in @ (esk93_3 @ X3150 @ X3151 @ X3152) @ X3150)|~(breln1 @ X3150 @ X3152)|~(breln1 @ X3150 @ X3151))&(~(in @ (kpair @ (esk95_3 @ X3150 @ X3151 @ X3152) @ (esk96_3 @ X3150 @ X3151 @ X3152)) @ X3151)|((X3151)=(X3152))|(in @ (esk93_3 @ X3150 @ X3151 @ X3152) @ X3150)|~(breln1 @ X3150 @ X3152)|~(breln1 @ X3150 @ X3151)))))&((((in @ (esk95_3 @ X3150 @ X3151 @ X3152) @ X3150)|((X3151)=(X3152))|(in @ (esk94_3 @ X3150 @ X3151 @ X3152) @ X3150)|~(breln1 @ X3150 @ X3152)|~(breln1 @ X3150 @ X3151))&(((in @ (esk96_3 @ X3150 @ X3151 @ X3152) @ X3150)|((X3151)=(X3152))|(in @ (esk94_3 @ X3150 @ X3151 @ X3152) @ X3150)|~(breln1 @ X3150 @ X3152)|~(breln1 @ X3150 @ X3151))&(((in @ (kpair @ (esk95_3 @ X3150 @ X3151 @ X3152) @ (esk96_3 @ X3150 @ X3151 @ X3152)) @ X3152)|((X3151)=(X3152))|(in @ (esk94_3 @ X3150 @ X3151 @ X3152) @ X3150)|~(breln1 @ X3150 @ X3152)|~(breln1 @ X3150 @ X3151))&(~(in @ (kpair @ (esk95_3 @ X3150 @ X3151 @ X3152) @ (esk96_3 @ X3150 @ X3151 @ X3152)) @ X3151)|((X3151)=(X3152))|(in @ (esk94_3 @ X3150 @ X3151 @ X3152) @ X3150)|~(breln1 @ X3150 @ X3152)|~(breln1 @ X3150 @ X3151)))))&((((in @ (esk95_3 @ X3150 @ X3151 @ X3152) @ X3150)|((X3151)=(X3152))|(in @ (kpair @ (esk93_3 @ X3150 @ X3151 @ X3152) @ (esk94_3 @ X3150 @ X3151 @ X3152)) @ X3151)|~(breln1 @ X3150 @ X3152)|~(breln1 @ X3150 @ X3151))&(((in @ (esk96_3 @ X3150 @ X3151 @ X3152) @ X3150)|((X3151)=(X3152))|(in @ (kpair @ (esk93_3 @ X3150 @ X3151 @ X3152) @ (esk94_3 @ X3150 @ X3151 @ X3152)) @ X3151)|~(breln1 @ X3150 @ X3152)|~(breln1 @ X3150 @ X3151))&(((in @ (kpair @ (esk95_3 @ X3150 @ X3151 @ X3152) @ (esk96_3 @ X3150 @ X3151 @ X3152)) @ X3152)|((X3151)=(X3152))|(in @ (kpair @ (esk93_3 @ X3150 @ X3151 @ X3152) @ (esk94_3 @ X3150 @ X3151 @ X3152)) @ X3151)|~(breln1 @ X3150 @ X3152)|~(breln1 @ X3150 @ X3151))&(~(in @ (kpair @ (esk95_3 @ X3150 @ X3151 @ X3152) @ (esk96_3 @ X3150 @ X3151 @ X3152)) @ X3151)|((X3151)=(X3152))|(in @ (kpair @ (esk93_3 @ X3150 @ X3151 @ X3152) @ (esk94_3 @ X3150 @ X3151 @ X3152)) @ X3151)|~(breln1 @ X3150 @ X3152)|~(breln1 @ X3150 @ X3151)))))&(((in @ (esk95_3 @ X3150 @ X3151 @ X3152) @ X3150)|((X3151)=(X3152))|~(in @ (kpair @ (esk93_3 @ X3150 @ X3151 @ X3152) @ (esk94_3 @ X3150 @ X3151 @ X3152)) @ X3152)|~(breln1 @ X3150 @ X3152)|~(breln1 @ X3150 @ X3151))&(((in @ (esk96_3 @ X3150 @ X3151 @ X3152) @ X3150)|((X3151)=(X3152))|~(in @ (kpair @ (esk93_3 @ X3150 @ X3151 @ X3152) @ (esk94_3 @ X3150 @ X3151 @ X3152)) @ X3152)|~(breln1 @ X3150 @ X3152)|~(breln1 @ X3150 @ X3151))&(((in @ (kpair @ (esk95_3 @ X3150 @ X3151 @ X3152) @ (esk96_3 @ X3150 @ X3151 @ X3152)) @ X3152)|((X3151)=(X3152))|~(in @ (kpair @ (esk93_3 @ X3150 @ X3151 @ X3152) @ (esk94_3 @ X3150 @ X3151 @ X3152)) @ X3152)|~(breln1 @ X3150 @ X3152)|~(breln1 @ X3150 @ X3151))&(~(in @ (kpair @ (esk95_3 @ X3150 @ X3151 @ X3152) @ (esk96_3 @ X3150 @ X3151 @ X3152)) @ X3151)|((X3151)=(X3152))|~(in @ (kpair @ (esk93_3 @ X3150 @ X3151 @ X3152) @ (esk94_3 @ X3150 @ X3151 @ X3152)) @ X3152)|~(breln1 @ X3150 @ X3152)|~(breln1 @ X3150 @ X3151))))))))&((~(breln1 @ X3157 @ X3158)|(breln1 @ X3157 @ (breln1invset @ X3157 @ X3158)))&((~(breln1 @ X3159 @ X3160)|(~(in @ X3161 @ X3159)|(~(in @ X3162 @ X3159)|(~(in @ (kpair @ X3161 @ X3162) @ X3160)|(in @ (kpair @ X3162 @ X3161) @ (breln1invset @ X3159 @ X3160))))))&((~(breln1 @ X3163 @ X3164)|(~(in @ X3165 @ X3163)|(~(in @ X3166 @ X3163)|(~(in @ (kpair @ X3166 @ X3165) @ (breln1invset @ X3163 @ X3164))|(in @ (kpair @ X3165 @ X3166) @ X3164)))))&((~(breln1 @ X3167 @ X3168)|(~(breln1 @ X3167 @ X3169)|(breln1 @ X3167 @ (breln1compset @ X3167 @ X3168 @ X3169))))&((~(breln1 @ X3170 @ X3171)|(~(breln1 @ X3170 @ X3172)|(~(in @ X3173 @ X3170)|(~(in @ X3174 @ X3170)|(~(in @ X3175 @ X3170)|(~(in @ (kpair @ X3173 @ X3175) @ X3171)|(~(in @ (kpair @ X3175 @ X3174) @ X3172)|(in @ (kpair @ X3173 @ X3174) @ (breln1compset @ X3170 @ X3171 @ X3172)))))))))&(((((in @ (esk97_5 @ X3176 @ X3177 @ X3178 @ X3179 @ X3180) @ X3176)|~(in @ (kpair @ X3179 @ X3180) @ (breln1compset @ X3176 @ X3177 @ X3178))|~(in @ X3180 @ X3176)|~(in @ X3179 @ X3176)|~(breln1 @ X3176 @ X3178)|~(breln1 @ X3176 @ X3177))&((in @ (kpair @ X3179 @ (esk97_5 @ X3176 @ X3177 @ X3178 @ X3179 @ X3180)) @ X3177)|~(in @ (kpair @ X3179 @ X3180) @ (breln1compset @ X3176 @ X3177 @ X3178))|~(in @ X3180 @ X3176)|~(in @ X3179 @ X3176)|~(breln1 @ X3176 @ X3178)|~(breln1 @ X3176 @ X3177)))&((in @ (kpair @ (esk97_5 @ X3176 @ X3177 @ X3178 @ X3179 @ X3180) @ X3180) @ X3178)|~(in @ (kpair @ X3179 @ X3180) @ (breln1compset @ X3176 @ X3177 @ X3178))|~(in @ X3180 @ X3176)|~(in @ X3179 @ X3176)|~(breln1 @ X3176 @ X3178)|~(breln1 @ X3176 @ X3177)))&((((in @ (esk98_6 @ X3182 @ X3183 @ X3184 @ X3185 @ X3186 @ X3187) @ X3182)|(X3187)|~(in @ (kpair @ X3185 @ X3186) @ (breln1compset @ X3182 @ X3183 @ X3184))|~(in @ X3186 @ X3182)|~(in @ X3185 @ X3182)|~(breln1 @ X3182 @ X3184)|~(breln1 @ X3182 @ X3183))&(((in @ (kpair @ X3185 @ (esk98_6 @ X3182 @ X3183 @ X3184 @ X3185 @ X3186 @ X3187)) @ X3183)|(X3187)|~(in @ (kpair @ X3185 @ X3186) @ (breln1compset @ X3182 @ X3183 @ X3184))|~(in @ X3186 @ X3182)|~(in @ X3185 @ X3182)|~(breln1 @ X3182 @ X3184)|~(breln1 @ X3182 @ X3183))&(((in @ (kpair @ (esk98_6 @ X3182 @ X3183 @ X3184 @ X3185 @ X3186 @ X3187) @ X3186) @ X3184)|(X3187)|~(in @ (kpair @ X3185 @ X3186) @ (breln1compset @ X3182 @ X3183 @ X3184))|~(in @ X3186 @ X3182)|~(in @ X3185 @ X3182)|~(breln1 @ X3182 @ X3184)|~(breln1 @ X3182 @ X3183))&(~(X3187)|(X3187)|~(in @ (kpair @ X3185 @ X3186) @ (breln1compset @ X3182 @ X3183 @ X3184))|~(in @ X3186 @ X3182)|~(in @ X3185 @ X3182)|~(breln1 @ X3182 @ X3184)|~(breln1 @ X3182 @ X3183)))))&((~(breln1 @ X3189 @ X3190)|(~(breln1 @ X3189 @ X3191)|(breln1 @ X3189 @ (binunion @ X3190 @ X3191))))&((~(breln1 @ X3192 @ X3193)|(~(breln1 @ X3192 @ X3194)|(~(in @ X3195 @ X3192)|(~(in @ X3196 @ X3192)|(~(in @ (kpair @ X3195 @ X3196) @ X3193)|(in @ (kpair @ X3195 @ X3196) @ (binunion @ X3193 @ X3194)))))))&((~(breln1 @ X3197 @ X3198)|(~(breln1 @ X3197 @ X3199)|(~(in @ X3200 @ X3197)|(~(in @ X3201 @ X3197)|(~(in @ (kpair @ X3200 @ X3201) @ X3199)|(in @ (kpair @ X3200 @ X3201) @ (binunion @ X3198 @ X3199)))))))&(((~(in @ (kpair @ X3205 @ X3206) @ X3203)|(in @ (kpair @ X3205 @ X3206) @ (binunion @ X3203 @ X3204))|~(in @ X3206 @ X3202)|~(in @ X3205 @ X3202)|~(breln1 @ X3202 @ X3204)|~(breln1 @ X3202 @ X3203))&(~(in @ (kpair @ X3205 @ X3206) @ X3204)|(in @ (kpair @ X3205 @ X3206) @ (binunion @ X3203 @ X3204))|~(in @ X3206 @ X3202)|~(in @ X3205 @ X3202)|~(breln1 @ X3202 @ X3204)|~(breln1 @ X3202 @ X3203)))&((~(breln1 @ X3207 @ X3208)|(~(breln1 @ X3207 @ X3209)|(~(in @ X3210 @ X3207)|(~(in @ X3211 @ X3207)|(~(in @ (kpair @ X3210 @ X3211) @ (binunion @ X3208 @ X3209))|((in @ (kpair @ X3210 @ X3211) @ X3208)|(in @ (kpair @ X3210 @ X3211) @ X3209)))))))&(((((in @ (kpair @ X3215 @ X3216) @ X3214)|(X3217)|(in @ (kpair @ X3215 @ X3216) @ X3213)|~(in @ (kpair @ X3215 @ X3216) @ (binunion @ X3213 @ X3214))|~(in @ X3216 @ X3212)|~(in @ X3215 @ X3212)|~(breln1 @ X3212 @ X3214)|~(breln1 @ X3212 @ X3213))&(~(X3217)|(X3217)|(in @ (kpair @ X3215 @ X3216) @ X3213)|~(in @ (kpair @ X3215 @ X3216) @ (binunion @ X3213 @ X3214))|~(in @ X3216 @ X3212)|~(in @ X3215 @ X3212)|~(breln1 @ X3212 @ X3214)|~(breln1 @ X3212 @ X3213)))&(((in @ (kpair @ X3215 @ X3216) @ X3214)|(X3217)|~(X3217)|~(in @ (kpair @ X3215 @ X3216) @ (binunion @ X3213 @ X3214))|~(in @ X3216 @ X3212)|~(in @ X3215 @ X3212)|~(breln1 @ X3212 @ X3214)|~(breln1 @ X3212 @ X3213))&(~(X3217)|(X3217)|~(X3217)|~(in @ (kpair @ X3215 @ X3216) @ (binunion @ X3213 @ X3214))|~(in @ X3216 @ X3212)|~(in @ X3215 @ X3212)|~(breln1 @ X3212 @ X3214)|~(breln1 @ X3212 @ X3213))))&((~(breln1 @ X3218 @ X3219)|(~(breln1 @ X3218 @ X3220)|((binunion @ X3219 @ X3220)=(binunion @ X3220 @ X3219))))&((~(breln1 @ X3221 @ X3222)|((X3222)=(breln1invset @ X3221 @ (breln1invset @ X3221 @ X3222))))&((~(breln1 @ X3223 @ X3224)|(~(breln1 @ X3223 @ X3225)|((breln1invset @ X3223 @ (breln1compset @ X3223 @ X3224 @ X3225))=(breln1compset @ X3223 @ (breln1invset @ X3223 @ X3225) @ (breln1invset @ X3223 @ X3224)))))&((~(breln1 @ X3226 @ X3227)|(~(breln1 @ X3226 @ X3228)|(~(breln1 @ X3226 @ X3229)|((breln1compset @ X3226 @ (binunion @ X3227 @ X3228) @ X3229)=(binunion @ (breln1compset @ X3226 @ X3227 @ X3229) @ (breln1compset @ X3226 @ X3228 @ X3229))))))&((~(breln1 @ X3230 @ X3231)|(~(breln1 @ X3230 @ X3232)|(~(breln1 @ X3230 @ X3233)|((breln1compset @ X3230 @ (binunion @ X3231 @ X3232) @ X3233)=(binunion @ (breln1invset @ X3230 @ (breln1compset @ X3230 @ (breln1invset @ X3230 @ X3233) @ (breln1invset @ X3230 @ X3232))) @ (breln1invset @ X3230 @ (breln1compset @ X3230 @ (breln1invset @ X3230 @ X3233) @ (breln1invset @ X3230 @ X3231))))))))&(((((in @ (esk100_3 @ X3234 @ X3235 @ X3237) @ X3234)|~(in @ X3237 @ (esk99_2 @ X3234 @ X3235)))&(((X3237)=(X3235 @ (esk100_3 @ X3234 @ X3235 @ X3237)))|~(in @ X3237 @ (esk99_2 @ X3234 @ X3235))))&(~(in @ X3240 @ X3234)|((X3239)!=(X3235 @ X3240))|(in @ X3239 @ (esk99_2 @ X3234 @ X3235))))&((((((in @ (esk102_3 @ X3241 @ X3242 @ X3244) @ X3241)|~(in @ X3244 @ (esk101_2 @ X3241 @ X3242)))&(((X3244)=(X3242 @ (esk102_3 @ X3241 @ X3242 @ X3244)))|~(in @ X3244 @ (esk101_2 @ X3241 @ X3242))))&(~(in @ X3247 @ X3241)|((X3246)!=(X3242 @ X3247))|(in @ X3246 @ (esk101_2 @ X3241 @ X3242))))&((~(in @ (esk103_3 @ X3241 @ X3242 @ X3248) @ X3248)|(~(in @ X3250 @ X3241)|((esk103_3 @ X3241 @ X3242 @ X3248)!=(X3242 @ X3250)))|((esk101_2 @ X3241 @ X3242)=(X3248)))&(((in @ (esk104_3 @ X3241 @ X3242 @ X3248) @ X3241)|(in @ (esk103_3 @ X3241 @ X3242 @ X3248) @ X3248)|((esk101_2 @ X3241 @ X3242)=(X3248)))&(((esk103_3 @ X3241 @ X3242 @ X3248)=(X3242 @ (esk104_3 @ X3241 @ X3242 @ X3248)))|(in @ (esk103_3 @ X3241 @ X3242 @ X3248) @ X3248)|((esk101_2 @ X3241 @ X3242)=(X3248))))))&(((((in @ (esk105_3 @ X3252 @ X3253 @ X3254) @ X3252)|~(in @ X3254 @ (image1 @ X3252 @ X3253)))&(((X3254)=(X3253 @ (esk105_3 @ X3252 @ X3253 @ X3254)))|~(in @ X3254 @ (image1 @ X3252 @ X3253))))&(~(in @ X3259 @ X3256)|((X3258)!=(X3257 @ X3259))|(in @ X3258 @ (image1 @ X3256 @ X3257))))&((((in @ (esk106_3 @ X3260 @ X3261 @ X3262) @ X3260)|~(in @ X3262 @ (image1 @ X3260 @ X3261)))&(((X3262)=(X3261 @ (esk106_3 @ X3260 @ X3261 @ X3262)))|~(in @ X3262 @ (image1 @ X3260 @ X3261))))&((~(in @ X3267 @ X3264)|((X3266)!=(X3265 @ X3267))|(in @ X3266 @ (image1 @ X3264 @ X3265)))&((~(in @ X3270 @ (funcSet @ X3268 @ X3269))|(~(injective @ X3268 @ X3269 @ X3270)|(in @ X3270 @ (dsetconstr @ (funcSet @ X3268 @ X3269) @ (^[Z0/* 3 */:$i]:((injective @ X3268 @ X3269 @ Z0)))))))&((~(in @ X3273 @ (dsetconstr @ (funcSet @ X3271 @ X3272) @ (^[Z0/* 3 */:$i]:((injective @ X3271 @ X3272 @ Z0)))))|(in @ X3273 @ (funcSet @ X3271 @ X3272)))&((in @ esk109_0 @ (dsetconstr @ (funcSet @ esk107_0 @ esk108_0) @ (^[Z0/* 3 */:$i]:((injective @ esk107_0 @ esk108_0 @ Z0)))))&~(injective @ esk107_0 @ esk108_0 @ esk109_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_397])])])])])])).
2.01/0.65	thf(c_0_399, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((X1 @ X2)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_398])).
2.01/0.65	thf(c_0_400, negated_conjecture, (in @ esk109_0 @ (dsetconstr @ (funcSet @ esk107_0 @ esk108_0) @ (injective @ esk107_0 @ esk108_0))), inference(split_conjunct,[status(thm)],[c_0_398])).
2.01/0.65	thf(c_0_401, negated_conjecture, ~((injective @ esk107_0 @ esk108_0 @ esk109_0)), inference(split_conjunct,[status(thm)],[c_0_398])).
2.01/0.65	thf(c_0_402, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_399, c_0_400]), c_0_401]), ['proof']).
2.01/0.65	# SZS output end CNFRefutation
2.01/0.65	# Parsed axioms                        : 687
2.01/0.65	# Removed by relevancy pruning/SinE    : 369
2.01/0.65	# Initial clauses                      : 544
2.01/0.65	# Removed in clause preprocessing      : 35
2.01/0.65	# Initial clauses in saturation        : 509
2.01/0.65	# Processed clauses                    : 589
2.01/0.65	# ...of these trivial                  : 9
2.01/0.65	# ...subsumed                          : 52
2.01/0.65	# ...remaining for further processing  : 528
2.01/0.65	# Other redundant clauses eliminated   : 22
2.01/0.65	# Clauses deleted for lack of memory   : 0
2.01/0.65	# Backward-subsumed                    : 2
2.01/0.65	# Backward-rewritten                   : 1
2.01/0.65	# Generated clauses                    : 160
2.01/0.65	# ...of the previous two non-redundant : 131
2.01/0.65	# ...aggressively subsumed             : 0
2.01/0.65	# Contextual simplify-reflections      : 14
2.01/0.65	# Paramodulations                      : 132
2.01/0.65	# Factorizations                       : 0
2.01/0.65	# NegExts                              : 0
2.01/0.65	# Equation resolutions                 : 25
2.01/0.65	# Total rewrite steps                  : 42
2.01/0.65	# Propositional unsat checks           : 0
2.01/0.65	#    Propositional check models        : 0
2.01/0.65	#    Propositional check unsatisfiable : 0
2.01/0.65	#    Propositional clauses             : 0
2.01/0.65	#    Propositional clauses after purity: 0
2.01/0.65	#    Propositional unsat core size     : 0
2.01/0.65	#    Propositional preprocessing time  : 0.000
2.01/0.65	#    Propositional encoding time       : 0.000
2.01/0.65	#    Propositional solver time         : 0.000
2.01/0.65	#    Success case prop preproc time    : 0.000
2.01/0.65	#    Success case prop encoding time   : 0.000
2.01/0.65	#    Success case prop solver time     : 0.000
2.01/0.65	# Current number of processed clauses  : 66
2.01/0.65	#    Positive orientable unit clauses  : 28
2.01/0.65	#    Positive unorientable unit clauses: 0
2.01/0.65	#    Negative unit clauses             : 3
2.01/0.65	#    Non-unit-clauses                  : 35
2.01/0.65	# Current number of unprocessed clauses: 491
2.01/0.65	# ...number of literals in the above   : 1677
2.01/0.65	# Current number of archived formulas  : 0
2.01/0.65	# Current number of archived clauses   : 443
2.01/0.65	# Clause-clause subsumption calls (NU) : 48267
2.01/0.65	# Rec. Clause-clause subsumption calls : 13687
2.01/0.65	# Non-unit clause-clause subsumptions  : 63
2.01/0.65	# Unit Clause-clause subsumption calls : 151
2.01/0.65	# Rewrite failures with RHS unbound    : 0
2.01/0.65	# BW rewrite match attempts            : 22
2.01/0.65	# BW rewrite match successes           : 1
2.01/0.65	# Condensation attempts                : 0
2.01/0.65	# Condensation successes               : 0
2.01/0.65	# Termbank termtop insertions          : 100154
2.01/0.65	
2.01/0.65	# -------------------------------------------------
2.01/0.65	# User time                : 0.212 s
2.01/0.65	# System time              : 0.027 s
2.01/0.65	# Total time               : 0.239 s
2.01/0.65	# Maximum resident set size: 10248 pages
2.01/0.67	
2.01/0.67	# -------------------------------------------------
2.01/0.67	# User time                : 0.221 s
2.01/0.67	# System time              : 0.030 s
2.01/0.67	# Total time               : 0.251 s
2.01/0.67	# Maximum resident set size: 2888 pages
2.01/0.68	% E---3.1 exiting
2.01/0.68	EOF