0.11/0.16	% Problem    : Vampire---4.8_20603 : TPTP v0.0.0. Released v0.0.0.
0.11/0.17	% Command    : run_E %s %d THM
0.16/0.38	% Computer : n013.cluster.edu
0.16/0.38	% Model    : x86_64 x86_64
0.16/0.38	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.16/0.38	% Memory   : 8042.1875MB
0.16/0.38	% OS       : Linux 3.10.0-693.el7.x86_64
0.16/0.38	% CPULimit   : 1440
0.16/0.38	% WCLimit    : 180
0.16/0.38	% DateTime   : Mon Jul  3 12:45:32 EDT 2023
0.16/0.38	% CPUTime    : 
0.23/0.55	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.r75cfSlgae/Vampire---4.8_20603
0.23/0.55	# Version: 3.1pre001-ho
0.39/0.64	# Preprocessing class: HSLMSLSSLLLCHSA.
0.39/0.64	# Scheduled 5 strats onto 8 cores with 180 seconds (1440 total)
0.39/0.64	# Starting ho_unfolding_5 with 720s (4) cores
0.39/0.64	# Starting pre_casc_3 with 180s (1) cores
0.39/0.64	# Starting new_ho_10_cnf2 with 180s (1) cores
0.39/0.64	# Starting full_lambda_10 with 180s (1) cores
0.39/0.64	# Starting ehoh_best_nonlift_rwall with 180s (1) cores
0.39/0.64	# full_lambda_10 with pid 20784 completed with status 0
0.39/0.64	# Result found by full_lambda_10
0.39/0.64	# Preprocessing class: HSLMSLSSLLLCHSA.
0.39/0.64	# Scheduled 5 strats onto 8 cores with 180 seconds (1440 total)
0.39/0.64	# Starting ho_unfolding_5 with 720s (4) cores
0.39/0.64	# Starting pre_casc_3 with 180s (1) cores
0.39/0.64	# Starting new_ho_10_cnf2 with 180s (1) cores
0.39/0.64	# Starting full_lambda_10 with 180s (1) cores
0.39/0.64	# SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
0.39/0.64	# Search class: HGHSM-FSLM32-DHSMMSBN
0.39/0.64	# partial match(1): HGHSM-FSLM32-MHSMMSBN
0.39/0.64	# Scheduled 12 strats onto 1 cores with 180 seconds (180 total)
0.39/0.64	# Starting full_lambda_5 with 15s (1) cores
0.39/0.64	# full_lambda_5 with pid 20786 completed with status 0
0.39/0.64	# Result found by full_lambda_5
0.39/0.64	# Preprocessing class: HSLMSLSSLLLCHSA.
0.39/0.64	# Scheduled 5 strats onto 8 cores with 180 seconds (1440 total)
0.39/0.64	# Starting ho_unfolding_5 with 720s (4) cores
0.39/0.64	# Starting pre_casc_3 with 180s (1) cores
0.39/0.64	# Starting new_ho_10_cnf2 with 180s (1) cores
0.39/0.64	# Starting full_lambda_10 with 180s (1) cores
0.39/0.64	# SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
0.39/0.64	# Search class: HGHSM-FSLM32-DHSMMSBN
0.39/0.64	# partial match(1): HGHSM-FSLM32-MHSMMSBN
0.39/0.64	# Scheduled 12 strats onto 1 cores with 180 seconds (180 total)
0.39/0.64	# Starting full_lambda_5 with 15s (1) cores
0.39/0.64	# Preprocessing time       : 0.009 s
0.39/0.64	# Presaturation interreduction done
0.39/0.64	
0.39/0.64	# Proof found!
0.39/0.64	# SZS status Theorem
0.39/0.64	# SZS output start CNFRefutation
0.39/0.64	thf(decl_22, type, in: $i > $i > $o).
0.39/0.64	thf(decl_23, type, exu: ($i > $o) > $o).
0.39/0.64	thf(decl_24, type, setextAx: $o).
0.39/0.64	thf(decl_25, type, emptyset: $i).
0.39/0.64	thf(decl_26, type, emptysetAx: $o).
0.39/0.64	thf(decl_27, type, setadjoin: $i > $i > $i).
0.39/0.64	thf(decl_28, type, setadjoinAx: $o).
0.39/0.64	thf(decl_29, type, powerset: $i > $i).
0.39/0.64	thf(decl_30, type, powersetAx: $o).
0.39/0.64	thf(decl_31, type, setunion: $i > $i).
0.39/0.64	thf(decl_32, type, setunionAx: $o).
0.39/0.64	thf(decl_33, type, omega: $i).
0.39/0.64	thf(decl_34, type, omega0Ax: $o).
0.39/0.64	thf(decl_35, type, omegaSAx: $o).
0.39/0.64	thf(decl_36, type, omegaIndAx: $o).
0.39/0.64	thf(decl_37, type, replAx: $o).
0.39/0.64	thf(decl_38, type, foundationAx: $o).
0.39/0.64	thf(decl_39, type, wellorderingAx: $o).
0.39/0.64	thf(decl_40, type, descr: ($i > $o) > $i).
0.39/0.64	thf(decl_41, type, descrp: $o).
0.39/0.64	thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
0.39/0.64	thf(decl_43, type, dsetconstrI: $o).
0.39/0.64	thf(decl_44, type, dsetconstrEL: $o).
0.39/0.64	thf(decl_45, type, dsetconstrER: $o).
0.39/0.64	thf(decl_46, type, exuE1: $o).
0.39/0.64	thf(decl_47, type, prop2set: $o > $i).
0.39/0.64	thf(decl_48, type, prop2setE: $o).
0.39/0.64	thf(decl_49, type, emptysetE: $o).
0.39/0.64	thf(decl_50, type, emptysetimpfalse: $o).
0.39/0.64	thf(decl_51, type, notinemptyset: $o).
0.39/0.64	thf(decl_52, type, exuE3e: $o).
0.39/0.64	thf(decl_53, type, setext: $o).
0.39/0.64	thf(decl_54, type, emptyI: $o).
0.39/0.64	thf(decl_55, type, noeltsimpempty: $o).
0.39/0.64	thf(decl_56, type, setbeta: $o).
0.39/0.64	thf(decl_57, type, nonempty: $i > $o).
0.39/0.64	thf(decl_58, type, nonemptyE1: $o).
0.39/0.64	thf(decl_59, type, nonemptyI: $o).
0.39/0.64	thf(decl_60, type, nonemptyI1: $o).
0.39/0.64	thf(decl_61, type, setadjoinIL: $o).
0.39/0.64	thf(decl_62, type, emptyinunitempty: $o).
0.39/0.64	thf(decl_63, type, setadjoinIR: $o).
0.39/0.64	thf(decl_64, type, setadjoinE: $o).
0.39/0.64	thf(decl_65, type, setadjoinOr: $o).
0.39/0.64	thf(decl_66, type, setoftrueEq: $o).
0.39/0.64	thf(decl_67, type, powersetI: $o).
0.39/0.64	thf(decl_68, type, emptyinPowerset: $o).
0.39/0.64	thf(decl_69, type, emptyInPowerset: $o).
0.39/0.64	thf(decl_70, type, powersetE: $o).
0.39/0.64	thf(decl_71, type, setunionI: $o).
0.39/0.64	thf(decl_72, type, setunionE: $o).
0.39/0.64	thf(decl_73, type, subPowSU: $o).
0.39/0.64	thf(decl_74, type, exuE2: $o).
0.39/0.64	thf(decl_75, type, nonemptyImpWitness: $o).
0.39/0.64	thf(decl_76, type, uniqinunit: $o).
0.39/0.64	thf(decl_77, type, notinsingleton: $o).
0.39/0.64	thf(decl_78, type, eqinunit: $o).
0.39/0.64	thf(decl_79, type, singletonsswitch: $o).
0.39/0.64	thf(decl_80, type, upairsetE: $o).
0.39/0.64	thf(decl_81, type, upairsetIL: $o).
0.39/0.64	thf(decl_82, type, upairsetIR: $o).
0.39/0.64	thf(decl_83, type, emptyE1: $o).
0.39/0.64	thf(decl_84, type, vacuousDall: $o).
0.39/0.64	thf(decl_85, type, quantDeMorgan1: $o).
0.39/0.64	thf(decl_86, type, quantDeMorgan2: $o).
0.39/0.64	thf(decl_87, type, quantDeMorgan3: $o).
0.39/0.64	thf(decl_88, type, quantDeMorgan4: $o).
0.39/0.64	thf(decl_89, type, prop2setI: $o).
0.39/0.64	thf(decl_90, type, set2prop: $i > $o).
0.39/0.64	thf(decl_91, type, prop2set2propI: $o).
0.39/0.64	thf(decl_92, type, notdexE: $o).
0.39/0.64	thf(decl_93, type, notdallE: $o).
0.39/0.64	thf(decl_94, type, exuI1: $o).
0.39/0.64	thf(decl_95, type, exuI3: $o).
0.39/0.64	thf(decl_96, type, exuI2: $o).
0.39/0.64	thf(decl_97, type, inCongP: $o).
0.39/0.64	thf(decl_98, type, in__Cong: $o).
0.39/0.64	thf(decl_99, type, exuE3u: $o).
0.39/0.64	thf(decl_100, type, exu__Cong: $o).
0.39/0.64	thf(decl_101, type, emptyset__Cong: $o).
0.39/0.64	thf(decl_102, type, setadjoin__Cong: $o).
0.39/0.64	thf(decl_103, type, powerset__Cong: $o).
0.39/0.64	thf(decl_104, type, setunion__Cong: $o).
0.39/0.64	thf(decl_105, type, omega__Cong: $o).
0.39/0.64	thf(decl_106, type, exuEu: $o).
0.39/0.64	thf(decl_107, type, descr__Cong: $o).
0.39/0.64	thf(decl_108, type, dsetconstr__Cong: $o).
0.39/0.64	thf(decl_109, type, subset: $i > $i > $o).
0.39/0.64	thf(decl_112, type, subsetI1: $o).
0.39/0.64	thf(decl_113, type, eqimpsubset2: $o).
0.39/0.64	thf(decl_114, type, eqimpsubset1: $o).
0.39/0.64	thf(decl_115, type, subsetI2: $o).
0.39/0.64	thf(decl_116, type, emptysetsubset: $o).
0.39/0.64	thf(decl_117, type, subsetE: $o).
0.39/0.64	thf(decl_118, type, subsetE2: $o).
0.39/0.64	thf(decl_119, type, notsubsetI: $o).
0.39/0.64	thf(decl_120, type, notequalI1: $o).
0.39/0.64	thf(decl_121, type, notequalI2: $o).
0.39/0.64	thf(decl_122, type, subsetRefl: $o).
0.39/0.64	thf(decl_123, type, subsetTrans: $o).
0.39/0.64	thf(decl_124, type, setadjoinSub: $o).
0.39/0.64	thf(decl_125, type, setadjoinSub2: $o).
0.39/0.64	thf(decl_126, type, subset2powerset: $o).
0.39/0.64	thf(decl_127, type, setextsub: $o).
0.39/0.64	thf(decl_128, type, subsetemptysetimpeq: $o).
0.39/0.64	thf(decl_129, type, powersetI1: $o).
0.39/0.64	thf(decl_130, type, powersetE1: $o).
0.39/0.64	thf(decl_131, type, inPowerset: $o).
0.39/0.64	thf(decl_132, type, powersetsubset: $o).
0.39/0.64	thf(decl_133, type, sepInPowerset: $o).
0.39/0.64	thf(decl_134, type, sepSubset: $o).
0.39/0.64	thf(decl_135, type, binunion: $i > $i > $i).
0.39/0.64	thf(decl_136, type, binunionIL: $o).
0.39/0.64	thf(decl_137, type, upairset2IR: $o).
0.39/0.64	thf(decl_138, type, binunionIR: $o).
0.39/0.64	thf(decl_139, type, binunionEcases: $o).
0.39/0.64	thf(decl_140, type, binunionE: $o).
0.39/0.64	thf(decl_141, type, binunionLsub: $o).
0.39/0.64	thf(decl_142, type, binunionRsub: $o).
0.39/0.64	thf(decl_143, type, binintersect: $i > $i > $i).
0.39/0.64	thf(decl_144, type, binintersectI: $o).
0.39/0.64	thf(decl_145, type, binintersectSubset5: $o).
0.39/0.64	thf(decl_146, type, binintersectEL: $o).
0.39/0.64	thf(decl_147, type, binintersectLsub: $o).
0.39/0.64	thf(decl_148, type, binintersectSubset2: $o).
0.39/0.64	thf(decl_149, type, binintersectSubset3: $o).
0.39/0.64	thf(decl_150, type, binintersectER: $o).
0.39/0.64	thf(decl_151, type, disjointsetsI1: $o).
0.39/0.64	thf(decl_152, type, binintersectRsub: $o).
0.39/0.64	thf(decl_153, type, binintersectSubset4: $o).
0.39/0.64	thf(decl_154, type, binintersectSubset1: $o).
0.39/0.64	thf(decl_155, type, bs114d: $o).
0.39/0.64	thf(decl_157, type, setminus: $i > $i > $i).
0.39/0.64	thf(decl_158, type, setminusI: $o).
0.39/0.64	thf(decl_159, type, setminusEL: $o).
0.39/0.64	thf(decl_160, type, setminusER: $o).
0.39/0.64	thf(decl_161, type, setminusSubset2: $o).
0.39/0.64	thf(decl_162, type, setminusERneg: $o).
0.39/0.64	thf(decl_163, type, setminusELneg: $o).
0.39/0.64	thf(decl_164, type, setminusILneg: $o).
0.39/0.64	thf(decl_165, type, setminusIRneg: $o).
0.39/0.64	thf(decl_166, type, setminusLsub: $o).
0.39/0.64	thf(decl_167, type, setminusSubset1: $o).
0.39/0.64	thf(decl_168, type, symdiff: $i > $i > $i).
0.39/0.64	thf(decl_169, type, symdiffE: $o).
0.39/0.64	thf(decl_170, type, symdiffI1: $o).
0.39/0.64	thf(decl_171, type, symdiffI2: $o).
0.39/0.64	thf(decl_172, type, symdiffIneg1: $o).
0.39/0.64	thf(decl_173, type, symdiffIneg2: $o).
0.39/0.64	thf(decl_174, type, iskpair: $i > $o).
0.39/0.64	thf(decl_175, type, secondinupair: $o).
0.39/0.64	thf(decl_176, type, setukpairIL: $o).
0.39/0.64	thf(decl_177, type, setukpairIR: $o).
0.39/0.64	thf(decl_178, type, kpairiskpair: $o).
0.39/0.64	thf(decl_179, type, kpair: $i > $i > $i).
0.39/0.64	thf(decl_180, type, kpairp: $o).
0.39/0.64	thf(decl_181, type, cartprod: $i > $i > $i).
0.39/0.64	thf(decl_182, type, singletonsubset: $o).
0.39/0.64	thf(decl_183, type, singletoninpowerset: $o).
0.39/0.64	thf(decl_184, type, singletoninpowunion: $o).
0.39/0.64	thf(decl_185, type, upairset2E: $o).
0.39/0.64	thf(decl_186, type, upairsubunion: $o).
0.39/0.64	thf(decl_187, type, upairinpowunion: $o).
0.39/0.64	thf(decl_188, type, ubforcartprodlem1: $o).
0.39/0.64	thf(decl_189, type, ubforcartprodlem2: $o).
0.39/0.64	thf(decl_190, type, ubforcartprodlem3: $o).
0.39/0.64	thf(decl_191, type, cartprodpairin: $o).
0.39/0.64	thf(decl_192, type, cartprodmempair1: $o).
0.39/0.64	thf(decl_193, type, cartprodmempair: $o).
0.39/0.64	thf(decl_194, type, setunionE2: $o).
0.39/0.64	thf(decl_195, type, setunionsingleton1: $o).
0.39/0.64	thf(decl_196, type, setunionsingleton2: $o).
0.39/0.64	thf(decl_197, type, setunionsingleton: $o).
0.39/0.64	thf(decl_198, type, singleton: $i > $o).
0.39/0.64	thf(decl_199, type, singletonprop: $o).
0.39/0.64	thf(decl_200, type, ex1: $i > ($i > $o) > $o).
0.39/0.64	thf(decl_201, type, ex1E1: $o).
0.39/0.64	thf(decl_202, type, ex1I: $o).
0.39/0.64	thf(decl_203, type, ex1I2: $o).
0.39/0.64	thf(decl_204, type, singletonsuniq: $o).
0.39/0.64	thf(decl_209, type, setukpairinjL1: $o).
0.39/0.64	thf(decl_210, type, kfstsingleton: $o).
0.39/0.64	thf(decl_211, type, theprop: $o).
0.39/0.64	thf(decl_212, type, kfst: $i > $i).
0.39/0.64	thf(decl_213, type, kfstpairEq: $o).
0.39/0.64	thf(decl_214, type, cartprodfstin: $o).
0.39/0.64	thf(decl_215, type, setukpairinjL2: $o).
0.39/0.64	thf(decl_216, type, setukpairinjL: $o).
0.39/0.64	thf(decl_217, type, setukpairinjR11: $o).
0.39/0.64	thf(decl_218, type, setukpairinjR12: $o).
0.39/0.64	thf(decl_219, type, setukpairinjR1: $o).
0.39/0.64	thf(decl_220, type, upairequniteq: $o).
0.39/0.64	thf(decl_221, type, setukpairinjR2: $o).
0.39/0.64	thf(decl_222, type, setukpairinjR: $o).
0.39/0.64	thf(decl_223, type, ksndsingleton: $o).
0.39/0.64	thf(decl_224, type, ksnd: $i > $i).
0.39/0.64	thf(decl_225, type, ksndpairEq: $o).
0.39/0.64	thf(decl_226, type, kpairsurjEq: $o).
0.39/0.64	thf(decl_227, type, cartprodsndin: $o).
0.39/0.64	thf(decl_228, type, cartprodpairmemEL: $o).
0.39/0.64	thf(decl_229, type, cartprodpairmemER: $o).
0.39/0.64	thf(decl_230, type, cartprodmempaircEq: $o).
0.39/0.64	thf(decl_231, type, cartprodfstpairEq: $o).
0.39/0.64	thf(decl_232, type, cartprodsndpairEq: $o).
0.39/0.64	thf(decl_233, type, cartprodpairsurjEq: $o).
0.39/0.64	thf(decl_234, type, breln: $i > $i > $i > $o).
0.39/0.64	thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
0.39/0.64	thf(decl_236, type, dpsetconstrI: $o).
0.39/0.64	thf(decl_237, type, dpsetconstrSub: $o).
0.39/0.64	thf(decl_238, type, setOfPairsIsBReln: $o).
0.39/0.64	thf(decl_239, type, dpsetconstrERa: $o).
0.39/0.64	thf(decl_240, type, dpsetconstrEL1: $o).
0.39/0.64	thf(decl_241, type, dpsetconstrEL2: $o).
0.39/0.64	thf(decl_242, type, dpsetconstrER: $o).
0.39/0.64	thf(decl_243, type, func: $i > $i > $i > $o).
0.39/0.64	thf(decl_244, type, funcSet: $i > $i > $i).
0.39/0.64	thf(decl_245, type, funcImageSingleton: $o).
0.39/0.64	thf(decl_246, type, apProp: $o).
0.39/0.64	thf(decl_247, type, ap: $i > $i > $i > $i > $i).
0.39/0.64	thf(decl_248, type, app: $o).
0.39/0.64	thf(decl_249, type, infuncsetfunc: $o).
0.39/0.64	thf(decl_250, type, ap2p: $o).
0.39/0.64	thf(decl_251, type, funcinfuncset: $o).
0.39/0.64	thf(decl_252, type, lamProp: $o).
0.39/0.64	thf(decl_253, type, lam: $i > $i > ($i > $i) > $i).
0.39/0.64	thf(decl_254, type, lamp: $o).
0.39/0.64	thf(decl_255, type, lam2p: $o).
0.39/0.64	thf(decl_256, type, brelnall1: $o).
0.39/0.64	thf(decl_257, type, brelnall2: $o).
0.39/0.64	thf(decl_258, type, ex1E2: $o).
0.39/0.64	thf(decl_259, type, funcGraphProp1: $o).
0.39/0.64	thf(decl_260, type, funcGraphProp3: $o).
0.39/0.64	thf(decl_261, type, funcGraphProp2: $o).
0.39/0.64	thf(decl_262, type, funcextLem: $o).
0.39/0.64	thf(decl_263, type, funcGraphProp4: $o).
0.39/0.64	thf(decl_264, type, subbreln: $o).
0.39/0.64	thf(decl_265, type, eqbreln: $o).
0.39/0.64	thf(decl_266, type, funcext: $o).
0.39/0.64	thf(decl_267, type, funcext2: $o).
0.39/0.64	thf(decl_268, type, ap2apEq1: $o).
0.39/0.64	thf(decl_269, type, ap2apEq2: $o).
0.39/0.64	thf(decl_270, type, beta1: $o).
0.39/0.64	thf(decl_271, type, eta1: $o).
0.39/0.64	thf(decl_272, type, epred1_0: $o).
0.39/0.64	thf(decl_273, type, esk1_2: $i > $i > $i).
0.39/0.64	thf(decl_274, type, esk2_2: $i > $i > $i).
0.39/0.64	thf(decl_275, type, esk3_2: $i > $i > $i).
0.39/0.64	thf(decl_276, type, esk4_1: $i > $i).
0.39/0.64	thf(decl_277, type, esk5_2: ($i > $i > $o) > $i > $i).
0.39/0.64	thf(decl_278, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
0.39/0.64	thf(decl_279, type, esk7_2: ($i > $i > $o) > $i > $i).
0.39/0.64	thf(decl_280, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
0.39/0.64	thf(decl_281, type, esk9_1: $i > $i).
0.39/0.64	thf(decl_282, type, esk10_2: ($i > $o) > $i > $i).
0.39/0.64	thf(decl_283, type, esk11_2: ($i > $o) > $i > $i).
0.39/0.64	thf(decl_284, type, esk12_1: ($i > $o) > $i).
0.39/0.64	thf(decl_285, type, esk13_2: ($i > $o) > $i > $i).
0.39/0.64	thf(decl_286, type, esk14_1: ($i > $o) > $i).
0.39/0.64	thf(decl_287, type, esk15_2: $i > $i > $i).
0.39/0.64	thf(decl_288, type, esk16_2: $i > $i > $i).
0.39/0.64	thf(decl_289, type, esk17_1: $i > $i).
0.39/0.64	thf(decl_290, type, esk18_1: $i > $i).
0.39/0.64	thf(decl_291, type, esk19_1: $i > $i).
0.39/0.64	thf(decl_292, type, esk20_2: $i > $i > $i).
0.39/0.64	thf(decl_293, type, esk21_3: $i > $i > $o > $i).
0.39/0.64	thf(decl_294, type, esk22_2: ($i > $o) > $i > $i).
0.39/0.64	thf(decl_295, type, esk23_1: ($i > $o) > $i).
0.39/0.64	thf(decl_296, type, esk24_1: $i > $i).
0.39/0.64	thf(decl_297, type, esk25_2: $i > ($i > $o) > $i).
0.39/0.64	thf(decl_298, type, esk26_2: $i > ($i > $o) > $i).
0.39/0.64	thf(decl_299, type, esk27_2: $i > ($i > $o) > $i).
0.39/0.64	thf(decl_300, type, esk28_2: $i > ($i > $o) > $i).
0.39/0.64	thf(decl_301, type, esk29_2: $i > ($i > $o) > $i).
0.39/0.64	thf(decl_302, type, esk30_2: $i > ($i > $o) > $i).
0.39/0.64	thf(decl_303, type, esk31_2: ($i > $o) > $i > $i).
0.39/0.64	thf(decl_304, type, esk32_1: ($i > $o) > $i).
0.39/0.64	thf(decl_305, type, esk33_1: ($i > $o) > $i).
0.39/0.64	thf(decl_306, type, esk34_1: ($i > $o) > $i).
0.39/0.64	thf(decl_307, type, esk35_1: ($i > $o) > $i).
0.39/0.64	thf(decl_308, type, esk36_2: ($i > $o) > $i > $i).
0.39/0.64	thf(decl_309, type, esk37_1: ($i > $o) > $i).
0.39/0.64	thf(decl_310, type, esk38_2: ($i > $o) > $i > $i).
0.39/0.64	thf(decl_311, type, esk39_2: ($i > $o) > ($i > $o) > $i).
0.39/0.64	thf(decl_312, type, esk40_2: ($i > $o) > ($i > $o) > $i).
0.39/0.64	thf(decl_313, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
0.39/0.64	thf(decl_314, type, esk42_2: ($i > $o) > ($i > $o) > $i).
0.39/0.64	thf(decl_315, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
0.39/0.64	thf(decl_316, type, esk44_2: ($i > $o) > ($i > $o) > $i).
0.39/0.64	thf(decl_317, type, esk45_2: ($i > $o) > $i > $i).
0.39/0.64	thf(decl_318, type, esk46_2: ($i > $o) > ($i > $o) > $i).
0.39/0.64	thf(decl_319, type, esk47_2: ($i > $o) > ($i > $o) > $i).
0.39/0.64	thf(decl_320, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
0.39/0.64	thf(decl_321, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
0.39/0.64	thf(decl_322, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
0.39/0.64	thf(decl_323, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
0.39/0.64	thf(decl_324, type, esk52_2: $i > $i > $i).
0.39/0.64	thf(decl_325, type, esk53_2: $i > $i > $i).
0.39/0.64	thf(decl_326, type, esk54_2: $i > $i > $i).
0.39/0.64	thf(decl_327, type, esk55_3: $i > $i > $i > $i).
0.39/0.64	thf(decl_328, type, esk56_3: $i > $i > $i > $i).
0.39/0.64	thf(decl_329, type, esk57_2: $i > $i > $i).
0.39/0.64	thf(decl_330, type, esk58_2: $i > ($i > $o) > $i).
0.39/0.64	thf(decl_331, type, esk59_2: $i > ($i > $o) > $i).
0.39/0.64	thf(decl_332, type, esk60_2: $i > ($i > $o) > $i).
0.39/0.64	thf(decl_333, type, esk61_2: $i > ($i > $o) > $i).
0.39/0.64	thf(decl_334, type, esk62_3: $i > ($i > $o) > $i > $i).
0.39/0.64	thf(decl_335, type, esk63_3: $i > ($i > $o) > $i > $i).
0.39/0.64	thf(decl_336, type, esk64_2: $i > ($i > $o) > $i).
0.39/0.64	thf(decl_337, type, esk65_2: $i > ($i > $o) > $i).
0.39/0.64	thf(decl_338, type, esk66_2: $i > ($i > $o) > $i).
0.39/0.64	thf(decl_339, type, esk67_1: $i > $i).
0.39/0.64	thf(decl_340, type, esk68_1: $i > $i).
0.39/0.64	thf(decl_341, type, esk69_4: $i > $i > $i > $i > $i).
0.39/0.64	thf(decl_342, type, esk70_3: $i > $i > ($i > $i) > $i).
0.39/0.64	thf(decl_343, type, esk71_3: $i > $i > ($i > $i) > $i).
0.39/0.64	thf(decl_344, type, esk72_3: $i > $i > ($i > $i) > $i).
0.39/0.64	thf(decl_345, type, esk73_4: $i > $i > $i > ($i > $o) > $i).
0.39/0.64	thf(decl_346, type, esk74_4: $i > $i > $i > ($i > $o) > $i).
0.39/0.64	thf(decl_347, type, esk75_4: $i > $i > $i > ($i > $o) > $i).
0.39/0.64	thf(decl_348, type, esk76_4: $i > $i > $i > ($i > $o) > $i).
0.39/0.64	thf(decl_349, type, esk77_4: $i > $i > $i > $i > $i).
0.39/0.64	thf(decl_350, type, esk78_4: $i > $i > $i > $i > $i).
0.39/0.64	thf(decl_351, type, esk79_4: $i > $i > $i > $i > $i).
0.39/0.64	thf(decl_352, type, esk80_4: $i > $i > $i > $i > $i).
0.39/0.64	thf(decl_353, type, esk81_4: $i > $i > $i > $i > $i).
0.39/0.64	thf(decl_354, type, esk82_4: $i > $i > $i > $i > $i).
0.39/0.64	thf(decl_355, type, esk83_4: $i > $i > $i > $i > $i).
0.39/0.64	thf(decl_356, type, esk84_4: $i > $i > $i > $i > $i).
0.39/0.64	thf(decl_357, type, esk85_4: $i > $i > $i > $i > $i).
0.39/0.64	thf(decl_358, type, esk86_3: $i > $i > ($i > $i) > $i).
0.39/0.64	thf(decl_359, type, esk87_0: $i).
0.39/0.64	thf(decl_360, type, esk88_0: $i).
0.39/0.64	thf(decl_361, type, esk89_0: $i > $i).
0.39/0.64	thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', ex1)).
0.39/0.64	thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', singleton)).
0.39/0.64	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', exuI3)).
0.39/0.64	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', exu)).
0.39/0.64	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', exuI1)).
0.39/0.64	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', nonempty)).
0.39/0.64	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', exuE2)).
0.39/0.64	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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', replAx)).
0.39/0.64	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', singletonprop)).
0.39/0.64	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', ex1E1)).
0.39/0.64	thf(ex1I, axiom, ((ex1I)<=>![X4:$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.r75cfSlgae/Vampire---4.8_20603', ex1I)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', ksndsingleton)).
0.39/0.64	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', breln)).
0.39/0.64	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.r75cfSlgae/Vampire---4.8_20603', ex1E2)).
0.39/0.64	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', funcImageSingleton)).
0.39/0.64	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setOfPairsIsBReln)).
0.39/0.64	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', kfstsingleton)).
0.39/0.64	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', ex1I2)).
0.39/0.64	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', descr__Cong)).
0.39/0.64	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', exuEu)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', exuE3u)).
0.39/0.64	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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', exu__Cong)).
0.39/0.64	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', exuI2)).
0.39/0.64	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', nonemptyI)).
0.39/0.64	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', exuE3e)).
0.39/0.64	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', exuE1)).
0.39/0.64	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', descrp)).
0.39/0.64	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.r75cfSlgae/Vampire---4.8_20603', emptyE1)).
0.39/0.64	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', nonemptyImpWitness)).
0.39/0.64	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setoftrueEq)).
0.39/0.64	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', dsetconstrER)).
0.39/0.64	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', dsetconstrEL)).
0.39/0.64	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', dsetconstrI)).
0.39/0.64	thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X37 @ X3))) @ X2)=(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', beta1)).
0.39/0.64	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', theprop)).
0.39/0.64	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', dpsetconstrI)).
0.39/0.64	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', dpsetconstrEL1)).
0.39/0.64	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', dpsetconstrEL2)).
0.39/0.64	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', dpsetconstrER)).
0.39/0.64	thf(lamProp, axiom, ((lamProp)<=>![X4:$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.r75cfSlgae/Vampire---4.8_20603', lamProp)).
0.39/0.64	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X34:$i]:(((breln @ X4 @ X5 @ X34)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X34)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', brelnall1)).
0.39/0.64	thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X34:$i]:(((breln @ X4 @ X5 @ X34)=>![X36:$i]:(((breln @ X4 @ X5 @ X36)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X36))))))=>(subset @ X34 @ X36))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', subbreln)).
0.39/0.64	thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X34:$i]:(((breln @ X4 @ X5 @ X34)=>![X36:$i]:(((breln @ X4 @ X5 @ X36)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X36))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X36)=>(in @ (kpair @ X2 @ X3) @ X34))))))=>((X34)=(X36))))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', eqbreln)).
0.39/0.64	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X33 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', lam2p)).
0.39/0.64	thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', eta1)).
0.39/0.64	thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X34:$i]:(((breln @ X4 @ X5 @ X34)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X34)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', brelnall2)).
0.39/0.64	thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', lamp)).
0.39/0.64	thf(apProp, axiom, ((apProp)<=>![X4:$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.r75cfSlgae/Vampire---4.8_20603', apProp)).
0.39/0.64	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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', dpsetconstrERa)).
0.39/0.64	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', dpsetconstrSub)).
0.39/0.64	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', sepSubset)).
0.39/0.64	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', sepInPowerset)).
0.39/0.64	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', dsetconstr__Cong)).
0.39/0.64	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', nonemptyI1)).
0.39/0.64	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', nonemptyE1)).
0.39/0.64	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setbeta)).
0.39/0.64	thf(lam2lamEq, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((((((foundationAx)=>(((descrp)=>(((((exuE1)=>(((emptysetE)=>(((notinemptyset)=>((exuE3e)=>(((emptyI)=>(((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>(((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>(((((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((((((notinsingleton)=>((((((upairsetIR)=>(((((quantDeMorgan2)=>((quantDeMorgan3)=>(((prop2setI)=>(((notdexE)=>((notdallE)=>((((exuI2)=>(((in__Cong)=>(((exu__Cong)=>((emptyset__Cong)=>((((((((dsetconstr__Cong)=>(((eqimpsubset2)=>((((emptysetsubset)=>((((((notequalI2)=>((((setadjoinSub)=>((setadjoinSub2)=>((((subsetemptysetimpeq)=>((powersetI1)=>(((inPowerset)=>((powersetsubset)=>((((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((((((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>(((setminusEL)=>((setminusER)=>(((setminusERneg)=>(((setminusILneg)=>((setminusIRneg)=>(((setminusSubset1)=>((((symdiffI2)=>(((symdiffIneg2)=>((secondinupair)=>((((((((singletoninpowunion)=>((upairset2E)=>((((ubforcartprodlem1)=>((((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((((setukpairinjL1)=>(((theprop)=>(((((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((((setukpairinjR2)=>(((ksndsingleton)=>(((kpairsurjEq)=>((cartprodsndin)=>(((cartprodpairmemER)=>(((((cartprodpairsurjEq)=>((dpsetconstrI)=>(((((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((((app)=>(((((lamProp)=>(((lam2p)=>((brelnall1)=>((((funcGraphProp1)=>(((funcGraphProp2)=>((funcextLem)=>(((subbreln)=>((eqbreln)=>((((ap2apEq1)=>((ap2apEq2)=>((![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ (X38 @ X2) @ X5)<=(in @ X2 @ X4)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X38 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X38 @ X2))))))<=(eta1))<=(beta1))))<=(funcext2))<=(funcext))))<=(funcGraphProp4))))<=(funcGraphProp3)))<=(ex1E2))<=(brelnall2))))<=(lamp)))<=(funcinfuncset))<=(ap2p))<=(infuncsetfunc)))<=(apProp))<=(funcImageSingleton)))))<=(dpsetconstrERa))<=(setOfPairsIsBReln))<=(dpsetconstrSub))))<=(cartprodsndpairEq))<=(cartprodfstpairEq))<=(cartprodmempaircEq)))<=(cartprodpairmemEL))))<=(ksndpairEq)))<=(setukpairinjR)))<=(upairequniteq))<=(setukpairinjR1)))))<=(setukpairinjL2))<=(cartprodfstin))<=(kfstpairEq)))<=(kfstsingleton)))<=(singletonsuniq))<=(ex1I2))))))<=(setunionsingleton2))<=(setunionsingleton1))))))<=(ubforcartprodlem3))<=(ubforcartprodlem2)))<=(upairinpowunion))<=(upairsubunion))))<=(singletoninpowerset))<=(singletonsubset))<=(kpairp))<=(kpairiskpair))<=(setukpairIR))<=(setukpairIL))))<=(symdiffIneg1)))<=(symdiffI1))<=(symdiffE)))<=(setminusLsub))))<=(setminusELneg)))<=(setminusSubset2))))<=(setminusI)))))))<=(binintersectER))<=(binintersectSubset3))))))<=(binintersectI))<=(binunionRsub))<=(binunionLsub))<=(binunionE))))))<=(sepSubset))<=(sepInPowerset))))<=(powersetE1))))<=(setextsub))<=(subset2powerset))))<=(subsetTrans))<=(subsetRefl)))<=(notequalI1))<=(notsubsetI))<=(subsetE2))<=(subsetE)))<=(subsetI2))<=(eqimpsubset1)))<=(subsetI1)))<=(descr__Cong))<=(exuEu))<=(omega__Cong))<=(setunion__Cong))<=(powerset__Cong))<=(setadjoin__Cong))))<=(exuE3u)))<=(inCongP)))<=(exuI3))<=(exuI1))))<=(prop2set2propI)))<=(quantDeMorgan4))))<=(quantDeMorgan1))<=(vacuousDall))<=(emptyE1)))<=(upairsetIL))<=(upairsetE))<=(singletonsswitch))<=(eqinunit)))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU))))))<=(emptyinPowerset))<=(powersetI))<=(setoftrueEq)))))<=(emptyinunitempty)))))))<=(noeltsimpempty)))<=(setext))))<=(emptysetimpfalse)))<=(prop2setE)))<=(dsetconstrER))<=(dsetconstrEL))<=(dsetconstrI)))<=(wellorderingAx)))<=(replAx))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', lam2lamEq)).
0.39/0.64	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', binintersectSubset5)).
0.39/0.64	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', noeltsimpempty)).
0.39/0.64	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', omega0Ax)).
0.39/0.64	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', inCongP)).
0.39/0.64	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', binunionEcases)).
0.39/0.64	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', disjointsetsI1)).
0.39/0.64	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', prop2set2propI)).
0.39/0.64	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', quantDeMorgan4)).
0.39/0.64	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', quantDeMorgan1)).
0.39/0.64	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', binintersectRsub)).
0.39/0.64	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', vacuousDall)).
0.39/0.64	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', binintersectSubset4)).
0.39/0.64	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', upairsetIL)).
0.39/0.64	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', upairsetE)).
0.39/0.64	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', singletonsswitch)).
0.39/0.64	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', binintersectSubset1)).
0.39/0.64	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', eqinunit)).
0.39/0.64	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', uniqinunit)).
0.39/0.64	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', bs114d)).
0.39/0.64	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', subPowSU)).
0.39/0.64	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', emptyinPowerset)).
0.39/0.64	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setminusEL)).
0.39/0.64	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', powersetI)).
0.39/0.64	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setminusER)).
0.39/0.64	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', emptyinunitempty)).
0.39/0.64	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setunionsingleton)).
0.39/0.64	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setext)).
0.39/0.64	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', emptysetimpfalse)).
0.39/0.64	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', prop2setE)).
0.39/0.64	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setminusERneg)).
0.39/0.64	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setminusILneg)).
0.39/0.64	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.r75cfSlgae/Vampire---4.8_20603', wellorderingAx)).
0.39/0.64	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setminusIRneg)).
0.39/0.64	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.r75cfSlgae/Vampire---4.8_20603', omegaIndAx)).
0.39/0.64	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', omegaSAx)).
0.39/0.64	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setminusSubset1)).
0.39/0.64	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', symdiffI2)).
0.39/0.64	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', symdiffIneg2)).
0.39/0.64	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', secondinupair)).
0.39/0.64	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', singletoninpowunion)).
0.39/0.64	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', binintersectEL)).
0.39/0.64	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', upairset2E)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', ubforcartprodlem1)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', cartprodpairin)).
0.39/0.64	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', cartprodmempair1)).
0.39/0.64	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', cartprodmempair)).
0.39/0.64	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setunionE2)).
0.39/0.64	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X35:$i]:(((in @ X35 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X35 @ X2))))=>((X29)=(X35)))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', funcext2)).
0.39/0.64	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setukpairinjL1)).
0.39/0.64	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setukpairinjL)).
0.39/0.64	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setukpairinjR11)).
0.39/0.64	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setukpairinjR12)).
0.39/0.64	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', binintersectLsub)).
0.39/0.64	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setukpairinjR2)).
0.39/0.64	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', kpairsurjEq)).
0.39/0.64	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', cartprodsndin)).
0.39/0.64	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', cartprodpairmemER)).
0.39/0.64	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', cartprodpairsurjEq)).
0.39/0.64	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', binintersectSubset2)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', app)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', funcGraphProp1)).
0.39/0.64	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', funcGraphProp2)).
0.39/0.64	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X35:$i]:(((func @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X35 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', funcextLem)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', ap2apEq1)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', ap2apEq2)).
0.39/0.64	thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X35:$i]:(((func @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X35 @ X2))))=>((X29)=(X35)))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', funcext)).
0.39/0.64	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.r75cfSlgae/Vampire---4.8_20603', funcGraphProp4)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', funcGraphProp3)).
0.39/0.64	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', funcinfuncset)).
0.39/0.64	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', ap2p)).
0.39/0.64	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', infuncsetfunc)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', cartprodsndpairEq)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', cartprodfstpairEq)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', cartprodmempaircEq)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', cartprodpairmemEL)).
0.39/0.64	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', ksndpairEq)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', setukpairinjR)).
0.39/0.64	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', upairequniteq)).
0.39/0.64	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setukpairinjR1)).
0.39/0.64	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setukpairinjL2)).
0.39/0.64	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', cartprodfstin)).
0.39/0.64	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', kfstpairEq)).
0.39/0.64	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', singletonsuniq)).
0.39/0.64	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setunionsingleton2)).
0.39/0.64	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setunionsingleton1)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', ubforcartprodlem3)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', ubforcartprodlem2)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', upairinpowunion)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', upairsubunion)).
0.39/0.64	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', singletoninpowerset)).
0.39/0.64	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', singletonsubset)).
0.39/0.64	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', kpairp)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', kpairiskpair)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', setukpairIR)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', setukpairIL)).
0.39/0.64	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', symdiffIneg1)).
0.39/0.64	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', symdiffI1)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', symdiffE)).
0.39/0.64	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setminusLsub)).
0.39/0.64	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setminusELneg)).
0.39/0.64	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setminusSubset2)).
0.39/0.64	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setminusI)).
0.39/0.64	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', binintersectER)).
0.39/0.64	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', binintersectSubset3)).
0.39/0.64	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', binintersectI)).
0.39/0.64	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', binunionRsub)).
0.39/0.64	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', binunionLsub)).
0.39/0.64	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', binunionE)).
0.39/0.64	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', powersetE1)).
0.39/0.64	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setextsub)).
0.39/0.64	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', subset2powerset)).
0.39/0.64	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', subsetTrans)).
0.39/0.64	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', subsetRefl)).
0.39/0.64	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', notequalI1)).
0.39/0.64	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', notsubsetI)).
0.39/0.64	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', subsetE2)).
0.39/0.64	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', subsetE)).
0.39/0.64	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', subsetI2)).
0.39/0.64	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', eqimpsubset1)).
0.39/0.64	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', subsetI1)).
0.39/0.64	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', omega__Cong)).
0.39/0.64	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setunion__Cong)).
0.39/0.64	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', powerset__Cong)).
0.39/0.64	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.r75cfSlgae/Vampire---4.8_20603', setadjoin__Cong)).
0.39/0.64	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', binunionIR)).
0.39/0.64	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', upairset2IR)).
0.39/0.64	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', binunionIL)).
0.39/0.64	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', powersetsubset)).
0.39/0.64	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', inPowerset)).
0.39/0.64	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', powersetI1)).
0.39/0.64	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', subsetemptysetimpeq)).
0.39/0.64	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setadjoinSub2)).
0.39/0.64	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setadjoinSub)).
0.39/0.64	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', notequalI2)).
0.39/0.64	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', emptysetsubset)).
0.39/0.64	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', eqimpsubset2)).
0.39/0.64	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', emptyset__Cong)).
0.39/0.64	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', in__Cong)).
0.39/0.64	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', notdallE)).
0.39/0.64	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', notdexE)).
0.39/0.64	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', prop2setI)).
0.39/0.64	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', quantDeMorgan3)).
0.39/0.64	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', quantDeMorgan2)).
0.39/0.64	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', upairsetIR)).
0.39/0.64	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', notinsingleton)).
0.39/0.64	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setunionE)).
0.39/0.64	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setunionI)).
0.39/0.64	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', powersetE)).
0.39/0.64	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', emptyInPowerset)).
0.39/0.64	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setadjoinOr)).
0.39/0.64	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setadjoinE)).
0.39/0.64	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setadjoinIR)).
0.39/0.64	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setadjoinIL)).
0.39/0.64	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', emptyI)).
0.39/0.64	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', notinemptyset)).
0.39/0.64	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', emptysetE)).
0.39/0.64	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', foundationAx)).
0.39/0.64	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setunionAx)).
0.39/0.64	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', powersetAx)).
0.39/0.64	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setadjoinAx)).
0.39/0.64	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', emptysetAx)).
0.39/0.64	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.r75cfSlgae/Vampire---4.8_20603', setextAx)).
0.39/0.64	thf(c_0_219, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X718:$i]:(((in @ X718 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X718 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])).
0.39/0.64	thf(c_0_220, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])).
0.39/0.64	thf(c_0_221, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
0.39/0.64	thf(c_0_222, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
0.39/0.64	thf(c_0_223, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
0.39/0.64	thf(c_0_224, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
0.39/0.64	thf(c_0_225, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
0.39/0.64	thf(c_0_226, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
0.39/0.64	thf(c_0_227, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
0.39/0.64	thf(c_0_228, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
0.39/0.64	thf(c_0_229, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X718:$i]:(((in @ X718 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X718 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_219, c_0_220])).
0.39/0.64	thf(c_0_230, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
0.39/0.64	thf(c_0_231, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
0.39/0.64	thf(c_0_232, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
0.39/0.64	thf(c_0_233, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
0.39/0.64	thf(c_0_234, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
0.39/0.64	thf(c_0_235, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
0.39/0.64	thf(c_0_236, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
0.39/0.64	thf(c_0_237, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
0.39/0.64	thf(c_0_238, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
0.39/0.64	thf(c_0_239, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
0.39/0.64	thf(c_0_240, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
0.39/0.64	thf(c_0_241, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
0.39/0.64	thf(c_0_242, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
0.39/0.64	thf(c_0_243, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
0.39/0.64	thf(c_0_244, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
0.39/0.64	thf(c_0_245, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
0.39/0.64	thf(c_0_246, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
0.39/0.64	thf(c_0_247, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X701:$i]:((((X1 @ X701))&![X702:$i]:((((X1 @ X702))=>((X701)=(X702)))))))))))), inference(apply_def,[status(thm)],[c_0_221, c_0_222])).
0.39/0.64	thf(c_0_248, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X699:$i]:((((X1 @ X699))&![X700:$i]:((((X1 @ X700))=>((X699)=(X700))))))))))), inference(apply_def,[status(thm)],[c_0_223, c_0_222])).
0.39/0.64	thf(c_0_249, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
0.39/0.64	thf(c_0_250, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_224])).
0.39/0.64	thf(c_0_251, plain, ((exuE2)=(![X1:$i > $o]:(((?[X697:$i]:((((X1 @ X697))&![X698:$i]:((((X1 @ X698))=>((X697)=(X698)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_225, c_0_222])).
0.39/0.64	thf(c_0_252, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
0.39/0.64	thf(c_0_253, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
0.39/0.64	thf(c_0_254, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
0.39/0.64	thf(c_0_255, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
0.39/0.64	thf(c_0_256, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X689:$i]:((((X6 @ X2 @ X689))&![X690:$i]:((((X6 @ X2 @ X690))=>((X689)=(X690)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_226, c_0_222])).
0.39/0.64	thf(c_0_257, plain, ((beta1)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))) @ X2)=(X37 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
0.39/0.64	thf(c_0_258, 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)))=>(?[X717:$i]:(((in @ X717 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X717 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_227, c_0_220])).
0.39/0.64	thf(c_0_259, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X719:$i]:(((in @ X719 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X719 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_228, c_0_229])).
0.39/0.64	thf(c_0_260, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X720:$i]:(((in @ X720 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X720 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_230, c_0_229])).
0.39/0.64	thf(c_0_261, axiom, ((theprop)=(![X21:$i]:(((?[X723:$i]:(((in @ X723 @ X21)&((X21)=(setadjoin @ X723 @ emptyset)))))=>(in @ (setunion @ X21) @ X21))))), inference(apply_def,[status(thm)],[theprop, c_0_220])).
0.39/0.64	thf(c_0_262, plain, ((ksndsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X724:$i]:(((in @ X724 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X724 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_231, c_0_220])).
0.39/0.64	thf(c_0_263, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
0.39/0.64	thf(c_0_264, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
0.39/0.64	thf(c_0_265, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
0.39/0.64	thf(c_0_266, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
0.39/0.64	thf(c_0_267, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
0.39/0.64	thf(c_0_268, axiom, ((brelnall1)=(![X4:$i, X5:$i, X34:$i]:((((subset @ X34 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X34)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_232])).
0.39/0.64	thf(c_0_269, axiom, ((subbreln)=(![X4:$i, X5:$i, X34:$i]:((((subset @ X34 @ (cartprod @ X4 @ X5)))=>![X36:$i]:((((subset @ X36 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X36))))))=>(subset @ X34 @ X36)))))))), inference(apply_def,[status(thm)],[subbreln, c_0_232])).
0.39/0.64	thf(c_0_270, axiom, ((eqbreln)=(![X4:$i, X5:$i, X34:$i]:((((subset @ X34 @ (cartprod @ X4 @ X5)))=>![X36:$i]:((((subset @ X36 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X36))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X36)=>(in @ (kpair @ X2 @ X3) @ X34))))))=>((X34)=(X36)))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_232])).
0.39/0.64	thf(c_0_271, plain, ((lam2p)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X33 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
0.39/0.64	thf(c_0_272, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
0.39/0.64	thf(c_0_273, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:(((?[X726:$i]:(((in @ X726 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X726 @ emptyset)))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_233, c_0_229])).
0.39/0.64	thf(c_0_274, axiom, ((brelnall2)=(![X4:$i, X5:$i, X34:$i]:((((subset @ X34 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X34)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_232])).
0.39/0.64	thf(c_0_275, plain, ((lamp)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
0.39/0.64	thf(c_0_276, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
0.39/0.64	thf(c_0_277, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(?[X725:$i]:(((in @ X725 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))=(setadjoin @ X725 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_234, c_0_220])).
0.39/0.64	thf(c_0_278, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
0.39/0.64	thf(c_0_279, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_235, c_0_232])).
0.39/0.64	thf(c_0_280, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
0.39/0.64	thf(c_0_281, plain, ((kfstsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X722:$i]:(((in @ X722 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X722 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_236, c_0_220])).
0.39/0.64	thf(c_0_282, plain, ((ex1I2)=(![X4:$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)))=>(?[X721:$i]:(((in @ X721 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X721 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_237, c_0_229])).
0.39/0.64	thf(c_0_283, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
0.39/0.64	thf(c_0_284, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
0.39/0.64	thf(c_0_285, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X713:$i]:((((X1 @ X713))&![X714:$i]:((((X1 @ X714))=>((X713)=(X714)))))))=>((?[X715:$i]:((((X17 @ X715))&![X716:$i]:((((X17 @ X716))=>((X715)=(X716)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_238, c_0_222])).
0.39/0.64	thf(c_0_286, plain, ((exuEu)=(![X1:$i > $o]:(((?[X711:$i]:((((X1 @ X711))&![X712:$i]:((((X1 @ X712))=>((X711)=(X712)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_239, c_0_222])).
0.39/0.64	thf(c_0_287, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X705:$i]:((((X1 @ X705))&![X706:$i]:((((X1 @ X706))=>((X705)=(X706)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_240, c_0_222])).
0.39/0.64	thf(c_0_288, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
0.39/0.64	thf(c_0_289, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X707:$i]:((((X1 @ X707))&![X708:$i]:((((X1 @ X708))=>((X707)=(X708)))))))<=>(?[X709:$i]:((((X17 @ X709))&![X710:$i]:((((X17 @ X710))=>((X709)=(X710)))))))))))), inference(apply_def,[status(thm)],[c_0_241, c_0_222])).
0.39/0.64	thf(c_0_290, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X703:$i]:((((X1 @ X703))&![X704:$i]:((((X1 @ X704))=>((X703)=(X704))))))))))), inference(apply_def,[status(thm)],[c_0_242, c_0_222])).
0.39/0.64	thf(c_0_291, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_224])).
0.39/0.64	thf(c_0_292, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_243, c_0_224])).
0.39/0.64	thf(c_0_293, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_224])).
0.39/0.64	thf(c_0_294, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
0.39/0.64	thf(c_0_295, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X695:$i]:((((X1 @ X695))&![X696:$i]:((((X1 @ X696))=>((X695)=(X696)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_244, c_0_222])).
0.39/0.64	thf(c_0_296, plain, ((exuE1)=(![X1:$i > $o]:(((?[X693:$i]:((((X1 @ X693))&![X694:$i]:((((X1 @ X694))=>((X693)=(X694)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_245, c_0_222])).
0.39/0.64	thf(c_0_297, plain, ((descrp)=(![X1:$i > $o]:(((?[X691:$i]:((((X1 @ X691))&![X692:$i]:((((X1 @ X692))=>((X691)=(X692)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_246, c_0_222])).
0.39/0.64	thf(c_0_298, plain, ((epred1_0)<=>![X1379:$i]:(?[X1380:$i]:((((![X1381:$i]:(((in @ X1381 @ X1380)=>![X1382:$i]:(((in @ X1382 @ X1381)=>(in @ X1382 @ X1379)))))&![X1383:$i, X1384:$i]:((((in @ X1383 @ X1379)&(in @ X1384 @ X1379))=>(![X1385:$i]:(((in @ X1385 @ X1380)=>((in @ X1383 @ X1385)<=>(in @ X1384 @ X1385))))=>((X1383)=(X1384))))))&![X1386:$i, X1387:$i]:((((in @ X1386 @ X1380)&(in @ X1387 @ X1380))=>(![X1388:$i]:(((in @ X1388 @ X1386)=>(in @ X1388 @ X1387)))|![X1389:$i]:(((in @ X1389 @ X1387)=>(in @ X1389 @ X1386)))))))&![X1390:$i]:(((![X1391:$i]:(((in @ X1391 @ X1390)=>(in @ X1391 @ X1379)))&?[X1392:$i]:((in @ X1392 @ X1390)))=>?[X1393:$i, X1394:$i]:(((((in @ X1393 @ X1380)&(in @ X1394 @ X1390))&~(?[X1395:$i]:(((in @ X1395 @ X1393)&(in @ X1395 @ X1390)))))&![X1396:$i]:(((in @ X1396 @ X1380)=>(![X1397:$i]:(((in @ X1397 @ X1396)=>(in @ X1397 @ X1393)))|(in @ X1394 @ X1396)))))))))))), introduced(definition)).
0.39/0.64	thf(c_0_299, negated_conjecture, ~((![X727:$i, X728:$i]:((![X729:$i]:(((in @ X729 @ X727)<=>(in @ X729 @ X728)))=>((X727)=(X728))))=>(![X730:$i]:(~(in @ X730 @ emptyset))=>(![X731:$i, X732:$i, X733:$i]:(((in @ X733 @ (setadjoin @ X731 @ X732))<=>(((X733)=(X731))|(in @ X733 @ X732))))=>(![X734:$i, X735:$i]:(((in @ X735 @ (powerset @ X734))<=>![X736:$i]:(((in @ X736 @ X735)=>(in @ X736 @ X734)))))=>(![X737:$i, X738:$i]:(((in @ X738 @ (setunion @ X737))<=>?[X739:$i]:(((in @ X738 @ X739)&(in @ X739 @ X737)))))=>((in @ emptyset @ omega)=>(![X1409:$i]:(((in @ X1409 @ omega)=>(in @ (setadjoin @ X1409 @ X1409) @ omega)))=>(![X1406:$i]:((((in @ emptyset @ X1406)&![X1407:$i]:((((in @ X1407 @ omega)&(in @ X1407 @ X1406))=>(in @ (setadjoin @ X1407 @ X1407) @ X1406))))=>![X1408:$i]:(((in @ X1408 @ omega)=>(in @ X1408 @ X1406)))))=>(![X1398:$i > $i > $o, X1399:$i]:((![X1400:$i]:(((in @ X1400 @ X1399)=>?[X1401:$i]:(((X1398 @ X1400 @ X1401)&![X1402:$i]:(((X1398 @ X1400 @ X1402)=>((X1401)=(X1402))))))))=>?[X1403:$i]:(![X1404:$i]:(((in @ X1404 @ X1403)<=>?[X1405:$i]:(((in @ X1405 @ X1399)&(X1398 @ X1405 @ X1404))))))))=>(![X740:$i]:((?[X741:$i]:((in @ X741 @ X740))=>?[X742:$i]:(((in @ X742 @ X740)&~(?[X743:$i]:(((in @ X743 @ X742)&(in @ X743 @ X740))))))))=>((epred1_0)=>(![X744:$i > $o]:((?[X745:$i]:(((X744 @ X745)&![X746:$i]:(((X744 @ X746)=>((X745)=(X746))))))=>(X744 @ (descr @ (^[Z0/* 3 */:$i]:((X744 @ Z0)))))))=>(![X1376:$i, X1377:$i > $o, X1378:$i]:(((in @ X1378 @ X1376)=>((X1377 @ X1378)=>(in @ X1378 @ (dsetconstr @ X1376 @ (^[Z0/* 3 */:$i]:((X1377 @ Z0))))))))=>(![X1373:$i, X1374:$i > $o, X1375:$i]:(((in @ X1375 @ (dsetconstr @ X1373 @ (^[Z0/* 3 */:$i]:((X1374 @ Z0)))))=>(in @ X1375 @ X1373)))=>(![X1370:$i, X1371:$i > $o, X1372:$i]:(((in @ X1372 @ (dsetconstr @ X1370 @ (^[Z0/* 3 */:$i]:((X1371 @ Z0)))))=>(X1371 @ X1372)))=>(![X747:$i > $o]:((?[X748:$i]:(((X747 @ X748)&![X749:$i]:(((X747 @ X749)=>((X748)=(X749))))))=>?[X750:$i]:(((X747 @ X750)&![X751:$i]:(((X747 @ X751)=>((X750)=(X751))))))))=>(![X1368:$o, X1369:$i]:(((in @ X1369 @ (prop2set @ ((X1368))))=>(X1368)))=>(![X752:$i]:(((in @ X752 @ emptyset)=>![X753:$o]:((X753))))=>(![X1367:$i]:(~(in @ X1367 @ emptyset))=>(![X754:$i]:(~(in @ X754 @ emptyset))=>(![X755:$i > $o]:((?[X756:$i]:(((X755 @ X756)&![X757:$i]:(((X755 @ X757)=>((X756)=(X757))))))=>?[X758:$i]:((X755 @ X758))))=>(![X1363:$i, X1364:$i]:((![X1365:$i]:(((in @ X1365 @ X1363)=>(in @ X1365 @ X1364)))=>(![X1366:$i]:(((in @ X1366 @ X1364)=>(in @ X1366 @ X1363)))=>((X1363)=(X1364)))))=>(![X759:$i]:((![X760:$i]:(~(in @ X760 @ X759))=>((X759)=(emptyset))))=>(![X1361:$i]:((![X1362:$i]:(~(in @ X1362 @ X1361))=>((X1361)=(emptyset))))=>(![X761:$i, X762:$i > $o, X763:$i]:(((in @ X763 @ X761)=>((in @ X763 @ (dsetconstr @ X761 @ (^[Z0/* 3 */:$i]:((X762 @ Z0)))))<=>(X762 @ X763))))=>(![X764:$i]:((((X764)!=(emptyset))=>?[X765:$i]:((in @ X765 @ X764))))=>(![X766:$i, X767:$i > $o, X768:$i]:(((in @ X768 @ X766)=>((X767 @ X768)=>((dsetconstr @ X766 @ (^[Z0/* 3 */:$i]:((X767 @ Z0))))!=(emptyset)))))=>(![X769:$i]:((?[X770:$i]:((in @ X770 @ X769))=>((X769)!=(emptyset))))=>(![X771:$i, X772:$i]:((in @ X771 @ (setadjoin @ X771 @ X772)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X773:$i, X774:$i, X775:$i]:(((in @ X775 @ X774)=>(in @ X775 @ (setadjoin @ X773 @ X774))))=>(![X776:$i, X777:$i, X778:$i]:(((in @ X778 @ (setadjoin @ X776 @ X777))=>![X779:$o]:(((((X778)=(X776))=>(X779))=>(((in @ X778 @ X777)=>(X779))=>(X779))))))=>(![X780:$i, X781:$i, X782:$i]:(((in @ X782 @ (setadjoin @ X780 @ X781))=>(((X782)=(X780))|(in @ X782 @ X781))))=>(![X1360:$i]:(((dsetconstr @ X1360 @ (^[Z0/* 3 */:$i]:(($true))))=(X1360)))=>(![X1357:$i, X1358:$i]:((![X1359:$i]:(((in @ X1359 @ X1358)=>(in @ X1359 @ X1357)))=>(in @ X1358 @ (powerset @ X1357))))=>(![X1356:$i]:((in @ emptyset @ (powerset @ X1356)))=>(![X783:$i]:((in @ emptyset @ (powerset @ X783)))=>(![X784:$i, X785:$i, X786:$i]:(((in @ X785 @ (powerset @ X784))=>((in @ X786 @ X785)=>(in @ X786 @ X784))))=>(![X787:$i, X788:$i, X789:$i]:(((in @ X788 @ X789)=>((in @ X789 @ X787)=>(in @ X788 @ (setunion @ X787)))))=>(![X790:$i, X791:$i]:(((in @ X791 @ (setunion @ X790))=>![X792:$o]:((![X793:$i]:(((in @ X791 @ X793)=>((in @ X793 @ X790)=>(X792))))=>(X792)))))=>(![X1354:$i, X1355:$i]:(((in @ X1355 @ X1354)=>(in @ X1355 @ (powerset @ (setunion @ X1354)))))=>(![X1349:$i > $o]:((?[X1350:$i]:(((X1349 @ X1350)&![X1351:$i]:(((X1349 @ X1351)=>((X1350)=(X1351))))))=>?[X1352:$i]:(![X1353:$i]:(((X1349 @ X1353)<=>((X1353)=(X1352)))))))=>(![X1347:$i]:((((X1347)!=(emptyset))=>?[X1348:$i]:((in @ X1348 @ X1347))))=>(![X1345:$i, X1346:$i]:(((in @ X1345 @ (setadjoin @ X1346 @ emptyset))=>((X1345)=(X1346))))=>(![X794:$i, X795:$i]:((((X794)!=(X795))=>~(in @ X795 @ (setadjoin @ X794 @ emptyset))))=>(![X1343:$i, X1344:$i]:((((X1343)=(X1344))=>(in @ X1343 @ (setadjoin @ X1344 @ emptyset))))=>(![X1341:$i, X1342:$i]:(((in @ X1341 @ (setadjoin @ X1342 @ emptyset))=>(in @ X1342 @ (setadjoin @ X1341 @ emptyset))))=>(![X1338:$i, X1339:$i, X1340:$i]:(((in @ X1340 @ (setadjoin @ X1338 @ (setadjoin @ X1339 @ emptyset)))=>(((X1340)=(X1338))|((X1340)=(X1339)))))=>(![X1336:$i, X1337:$i]:((in @ X1336 @ (setadjoin @ X1336 @ (setadjoin @ X1337 @ emptyset))))=>(![X796:$i, X797:$i]:((in @ X797 @ (setadjoin @ X796 @ (setadjoin @ X797 @ emptyset))))=>(![X1333:$i, X1334:$i > $o]:((?[X1335:$i]:(((in @ X1335 @ X1333)&(X1334 @ X1335)))=>((dsetconstr @ X1333 @ (^[Z0/* 3 */:$i]:((X1334 @ Z0))))!=(emptyset))))=>(![X1331:$i > $o, X1332:$i]:(((in @ X1332 @ emptyset)=>(X1331 @ X1332)))=>(![X1327:$i, X1328:$i > $o]:((~(![X1329:$i]:(((in @ X1329 @ X1327)=>(X1328 @ X1329))))=>?[X1330:$i]:(((in @ X1330 @ X1327)&~(X1328 @ X1330)))))=>(![X798:$i, X799:$i > $o]:((![X800:$i]:(((in @ X800 @ X798)=>~(X799 @ X800)))=>~(?[X801:$i]:(((in @ X801 @ X798)&(X799 @ X801))))))=>(![X802:$i, X803:$i > $o]:((~(?[X804:$i]:(((in @ X804 @ X802)&(X803 @ X804))))=>![X805:$i]:(((in @ X805 @ X802)=>~(X803 @ X805)))))=>(![X1323:$i, X1324:$i > $o]:((?[X1325:$i]:(((in @ X1325 @ X1323)&~(X1324 @ X1325)))=>~(![X1326:$i]:(((in @ X1326 @ X1323)=>(X1324 @ X1326))))))=>(![X806:$o]:(((X806)=>(in @ emptyset @ (prop2set @ ((X806))))))=>(![X1322:$o]:(((X1322)=>(set2prop @ (prop2set @ ((X1322))))))=>(![X807:$i, X808:$i > $o]:((~(?[X809:$i]:(((in @ X809 @ X807)&(X808 @ X809))))=>![X810:$i]:(((in @ X810 @ X807)=>~(X808 @ X810)))))=>(![X811:$i, X812:$i > $o]:((~(![X813:$i]:(((in @ X813 @ X811)=>(X812 @ X813))))=>?[X814:$i]:(((in @ X814 @ X811)&~(X812 @ X814)))))=>(![X1317:$i > $o]:((?[X1318:$i]:(((X1317 @ X1318)&![X1319:$i]:(((X1317 @ X1319)=>((X1318)=(X1319))))))=>?[X1320:$i]:(((X1317 @ X1320)&![X1321:$i]:(((X1317 @ X1321)=>((X1320)=(X1321))))))))=>(![X1311:$i > $o]:((?[X1312:$i]:((X1311 @ X1312))=>(![X1313:$i, X1314:$i]:(((X1311 @ X1313)=>((X1311 @ X1314)=>((X1313)=(X1314)))))=>?[X1315:$i]:(((X1311 @ X1315)&![X1316:$i]:(((X1311 @ X1316)=>((X1315)=(X1316)))))))))=>(![X815:$i > 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binintersectSubset5]), noeltsimpempty]), omega0Ax]), inCongP]), binunionEcases]), c_0_247]), c_0_248]), disjointsetsI1]), prop2set2propI]), quantDeMorgan4]), quantDeMorgan1]), binintersectRsub]), vacuousDall]), c_0_249]), binintersectSubset4]), upairsetIL]), upairsetE]), singletonsswitch]), binintersectSubset1]), eqinunit]), uniqinunit]), bs114d]), c_0_250]), c_0_251]), subPowSU]), emptyinPowerset]), setminusEL]), powersetI]), c_0_252]), setminusER]), emptyinunitempty]), setunionsingleton]), setext]), emptysetimpfalse]), prop2setE]), setminusERneg]), c_0_253]), c_0_254]), setminusILneg]), c_0_255]), wellorderingAx]), c_0_256]), setminusIRneg]), omegaIndAx]), omegaSAx]), setminusSubset1]), symdiffI2]), symdiffIneg2]), secondinupair]), singletoninpowunion]), binintersectEL]), upairset2E]), ubforcartprodlem1]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), c_0_257]), funcext2]), c_0_258]), c_0_259]), c_0_260]), setukpairinjL1]), c_0_261]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), binintersectLsub]), setukpairinjR2]), c_0_262]), kpairsurjEq]), cartprodsndin]), cartprodpairmemER]), cartprodpairsurjEq]), c_0_263]), c_0_264]), c_0_265]), c_0_266]), binintersectSubset2]), app]), c_0_267]), c_0_268]), funcGraphProp1]), funcGraphProp2]), funcextLem]), c_0_269]), c_0_270]), ap2apEq1]), ap2apEq2]), c_0_271]), c_0_272]), funcext]), funcGraphProp4]), funcGraphProp3]), c_0_273]), c_0_274]), c_0_275]), funcinfuncset]), ap2p]), infuncsetfunc]), c_0_276]), c_0_277]), c_0_278]), c_0_279]), c_0_280]), cartprodsndpairEq]), cartprodfstpairEq]), cartprodmempaircEq]), cartprodpairmemEL]), ksndpairEq]), setukpairinjR]), upairequniteq]), setukpairinjR1]), setukpairinjL2]), cartprodfstin]), kfstpairEq]), c_0_281]), singletonsuniq]), c_0_282]), setunionsingleton2]), setunionsingleton1]), ubforcartprodlem3]), ubforcartprodlem2]), upairinpowunion]), upairsubunion]), singletoninpowerset]), singletonsubset]), kpairp]), kpairiskpair]), setukpairIR]), setukpairIL]), symdiffIneg1]), symdiffI1]), symdiffE]), setminusLsub]), setminusELneg]), setminusSubset2]), setminusI]), binintersectER]), binintersectSubset3]), binintersectI]), binunionRsub]), binunionLsub]), binunionE]), c_0_283]), c_0_284]), powersetE1]), setextsub]), subset2powerset]), subsetTrans]), subsetRefl]), notequalI1]), notsubsetI]), subsetE2]), subsetE]), subsetI2]), eqimpsubset1]), subsetI1]), c_0_285]), c_0_286]), omega__Cong]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), c_0_287]), binunionIR]), upairset2IR]), binunionIL]), powersetsubset]), inPowerset]), powersetI1]), subsetemptysetimpeq]), setadjoinSub2]), setadjoinSub]), notequalI2]), emptysetsubset]), eqimpsubset2]), c_0_288]), emptyset__Cong]), c_0_289]), in__Cong]), c_0_290]), notdallE]), notdexE]), prop2setI]), quantDeMorgan3]), quantDeMorgan2]), upairsetIR]), notinsingleton]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), setadjoinOr]), setadjoinE]), setadjoinIR]), setadjoinIL]), c_0_291]), c_0_292]), c_0_293]), c_0_294]), emptyI]), c_0_295]), notinemptyset]), emptysetE]), c_0_296]), c_0_297]), foundationAx]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_298])).
0.39/0.64	thf(c_0_300, negated_conjecture, ![X1410:$i, X1411:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1417:$i, X1418:$i, X1419:$i, X1420:$i, X1421:$i, X1423:$i, X1424:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1432:$i, X1433:$i > $i > $o, X1434:$i, X1436:$i, X1439:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1446:$i, X1447:$i > $o, X1448:$i, X1450:$i, X1451:$i > $o, X1452:$i, X1453:$i, X1454:$i > $o, X1455:$i, X1456:$i, X1457:$i > $o, X1458:$i, X1459:$i > $o, X1460:$i, X1463:$i, X1464:$o, X1465:$i, X1466:$i, X1467:$o, X1468:$i, X1469:$i, X1470:$i > $o, X1471:$i, X1474:$i, X1475:$i, X1478:$i, X1480:$i, X1482:$i, X1483:$i > $o, X1484:$i, X1485:$i, X1487:$i, X1488:$i > $o, X1489:$i, X1490:$i, X1491:$i, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$o, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i, X1506:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1512:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$o, X1520:$i, X1521:$i, X1522:$i > $o, X1523:$i, X1526:$i, X1527:$i, X1528:$i, X1530:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i > $o, X1547:$i, X1548:$i > $o, X1549:$i, X1550:$i, X1551:$i > $o, X1552:$i, X1554:$i, X1555:$i > $o, X1557:$i, X1558:$i, X1559:$i > $o, X1561:$i, X1562:$i, X1563:$i > $o, X1564:$i, X1566:$o, X1567:$o, X1568:$i, X1569:$i > $o, X1571:$i, X1572:$i, X1573:$i > $o, X1574:$i, X1576:$i > $o, X1577:$i, X1580:$i, X1581:$i > $o, X1582:$i, X1586:$i, X1587:$i > $o, X1588:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1599:$i, X1600:$i > $o, X1601:$i, X1603:$i, X1604:$i, X1605:$i > $o, X1606:$i > $o, X1609:$i, X1612:$i, X1613:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i > $o, X1626:$i, X1628:$i, X1629:$i, X1630:$i > $o, X1631:$i > $o, X1634:$i, X1636:$i, X1638:$i, X1639:$i, X1640:$i > $o, X1641:$i > $o, X1644:$i, X1645:$i, X1647:$i, X1648:$i, X1649:$i, X1650:$i, X1651:$i, X1652:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$i, X1685:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i > $o, X1692:$i, X1693:$i > $o, X1694:$i, X1695:$i, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$o, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i, X1773:$o, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i > $o, X1848:$i, X1850:$i, X1851:$i > $o, X1852:$i, X1854:$i, X1855:$i > $o, X1856:$i, X1859:$i, X1860:$i > $o, X1863:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i > $i > $o, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i > $i > $o, X1945:$i, X1946:$i, X1947:$i > $i > $o, X1948:$i, X1949:$i, X1950:$i > $i > $o, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i > $i > $o, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i > $i > $o, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i > $i > $o, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i > $i, X1995:$i, X1996:$i, X1997:$i > $i, X1999:$i, X2000:$i, X2001:$i > $i, X2003:$i, X2004:$i, X2005:$i, X2006:$i > $o, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i > $o, X2016:$i, X2017:$i, X2018:$i > $o, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i > $i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2090:$i]:((((~(in @ (esk1_2 @ X1410 @ X1411) @ X1410)|~(in @ (esk1_2 @ X1410 @ X1411) @ X1411)|((X1410)=(X1411)))&((in @ (esk1_2 @ X1410 @ X1411) @ X1410)|(in @ (esk1_2 @ X1410 @ X1411) @ X1411)|((X1410)=(X1411))))&(~(in @ X1413 @ emptyset)&(((~(in @ X1416 @ (setadjoin @ X1414 @ X1415))|(((X1416)=(X1414))|(in @ X1416 @ X1415)))&((((X1416)!=(X1414))|(in @ X1416 @ (setadjoin @ X1414 @ X1415)))&(~(in @ X1416 @ X1415)|(in @ X1416 @ (setadjoin @ X1414 @ X1415)))))&(((~(in @ X1418 @ (powerset @ X1417))|(~(in @ X1419 @ X1418)|(in @ X1419 @ X1417)))&(((in @ (esk2_2 @ X1420 @ X1421) @ X1421)|(in @ X1421 @ (powerset @ X1420)))&(~(in @ (esk2_2 @ X1420 @ X1421) @ X1420)|(in @ X1421 @ (powerset @ X1420)))))&(((((in @ X1424 @ (esk3_2 @ X1423 @ X1424))|~(in @ 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@ X2050 @ (cartprod @ X2047 @ X2048))|~(subset @ X2049 @ (cartprod @ X2047 @ X2048)))&(((in @ (kpair @ (esk78_4 @ X2047 @ X2048 @ X2049 @ X2050) @ (esk79_4 @ X2047 @ X2048 @ X2049 @ X2050)) @ X2049)|(subset @ X2049 @ X2050)|~(subset @ X2050 @ (cartprod @ X2047 @ X2048))|~(subset @ X2049 @ (cartprod @ X2047 @ X2048)))&(~(in @ (kpair @ (esk78_4 @ X2047 @ X2048 @ X2049 @ X2050) @ (esk79_4 @ X2047 @ X2048 @ X2049 @ X2050)) @ X2050)|(subset @ X2049 @ X2050)|~(subset @ X2050 @ (cartprod @ X2047 @ X2048))|~(subset @ X2049 @ (cartprod @ X2047 @ X2048))))))&(((((in @ (esk82_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2053)|((X2055)=(X2056))|(in @ (esk80_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2053)|~(subset @ X2056 @ (cartprod @ X2053 @ X2054))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))&(((in @ (esk83_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2054)|((X2055)=(X2056))|(in @ (esk80_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2053)|~(subset @ X2056 @ (cartprod @ X2053 @ X2054))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))&(((in @ (kpair @ (esk82_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk83_4 @ X2053 @ X2054 @ X2055 @ X2056)) @ X2056)|((X2055)=(X2056))|(in @ (esk80_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2053)|~(subset @ X2056 @ (cartprod @ X2053 @ X2054))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))&(~(in @ (kpair @ (esk82_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk83_4 @ X2053 @ X2054 @ X2055 @ X2056)) @ X2055)|((X2055)=(X2056))|(in @ (esk80_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2053)|~(subset @ X2056 @ (cartprod @ X2053 @ X2054))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054))))))&((((in @ (esk82_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2053)|((X2055)=(X2056))|(in @ (esk81_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2054)|~(subset @ X2056 @ (cartprod @ X2053 @ X2054))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))&(((in @ (esk83_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2054)|((X2055)=(X2056))|(in @ (esk81_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2054)|~(subset @ X2056 @ (cartprod @ X2053 @ X2054))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))&(((in @ (kpair @ (esk82_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk83_4 @ X2053 @ X2054 @ X2055 @ X2056)) @ X2056)|((X2055)=(X2056))|(in @ (esk81_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2054)|~(subset @ X2056 @ (cartprod @ X2053 @ X2054))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))&(~(in @ (kpair @ (esk82_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk83_4 @ X2053 @ X2054 @ X2055 @ X2056)) @ X2055)|((X2055)=(X2056))|(in @ (esk81_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2054)|~(subset @ X2056 @ (cartprod @ X2053 @ X2054))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054))))))&((((in @ (esk82_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2053)|((X2055)=(X2056))|(in @ (kpair @ (esk80_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk81_4 @ X2053 @ X2054 @ X2055 @ X2056)) @ X2055)|~(subset @ X2056 @ (cartprod @ X2053 @ X2054))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))&(((in @ (esk83_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2054)|((X2055)=(X2056))|(in @ (kpair @ (esk80_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk81_4 @ X2053 @ X2054 @ X2055 @ X2056)) @ X2055)|~(subset @ X2056 @ (cartprod @ X2053 @ X2054))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))&(((in @ (kpair @ (esk82_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk83_4 @ X2053 @ X2054 @ X2055 @ X2056)) @ X2056)|((X2055)=(X2056))|(in @ (kpair @ (esk80_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk81_4 @ X2053 @ X2054 @ X2055 @ X2056)) @ X2055)|~(subset @ X2056 @ (cartprod @ X2053 @ X2054))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))&(~(in @ (kpair @ (esk82_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk83_4 @ X2053 @ X2054 @ X2055 @ X2056)) @ X2055)|((X2055)=(X2056))|(in @ (kpair @ (esk80_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk81_4 @ X2053 @ X2054 @ X2055 @ X2056)) @ X2055)|~(subset @ X2056 @ (cartprod @ X2053 @ X2054))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054))))))&(((in @ (esk82_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2053)|((X2055)=(X2056))|~(in @ (kpair @ (esk80_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk81_4 @ X2053 @ X2054 @ X2055 @ X2056)) @ X2056)|~(subset @ X2056 @ (cartprod @ X2053 @ X2054))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))&(((in @ (esk83_4 @ X2053 @ X2054 @ X2055 @ X2056) @ X2054)|((X2055)=(X2056))|~(in @ (kpair @ (esk80_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk81_4 @ X2053 @ X2054 @ X2055 @ X2056)) @ X2056)|~(subset @ X2056 @ (cartprod @ X2053 @ X2054))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))&(((in @ (kpair @ (esk82_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk83_4 @ X2053 @ X2054 @ X2055 @ X2056)) @ X2056)|((X2055)=(X2056))|~(in @ (kpair @ (esk80_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk81_4 @ X2053 @ X2054 @ X2055 @ X2056)) @ X2056)|~(subset @ X2056 @ (cartprod @ X2053 @ X2054))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))&(~(in @ (kpair @ (esk82_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk83_4 @ X2053 @ X2054 @ X2055 @ X2056)) @ X2055)|((X2055)=(X2056))|~(in @ (kpair @ (esk80_4 @ X2053 @ X2054 @ X2055 @ X2056) @ (esk81_4 @ X2053 @ X2054 @ X2055 @ X2056)) @ X2056)|~(subset @ X2056 @ (cartprod @ X2053 @ X2054))|~(subset @ X2055 @ (cartprod @ X2053 @ X2054)))))))))&((((in @ (esk84_4 @ X2061 @ X2062 @ X2063 @ X2064) @ X2061)|((X2063)=(X2064))|~(func @ X2061 @ X2062 @ X2064)|~(func @ X2061 @ X2062 @ X2063))&(((ap @ X2061 @ X2062 @ X2063 @ (esk84_4 @ X2061 @ X2062 @ X2063 @ X2064))!=(ap @ X2061 @ X2062 @ X2064 @ (esk84_4 @ X2061 @ X2062 @ X2063 @ X2064)))|((X2063)=(X2064))|~(func @ X2061 @ X2062 @ X2064)|~(func @ X2061 @ X2062 @ X2063)))&((((in @ (esk85_4 @ X2066 @ X2067 @ X2068 @ X2069) @ X2066)|((X2068)=(X2069))|~(in @ X2069 @ (funcSet @ X2066 @ X2067))|~(in @ X2068 @ (funcSet @ X2066 @ X2067)))&(((ap @ X2066 @ X2067 @ X2068 @ (esk85_4 @ X2066 @ X2067 @ X2068 @ X2069))!=(ap @ X2066 @ X2067 @ X2069 @ (esk85_4 @ X2066 @ X2067 @ X2068 @ X2069)))|((X2068)=(X2069))|~(in @ X2069 @ (funcSet @ X2066 @ X2067))|~(in @ X2068 @ (funcSet @ X2066 @ X2067))))&((~(in @ X2073 @ (funcSet @ X2071 @ X2072))|(~(in @ X2074 @ X2071)|((ap @ X2071 @ X2072 @ X2073 @ X2074)=(ap @ X2071 @ X2072 @ X2073 @ X2074))))&((~(func @ X2075 @ X2076 @ X2077)|(~(in @ X2078 @ X2075)|((ap @ X2075 @ X2076 @ X2077 @ X2078)=(ap @ X2075 @ X2076 @ X2077 @ X2078))))&((((in @ (esk86_3 @ X2079 @ X2080 @ X2081) @ X2079)|(~(in @ X2083 @ X2079)|((ap @ X2079 @ X2080 @ (lam @ X2079 @ X2080 @ X2081) @ X2083)=(X2081 @ X2083))))&(~(in @ (X2081 @ (esk86_3 @ X2079 @ X2080 @ X2081)) @ X2080)|(~(in @ X2083 @ X2079)|((ap @ X2079 @ X2080 @ (lam @ X2079 @ X2080 @ X2081) @ X2083)=(X2081 @ X2083)))))&((~(func @ X2084 @ X2085 @ X2086)|((lam @ X2084 @ X2085 @ (ap @ X2084 @ X2085 @ X2086))=(X2086)))&((~(in @ X2090 @ esk87_0)|(in @ (esk89_0 @ X2090) @ esk88_0))&((lam @ esk87_0 @ esk88_0 @ esk89_0)!=(lam @ esk87_0 @ esk88_0 @ esk89_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_299])])])])])])).
0.39/0.64	thf(c_0_301, negated_conjecture, ((lam @ esk87_0 @ esk88_0 @ esk89_0)!=(lam @ esk87_0 @ esk88_0 @ esk89_0)), inference(split_conjunct,[status(thm)],[c_0_300])).
0.39/0.64	thf(c_0_302, negated_conjecture, ($false), inference(cn,[status(thm)],[c_0_301]), ['proof']).
0.39/0.64	# SZS output end CNFRefutation
0.39/0.64	# Parsed axioms                        : 470
0.39/0.64	# Removed by relevancy pruning/SinE    : 250
0.39/0.64	# Initial clauses                      : 398
0.39/0.64	# Removed in clause preprocessing      : 26
0.39/0.64	# Initial clauses in saturation        : 372
0.39/0.64	# Processed clauses                    : 1
0.39/0.64	# ...of these trivial                  : 0
0.39/0.64	# ...subsumed                          : 0
0.39/0.64	# ...remaining for further processing  : 0
0.39/0.64	# Other redundant clauses eliminated   : 0
0.39/0.64	# Clauses deleted for lack of memory   : 0
0.39/0.64	# Backward-subsumed                    : 0
0.39/0.64	# Backward-rewritten                   : 0
0.39/0.64	# Generated clauses                    : 0
0.39/0.64	# ...of the previous two non-redundant : 0
0.39/0.64	# ...aggressively subsumed             : 0
0.39/0.64	# Contextual simplify-reflections      : 0
0.39/0.64	# Paramodulations                      : 0
0.39/0.64	# Factorizations                       : 0
0.39/0.64	# NegExts                              : 0
0.39/0.64	# Equation resolutions                 : 0
0.39/0.64	# Total rewrite steps                  : 0
0.39/0.64	# Propositional unsat checks           : 0
0.39/0.64	#    Propositional check models        : 0
0.39/0.64	#    Propositional check unsatisfiable : 0
0.39/0.64	#    Propositional clauses             : 0
0.39/0.64	#    Propositional clauses after purity: 0
0.39/0.64	#    Propositional unsat core size     : 0
0.39/0.64	#    Propositional preprocessing time  : 0.000
0.39/0.64	#    Propositional encoding time       : 0.000
0.39/0.64	#    Propositional solver time         : 0.000
0.39/0.64	#    Success case prop preproc time    : 0.000
0.39/0.64	#    Success case prop encoding time   : 0.000
0.39/0.64	#    Success case prop solver time     : 0.000
0.39/0.64	# Current number of processed clauses  : 0
0.39/0.64	#    Positive orientable unit clauses  : 0
0.39/0.64	#    Positive unorientable unit clauses: 0
0.39/0.64	#    Negative unit clauses             : 0
0.39/0.64	#    Non-unit-clauses                  : 0
0.39/0.64	# Current number of unprocessed clauses: 371
0.39/0.64	# ...number of literals in the above   : 1185
0.39/0.64	# Current number of archived formulas  : 0
0.39/0.64	# Current number of archived clauses   : 0
0.39/0.64	# Clause-clause subsumption calls (NU) : 0
0.39/0.64	# Rec. Clause-clause subsumption calls : 0
0.39/0.64	# Non-unit clause-clause subsumptions  : 0
0.39/0.64	# Unit Clause-clause subsumption calls : 0
0.39/0.64	# Rewrite failures with RHS unbound    : 0
0.39/0.64	# BW rewrite match attempts            : 0
0.39/0.64	# BW rewrite match successes           : 0
0.39/0.64	# Condensation attempts                : 0
0.39/0.64	# Condensation successes               : 0
0.39/0.64	# Termbank termtop insertions          : 50925
0.39/0.64	
0.39/0.64	# -------------------------------------------------
0.39/0.64	# User time                : 0.059 s
0.39/0.64	# System time              : 0.013 s
0.39/0.64	# Total time               : 0.071 s
0.39/0.64	# Maximum resident set size: 7104 pages
0.75/180.02	
0.75/180.02	# -------------------------------------------------
0.75/180.02	# User time                : 0.070 s
0.75/180.02	# System time              : 0.017 s
0.75/180.02	# Total time               : 0.087 s
0.75/180.02	# Maximum resident set size: 2604 pages
0.75/180.02	% E---3.1 exiting
0.75/180.02	EOF