0.09/0.13	% Problem    : Vampire---4.8_7426 : TPTP v0.0.0. Released v0.0.0.
0.09/0.14	% Command    : run_E %s %d THM
0.13/0.34	% Computer : n024.cluster.edu
0.13/0.34	% Model    : x86_64 x86_64
0.13/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory   : 8042.1875MB
0.13/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 1440
0.13/0.34	% WCLimit    : 180
0.13/0.34	% DateTime   : Mon Jul  3 12:58:53 EDT 2023
0.13/0.34	% CPUTime    : 
0.18/0.48	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.v9GU9nN78k/Vampire---4.8_7426
0.18/0.48	# Version: 3.1pre001-ho
164.62/21.20	# Preprocessing class: HSLMSLSSLLLCHSA.
164.62/21.20	# Scheduled 5 strats onto 8 cores with 180 seconds (1440 total)
164.62/21.20	# Starting ho_unfolding_5 with 720s (4) cores
164.62/21.20	# Starting pre_casc_3 with 180s (1) cores
164.62/21.20	# Starting new_ho_10_cnf2 with 180s (1) cores
164.62/21.20	# Starting full_lambda_10 with 180s (1) cores
164.62/21.20	# Starting ehoh_best_nonlift_rwall with 180s (1) cores
164.62/21.20	# full_lambda_10 with pid 7609 completed with status 0
164.62/21.20	# Result found by full_lambda_10
164.62/21.20	# Preprocessing class: HSLMSLSSLLLCHSA.
164.62/21.20	# Scheduled 5 strats onto 8 cores with 180 seconds (1440 total)
164.62/21.20	# Starting ho_unfolding_5 with 720s (4) cores
164.62/21.20	# Starting pre_casc_3 with 180s (1) cores
164.62/21.20	# Starting new_ho_10_cnf2 with 180s (1) cores
164.62/21.20	# Starting full_lambda_10 with 180s (1) cores
164.62/21.20	# SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
164.62/21.20	# Search class: HGHSM-FSLM32-DHSMMSBN
164.62/21.20	# partial match(1): HGHSM-FSLM32-MHSMMSBN
164.62/21.20	# Scheduled 12 strats onto 1 cores with 180 seconds (180 total)
164.62/21.20	# Starting full_lambda_5 with 15s (1) cores
164.62/21.20	# full_lambda_5 with pid 7611 completed with status 7
164.62/21.20	# Starting full_lambda_10 with 19s (1) cores
164.62/21.20	# full_lambda_10 with pid 7625 completed with status 0
164.62/21.20	# Result found by full_lambda_10
164.62/21.20	# Preprocessing class: HSLMSLSSLLLCHSA.
164.62/21.20	# Scheduled 5 strats onto 8 cores with 180 seconds (1440 total)
164.62/21.20	# Starting ho_unfolding_5 with 720s (4) cores
164.62/21.20	# Starting pre_casc_3 with 180s (1) cores
164.62/21.20	# Starting new_ho_10_cnf2 with 180s (1) cores
164.62/21.20	# Starting full_lambda_10 with 180s (1) cores
164.62/21.20	# SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
164.62/21.20	# Search class: HGHSM-FSLM32-DHSMMSBN
164.62/21.20	# partial match(1): HGHSM-FSLM32-MHSMMSBN
164.62/21.20	# Scheduled 12 strats onto 1 cores with 180 seconds (180 total)
164.62/21.20	# Starting full_lambda_5 with 15s (1) cores
164.62/21.20	# full_lambda_5 with pid 7611 completed with status 7
164.62/21.20	# Starting full_lambda_10 with 19s (1) cores
164.62/21.20	# Preprocessing time       : 0.008 s
164.62/21.20	# Presaturation interreduction done
164.62/21.20	
164.62/21.20	# Proof found!
164.62/21.20	# SZS status Theorem
164.62/21.20	# SZS output start CNFRefutation
164.62/21.20	thf(decl_22, type, in: $i > $i > $o).
164.62/21.20	thf(decl_23, type, exu: ($i > $o) > $o).
164.62/21.20	thf(decl_24, type, setextAx: $o).
164.62/21.20	thf(decl_25, type, emptyset: $i).
164.62/21.20	thf(decl_26, type, emptysetAx: $o).
164.62/21.20	thf(decl_27, type, setadjoin: $i > $i > $i).
164.62/21.20	thf(decl_28, type, setadjoinAx: $o).
164.62/21.20	thf(decl_29, type, powerset: $i > $i).
164.62/21.20	thf(decl_30, type, powersetAx: $o).
164.62/21.20	thf(decl_31, type, setunion: $i > $i).
164.62/21.20	thf(decl_32, type, setunionAx: $o).
164.62/21.20	thf(decl_33, type, omega: $i).
164.62/21.20	thf(decl_34, type, omega0Ax: $o).
164.62/21.20	thf(decl_35, type, omegaSAx: $o).
164.62/21.20	thf(decl_36, type, omegaIndAx: $o).
164.62/21.20	thf(decl_37, type, replAx: $o).
164.62/21.20	thf(decl_38, type, foundationAx: $o).
164.62/21.20	thf(decl_39, type, wellorderingAx: $o).
164.62/21.20	thf(decl_40, type, descr: ($i > $o) > $i).
164.62/21.20	thf(decl_41, type, descrp: $o).
164.62/21.20	thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
164.62/21.20	thf(decl_43, type, dsetconstrI: $o).
164.62/21.20	thf(decl_44, type, dsetconstrEL: $o).
164.62/21.20	thf(decl_45, type, dsetconstrER: $o).
164.62/21.20	thf(decl_46, type, exuE1: $o).
164.62/21.20	thf(decl_47, type, prop2set: $o > $i).
164.62/21.20	thf(decl_48, type, prop2setE: $o).
164.62/21.20	thf(decl_49, type, emptysetE: $o).
164.62/21.20	thf(decl_50, type, emptysetimpfalse: $o).
164.62/21.20	thf(decl_51, type, notinemptyset: $o).
164.62/21.20	thf(decl_52, type, exuE3e: $o).
164.62/21.20	thf(decl_53, type, setext: $o).
164.62/21.20	thf(decl_54, type, emptyI: $o).
164.62/21.20	thf(decl_55, type, noeltsimpempty: $o).
164.62/21.20	thf(decl_56, type, setbeta: $o).
164.62/21.20	thf(decl_57, type, nonempty: $i > $o).
164.62/21.20	thf(decl_58, type, nonemptyE1: $o).
164.62/21.20	thf(decl_59, type, nonemptyI: $o).
164.62/21.20	thf(decl_60, type, nonemptyI1: $o).
164.62/21.20	thf(decl_61, type, setadjoinIL: $o).
164.62/21.20	thf(decl_62, type, emptyinunitempty: $o).
164.62/21.20	thf(decl_63, type, setadjoinIR: $o).
164.62/21.20	thf(decl_64, type, setadjoinE: $o).
164.62/21.20	thf(decl_65, type, setadjoinOr: $o).
164.62/21.20	thf(decl_66, type, setoftrueEq: $o).
164.62/21.20	thf(decl_67, type, powersetI: $o).
164.62/21.20	thf(decl_68, type, emptyinPowerset: $o).
164.62/21.20	thf(decl_69, type, emptyInPowerset: $o).
164.62/21.20	thf(decl_70, type, powersetE: $o).
164.62/21.20	thf(decl_71, type, setunionI: $o).
164.62/21.20	thf(decl_72, type, setunionE: $o).
164.62/21.20	thf(decl_73, type, subPowSU: $o).
164.62/21.20	thf(decl_74, type, exuE2: $o).
164.62/21.20	thf(decl_75, type, nonemptyImpWitness: $o).
164.62/21.20	thf(decl_76, type, uniqinunit: $o).
164.62/21.20	thf(decl_77, type, notinsingleton: $o).
164.62/21.20	thf(decl_78, type, eqinunit: $o).
164.62/21.20	thf(decl_79, type, singletonsswitch: $o).
164.62/21.20	thf(decl_80, type, upairsetE: $o).
164.62/21.20	thf(decl_81, type, upairsetIL: $o).
164.62/21.20	thf(decl_82, type, upairsetIR: $o).
164.62/21.20	thf(decl_83, type, emptyE1: $o).
164.62/21.20	thf(decl_84, type, vacuousDall: $o).
164.62/21.20	thf(decl_85, type, quantDeMorgan1: $o).
164.62/21.20	thf(decl_86, type, quantDeMorgan2: $o).
164.62/21.20	thf(decl_87, type, quantDeMorgan3: $o).
164.62/21.20	thf(decl_88, type, quantDeMorgan4: $o).
164.62/21.20	thf(decl_89, type, prop2setI: $o).
164.62/21.20	thf(decl_90, type, set2prop: $i > $o).
164.62/21.20	thf(decl_91, type, prop2set2propI: $o).
164.62/21.20	thf(decl_92, type, notdexE: $o).
164.62/21.20	thf(decl_93, type, notdallE: $o).
164.62/21.20	thf(decl_94, type, exuI1: $o).
164.62/21.20	thf(decl_95, type, exuI3: $o).
164.62/21.20	thf(decl_96, type, exuI2: $o).
164.62/21.20	thf(decl_97, type, inCongP: $o).
164.62/21.20	thf(decl_98, type, in__Cong: $o).
164.62/21.20	thf(decl_99, type, exuE3u: $o).
164.62/21.20	thf(decl_100, type, exu__Cong: $o).
164.62/21.20	thf(decl_101, type, emptyset__Cong: $o).
164.62/21.20	thf(decl_102, type, setadjoin__Cong: $o).
164.62/21.20	thf(decl_103, type, powerset__Cong: $o).
164.62/21.20	thf(decl_104, type, setunion__Cong: $o).
164.62/21.20	thf(decl_105, type, omega__Cong: $o).
164.62/21.20	thf(decl_106, type, exuEu: $o).
164.62/21.20	thf(decl_107, type, descr__Cong: $o).
164.62/21.20	thf(decl_108, type, dsetconstr__Cong: $o).
164.62/21.20	thf(decl_109, type, subset: $i > $i > $o).
164.62/21.20	thf(decl_112, type, subsetI1: $o).
164.62/21.20	thf(decl_113, type, eqimpsubset2: $o).
164.62/21.20	thf(decl_114, type, eqimpsubset1: $o).
164.62/21.20	thf(decl_115, type, subsetI2: $o).
164.62/21.20	thf(decl_116, type, emptysetsubset: $o).
164.62/21.20	thf(decl_117, type, subsetE: $o).
164.62/21.20	thf(decl_118, type, subsetE2: $o).
164.62/21.20	thf(decl_119, type, notsubsetI: $o).
164.62/21.20	thf(decl_120, type, notequalI1: $o).
164.62/21.20	thf(decl_121, type, notequalI2: $o).
164.62/21.20	thf(decl_122, type, subsetRefl: $o).
164.62/21.20	thf(decl_123, type, subsetTrans: $o).
164.62/21.20	thf(decl_124, type, setadjoinSub: $o).
164.62/21.20	thf(decl_125, type, setadjoinSub2: $o).
164.62/21.20	thf(decl_126, type, subset2powerset: $o).
164.62/21.20	thf(decl_127, type, setextsub: $o).
164.62/21.20	thf(decl_128, type, subsetemptysetimpeq: $o).
164.62/21.20	thf(decl_129, type, powersetI1: $o).
164.62/21.20	thf(decl_130, type, powersetE1: $o).
164.62/21.20	thf(decl_131, type, inPowerset: $o).
164.62/21.20	thf(decl_132, type, powersetsubset: $o).
164.62/21.20	thf(decl_133, type, sepInPowerset: $o).
164.62/21.20	thf(decl_134, type, sepSubset: $o).
164.62/21.20	thf(decl_135, type, binunion: $i > $i > $i).
164.62/21.20	thf(decl_136, type, binunionIL: $o).
164.62/21.20	thf(decl_137, type, upairset2IR: $o).
164.62/21.20	thf(decl_138, type, binunionIR: $o).
164.62/21.20	thf(decl_139, type, binunionEcases: $o).
164.62/21.20	thf(decl_140, type, binunionE: $o).
164.62/21.20	thf(decl_141, type, binunionLsub: $o).
164.62/21.20	thf(decl_142, type, binunionRsub: $o).
164.62/21.20	thf(decl_143, type, binintersect: $i > $i > $i).
164.62/21.20	thf(decl_144, type, binintersectI: $o).
164.62/21.20	thf(decl_145, type, binintersectSubset5: $o).
164.62/21.20	thf(decl_146, type, binintersectEL: $o).
164.62/21.20	thf(decl_147, type, binintersectLsub: $o).
164.62/21.20	thf(decl_148, type, binintersectSubset2: $o).
164.62/21.20	thf(decl_149, type, binintersectSubset3: $o).
164.62/21.20	thf(decl_150, type, binintersectER: $o).
164.62/21.20	thf(decl_151, type, disjointsetsI1: $o).
164.62/21.20	thf(decl_152, type, binintersectRsub: $o).
164.62/21.20	thf(decl_153, type, binintersectSubset4: $o).
164.62/21.20	thf(decl_154, type, binintersectSubset1: $o).
164.62/21.20	thf(decl_155, type, bs114d: $o).
164.62/21.20	thf(decl_157, type, setminus: $i > $i > $i).
164.62/21.20	thf(decl_158, type, setminusI: $o).
164.62/21.20	thf(decl_159, type, setminusEL: $o).
164.62/21.20	thf(decl_160, type, setminusER: $o).
164.62/21.20	thf(decl_161, type, setminusSubset2: $o).
164.62/21.20	thf(decl_162, type, setminusERneg: $o).
164.62/21.20	thf(decl_163, type, setminusELneg: $o).
164.62/21.20	thf(decl_164, type, setminusILneg: $o).
164.62/21.20	thf(decl_165, type, setminusIRneg: $o).
164.62/21.20	thf(decl_166, type, setminusLsub: $o).
164.62/21.20	thf(decl_167, type, setminusSubset1: $o).
164.62/21.20	thf(decl_168, type, symdiff: $i > $i > $i).
164.62/21.20	thf(decl_169, type, symdiffE: $o).
164.62/21.20	thf(decl_170, type, symdiffI1: $o).
164.62/21.20	thf(decl_171, type, symdiffI2: $o).
164.62/21.20	thf(decl_172, type, symdiffIneg1: $o).
164.62/21.20	thf(decl_173, type, symdiffIneg2: $o).
164.62/21.20	thf(decl_174, type, iskpair: $i > $o).
164.62/21.20	thf(decl_175, type, secondinupair: $o).
164.62/21.20	thf(decl_176, type, setukpairIL: $o).
164.62/21.20	thf(decl_177, type, setukpairIR: $o).
164.62/21.20	thf(decl_178, type, kpairiskpair: $o).
164.62/21.20	thf(decl_179, type, kpair: $i > $i > $i).
164.62/21.20	thf(decl_180, type, kpairp: $o).
164.62/21.20	thf(decl_181, type, cartprod: $i > $i > $i).
164.62/21.20	thf(decl_182, type, singletonsubset: $o).
164.62/21.20	thf(decl_183, type, singletoninpowerset: $o).
164.62/21.20	thf(decl_184, type, singletoninpowunion: $o).
164.62/21.20	thf(decl_185, type, upairset2E: $o).
164.62/21.20	thf(decl_186, type, upairsubunion: $o).
164.62/21.20	thf(decl_187, type, upairinpowunion: $o).
164.62/21.20	thf(decl_188, type, ubforcartprodlem1: $o).
164.62/21.20	thf(decl_189, type, ubforcartprodlem2: $o).
164.62/21.20	thf(decl_190, type, ubforcartprodlem3: $o).
164.62/21.20	thf(decl_191, type, cartprodpairin: $o).
164.62/21.20	thf(decl_192, type, cartprodmempair1: $o).
164.62/21.20	thf(decl_193, type, cartprodmempair: $o).
164.62/21.20	thf(decl_194, type, setunionE2: $o).
164.62/21.20	thf(decl_195, type, setunionsingleton1: $o).
164.62/21.20	thf(decl_196, type, setunionsingleton2: $o).
164.62/21.20	thf(decl_197, type, setunionsingleton: $o).
164.62/21.20	thf(decl_198, type, singleton: $i > $o).
164.62/21.20	thf(decl_199, type, singletonprop: $o).
164.62/21.20	thf(decl_200, type, ex1: $i > ($i > $o) > $o).
164.62/21.20	thf(decl_201, type, ex1E1: $o).
164.62/21.20	thf(decl_202, type, ex1I: $o).
164.62/21.20	thf(decl_203, type, ex1I2: $o).
164.62/21.20	thf(decl_204, type, singletonsuniq: $o).
164.62/21.20	thf(decl_209, type, setukpairinjL1: $o).
164.62/21.20	thf(decl_210, type, kfstsingleton: $o).
164.62/21.20	thf(decl_211, type, theprop: $o).
164.62/21.20	thf(decl_212, type, kfst: $i > $i).
164.62/21.20	thf(decl_213, type, kfstpairEq: $o).
164.62/21.20	thf(decl_214, type, cartprodfstin: $o).
164.62/21.20	thf(decl_215, type, setukpairinjL2: $o).
164.62/21.20	thf(decl_216, type, setukpairinjL: $o).
164.62/21.20	thf(decl_217, type, setukpairinjR11: $o).
164.62/21.20	thf(decl_218, type, setukpairinjR12: $o).
164.62/21.20	thf(decl_219, type, setukpairinjR1: $o).
164.62/21.20	thf(decl_220, type, upairequniteq: $o).
164.62/21.20	thf(decl_221, type, setukpairinjR2: $o).
164.62/21.20	thf(decl_222, type, setukpairinjR: $o).
164.62/21.20	thf(decl_223, type, ksndsingleton: $o).
164.62/21.20	thf(decl_224, type, ksnd: $i > $i).
164.62/21.20	thf(decl_225, type, ksndpairEq: $o).
164.62/21.20	thf(decl_226, type, kpairsurjEq: $o).
164.62/21.20	thf(decl_227, type, cartprodsndin: $o).
164.62/21.20	thf(decl_228, type, cartprodpairmemEL: $o).
164.62/21.20	thf(decl_229, type, cartprodpairmemER: $o).
164.62/21.20	thf(decl_230, type, cartprodmempaircEq: $o).
164.62/21.20	thf(decl_231, type, cartprodfstpairEq: $o).
164.62/21.20	thf(decl_232, type, cartprodsndpairEq: $o).
164.62/21.20	thf(decl_233, type, cartprodpairsurjEq: $o).
164.62/21.20	thf(decl_234, type, breln: $i > $i > $i > $o).
164.62/21.20	thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
164.62/21.20	thf(decl_236, type, dpsetconstrI: $o).
164.62/21.20	thf(decl_237, type, dpsetconstrSub: $o).
164.62/21.20	thf(decl_238, type, setOfPairsIsBReln: $o).
164.62/21.20	thf(decl_239, type, dpsetconstrERa: $o).
164.62/21.20	thf(decl_240, type, dpsetconstrEL1: $o).
164.62/21.20	thf(decl_241, type, dpsetconstrEL2: $o).
164.62/21.20	thf(decl_242, type, dpsetconstrER: $o).
164.62/21.20	thf(decl_243, type, func: $i > $i > $i > $o).
164.62/21.20	thf(decl_244, type, funcSet: $i > $i > $i).
164.62/21.20	thf(decl_245, type, funcImageSingleton: $o).
164.62/21.20	thf(decl_246, type, apProp: $o).
164.62/21.20	thf(decl_247, type, ap: $i > $i > $i > $i > $i).
164.62/21.20	thf(decl_248, type, app: $o).
164.62/21.20	thf(decl_249, type, infuncsetfunc: $o).
164.62/21.20	thf(decl_250, type, ap2p: $o).
164.62/21.20	thf(decl_251, type, funcinfuncset: $o).
164.62/21.20	thf(decl_252, type, lamProp: $o).
164.62/21.20	thf(decl_253, type, lam: $i > $i > ($i > $i) > $i).
164.62/21.20	thf(decl_254, type, lamp: $o).
164.62/21.20	thf(decl_255, type, lam2p: $o).
164.62/21.20	thf(decl_256, type, brelnall1: $o).
164.62/21.20	thf(decl_257, type, brelnall2: $o).
164.62/21.20	thf(decl_258, type, ex1E2: $o).
164.62/21.20	thf(decl_259, type, funcGraphProp1: $o).
164.62/21.20	thf(decl_260, type, funcGraphProp3: $o).
164.62/21.20	thf(decl_261, type, funcGraphProp2: $o).
164.62/21.20	thf(decl_262, type, funcextLem: $o).
164.62/21.20	thf(decl_263, type, funcGraphProp4: $o).
164.62/21.20	thf(decl_264, type, subbreln: $o).
164.62/21.20	thf(decl_265, type, eqbreln: $o).
164.62/21.20	thf(decl_266, type, funcext: $o).
164.62/21.20	thf(decl_267, type, funcext2: $o).
164.62/21.20	thf(decl_268, type, ap2apEq1: $o).
164.62/21.20	thf(decl_269, type, ap2apEq2: $o).
164.62/21.20	thf(decl_270, type, beta1: $o).
164.62/21.20	thf(decl_271, type, eta1: $o).
164.62/21.20	thf(decl_272, type, lam2lamEq: $o).
164.62/21.20	thf(decl_273, type, epred1_0: $o).
164.62/21.20	thf(decl_274, type, esk1_2: $i > $i > $i).
164.62/21.20	thf(decl_275, type, esk2_2: $i > $i > $i).
164.62/21.20	thf(decl_276, type, esk3_2: $i > $i > $i).
164.62/21.20	thf(decl_277, type, esk4_1: $i > $i).
164.62/21.20	thf(decl_278, type, esk5_2: ($i > $i > $o) > $i > $i).
164.62/21.20	thf(decl_279, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
164.62/21.20	thf(decl_280, type, esk7_2: ($i > $i > $o) > $i > $i).
164.62/21.20	thf(decl_281, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
164.62/21.20	thf(decl_282, type, esk9_1: $i > $i).
164.62/21.20	thf(decl_283, type, esk10_2: ($i > $o) > $i > $i).
164.62/21.20	thf(decl_284, type, esk11_2: ($i > $o) > $i > $i).
164.62/21.20	thf(decl_285, type, esk12_1: ($i > $o) > $i).
164.62/21.20	thf(decl_286, type, esk13_2: ($i > $o) > $i > $i).
164.62/21.20	thf(decl_287, type, esk14_1: ($i > $o) > $i).
164.62/21.20	thf(decl_288, type, esk15_2: $i > $i > $i).
164.62/21.20	thf(decl_289, type, esk16_2: $i > $i > $i).
164.62/21.20	thf(decl_290, type, esk17_1: $i > $i).
164.62/21.20	thf(decl_291, type, esk18_1: $i > $i).
164.62/21.20	thf(decl_292, type, esk19_1: $i > $i).
164.62/21.20	thf(decl_293, type, esk20_2: $i > $i > $i).
164.62/21.20	thf(decl_294, type, esk21_3: $i > $i > $o > $i).
164.62/21.20	thf(decl_295, type, esk22_2: ($i > $o) > $i > $i).
164.62/21.20	thf(decl_296, type, esk23_1: ($i > $o) > $i).
164.62/21.20	thf(decl_297, type, esk24_1: $i > $i).
164.62/21.20	thf(decl_298, type, esk25_2: $i > ($i > $o) > $i).
164.62/21.20	thf(decl_299, type, esk26_2: $i > ($i > $o) > $i).
164.62/21.20	thf(decl_300, type, esk27_2: $i > ($i > $o) > $i).
164.62/21.20	thf(decl_301, type, esk28_2: $i > ($i > $o) > $i).
164.62/21.20	thf(decl_302, type, esk29_2: $i > ($i > $o) > $i).
164.62/21.20	thf(decl_303, type, esk30_2: $i > ($i > $o) > $i).
164.62/21.20	thf(decl_304, type, esk31_2: ($i > $o) > $i > $i).
164.62/21.20	thf(decl_305, type, esk32_1: ($i > $o) > $i).
164.62/21.20	thf(decl_306, type, esk33_1: ($i > $o) > $i).
164.62/21.20	thf(decl_307, type, esk34_1: ($i > $o) > $i).
164.62/21.20	thf(decl_308, type, esk35_1: ($i > $o) > $i).
164.62/21.20	thf(decl_309, type, esk36_2: ($i > $o) > $i > $i).
164.62/21.20	thf(decl_310, type, esk37_1: ($i > $o) > $i).
164.62/21.20	thf(decl_311, type, esk38_2: ($i > $o) > $i > $i).
164.62/21.20	thf(decl_312, type, esk39_2: ($i > $o) > ($i > $o) > $i).
164.62/21.20	thf(decl_313, type, esk40_2: ($i > $o) > ($i > $o) > $i).
164.62/21.20	thf(decl_314, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
164.62/21.20	thf(decl_315, type, esk42_2: ($i > $o) > ($i > $o) > $i).
164.62/21.20	thf(decl_316, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
164.62/21.20	thf(decl_317, type, esk44_2: ($i > $o) > ($i > $o) > $i).
164.62/21.20	thf(decl_318, type, esk45_2: ($i > $o) > $i > $i).
164.62/21.20	thf(decl_319, type, esk46_2: ($i > $o) > ($i > $o) > $i).
164.62/21.20	thf(decl_320, type, esk47_2: ($i > $o) > ($i > $o) > $i).
164.62/21.20	thf(decl_321, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
164.62/21.20	thf(decl_322, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
164.62/21.20	thf(decl_323, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
164.62/21.20	thf(decl_324, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
164.62/21.20	thf(decl_325, type, esk52_2: $i > $i > $i).
164.62/21.20	thf(decl_326, type, esk53_2: $i > $i > $i).
164.62/21.20	thf(decl_327, type, esk54_2: $i > $i > $i).
164.62/21.20	thf(decl_328, type, esk55_3: $i > $i > $i > $i).
164.62/21.20	thf(decl_329, type, esk56_3: $i > $i > $i > $i).
164.62/21.20	thf(decl_330, type, esk57_2: $i > $i > $i).
164.62/21.20	thf(decl_331, type, esk58_2: $i > ($i > $o) > $i).
164.62/21.20	thf(decl_332, type, esk59_2: $i > ($i > $o) > $i).
164.62/21.20	thf(decl_333, type, esk60_2: $i > ($i > $o) > $i).
164.62/21.20	thf(decl_334, type, esk61_2: $i > ($i > $o) > $i).
164.62/21.20	thf(decl_335, type, esk62_3: $i > ($i > $o) > $i > $i).
164.62/21.20	thf(decl_336, type, esk63_3: $i > ($i > $o) > $i > $i).
164.62/21.20	thf(decl_337, type, esk64_2: $i > ($i > $o) > $i).
164.62/21.20	thf(decl_338, type, esk65_2: $i > ($i > $o) > $i).
164.62/21.20	thf(decl_339, type, esk66_2: $i > ($i > $o) > $i).
164.62/21.20	thf(decl_340, type, esk67_1: $i > $i).
164.62/21.20	thf(decl_341, type, esk68_1: $i > $i).
164.62/21.20	thf(decl_342, type, esk69_4: $i > $i > $i > $i > $i).
164.62/21.20	thf(decl_343, type, esk70_3: $i > $i > ($i > $i) > $i).
164.62/21.20	thf(decl_344, type, esk71_3: $i > $i > ($i > $i) > $i).
164.62/21.20	thf(decl_345, type, esk72_3: $i > $i > ($i > $i) > $i).
164.62/21.20	thf(decl_346, type, esk73_4: $i > $i > $i > ($i > $o) > $i).
164.62/21.20	thf(decl_347, type, esk74_4: $i > $i > $i > ($i > $o) > $i).
164.62/21.20	thf(decl_348, type, esk75_4: $i > $i > $i > ($i > $o) > $i).
164.62/21.20	thf(decl_349, type, esk76_4: $i > $i > $i > ($i > $o) > $i).
164.62/21.20	thf(decl_350, type, esk77_4: $i > $i > $i > $i > $i).
164.62/21.20	thf(decl_351, type, esk78_4: $i > $i > $i > $i > $i).
164.62/21.20	thf(decl_352, type, esk79_4: $i > $i > $i > $i > $i).
164.62/21.20	thf(decl_353, type, esk80_4: $i > $i > $i > $i > $i).
164.62/21.20	thf(decl_354, type, esk81_4: $i > $i > $i > $i > $i).
164.62/21.20	thf(decl_355, type, esk82_4: $i > $i > $i > $i > $i).
164.62/21.20	thf(decl_356, type, esk83_4: $i > $i > $i > $i > $i).
164.62/21.20	thf(decl_357, type, esk84_4: $i > $i > $i > $i > $i).
164.62/21.20	thf(decl_358, type, esk85_4: $i > $i > $i > $i > $i).
164.62/21.20	thf(decl_359, type, esk86_3: $i > $i > ($i > $i) > $i).
164.62/21.20	thf(decl_360, type, esk87_3: $i > $i > ($i > $i) > $i).
164.62/21.20	thf(decl_361, type, esk88_0: $i).
164.62/21.20	thf(decl_362, type, esk89_0: $i).
164.62/21.20	thf(decl_363, type, esk90_0: $i > $i).
164.62/21.20	thf(decl_364, type, esk91_0: $i).
164.62/21.20	thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', ex1)).
164.62/21.20	thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', singleton)).
164.62/21.20	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', nonempty)).
164.62/21.20	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', exuE3u)).
164.62/21.20	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', exu)).
164.62/21.20	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', exuI2)).
164.62/21.20	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', exuI3)).
164.62/21.20	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', exuE2)).
164.62/21.20	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', nonemptyI)).
164.62/21.20	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', exuE1)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', ex1I)).
164.62/21.20	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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', ex1I2)).
164.62/21.20	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', kfstsingleton)).
164.62/21.20	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', ksndsingleton)).
164.62/21.20	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setOfPairsIsBReln)).
164.62/21.20	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', breln)).
164.62/21.20	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', funcImageSingleton)).
164.62/21.20	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.v9GU9nN78k/Vampire---4.8_7426', ex1E2)).
164.62/21.20	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', ex1E1)).
164.62/21.20	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', singletonprop)).
164.62/21.20	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', descr__Cong)).
164.62/21.20	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', exuEu)).
164.62/21.20	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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', exu__Cong)).
164.62/21.20	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', exuI1)).
164.62/21.20	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', exuE3e)).
164.62/21.20	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', descrp)).
164.62/21.20	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', replAx)).
164.62/21.20	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', nonemptyI1)).
164.62/21.20	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setoftrueEq)).
164.62/21.20	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', sepSubset)).
164.62/21.20	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', nonemptyE1)).
164.62/21.20	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', dsetconstrI)).
164.62/21.20	thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X38 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', lam2lamEq)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', eta1)).
164.62/21.20	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', theprop)).
164.62/21.20	thf(apProp, axiom, ((apProp)<=>![X4:$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.v9GU9nN78k/Vampire---4.8_7426', apProp)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', brelnall1)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', brelnall2)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', eqbreln)).
164.62/21.20	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:$i]:(X33 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', lam2p)).
164.62/21.20	thf(beta1, axiom, ((beta1)<=>![X4:$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.v9GU9nN78k/Vampire---4.8_7426', beta1)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', subbreln)).
164.62/21.20	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:$i]:(X32 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', lamp)).
164.62/21.20	thf(lamProp, axiom, ((lamProp)<=>![X4:$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.v9GU9nN78k/Vampire---4.8_7426', lamProp)).
164.62/21.20	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:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', dpsetconstrER)).
164.62/21.20	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', dpsetconstrEL2)).
164.62/21.20	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', dpsetconstrEL1)).
164.62/21.20	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', dpsetconstrERa)).
164.62/21.20	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', dpsetconstrSub)).
164.62/21.20	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', dpsetconstrI)).
164.62/21.20	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', sepInPowerset)).
164.62/21.20	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', dsetconstr__Cong)).
164.62/21.20	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.v9GU9nN78k/Vampire---4.8_7426', emptyE1)).
164.62/21.20	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', nonemptyImpWitness)).
164.62/21.20	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setbeta)).
164.62/21.20	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', dsetconstrER)).
164.62/21.20	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', dsetconstrEL)).
164.62/21.20	thf(beta2, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>(((setunionAx)=>(((omegaSAx)=>(((replAx)=>((((descrp)=>(((dsetconstrEL)=>((dsetconstrER)=>(((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>(((exuE3e)=>((setext)=>(((noeltsimpempty)=>((setbeta)=>((((((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((((emptyinPowerset)=>((((setunionI)=>(((((nonemptyImpWitness)=>((uniqinunit)=>((((((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((((((prop2setI)=>((prop2set2propI)=>(((notdallE)=>((exuI1)=>((((inCongP)=>((in__Cong)=>(((exu__Cong)=>(((setadjoin__Cong)=>((powerset__Cong)=>((((exuEu)=>((((subsetI1)=>((((subsetI2)=>(((subsetE)=>((((notequalI1)=>(((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>(((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>(((((sepSubset)=>((binunionIL)=>(((binunionIR)=>((binunionEcases)=>(((((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>(((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>(((binintersectSubset4)=>(((bs114d)=>((setminusI)=>(((setminusER)=>((((setminusELneg)=>(((setminusIRneg)=>(((setminusSubset1)=>((symdiffE)=>(((symdiffI2)=>((((secondinupair)=>(((((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>(((((((ubforcartprodlem3)=>((cartprodpairin)=>(((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((((ex1I)=>((ex1I2)=>((singletonsuniq)=>(((kfstsingleton)=>((theprop)=>((kfstpairEq)=>(((((((((((ksndsingleton)=>((ksndpairEq)=>(((((cartprodpairmemER)=>((cartprodmempaircEq)=>(((cartprodsndpairEq)=>(((((setOfPairsIsBReln)=>((((((funcImageSingleton)=>((apProp)=>(((((funcinfuncset)=>((((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>(((funcGraphProp3)=>(((funcextLem)=>((((eqbreln)=>(((funcext2)=>((ap2apEq1)=>((((eta1)=>((lam2lamEq)=>![X4:$i, X5:$i, X39:$i > $i]:((![X2:$i]:((((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X39 @ X3))) @ X2)=(X39 @ X2))<=(in @ X2 @ X4)))<=![X2:$i]:(((in @ (X39 @ X2) @ X5)<=(in @ X2 @ X4)))))))<=(beta1))<=(ap2apEq2))))<=(funcext)))<=(subbreln))<=(funcGraphProp4)))<=(funcGraphProp2)))<=(funcGraphProp1))))))<=(lamp))<=(lamProp)))<=(ap2p))<=(infuncsetfunc))<=(app))))<=(dpsetconstrER))<=(dpsetconstrEL2))<=(dpsetconstrEL1))<=(dpsetconstrERa)))<=(dpsetconstrSub))<=(dpsetconstrI))<=(cartprodpairsurjEq)))<=(cartprodfstpairEq))))<=(cartprodpairmemEL))<=(cartprodsndin))<=(kpairsurjEq))))<=(setukpairinjR))<=(setukpairinjR2))<=(upairequniteq))<=(setukpairinjR1))<=(setukpairinjR12))<=(setukpairinjR11))<=(setukpairinjL))<=(setukpairinjL2))<=(cartprodfstin)))))<=(setukpairinjL1)))))<=(ex1E1))<=(singletonprop)))))))<=(cartprodmempair1))))<=(ubforcartprodlem2))<=(ubforcartprodlem1))<=(upairinpowunion))<=(upairsubunion))<=(upairset2E))))))<=(kpairiskpair))<=(setukpairIR))<=(setukpairIL)))<=(symdiffIneg2))<=(symdiffIneg1)))<=(symdiffI1))))<=(setminusLsub)))<=(setminusILneg)))<=(setminusERneg))<=(setminusSubset2)))<=(setminusEL))))<=(binintersectSubset1)))<=(binintersectRsub)))))<=(binintersectSubset2))))))<=(binunionRsub))<=(binunionLsub))<=(binunionE))))<=(upairset2IR))))<=(sepInPowerset))<=(powersetsubset))<=(inPowerset)))))<=(setextsub)))))))<=(notequalI2)))<=(notsubsetI))<=(subsetE2)))<=(emptysetsubset)))<=(eqimpsubset1))<=(eqimpsubset2)))<=(dsetconstr__Cong))<=(descr__Cong)))<=(omega__Cong))<=(setunion__Cong))))<=(emptyset__Cong)))<=(exuE3u))))<=(exuI2))<=(exuI3))))<=(notdexE))))<=(quantDeMorgan4))<=(quantDeMorgan3))<=(quantDeMorgan2))<=(quantDeMorgan1))))))<=(upairsetE))<=(singletonsswitch))<=(eqinunit))<=(notinsingleton))))<=(exuE2))<=(subPowSU))<=(setunionE)))<=(powersetE))<=(emptyInPowerset)))<=(powersetI))<=(setoftrueEq))))))<=(setadjoinIL))<=(nonemptyI1))<=(nonemptyI))<=(nonemptyE1))))<=(emptyI))))<=(notinemptyset)))))<=(exuE1))))<=(dsetconstrI)))<=(wellorderingAx))<=(foundationAx)))<=(omegaIndAx)))<=(omega0Ax)))<=(powersetAx))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', beta2)).
164.62/21.20	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', powersetE1)).
164.62/21.20	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', powersetAx)).
164.62/21.20	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', powersetI1)).
164.62/21.20	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', binunionEcases)).
164.62/21.20	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', notdexE)).
164.62/21.20	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', quantDeMorgan4)).
164.62/21.20	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', binintersectI)).
164.62/21.20	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', quantDeMorgan3)).
164.62/21.20	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', quantDeMorgan2)).
164.62/21.20	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', quantDeMorgan1)).
164.62/21.20	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', binintersectSubset5)).
164.62/21.20	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', upairsetE)).
164.62/21.20	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', singletonsswitch)).
164.62/21.20	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', binintersectEL)).
164.62/21.20	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', eqinunit)).
164.62/21.20	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', notinsingleton)).
164.62/21.20	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', binintersectLsub)).
164.62/21.20	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', subPowSU)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', setunionE)).
164.62/21.20	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', powersetE)).
164.62/21.20	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', binintersectSubset3)).
164.62/21.20	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', emptyInPowerset)).
164.62/21.20	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', powersetI)).
164.62/21.20	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', binintersectER)).
164.62/21.20	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setadjoinIL)).
164.62/21.20	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', disjointsetsI1)).
164.62/21.20	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', emptyI)).
164.62/21.20	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', notinemptyset)).
164.62/21.20	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', binintersectSubset4)).
164.62/21.20	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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', wellorderingAx)).
164.62/21.20	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', bs114d)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', foundationAx)).
164.62/21.20	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', omegaIndAx)).
164.62/21.20	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', omega0Ax)).
164.62/21.20	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setminusI)).
164.62/21.20	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setminusER)).
164.62/21.20	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setminusELneg)).
164.62/21.20	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setminusIRneg)).
164.62/21.20	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setminusSubset1)).
164.62/21.20	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', symdiffE)).
164.62/21.20	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', symdiffI2)).
164.62/21.20	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', secondinupair)).
164.62/21.20	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', kpairp)).
164.62/21.20	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', singletonsubset)).
164.62/21.20	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', singletoninpowerset)).
164.62/21.20	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', singletoninpowunion)).
164.62/21.20	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', ubforcartprodlem3)).
164.62/21.20	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', cartprodpairin)).
164.62/21.20	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', cartprodmempair)).
164.62/21.20	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setunionE2)).
164.62/21.20	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setunionsingleton1)).
164.62/21.20	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setunionsingleton2)).
164.62/21.20	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setunionsingleton)).
164.62/21.20	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', binunionIL)).
164.62/21.20	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', singletonsuniq)).
164.62/21.20	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', kfstpairEq)).
164.62/21.20	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', ksndpairEq)).
164.62/21.20	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', cartprodpairmemER)).
164.62/21.20	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', cartprodmempaircEq)).
164.62/21.20	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', cartprodsndpairEq)).
164.62/21.20	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', binunionIR)).
164.62/21.20	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', funcinfuncset)).
164.62/21.20	thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', funcGraphProp3)).
164.62/21.20	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.v9GU9nN78k/Vampire---4.8_7426', funcextLem)).
164.62/21.20	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X35:$i]:(((in @ X35 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X35 @ X2))))=>((X29)=(X35)))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', funcext2)).
164.62/21.20	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', ap2apEq1)).
164.62/21.20	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', ap2apEq2)).
164.62/21.20	thf(funcext, axiom, ((funcext)<=>![X4:$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.v9GU9nN78k/Vampire---4.8_7426', funcext)).
164.62/21.20	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', funcGraphProp4)).
164.62/21.20	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$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.v9GU9nN78k/Vampire---4.8_7426', funcGraphProp2)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', funcGraphProp1)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', ap2p)).
164.62/21.20	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', infuncsetfunc)).
164.62/21.20	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', app)).
164.62/21.20	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', cartprodpairsurjEq)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', cartprodfstpairEq)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', cartprodpairmemEL)).
164.62/21.20	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', cartprodsndin)).
164.62/21.20	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', kpairsurjEq)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', setukpairinjR)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', setukpairinjR2)).
164.62/21.20	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', upairequniteq)).
164.62/21.20	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setukpairinjR1)).
164.62/21.20	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setukpairinjR12)).
164.62/21.20	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setukpairinjR11)).
164.62/21.20	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setukpairinjL)).
164.62/21.20	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setukpairinjL2)).
164.62/21.20	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', cartprodfstin)).
164.62/21.20	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setukpairinjL1)).
164.62/21.20	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.v9GU9nN78k/Vampire---4.8_7426', cartprodmempair1)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', ubforcartprodlem2)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', ubforcartprodlem1)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', upairinpowunion)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', upairsubunion)).
164.62/21.20	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', upairset2E)).
164.62/21.20	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', kpairiskpair)).
164.62/21.20	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setukpairIR)).
164.62/21.20	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setukpairIL)).
164.62/21.20	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', symdiffIneg2)).
164.62/21.20	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', symdiffIneg1)).
164.62/21.20	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', symdiffI1)).
164.62/21.20	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setminusLsub)).
164.62/21.20	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setminusILneg)).
164.62/21.20	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setminusERneg)).
164.62/21.20	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setminusSubset2)).
164.62/21.20	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setminusEL)).
164.62/21.20	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', binintersectSubset1)).
164.62/21.20	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', binintersectRsub)).
164.62/21.20	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', binintersectSubset2)).
164.62/21.20	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', binunionRsub)).
164.62/21.20	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', binunionLsub)).
164.62/21.20	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', binunionE)).
164.62/21.20	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', upairset2IR)).
164.62/21.20	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', powersetsubset)).
164.62/21.20	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', inPowerset)).
164.62/21.20	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setextsub)).
164.62/21.20	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', notequalI2)).
164.62/21.20	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', notsubsetI)).
164.62/21.20	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', subsetE2)).
164.62/21.20	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', emptysetsubset)).
164.62/21.20	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', eqimpsubset1)).
164.62/21.20	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', eqimpsubset2)).
164.62/21.20	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', omega__Cong)).
164.62/21.20	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setunion__Cong)).
164.62/21.20	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', emptyset__Cong)).
164.62/21.20	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', subsetemptysetimpeq)).
164.62/21.20	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', subset2powerset)).
164.62/21.20	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setadjoinSub2)).
164.62/21.20	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setadjoinSub)).
164.62/21.20	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', subsetTrans)).
164.62/21.20	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', subsetRefl)).
164.62/21.20	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', notequalI1)).
164.62/21.20	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', subsetE)).
164.62/21.20	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', subsetI2)).
164.62/21.20	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', subsetI1)).
164.62/21.20	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', powerset__Cong)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', setadjoin__Cong)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', in__Cong)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', inCongP)).
164.62/21.20	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', notdallE)).
164.62/21.20	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', prop2set2propI)).
164.62/21.20	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', prop2setI)).
164.62/21.20	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', vacuousDall)).
164.62/21.20	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', upairsetIR)).
164.62/21.20	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', upairsetIL)).
164.62/21.20	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', uniqinunit)).
164.62/21.20	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setunionI)).
164.62/21.20	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', emptyinPowerset)).
164.62/21.20	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setadjoinOr)).
164.62/21.20	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setadjoinE)).
164.62/21.20	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setadjoinIR)).
164.62/21.20	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', emptyinunitempty)).
164.62/21.20	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', noeltsimpempty)).
164.62/21.20	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.v9GU9nN78k/Vampire---4.8_7426', setext)).
164.62/21.20	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', emptysetimpfalse)).
164.62/21.20	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', emptysetE)).
164.62/21.20	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', prop2setE)).
164.62/21.20	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', omegaSAx)).
164.62/21.20	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setunionAx)).
164.62/21.20	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setadjoinAx)).
164.62/21.20	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', emptysetAx)).
164.62/21.20	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.v9GU9nN78k/Vampire---4.8_7426', setextAx)).
164.62/21.20	thf(c_0_220, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X724:$i]:(((in @ X724 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X724 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])).
164.62/21.20	thf(c_0_221, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])).
164.62/21.20	thf(c_0_222, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
164.62/21.20	thf(c_0_223, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
164.62/21.20	thf(c_0_224, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
164.62/21.20	thf(c_0_225, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
164.62/21.20	thf(c_0_226, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
164.62/21.20	thf(c_0_227, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
164.62/21.20	thf(c_0_228, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
164.62/21.20	thf(c_0_229, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
164.62/21.20	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])).
164.62/21.20	thf(c_0_231, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X724:$i]:(((in @ X724 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X724 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_220, c_0_221])).
164.62/21.20	thf(c_0_232, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
164.62/21.20	thf(c_0_233, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
164.62/21.20	thf(c_0_234, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
164.62/21.20	thf(c_0_235, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
164.62/21.20	thf(c_0_236, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
164.62/21.20	thf(c_0_237, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
164.62/21.20	thf(c_0_238, plain, ((ex1E2)<=>![X4:$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])).
164.62/21.20	thf(c_0_239, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
164.62/21.20	thf(c_0_240, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
164.62/21.20	thf(c_0_241, plain, ((descr__Cong)<=>![X1:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
164.62/21.20	thf(c_0_242, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
164.62/21.20	thf(c_0_243, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
164.62/21.20	thf(c_0_244, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
164.62/21.20	thf(c_0_245, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
164.62/21.20	thf(c_0_246, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
164.62/21.20	thf(c_0_247, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
164.62/21.20	thf(c_0_248, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_222])).
164.62/21.20	thf(c_0_249, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X711:$i]:((((X1 @ X711))&![X712:$i]:((((X1 @ X712))=>((X711)=(X712)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_223, c_0_224])).
164.62/21.20	thf(c_0_250, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X709:$i]:((((X1 @ X709))&![X710:$i]:((((X1 @ X710))=>((X709)=(X710))))))))))), inference(apply_def,[status(thm)],[c_0_225, c_0_224])).
164.62/21.20	thf(c_0_251, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X707:$i]:((((X1 @ X707))&![X708:$i]:((((X1 @ X708))=>((X707)=(X708)))))))))))), inference(apply_def,[status(thm)],[c_0_226, c_0_224])).
164.62/21.20	thf(c_0_252, plain, ((exuE2)=(![X1:$i > $o]:(((?[X703:$i]:((((X1 @ X703))&![X704:$i]:((((X1 @ X704))=>((X703)=(X704)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_227, c_0_224])).
164.62/21.20	thf(c_0_253, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
164.62/21.20	thf(c_0_254, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
164.62/21.20	thf(c_0_255, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_228, c_0_222])).
164.62/21.20	thf(c_0_256, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_222])).
164.62/21.20	thf(c_0_257, plain, ((exuE1)=(![X1:$i > $o]:(((?[X699:$i]:((((X1 @ X699))&![X700:$i]:((((X1 @ X700))=>((X699)=(X700)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_229, c_0_224])).
164.62/21.20	thf(c_0_258, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
164.62/21.20	thf(c_0_259, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
164.62/21.20	thf(c_0_260, 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])).
164.62/21.20	thf(c_0_261, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X726:$i]:(((in @ X726 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X726 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_230, c_0_231])).
164.62/21.20	thf(c_0_262, 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)))=>(?[X727:$i]:(((in @ X727 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X727 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_232, c_0_231])).
164.62/21.20	thf(c_0_263, plain, ((kfstsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X728:$i]:(((in @ X728 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X728 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_233, c_0_221])).
164.62/21.20	thf(c_0_264, axiom, ((theprop)=(![X21:$i]:(((?[X729:$i]:(((in @ X729 @ X21)&((X21)=(setadjoin @ X729 @ emptyset)))))=>(in @ (setunion @ X21) @ X21))))), inference(apply_def,[status(thm)],[theprop, c_0_221])).
164.62/21.20	thf(c_0_265, plain, ((ksndsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X730:$i]:(((in @ X730 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X730 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_234, c_0_221])).
164.62/21.20	thf(c_0_266, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_235, c_0_236])).
164.62/21.20	thf(c_0_267, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(?[X731:$i]:(((in @ X731 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))=(setadjoin @ X731 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_237, c_0_221])).
164.62/21.20	thf(c_0_268, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
164.62/21.20	thf(c_0_269, axiom, ((brelnall1)=(![X4:$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_236])).
164.62/21.20	thf(c_0_270, 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_236])).
164.62/21.20	thf(c_0_271, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:(((?[X732:$i]:(((in @ X732 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X732 @ emptyset)))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_238, c_0_231])).
164.62/21.20	thf(c_0_272, 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_236])).
164.62/21.20	thf(c_0_273, plain, ((lam2p)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X33 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
164.62/21.20	thf(c_0_274, plain, ((beta1)<=>![X4:$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])).
164.62/21.20	thf(c_0_275, 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_236])).
164.62/21.20	thf(c_0_276, 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 */:$i]:(X32 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
164.62/21.20	thf(c_0_277, plain, ((lamProp)<=>![X4:$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])).
164.62/21.20	thf(c_0_278, 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:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
164.62/21.20	thf(c_0_279, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
164.62/21.20	thf(c_0_280, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
164.62/21.20	thf(c_0_281, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
164.62/21.20	thf(c_0_282, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
164.62/21.20	thf(c_0_283, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
164.62/21.20	thf(c_0_284, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X725:$i]:(((in @ X725 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X725 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_239, c_0_231])).
164.62/21.20	thf(c_0_285, plain, ((singletonprop)=(![X4:$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)))=>(?[X723:$i]:(((in @ X723 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X723 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_240, c_0_221])).
164.62/21.20	thf(c_0_286, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
164.62/21.20	thf(c_0_287, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
164.62/21.20	thf(c_0_288, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X719:$i]:((((X1 @ X719))&![X720:$i]:((((X1 @ X720))=>((X719)=(X720)))))))=>((?[X721:$i]:((((X17 @ X721))&![X722:$i]:((((X17 @ X722))=>((X721)=(X722)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_241, c_0_224])).
164.62/21.20	thf(c_0_289, plain, ((exuEu)=(![X1:$i > $o]:(((?[X717:$i]:((((X1 @ X717))&![X718:$i]:((((X1 @ X718))=>((X717)=(X718)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_242, c_0_224])).
164.62/21.20	thf(c_0_290, plain, ((exu__Cong)=(![X1:$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:$i]:((((X17 @ X716))=>((X715)=(X716)))))))))))), inference(apply_def,[status(thm)],[c_0_243, c_0_224])).
164.62/21.20	thf(c_0_291, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X705:$i]:((((X1 @ X705))&![X706:$i]:((((X1 @ X706))=>((X705)=(X706))))))))))), inference(apply_def,[status(thm)],[c_0_244, c_0_224])).
164.62/21.20	thf(c_0_292, plain, ((emptyE1)<=>![X4:$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])).
164.62/21.20	thf(c_0_293, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_222])).
164.62/21.20	thf(c_0_294, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
164.62/21.20	thf(c_0_295, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X701:$i]:((((X1 @ X701))&![X702:$i]:((((X1 @ X702))=>((X701)=(X702)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_245, c_0_224])).
164.62/21.20	thf(c_0_296, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
164.62/21.20	thf(c_0_297, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
164.62/21.20	thf(c_0_298, plain, ((descrp)=(![X1:$i > $o]:(((?[X697:$i]:((((X1 @ X697))&![X698:$i]:((((X1 @ X698))=>((X697)=(X698)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_246, c_0_224])).
164.62/21.20	thf(c_0_299, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X695:$i]:((((X6 @ X2 @ X695))&![X696:$i]:((((X6 @ X2 @ X696))=>((X695)=(X696)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_247, c_0_224])).
164.62/21.20	thf(c_0_300, plain, ((epred1_0)<=>![X1391:$i]:(?[X1392:$i]:((((![X1393:$i]:(((in @ X1393 @ X1392)=>![X1394:$i]:(((in @ X1394 @ X1393)=>(in @ X1394 @ X1391)))))&![X1395:$i, X1396:$i]:((((in @ X1395 @ X1391)&(in @ X1396 @ X1391))=>(![X1397:$i]:(((in @ X1397 @ X1392)=>((in @ X1395 @ X1397)<=>(in @ X1396 @ X1397))))=>((X1395)=(X1396))))))&![X1398:$i, X1399:$i]:((((in @ X1398 @ X1392)&(in @ X1399 @ X1392))=>(![X1400:$i]:(((in @ X1400 @ X1398)=>(in @ X1400 @ X1399)))|![X1401:$i]:(((in @ X1401 @ X1399)=>(in @ X1401 @ X1398)))))))&![X1402:$i]:(((![X1403:$i]:(((in @ X1403 @ X1402)=>(in @ X1403 @ X1391)))&?[X1404:$i]:((in @ X1404 @ X1402)))=>?[X1405:$i, X1406:$i]:(((((in @ X1405 @ X1392)&(in @ X1406 @ X1402))&~(?[X1407:$i]:(((in @ X1407 @ X1405)&(in @ X1407 @ X1402)))))&![X1408:$i]:(((in @ X1408 @ X1392)=>(![X1409:$i]:(((in @ X1409 @ X1408)=>(in @ X1409 @ X1405)))|(in @ X1406 @ X1408)))))))))))), introduced(definition)).
164.62/21.20	thf(c_0_301, negated_conjecture, ~((![X733:$i, X734:$i]:((![X735:$i]:(((in @ X735 @ X733)<=>(in @ X735 @ X734)))=>((X733)=(X734))))=>(![X736:$i]:(~(in @ X736 @ emptyset))=>(![X737:$i, X738:$i, X739:$i]:(((in @ X739 @ (setadjoin @ X737 @ X738))<=>(((X739)=(X737))|(in @ X739 @ X738))))=>(![X1417:$i, X1418:$i]:(((in @ X1418 @ (powerset @ X1417))<=>![X1419:$i]:(((in @ X1419 @ X1418)=>(in @ X1419 @ X1417)))))=>(![X740:$i, X741:$i]:(((in @ X741 @ (setunion @ X740))<=>?[X742:$i]:(((in @ X741 @ X742)&(in @ X742 @ X740)))))=>((in @ emptyset @ omega)=>(![X743:$i]:(((in @ X743 @ omega)=>(in @ (setadjoin @ X743 @ X743) @ omega)))=>(![X1414:$i]:((((in @ emptyset @ X1414)&![X1415:$i]:((((in @ X1415 @ omega)&(in @ X1415 @ X1414))=>(in @ (setadjoin @ X1415 @ X1415) @ X1414))))=>![X1416:$i]:(((in @ X1416 @ omega)=>(in @ X1416 @ X1414)))))=>(![X744:$i > $i > $o, X745:$i]:((![X746:$i]:(((in @ X746 @ X745)=>?[X747:$i]:(((X744 @ X746 @ X747)&![X748:$i]:(((X744 @ X746 @ X748)=>((X747)=(X748))))))))=>?[X749:$i]:(![X750:$i]:(((in @ X750 @ X749)<=>?[X751:$i]:(((in @ X751 @ X745)&(X744 @ X751 @ X750))))))))=>(![X1410:$i]:((?[X1411:$i]:((in @ X1411 @ X1410))=>?[X1412:$i]:(((in @ X1412 @ X1410)&~(?[X1413:$i]:(((in @ X1413 @ X1412)&(in @ X1413 @ X1410))))))))=>((epred1_0)=>(![X752:$i > $o]:((?[X753:$i]:(((X752 @ X753)&![X754:$i]:(((X752 @ X754)=>((X753)=(X754))))))=>(X752 @ (descr @ (^[Z0/* 3 */:$i]:((X752 @ Z0)))))))=>(![X1388:$i, X1389:$i > $o, X1390:$i]:(((in @ X1390 @ X1388)=>((X1389 @ X1390)=>(in @ X1390 @ (dsetconstr @ X1388 @ (^[Z0/* 3 */:$i]:((X1389 @ Z0))))))))=>(![X755:$i, X756:$i > $o, X757:$i]:(((in @ X757 @ (dsetconstr @ X755 @ (^[Z0/* 3 */:$i]:((X756 @ Z0)))))=>(in @ X757 @ X755)))=>(![X758:$i, X759:$i > $o, X760:$i]:(((in @ X760 @ (dsetconstr @ X758 @ (^[Z0/* 3 */:$i]:((X759 @ Z0)))))=>(X759 @ X760)))=>(![X1383:$i > $o]:((?[X1384:$i]:(((X1383 @ X1384)&![X1385:$i]:(((X1383 @ X1385)=>((X1384)=(X1385))))))=>?[X1386:$i]:(((X1383 @ X1386)&![X1387:$i]:(((X1383 @ X1387)=>((X1386)=(X1387))))))))=>(![X761:$o, X762:$i]:(((in @ X762 @ (prop2set @ ((X761))))=>(X761)))=>(![X763:$i]:(((in @ X763 @ emptyset)=>![X764:$o]:((X764))))=>(![X765:$i]:(~(in @ X765 @ emptyset))=>(![X1382:$i]:(~(in @ X1382 @ emptyset))=>(![X766:$i > $o]:((?[X767:$i]:(((X766 @ X767)&![X768:$i]:(((X766 @ X768)=>((X767)=(X768))))))=>?[X769:$i]:((X766 @ X769))))=>(![X770:$i, X771:$i]:((![X772:$i]:(((in @ X772 @ X770)=>(in @ X772 @ X771)))=>(![X773:$i]:(((in @ X773 @ X771)=>(in @ X773 @ X770)))=>((X770)=(X771)))))=>(![X1380:$i]:((![X1381:$i]:(~(in @ X1381 @ X1380))=>((X1380)=(emptyset))))=>(![X774:$i]:((![X775:$i]:(~(in @ X775 @ X774))=>((X774)=(emptyset))))=>(![X776:$i, X777:$i > $o, X778:$i]:(((in @ X778 @ X776)=>((in @ X778 @ (dsetconstr @ X776 @ (^[Z0/* 3 */:$i]:((X777 @ Z0)))))<=>(X777 @ X778))))=>(![X1378:$i]:((((X1378)!=(emptyset))=>?[X1379:$i]:((in @ X1379 @ X1378))))=>(![X1375:$i, X1376:$i > $o, X1377:$i]:(((in @ X1377 @ X1375)=>((X1376 @ X1377)=>((dsetconstr @ X1375 @ (^[Z0/* 3 */:$i]:((X1376 @ Z0))))!=(emptyset)))))=>(![X1373:$i]:((?[X1374:$i]:((in @ X1374 @ X1373))=>((X1373)!=(emptyset))))=>(![X1371:$i, X1372:$i]:((in @ X1371 @ (setadjoin @ X1371 @ X1372)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X779:$i, X780:$i, X781:$i]:(((in @ X781 @ X780)=>(in @ X781 @ (setadjoin @ X779 @ X780))))=>(![X782:$i, X783:$i, X784:$i]:(((in @ X784 @ (setadjoin @ X782 @ X783))=>![X785:$o]:(((((X784)=(X782))=>(X785))=>(((in @ X784 @ X783)=>(X785))=>(X785))))))=>(![X786:$i, X787:$i, X788:$i]:(((in @ X788 @ (setadjoin @ X786 @ X787))=>(((X788)=(X786))|(in @ X788 @ X787))))=>(![X1370:$i]:(((dsetconstr @ X1370 @ (^[Z0/* 3 */:$i]:(($true))))=(X1370)))=>(![X1367:$i, X1368:$i]:((![X1369:$i]:(((in @ X1369 @ X1368)=>(in @ X1369 @ X1367)))=>(in @ X1368 @ (powerset @ X1367))))=>(![X789:$i]:((in @ emptyset @ (powerset @ X789)))=>(![X1366:$i]:((in @ emptyset @ (powerset @ X1366)))=>(![X1363:$i, X1364:$i, X1365:$i]:(((in @ X1364 @ 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inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[beta2])]), powersetE1]), c_0_248]), powersetAx]), c_0_249]), powersetI1]), c_0_250]), c_0_251]), binunionEcases]), notdexE]), quantDeMorgan4]), binintersectI]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), binintersectSubset5]), upairsetE]), singletonsswitch]), binintersectEL]), eqinunit]), notinsingleton]), c_0_252]), binintersectLsub]), subPowSU]), setunionE]), powersetE]), binintersectSubset3]), emptyInPowerset]), powersetI]), c_0_253]), binintersectER]), setadjoinIL]), c_0_254]), c_0_255]), c_0_256]), disjointsetsI1]), emptyI]), notinemptyset]), c_0_257]), binintersectSubset4]), c_0_258]), wellorderingAx]), bs114d]), foundationAx]), omegaIndAx]), omega0Ax]), setminusI]), setminusER]), setminusELneg]), setminusIRneg]), setminusSubset1]), symdiffE]), symdiffI2]), secondinupair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), c_0_259]), c_0_260]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_261]), binunionIL]), c_0_262]), singletonsuniq]), c_0_263]), c_0_264]), kfstpairEq]), c_0_265]), ksndpairEq]), cartprodpairmemER]), cartprodmempaircEq]), cartprodsndpairEq]), binunionIR]), c_0_266]), c_0_267]), c_0_268]), funcinfuncset]), c_0_269]), c_0_270]), c_0_271]), funcGraphProp3]), funcextLem]), c_0_272]), funcext2]), ap2apEq1]), c_0_273]), c_0_274]), ap2apEq2]), funcext]), c_0_275]), funcGraphProp4]), funcGraphProp2]), funcGraphProp1]), c_0_276]), c_0_277]), ap2p]), infuncsetfunc]), app]), c_0_278]), c_0_279]), c_0_280]), c_0_281]), c_0_282]), c_0_283]), cartprodpairsurjEq]), cartprodfstpairEq]), cartprodpairmemEL]), cartprodsndin]), kpairsurjEq]), setukpairinjR]), setukpairinjR2]), upairequniteq]), setukpairinjR1]), setukpairinjR12]), setukpairinjR11]), setukpairinjL]), setukpairinjL2]), cartprodfstin]), setukpairinjL1]), c_0_284]), c_0_285]), cartprodmempair1]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), upairsubunion]), upairset2E]), kpairiskpair]), setukpairIR]), setukpairIL]), symdiffIneg2]), symdiffIneg1]), symdiffI1]), setminusLsub]), setminusILneg]), setminusERneg]), setminusSubset2]), setminusEL]), binintersectSubset1]), binintersectRsub]), binintersectSubset2]), binunionRsub]), binunionLsub]), binunionE]), upairset2IR]), c_0_286]), powersetsubset]), inPowerset]), setextsub]), notequalI2]), notsubsetI]), subsetE2]), emptysetsubset]), eqimpsubset1]), eqimpsubset2]), c_0_287]), c_0_288]), omega__Cong]), setunion__Cong]), emptyset__Cong]), subsetemptysetimpeq]), subset2powerset]), setadjoinSub2]), setadjoinSub]), subsetTrans]), subsetRefl]), notequalI1]), subsetE]), subsetI2]), subsetI1]), c_0_289]), powerset__Cong]), setadjoin__Cong]), c_0_290]), in__Cong]), inCongP]), c_0_291]), notdallE]), prop2set2propI]), prop2setI]), vacuousDall]), c_0_292]), upairsetIR]), upairsetIL]), uniqinunit]), c_0_293]), setunionI]), emptyinPowerset]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), c_0_294]), noeltsimpempty]), setext]), c_0_295]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_296]), c_0_297]), c_0_298]), c_0_299]), omegaSAx]), setunionAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_300])).
164.62/21.20	thf(c_0_302, negated_conjecture, ![X1420:$i, X1421:$i, X1423:$i, X1424:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$i, X1433:$i, X1434:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1442:$i, X1443:$i > $i > $o, X1444:$i, X1446:$i, X1449:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1456:$i, X1457:$i > $o, X1458:$i, X1460:$i, X1461:$i > $o, X1462:$i, X1463:$i, X1464:$i > $o, X1465:$i, X1466:$i, X1467:$i > $o, X1468:$i, X1469:$i > $o, X1470:$i, X1473:$i, X1474:$o, X1475:$i, X1476:$i, X1477:$o, X1478:$i, X1479:$i, X1480:$i > $o, X1481:$i, X1484:$i, X1485:$i, X1488:$i, X1490:$i, X1492:$i, X1493:$i > $o, X1494:$i, X1495:$i, X1497:$i, X1498:$i > $o, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$o, X1511:$i, X1512:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$o, X1530:$i, X1531:$i, X1532:$i > $o, X1533:$i, X1536:$i, X1537:$i, X1538:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i > $o, X1557:$i, X1558:$i > $o, X1559:$i, X1560:$i, X1561:$i > $o, X1562:$i, X1564:$i, X1565:$i > $o, X1567:$i, X1568:$i, X1569:$i > $o, X1571:$i, X1572:$i, X1573:$i > $o, X1574:$i, X1576:$o, X1577:$o, X1578:$i, X1579:$i > $o, X1581:$i, X1582:$i, X1583:$i > $o, X1584:$i, X1586:$i > $o, X1587:$i, X1590:$i, X1591:$i > $o, X1592:$i, X1596:$i, X1597:$i > $o, X1598:$i, X1601:$i, X1602:$i, X1603:$i, X1604:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i, X1610:$i > $o, X1611:$i, X1613:$i, X1614:$i, X1615:$i > $o, X1616:$i > $o, X1619:$i, X1622:$i, X1623:$i, X1626:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i, X1633:$i, X1634:$i, X1635:$i > $o, X1636:$i, X1638:$i, X1639:$i, X1640:$i > $o, X1641:$i > $o, X1644:$i, X1646:$i, X1648:$i, X1649:$i, X1650:$i > $o, X1651:$i > $o, X1654:$i, X1655:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1664:$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:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i > $o, X1702:$i, X1703:$i > $o, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$o, X1716:$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, X1733:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$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:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$o, 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:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i > $o, X1858:$i, X1860:$i, X1861:$i > $o, X1862:$i, X1864:$i, X1865:$i > $o, X1866:$i, X1869:$i, X1870:$i > $o, X1873:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1918:$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:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i > $i > $o, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i > $i > $o, X1955:$i, X1956:$i, X1957:$i > $i > $o, X1958:$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 > $i > $o, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i > $i > $o, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i > $i, X2005:$i, X2006:$i, X2007:$i > $i, X2009:$i, X2010:$i, X2011:$i > $i, X2013:$i, X2014:$i, X2015:$i, X2016:$i > $o, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i > $o, X2026:$i, X2027:$i, X2028:$i > $o, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i > $i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i > $i, X2104:$i]:((((~(in @ (esk1_2 @ X1420 @ X1421) @ X1420)|~(in @ (esk1_2 @ X1420 @ X1421) @ X1421)|((X1420)=(X1421)))&((in @ (esk1_2 @ X1420 @ X1421) @ X1420)|(in @ (esk1_2 @ X1420 @ X1421) @ X1421)|((X1420)=(X1421))))&(~(in @ X1423 @ emptyset)&(((~(in @ X1426 @ (setadjoin @ X1424 @ X1425))|(((X1426)=(X1424))|(in @ X1426 @ X1425)))&((((X1426)!=(X1424))|(in @ X1426 @ (setadjoin @ X1424 @ X1425)))&(~(in @ X1426 @ X1425)|(in @ X1426 @ (setadjoin @ X1424 @ X1425)))))&(((~(in @ X1428 @ (powerset @ X1427))|(~(in @ X1429 @ X1428)|(in @ X1429 @ X1427)))&(((in @ (esk2_2 @ X1430 @ X1431) @ X1431)|(in @ X1431 @ (powerset @ X1430)))&(~(in @ (esk2_2 @ X1430 @ X1431) @ X1430)|(in @ X1431 @ (powerset @ X1430)))))&(((((in @ X1434 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X2045)|(~(in @ X2050 @ X2045)|(~(in @ X2051 @ X2046)|(~(in @ (kpair @ X2050 @ X2051) @ X2048)|(in @ (kpair @ X2050 @ X2051) @ X2047))))|~(func @ X2045 @ X2046 @ X2048)|~(func @ X2045 @ X2046 @ X2047))&(((ap @ X2045 @ X2046 @ X2047 @ (esk77_4 @ X2045 @ X2046 @ X2047 @ X2048))!=(ap @ X2045 @ X2046 @ X2048 @ (esk77_4 @ X2045 @ X2046 @ X2047 @ X2048)))|(~(in @ X2050 @ X2045)|(~(in @ X2051 @ X2046)|(~(in @ (kpair @ X2050 @ X2051) @ X2048)|(in @ (kpair @ X2050 @ X2051) @ X2047))))|~(func @ X2045 @ X2046 @ X2048)|~(func @ X2045 @ X2046 @ X2047)))&((~(in @ X2054 @ (funcSet @ X2052 @ X2053))|(~(in @ X2055 @ X2052)|(~(in @ X2056 @ X2053)|(~(in @ (kpair @ X2055 @ X2056) @ X2054)|((ap @ X2052 @ X2053 @ X2054 @ X2055)=(X2056))))))&((((in @ (esk78_4 @ X2057 @ X2058 @ X2059 @ X2060) @ X2057)|(subset @ X2059 @ X2060)|~(subset @ X2060 @ (cartprod @ X2057 @ X2058))|~(subset @ X2059 @ (cartprod @ X2057 @ X2058)))&(((in @ (esk79_4 @ X2057 @ X2058 @ X2059 @ X2060) @ X2058)|(subset @ X2059 @ X2060)|~(subset @ X2060 @ (cartprod @ X2057 @ X2058))|~(subset @ X2059 @ (cartprod @ X2057 @ X2058)))&(((in @ (kpair @ (esk78_4 @ X2057 @ X2058 @ X2059 @ X2060) @ (esk79_4 @ X2057 @ X2058 @ X2059 @ X2060)) @ X2059)|(subset @ X2059 @ X2060)|~(subset @ X2060 @ (cartprod @ X2057 @ X2058))|~(subset @ X2059 @ (cartprod @ X2057 @ X2058)))&(~(in @ (kpair @ (esk78_4 @ X2057 @ X2058 @ X2059 @ X2060) @ (esk79_4 @ X2057 @ X2058 @ X2059 @ X2060)) @ X2060)|(subset @ X2059 @ X2060)|~(subset @ X2060 @ (cartprod @ X2057 @ X2058))|~(subset @ X2059 @ (cartprod @ X2057 @ X2058))))))&(((((in @ (esk82_4 @ X2063 @ X2064 @ X2065 @ X2066) @ X2063)|((X2065)=(X2066))|(in @ (esk80_4 @ X2063 @ X2064 @ X2065 @ X2066) @ X2063)|~(subset @ X2066 @ (cartprod @ X2063 @ X2064))|~(subset @ X2065 @ (cartprod @ X2063 @ X2064)))&(((in @ (esk83_4 @ X2063 @ X2064 @ X2065 @ X2066) @ X2064)|((X2065)=(X2066))|(in @ (esk80_4 @ X2063 @ X2064 @ X2065 @ X2066) @ X2063)|~(subset @ X2066 @ (cartprod @ X2063 @ X2064))|~(subset @ X2065 @ (cartprod @ X2063 @ X2064)))&(((in @ (kpair @ (esk82_4 @ X2063 @ X2064 @ X2065 @ X2066) @ (esk83_4 @ X2063 @ X2064 @ X2065 @ X2066)) @ X2066)|((X2065)=(X2066))|(in @ (esk80_4 @ X2063 @ X2064 @ X2065 @ X2066) @ X2063)|~(subset @ X2066 @ (cartprod @ X2063 @ X2064))|~(subset @ X2065 @ (cartprod @ X2063 @ X2064)))&(~(in @ (kpair @ (esk82_4 @ X2063 @ X2064 @ X2065 @ X2066) @ (esk83_4 @ X2063 @ X2064 @ X2065 @ X2066)) @ X2065)|((X2065)=(X2066))|(in @ (esk80_4 @ X2063 @ X2064 @ X2065 @ X2066) @ X2063)|~(subset @ X2066 @ (cartprod @ X2063 @ X2064))|~(subset @ X2065 @ (cartprod @ X2063 @ X2064))))))&((((in @ (esk82_4 @ X2063 @ X2064 @ X2065 @ X2066) @ X2063)|((X2065)=(X2066))|(in @ (esk81_4 @ X2063 @ X2064 @ X2065 @ X2066) @ X2064)|~(subset @ X2066 @ (cartprod @ X2063 @ X2064))|~(subset @ X2065 @ (cartprod @ X2063 @ X2064)))&(((in @ (esk83_4 @ X2063 @ X2064 @ X2065 @ X2066) @ X2064)|((X2065)=(X2066))|(in @ (esk81_4 @ X2063 @ X2064 @ X2065 @ X2066) @ X2064)|~(subset @ X2066 @ (cartprod @ X2063 @ X2064))|~(subset @ X2065 @ (cartprod @ X2063 @ X2064)))&(((in @ (kpair @ (esk82_4 @ X2063 @ X2064 @ X2065 @ X2066) @ (esk83_4 @ X2063 @ X2064 @ X2065 @ X2066)) @ X2066)|((X2065)=(X2066))|(in @ (esk81_4 @ X2063 @ X2064 @ X2065 @ X2066) @ X2064)|~(subset @ X2066 @ (cartprod @ X2063 @ X2064))|~(subset @ X2065 @ (cartprod @ X2063 @ X2064)))&(~(in @ (kpair @ (esk82_4 @ X2063 @ X2064 @ X2065 @ X2066) @ (esk83_4 @ X2063 @ X2064 @ X2065 @ X2066)) @ X2065)|((X2065)=(X2066))|(in @ (esk81_4 @ X2063 @ X2064 @ X2065 @ X2066) @ X2064)|~(subset @ X2066 @ (cartprod @ X2063 @ X2064))|~(subset @ X2065 @ (cartprod @ X2063 @ X2064))))))&((((in @ (esk82_4 @ X2063 @ X2064 @ X2065 @ X2066) @ X2063)|((X2065)=(X2066))|(in @ (kpair @ (esk80_4 @ X2063 @ X2064 @ X2065 @ X2066) @ (esk81_4 @ X2063 @ X2064 @ X2065 @ X2066)) @ X2065)|~(subset @ X2066 @ (cartprod @ X2063 @ X2064))|~(subset @ X2065 @ (cartprod @ X2063 @ X2064)))&(((in @ (esk83_4 @ X2063 @ X2064 @ X2065 @ X2066) @ X2064)|((X2065)=(X2066))|(in @ (kpair @ (esk80_4 @ X2063 @ X2064 @ X2065 @ X2066) @ (esk81_4 @ X2063 @ X2064 @ X2065 @ X2066)) @ X2065)|~(subset @ X2066 @ (cartprod @ X2063 @ X2064))|~(subset @ X2065 @ (cartprod @ X2063 @ X2064)))&(((in @ (kpair @ (esk82_4 @ X2063 @ X2064 @ X2065 @ X2066) @ (esk83_4 @ X2063 @ X2064 @ X2065 @ X2066)) @ X2066)|((X2065)=(X2066))|(in @ (kpair @ (esk80_4 @ X2063 @ X2064 @ X2065 @ X2066) @ (esk81_4 @ X2063 @ X2064 @ X2065 @ X2066)) @ X2065)|~(subset @ X2066 @ (cartprod @ X2063 @ X2064))|~(subset @ X2065 @ (cartprod @ X2063 @ X2064)))&(~(in @ (kpair @ (esk82_4 @ X2063 @ X2064 @ X2065 @ X2066) @ (esk83_4 @ X2063 @ X2064 @ X2065 @ X2066)) @ X2065)|((X2065)=(X2066))|(in @ (kpair @ (esk80_4 @ X2063 @ X2064 @ X2065 @ X2066) @ (esk81_4 @ X2063 @ X2064 @ X2065 @ X2066)) @ X2065)|~(subset @ X2066 @ (cartprod @ X2063 @ X2064))|~(subset @ X2065 @ (cartprod @ X2063 @ X2064))))))&(((in @ (esk82_4 @ X2063 @ X2064 @ X2065 @ X2066) @ X2063)|((X2065)=(X2066))|~(in @ (kpair @ (esk80_4 @ X2063 @ X2064 @ X2065 @ X2066) @ (esk81_4 @ X2063 @ X2064 @ X2065 @ X2066)) @ X2066)|~(subset @ X2066 @ (cartprod @ X2063 @ X2064))|~(subset @ X2065 @ (cartprod @ X2063 @ X2064)))&(((in @ (esk83_4 @ X2063 @ X2064 @ X2065 @ X2066) @ X2064)|((X2065)=(X2066))|~(in @ (kpair @ (esk80_4 @ X2063 @ X2064 @ X2065 @ X2066) @ (esk81_4 @ X2063 @ X2064 @ X2065 @ X2066)) @ X2066)|~(subset @ X2066 @ (cartprod @ X2063 @ X2064))|~(subset @ X2065 @ (cartprod @ X2063 @ X2064)))&(((in @ (kpair @ (esk82_4 @ X2063 @ X2064 @ X2065 @ X2066) @ (esk83_4 @ X2063 @ X2064 @ X2065 @ X2066)) @ X2066)|((X2065)=(X2066))|~(in @ (kpair @ (esk80_4 @ X2063 @ X2064 @ X2065 @ X2066) @ (esk81_4 @ X2063 @ X2064 @ X2065 @ X2066)) @ X2066)|~(subset @ X2066 @ (cartprod @ X2063 @ X2064))|~(subset @ X2065 @ (cartprod @ X2063 @ X2064)))&(~(in @ (kpair @ (esk82_4 @ X2063 @ X2064 @ X2065 @ X2066) @ (esk83_4 @ X2063 @ X2064 @ X2065 @ X2066)) @ X2065)|((X2065)=(X2066))|~(in @ (kpair @ (esk80_4 @ X2063 @ X2064 @ X2065 @ X2066) @ (esk81_4 @ X2063 @ X2064 @ X2065 @ X2066)) @ X2066)|~(subset @ X2066 @ (cartprod @ X2063 @ X2064))|~(subset @ X2065 @ (cartprod @ X2063 @ X2064)))))))))&((((in @ (esk84_4 @ X2071 @ X2072 @ X2073 @ X2074) @ X2071)|((X2073)=(X2074))|~(func @ X2071 @ X2072 @ X2074)|~(func @ X2071 @ X2072 @ X2073))&(((ap @ X2071 @ X2072 @ X2073 @ (esk84_4 @ X2071 @ X2072 @ X2073 @ X2074))!=(ap @ X2071 @ X2072 @ X2074 @ (esk84_4 @ X2071 @ X2072 @ X2073 @ X2074)))|((X2073)=(X2074))|~(func @ X2071 @ X2072 @ X2074)|~(func @ X2071 @ X2072 @ X2073)))&((((in @ (esk85_4 @ X2076 @ X2077 @ X2078 @ X2079) @ X2076)|((X2078)=(X2079))|~(in @ X2079 @ (funcSet @ X2076 @ X2077))|~(in @ X2078 @ (funcSet @ X2076 @ X2077)))&(((ap @ X2076 @ X2077 @ X2078 @ (esk85_4 @ X2076 @ X2077 @ X2078 @ X2079))!=(ap @ X2076 @ X2077 @ X2079 @ (esk85_4 @ X2076 @ X2077 @ X2078 @ X2079)))|((X2078)=(X2079))|~(in @ X2079 @ (funcSet @ X2076 @ X2077))|~(in @ X2078 @ (funcSet @ X2076 @ X2077))))&((~(in @ X2083 @ (funcSet @ X2081 @ X2082))|(~(in @ X2084 @ X2081)|((ap @ X2081 @ X2082 @ X2083 @ X2084)=(ap @ X2081 @ X2082 @ X2083 @ X2084))))&((~(func @ X2085 @ X2086 @ X2087)|(~(in @ X2088 @ X2085)|((ap @ X2085 @ X2086 @ X2087 @ X2088)=(ap @ X2085 @ X2086 @ X2087 @ X2088))))&((((in @ (esk86_3 @ X2089 @ X2090 @ X2091) @ X2089)|(~(in @ X2093 @ X2089)|((ap @ X2089 @ X2090 @ (lam @ X2089 @ X2090 @ X2091) @ X2093)=(X2091 @ X2093))))&(~(in @ (X2091 @ (esk86_3 @ X2089 @ X2090 @ X2091)) @ X2090)|(~(in @ X2093 @ X2089)|((ap @ X2089 @ X2090 @ (lam @ X2089 @ X2090 @ X2091) @ X2093)=(X2091 @ X2093)))))&((~(func @ X2094 @ X2095 @ X2096)|((lam @ X2094 @ X2095 @ (ap @ X2094 @ X2095 @ X2096))=(X2096)))&((((in @ (esk87_3 @ X2097 @ X2098 @ X2099) @ X2097)|((lam @ X2097 @ X2098 @ X2099)=(lam @ X2097 @ X2098 @ X2099)))&(~(in @ (X2099 @ (esk87_3 @ X2097 @ X2098 @ X2099)) @ X2098)|((lam @ X2097 @ X2098 @ X2099)=(lam @ X2097 @ X2098 @ X2099))))&((~(in @ X2104 @ esk88_0)|(in @ (esk90_0 @ X2104) @ esk89_0))&((in @ esk91_0 @ esk88_0)&((ap @ esk88_0 @ esk89_0 @ (lam @ esk88_0 @ esk89_0 @ esk90_0) @ esk91_0)!=(esk90_0 @ esk91_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_301])])])])])])).
164.62/21.20	thf(c_0_303, negated_conjecture, ![X30:$i > $i, X4:$i, X3:$i, X2:$i]:((((ap @ X2 @ X3 @ (lam @ X2 @ X3 @ X30) @ X4)=(X30 @ X4))|~((in @ (X30 @ (esk86_3 @ X2 @ X3 @ X30)) @ X3))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_302])).
164.62/21.20	thf(c_0_304, negated_conjecture, ![X2:$i]:(((in @ (esk90_0 @ X2) @ esk89_0)|~((in @ X2 @ esk88_0)))), inference(split_conjunct,[status(thm)],[c_0_302])).
164.62/21.20	thf(c_0_305, negated_conjecture, ((ap @ esk88_0 @ esk89_0 @ (lam @ esk88_0 @ esk89_0 @ esk90_0) @ esk91_0)!=(esk90_0 @ esk91_0)), inference(split_conjunct,[status(thm)],[c_0_302])).
164.62/21.20	thf(c_0_306, negated_conjecture, ![X30:$i > $i, X4:$i, X3:$i, X2:$i]:(((in @ (esk86_3 @ X2 @ X3 @ X30) @ X2)|((ap @ X2 @ X3 @ (lam @ X2 @ X3 @ X30) @ X4)=(X30 @ X4))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_302])).
164.62/21.20	thf(c_0_307, negated_conjecture, (in @ esk91_0 @ esk88_0), inference(split_conjunct,[status(thm)],[c_0_302])).
164.62/21.20	thf(c_0_308, negated_conjecture, ![X3:$i, X2:$i]:((((ap @ X2 @ esk89_0 @ (lam @ X2 @ esk89_0 @ esk90_0) @ X3)=(esk90_0 @ X3))|~((in @ (esk86_3 @ X2 @ esk89_0 @ esk90_0) @ esk88_0))|~((in @ X3 @ X2)))), inference(spm,[status(thm)],[c_0_303, c_0_304])).
164.62/21.20	thf(c_0_309, negated_conjecture, (in @ (esk86_3 @ esk88_0 @ esk89_0 @ esk90_0) @ esk88_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_305, c_0_306]), c_0_307])])).
164.62/21.20	thf(c_0_310, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_305, c_0_308]), c_0_309]), c_0_307])]), ['proof']).
164.62/21.20	# SZS output end CNFRefutation
164.62/21.20	# Parsed axioms                        : 472
164.62/21.20	# Removed by relevancy pruning/SinE    : 251
164.62/21.20	# Initial clauses                      : 401
164.62/21.20	# Removed in clause preprocessing      : 28
164.62/21.20	# Initial clauses in saturation        : 373
164.62/21.20	# Processed clauses                    : 3068
164.62/21.20	# ...of these trivial                  : 61
164.62/21.20	# ...subsumed                          : 861
164.62/21.20	# ...remaining for further processing  : 2146
164.62/21.20	# Other redundant clauses eliminated   : 78
164.62/21.20	# Clauses deleted for lack of memory   : 0
164.62/21.20	# Backward-subsumed                    : 9
164.62/21.20	# Backward-rewritten                   : 11
164.62/21.20	# Generated clauses                    : 170405
164.62/21.20	# ...of the previous two non-redundant : 165099
164.62/21.20	# ...aggressively subsumed             : 0
164.62/21.20	# Contextual simplify-reflections      : 2
164.62/21.20	# Paramodulations                      : 170280
164.62/21.20	# Factorizations                       : 4
164.62/21.20	# NegExts                              : 0
164.62/21.20	# Equation resolutions                 : 85
164.62/21.20	# Total rewrite steps                  : 26532
164.62/21.20	# Propositional unsat checks           : 0
164.62/21.20	#    Propositional check models        : 0
164.62/21.20	#    Propositional check unsatisfiable : 0
164.62/21.20	#    Propositional clauses             : 0
164.62/21.20	#    Propositional clauses after purity: 0
164.62/21.20	#    Propositional unsat core size     : 0
164.62/21.20	#    Propositional preprocessing time  : 0.000
164.62/21.20	#    Propositional encoding time       : 0.000
164.62/21.20	#    Propositional solver time         : 0.000
164.62/21.20	#    Success case prop preproc time    : 0.000
164.62/21.20	#    Success case prop encoding time   : 0.000
164.62/21.20	#    Success case prop solver time     : 0.000
164.62/21.20	# Current number of processed clauses  : 1781
164.62/21.20	#    Positive orientable unit clauses  : 128
164.62/21.20	#    Positive unorientable unit clauses: 3
164.62/21.20	#    Negative unit clauses             : 71
164.62/21.20	#    Non-unit-clauses                  : 1579
164.62/21.20	# Current number of unprocessed clauses: 162628
164.62/21.20	# ...number of literals in the above   : 565118
164.62/21.20	# Current number of archived formulas  : 0
164.62/21.20	# Current number of archived clauses   : 349
164.62/21.20	# Clause-clause subsumption calls (NU) : 246318
164.62/21.20	# Rec. Clause-clause subsumption calls : 161400
164.62/21.20	# Non-unit clause-clause subsumptions  : 605
164.62/21.20	# Unit Clause-clause subsumption calls : 20757
164.62/21.20	# Rewrite failures with RHS unbound    : 0
164.62/21.20	# BW rewrite match attempts            : 74
164.62/21.20	# BW rewrite match successes           : 13
164.62/21.20	# Condensation attempts                : 3068
164.62/21.20	# Condensation successes               : 60
164.62/21.20	# Termbank termtop insertions          : 10902409
164.62/21.20	
164.62/21.20	# -------------------------------------------------
164.62/21.20	# User time                : 20.107 s
164.62/21.20	# System time              : 0.597 s
164.62/21.20	# Total time               : 20.704 s
164.62/21.20	# Maximum resident set size: 7336 pages
166.00/21.52	
166.00/21.52	# -------------------------------------------------
166.00/21.52	# User time                : 20.119 s
166.00/21.52	# System time              : 0.600 s
166.00/21.52	# Total time               : 20.719 s
166.00/21.52	# Maximum resident set size: 2348 pages
166.00/21.52	% E---3.1 exiting
166.00/21.53	EOF