0.11/0.12	% Problem    : Vampire---4.8_3218 : TPTP v0.0.0. Released v0.0.0.
0.11/0.13	% Command    : run_E %s %d THM
0.12/0.33	% Computer : n023.cluster.edu
0.12/0.33	% Model    : x86_64 x86_64
0.12/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory   : 8042.1875MB
0.12/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 1440
0.12/0.33	% WCLimit    : 180
0.12/0.33	% DateTime   : Mon Jul  3 13:15:06 EDT 2023
0.12/0.33	% CPUTime    : 
0.17/0.46	Running higher-order theorem provingRunning: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218
0.17/0.46	# Version: 3.1pre001-ho
12.26/2.01	# Preprocessing class: HSLMSLSSLLLCHFA.
12.26/2.01	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
12.26/2.01	# Starting ehoh_best5 with 180s (1) cores
12.26/2.01	# Starting almost_fo_3_lam with 180s (1) cores
12.26/2.01	# Starting new_bool_5 with 180s (1) cores
12.26/2.01	# Starting pre_casc_3 with 180s (1) cores
12.26/2.01	# Starting ho_unfolding_8 with 180s (1) cores
12.26/2.01	# Starting new_ho_10_cnf2 with 180s (1) cores
12.26/2.01	# Starting new_bool_3 with 180s (1) cores
12.26/2.01	# Starting new_ho_5 with 180s (1) cores
12.26/2.01	# new_bool_5 with pid 3399 completed with status 0
12.26/2.01	# Result found by new_bool_5
12.26/2.01	# Preprocessing class: HSLMSLSSLLLCHFA.
12.26/2.01	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
12.26/2.01	# Starting ehoh_best5 with 180s (1) cores
12.26/2.01	# Starting almost_fo_3_lam with 180s (1) cores
12.26/2.01	# Starting new_bool_5 with 180s (1) cores
12.26/2.01	# SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
12.26/2.01	# Search class: HGHSM-FSLM31-MHFMMSBN
12.26/2.01	# Scheduled 6 strats onto 1 cores with 180 seconds (180 total)
12.26/2.01	# Starting new_ho_10_cnf2 with 98s (1) cores
12.26/2.01	# new_ho_10_cnf2 with pid 3405 completed with status 0
12.26/2.01	# Result found by new_ho_10_cnf2
12.26/2.01	# Preprocessing class: HSLMSLSSLLLCHFA.
12.26/2.01	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
12.26/2.01	# Starting ehoh_best5 with 180s (1) cores
12.26/2.01	# Starting almost_fo_3_lam with 180s (1) cores
12.26/2.01	# Starting new_bool_5 with 180s (1) cores
12.26/2.01	# SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
12.26/2.01	# Search class: HGHSM-FSLM31-MHFMMSBN
12.26/2.01	# Scheduled 6 strats onto 1 cores with 180 seconds (180 total)
12.26/2.01	# Starting new_ho_10_cnf2 with 98s (1) cores
12.26/2.01	# Preprocessing time       : 0.005 s
12.26/2.01	# Presaturation interreduction done
12.26/2.01	
12.26/2.01	# Proof found!
12.26/2.01	# SZS status Theorem
12.26/2.01	# SZS output start CNFRefutation
12.26/2.01	thf(decl_22, type, in: $i > $i > $o).
12.26/2.01	thf(decl_23, type, exu: ($i > $o) > $o).
12.26/2.01	thf(decl_24, type, setextAx: $o).
12.26/2.01	thf(decl_25, type, emptyset: $i).
12.26/2.01	thf(decl_26, type, emptysetAx: $o).
12.26/2.01	thf(decl_27, type, setadjoin: $i > $i > $i).
12.26/2.01	thf(decl_28, type, setadjoinAx: $o).
12.26/2.01	thf(decl_29, type, powerset: $i > $i).
12.26/2.01	thf(decl_30, type, powersetAx: $o).
12.26/2.01	thf(decl_31, type, setunion: $i > $i).
12.26/2.01	thf(decl_32, type, setunionAx: $o).
12.26/2.01	thf(decl_33, type, omega: $i).
12.26/2.01	thf(decl_34, type, omega0Ax: $o).
12.26/2.01	thf(decl_35, type, omegaSAx: $o).
12.26/2.01	thf(decl_36, type, omegaIndAx: $o).
12.26/2.01	thf(decl_37, type, replAx: $o).
12.26/2.01	thf(decl_38, type, foundationAx: $o).
12.26/2.01	thf(decl_39, type, wellorderingAx: $o).
12.26/2.01	thf(decl_40, type, descr: ($i > $o) > $i).
12.26/2.01	thf(decl_41, type, descrp: $o).
12.26/2.01	thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
12.26/2.01	thf(decl_43, type, dsetconstrI: $o).
12.26/2.01	thf(decl_44, type, dsetconstrEL: $o).
12.26/2.01	thf(decl_45, type, dsetconstrER: $o).
12.26/2.01	thf(decl_46, type, exuE1: $o).
12.26/2.01	thf(decl_47, type, prop2set: $o > $i).
12.26/2.01	thf(decl_48, type, prop2setE: $o).
12.26/2.01	thf(decl_49, type, emptysetE: $o).
12.26/2.01	thf(decl_50, type, emptysetimpfalse: $o).
12.26/2.01	thf(decl_51, type, notinemptyset: $o).
12.26/2.01	thf(decl_52, type, exuE3e: $o).
12.26/2.01	thf(decl_53, type, setext: $o).
12.26/2.01	thf(decl_54, type, emptyI: $o).
12.26/2.01	thf(decl_55, type, noeltsimpempty: $o).
12.26/2.01	thf(decl_56, type, setbeta: $o).
12.26/2.01	thf(decl_57, type, nonempty: $i > $o).
12.26/2.01	thf(decl_58, type, nonemptyE1: $o).
12.26/2.01	thf(decl_59, type, nonemptyI: $o).
12.26/2.01	thf(decl_60, type, nonemptyI1: $o).
12.26/2.01	thf(decl_61, type, setadjoinIL: $o).
12.26/2.01	thf(decl_62, type, emptyinunitempty: $o).
12.26/2.01	thf(decl_63, type, setadjoinIR: $o).
12.26/2.01	thf(decl_64, type, setadjoinE: $o).
12.26/2.01	thf(decl_65, type, setadjoinOr: $o).
12.26/2.01	thf(decl_66, type, setoftrueEq: $o).
12.26/2.01	thf(decl_67, type, powersetI: $o).
12.26/2.01	thf(decl_68, type, emptyinPowerset: $o).
12.26/2.01	thf(decl_69, type, emptyInPowerset: $o).
12.26/2.01	thf(decl_70, type, powersetE: $o).
12.26/2.01	thf(decl_71, type, setunionI: $o).
12.26/2.01	thf(decl_72, type, setunionE: $o).
12.26/2.01	thf(decl_73, type, subPowSU: $o).
12.26/2.01	thf(decl_74, type, exuE2: $o).
12.26/2.01	thf(decl_75, type, nonemptyImpWitness: $o).
12.26/2.01	thf(decl_76, type, uniqinunit: $o).
12.26/2.01	thf(decl_77, type, notinsingleton: $o).
12.26/2.01	thf(decl_78, type, eqinunit: $o).
12.26/2.01	thf(decl_79, type, singletonsswitch: $o).
12.26/2.01	thf(decl_80, type, upairsetE: $o).
12.26/2.01	thf(decl_81, type, upairsetIL: $o).
12.26/2.01	thf(decl_82, type, upairsetIR: $o).
12.26/2.01	thf(decl_83, type, emptyE1: $o).
12.26/2.01	thf(decl_84, type, vacuousDall: $o).
12.26/2.01	thf(decl_85, type, quantDeMorgan1: $o).
12.26/2.01	thf(decl_86, type, quantDeMorgan2: $o).
12.26/2.01	thf(decl_87, type, quantDeMorgan3: $o).
12.26/2.01	thf(decl_88, type, quantDeMorgan4: $o).
12.26/2.01	thf(decl_89, type, prop2setI: $o).
12.26/2.01	thf(decl_91, type, prop2set2propI: $o).
12.26/2.01	thf(decl_92, type, notdexE: $o).
12.26/2.01	thf(decl_93, type, notdallE: $o).
12.26/2.01	thf(decl_94, type, exuI1: $o).
12.26/2.01	thf(decl_95, type, exuI3: $o).
12.26/2.01	thf(decl_96, type, exuI2: $o).
12.26/2.01	thf(decl_97, type, inCongP: $o).
12.26/2.01	thf(decl_98, type, in__Cong: $o).
12.26/2.01	thf(decl_99, type, exuE3u: $o).
12.26/2.01	thf(decl_100, type, exu__Cong: $o).
12.26/2.01	thf(decl_101, type, emptyset__Cong: $o).
12.26/2.01	thf(decl_102, type, setadjoin__Cong: $o).
12.26/2.01	thf(decl_103, type, powerset__Cong: $o).
12.26/2.01	thf(decl_104, type, setunion__Cong: $o).
12.26/2.01	thf(decl_105, type, omega__Cong: $o).
12.26/2.01	thf(decl_106, type, exuEu: $o).
12.26/2.01	thf(decl_107, type, descr__Cong: $o).
12.26/2.01	thf(decl_108, type, dsetconstr__Cong: $o).
12.26/2.01	thf(decl_109, type, subset: $i > $i > $o).
12.26/2.01	thf(decl_112, type, subsetI1: $o).
12.26/2.01	thf(decl_113, type, eqimpsubset2: $o).
12.26/2.01	thf(decl_114, type, eqimpsubset1: $o).
12.26/2.01	thf(decl_115, type, subsetI2: $o).
12.26/2.01	thf(decl_116, type, emptysetsubset: $o).
12.26/2.01	thf(decl_117, type, subsetE: $o).
12.26/2.01	thf(decl_118, type, subsetE2: $o).
12.26/2.01	thf(decl_119, type, notsubsetI: $o).
12.26/2.01	thf(decl_120, type, notequalI1: $o).
12.26/2.01	thf(decl_121, type, notequalI2: $o).
12.26/2.01	thf(decl_122, type, subsetRefl: $o).
12.26/2.01	thf(decl_123, type, subsetTrans: $o).
12.26/2.01	thf(decl_124, type, setadjoinSub: $o).
12.26/2.01	thf(decl_125, type, setadjoinSub2: $o).
12.26/2.01	thf(decl_126, type, subset2powerset: $o).
12.26/2.01	thf(decl_127, type, setextsub: $o).
12.26/2.01	thf(decl_128, type, subsetemptysetimpeq: $o).
12.26/2.01	thf(decl_129, type, powersetI1: $o).
12.26/2.01	thf(decl_130, type, powersetE1: $o).
12.26/2.01	thf(decl_131, type, inPowerset: $o).
12.26/2.01	thf(decl_132, type, powersetsubset: $o).
12.26/2.01	thf(decl_133, type, sepInPowerset: $o).
12.26/2.01	thf(decl_134, type, sepSubset: $o).
12.26/2.01	thf(decl_135, type, binunion: $i > $i > $i).
12.26/2.01	thf(decl_136, type, binunionIL: $o).
12.26/2.01	thf(decl_137, type, upairset2IR: $o).
12.26/2.01	thf(decl_138, type, binunionIR: $o).
12.26/2.01	thf(decl_139, type, binunionEcases: $o).
12.26/2.01	thf(decl_140, type, binunionE: $o).
12.26/2.01	thf(decl_141, type, binunionLsub: $o).
12.26/2.01	thf(decl_142, type, binunionRsub: $o).
12.26/2.01	thf(decl_143, type, binintersect: $i > $i > $i).
12.26/2.01	thf(decl_144, type, binintersectI: $o).
12.26/2.01	thf(decl_145, type, binintersectSubset5: $o).
12.26/2.01	thf(decl_146, type, binintersectEL: $o).
12.26/2.01	thf(decl_147, type, binintersectLsub: $o).
12.26/2.01	thf(decl_148, type, binintersectSubset2: $o).
12.26/2.01	thf(decl_149, type, binintersectSubset3: $o).
12.26/2.01	thf(decl_150, type, binintersectER: $o).
12.26/2.01	thf(decl_151, type, disjointsetsI1: $o).
12.26/2.01	thf(decl_152, type, binintersectRsub: $o).
12.26/2.01	thf(decl_153, type, binintersectSubset4: $o).
12.26/2.01	thf(decl_154, type, binintersectSubset1: $o).
12.26/2.01	thf(decl_155, type, bs114d: $o).
12.26/2.01	thf(decl_157, type, setminus: $i > $i > $i).
12.26/2.01	thf(decl_158, type, setminusI: $o).
12.26/2.01	thf(decl_159, type, setminusEL: $o).
12.26/2.01	thf(decl_160, type, setminusER: $o).
12.26/2.01	thf(decl_161, type, setminusSubset2: $o).
12.26/2.01	thf(decl_162, type, setminusERneg: $o).
12.26/2.01	thf(decl_163, type, setminusELneg: $o).
12.26/2.01	thf(decl_164, type, setminusILneg: $o).
12.26/2.01	thf(decl_165, type, setminusIRneg: $o).
12.26/2.01	thf(decl_166, type, setminusLsub: $o).
12.26/2.01	thf(decl_167, type, setminusSubset1: $o).
12.26/2.01	thf(decl_168, type, symdiff: $i > $i > $i).
12.26/2.01	thf(decl_169, type, symdiffE: $o).
12.26/2.01	thf(decl_170, type, symdiffI1: $o).
12.26/2.01	thf(decl_171, type, symdiffI2: $o).
12.26/2.01	thf(decl_172, type, symdiffIneg1: $o).
12.26/2.01	thf(decl_173, type, symdiffIneg2: $o).
12.26/2.01	thf(decl_174, type, iskpair: $i > $o).
12.26/2.01	thf(decl_175, type, secondinupair: $o).
12.26/2.01	thf(decl_176, type, setukpairIL: $o).
12.26/2.01	thf(decl_177, type, setukpairIR: $o).
12.26/2.01	thf(decl_178, type, kpairiskpair: $o).
12.26/2.01	thf(decl_179, type, kpair: $i > $i > $i).
12.26/2.01	thf(decl_180, type, kpairp: $o).
12.26/2.01	thf(decl_181, type, cartprod: $i > $i > $i).
12.26/2.01	thf(decl_182, type, singletonsubset: $o).
12.26/2.01	thf(decl_183, type, singletoninpowerset: $o).
12.26/2.01	thf(decl_184, type, singletoninpowunion: $o).
12.26/2.01	thf(decl_185, type, upairset2E: $o).
12.26/2.01	thf(decl_186, type, upairsubunion: $o).
12.26/2.01	thf(decl_187, type, upairinpowunion: $o).
12.26/2.01	thf(decl_188, type, ubforcartprodlem1: $o).
12.26/2.01	thf(decl_189, type, ubforcartprodlem2: $o).
12.26/2.01	thf(decl_190, type, ubforcartprodlem3: $o).
12.26/2.01	thf(decl_191, type, cartprodpairin: $o).
12.26/2.01	thf(decl_192, type, cartprodmempair1: $o).
12.26/2.01	thf(decl_193, type, cartprodmempair: $o).
12.26/2.01	thf(decl_194, type, setunionE2: $o).
12.26/2.01	thf(decl_195, type, setunionsingleton1: $o).
12.26/2.01	thf(decl_196, type, setunionsingleton2: $o).
12.26/2.01	thf(decl_197, type, setunionsingleton: $o).
12.26/2.01	thf(decl_198, type, singleton: $i > $o).
12.26/2.01	thf(decl_199, type, singletonprop: $o).
12.26/2.01	thf(decl_200, type, ex1: $i > ($i > $o) > $o).
12.26/2.01	thf(decl_201, type, ex1E1: $o).
12.26/2.01	thf(decl_202, type, ex1I: $o).
12.26/2.01	thf(decl_203, type, ex1I2: $o).
12.26/2.01	thf(decl_204, type, singletonsuniq: $o).
12.26/2.01	thf(decl_209, type, setukpairinjL1: $o).
12.26/2.01	thf(decl_210, type, kfstsingleton: $o).
12.26/2.01	thf(decl_211, type, theprop: $o).
12.26/2.01	thf(decl_212, type, kfst: $i > $i).
12.26/2.01	thf(decl_213, type, kfstpairEq: $o).
12.26/2.01	thf(decl_214, type, cartprodfstin: $o).
12.26/2.01	thf(decl_215, type, setukpairinjL2: $o).
12.26/2.01	thf(decl_216, type, setukpairinjL: $o).
12.26/2.01	thf(decl_217, type, setukpairinjR11: $o).
12.26/2.01	thf(decl_218, type, setukpairinjR12: $o).
12.26/2.01	thf(decl_219, type, setukpairinjR1: $o).
12.26/2.01	thf(decl_220, type, upairequniteq: $o).
12.26/2.01	thf(decl_221, type, setukpairinjR2: $o).
12.26/2.01	thf(decl_222, type, setukpairinjR: $o).
12.26/2.01	thf(decl_223, type, ksndsingleton: $o).
12.26/2.01	thf(decl_224, type, ksnd: $i > $i).
12.26/2.01	thf(decl_225, type, ksndpairEq: $o).
12.26/2.01	thf(decl_226, type, kpairsurjEq: $o).
12.26/2.01	thf(decl_227, type, cartprodsndin: $o).
12.26/2.01	thf(decl_228, type, cartprodpairmemEL: $o).
12.26/2.01	thf(decl_229, type, cartprodpairmemER: $o).
12.26/2.01	thf(decl_230, type, cartprodmempaircEq: $o).
12.26/2.01	thf(decl_231, type, cartprodfstpairEq: $o).
12.26/2.01	thf(decl_232, type, cartprodsndpairEq: $o).
12.26/2.01	thf(decl_233, type, cartprodpairsurjEq: $o).
12.26/2.01	thf(decl_234, type, breln: $i > $i > $i > $o).
12.26/2.01	thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
12.26/2.01	thf(decl_236, type, dpsetconstrI: $o).
12.26/2.01	thf(decl_237, type, dpsetconstrSub: $o).
12.26/2.01	thf(decl_238, type, setOfPairsIsBReln: $o).
12.26/2.01	thf(decl_239, type, dpsetconstrERa: $o).
12.26/2.01	thf(decl_240, type, dpsetconstrEL1: $o).
12.26/2.01	thf(decl_241, type, dpsetconstrEL2: $o).
12.26/2.01	thf(decl_242, type, dpsetconstrER: $o).
12.26/2.01	thf(decl_243, type, func: $i > $i > $i > $o).
12.26/2.01	thf(decl_244, type, funcSet: $i > $i > $i).
12.26/2.01	thf(decl_245, type, funcImageSingleton: $o).
12.26/2.01	thf(decl_246, type, apProp: $o).
12.26/2.01	thf(decl_247, type, ap: $i > $i > $i > $i > $i).
12.26/2.01	thf(decl_248, type, app: $o).
12.26/2.01	thf(decl_249, type, infuncsetfunc: $o).
12.26/2.01	thf(decl_250, type, epred1_0: $o).
12.26/2.01	thf(decl_251, type, esk1_2: $i > $i > $i).
12.26/2.01	thf(decl_252, type, esk2_2: $i > $i > $i).
12.26/2.01	thf(decl_253, type, esk3_2: $i > $i > $i).
12.26/2.01	thf(decl_254, type, esk4_1: $i > $i).
12.26/2.01	thf(decl_255, type, esk5_2: ($i > $i > $o) > $i > $i).
12.26/2.01	thf(decl_256, type, esk6_2: ($i > $i > $o) > $i > $i).
12.26/2.01	thf(decl_257, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
12.26/2.01	thf(decl_258, type, esk8_1: $i > $i).
12.26/2.01	thf(decl_259, type, esk9_1: ($i > $o) > $i).
12.26/2.01	thf(decl_260, type, esk10_1: ($i > $o) > $i).
12.26/2.01	thf(decl_261, type, esk11_2: $i > $i > $i).
12.26/2.01	thf(decl_262, type, esk12_2: $i > $i > $i).
12.26/2.01	thf(decl_263, type, esk13_1: $i > $i).
12.26/2.01	thf(decl_264, type, esk14_1: $i > $i).
12.26/2.01	thf(decl_265, type, esk15_1: $i > $i).
12.26/2.01	thf(decl_266, type, esk16_2: $i > $i > $i).
12.26/2.01	thf(decl_267, type, esk17_3: $i > $i > $o > $i).
12.26/2.01	thf(decl_268, type, esk18_1: ($i > $o) > $i).
12.26/2.01	thf(decl_269, type, esk19_1: $i > $i).
12.26/2.01	thf(decl_270, type, esk20_2: $i > ($i > $o) > $i).
12.26/2.01	thf(decl_271, type, esk21_2: $i > ($i > $o) > $i).
12.26/2.01	thf(decl_272, type, esk22_2: $i > ($i > $o) > $i).
12.26/2.01	thf(decl_273, type, esk23_2: $i > ($i > $o) > $i).
12.26/2.01	thf(decl_274, type, esk24_2: $i > ($i > $o) > $i).
12.26/2.01	thf(decl_275, type, esk25_2: $i > ($i > $o) > $i).
12.26/2.01	thf(decl_276, type, esk26_2: ($i > $o) > $i > $i).
12.26/2.01	thf(decl_277, type, esk27_1: ($i > $o) > $i).
12.26/2.01	thf(decl_278, type, esk28_1: ($i > $o) > $i).
12.26/2.01	thf(decl_279, type, esk29_2: ($i > $o) > $i > $i).
12.26/2.01	thf(decl_280, type, esk30_2: ($i > $o) > ($i > $o) > $i).
12.26/2.01	thf(decl_281, type, esk31_2: ($i > $o) > ($i > $o) > $i).
12.26/2.01	thf(decl_282, type, esk32_2: ($i > $o) > ($i > $o) > $i).
12.26/2.01	thf(decl_283, type, esk33_2: ($i > $o) > ($i > $o) > $i).
12.26/2.01	thf(decl_284, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
12.26/2.01	thf(decl_285, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
12.26/2.01	thf(decl_286, type, esk36_2: $i > $i > $i).
12.26/2.01	thf(decl_287, type, esk37_2: $i > $i > $i).
12.26/2.01	thf(decl_288, type, esk38_2: $i > $i > $i).
12.26/2.01	thf(decl_289, type, esk39_3: $i > $i > $i > $i).
12.26/2.01	thf(decl_290, type, esk40_3: $i > $i > $i > $i).
12.26/2.01	thf(decl_291, type, esk41_2: $i > $i > $i).
12.26/2.01	thf(decl_292, type, esk42_2: $i > ($i > $o) > $i).
12.26/2.01	thf(decl_293, type, esk43_2: $i > ($i > $o) > $i).
12.26/2.01	thf(decl_294, type, esk44_2: $i > ($i > $o) > $i).
12.26/2.01	thf(decl_295, type, esk45_3: $i > ($i > $o) > $i > $i).
12.26/2.01	thf(decl_296, type, esk46_2: $i > ($i > $o) > $i).
12.26/2.01	thf(decl_297, type, esk47_2: $i > ($i > $o) > $i).
12.26/2.01	thf(decl_298, type, esk48_0: $i).
12.26/2.01	thf(decl_299, type, esk49_0: $i).
12.26/2.01	thf(decl_300, type, esk50_0: $i).
12.26/2.01	thf(decl_301, type, esk51_0: $i).
12.26/2.01	thf(decl_307, type, epred2_2: $i > $i > $i > $o).
12.26/2.01	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', dsetconstr__Cong)).
12.26/2.01	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', descr__Cong)).
12.26/2.01	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', exu__Cong)).
12.26/2.01	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', exuI1)).
12.26/2.01	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', exuE3u)).
12.26/2.01	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', exuE2)).
12.26/2.01	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setoftrueEq)).
12.26/2.01	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', sepInPowerset)).
12.26/2.01	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', nonemptyI)).
12.26/2.01	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setbeta)).
12.26/2.01	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', sepSubset)).
12.26/2.01	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', exuE3e)).
12.26/2.01	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', dsetconstrI)).
12.26/2.01	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', descrp)).
12.26/2.01	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', replAx)).
12.26/2.01	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', apProp)).
12.26/2.01	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', singletonprop)).
12.26/2.01	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', exuEu)).
12.26/2.01	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', ex1E1)).
12.26/2.01	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', dpsetconstrI)).
12.26/2.01	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30)))))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', funcImageSingleton)).
12.26/2.01	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', dpsetconstrER)).
12.26/2.01	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', dpsetconstrEL2)).
12.26/2.01	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', dpsetconstrEL1)).
12.26/2.01	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', dpsetconstrERa)).
12.26/2.01	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setOfPairsIsBReln)).
12.26/2.01	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', dpsetconstrSub)).
12.26/2.01	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', ksndsingleton)).
12.26/2.01	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', kfstsingleton)).
12.26/2.01	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', ex1I2)).
12.26/2.01	thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', ex1I)).
12.26/2.01	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', exuI2)).
12.26/2.01	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', exuI3)).
12.26/2.01	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', emptyE1)).
12.26/2.01	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', exuE1)).
12.26/2.01	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', dsetconstrER)).
12.26/2.01	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', dsetconstrEL)).
12.26/2.01	thf(ap, axiom, ((ap)=(^[X4:$i, X5:$i, X30:$i, X2:$i]:(setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', ap)).
12.26/2.01	thf(ap2p, conjecture, ((setextAx)=>(((setadjoinAx)=>(((setunionAx)=>(((omegaSAx)=>((((((((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>(((emptysetE)=>(((((setext)=>(((((nonemptyE1)=>((((setadjoinIL)=>((emptyinunitempty)=>((((setadjoinOr)=>(((((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((((uniqinunit)=>((notinsingleton)=>((eqinunit)=>(((upairsetE)=>(((upairsetIR)=>((emptyE1)=>((((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>(((notdexE)=>((notdallE)=>(((exuI3)=>((exuI2)=>((((exuE3u)=>(((emptyset__Cong)=>((setadjoin__Cong)=>((((omega__Cong)=>((exuEu)=>((((subsetI1)=>(((((((subsetE2)=>((((notequalI2)=>(((subsetTrans)=>((setadjoinSub)=>((((setextsub)=>((subsetemptysetimpeq)=>(((powersetE1)=>((((sepInPowerset)=>((sepSubset)=>(((upairset2IR)=>((binunionIR)=>((binunionEcases)=>(((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((((((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>(((setminusSubset2)=>((setminusERneg)=>(((setminusILneg)=>((((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((((symdiffIneg2)=>((secondinupair)=>((((kpairiskpair)=>((kpairp)=>((((((((ubforcartprodlem1)=>(((ubforcartprodlem3)=>((cartprodpairin)=>(((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>(((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((((((((kfstpairEq)=>((((setukpairinjL)=>(((((upairequniteq)=>((setukpairinjR2)=>((((((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>(((((dpsetconstrI)=>((((((((funcImageSingleton)=>(((app)=>(![X4:$i, X5:$i, X30:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))<=(in @ X30 @ (funcSet @ X4 @ X5))))<=(infuncsetfunc)))<=(apProp)))<=(dpsetconstrER))<=(dpsetconstrEL2))<=(dpsetconstrEL1))<=(dpsetconstrERa))<=(setOfPairsIsBReln))<=(dpsetconstrSub)))<=(cartprodpairsurjEq))<=(cartprodsndpairEq))<=(cartprodfstpairEq))))))<=(kpairsurjEq))<=(ksndpairEq))<=(ksndsingleton))<=(setukpairinjR))))<=(setukpairinjR1))<=(setukpairinjR12))<=(setukpairinjR11)))<=(setukpairinjL2))<=(cartprodfstin)))<=(theprop))<=(kfstsingleton))<=(setukpairinjL1))<=(singletonsuniq))<=(ex1I2))<=(ex1I)))))<=(setunionsingleton2)))))<=(cartprodmempair1))))<=(ubforcartprodlem2)))<=(upairinpowunion))<=(upairsubunion))<=(upairset2E))<=(singletoninpowunion))<=(singletoninpowerset))<=(singletonsubset))))<=(setukpairIR))<=(setukpairIL))))<=(symdiffIneg1))<=(symdiffI2)))))<=(setminusLsub))<=(setminusIRneg)))<=(setminusELneg))))<=(setminusER))))))<=(binintersectSubset4))<=(binintersectRsub)))))<=(binintersectSubset2))<=(binintersectLsub))<=(binintersectEL))<=(binintersectSubset5)))))<=(binunionE)))))<=(binunionIL))))<=(powersetsubset))<=(inPowerset)))<=(powersetI1))))<=(subset2powerset))<=(setadjoinSub2))))<=(subsetRefl)))<=(notequalI1))<=(notsubsetI)))<=(subsetE))<=(emptysetsubset))<=(subsetI2))<=(eqimpsubset1))<=(eqimpsubset2)))<=(dsetconstr__Cong))<=(descr__Cong))))<=(setunion__Cong))<=(powerset__Cong))))<=(exu__Cong)))<=(in__Cong))<=(inCongP))))<=(exuI1))))<=(prop2set2propI))))))<=(quantDeMorgan1))<=(vacuousDall))))<=(upairsetIL)))<=(singletonsswitch)))))<=(nonemptyImpWitness))<=(exuE2)))))))<=(emptyinPowerset))<=(powersetI))<=(setoftrueEq)))<=(setadjoinE))<=(setadjoinIR))))<=(nonemptyI1))<=(nonemptyI)))<=(setbeta))<=(noeltsimpempty))<=(emptyI)))<=(exuE3e))<=(notinemptyset))<=(emptysetimpfalse)))<=(prop2setE)))))<=(dsetconstrI))<=(descrp))<=(wellorderingAx))<=(foundationAx))<=(replAx))<=(omegaIndAx)))<=(omega0Ax)))<=(powersetAx)))<=(emptysetAx))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', ap2p)).
12.26/2.01	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', emptyset__Cong)).
12.26/2.01	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', powersetI)).
12.26/2.01	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', emptysetAx)).
12.26/2.01	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', notsubsetI)).
12.26/2.01	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', subsetE)).
12.26/2.01	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', subsetI1)).
12.26/2.01	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', emptysetsubset)).
12.26/2.01	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', subsetI2)).
12.26/2.01	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', eqimpsubset1)).
12.26/2.01	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', subsetE2)).
12.26/2.01	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', eqimpsubset2)).
12.26/2.01	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', notequalI2)).
12.26/2.01	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setunion__Cong)).
12.26/2.01	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', powerset__Cong)).
12.26/2.01	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', subsetTrans)).
12.26/2.01	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', in__Cong)).
12.26/2.01	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setadjoinSub)).
12.26/2.01	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', inCongP)).
12.26/2.01	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', quantDeMorgan1)).
12.26/2.01	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', vacuousDall)).
12.26/2.01	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setextsub)).
12.26/2.01	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', upairsetIL)).
12.26/2.01	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', singletonsswitch)).
12.26/2.01	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', subsetemptysetimpeq)).
12.26/2.01	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', nonemptyImpWitness)).
12.26/2.01	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', emptyinPowerset)).
12.26/2.01	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', powersetE1)).
12.26/2.01	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setadjoinE)).
12.26/2.01	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setadjoinIR)).
12.26/2.01	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', nonemptyI1)).
12.26/2.01	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', noeltsimpempty)).
12.26/2.01	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', emptyI)).
12.26/2.01	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', upairset2IR)).
12.26/2.01	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', notinemptyset)).
12.26/2.01	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', emptysetimpfalse)).
12.26/2.01	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', binunionIR)).
12.26/2.01	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', prop2setE)).
12.26/2.01	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', binunionEcases)).
12.26/2.01	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', wellorderingAx)).
12.26/2.01	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', foundationAx)).
12.26/2.01	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', binunionLsub)).
12.26/2.01	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', omegaIndAx)).
12.26/2.01	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', binunionRsub)).
12.26/2.01	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', omega0Ax)).
12.26/2.01	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', powersetAx)).
12.26/2.01	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', binintersectI)).
12.26/2.01	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setadjoin__Cong)).
12.26/2.01	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', binintersectSubset3)).
12.26/2.01	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', binintersectER)).
12.26/2.01	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', disjointsetsI1)).
12.26/2.01	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', binintersectSubset1)).
12.26/2.01	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', bs114d)).
12.26/2.01	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setminusI)).
12.26/2.01	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setminusEL)).
12.26/2.01	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setminusSubset2)).
12.26/2.01	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setminusERneg)).
12.26/2.01	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setminusILneg)).
12.26/2.01	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setminusSubset1)).
12.26/2.01	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', symdiffE)).
12.26/2.01	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', symdiffI1)).
12.26/2.01	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', symdiffIneg2)).
12.26/2.01	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', secondinupair)).
12.26/2.01	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', kpairiskpair)).
12.26/2.01	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', kpairp)).
12.26/2.01	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', omega__Cong)).
12.26/2.01	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', ubforcartprodlem1)).
12.26/2.01	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', ubforcartprodlem3)).
12.26/2.01	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', cartprodpairin)).
12.26/2.01	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', cartprodmempair)).
12.26/2.01	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setunionE2)).
12.26/2.01	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setunionsingleton1)).
12.26/2.01	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setunionsingleton)).
12.26/2.01	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', kfstpairEq)).
12.26/2.01	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setukpairinjL)).
12.26/2.01	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', upairequniteq)).
12.26/2.01	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setukpairinjR2)).
12.26/2.01	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', cartprodsndin)).
12.26/2.01	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', cartprodpairmemEL)).
12.26/2.01	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', cartprodpairmemER)).
12.26/2.01	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', cartprodmempaircEq)).
12.26/2.01	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', app)).
12.26/2.01	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X30)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', infuncsetfunc)).
12.26/2.01	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', cartprodpairsurjEq)).
12.26/2.01	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', cartprodsndpairEq)).
12.26/2.01	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', cartprodfstpairEq)).
12.26/2.01	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', kpairsurjEq)).
12.26/2.01	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', ksndpairEq)).
12.26/2.01	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setukpairinjR)).
12.26/2.01	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setukpairinjR1)).
12.26/2.01	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setukpairinjR12)).
12.26/2.01	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setukpairinjR11)).
12.26/2.01	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setukpairinjL2)).
12.26/2.01	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', cartprodfstin)).
12.26/2.01	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', theprop)).
12.26/2.01	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setukpairinjL1)).
12.26/2.01	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', singletonsuniq)).
12.26/2.01	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setunionsingleton2)).
12.26/2.01	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', cartprodmempair1)).
12.26/2.01	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', ubforcartprodlem2)).
12.26/2.01	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', upairinpowunion)).
12.26/2.01	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', upairsubunion)).
12.26/2.01	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', upairset2E)).
12.26/2.01	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', singletoninpowunion)).
12.26/2.01	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', singletoninpowerset)).
12.26/2.01	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', singletonsubset)).
12.26/2.01	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setukpairIR)).
12.26/2.01	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setukpairIL)).
12.26/2.01	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', symdiffIneg1)).
12.26/2.01	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', symdiffI2)).
12.26/2.01	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setminusLsub)).
12.26/2.01	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setminusIRneg)).
12.26/2.01	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setminusELneg)).
12.26/2.01	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setminusER)).
12.26/2.01	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', binintersectSubset4)).
12.26/2.01	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', binintersectRsub)).
12.26/2.01	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', binintersectSubset2)).
12.26/2.01	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', binintersectLsub)).
12.26/2.01	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', binintersectEL)).
12.26/2.01	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', binintersectSubset5)).
12.26/2.01	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', binunionE)).
12.26/2.01	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', binunionIL)).
12.26/2.01	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', powersetsubset)).
12.26/2.01	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', inPowerset)).
12.26/2.01	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', powersetI1)).
12.26/2.01	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', subset2powerset)).
12.26/2.01	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setadjoinSub2)).
12.26/2.01	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', subsetRefl)).
12.26/2.01	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', notequalI1)).
12.26/2.01	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', notdallE)).
12.26/2.01	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', notdexE)).
12.26/2.01	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', prop2setI)).
12.26/2.01	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', quantDeMorgan4)).
12.26/2.01	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', quantDeMorgan3)).
12.26/2.01	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', quantDeMorgan2)).
12.26/2.01	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', upairsetIR)).
12.26/2.01	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', upairsetE)).
12.26/2.01	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', eqinunit)).
12.26/2.01	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', notinsingleton)).
12.26/2.01	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', uniqinunit)).
12.26/2.01	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', subPowSU)).
12.26/2.01	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setunionE)).
12.26/2.01	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setunionI)).
12.26/2.01	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', powersetE)).
12.26/2.01	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', emptyInPowerset)).
12.26/2.01	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setadjoinOr)).
12.26/2.01	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', emptyinunitempty)).
12.26/2.01	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setadjoinIL)).
12.26/2.01	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', nonemptyE1)).
12.26/2.01	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setext)).
12.26/2.01	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', emptysetE)).
12.26/2.01	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', omegaSAx)).
12.26/2.01	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setunionAx)).
12.26/2.01	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setadjoinAx)).
12.26/2.01	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.kqzMh3YR4E/Vampire---4.8_3218', setextAx)).
12.26/2.01	thf(c_0_193, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
12.26/2.01	thf(c_0_194, plain, ((descr__Cong)<=>![X1:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
12.26/2.01	thf(c_0_195, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
12.26/2.01	thf(c_0_196, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
12.26/2.01	thf(c_0_197, 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])).
12.26/2.01	thf(c_0_198, 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])).
12.26/2.01	thf(c_0_199, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
12.26/2.01	thf(c_0_200, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
12.26/2.01	thf(c_0_201, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
12.26/2.01	thf(c_0_202, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
12.26/2.01	thf(c_0_203, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
12.26/2.01	thf(c_0_204, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
12.26/2.01	thf(c_0_205, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
12.26/2.01	thf(c_0_206, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
12.26/2.01	thf(c_0_207, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
12.26/2.01	thf(c_0_208, plain, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
12.26/2.01	thf(c_0_209, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
12.26/2.01	thf(c_0_210, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
12.26/2.01	thf(c_0_211, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
12.26/2.01	thf(c_0_212, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
12.26/2.01	thf(c_0_213, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
12.26/2.01	thf(c_0_214, 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:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
12.26/2.01	thf(c_0_215, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
12.26/2.01	thf(c_0_216, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
12.26/2.01	thf(c_0_217, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
12.26/2.01	thf(c_0_218, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
12.26/2.01	thf(c_0_219, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
12.26/2.01	thf(c_0_220, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
12.26/2.01	thf(c_0_221, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
12.26/2.01	thf(c_0_222, plain, ((ex1I2)<=>![X4:$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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
12.26/2.01	thf(c_0_223, plain, ((ex1I)<=>![X4:$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])).
12.26/2.01	thf(c_0_224, 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])).
12.26/2.01	thf(c_0_225, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
12.26/2.01	thf(c_0_226, plain, ((emptyE1)<=>![X4:$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])).
12.26/2.01	thf(c_0_227, 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])).
12.26/2.01	thf(c_0_228, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
12.26/2.01	thf(c_0_229, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
12.26/2.01	thf(c_0_230, plain, ((epred1_0)<=>![X1085:$i]:(?[X1086:$i]:((((![X1087:$i]:(((in @ X1087 @ X1086)=>![X1088:$i]:(((in @ X1088 @ X1087)=>(in @ X1088 @ X1085)))))&![X1089:$i, X1090:$i]:((((in @ X1089 @ X1085)&(in @ X1090 @ X1085))=>(![X1091:$i]:(((in @ X1091 @ X1086)=>((in @ X1089 @ X1091)<=>(in @ X1090 @ X1091))))=>((X1089)=(X1090))))))&![X1092:$i, X1093:$i]:((((in @ X1092 @ X1086)&(in @ X1093 @ X1086))=>(![X1094:$i]:(((in @ X1094 @ X1092)=>(in @ X1094 @ X1093)))|![X1095:$i]:(((in @ X1095 @ X1093)=>(in @ X1095 @ X1092)))))))&![X1096:$i]:(((![X1097:$i]:(((in @ X1097 @ X1096)=>(in @ X1097 @ X1085)))&?[X1098:$i]:((in @ X1098 @ X1096)))=>?[X1099:$i, X1100:$i]:(((((in @ X1099 @ X1086)&(in @ X1100 @ X1096))&~(?[X1101:$i]:(((in @ X1101 @ X1099)&(in @ X1101 @ X1096)))))&![X1102:$i]:(((in @ X1102 @ X1086)=>(![X1103:$i]:(((in @ X1103 @ X1102)=>(in @ X1103 @ X1099)))|(in @ X1100 @ X1102)))))))))))), introduced(definition)).
12.26/2.01	thf(c_0_231, plain, ![X1123:$i, X1124:$i, X1125:$i, X1126:$i]:(((ap @ X1123 @ X1124 @ X1125 @ X1126)=(setunion @ (dsetconstr @ X1124 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1126 @ Z0) @ X1125))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ap])])).
12.26/2.01	thf(c_0_232, negated_conjecture, ~((![X578:$i, X579:$i]:((![X580:$i]:(((in @ X580 @ X578)<=>(in @ X580 @ X579)))=>((X578)=(X579))))=>(![X1120:$i]:(~(in @ X1120 @ emptyset))=>(![X581:$i, X582:$i, X583:$i]:(((in @ X583 @ (setadjoin @ X581 @ X582))<=>(((X583)=(X581))|(in @ X583 @ X582))))=>(![X1117:$i, X1118:$i]:(((in @ X1118 @ (powerset @ X1117))<=>![X1119:$i]:(((in @ X1119 @ X1118)=>(in @ X1119 @ X1117)))))=>(![X584:$i, X585:$i]:(((in @ X585 @ (setunion @ X584))<=>?[X586:$i]:(((in @ X585 @ X586)&(in @ X586 @ X584)))))=>((in @ emptyset @ omega)=>(![X587:$i]:(((in @ X587 @ omega)=>(in @ (setadjoin @ X587 @ X587) @ omega)))=>(![X1114:$i]:((((in @ emptyset @ X1114)&![X1115:$i]:((((in @ X1115 @ omega)&(in @ X1115 @ X1114))=>(in @ (setadjoin @ X1115 @ X1115) @ X1114))))=>![X1116:$i]:(((in @ X1116 @ omega)=>(in @ X1116 @ X1114)))))=>(![X1108:$i > $i > $o, X1109:$i]:((![X1110:$i]:(((in @ X1110 @ X1109)=>(exu @ (^[Z0/* 3 */:$i]:((X1108 @ X1110 @ Z0))))))=>?[X1111:$i]:(![X1112:$i]:(((in @ X1112 @ X1111)<=>?[X1113:$i]:(((in @ X1113 @ X1109)&(X1108 @ X1113 @ X1112))))))))=>(![X1104:$i]:((?[X1105:$i]:((in @ X1105 @ X1104))=>?[X1106:$i]:(((in @ X1106 @ X1104)&~(?[X1107:$i]:(((in @ X1107 @ X1106)&(in @ X1107 @ X1104))))))))=>((epred1_0)=>(![X1084:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1084 @ Z0))))=>(X1084 @ (descr @ (^[Z0/* 3 */:$i]:((X1084 @ Z0)))))))=>(![X1081:$i, X1082:$i > $o, X1083:$i]:(((in @ X1083 @ X1081)=>((X1082 @ X1083)=>(in @ X1083 @ (dsetconstr @ X1081 @ (^[Z0/* 3 */:$i]:((X1082 @ Z0))))))))=>(![X588:$i, X589:$i > $o, X590:$i]:(((in @ X590 @ (dsetconstr @ X588 @ (^[Z0/* 3 */:$i]:((X589 @ Z0)))))=>(in @ X590 @ X588)))=>(![X591:$i, X592:$i > $o, X593:$i]:(((in @ X593 @ (dsetconstr @ X591 @ (^[Z0/* 3 */:$i]:((X592 @ Z0)))))=>(X592 @ X593)))=>(![X594:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X594 @ Z0))))=>?[X595:$i]:(((X594 @ X595)&![X596:$i]:(((X594 @ X596)=>((X595)=(X596))))))))=>(![X1079:$o, X1080:$i]:(((in @ X1080 @ (prop2set @ ((X1079))))=>(X1079)))=>(![X597:$i]:(((in @ X597 @ emptyset)=>![X598:$o]:((X598))))=>(![X1078:$i]:(~(in @ X1078 @ emptyset))=>(![X1077:$i]:(~(in @ X1077 @ emptyset))=>(![X1075:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1075 @ Z0))))=>?[X1076:$i]:((X1075 @ X1076))))=>(![X599:$i, X600:$i]:((![X601:$i]:(((in @ X601 @ X599)=>(in @ X601 @ X600)))=>(![X602:$i]:(((in @ X602 @ X600)=>(in @ X602 @ X599)))=>((X599)=(X600)))))=>(![X1073:$i]:((![X1074:$i]:(~(in @ X1074 @ X1073))=>((X1073)=(emptyset))))=>(![X1071:$i]:((![X1072:$i]:(~(in @ X1072 @ X1071))=>((X1071)=(emptyset))))=>(![X1068:$i, X1069:$i > $o, X1070:$i]:(((in @ X1070 @ X1068)=>((in @ X1070 @ (dsetconstr @ X1068 @ (^[Z0/* 3 */:$i]:((X1069 @ Z0)))))<=>(X1069 @ X1070))))=>(![X603:$i]:(((nonempty @ X603)=>?[X604:$i]:((in @ X604 @ X603))))=>(![X1065:$i, X1066:$i > $o, X1067:$i]:(((in @ X1067 @ X1065)=>((X1066 @ X1067)=>(nonempty @ (dsetconstr @ X1065 @ (^[Z0/* 3 */:$i]:((X1066 @ Z0))))))))=>(![X1063:$i]:((?[X1064:$i]:((in @ X1064 @ X1063))=>(nonempty @ X1063)))=>(![X605:$i, X606:$i]:((in @ X605 @ (setadjoin @ X605 @ X606)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1060:$i, X1061:$i, X1062:$i]:(((in @ X1062 @ X1061)=>(in @ X1062 @ (setadjoin @ X1060 @ X1061))))=>(![X1056:$i, X1057:$i, X1058:$i]:(((in @ X1058 @ (setadjoin @ X1056 @ X1057))=>![X1059:$o]:(((((X1058)=(X1056))=>(X1059))=>(((in @ X1058 @ X1057)=>(X1059))=>(X1059))))))=>(![X607:$i, X608:$i, X609:$i]:(((in @ X609 @ (setadjoin @ X607 @ X608))=>(((X609)=(X607))|(in @ X609 @ X608))))=>(![X1055:$i]:(((dsetconstr @ X1055 @ (^[Z0/* 3 */:$i]:(($true))))=(X1055)))=>(![X1052:$i, X1053:$i]:((![X1054:$i]:(((in @ X1054 @ X1053)=>(in @ X1054 @ X1052)))=>(in @ X1053 @ (powerset @ X1052))))=>(![X1051:$i]:((in @ emptyset @ (powerset @ X1051)))=>(![X610:$i]:((in @ emptyset @ (powerset @ X610)))=>(![X611:$i, X612:$i, X613:$i]:(((in @ X612 @ (powerset @ X611))=>((in @ X613 @ X612)=>(in @ X613 @ X611))))=>(![X614:$i, X615:$i, X616:$i]:(((in @ X615 @ X616)=>((in @ X616 @ X614)=>(in @ X615 @ (setunion @ X614)))))=>(![X617:$i, X618:$i]:(((in @ X618 @ (setunion @ X617))=>![X619:$o]:((![X620:$i]:(((in @ X618 @ X620)=>((in @ X620 @ X617)=>(X619))))=>(X619)))))=>(![X621:$i, X622:$i]:(((in @ X622 @ X621)=>(in @ X622 @ (powerset @ (setunion @ X621)))))=>(![X1048:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1048 @ Z0))))=>?[X1049:$i]:(![X1050:$i]:(((X1048 @ X1050)<=>((X1050)=(X1049)))))))=>(![X1046:$i]:(((nonempty @ X1046)=>?[X1047:$i]:((in @ X1047 @ X1046))))=>(![X623:$i, X624:$i]:(((in @ X623 @ (setadjoin @ X624 @ emptyset))=>((X623)=(X624))))=>(![X625:$i, X626:$i]:((((X625)!=(X626))=>~(in @ X626 @ (setadjoin @ X625 @ emptyset))))=>(![X627:$i, X628:$i]:((((X627)=(X628))=>(in @ X627 @ (setadjoin @ X628 @ emptyset))))=>(![X1044:$i, X1045:$i]:(((in @ X1044 @ (setadjoin @ X1045 @ emptyset))=>(in @ X1045 @ (setadjoin @ X1044 @ emptyset))))=>(![X629:$i, X630:$i, X631:$i]:(((in @ X631 @ (setadjoin @ X629 @ (setadjoin @ X630 @ emptyset)))=>(((X631)=(X629))|((X631)=(X630)))))=>(![X1042:$i, X1043:$i]:((in @ X1042 @ (setadjoin @ X1042 @ (setadjoin @ X1043 @ emptyset))))=>(![X632:$i, X633:$i]:((in @ X633 @ (setadjoin @ X632 @ (setadjoin @ X633 @ emptyset))))=>(![X634:$i, X635:$i > $o]:((?[X636:$i]:(((in @ X636 @ X634)&(X635 @ X636)))=>((dsetconstr @ X634 @ (^[Z0/* 3 */:$i]:((X635 @ Z0))))!=(emptyset))))=>(![X1040:$i > $o, X1041:$i]:(((in @ X1041 @ emptyset)=>(X1040 @ X1041)))=>(![X1036:$i, X1037:$i > $o]:((~(![X1038:$i]:(((in @ X1038 @ X1036)=>(X1037 @ X1038))))=>?[X1039:$i]:(((in @ X1039 @ X1036)&~(X1037 @ X1039)))))=>(![X637:$i, X638:$i > $o]:((![X639:$i]:(((in @ X639 @ X637)=>~(X638 @ X639)))=>~(?[X640:$i]:(((in @ X640 @ X637)&(X638 @ X640))))))=>(![X641:$i, X642:$i > $o]:((~(?[X643:$i]:(((in @ X643 @ X641)&(X642 @ X643))))=>![X644:$i]:(((in @ X644 @ X641)=>~(X642 @ X644)))))=>(![X645:$i, X646:$i > $o]:((?[X647:$i]:(((in @ X647 @ X645)&~(X646 @ X647)))=>~(![X648:$i]:(((in @ X648 @ X645)=>(X646 @ X648))))))=>(![X649:$o]:(((X649)=>(in @ emptyset @ (prop2set @ ((X649))))))=>((prop2set2propI)=>(![X650:$i, X651:$i > $o]:((~(?[X652:$i]:(((in @ X652 @ X650)&(X651 @ X652))))=>![X653:$i]:(((in @ X653 @ X650)=>~(X651 @ X653)))))=>(![X654:$i, X655:$i > $o]:((~(![X656:$i]:(((in @ X656 @ X654)=>(X655 @ X656))))=>?[X657:$i]:(((in @ X657 @ X654)&~(X655 @ X657)))))=>(![X1033:$i > $o]:((?[X1034:$i]:(((X1033 @ X1034)&![X1035:$i]:(((X1033 @ X1035)=>((X1034)=(X1035))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1033 @ Z0))))))=>(![X658:$i > $o]:((?[X659:$i]:((X658 @ X659))=>(![X660:$i, X661:$i]:(((X658 @ X660)=>((X658 @ X661)=>((X660)=(X661)))))=>(exu @ (^[Z0/* 3 */:$i]:((X658 @ Z0)))))))=>(![X662:$i > $o]:((?[X663:$i]:(![X664:$i]:(((X662 @ X664)<=>((X664)=(X663)))))=>(exu @ (^[Z0/* 3 */:$i]:((X662 @ Z0))))))=>(![X1029:$i, X1030:$i]:((((X1029)=(X1030))=>![X1031:$i, X1032:$i]:((((X1031)=(X1032))=>((in @ X1031 @ X1029)=>(in @ X1032 @ X1030))))))=>(![X1025:$i, X1026:$i]:((((X1025)=(X1026))=>![X1027:$i, X1028:$i]:((((X1027)=(X1028))=>((in @ X1027 @ X1025)<=>(in @ X1028 @ X1026))))))=>(![X665:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X665 @ Z0))))=>![X666:$i, X667:$i]:(((X665 @ X666)=>((X665 @ X667)=>((X666)=(X667)))))))=>(![X1021:$i > $o, X1022:$i > $o]:((![X1023:$i, X1024:$i]:((((X1023)=(X1024))=>((X1021 @ X1023)<=>(X1022 @ X1024))))=>((exu @ (^[Z0/* 3 */:$i]:((X1021 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X1022 @ Z0)))))))=>(((emptyset)=(emptyset))=>(![X668:$i, X669:$i]:((((X668)=(X669))=>![X670:$i, X671:$i]:((((X670)=(X671))=>((setadjoin @ X668 @ X670)=(setadjoin @ X669 @ X671))))))=>(![X1019:$i, X1020:$i]:((((X1019)=(X1020))=>((powerset @ X1019)=(powerset @ X1020))))=>(![X1017:$i, X1018:$i]:((((X1017)=(X1018))=>((setunion @ X1017)=(setunion @ X1018))))=>(((omega)=(omega))=>(![X672:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X672 @ Z0))))=>![X673:$i, X674:$i]:(((X672 @ X673)=>((X672 @ X674)=>((X673)=(X674)))))))=>(![X1013:$i > $o, X1014:$i > $o]:((![X1015:$i, X1016:$i]:((((X1015)=(X1016))=>((X1013 @ X1015)<=>(X1014 @ X1016))))=>((exu @ (^[Z0/* 3 */:$i]:((X1013 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X1014 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1013 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X1014 @ Z0)))))))))=>(![X1007:$i, X1008:$i]:((((X1007)=(X1008))=>![X1009:$i > $o, X1010:$i > $o]:((![X1011:$i]:(((in @ X1011 @ X1007)=>![X1012:$i]:(((in @ X1012 @ X1008)=>(((X1011)=(X1012))=>((X1009 @ X1011)<=>(X1010 @ X1012)))))))=>((dsetconstr @ X1007 @ (^[Z0/* 3 */:$i]:((X1009 @ Z0))))=(dsetconstr @ X1008 @ (^[Z0/* 3 */:$i]:((X1010 @ Z0)))))))))=>(![X675:$i, X676:$i]:((![X677:$i]:(((in @ X677 @ X675)=>(in @ X677 @ X676)))=>(subset @ X675 @ X676)))=>(![X1005:$i, X1006:$i]:((((X1005)=(X1006))=>(subset @ X1006 @ X1005)))=>(![X1003:$i, X1004:$i]:((((X1003)=(X1004))=>(subset @ X1003 @ X1004)))=>(![X1000:$i, X1001:$i]:((![X1002:$i]:(((in @ X1002 @ X1000)=>(in @ X1002 @ X1001)))=>(subset @ X1000 @ X1001)))=>(![X999:$i]:((subset @ emptyset @ X999))=>(![X996:$i, X997:$i, X998:$i]:(((subset @ X996 @ X997)=>((in @ X998 @ X996)=>(in @ X998 @ X997))))=>(![X678:$i, X679:$i, X680:$i]:(((subset @ X678 @ X679)=>(~(in @ X680 @ X679)=>~(in @ X680 @ X678))))=>(![X993:$i, X994:$i, X995:$i]:(((in @ X995 @ X993)=>(~(in @ X995 @ X994)=>~(subset @ X993 @ X994))))=>(![X991:$i, X992:$i]:((~(subset @ X991 @ X992)=>((X991)!=(X992))))=>(![X681:$i, X682:$i, X683:$i]:(((in @ X683 @ X681)=>(~(in @ X683 @ X682)=>((X681)!=(X682)))))=>(![X990:$i]:((subset @ X990 @ X990))=>(![X684:$i, X685:$i, X686:$i]:(((subset @ X684 @ X685)=>((subset @ X685 @ X686)=>(subset @ X684 @ X686))))=>(![X687:$i, X688:$i]:((subset @ X688 @ (setadjoin @ X687 @ X688)))=>(![X987:$i, X988:$i, X989:$i]:(((subset @ X987 @ X989)=>(subset @ X987 @ (setadjoin @ X988 @ X989))))=>(![X985:$i, X986:$i]:(((subset @ X985 @ X986)=>(in @ X985 @ (powerset @ X986))))=>(![X689:$i, X690:$i]:(((subset @ X689 @ X690)=>((subset @ X690 @ X689)=>((X689)=(X690)))))=>(![X691:$i]:(((subset @ X691 @ emptyset)=>((X691)=(emptyset))))=>(![X983:$i, X984:$i]:(((subset @ X984 @ X983)=>(in @ X984 @ (powerset @ X983))))=>(![X692:$i, X693:$i]:(((in @ X693 @ (powerset @ X692))=>(subset @ X693 @ X692)))=>(![X982:$i]:((in @ X982 @ (powerset @ X982)))=>(![X980:$i, X981:$i]:(((subset @ X980 @ X981)=>(subset @ (powerset @ X980) @ (powerset @ X981))))=>(![X694:$i, X695:$i > $o]:((in @ (dsetconstr @ X694 @ (^[Z0/* 3 */:$i]:((X695 @ Z0)))) @ (powerset @ X694)))=>(![X696:$i, X697:$i > $o]:((subset @ (dsetconstr @ X696 @ (^[Z0/* 3 */:$i]:((X697 @ Z0)))) @ X696))=>(![X977:$i, X978:$i, X979:$i]:(((in @ X979 @ X977)=>(in @ X979 @ (binunion @ X977 @ X978))))=>(![X698:$i, X699:$i]:((in @ X699 @ (setadjoin @ X698 @ (setadjoin @ X699 @ emptyset))))=>(![X700:$i, X701:$i, X702:$i]:(((in @ X702 @ X701)=>(in @ X702 @ (binunion @ X700 @ X701))))=>(![X703:$i, X704:$i, X705:$i, X706:$o]:(((in @ X705 @ (binunion @ X703 @ X704))=>(((in @ X705 @ X703)=>(X706))=>(((in @ X705 @ X704)=>(X706))=>(X706)))))=>(![X974:$i, X975:$i, X976:$i]:(((in @ X976 @ (binunion @ X974 @ X975))=>((in @ X976 @ X974)|(in @ X976 @ X975))))=>(![X707:$i, X708:$i]:((subset @ X707 @ (binunion @ X707 @ X708)))=>(![X709:$i, X710:$i]:((subset @ X710 @ (binunion @ X709 @ X710)))=>(![X711:$i, X712:$i, X713:$i]:(((in @ X713 @ X711)=>((in @ X713 @ X712)=>(in @ X713 @ (binintersect @ X711 @ X712)))))=>(![X971:$i, X972:$i, X973:$i]:(((subset @ X973 @ X971)=>((subset @ X973 @ X972)=>(subset @ X973 @ (binintersect @ X971 @ X972)))))=>(![X968:$i, X969:$i, X970:$i]:(((in @ X970 @ (binintersect @ X968 @ X969))=>(in @ X970 @ X968)))=>(![X966:$i, X967:$i]:((subset @ (binintersect @ X966 @ X967) @ X966))=>(![X964:$i, X965:$i]:(((subset @ X964 @ X965)=>((binintersect @ X964 @ X965)=(X964))))=>(![X714:$i, X715:$i]:((((binintersect @ X714 @ X715)=(X715))=>(subset @ X715 @ X714)))=>(![X716:$i, X717:$i, X718:$i]:(((in @ X718 @ (binintersect @ X716 @ X717))=>(in @ X718 @ X717)))=>(![X719:$i, X720:$i]:((~(?[X721:$i]:(((in @ X721 @ X719)&(in @ X721 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X831 @ X832 @ X833)=>![X834:$i]:(((in @ X834 @ X831)=>(in @ (setunion @ (dsetconstr @ X832 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X834 @ Z0) @ X833))))) @ X832)))))=>(![X824:$i, X825:$i, X826:$i]:(((func @ X824 @ X825 @ X826)=>![X827:$i]:(((in @ X827 @ X824)=>(in @ (ap @ X824 @ X825 @ X826 @ X827) @ X825)))))=>(![X828:$i, X829:$i, X830:$i]:(((in @ X830 @ (funcSet @ X828 @ X829))=>(func @ X828 @ X829 @ X830)))=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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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(assume_negation,[status(cth)],[ap2p]), emptyset__Cong]), powersetI]), emptysetAx]), notsubsetI]), subsetE]), subsetI1]), emptysetsubset]), subsetI2]), eqimpsubset1]), subsetE2]), eqimpsubset2]), c_0_193]), notequalI2]), c_0_194]), setunion__Cong]), powerset__Cong]), subsetTrans]), c_0_195]), in__Cong]), setadjoinSub]), inCongP]), c_0_196]), quantDeMorgan1]), c_0_197]), vacuousDall]), setextsub]), upairsetIL]), singletonsswitch]), subsetemptysetimpeq]), nonemptyImpWitness]), c_0_198]), emptyinPowerset]), c_0_199]), powersetE1]), setadjoinE]), setadjoinIR]), c_0_200]), nonemptyI1]), c_0_201]), c_0_202]), c_0_203]), noeltsimpempty]), emptyI]), upairset2IR]), c_0_204]), notinemptyset]), emptysetimpfalse]), binunionIR]), prop2setE]), c_0_205]), binunionEcases]), c_0_206]), wellorderingAx]), foundationAx]), binunionLsub]), c_0_207]), omegaIndAx]), binunionRsub]), omega0Ax]), powersetAx]), binintersectI]), setadjoin__Cong]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), c_0_208]), setminusSubset2]), setminusERneg]), setminusILneg]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffIneg2]), secondinupair]), kpairiskpair]), kpairp]), omega__Cong]), ubforcartprodlem1]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton]), c_0_209]), c_0_210]), c_0_211]), kfstpairEq]), setukpairinjL]), upairequniteq]), setukpairinjR2]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), c_0_212]), c_0_213]), app]), infuncsetfunc]), c_0_214]), c_0_215]), c_0_216]), c_0_217]), c_0_218]), c_0_219]), cartprodpairsurjEq]), cartprodsndpairEq]), cartprodfstpairEq]), kpairsurjEq]), ksndpairEq]), c_0_220]), setukpairinjR]), setukpairinjR1]), setukpairinjR12]), setukpairinjR11]), setukpairinjL2]), cartprodfstin]), theprop]), c_0_221]), setukpairinjL1]), singletonsuniq]), c_0_222]), c_0_223]), setunionsingleton2]), cartprodmempair1]), ubforcartprodlem2]), upairinpowunion]), upairsubunion]), upairset2E]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), setukpairIR]), setukpairIL]), symdiffIneg1]), symdiffI2]), setminusLsub]), setminusIRneg]), setminusELneg]), setminusER]), binintersectSubset4]), binintersectRsub]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binunionE]), binunionIL]), powersetsubset]), inPowerset]), powersetI1]), subset2powerset]), setadjoinSub2]), subsetRefl]), notequalI1]), c_0_224]), c_0_225]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), c_0_226]), upairsetIR]), upairsetE]), eqinunit]), notinsingleton]), uniqinunit]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), setadjoinOr]), emptyinunitempty]), setadjoinIL]), nonemptyE1]), setext]), emptysetE]), c_0_227]), c_0_228]), c_0_229]), omegaSAx]), setunionAx]), setadjoinAx]), setextAx])]), c_0_230])).
12.26/2.01	thf(c_0_233, plain, ![X1666:$i, X1667:$i, X1668:$i, X1669:$i]:(((ap @ X1666 @ X1667 @ X1668 @ X1669)=(setunion @ (dsetconstr @ X1667 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1669 @ Z0) @ X1668))))))), inference(variable_rename,[status(thm)],[c_0_231])).
12.26/2.01	thf(c_0_234, plain, ![X1689:$i, X5:$i, X4:$i]:(((epred2_2 @ X4 @ X5 @ X1689)<=>(in @ (kpair @ X5 @ X1689) @ X4))), introduced(definition)).
12.26/2.01	thf(c_0_235, negated_conjecture, ![X1127:$i, X1128:$i, X1130:$i, X1131:$i, X1132:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1137:$i, X1138:$i, X1140:$i, X1141:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1147:$i, X1149:$i, X1150:$i > $i > $o, X1151:$i, X1154:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1161:$i, X1162:$i > $o, X1163:$i, X1164:$i > $o, X1165:$i, X1166:$i, X1167:$i > $o, X1168:$i, X1169:$i, X1170:$i > $o, X1171:$i, X1172:$i > $o, X1174:$i, X1175:$o, X1176:$i, X1177:$i, X1178:$o, X1179:$i, X1180:$i, X1181:$i > $o, X1183:$i, X1184:$i, X1187:$i, X1189:$i, X1191:$i, X1192:$i > $o, X1193:$i, X1194:$i, X1196:$i, X1197:$i > $o, X1198:$i, X1199:$i, X1200:$i, X1201:$i, X1202:$i, X1203:$i, X1204:$i, X1205:$i, X1206:$i, X1207:$i, X1208:$i, X1209:$o, X1210:$i, X1211:$i, X1212:$i, X1213:$i, X1214:$i, X1215:$i, X1217:$i, X1218:$i, X1219:$i, X1220:$i, X1221:$i, X1222:$i, X1223:$i, X1224:$i, X1225:$i, X1226:$i, X1227:$o, X1229:$i, X1230:$i, X1231:$i > $o, X1233:$i, X1234:$i, X1235:$i, X1237:$i, X1238:$i, X1239:$i, X1240:$i, X1241:$i, X1242:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i, X1251:$i, X1252:$i, X1253:$i > $o, X1254:$i, X1255:$i > $o, X1256:$i, X1257:$i, X1258:$i > $o, X1259:$i, X1261:$i, X1262:$i > $o, X1264:$i, X1265:$i, X1266:$i > $o, X1268:$i, X1269:$i, X1270:$i > $o, X1271:$i, X1273:$o, X1274:$i, X1275:$i > $o, X1277:$i, X1278:$i, X1279:$i > $o, X1280:$i, X1282:$i > $o, X1283:$i, X1285:$i > $o, X1286:$i, X1289:$i > $o, X1290:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i > $o, X1301:$i, X1302:$i, X1303:$i > $o, X1304:$i > $o, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i > $o, X1316:$i, X1317:$i, X1318:$i > $o, X1319:$i > $o, X1322:$i, X1323:$i, X1324:$i > $o, X1325:$i > $o, X1328:$i, X1329:$i, X1331:$i, X1332:$i, X1333:$i, X1334:$i, X1335:$i, X1336:$i, X1338:$i, X1339:$i, X1340:$i, X1341:$i, X1342:$i, X1343:$i, X1344:$i, X1345:$i, X1346:$i, X1347:$i, X1348:$i, X1349:$i, X1350:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i, X1356:$i, X1357:$i, X1358:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i, X1365:$i, X1366:$i, X1367:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i > $o, X1376:$i, X1377:$i > $o, X1378:$i, X1379:$i, X1380:$i, X1381:$i, X1382:$i, X1383:$i, X1384:$i, X1385:$i, X1386:$i, X1387:$i, X1388:$i, X1389:$o, X1390:$i, X1391:$i, X1392:$i, X1393:$i, X1394:$i, X1395:$i, X1396:$i, X1397:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i, X1403:$i, X1404:$i, X1405:$i, X1406:$i, X1407:$i, X1408:$i, X1409:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1418:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1423:$i, X1424:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$i, X1432:$i, X1433:$i, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1456:$i, X1457:$o, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1470:$i, X1471:$i, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$i, X1483:$i, X1484:$i, X1485:$i, X1486:$i, X1487:$i, X1488:$i, X1489:$i, X1490:$i, X1491:$i, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1512:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i > $o, X1532:$i, X1533:$i, X1534:$i > $o, X1536:$i, X1537:$i > $o, X1538:$i, X1540:$i, X1541:$i > $o, X1544:$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, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1599:$i, X1600:$i, X1601:$i, X1602:$i, X1603:$i, X1604:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i, X1610:$i, X1611:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$i > $i > $o, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i > $i > $o, X1622:$i, X1623:$i, X1624:$i > $i > $o, X1625:$i, X1626:$i, X1627:$i > $i > $o, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i > $i > $o, X1633:$i, X1634:$i, X1635:$i, X1636:$i, X1637:$i > $i > $o, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i > $i > $o, X1643:$i, X1644:$i, X1645:$i, X1646:$i, X1647:$i, X1648:$i, X1649:$i, X1650:$i, X1651:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i]:((((~(in @ (esk1_2 @ X1127 @ X1128) @ X1127)|~(in @ (esk1_2 @ X1127 @ X1128) @ X1128)|((X1127)=(X1128)))&((in @ (esk1_2 @ X1127 @ X1128) @ X1127)|(in @ (esk1_2 @ X1127 @ X1128) @ X1128)|((X1127)=(X1128))))&(~(in @ X1130 @ emptyset)&(((~(in @ X1133 @ (setadjoin @ X1131 @ X1132))|(((X1133)=(X1131))|(in @ X1133 @ X1132)))&((((X1133)!=(X1131))|(in @ X1133 @ (setadjoin @ X1131 @ X1132)))&(~(in @ X1133 @ X1132)|(in @ X1133 @ (setadjoin @ X1131 @ X1132)))))&(((~(in @ X1135 @ (powerset @ X1134))|(~(in @ X1136 @ X1135)|(in @ X1136 @ X1134)))&(((in @ (esk2_2 @ X1137 @ X1138) @ X1138)|(in @ X1138 @ (powerset @ X1137)))&(~(in @ (esk2_2 @ X1137 @ X1138) @ X1137)|(in @ X1138 @ (powerset @ X1137)))))&(((((in @ X1141 @ (esk3_2 @ X1140 @ X1141))|~(in @ X1141 @ (setunion @ X1140)))&((in @ (esk3_2 @ X1140 @ X1141) @ X1140)|~(in @ X1141 @ (setunion @ X1140))))&(~(in @ X1144 @ X1145)|~(in @ X1145 @ X1143)|(in @ X1144 @ (setunion @ X1143))))&((in @ emptyset @ omega)&((~(in @ X1146 @ omega)|(in @ (setadjoin @ X1146 @ X1146) @ omega))&(((((in @ (esk4_1 @ X1147) @ omega)|~(in @ emptyset @ X1147)|(~(in @ X1149 @ omega)|(in @ X1149 @ X1147)))&((in @ (esk4_1 @ X1147) @ X1147)|~(in @ emptyset @ X1147)|(~(in @ X1149 @ omega)|(in @ X1149 @ X1147))))&(~(in @ (setadjoin @ (esk4_1 @ X1147) @ (esk4_1 @ X1147)) @ X1147)|~(in @ emptyset @ X1147)|(~(in @ X1149 @ omega)|(in @ X1149 @ X1147))))&((((((in @ (esk7_3 @ X1150 @ X1151 @ X1154) @ X1151)|~(in @ X1154 @ (esk6_2 @ X1150 @ X1151))|(in @ (esk5_2 @ X1150 @ X1151) @ X1151))&((X1150 @ (esk7_3 @ X1150 @ X1151 @ X1154) @ X1154)|~(in @ X1154 @ (esk6_2 @ X1150 @ X1151))|(in @ (esk5_2 @ X1150 @ X1151) @ X1151)))&(~(in @ X1157 @ X1151)|~(X1150 @ X1157 @ X1156)|(in @ X1156 @ (esk6_2 @ X1150 @ X1151))|(in @ (esk5_2 @ X1150 @ X1151) @ X1151)))&((((in @ (esk7_3 @ X1150 @ X1151 @ X1154) @ X1151)|~(in @ X1154 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X1387)))&(~(X1389)|(X1389)|~(X1389)|~(in @ X1388 @ (binunion @ X1386 @ X1387)))))&((~(in @ X1392 @ (binunion @ X1390 @ X1391))|((in @ X1392 @ X1390)|(in @ X1392 @ X1391)))&((subset @ X1393 @ (binunion @ X1393 @ X1394))&((subset @ X1396 @ (binunion @ X1395 @ X1396))&((~(in @ X1399 @ X1397)|(~(in @ X1399 @ X1398)|(in @ X1399 @ (binintersect @ X1397 @ X1398))))&((~(subset @ X1402 @ X1400)|(~(subset @ X1402 @ X1401)|(subset @ X1402 @ (binintersect @ X1400 @ X1401))))&((~(in @ X1405 @ (binintersect @ X1403 @ X1404))|(in @ X1405 @ X1403))&((subset @ (binintersect @ X1406 @ X1407) @ X1406)&((~(subset @ X1408 @ X1409)|((binintersect @ X1408 @ X1409)=(X1408)))&((((binintersect @ X1410 @ X1411)!=(X1411))|(subset @ X1411 @ X1410))&((~(in @ X1414 @ (binintersect @ X1412 @ X1413))|(in @ X1414 @ X1413))&((((in @ (esk38_2 @ X1415 @ X1416) @ X1415)|((binintersect @ X1415 @ X1416)=(emptyset)))&((in @ (esk38_2 @ X1415 @ X1416) @ X1416)|((binintersect @ X1415 @ X1416)=(emptyset))))&((subset @ (binintersect @ X1418 @ X1419) @ X1419)&((~(subset @ X1421 @ X1420)|((binintersect @ X1420 @ X1421)=(X1421)))&((((binintersect @ X1422 @ X1423)!=(X1422))|(subset @ X1422 @ X1423))&(((binintersect @ X1424 @ (binunion @ X1425 @ X1426))=(binunion @ (binintersect @ X1424 @ X1425) @ (binintersect @ X1424 @ X1426)))&((~(in @ X1429 @ X1427)|((in @ X1429 @ X1428)|(in @ X1429 @ (setminus @ X1427 @ X1428))))&((~(in @ X1432 @ (setminus @ X1430 @ X1431))|(in @ X1432 @ X1430))&((~(in @ X1435 @ (setminus @ X1433 @ X1434))|~(in @ X1435 @ X1434))&((~(subset @ X1436 @ X1437)|((setminus @ X1436 @ X1437)=(emptyset)))&(((in @ X1440 @ (setminus @ X1438 @ X1439))|(~(in @ X1440 @ X1438)|(in @ X1440 @ X1439)))&(((in @ X1443 @ (setminus @ X1441 @ X1442))|((in @ X1443 @ X1442)|~(in @ X1443 @ X1441)))&(((in @ X1446 @ X1444)|~(in @ X1446 @ (setminus @ X1444 @ X1445)))&((~(in @ X1449 @ X1448)|~(in @ X1449 @ (setminus @ X1447 @ X1448)))&((subset @ (setminus @ X1450 @ X1451) @ X1450)&((((setminus @ X1452 @ X1453)!=(emptyset))|(subset @ X1452 @ X1453))&((((~(in @ X1456 @ X1454)|(X1457)|(in @ X1456 @ X1454)|~(in @ X1456 @ (symdiff @ X1454 @ X1455)))&(((in @ X1456 @ X1455)|(X1457)|(in @ X1456 @ X1454)|~(in @ X1456 @ (symdiff @ X1454 @ X1455)))&(~(X1457)|(X1457)|(in @ X1456 @ X1454)|~(in @ X1456 @ (symdiff @ X1454 @ X1455)))))&(((~(in @ X1456 @ X1454)|(X1457)|~(in @ X1456 @ X1455)|~(in @ X1456 @ (symdiff @ X1454 @ X1455)))&(((in @ X1456 @ X1455)|(X1457)|~(in @ X1456 @ X1455)|~(in @ X1456 @ (symdiff @ X1454 @ X1455)))&(~(X1457)|(X1457)|~(in @ X1456 @ X1455)|~(in @ X1456 @ (symdiff @ X1454 @ X1455)))))&((~(in @ X1456 @ X1454)|(X1457)|~(X1457)|~(in @ X1456 @ (symdiff @ X1454 @ X1455)))&(((in @ X1456 @ X1455)|(X1457)|~(X1457)|~(in @ X1456 @ (symdiff @ X1454 @ X1455)))&(~(X1457)|(X1457)|~(X1457)|~(in @ X1456 @ (symdiff @ X1454 @ X1455)))))))&((~(in @ X1460 @ X1458)|((in @ X1460 @ X1459)|(in @ X1460 @ (symdiff @ X1458 @ X1459))))&(((in @ X1463 @ X1461)|(~(in @ X1463 @ X1462)|(in @ X1463 @ (symdiff @ X1461 @ X1462))))&((~(in @ X1466 @ X1464)|(~(in @ X1466 @ X1465)|~(in @ X1466 @ (symdiff @ X1464 @ X1465))))&(((in @ X1469 @ X1467)|((in @ X1469 @ X1468)|~(in @ X1469 @ (symdiff @ X1467 @ X1468))))&((in @ X1471 @ (setadjoin @ X1470 @ (setadjoin @ X1471 @ emptyset)))&((in @ X1472 @ (setunion @ (setadjoin @ (setadjoin @ X1472 @ emptyset) @ (setadjoin @ (setadjoin @ X1472 @ (setadjoin @ X1473 @ emptyset)) @ emptyset))))&((in @ X1475 @ (setunion @ (setadjoin @ (setadjoin @ X1474 @ emptyset) @ (setadjoin @ (setadjoin @ X1474 @ (setadjoin @ X1475 @ emptyset)) @ emptyset))))&((iskpair @ (setadjoin @ (setadjoin @ X1476 @ emptyset) @ (setadjoin @ (setadjoin @ X1476 @ (setadjoin @ X1477 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X1478 @ X1479))&((~(in @ X1481 @ X1480)|(subset @ (setadjoin @ X1481 @ emptyset) @ X1480))&((~(in @ X1483 @ X1482)|(in @ (setadjoin @ X1483 @ emptyset) @ (powerset @ X1482)))&((~(in @ X1486 @ X1484)|(in @ (setadjoin @ X1486 @ emptyset) @ (powerset @ (binunion @ X1484 @ X1485))))&((~(in @ X1489 @ (setadjoin @ X1487 @ (setadjoin @ X1488 @ emptyset)))|(((X1489)=(X1487))|((X1489)=(X1488))))&((~(in @ X1492 @ X1490)|(~(in @ X1493 @ X1491)|(subset @ (setadjoin @ X1492 @ (setadjoin @ X1493 @ emptyset)) @ (binunion @ X1490 @ X1491))))&((~(in @ X1496 @ X1494)|(~(in @ X1497 @ X1495)|(in @ (setadjoin @ X1496 @ (setadjoin @ X1497 @ emptyset)) @ (powerset @ (binunion @ X1494 @ X1495)))))&((~(in @ X1500 @ X1498)|(~(in @ X1501 @ X1499)|(subset @ (setadjoin @ (setadjoin @ X1500 @ emptyset) @ (setadjoin @ (setadjoin @ X1500 @ (setadjoin @ X1501 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1498 @ X1499)))))&((~(in @ X1504 @ X1502)|(~(in @ X1505 @ X1503)|(in @ (setadjoin @ (setadjoin @ X1504 @ emptyset) @ (setadjoin @ (setadjoin @ X1504 @ (setadjoin @ X1505 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1502 @ X1503))))))&((~(in @ X1508 @ X1506)|(~(in @ X1509 @ X1507)|(in @ (kpair @ X1508 @ X1509) @ (powerset @ (powerset @ (binunion @ X1506 @ X1507))))))&((~(in @ X1512 @ X1510)|(~(in @ X1513 @ X1511)|(in @ (kpair @ X1512 @ X1513) @ (cartprod @ X1510 @ X1511))))&((((in @ (esk39_3 @ X1514 @ X1515 @ X1516) @ X1514)|~(in @ X1516 @ (cartprod @ X1514 @ X1515)))&(((in @ (esk40_3 @ X1514 @ X1515 @ X1516) @ X1515)|~(in @ X1516 @ (cartprod @ X1514 @ X1515)))&(((X1516)=(kpair @ (esk39_3 @ X1514 @ X1515 @ X1516) @ (esk40_3 @ X1514 @ X1515 @ X1516)))|~(in @ X1516 @ (cartprod @ X1514 @ X1515)))))&((~(in @ X1521 @ (cartprod @ X1519 @ X1520))|(iskpair @ X1521))&((((in @ (esk41_2 @ X1522 @ X1523) @ X1522)|~(in @ X1523 @ (setunion @ X1522)))&((in @ X1523 @ (esk41_2 @ X1522 @ X1523))|~(in @ X1523 @ (setunion @ X1522))))&((subset @ (setunion @ (setadjoin @ X1525 @ emptyset)) @ X1525)&((subset @ X1526 @ (setunion @ (setadjoin @ X1526 @ emptyset)))&(((setunion @ (setadjoin @ X1527 @ emptyset))=(X1527))&((((in @ (esk42_2 @ X1528 @ X1529) @ X1528)|(~(in @ X1532 @ X1528)|~(X1529 @ X1532)|(singleton @ (dsetconstr @ X1528 @ (^[Z0/* 3 */:$i]:((X1529 @ Z0)))))))&(((in @ (esk43_2 @ X1528 @ X1529) @ X1528)|(~(in @ X1532 @ X1528)|~(X1529 @ X1532)|(singleton @ (dsetconstr @ X1528 @ (^[Z0/* 3 */:$i]:((X1529 @ Z0)))))))&(((X1529 @ (esk42_2 @ X1528 @ X1529))|(~(in @ X1532 @ X1528)|~(X1529 @ X1532)|(singleton @ (dsetconstr @ X1528 @ (^[Z0/* 3 */:$i]:((X1529 @ Z0)))))))&(((X1529 @ (esk43_2 @ X1528 @ X1529))|(~(in @ X1532 @ X1528)|~(X1529 @ X1532)|(singleton @ (dsetconstr @ X1528 @ (^[Z0/* 3 */:$i]:((X1529 @ Z0)))))))&(((esk42_2 @ X1528 @ X1529)!=(esk43_2 @ X1528 @ X1529))|(~(in @ X1532 @ X1528)|~(X1529 @ X1532)|(singleton @ (dsetconstr @ X1528 @ (^[Z0/* 3 */:$i]:((X1529 @ Z0)))))))))))&((((in @ (esk44_2 @ X1533 @ X1534) @ X1533)|~(ex1 @ X1533 @ (^[Z0/* 3 */:$i]:((X1534 @ Z0)))))&((X1534 @ (esk44_2 @ X1533 @ X1534))|~(ex1 @ X1533 @ (^[Z0/* 3 */:$i]:((X1534 @ Z0))))))&((((in @ (esk45_3 @ X1536 @ X1537 @ X1538) @ X1536)|(ex1 @ X1536 @ (^[Z0/* 3 */:$i]:((X1537 @ Z0))))|~(X1537 @ X1538)|~(in @ X1538 @ X1536))&(((X1537 @ (esk45_3 @ X1536 @ X1537 @ X1538))|(ex1 @ X1536 @ (^[Z0/* 3 */:$i]:((X1537 @ Z0))))|~(X1537 @ X1538)|~(in @ X1538 @ X1536))&(((esk45_3 @ X1536 @ X1537 @ X1538)!=(X1538))|(ex1 @ X1536 @ (^[Z0/* 3 */:$i]:((X1537 @ Z0))))|~(X1537 @ X1538)|~(in @ X1538 @ X1536))))&((((in @ (esk46_2 @ X1540 @ X1541) @ X1540)|(~(in @ X1544 @ X1540)|~(X1541 @ X1544)|(ex1 @ X1540 @ (^[Z0/* 3 */:$i]:((X1541 @ Z0))))))&(((in @ (esk47_2 @ X1540 @ X1541) @ X1540)|(~(in @ X1544 @ X1540)|~(X1541 @ X1544)|(ex1 @ X1540 @ (^[Z0/* 3 */:$i]:((X1541 @ Z0))))))&(((X1541 @ (esk46_2 @ X1540 @ X1541))|(~(in @ X1544 @ X1540)|~(X1541 @ X1544)|(ex1 @ X1540 @ (^[Z0/* 3 */:$i]:((X1541 @ Z0))))))&(((X1541 @ (esk47_2 @ X1540 @ X1541))|(~(in @ X1544 @ X1540)|~(X1541 @ X1544)|(ex1 @ X1540 @ (^[Z0/* 3 */:$i]:((X1541 @ Z0))))))&(((esk46_2 @ X1540 @ X1541)!=(esk47_2 @ X1540 @ X1541))|(~(in @ X1544 @ X1540)|~(X1541 @ X1544)|(ex1 @ X1540 @ (^[Z0/* 3 */:$i]:((X1541 @ Z0))))))))))&((((setadjoin @ X1545 @ emptyset)!=(setadjoin @ X1546 @ emptyset))|((X1545)=(X1546)))&((~(in @ (setadjoin @ X1549 @ emptyset) @ (setadjoin @ (setadjoin @ X1547 @ emptyset) @ (setadjoin @ (setadjoin @ X1547 @ (setadjoin @ X1548 @ emptyset)) @ emptyset)))|((X1547)=(X1549)))&((~(iskpair @ X1550)|(singleton @ (dsetconstr @ (setunion @ X1550) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1550))))))&((~(singleton @ X1551)|(in @ (setunion @ X1551) @ X1551))&(((kfst @ (kpair @ X1552 @ X1553))=(X1552))&((~(in @ X1556 @ (cartprod @ X1554 @ X1555))|(in @ (kfst @ X1556) @ X1554))&((((setadjoin @ (setadjoin @ X1557 @ emptyset) @ (setadjoin @ (setadjoin @ X1557 @ (setadjoin @ X1558 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1559 @ emptyset) @ (setadjoin @ (setadjoin @ X1559 @ (setadjoin @ X1560 @ emptyset)) @ emptyset)))|((X1557)=(X1559)))&((((kpair @ X1561 @ X1562)!=(kpair @ X1563 @ X1564))|((X1561)=(X1563)))&((((X1565)!=(X1566))|((setadjoin @ X1565 @ (setadjoin @ X1566 @ emptyset))=(setadjoin @ X1565 @ emptyset)))&((((X1567)!=(X1568))|((setadjoin @ (setadjoin @ X1567 @ emptyset) @ (setadjoin @ (setadjoin @ X1567 @ (setadjoin @ X1568 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1567 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1569 @ emptyset) @ (setadjoin @ (setadjoin @ X1569 @ (setadjoin @ X1570 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1571 @ emptyset) @ (setadjoin @ (setadjoin @ X1571 @ (setadjoin @ X1572 @ emptyset)) @ emptyset)))|(((X1571)!=(X1572))|((X1570)=(X1572))))&((((setadjoin @ X1573 @ (setadjoin @ X1574 @ emptyset))!=(setadjoin @ X1575 @ emptyset))|((X1573)=(X1574)))&((((setadjoin @ (setadjoin @ X1576 @ emptyset) @ (setadjoin @ (setadjoin @ X1576 @ (setadjoin @ X1577 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1578 @ emptyset) @ (setadjoin @ (setadjoin @ X1578 @ (setadjoin @ X1579 @ emptyset)) @ emptyset)))|((X1577)=(X1579)))&((((kpair @ X1580 @ X1581)!=(kpair @ X1582 @ X1583))|((X1581)=(X1583)))&((~(iskpair @ X1584)|(singleton @ (dsetconstr @ (setunion @ X1584) @ (^[Z0/* 3 */:$i]:(((X1584)=(kpair @ (kfst @ X1584) @ Z0)))))))&(((ksnd @ (kpair @ X1585 @ X1586))=(X1586))&((~(iskpair @ X1587)|((kpair @ (kfst @ X1587) @ (ksnd @ X1587))=(X1587)))&((~(in @ X1590 @ (cartprod @ X1588 @ X1589))|(in @ (ksnd @ X1590) @ X1589))&((~(in @ (kpair @ X1593 @ X1594) @ (cartprod @ X1591 @ X1592))|(in @ X1593 @ X1591))&((~(in @ (kpair @ X1597 @ X1598) @ (cartprod @ X1595 @ X1596))|(in @ X1598 @ X1596))&((~(in @ X1601 @ X1599)|(~(in @ X1602 @ X1600)|((kpair @ X1601 @ X1602)=(kpair @ X1601 @ X1602))))&((~(in @ X1605 @ X1603)|(~(in @ X1606 @ X1604)|((kfst @ (kpair @ X1605 @ X1606))=(X1605))))&((~(in @ X1609 @ X1607)|(~(in @ X1610 @ X1608)|((ksnd @ (kpair @ X1609 @ X1610))=(X1610))))&((~(in @ X1613 @ (cartprod @ X1611 @ X1612))|((kpair @ (kfst @ X1613) @ (ksnd @ X1613))=(X1613)))&((~(in @ X1617 @ X1614)|(~(in @ X1618 @ X1615)|(~(X1616 @ X1617 @ X1618)|(in @ (kpair @ X1617 @ X1618) @ (dpsetconstr @ X1614 @ X1615 @ (^[Z0/* 19 */:$i, Z1:$i]:((X1616 @ Z0 @ Z1))))))))&((subset @ (dpsetconstr @ X1619 @ X1620 @ (^[Z0/* 19 */:$i, Z1:$i]:((X1621 @ Z0 @ Z1)))) @ (cartprod @ X1619 @ X1620))&((breln @ X1622 @ X1623 @ (dpsetconstr @ X1622 @ X1623 @ (^[Z0/* 19 */:$i, Z1:$i]:((X1624 @ Z0 @ Z1)))))&((~(in @ X1628 @ X1625)|(~(in @ X1629 @ X1626)|(~(in @ (kpair @ X1628 @ X1629) @ (dpsetconstr @ X1625 @ X1626 @ (^[Z0/* 19 */:$i, Z1:$i]:((X1627 @ Z0 @ Z1)))))|(X1627 @ X1628 @ X1629))))&((~(in @ (kpair @ X1633 @ X1634) @ (dpsetconstr @ X1630 @ X1631 @ (^[Z0/* 19 */:$i, Z1:$i]:((X1632 @ Z0 @ Z1)))))|(in @ X1633 @ X1630))&((~(in @ (kpair @ X1638 @ X1639) @ (dpsetconstr @ X1635 @ X1636 @ (^[Z0/* 19 */:$i, Z1:$i]:((X1637 @ Z0 @ Z1)))))|(in @ X1639 @ X1636))&((~(in @ (kpair @ X1643 @ X1644) @ (dpsetconstr @ X1640 @ X1641 @ (^[Z0/* 19 */:$i, Z1:$i]:((X1642 @ Z0 @ Z1)))))|(X1642 @ X1643 @ X1644))&((~(func @ X1645 @ X1646 @ X1647)|(~(in @ X1648 @ X1645)|(singleton @ (dsetconstr @ X1646 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1648 @ Z0) @ X1647)))))))&((~(func @ X1649 @ X1650 @ X1651)|(~(in @ X1652 @ X1649)|(in @ (setunion @ (dsetconstr @ X1650 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1652 @ Z0) @ X1651))))) @ X1650)))&((~(func @ X1653 @ X1654 @ X1655)|(~(in @ X1656 @ X1653)|(in @ (ap @ X1653 @ X1654 @ X1655 @ X1656) @ X1654)))&((~(in @ X1659 @ (funcSet @ X1657 @ X1658))|(func @ X1657 @ X1658 @ X1659))&((in @ esk50_0 @ (funcSet @ esk48_0 @ esk49_0))&((in @ esk51_0 @ esk48_0)&~(in @ (ap @ esk48_0 @ esk49_0 @ esk50_0 @ esk51_0) @ esk49_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_232])])])])])])).
12.26/2.01	thf(c_0_236, plain, ![X2:$i, X3:$i, X4:$i, X5:$i]:(((ap @ X2 @ X3 @ X4 @ X5)=(setunion @ (dsetconstr @ X3 @ (epred2_2 @ X4 @ X5))))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_233]), c_0_234])).
12.26/2.01	thf(c_0_237, negated_conjecture, ~((in @ (ap @ esk48_0 @ esk49_0 @ esk50_0 @ esk51_0) @ esk49_0)), inference(split_conjunct,[status(thm)],[c_0_235])).
12.26/2.01	thf(c_0_238, plain, ![X2:$i, X3:$i, X4:$i, X5:$i]:(((ap @ X2 @ X3 @ X4 @ X5)=(ap @ emptyset @ X3 @ X4 @ X5))), inference(rw,[status(thm)],[c_0_236, c_0_236])).
12.26/2.01	thf(c_0_239, negated_conjecture, ~((in @ (ap @ emptyset @ esk49_0 @ esk50_0 @ esk51_0) @ esk49_0)), inference(rw,[status(thm)],[c_0_237, c_0_238])).
12.26/2.01	thf(c_0_240, negated_conjecture, ![X2:$i]:(~((in @ (ap @ X2 @ esk49_0 @ esk50_0 @ esk51_0) @ esk49_0))), inference(spm,[status(thm)],[c_0_239, c_0_238])).
12.26/2.01	thf(c_0_241, negated_conjecture, ![X3:$i, X5:$i, X4:$i, X2:$i]:(((in @ (ap @ X2 @ X3 @ X4 @ X5) @ X3)|~((func @ X2 @ X3 @ X4))|~((in @ X5 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_235])).
12.26/2.01	thf(c_0_242, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((func @ X3 @ X4 @ X2)|~((in @ X2 @ (funcSet @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_235])).
12.26/2.01	thf(c_0_243, negated_conjecture, (in @ esk50_0 @ (funcSet @ esk48_0 @ esk49_0)), inference(split_conjunct,[status(thm)],[c_0_235])).
12.26/2.01	thf(c_0_244, negated_conjecture, ![X2:$i]:((~((func @ X2 @ esk49_0 @ esk50_0))|~((in @ esk51_0 @ X2)))), inference(spm,[status(thm)],[c_0_240, c_0_241])).
12.26/2.01	thf(c_0_245, negated_conjecture, (func @ esk48_0 @ esk49_0 @ esk50_0), inference(spm,[status(thm)],[c_0_242, c_0_243])).
12.26/2.01	thf(c_0_246, negated_conjecture, (in @ esk51_0 @ esk48_0), inference(split_conjunct,[status(thm)],[c_0_235])).
12.26/2.01	thf(c_0_247, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244, c_0_245]), c_0_246])]), ['proof']).
12.26/2.01	# SZS output end CNFRefutation
12.26/2.01	# Parsed axioms                        : 429
12.26/2.01	# Removed by relevancy pruning/SinE    : 235
12.26/2.01	# Initial clauses                      : 294
12.26/2.01	# Removed in clause preprocessing      : 24
12.26/2.01	# Initial clauses in saturation        : 270
12.26/2.01	# Processed clauses                    : 2327
12.26/2.01	# ...of these trivial                  : 30
12.26/2.01	# ...subsumed                          : 784
12.26/2.01	# ...remaining for further processing  : 1513
12.26/2.01	# Other redundant clauses eliminated   : 142
12.26/2.01	# Clauses deleted for lack of memory   : 0
12.26/2.01	# Backward-subsumed                    : 67
12.26/2.01	# Backward-rewritten                   : 19
12.26/2.01	# Generated clauses                    : 69912
12.26/2.01	# ...of the previous two non-redundant : 68670
12.26/2.01	# ...aggressively subsumed             : 0
12.26/2.01	# Contextual simplify-reflections      : 0
12.26/2.01	# Paramodulations                      : 69741
12.26/2.01	# Factorizations                       : 6
12.26/2.01	# NegExts                              : 0
12.26/2.01	# Equation resolutions                 : 147
12.26/2.01	# Total rewrite steps                  : 2171
12.26/2.01	# Propositional unsat checks           : 0
12.26/2.01	#    Propositional check models        : 0
12.26/2.01	#    Propositional check unsatisfiable : 0
12.26/2.01	#    Propositional clauses             : 0
12.26/2.01	#    Propositional clauses after purity: 0
12.26/2.01	#    Propositional unsat core size     : 0
12.26/2.01	#    Propositional preprocessing time  : 0.000
12.26/2.01	#    Propositional encoding time       : 0.000
12.26/2.01	#    Propositional solver time         : 0.000
12.26/2.01	#    Success case prop preproc time    : 0.000
12.26/2.01	#    Success case prop encoding time   : 0.000
12.26/2.01	#    Success case prop solver time     : 0.000
12.26/2.01	# Current number of processed clauses  : 1185
12.26/2.01	#    Positive orientable unit clauses  : 89
12.26/2.01	#    Positive unorientable unit clauses: 4
12.26/2.01	#    Negative unit clauses             : 11
12.26/2.01	#    Non-unit-clauses                  : 1081
12.26/2.01	# Current number of unprocessed clauses: 66732
12.26/2.01	# ...number of literals in the above   : 227194
12.26/2.01	# Current number of archived formulas  : 0
12.26/2.01	# Current number of archived clauses   : 315
12.26/2.01	# Clause-clause subsumption calls (NU) : 122159
12.26/2.01	# Rec. Clause-clause subsumption calls : 93530
12.26/2.01	# Non-unit clause-clause subsumptions  : 499
12.26/2.01	# Unit Clause-clause subsumption calls : 2846
12.26/2.01	# Rewrite failures with RHS unbound    : 0
12.26/2.01	# BW rewrite match attempts            : 76
12.26/2.01	# BW rewrite match successes           : 23
12.26/2.01	# Condensation attempts                : 2327
12.26/2.01	# Condensation successes               : 18
12.26/2.01	# Termbank termtop insertions          : 1111691
12.26/2.01	
12.26/2.01	# -------------------------------------------------
12.26/2.01	# User time                : 1.481 s
12.26/2.01	# System time              : 0.058 s
12.26/2.01	# Total time               : 1.539 s
12.26/2.01	# Maximum resident set size: 5992 pages
12.26/2.06	
12.26/2.06	# -------------------------------------------------
12.26/2.06	# User time                : 1.493 s
12.26/2.06	# System time              : 0.059 s
12.26/2.06	# Total time               : 1.551 s
12.26/2.06	# Maximum resident set size: 2212 pages
12.26/2.06	% E---3.1 exiting
12.26/2.07	EOF