0.10/0.17	% Problem    : Vampire---4.8_21359 : TPTP v0.0.0. Released v0.0.0.
0.10/0.18	% Command    : run_E %s %d THM
0.17/0.38	% Computer : n004.cluster.edu
0.17/0.38	% Model    : x86_64 x86_64
0.17/0.38	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.17/0.38	% Memory   : 8042.1875MB
0.17/0.38	% OS       : Linux 3.10.0-693.el7.x86_64
0.17/0.38	% CPULimit   : 1440
0.17/0.38	% WCLimit    : 180
0.17/0.38	% DateTime   : Mon Jul  3 12:49:15 EDT 2023
0.17/0.38	% CPUTime    : 
0.22/0.56	Running higher-order theorem provingRunning: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359
0.22/0.56	# Version: 3.1pre001-ho
85.14/11.36	# Preprocessing class: HSLMSLSSLLLCHFA.
85.14/11.36	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
85.14/11.36	# Starting ehoh_best5 with 180s (1) cores
85.14/11.36	# Starting almost_fo_3_lam with 180s (1) cores
85.14/11.36	# Starting new_bool_5 with 180s (1) cores
85.14/11.36	# Starting pre_casc_3 with 180s (1) cores
85.14/11.36	# Starting ho_unfolding_8 with 180s (1) cores
85.14/11.36	# Starting new_ho_10_cnf2 with 180s (1) cores
85.14/11.36	# Starting new_bool_3 with 180s (1) cores
85.14/11.36	# Starting new_ho_5 with 180s (1) cores
85.14/11.36	# ehoh_best5 with pid 21537 completed with status 0
85.14/11.36	# Result found by ehoh_best5
85.14/11.36	# Preprocessing class: HSLMSLSSLLLCHFA.
85.14/11.36	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
85.14/11.36	# Starting ehoh_best5 with 180s (1) cores
85.14/11.36	# No SInE strategy applied
85.14/11.36	# Search class: HGHSM-FSLM32-MHFMMSBN
85.14/11.36	# Scheduled 10 strats onto 1 cores with 180 seconds (180 total)
85.14/11.36	# Starting ho_unfolding_8 with 33s (1) cores
85.14/11.36	# ho_unfolding_8 with pid 21550 completed with status 0
85.14/11.36	# Result found by ho_unfolding_8
85.14/11.36	# Preprocessing class: HSLMSLSSLLLCHFA.
85.14/11.36	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
85.14/11.36	# Starting ehoh_best5 with 180s (1) cores
85.14/11.36	# No SInE strategy applied
85.14/11.36	# Search class: HGHSM-FSLM32-MHFMMSBN
85.14/11.36	# Scheduled 10 strats onto 1 cores with 180 seconds (180 total)
85.14/11.36	# Starting ho_unfolding_8 with 33s (1) cores
85.14/11.36	# Preprocessing time       : 0.091 s
85.14/11.36	# Presaturation interreduction done
85.14/11.36	
85.14/11.36	# Proof found!
85.14/11.36	# SZS status Theorem
85.14/11.36	# SZS output start CNFRefutation
85.14/11.36	thf(decl_22, type, in: $i > $i > $o).
85.14/11.36	thf(decl_23, type, exu: ($i > $o) > $o).
85.14/11.36	thf(decl_24, type, setextAx: $o).
85.14/11.36	thf(decl_25, type, emptyset: $i).
85.14/11.36	thf(decl_26, type, emptysetAx: $o).
85.14/11.36	thf(decl_27, type, setadjoin: $i > $i > $i).
85.14/11.36	thf(decl_28, type, setadjoinAx: $o).
85.14/11.36	thf(decl_29, type, powerset: $i > $i).
85.14/11.36	thf(decl_30, type, powersetAx: $o).
85.14/11.36	thf(decl_31, type, setunion: $i > $i).
85.14/11.36	thf(decl_32, type, setunionAx: $o).
85.14/11.36	thf(decl_33, type, omega: $i).
85.14/11.36	thf(decl_34, type, omega0Ax: $o).
85.14/11.36	thf(decl_35, type, omegaSAx: $o).
85.14/11.36	thf(decl_36, type, omegaIndAx: $o).
85.14/11.36	thf(decl_37, type, replAx: $o).
85.14/11.36	thf(decl_38, type, foundationAx: $o).
85.14/11.36	thf(decl_39, type, wellorderingAx: $o).
85.14/11.36	thf(decl_40, type, descr: ($i > $o) > $i).
85.14/11.36	thf(decl_41, type, descrp: $o).
85.14/11.36	thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
85.14/11.36	thf(decl_43, type, dsetconstrI: $o).
85.14/11.36	thf(decl_44, type, dsetconstrEL: $o).
85.14/11.36	thf(decl_45, type, dsetconstrER: $o).
85.14/11.36	thf(decl_46, type, exuE1: $o).
85.14/11.36	thf(decl_47, type, prop2set: $o > $i).
85.14/11.36	thf(decl_48, type, prop2setE: $o).
85.14/11.36	thf(decl_49, type, emptysetE: $o).
85.14/11.36	thf(decl_50, type, emptysetimpfalse: $o).
85.14/11.36	thf(decl_51, type, notinemptyset: $o).
85.14/11.36	thf(decl_52, type, exuE3e: $o).
85.14/11.36	thf(decl_53, type, setext: $o).
85.14/11.36	thf(decl_54, type, emptyI: $o).
85.14/11.36	thf(decl_55, type, noeltsimpempty: $o).
85.14/11.36	thf(decl_56, type, setbeta: $o).
85.14/11.36	thf(decl_57, type, nonempty: $i > $o).
85.14/11.36	thf(decl_58, type, nonemptyE1: $o).
85.14/11.36	thf(decl_59, type, nonemptyI: $o).
85.14/11.36	thf(decl_60, type, nonemptyI1: $o).
85.14/11.36	thf(decl_61, type, setadjoinIL: $o).
85.14/11.36	thf(decl_62, type, emptyinunitempty: $o).
85.14/11.36	thf(decl_63, type, setadjoinIR: $o).
85.14/11.36	thf(decl_64, type, setadjoinE: $o).
85.14/11.36	thf(decl_65, type, setadjoinOr: $o).
85.14/11.36	thf(decl_66, type, setoftrueEq: $o).
85.14/11.36	thf(decl_67, type, powersetI: $o).
85.14/11.36	thf(decl_68, type, emptyinPowerset: $o).
85.14/11.36	thf(decl_69, type, emptyInPowerset: $o).
85.14/11.36	thf(decl_70, type, powersetE: $o).
85.14/11.36	thf(decl_71, type, setunionI: $o).
85.14/11.36	thf(decl_72, type, setunionE: $o).
85.14/11.36	thf(decl_73, type, subPowSU: $o).
85.14/11.36	thf(decl_74, type, exuE2: $o).
85.14/11.36	thf(decl_75, type, nonemptyImpWitness: $o).
85.14/11.36	thf(decl_76, type, uniqinunit: $o).
85.14/11.36	thf(decl_77, type, notinsingleton: $o).
85.14/11.36	thf(decl_78, type, eqinunit: $o).
85.14/11.36	thf(decl_79, type, singletonsswitch: $o).
85.14/11.36	thf(decl_80, type, upairsetE: $o).
85.14/11.36	thf(decl_81, type, upairsetIL: $o).
85.14/11.36	thf(decl_82, type, upairsetIR: $o).
85.14/11.36	thf(decl_83, type, emptyE1: $o).
85.14/11.36	thf(decl_84, type, vacuousDall: $o).
85.14/11.36	thf(decl_85, type, quantDeMorgan1: $o).
85.14/11.36	thf(decl_86, type, quantDeMorgan2: $o).
85.14/11.36	thf(decl_87, type, quantDeMorgan3: $o).
85.14/11.36	thf(decl_88, type, quantDeMorgan4: $o).
85.14/11.36	thf(decl_89, type, prop2setI: $o).
85.14/11.36	thf(decl_90, type, set2prop: $i > $o).
85.14/11.36	thf(decl_91, type, prop2set2propI: $o).
85.14/11.36	thf(decl_92, type, notdexE: $o).
85.14/11.36	thf(decl_93, type, notdallE: $o).
85.14/11.36	thf(decl_94, type, exuI1: $o).
85.14/11.36	thf(decl_95, type, exuI3: $o).
85.14/11.36	thf(decl_96, type, exuI2: $o).
85.14/11.36	thf(decl_97, type, inCongP: $o).
85.14/11.36	thf(decl_98, type, in__Cong: $o).
85.14/11.36	thf(decl_99, type, exuE3u: $o).
85.14/11.36	thf(decl_100, type, exu__Cong: $o).
85.14/11.36	thf(decl_101, type, emptyset__Cong: $o).
85.14/11.36	thf(decl_102, type, setadjoin__Cong: $o).
85.14/11.36	thf(decl_103, type, powerset__Cong: $o).
85.14/11.36	thf(decl_104, type, setunion__Cong: $o).
85.14/11.36	thf(decl_105, type, omega__Cong: $o).
85.14/11.36	thf(decl_106, type, exuEu: $o).
85.14/11.36	thf(decl_107, type, descr__Cong: $o).
85.14/11.36	thf(decl_108, type, dsetconstr__Cong: $o).
85.14/11.36	thf(decl_109, type, subset: $i > $i > $o).
85.14/11.36	thf(decl_112, type, subsetI1: $o).
85.14/11.36	thf(decl_113, type, eqimpsubset2: $o).
85.14/11.36	thf(decl_114, type, eqimpsubset1: $o).
85.14/11.36	thf(decl_115, type, subsetI2: $o).
85.14/11.36	thf(decl_116, type, emptysetsubset: $o).
85.14/11.36	thf(decl_117, type, subsetE: $o).
85.14/11.36	thf(decl_118, type, subsetE2: $o).
85.14/11.36	thf(decl_119, type, notsubsetI: $o).
85.14/11.36	thf(decl_120, type, notequalI1: $o).
85.14/11.36	thf(decl_121, type, notequalI2: $o).
85.14/11.36	thf(decl_122, type, subsetRefl: $o).
85.14/11.36	thf(decl_123, type, subsetTrans: $o).
85.14/11.36	thf(decl_124, type, setadjoinSub: $o).
85.14/11.36	thf(decl_125, type, setadjoinSub2: $o).
85.14/11.36	thf(decl_126, type, subset2powerset: $o).
85.14/11.36	thf(decl_127, type, setextsub: $o).
85.14/11.36	thf(decl_128, type, subsetemptysetimpeq: $o).
85.14/11.36	thf(decl_129, type, powersetI1: $o).
85.14/11.36	thf(decl_130, type, powersetE1: $o).
85.14/11.36	thf(decl_131, type, inPowerset: $o).
85.14/11.36	thf(decl_132, type, powersetsubset: $o).
85.14/11.36	thf(decl_133, type, sepInPowerset: $o).
85.14/11.36	thf(decl_134, type, sepSubset: $o).
85.14/11.36	thf(decl_135, type, binunion: $i > $i > $i).
85.14/11.36	thf(decl_136, type, binunionIL: $o).
85.14/11.36	thf(decl_137, type, upairset2IR: $o).
85.14/11.36	thf(decl_138, type, binunionIR: $o).
85.14/11.36	thf(decl_139, type, binunionEcases: $o).
85.14/11.36	thf(decl_140, type, binunionE: $o).
85.14/11.36	thf(decl_141, type, binunionLsub: $o).
85.14/11.36	thf(decl_142, type, binunionRsub: $o).
85.14/11.36	thf(decl_143, type, binintersect: $i > $i > $i).
85.14/11.36	thf(decl_144, type, binintersectI: $o).
85.14/11.36	thf(decl_145, type, binintersectSubset5: $o).
85.14/11.36	thf(decl_146, type, binintersectEL: $o).
85.14/11.36	thf(decl_147, type, binintersectLsub: $o).
85.14/11.36	thf(decl_148, type, binintersectSubset2: $o).
85.14/11.36	thf(decl_149, type, binintersectSubset3: $o).
85.14/11.36	thf(decl_150, type, binintersectER: $o).
85.14/11.36	thf(decl_151, type, disjointsetsI1: $o).
85.14/11.36	thf(decl_152, type, binintersectRsub: $o).
85.14/11.36	thf(decl_153, type, binintersectSubset4: $o).
85.14/11.36	thf(decl_154, type, binintersectSubset1: $o).
85.14/11.36	thf(decl_155, type, bs114d: $o).
85.14/11.36	thf(decl_157, type, setminus: $i > $i > $i).
85.14/11.36	thf(decl_158, type, setminusI: $o).
85.14/11.36	thf(decl_159, type, setminusEL: $o).
85.14/11.36	thf(decl_160, type, setminusER: $o).
85.14/11.36	thf(decl_161, type, setminusSubset2: $o).
85.14/11.36	thf(decl_162, type, setminusERneg: $o).
85.14/11.36	thf(decl_163, type, setminusELneg: $o).
85.14/11.36	thf(decl_164, type, setminusILneg: $o).
85.14/11.36	thf(decl_165, type, setminusIRneg: $o).
85.14/11.36	thf(decl_166, type, setminusLsub: $o).
85.14/11.36	thf(decl_167, type, setminusSubset1: $o).
85.14/11.36	thf(decl_168, type, symdiff: $i > $i > $i).
85.14/11.36	thf(decl_169, type, symdiffE: $o).
85.14/11.36	thf(decl_170, type, symdiffI1: $o).
85.14/11.36	thf(decl_171, type, symdiffI2: $o).
85.14/11.36	thf(decl_172, type, symdiffIneg1: $o).
85.14/11.36	thf(decl_173, type, symdiffIneg2: $o).
85.14/11.36	thf(decl_174, type, iskpair: $i > $o).
85.14/11.36	thf(decl_175, type, secondinupair: $o).
85.14/11.36	thf(decl_176, type, setukpairIL: $o).
85.14/11.36	thf(decl_177, type, setukpairIR: $o).
85.14/11.36	thf(decl_178, type, kpairiskpair: $o).
85.14/11.36	thf(decl_179, type, kpair: $i > $i > $i).
85.14/11.36	thf(decl_180, type, kpairp: $o).
85.14/11.36	thf(decl_181, type, cartprod: $i > $i > $i).
85.14/11.36	thf(decl_182, type, singletonsubset: $o).
85.14/11.36	thf(decl_183, type, singletoninpowerset: $o).
85.14/11.36	thf(decl_184, type, singletoninpowunion: $o).
85.14/11.36	thf(decl_185, type, upairset2E: $o).
85.14/11.36	thf(decl_186, type, upairsubunion: $o).
85.14/11.36	thf(decl_187, type, upairinpowunion: $o).
85.14/11.36	thf(decl_188, type, ubforcartprodlem1: $o).
85.14/11.36	thf(decl_189, type, ubforcartprodlem2: $o).
85.14/11.36	thf(decl_190, type, ubforcartprodlem3: $o).
85.14/11.36	thf(decl_191, type, cartprodpairin: $o).
85.14/11.36	thf(decl_192, type, cartprodmempair1: $o).
85.14/11.36	thf(decl_193, type, cartprodmempair: $o).
85.14/11.36	thf(decl_194, type, setunionE2: $o).
85.14/11.36	thf(decl_195, type, setunionsingleton1: $o).
85.14/11.36	thf(decl_196, type, setunionsingleton2: $o).
85.14/11.36	thf(decl_197, type, setunionsingleton: $o).
85.14/11.36	thf(decl_198, type, singleton: $i > $o).
85.14/11.36	thf(decl_199, type, singletonprop: $o).
85.14/11.36	thf(decl_200, type, ex1: $i > ($i > $o) > $o).
85.14/11.36	thf(decl_201, type, ex1E1: $o).
85.14/11.36	thf(decl_202, type, ex1I: $o).
85.14/11.36	thf(decl_203, type, ex1I2: $o).
85.14/11.36	thf(decl_204, type, singletonsuniq: $o).
85.14/11.36	thf(decl_209, type, setukpairinjL1: $o).
85.14/11.36	thf(decl_210, type, kfstsingleton: $o).
85.14/11.36	thf(decl_211, type, theprop: $o).
85.14/11.36	thf(decl_212, type, kfst: $i > $i).
85.14/11.36	thf(decl_213, type, kfstpairEq: $o).
85.14/11.36	thf(decl_214, type, cartprodfstin: $o).
85.14/11.36	thf(decl_215, type, setukpairinjL2: $o).
85.14/11.36	thf(decl_216, type, setukpairinjL: $o).
85.14/11.36	thf(decl_217, type, setukpairinjR11: $o).
85.14/11.36	thf(decl_218, type, setukpairinjR12: $o).
85.14/11.36	thf(decl_219, type, setukpairinjR1: $o).
85.14/11.36	thf(decl_220, type, upairequniteq: $o).
85.14/11.36	thf(decl_221, type, setukpairinjR2: $o).
85.14/11.36	thf(decl_222, type, setukpairinjR: $o).
85.14/11.36	thf(decl_223, type, ksndsingleton: $o).
85.14/11.36	thf(decl_224, type, ksnd: $i > $i).
85.14/11.36	thf(decl_225, type, ksndpairEq: $o).
85.14/11.36	thf(decl_226, type, kpairsurjEq: $o).
85.14/11.36	thf(decl_227, type, cartprodsndin: $o).
85.14/11.36	thf(decl_228, type, cartprodpairmemEL: $o).
85.14/11.36	thf(decl_229, type, cartprodpairmemER: $o).
85.14/11.36	thf(decl_230, type, cartprodmempaircEq: $o).
85.14/11.36	thf(decl_231, type, cartprodfstpairEq: $o).
85.14/11.36	thf(decl_232, type, cartprodsndpairEq: $o).
85.14/11.36	thf(decl_233, type, cartprodpairsurjEq: $o).
85.14/11.36	thf(decl_234, type, breln: $i > $i > $i > $o).
85.14/11.36	thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
85.14/11.36	thf(decl_236, type, dpsetconstrI: $o).
85.14/11.36	thf(decl_237, type, dpsetconstrSub: $o).
85.14/11.36	thf(decl_238, type, setOfPairsIsBReln: $o).
85.14/11.36	thf(decl_239, type, dpsetconstrERa: $o).
85.14/11.36	thf(decl_240, type, dpsetconstrEL1: $o).
85.14/11.36	thf(decl_241, type, dpsetconstrEL2: $o).
85.14/11.36	thf(decl_242, type, dpsetconstrER: $o).
85.14/11.36	thf(decl_243, type, func: $i > $i > $i > $o).
85.14/11.36	thf(decl_244, type, funcSet: $i > $i > $i).
85.14/11.36	thf(decl_245, type, funcImageSingleton: $o).
85.14/11.36	thf(decl_246, type, apProp: $o).
85.14/11.36	thf(decl_247, type, ap: $i > $i > $i > $i > $i).
85.14/11.36	thf(decl_248, type, app: $o).
85.14/11.36	thf(decl_249, type, infuncsetfunc: $o).
85.14/11.36	thf(decl_250, type, ap2p: $o).
85.14/11.36	thf(decl_251, type, funcinfuncset: $o).
85.14/11.36	thf(decl_252, type, lamProp: $o).
85.14/11.36	thf(decl_253, type, lam: $i > $i > ($i > $i) > $i).
85.14/11.36	thf(decl_254, type, lamp: $o).
85.14/11.36	thf(decl_255, type, lam2p: $o).
85.14/11.36	thf(decl_256, type, brelnall1: $o).
85.14/11.36	thf(decl_257, type, brelnall2: $o).
85.14/11.36	thf(decl_258, type, ex1E2: $o).
85.14/11.36	thf(decl_259, type, funcGraphProp1: $o).
85.14/11.36	thf(decl_260, type, funcGraphProp3: $o).
85.14/11.36	thf(decl_261, type, funcGraphProp2: $o).
85.14/11.36	thf(decl_262, type, funcextLem: $o).
85.14/11.36	thf(decl_263, type, funcGraphProp4: $o).
85.14/11.36	thf(decl_264, type, subbreln: $o).
85.14/11.36	thf(decl_265, type, eqbreln: $o).
85.14/11.36	thf(decl_266, type, funcext: $o).
85.14/11.36	thf(decl_267, type, funcext2: $o).
85.14/11.36	thf(decl_268, type, ap2apEq1: $o).
85.14/11.36	thf(decl_269, type, ap2apEq2: $o).
85.14/11.36	thf(decl_270, type, beta1: $o).
85.14/11.36	thf(decl_271, type, eta1: $o).
85.14/11.36	thf(decl_272, type, lam2lamEq: $o).
85.14/11.36	thf(decl_273, type, beta2: $o).
85.14/11.36	thf(decl_274, type, eta2: $o).
85.14/11.36	thf(decl_275, type, iffalseProp1: $o).
85.14/11.36	thf(decl_276, type, iffalseProp2: $o).
85.14/11.36	thf(decl_277, type, iftrueProp1: $o).
85.14/11.36	thf(decl_278, type, iftrueProp2: $o).
85.14/11.36	thf(decl_279, type, ifSingleton: $o).
85.14/11.36	thf(decl_280, type, if: $i > $o > $i > $i > $i).
85.14/11.36	thf(decl_281, type, ifp: $o).
85.14/11.36	thf(decl_282, type, theeq: $o).
85.14/11.36	thf(decl_283, type, iftrue: $o).
85.14/11.36	thf(decl_284, type, iffalse: $o).
85.14/11.36	thf(decl_285, type, iftrueorfalse: $o).
85.14/11.36	thf(decl_286, type, binintersectT_lem: $o).
85.14/11.36	thf(decl_287, type, binunionT_lem: $o).
85.14/11.36	thf(decl_288, type, powersetT_lem: $o).
85.14/11.36	thf(decl_289, type, setminusT_lem: $o).
85.14/11.36	thf(decl_290, type, complementT_lem: $o).
85.14/11.36	thf(decl_291, type, setextT: $o).
85.14/11.36	thf(decl_292, type, subsetTI: $o).
85.14/11.36	thf(decl_293, type, powersetTI1: $o).
85.14/11.36	thf(decl_294, type, powersetTE1: $o).
85.14/11.36	thf(decl_295, type, complementTI1: $o).
85.14/11.36	thf(decl_296, type, complementTE1: $o).
85.14/11.36	thf(decl_297, type, binintersectTELcontra: $o).
85.14/11.36	thf(decl_298, type, binintersectTERcontra: $o).
85.14/11.36	thf(decl_299, type, contrasubsetT: $o).
85.14/11.36	thf(decl_300, type, contrasubsetT1: $o).
85.14/11.36	thf(decl_301, type, contrasubsetT2: $o).
85.14/11.36	thf(decl_302, type, contrasubsetT3: $o).
85.14/11.36	thf(decl_303, type, doubleComplementI1: $o).
85.14/11.36	thf(decl_304, type, doubleComplementE1: $o).
85.14/11.36	thf(decl_305, type, doubleComplementSub1: $o).
85.14/11.36	thf(decl_306, type, doubleComplementSub2: $o).
85.14/11.36	thf(decl_307, type, doubleComplementEq: $o).
85.14/11.36	thf(decl_308, type, complementTnotintersectT: $o).
85.14/11.36	thf(decl_309, type, complementImpComplementIntersect: $o).
85.14/11.36	thf(decl_310, type, complementSubsetComplementIntersect: $o).
85.14/11.36	thf(decl_311, type, complementInPowersetComplementIntersect: $o).
85.14/11.36	thf(decl_312, type, contraSubsetComplement: $o).
85.14/11.36	thf(decl_313, type, complementTcontraSubset: $o).
85.14/11.36	thf(decl_314, type, binunionTILcontra: $o).
85.14/11.36	thf(decl_315, type, binunionTIRcontra: $o).
85.14/11.36	thf(decl_316, type, inIntersectImpInUnion: $o).
85.14/11.36	thf(decl_317, type, inIntersectImpInUnion2: $o).
85.14/11.36	thf(decl_318, type, inIntersectImpInIntersectUnions: $o).
85.14/11.36	thf(decl_319, type, intersectInPowersetIntersectUnions: $o).
85.14/11.36	thf(decl_320, type, inComplementUnionImpNotIn1: $o).
85.14/11.36	thf(decl_321, type, inComplementUnionImpInComplement1: $o).
85.14/11.36	thf(decl_322, type, binunionTE: $o).
85.14/11.36	thf(decl_323, type, binunionTEcontra: $o).
85.14/11.36	thf(decl_324, type, demorgan2a1: $o).
85.14/11.36	thf(decl_325, type, complementUnionInPowersetComplement: $o).
85.14/11.36	thf(decl_326, type, demorgan2a2: $o).
85.14/11.36	thf(decl_327, type, demorgan1a: $o).
85.14/11.36	thf(decl_328, type, demorgan1b: $o).
85.14/11.36	thf(decl_329, type, demorgan1: $o).
85.14/11.36	thf(decl_330, type, demorgan2a: $o).
85.14/11.36	thf(decl_331, type, demorgan2b2: $o).
85.14/11.36	thf(decl_332, type, demorgan2b: $o).
85.14/11.36	thf(decl_333, type, demorgan2: $o).
85.14/11.36	thf(decl_334, type, woz13rule0: $o).
85.14/11.36	thf(decl_335, type, woz13rule1: $o).
85.14/11.36	thf(decl_336, type, woz13rule2: $o).
85.14/11.36	thf(decl_337, type, woz13rule3: $o).
85.14/11.36	thf(decl_338, type, woz13rule4: $o).
85.14/11.36	thf(decl_339, type, woz1_1: $o).
85.14/11.36	thf(decl_340, type, woz1_2: $o).
85.14/11.36	thf(decl_341, type, woz1_3: $o).
85.14/11.36	thf(decl_342, type, woz1_4: $o).
85.14/11.36	thf(decl_343, type, woz1_5: $o).
85.14/11.36	thf(decl_344, type, breln1: $i > $i > $o).
85.14/11.36	thf(decl_345, type, breln1all2: $o).
85.14/11.36	thf(decl_346, type, breln1Set: $i > $i).
85.14/11.36	thf(decl_347, type, breln1SetBreln1: $o).
85.14/11.36	thf(decl_353, type, reflwellordering: $i > $i > $o).
85.14/11.36	thf(decl_354, type, choice2fnsingleton: $o).
85.14/11.36	thf(decl_355, type, setOfPairsIsBReln1: $o).
85.14/11.36	thf(decl_356, type, breln1all1: $o).
85.14/11.36	thf(decl_357, type, subbreln1: $o).
85.14/11.36	thf(decl_358, type, eqbreln1: $o).
85.14/11.36	thf(decl_359, type, breln1invset: $i > $i > $i).
85.14/11.36	thf(decl_360, type, breln1invprop: $o).
85.14/11.36	thf(decl_361, type, breln1invI: $o).
85.14/11.36	thf(decl_362, type, breln1invE: $o).
85.14/11.36	thf(decl_363, type, breln1compset: $i > $i > $i > $i).
85.14/11.36	thf(decl_364, type, breln1compprop: $o).
85.14/11.36	thf(decl_365, type, breln1compI: $o).
85.14/11.36	thf(decl_366, type, breln1compE: $o).
85.14/11.36	thf(decl_367, type, breln1compEex: $o).
85.14/11.36	thf(decl_368, type, epred1_0: $o).
85.14/11.36	thf(decl_369, type, esk1_2: $i > $i > $i).
85.14/11.36	thf(decl_370, type, esk2_2: $i > $i > $i).
85.14/11.36	thf(decl_371, type, esk3_2: $i > $i > $i).
85.14/11.36	thf(decl_372, type, esk4_1: $i > $i).
85.14/11.36	thf(decl_373, type, esk5_2: ($i > $i > $o) > $i > $i).
85.14/11.36	thf(decl_374, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
85.14/11.36	thf(decl_375, type, esk7_2: ($i > $i > $o) > $i > $i).
85.14/11.36	thf(decl_376, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
85.14/11.36	thf(decl_377, type, esk9_1: $i > $i).
85.14/11.36	thf(decl_378, type, esk10_2: ($i > $o) > $i > $i).
85.14/11.36	thf(decl_379, type, esk11_2: ($i > $o) > $i > $i).
85.14/11.36	thf(decl_380, type, esk12_1: ($i > $o) > $i).
85.14/11.36	thf(decl_381, type, esk13_2: ($i > $o) > $i > $i).
85.14/11.36	thf(decl_382, type, esk14_1: ($i > $o) > $i).
85.14/11.36	thf(decl_383, type, esk15_2: $i > $i > $i).
85.14/11.36	thf(decl_384, type, esk16_2: $i > $i > $i).
85.14/11.36	thf(decl_385, type, esk17_1: $i > $i).
85.14/11.36	thf(decl_386, type, esk18_1: $i > $i).
85.14/11.36	thf(decl_387, type, esk19_1: $i > $i).
85.14/11.36	thf(decl_388, type, esk20_2: $i > $i > $i).
85.14/11.36	thf(decl_389, type, esk21_3: $i > $i > $o > $i).
85.14/11.36	thf(decl_390, type, esk22_2: ($i > $o) > $i > $i).
85.14/11.36	thf(decl_391, type, esk23_1: ($i > $o) > $i).
85.14/11.36	thf(decl_392, type, esk24_1: $i > $i).
85.14/11.36	thf(decl_393, type, esk25_2: $i > ($i > $o) > $i).
85.14/11.36	thf(decl_394, type, esk26_2: $i > ($i > $o) > $i).
85.14/11.36	thf(decl_395, type, esk27_2: $i > ($i > $o) > $i).
85.14/11.36	thf(decl_396, type, esk28_2: $i > ($i > $o) > $i).
85.14/11.36	thf(decl_397, type, esk29_2: $i > ($i > $o) > $i).
85.14/11.36	thf(decl_398, type, esk30_2: $i > ($i > $o) > $i).
85.14/11.36	thf(decl_399, type, esk31_2: ($i > $o) > $i > $i).
85.14/11.36	thf(decl_400, type, esk32_1: ($i > $o) > $i).
85.14/11.36	thf(decl_401, type, esk33_1: ($i > $o) > $i).
85.14/11.36	thf(decl_402, type, esk34_1: ($i > $o) > $i).
85.14/11.36	thf(decl_403, type, esk35_1: ($i > $o) > $i).
85.14/11.36	thf(decl_404, type, esk36_2: ($i > $o) > $i > $i).
85.14/11.36	thf(decl_405, type, esk37_1: ($i > $o) > $i).
85.14/11.36	thf(decl_406, type, esk38_2: ($i > $o) > $i > $i).
85.14/11.36	thf(decl_407, type, esk39_2: ($i > $o) > ($i > $o) > $i).
85.14/11.36	thf(decl_408, type, esk40_2: ($i > $o) > ($i > $o) > $i).
85.14/11.36	thf(decl_409, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
85.14/11.36	thf(decl_410, type, esk42_2: ($i > $o) > ($i > $o) > $i).
85.14/11.36	thf(decl_411, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
85.14/11.36	thf(decl_412, type, esk44_2: ($i > $o) > ($i > $o) > $i).
85.14/11.36	thf(decl_413, type, esk45_2: ($i > $o) > $i > $i).
85.14/11.36	thf(decl_414, type, esk46_2: ($i > $o) > ($i > $o) > $i).
85.14/11.36	thf(decl_415, type, esk47_2: ($i > $o) > ($i > $o) > $i).
85.14/11.36	thf(decl_416, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
85.14/11.36	thf(decl_417, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
85.14/11.36	thf(decl_418, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
85.14/11.36	thf(decl_419, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
85.14/11.36	thf(decl_420, type, esk52_2: $i > $i > $i).
85.14/11.36	thf(decl_421, type, esk53_2: $i > $i > $i).
85.14/11.36	thf(decl_422, type, esk54_2: $i > $i > $i).
85.14/11.36	thf(decl_423, type, esk55_3: $i > $i > $i > $i).
85.14/11.36	thf(decl_424, type, esk56_3: $i > $i > $i > $i).
85.14/11.36	thf(decl_425, type, esk57_2: $i > $i > $i).
85.14/11.36	thf(decl_426, type, esk58_2: $i > ($i > $o) > $i).
85.14/11.36	thf(decl_427, type, esk59_2: $i > ($i > $o) > $i).
85.14/11.36	thf(decl_428, type, esk60_2: $i > ($i > $o) > $i).
85.14/11.36	thf(decl_429, type, esk61_3: $i > ($i > $o) > $i > $i).
85.14/11.36	thf(decl_430, type, esk62_2: $i > ($i > $o) > $i).
85.14/11.36	thf(decl_431, type, esk63_2: $i > ($i > $o) > $i).
85.14/11.36	thf(decl_432, type, esk64_3: $i > $i > ($i > $i) > $i).
85.14/11.36	thf(decl_433, type, esk65_3: $i > $i > ($i > $i) > $i).
85.14/11.36	thf(decl_434, type, esk66_3: $i > $i > ($i > $i) > $i).
85.14/11.36	thf(decl_435, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
85.14/11.36	thf(decl_436, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
85.14/11.36	thf(decl_437, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
85.14/11.36	thf(decl_438, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
85.14/11.36	thf(decl_439, type, esk71_4: $i > $i > $i > $i > $i).
85.14/11.36	thf(decl_440, type, esk72_4: $i > $i > $i > $i > $i).
85.14/11.36	thf(decl_441, type, esk73_4: $i > $i > $i > $i > $i).
85.14/11.36	thf(decl_442, type, esk74_4: $i > $i > $i > $i > $i).
85.14/11.36	thf(decl_443, type, esk75_4: $i > $i > $i > $i > $i).
85.14/11.36	thf(decl_444, type, esk76_4: $i > $i > $i > $i > $i).
85.14/11.36	thf(decl_445, type, esk77_4: $i > $i > $i > $i > $i).
85.14/11.36	thf(decl_446, type, esk78_4: $i > $i > $i > $i > $i).
85.14/11.36	thf(decl_447, type, esk79_4: $i > $i > $i > $i > $i).
85.14/11.36	thf(decl_448, type, esk80_3: $i > $i > ($i > $i) > $i).
85.14/11.36	thf(decl_449, type, esk81_3: $i > $i > ($i > $i) > $i).
85.14/11.36	thf(decl_450, type, esk82_3: $i > $i > ($i > $i) > $i).
85.14/11.36	thf(decl_451, type, esk83_3: $i > $i > $i > $i).
85.14/11.36	thf(decl_452, type, esk84_3: $i > $i > $i > $i).
85.14/11.36	thf(decl_453, type, esk85_3: $i > $i > $i > $i).
85.14/11.36	thf(decl_454, type, esk86_3: $i > $i > $i > $i).
85.14/11.36	thf(decl_455, type, esk87_3: $i > $i > ($i > $o) > $i).
85.14/11.36	thf(decl_456, type, esk88_3: $i > $i > ($i > $o) > $i).
85.14/11.36	thf(decl_457, type, esk89_3: $i > $i > ($i > $i > $o) > $i).
85.14/11.36	thf(decl_458, type, esk90_3: $i > $i > ($i > $o) > $i).
85.14/11.36	thf(decl_459, type, esk91_3: $i > $i > ($i > $o) > $i).
85.14/11.36	thf(decl_460, type, esk92_3: $i > $i > $i > $i).
85.14/11.36	thf(decl_461, type, esk93_3: $i > $i > $i > $i).
85.14/11.36	thf(decl_462, type, esk94_3: $i > $i > $i > $i).
85.14/11.36	thf(decl_463, type, esk95_3: $i > $i > $i > $i).
85.14/11.36	thf(decl_464, type, esk96_3: $i > $i > $i > $i).
85.14/11.36	thf(decl_465, type, esk97_3: $i > $i > $i > $i).
85.14/11.36	thf(decl_466, type, esk98_5: $i > $i > $i > $i > $i > $i).
85.14/11.36	thf(decl_467, type, esk99_6: $i > $i > $i > $i > $i > $o > $i).
85.14/11.36	thf(decl_468, type, esk100_0: $i).
85.14/11.36	thf(decl_469, type, esk101_0: $i).
85.14/11.36	thf(decl_470, type, esk102_0: $i).
85.14/11.36	thf(breln1, axiom, ((breln1)=(^[X4:$i, X33:$i]:((breln @ X4 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', breln1)).
85.14/11.36	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', breln)).
85.14/11.36	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', replAx)).
85.14/11.36	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', exu)).
85.14/11.36	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', descrp)).
85.14/11.36	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', exuE1)).
85.14/11.36	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', exuE3e)).
85.14/11.36	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', nonempty)).
85.14/11.36	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', nonemptyI)).
85.14/11.36	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', exuE2)).
85.14/11.36	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', exuI1)).
85.14/11.36	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', exuI3)).
85.14/11.36	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', exuI2)).
85.14/11.36	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', exuE3u)).
85.14/11.36	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', exu__Cong)).
85.14/11.36	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', exuEu)).
85.14/11.36	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', descr__Cong)).
85.14/11.36	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setOfPairsIsBReln)).
85.14/11.36	thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setOfPairsIsBReln1)).
85.14/11.36	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', dsetconstrI)).
85.14/11.36	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', dsetconstrEL)).
85.14/11.36	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', dsetconstrER)).
85.14/11.36	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setbeta)).
85.14/11.36	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', nonemptyE1)).
85.14/11.36	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', nonemptyI1)).
85.14/11.36	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setoftrueEq)).
85.14/11.36	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', nonemptyImpWitness)).
85.14/11.36	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', emptyE1)).
85.14/11.36	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', dsetconstr__Cong)).
85.14/11.36	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', sepInPowerset)).
85.14/11.36	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', sepSubset)).
85.14/11.36	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', singletonprop)).
85.14/11.36	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', ex1E1)).
85.14/11.36	thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', ex1I)).
85.14/11.36	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', ex1I2)).
85.14/11.36	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', kfstsingleton)).
85.14/11.36	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', ksndsingleton)).
85.14/11.36	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', dpsetconstrI)).
85.14/11.36	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', dpsetconstrSub)).
85.14/11.36	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', dpsetconstrERa)).
85.14/11.36	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', dpsetconstrEL1)).
85.14/11.36	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', dpsetconstrEL2)).
85.14/11.36	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', dpsetconstrER)).
85.14/11.36	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', funcImageSingleton)).
85.14/11.36	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', apProp)).
85.14/11.36	thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', lamProp)).
85.14/11.36	thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', lamp)).
85.14/11.36	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', lam2p)).
85.14/11.36	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', brelnall1)).
85.14/11.36	thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', brelnall2)).
85.14/11.36	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', ex1E2)).
85.14/11.36	thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', subbreln)).
85.14/11.36	thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', eqbreln)).
85.14/11.36	thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', beta1)).
85.14/11.36	thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', eta1)).
85.14/11.36	thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', lam2lamEq)).
85.14/11.36	thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', beta2)).
85.14/11.36	thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', eta2)).
85.14/11.36	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', iffalseProp1)).
85.14/11.36	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', iffalseProp2)).
85.14/11.36	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', iftrueProp1)).
85.14/11.36	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', iftrueProp2)).
85.14/11.36	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', ifSingleton)).
85.14/11.36	thf(breln1all2, axiom, ((breln1all2)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', breln1all2)).
85.14/11.36	thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', breln1SetBreln1)).
85.14/11.36	thf(choice2fnsingleton, axiom, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:(((X52 @ X2 @ X3)&![X14:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ X3 @ X14) @ X33))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', choice2fnsingleton)).
85.14/11.36	thf(breln1all1, axiom, ((breln1all1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', breln1all1)).
85.14/11.36	thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', subbreln1)).
85.14/11.36	thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', eqbreln1)).
85.14/11.36	thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', breln1invprop)).
85.14/11.36	thf(breln1invI, axiom, ((breln1invI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', breln1invI)).
85.14/11.36	thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', breln1invE)).
85.14/11.36	thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', breln1compprop)).
85.14/11.36	thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', breln1compI)).
85.14/11.36	thf(breln1compE, axiom, ((breln1compE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35))))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', breln1compE)).
85.14/11.36	thf(breln1compEex, axiom, ((breln1compEex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>![X54:$o]:((![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(X54)))))=>(X54))))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', breln1compEex)).
85.14/11.36	thf(breln1unionprop, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>(((((replAx)=>(((wellorderingAx)=>((descrp)=>(((dsetconstrEL)=>((dsetconstrER)=>(((prop2setE)=>(((emptysetimpfalse)=>((((((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>(((setadjoinIR)=>((setadjoinE)=>((((((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>(((((((((((((quantDeMorgan3)=>(((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((((inCongP)=>(((exuE3u)=>(((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>(((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>(((subsetE2)=>((notsubsetI)=>((notequalI1)=>(((subsetRefl)=>(((setadjoinSub)=>((setadjoinSub2)=>((((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>(((powersetsubset)=>((sepInPowerset)=>(((binunionIL)=>((upairset2IR)=>((((binunionE)=>(((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>(((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>(((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((((setminusI)=>(((setminusER)=>(((setminusERneg)=>((((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>(((symdiffIneg1)=>((symdiffIneg2)=>((((((kpairp)=>((singletonsubset)=>(((((((((ubforcartprodlem3)=>((cartprodpairin)=>((((setunionE2)=>((((setunionsingleton)=>((((ex1I)=>((ex1I2)=>(((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>(((setukpairinjL2)=>((((((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>(((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>(((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>(((((infuncsetfunc)=>(((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((((ex1E2)=>((((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((((ap2apEq2)=>(((((((((((ifSingleton)=>((((iftrue)=>(((((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>(((subsetTI)=>(((powersetTE1)=>((complementTI1)=>((((binintersectTERcontra)=>((contrasubsetT)=>(((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>(((complementInPowersetComplementIntersect)=>(((complementTcontraSubset)=>((((((inIntersectImpInIntersectUnions)=>((((inComplementUnionImpInComplement1)=>(((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>(((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>(((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((((woz13rule3)=>(((woz1_1)=>((woz1_2)=>((((woz1_5)=>((((choice2fnsingleton)=>((setOfPairsIsBReln1)=>((breln1all1)=>((subbreln1)=>((eqbreln1)=>(((breln1invI)=>((breln1invE)=>(((breln1compI)=>((breln1compE)=>(![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ (binunion @ X33 @ X35))<=(breln1 @ X4 @ X35)))))<=(breln1compEex))))<=(breln1compprop))))<=(breln1invprop)))))))<=(breln1SetBreln1))<=(breln1all2)))<=(woz1_4))<=(woz1_3))))<=(woz13rule4)))<=(woz13rule2))<=(woz13rule1)))))<=(demorgan2b2))))))<=(demorgan2a2)))))<=(binunionTE)))<=(inComplementUnionImpNotIn1))<=(intersectInPowersetIntersectUnions)))<=(inIntersectImpInUnion2))<=(inIntersectImpInUnion))<=(binunionTIRcontra))<=(binunionTILcontra)))<=(contraSubsetComplement)))<=(complementSubsetComplementIntersect)))))))))))<=(contrasubsetT1))))<=(binintersectTELcontra))<=(complementTE1))))<=(powersetTI1)))<=(setextT))))))<=(binintersectT_lem))<=(iftrueorfalse))<=(iffalse)))<=(theeq))<=(ifp)))<=(iftrueProp2))<=(iftrueProp1))<=(iffalseProp2))<=(iffalseProp1))<=(eta2))<=(beta2))<=(lam2lamEq))<=(eta1))<=(beta1)))<=(ap2apEq1))<=(funcext2))))))))<=(funcGraphProp3))<=(funcGraphProp1)))<=(brelnall2))<=(brelnall1))))))<=(ap2p)))<=(app))<=(apProp))<=(funcImageSingleton)))))<=(dpsetconstrERa))<=(setOfPairsIsBReln))))))<=(cartprodfstpairEq))))))<=(kpairsurjEq)))))))<=(setukpairinjR1))<=(setukpairinjR12))<=(setukpairinjR11))<=(setukpairinjL)))<=(cartprodfstin))))))<=(singletonsuniq))))<=(ex1E1))<=(singletonprop)))<=(setunionsingleton2))<=(setunionsingleton1)))<=(cartprodmempair))<=(cartprodmempair1))))<=(ubforcartprodlem2))<=(ubforcartprodlem1))<=(upairinpowunion))<=(upairsubunion))<=(upairset2E))<=(singletoninpowunion))<=(singletoninpowerset))))<=(kpairiskpair))<=(setukpairIR))<=(setukpairIL))<=(secondinupair))))<=(symdiffI2)))))))<=(setminusILneg))<=(setminusELneg)))<=(setminusSubset2)))<=(setminusEL)))<=(bs114d))<=(binintersectSubset1)))))<=(binintersectER)))))<=(binintersectEL)))))<=(binunionLsub)))<=(binunionEcases))<=(binunionIR))))<=(sepSubset))))<=(inPowerset)))))<=(setextsub))<=(subset2powerset))))<=(subsetTrans)))<=(notequalI2)))))<=(subsetE)))))))))<=(exuEu)))))))<=(exu__Cong)))<=(in__Cong)))<=(exuI2))<=(exuI3)))))))<=(quantDeMorgan4)))<=(quantDeMorgan2))<=(quantDeMorgan1))<=(vacuousDall))<=(emptyE1))<=(upairsetIR))<=(upairsetIL))<=(upairsetE))<=(singletonsswitch))<=(eqinunit))<=(notinsingleton))<=(uniqinunit)))))))))<=(emptyinPowerset))<=(powersetI))<=(setoftrueEq))<=(setadjoinOr))))<=(emptyinunitempty))))))))<=(emptyI))<=(setext))<=(exuE3e))<=(notinemptyset)))<=(emptysetE)))<=(exuE1))))<=(dsetconstrI))))<=(foundationAx)))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', breln1unionprop)).
85.14/11.36	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setextAx)).
85.14/11.36	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', emptysetAx)).
85.14/11.36	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setadjoinAx)).
85.14/11.36	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', powersetAx)).
85.14/11.36	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setunionAx)).
85.14/11.36	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', omega0Ax)).
85.14/11.36	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', omegaSAx)).
85.14/11.36	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', omegaIndAx)).
85.14/11.36	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', foundationAx)).
85.14/11.36	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', wellorderingAx)).
85.14/11.36	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', prop2setE)).
85.14/11.36	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', emptysetE)).
85.14/11.36	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', emptysetimpfalse)).
85.14/11.36	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', notinemptyset)).
85.14/11.36	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setext)).
85.14/11.36	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', emptyI)).
85.14/11.36	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', noeltsimpempty)).
85.14/11.36	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setadjoinIL)).
85.14/11.36	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', emptyinunitempty)).
85.14/11.36	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setadjoinIR)).
85.14/11.36	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setadjoinE)).
85.14/11.36	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setadjoinOr)).
85.14/11.36	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', powersetI)).
85.14/11.36	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', emptyinPowerset)).
85.14/11.36	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', emptyInPowerset)).
85.14/11.36	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', powersetE)).
85.14/11.36	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setunionI)).
85.14/11.36	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setunionE)).
85.14/11.36	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', subPowSU)).
85.14/11.36	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', uniqinunit)).
85.14/11.36	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', notinsingleton)).
85.14/11.36	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', eqinunit)).
85.14/11.36	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', singletonsswitch)).
85.14/11.36	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', upairsetE)).
85.14/11.36	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', upairsetIL)).
85.14/11.36	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', upairsetIR)).
85.14/11.36	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', vacuousDall)).
85.14/11.36	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', quantDeMorgan1)).
85.14/11.36	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', quantDeMorgan2)).
85.14/11.36	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', quantDeMorgan3)).
85.14/11.36	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', quantDeMorgan4)).
85.14/11.36	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', prop2setI)).
85.14/11.36	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', prop2set2propI)).
85.14/11.36	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', notdexE)).
85.14/11.36	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', notdallE)).
85.14/11.36	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', inCongP)).
85.14/11.36	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', in__Cong)).
85.14/11.36	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', emptyset__Cong)).
85.14/11.36	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setadjoin__Cong)).
85.14/11.36	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', powerset__Cong)).
85.14/11.36	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setunion__Cong)).
85.14/11.36	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', omega__Cong)).
85.14/11.36	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', subsetI1)).
85.14/11.36	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', eqimpsubset2)).
85.14/11.36	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', eqimpsubset1)).
85.14/11.36	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', subsetI2)).
85.14/11.36	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', emptysetsubset)).
85.14/11.36	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', subsetE)).
85.14/11.36	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', subsetE2)).
85.14/11.36	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', notsubsetI)).
85.14/11.36	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', notequalI1)).
85.14/11.36	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', notequalI2)).
85.14/11.36	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', subsetRefl)).
85.14/11.36	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', subsetTrans)).
85.14/11.36	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setadjoinSub)).
85.14/11.36	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setadjoinSub2)).
85.14/11.36	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', subset2powerset)).
85.14/11.36	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setextsub)).
85.14/11.36	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', subsetemptysetimpeq)).
85.14/11.36	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', powersetI1)).
85.14/11.36	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', powersetE1)).
85.14/11.36	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', inPowerset)).
85.14/11.36	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', powersetsubset)).
85.14/11.36	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binunionIL)).
85.14/11.36	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', upairset2IR)).
85.14/11.36	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binunionIR)).
85.14/11.36	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binunionEcases)).
85.14/11.36	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binunionE)).
85.14/11.36	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binunionLsub)).
85.14/11.36	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binunionRsub)).
85.14/11.36	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binintersectI)).
85.14/11.36	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binintersectSubset5)).
85.14/11.36	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binintersectEL)).
85.14/11.36	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binintersectLsub)).
85.14/11.36	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binintersectSubset2)).
85.14/11.36	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binintersectSubset3)).
85.14/11.36	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binintersectER)).
85.14/11.36	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', disjointsetsI1)).
85.14/11.36	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binintersectRsub)).
85.14/11.36	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binintersectSubset4)).
85.14/11.36	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binintersectSubset1)).
85.14/11.36	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', bs114d)).
85.14/11.36	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setminusI)).
85.14/11.36	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setminusEL)).
85.14/11.36	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setminusER)).
85.14/11.36	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setminusSubset2)).
85.14/11.36	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setminusERneg)).
85.14/11.36	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setminusELneg)).
85.14/11.36	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setminusILneg)).
85.14/11.36	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setminusIRneg)).
85.14/11.36	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setminusLsub)).
85.14/11.36	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setminusSubset1)).
85.14/11.36	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', symdiffE)).
85.14/11.36	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', symdiffI1)).
85.14/11.36	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', symdiffI2)).
85.14/11.36	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', symdiffIneg1)).
85.14/11.36	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', symdiffIneg2)).
85.14/11.36	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', secondinupair)).
85.14/11.36	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setukpairIL)).
85.14/11.36	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setukpairIR)).
85.14/11.36	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', kpairiskpair)).
85.14/11.36	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', kpairp)).
85.14/11.36	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', singletonsubset)).
85.14/11.36	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', singletoninpowerset)).
85.14/11.36	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', singletoninpowunion)).
85.14/11.36	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', upairset2E)).
85.14/11.36	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', upairsubunion)).
85.14/11.36	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', upairinpowunion)).
85.14/11.36	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', ubforcartprodlem1)).
85.14/11.36	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', ubforcartprodlem2)).
85.14/11.36	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', ubforcartprodlem3)).
85.14/11.36	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', cartprodpairin)).
85.14/11.36	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', cartprodmempair1)).
85.14/11.36	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', cartprodmempair)).
85.14/11.36	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setunionE2)).
85.14/11.36	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setunionsingleton1)).
85.14/11.36	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setunionsingleton2)).
85.14/11.36	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setunionsingleton)).
85.14/11.36	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', singletonsuniq)).
85.14/11.36	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setukpairinjL1)).
85.14/11.36	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', theprop)).
85.14/11.36	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', kfstpairEq)).
85.14/11.36	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', cartprodfstin)).
85.14/11.36	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setukpairinjL2)).
85.14/11.36	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setukpairinjL)).
85.14/11.36	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setukpairinjR11)).
85.14/11.36	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setukpairinjR12)).
85.14/11.36	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setukpairinjR1)).
85.14/11.36	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', upairequniteq)).
85.14/11.36	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setukpairinjR2)).
85.14/11.36	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setukpairinjR)).
85.14/11.36	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', ksndpairEq)).
85.14/11.36	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', kpairsurjEq)).
85.14/11.36	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', cartprodsndin)).
85.14/11.36	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', cartprodpairmemEL)).
85.14/11.36	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', cartprodpairmemER)).
85.14/11.36	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', cartprodmempaircEq)).
85.14/11.36	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', cartprodfstpairEq)).
85.14/11.36	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', cartprodsndpairEq)).
85.14/11.36	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', cartprodpairsurjEq)).
85.14/11.36	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', app)).
85.14/11.36	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', infuncsetfunc)).
85.14/11.36	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', ap2p)).
85.14/11.36	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', funcinfuncset)).
85.14/11.36	thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', funcGraphProp1)).
85.14/11.36	thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', funcGraphProp3)).
85.14/11.36	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', funcGraphProp2)).
85.14/11.36	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', funcextLem)).
85.14/11.36	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', funcGraphProp4)).
85.14/11.36	thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', funcext)).
85.14/11.36	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', funcext2)).
85.14/11.36	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', ap2apEq1)).
85.14/11.36	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', ap2apEq2)).
85.14/11.36	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', ifp)).
85.14/11.36	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', theeq)).
85.14/11.36	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', iftrue)).
85.14/11.36	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', iffalse)).
85.14/11.36	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', iftrueorfalse)).
85.14/11.36	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binintersectT_lem)).
85.14/11.36	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binunionT_lem)).
85.14/11.36	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', powersetT_lem)).
85.14/11.36	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setminusT_lem)).
85.14/11.36	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', complementT_lem)).
85.14/11.36	thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', setextT)).
85.14/11.36	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', subsetTI)).
85.14/11.36	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', powersetTI1)).
85.14/11.36	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', powersetTE1)).
85.14/11.36	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', complementTI1)).
85.14/11.36	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', complementTE1)).
85.14/11.36	thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binintersectTELcontra)).
85.14/11.36	thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binintersectTERcontra)).
85.14/11.36	thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', contrasubsetT)).
85.14/11.36	thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', contrasubsetT1)).
85.14/11.36	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', contrasubsetT2)).
85.14/11.36	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', contrasubsetT3)).
85.14/11.36	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', doubleComplementI1)).
85.14/11.36	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', doubleComplementE1)).
85.14/11.36	thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', doubleComplementSub1)).
85.14/11.36	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', doubleComplementSub2)).
85.14/11.36	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', doubleComplementEq)).
85.14/11.36	thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', complementTnotintersectT)).
85.14/11.36	thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', complementImpComplementIntersect)).
85.14/11.36	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', complementSubsetComplementIntersect)).
85.14/11.36	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', complementInPowersetComplementIntersect)).
85.14/11.36	thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', contraSubsetComplement)).
85.14/11.36	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', complementTcontraSubset)).
85.14/11.36	thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binunionTILcontra)).
85.14/11.36	thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binunionTIRcontra)).
85.14/11.36	thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', inIntersectImpInUnion)).
85.14/11.36	thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', inIntersectImpInUnion2)).
85.14/11.36	thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', inIntersectImpInIntersectUnions)).
85.14/11.36	thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', intersectInPowersetIntersectUnions)).
85.14/11.36	thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', inComplementUnionImpNotIn1)).
85.14/11.36	thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', inComplementUnionImpInComplement1)).
85.14/11.36	thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binunionTE)).
85.14/11.36	thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', binunionTEcontra)).
85.14/11.36	thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', demorgan2a1)).
85.14/11.36	thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', complementUnionInPowersetComplement)).
85.14/11.36	thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', demorgan2a2)).
85.14/11.36	thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', demorgan1a)).
85.14/11.36	thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', demorgan1b)).
85.14/11.36	thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', demorgan1)).
85.14/11.36	thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', demorgan2a)).
85.14/11.36	thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', demorgan2b2)).
85.14/11.36	thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', demorgan2b)).
85.14/11.36	thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', demorgan2)).
85.14/11.36	thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', woz13rule0)).
85.14/11.36	thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', woz13rule1)).
85.14/11.36	thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', woz13rule2)).
85.14/11.36	thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', woz13rule3)).
85.14/11.36	thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', woz13rule4)).
85.14/11.36	thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', woz1_1)).
85.14/11.36	thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', woz1_2)).
85.14/11.36	thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', woz1_3)).
85.14/11.36	thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', woz1_4)).
85.14/11.36	thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.0ur87Z6JG6/Vampire---4.8_21359', woz1_5)).
85.14/11.36	thf(c_0_303, plain, ((breln1)=(^[Z0/* 19 */:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(fof_simplification,[status(thm)],[breln1])).
85.14/11.36	thf(c_0_304, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
85.14/11.36	thf(c_0_305, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
85.14/11.36	thf(c_0_306, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
85.14/11.36	thf(c_0_307, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
85.14/11.36	thf(c_0_308, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
85.14/11.36	thf(c_0_309, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
85.14/11.36	thf(c_0_310, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
85.14/11.36	thf(c_0_311, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
85.14/11.36	thf(c_0_312, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
85.14/11.36	thf(c_0_313, 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])).
85.14/11.36	thf(c_0_314, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
85.14/11.36	thf(c_0_315, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
85.14/11.36	thf(c_0_316, 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])).
85.14/11.36	thf(c_0_317, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
85.14/11.36	thf(c_0_318, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
85.14/11.36	thf(c_0_319, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
85.14/11.36	thf(c_0_320, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
85.14/11.36	thf(c_0_321, plain, ((breln1)=(^[Z0/* 19 */:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(apply_def,[status(thm)],[c_0_303, c_0_304])).
85.14/11.36	thf(c_0_322, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
85.14/11.36	thf(c_0_323, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X1032:$i]:((((X6 @ X2 @ X1032))&![X1033:$i]:((((X6 @ X2 @ X1033))=>((X1032)=(X1033)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_305, c_0_306])).
85.14/11.36	thf(c_0_324, plain, ((descrp)=(![X1:$i > $o]:(((?[X1034:$i]:((((X1 @ X1034))&![X1035:$i]:((((X1 @ X1035))=>((X1034)=(X1035)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_307, c_0_306])).
85.14/11.36	thf(c_0_325, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
85.14/11.36	thf(c_0_326, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
85.14/11.36	thf(c_0_327, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
85.14/11.36	thf(c_0_328, plain, ((exuE1)=(![X1:$i > $o]:(((?[X1036:$i]:((((X1 @ X1036))&![X1037:$i]:((((X1 @ X1037))=>((X1036)=(X1037)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_308, c_0_306])).
85.14/11.36	thf(c_0_329, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X1038:$i]:((((X1 @ X1038))&![X1039:$i]:((((X1 @ X1039))=>((X1038)=(X1039)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_309, c_0_306])).
85.14/11.36	thf(c_0_330, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
85.14/11.36	thf(c_0_331, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_310])).
85.14/11.36	thf(c_0_332, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_311, c_0_310])).
85.14/11.36	thf(c_0_333, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_310])).
85.14/11.36	thf(c_0_334, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
85.14/11.36	thf(c_0_335, plain, ((exuE2)=(![X1:$i > $o]:(((?[X1040:$i]:((((X1 @ X1040))&![X1041:$i]:((((X1 @ X1041))=>((X1040)=(X1041)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_312, c_0_306])).
85.14/11.36	thf(c_0_336, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_310])).
85.14/11.36	thf(c_0_337, 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])).
85.14/11.36	thf(c_0_338, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X1042:$i]:((((X1 @ X1042))&![X1043:$i]:((((X1 @ X1043))=>((X1042)=(X1043))))))))))), inference(apply_def,[status(thm)],[c_0_313, c_0_306])).
85.14/11.36	thf(c_0_339, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X1044:$i]:((((X1 @ X1044))&![X1045:$i]:((((X1 @ X1045))=>((X1044)=(X1045)))))))))))), inference(apply_def,[status(thm)],[c_0_314, c_0_306])).
85.14/11.36	thf(c_0_340, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X1046:$i]:((((X1 @ X1046))&![X1047:$i]:((((X1 @ X1047))=>((X1046)=(X1047))))))))))), inference(apply_def,[status(thm)],[c_0_315, c_0_306])).
85.14/11.36	thf(c_0_341, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X1048:$i]:((((X1 @ X1048))&![X1049:$i]:((((X1 @ X1049))=>((X1048)=(X1049)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_316, c_0_306])).
85.14/11.36	thf(c_0_342, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1050:$i]:((((X1 @ X1050))&![X1051:$i]:((((X1 @ X1051))=>((X1050)=(X1051)))))))<=>(?[X1052:$i]:((((X17 @ X1052))&![X1053:$i]:((((X17 @ X1053))=>((X1052)=(X1053)))))))))))), inference(apply_def,[status(thm)],[c_0_317, c_0_306])).
85.14/11.36	thf(c_0_343, plain, ((exuEu)=(![X1:$i > $o]:(((?[X1054:$i]:((((X1 @ X1054))&![X1055:$i]:((((X1 @ X1055))=>((X1054)=(X1055)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_318, c_0_306])).
85.14/11.36	thf(c_0_344, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1056:$i]:((((X1 @ X1056))&![X1057:$i]:((((X1 @ X1057))=>((X1056)=(X1057)))))))=>((?[X1058:$i]:((((X17 @ X1058))&![X1059:$i]:((((X17 @ X1059))=>((X1058)=(X1059)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_319, c_0_306])).
85.14/11.36	thf(c_0_345, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
85.14/11.36	thf(c_0_346, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
85.14/11.36	thf(c_0_347, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
85.14/11.36	thf(c_0_348, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
85.14/11.36	thf(c_0_349, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
85.14/11.36	thf(c_0_350, plain, ((ex1I)<=>![X4:$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])).
85.14/11.36	thf(c_0_351, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
85.14/11.36	thf(c_0_352, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
85.14/11.36	thf(c_0_353, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
85.14/11.36	thf(c_0_354, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
85.14/11.36	thf(c_0_355, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
85.14/11.36	thf(c_0_356, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_320, c_0_304])).
85.14/11.36	thf(c_0_357, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
85.14/11.36	thf(c_0_358, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
85.14/11.36	thf(c_0_359, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
85.14/11.36	thf(c_0_360, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
85.14/11.36	thf(c_0_361, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
85.14/11.36	thf(c_0_362, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
85.14/11.36	thf(c_0_363, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
85.14/11.36	thf(c_0_364, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
85.14/11.36	thf(c_0_365, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
85.14/11.36	thf(c_0_366, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_304])).
85.14/11.36	thf(c_0_367, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_304])).
85.14/11.36	thf(c_0_368, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
85.14/11.36	thf(c_0_369, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln, c_0_304])).
85.14/11.36	thf(c_0_370, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_304])).
85.14/11.36	thf(c_0_371, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
85.14/11.36	thf(c_0_372, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
85.14/11.36	thf(c_0_373, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
85.14/11.36	thf(c_0_374, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
85.14/11.36	thf(c_0_375, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
85.14/11.36	thf(c_0_376, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
85.14/11.36	thf(c_0_377, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
85.14/11.36	thf(c_0_378, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
85.14/11.36	thf(c_0_379, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
85.14/11.36	thf(c_0_380, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
85.14/11.36	thf(c_0_381, axiom, ((breln1all2)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[breln1all2, c_0_321])).
85.14/11.36	thf(c_0_382, axiom, ((breln1SetBreln1)=(![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>((subset @ X33 @ (cartprod @ X4 @ X4))))))), inference(apply_def,[status(thm)],[breln1SetBreln1, c_0_321])).
85.14/11.36	thf(c_0_383, plain, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 8 */:$i]:(((X52 @ X2 @ Z0)&![X14:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ Z0 @ X14) @ X33))))))))))))))))), inference(fof_simplification,[status(thm)],[choice2fnsingleton])).
85.14/11.36	thf(c_0_384, plain, ((setOfPairsIsBReln1)=(![X4:$i, X53:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X4)))))), inference(apply_def,[status(thm)],[c_0_322, c_0_321])).
85.14/11.36	thf(c_0_385, axiom, ((breln1all1)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[breln1all1, c_0_321])).
85.14/11.36	thf(c_0_386, axiom, ((subbreln1)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X4)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln1, c_0_321])).
85.14/11.36	thf(c_0_387, axiom, ((eqbreln1)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X4)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln1, c_0_321])).
85.14/11.36	thf(c_0_388, axiom, ((breln1invprop)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>((subset @ (breln1invset @ X4 @ X33) @ (cartprod @ X4 @ X4))))))), inference(apply_def,[status(thm)],[breln1invprop, c_0_321])).
85.14/11.36	thf(c_0_389, axiom, ((breln1invI)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))))))))))), inference(apply_def,[status(thm)],[breln1invI, c_0_321])).
85.14/11.36	thf(c_0_390, axiom, ((breln1invE)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33)))))))))), inference(apply_def,[status(thm)],[breln1invE, c_0_321])).
85.14/11.36	thf(c_0_391, axiom, ((breln1compprop)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X4)))=>((subset @ (breln1compset @ X4 @ X33 @ X35) @ (cartprod @ X4 @ X4))))))))), inference(apply_def,[status(thm)],[breln1compprop, c_0_321])).
85.14/11.36	thf(c_0_392, axiom, ((breln1compI)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X4)))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35)))))))))))))))), inference(apply_def,[status(thm)],[breln1compI, c_0_321])).
85.14/11.36	thf(c_0_393, axiom, ((breln1compE)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X4)))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35)))))))))))))), inference(apply_def,[status(thm)],[breln1compE, c_0_321])).
85.14/11.36	thf(c_0_394, axiom, ((breln1compEex)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X4)))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>![X54:$o]:((![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(X54)))))=>(X54)))))))))))))), inference(apply_def,[status(thm)],[breln1compEex, c_0_321])).
85.14/11.36	thf(c_0_395, plain, ((epred1_0)<=>![X1081:$i]:(?[X1082:$i]:((((![X1083:$i]:(((in @ X1083 @ X1082)=>![X1084:$i]:(((in @ X1084 @ X1083)=>(in @ X1084 @ X1081)))))&![X1085:$i, X1086:$i]:((((in @ X1085 @ X1081)&(in @ X1086 @ X1081))=>(![X1087:$i]:(((in @ X1087 @ X1082)=>((in @ X1085 @ X1087)<=>(in @ X1086 @ X1087))))=>((X1085)=(X1086))))))&![X1088:$i, X1089:$i]:((((in @ X1088 @ X1082)&(in @ X1089 @ X1082))=>(![X1090:$i]:(((in @ X1090 @ X1088)=>(in @ X1090 @ X1089)))|![X1091:$i]:(((in @ X1091 @ X1089)=>(in @ X1091 @ X1088)))))))&![X1092:$i]:(((![X1093:$i]:(((in @ X1093 @ X1092)=>(in @ X1093 @ X1081)))&?[X1094:$i]:((in @ X1094 @ X1092)))=>?[X1095:$i, X1096:$i]:(((((in @ X1095 @ X1082)&(in @ X1096 @ X1092))&~(?[X1097:$i]:(((in @ X1097 @ X1095)&(in @ X1097 @ X1092)))))&![X1098:$i]:(((in @ X1098 @ X1082)=>(![X1099:$i]:(((in @ X1099 @ X1098)=>(in @ X1099 @ X1095)))|(in @ X1096 @ X1098)))))))))))), introduced(definition)).
85.14/11.36	thf(c_0_396, negated_conjecture, ~((![X1060:$i, X1061:$i]:((![X1062:$i]:(((in @ X1062 @ X1060)<=>(in @ X1062 @ X1061)))=>((X1060)=(X1061))))=>(![X1063:$i]:(~(in @ X1063 @ emptyset))=>(![X1064:$i, X1065:$i, X1066:$i]:(((in @ X1066 @ (setadjoin @ X1064 @ X1065))<=>(((X1066)=(X1064))|(in @ X1066 @ X1065))))=>(![X1067:$i, X1068:$i]:(((in @ X1068 @ (powerset @ X1067))<=>![X1069:$i]:(((in @ X1069 @ X1068)=>(in @ X1069 @ X1067)))))=>(![X1070:$i, X1071:$i]:(((in @ X1071 @ (setunion @ X1070))<=>?[X1072:$i]:(((in @ X1071 @ X1072)&(in @ X1072 @ X1070)))))=>((in @ emptyset @ omega)=>(![X2062:$i]:(((in @ X2062 @ omega)=>(in @ (setadjoin @ X2062 @ X2062) @ omega)))=>(![X2059:$i]:((((in @ emptyset @ X2059)&![X2060:$i]:((((in @ X2060 @ omega)&(in @ X2060 @ X2059))=>(in @ (setadjoin @ X2060 @ X2060) @ X2059))))=>![X2061:$i]:(((in @ X2061 @ omega)=>(in @ X2061 @ X2059)))))=>(![X1073:$i > $i > $o, X1074:$i]:((![X1075:$i]:(((in @ X1075 @ X1074)=>?[X1076:$i]:(((X1073 @ X1075 @ X1076)&![X1077:$i]:(((X1073 @ X1075 @ X1077)=>((X1076)=(X1077))))))))=>?[X1078:$i]:(![X1079:$i]:(((in @ X1079 @ X1078)<=>?[X1080:$i]:(((in @ X1080 @ X1074)&(X1073 @ X1080 @ X1079))))))))=>(![X2055:$i]:((?[X2056:$i]:((in @ X2056 @ X2055))=>?[X2057:$i]:(((in @ X2057 @ X2055)&~(?[X2058:$i]:(((in @ X2058 @ X2057)&(in @ X2058 @ X2055))))))))=>((epred1_0)=>(![X1100:$i > $o]:((?[X1101:$i]:(((X1100 @ X1101)&![X1102:$i]:(((X1100 @ X1102)=>((X1101)=(X1102))))))=>(X1100 @ (descr @ (^[Z0/* 3 */:$i]:((X1100 @ Z0)))))))=>(![X2052:$i, X2053:$i > $o, X2054:$i]:(((in @ X2054 @ X2052)=>((X2053 @ X2054)=>(in @ X2054 @ (dsetconstr @ X2052 @ (^[Z0/* 3 */:$i]:((X2053 @ Z0))))))))=>(![X1103:$i, X1104:$i > $o, X1105:$i]:(((in @ X1105 @ (dsetconstr @ X1103 @ (^[Z0/* 3 */:$i]:((X1104 @ Z0)))))=>(in @ X1105 @ X1103)))=>(![X1106:$i, X1107:$i > $o, X1108:$i]:(((in @ X1108 @ (dsetconstr @ X1106 @ (^[Z0/* 3 */:$i]:((X1107 @ Z0)))))=>(X1107 @ X1108)))=>(![X2047:$i > $o]:((?[X2048:$i]:(((X2047 @ X2048)&![X2049:$i]:(((X2047 @ X2049)=>((X2048)=(X2049))))))=>?[X2050:$i]:(((X2047 @ X2050)&![X2051:$i]:(((X2047 @ X2051)=>((X2050)=(X2051))))))))=>(![X1109:$o, X1110:$i]:(((in @ X1110 @ (prop2set @ ((X1109))))=>(X1109)))=>(![X2045:$i]:(((in @ X2045 @ emptyset)=>![X2046:$o]:((X2046))))=>(![X1111:$i]:(~(in @ X1111 @ emptyset))=>(![X2044:$i]:(~(in @ X2044 @ emptyset))=>(![X2040:$i > $o]:((?[X2041:$i]:(((X2040 @ X2041)&![X2042:$i]:(((X2040 @ X2042)=>((X2041)=(X2042))))))=>?[X2043:$i]:((X2040 @ X2043))))=>(![X2036:$i, X2037:$i]:((![X2038:$i]:(((in @ X2038 @ X2036)=>(in @ X2038 @ X2037)))=>(![X2039:$i]:(((in @ X2039 @ X2037)=>(in @ X2039 @ X2036)))=>((X2036)=(X2037)))))=>(![X2034:$i]:((![X2035:$i]:(~(in @ X2035 @ X2034))=>((X2034)=(emptyset))))=>(![X1112:$i]:((![X1113:$i]:(~(in @ X1113 @ X1112))=>((X1112)=(emptyset))))=>(![X1114:$i, X1115:$i > $o, X1116:$i]:(((in @ X1116 @ X1114)=>((in @ X1116 @ (dsetconstr @ X1114 @ (^[Z0/* 3 */:$i]:((X1115 @ Z0)))))<=>(X1115 @ X1116))))=>(![X1117:$i]:((((X1117)!=(emptyset))=>?[X1118:$i]:((in @ X1118 @ X1117))))=>(![X1119:$i, X1120:$i > $o, X1121:$i]:(((in @ X1121 @ X1119)=>((X1120 @ X1121)=>((dsetconstr @ X1119 @ (^[Z0/* 3 */:$i]:((X1120 @ Z0))))!=(emptyset)))))=>(![X1122:$i]:((?[X1123:$i]:((in @ X1123 @ X1122))=>((X1122)!=(emptyset))))=>(![X1124:$i, X1125:$i]:((in @ X1124 @ (setadjoin @ X1124 @ X1125)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1126:$i, X1127:$i, X1128:$i]:(((in @ X1128 @ X1127)=>(in @ X1128 @ (setadjoin @ X1126 @ X1127))))=>(![X1129:$i, X1130:$i, X1131:$i]:(((in @ X1131 @ (setadjoin @ X1129 @ X1130))=>![X1132:$o]:(((((X1131)=(X1129))=>(X1132))=>(((in @ X1131 @ X1130)=>(X1132))=>(X1132))))))=>(![X2031:$i, X2032:$i, X2033:$i]:(((in @ X2033 @ (setadjoin @ X2031 @ X2032))=>(((X2033)=(X2031))|(in @ X2033 @ X2032))))=>(![X2030:$i]:(((dsetconstr @ X2030 @ (^[Z0/* 3 */:$i]:(($true))))=(X2030)))=>(![X2027:$i, X2028:$i]:((![X2029:$i]:(((in @ X2029 @ X2028)=>(in @ X2029 @ X2027)))=>(in @ X2028 @ (powerset @ X2027))))=>(![X2026:$i]:((in @ emptyset @ (powerset @ X2026)))=>(![X1133:$i]:((in @ emptyset @ (powerset @ X1133)))=>(![X1134:$i, X1135:$i, X1136:$i]:(((in @ X1135 @ (powerset @ X1134))=>((in @ X1136 @ X1135)=>(in @ X1136 @ X1134))))=>(![X1137:$i, X1138:$i, X1139:$i]:(((in @ X1138 @ X1139)=>((in @ X1139 @ X1137)=>(in @ X1138 @ (setunion @ X1137)))))=>(![X1140:$i, X1141:$i]:(((in @ X1141 @ (setunion @ X1140))=>![X1142:$o]:((![X1143:$i]:(((in @ X1141 @ X1143)=>((in @ X1143 @ X1140)=>(X1142))))=>(X1142)))))=>(![X1144:$i, X1145:$i]:(((in @ X1145 @ X1144)=>(in @ X1145 @ (powerset @ (setunion @ X1144)))))=>(![X1146:$i > $o]:((?[X1147:$i]:(((X1146 @ X1147)&![X1148:$i]:(((X1146 @ X1148)=>((X1147)=(X1148))))))=>?[X1149:$i]:(![X1150:$i]:(((X1146 @ X1150)<=>((X1150)=(X1149)))))))=>(![X1151:$i]:((((X1151)!=(emptyset))=>?[X1152:$i]:((in @ X1152 @ X1151))))=>(![X2024:$i, X2025:$i]:(((in @ X2024 @ (setadjoin @ X2025 @ emptyset))=>((X2024)=(X2025))))=>(![X2022:$i, X2023:$i]:((((X2022)!=(X2023))=>~(in @ X2023 @ (setadjoin @ X2022 @ emptyset))))=>(![X2020:$i, X2021:$i]:((((X2020)=(X2021))=>(in @ X2020 @ (setadjoin @ X2021 @ emptyset))))=>(![X2018:$i, X2019:$i]:(((in @ X2018 @ (setadjoin @ X2019 @ emptyset))=>(in @ X2019 @ (setadjoin @ X2018 @ emptyset))))=>(![X2015:$i, X2016:$i, X2017:$i]:(((in @ X2017 @ (setadjoin @ X2015 @ (setadjoin @ X2016 @ emptyset)))=>(((X2017)=(X2015))|((X2017)=(X2016)))))=>(![X2013:$i, X2014:$i]:((in @ X2013 @ (setadjoin @ X2013 @ (setadjoin @ X2014 @ emptyset))))=>(![X2011:$i, X2012:$i]:((in @ X2012 @ (setadjoin @ X2011 @ (setadjoin @ X2012 @ emptyset))))=>(![X2008:$i, X2009:$i > $o]:((?[X2010:$i]:(((in @ X2010 @ X2008)&(X2009 @ X2010)))=>((dsetconstr @ X2008 @ (^[Z0/* 3 */:$i]:((X2009 @ Z0))))!=(emptyset))))=>(![X2006:$i > $o, X2007:$i]:(((in @ X2007 @ emptyset)=>(X2006 @ X2007)))=>(![X2002:$i, X2003:$i > $o]:((~(![X2004:$i]:(((in @ X2004 @ X2002)=>(X2003 @ X2004))))=>?[X2005:$i]:(((in @ X2005 @ X2002)&~(X2003 @ X2005)))))=>(![X1998:$i, X1999:$i > $o]:((![X2000:$i]:(((in @ X2000 @ X1998)=>~(X1999 @ X2000)))=>~(?[X2001:$i]:(((in @ X2001 @ X1998)&(X1999 @ X2001))))))=>(![X1153:$i, X1154:$i > $o]:((~(?[X1155:$i]:(((in @ X1155 @ X1153)&(X1154 @ X1155))))=>![X1156:$i]:(((in @ X1156 @ X1153)=>~(X1154 @ X1156)))))=>(![X1994:$i, X1995:$i > $o]:((?[X1996:$i]:(((in @ X1996 @ X1994)&~(X1995 @ X1996)))=>~(![X1997:$i]:(((in @ X1997 @ X1994)=>(X1995 @ X1997))))))=>(![X1157:$o]:(((X1157)=>(in @ emptyset @ (prop2set @ ((X1157))))))=>(![X1158:$o]:(((X1158)=>(set2prop @ (prop2set @ ((X1158))))))=>(![X1159:$i, X1160:$i > $o]:((~(?[X1161:$i]:(((in @ X1161 @ X1159)&(X1160 @ X1161))))=>![X1162:$i]:(((in @ X1162 @ X1159)=>~(X1160 @ X1162)))))=>(![X1163:$i, X1164:$i > $o]:((~(![X1165:$i]:(((in @ X1165 @ X1163)=>(X1164 @ X1165))))=>?[X1166:$i]:(((in @ X1166 @ X1163)&~(X1164 @ X1166)))))=>(![X1167:$i > $o]:((?[X1168:$i]:(((X1167 @ X1168)&![X1169:$i]:(((X1167 @ X1169)=>((X1168)=(X1169))))))=>?[X1170:$i]:(((X1167 @ X1170)&![X1171:$i]:(((X1167 @ X1171)=>((X1170)=(X1171))))))))=>(![X1988:$i > $o]:((?[X1989:$i]:((X1988 @ X1989))=>(![X1990:$i, X1991:$i]:(((X1988 @ X1990)=>((X1988 @ X1991)=>((X1990)=(X1991)))))=>?[X1992:$i]:(((X1988 @ X1992)&![X1993:$i]:(((X1988 @ X1993)=>((X1992)=(X1993)))))))))=>(![X1983:$i > $o]:((?[X1984:$i]:(![X1985:$i]:(((X1983 @ X1985)<=>((X1985)=(X1984)))))=>?[X1986:$i]:(((X1983 @ X1986)&![X1987:$i]:(((X1983 @ X1987)=>((X1986)=(X1987))))))))=>(![X1172:$i, X1173:$i]:((((X1172)=(X1173))=>![X1174:$i, X1175:$i]:((((X1174)=(X1175))=>((in @ X1174 @ X1172)=>(in @ X1175 @ X1173))))))=>(![X1979:$i, X1980:$i]:((((X1979)=(X1980))=>![X1981:$i, X1982:$i]:((((X1981)=(X1982))=>((in @ X1981 @ X1979)<=>(in @ X1982 @ X1980))))))=>(![X1176:$i > $o]:((?[X1177:$i]:(((X1176 @ X1177)&![X1178:$i]:(((X1176 @ X1178)=>((X1177)=(X1178))))))=>![X1179:$i, X1180:$i]:(((X1176 @ X1179)=>((X1176 @ X1180)=>((X1179)=(X1180)))))))=>(![X1971:$i > $o, X1972:$i > $o]:((![X1973:$i, X1974:$i]:((((X1973)=(X1974))=>((X1971 @ X1973)<=>(X1972 @ X1974))))=>(?[X1975:$i]:(((X1971 @ X1975)&![X1976:$i]:(((X1971 @ X1976)=>((X1975)=(X1976))))))<=>?[X1977:$i]:(((X1972 @ X1977)&![X1978:$i]:(((X1972 @ X1978)=>((X1977)=(X1978)))))))))=>(((emptyset)=(emptyset))=>(![X1181:$i, X1182:$i]:((((X1181)=(X1182))=>![X1183:$i, X1184:$i]:((((X1183)=(X1184))=>((setadjoin @ X1181 @ X1183)=(setadjoin @ X1182 @ X1184))))))=>(![X1185:$i, X1186:$i]:((((X1185)=(X1186))=>((powerset @ X1185)=(powerset @ X1186))))=>(![X1187:$i, X1188:$i]:((((X1187)=(X1188))=>((setunion @ X1187)=(setunion @ X1188))))=>(((omega)=(omega))=>(![X1966:$i > $o]:((?[X1967:$i]:(((X1966 @ X1967)&![X1968:$i]:(((X1966 @ X1968)=>((X1967)=(X1968))))))=>![X1969:$i, X1970:$i]:(((X1966 @ X1969)=>((X1966 @ X1970)=>((X1969)=(X1970)))))))=>(![X1189:$i > $o, X1190:$i > $o]:((![X1191:$i, X1192:$i]:((((X1191)=(X1192))=>((X1189 @ X1191)<=>(X1190 @ X1192))))=>(?[X1193:$i]:(((X1189 @ X1193)&![X1194:$i]:(((X1189 @ X1194)=>((X1193)=(X1194))))))=>(?[X1195:$i]:(((X1190 @ X1195)&![X1196:$i]:(((X1190 @ X1196)=>((X1195)=(X1196))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1189 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X1190 @ Z0)))))))))=>(![X1197:$i, X1198:$i]:((((X1197)=(X1198))=>![X1199:$i > $o, X1200:$i > $o]:((![X1201:$i]:(((in @ X1201 @ X1197)=>![X1202:$i]:(((in @ X1202 @ X1198)=>(((X1201)=(X1202))=>((X1199 @ X1201)<=>(X1200 @ X1202)))))))=>((dsetconstr @ X1197 @ (^[Z0/* 3 */:$i]:((X1199 @ Z0))))=(dsetconstr @ X1198 @ (^[Z0/* 3 */:$i]:((X1200 @ Z0)))))))))=>(![X1203:$i, X1204:$i]:((![X1205:$i]:(((in @ X1205 @ X1203)=>(in @ X1205 @ X1204)))=>(subset @ X1203 @ X1204)))=>(![X1206:$i, X1207:$i]:((((X1206)=(X1207))=>(subset @ X1207 @ X1206)))=>(![X1208:$i, X1209:$i]:((((X1208)=(X1209))=>(subset @ X1208 @ X1209)))=>(![X1210:$i, X1211:$i]:((![X1212:$i]:(((in @ X1212 @ X1210)=>(in @ X1212 @ X1211)))=>(subset @ X1210 @ X1211)))=>(![X1213:$i]:((subset @ emptyset @ X1213))=>(![X1963:$i, X1964:$i, X1965:$i]:(((subset @ X1963 @ X1964)=>((in @ X1965 @ X1963)=>(in @ X1965 @ X1964))))=>(![X1214:$i, X1215:$i, X1216:$i]:(((subset @ X1214 @ X1215)=>(~(in @ X1216 @ X1215)=>~(in @ X1216 @ X1214))))=>(![X1217:$i, X1218:$i, X1219:$i]:(((in @ X1219 @ X1217)=>(~(in @ X1219 @ X1218)=>~(subset @ X1217 @ X1218))))=>(![X1220:$i, X1221:$i]:((~(subset @ X1220 @ X1221)=>((X1220)!=(X1221))))=>(![X1960:$i, X1961:$i, X1962:$i]:(((in @ X1962 @ X1960)=>(~(in @ X1962 @ X1961)=>((X1960)!=(X1961)))))=>(![X1222:$i]:((subset @ X1222 @ X1222))=>(![X1957:$i, X1958:$i, X1959:$i]:(((subset @ X1957 @ X1958)=>((subset @ X1958 @ X1959)=>(subset @ X1957 @ X1959))))=>(![X1223:$i, X1224:$i]:((subset @ X1224 @ (setadjoin @ X1223 @ X1224)))=>(![X1225:$i, X1226:$i, X1227:$i]:(((subset @ X1225 @ X1227)=>(subset @ X1225 @ (setadjoin @ X1226 @ X1227))))=>(![X1955:$i, X1956:$i]:(((subset @ X1955 @ X1956)=>(in @ X1955 @ (powerset @ X1956))))=>(![X1953:$i, X1954:$i]:(((subset @ X1953 @ X1954)=>((subset @ X1954 @ X1953)=>((X1953)=(X1954)))))=>(![X1228:$i]:(((subset @ X1228 @ emptyset)=>((X1228)=(emptyset))))=>(![X1229:$i, X1230:$i]:(((subset @ X1230 @ X1229)=>(in @ X1230 @ (powerset @ X1229))))=>(![X1231:$i, X1232:$i]:(((in @ X1232 @ (powerset @ X1231))=>(subset @ X1232 @ X1231)))=>(![X1952:$i]:((in @ X1952 @ (powerset @ X1952)))=>(![X1233:$i, X1234:$i]:(((subset @ X1233 @ X1234)=>(subset @ (powerset @ X1233) @ (powerset @ X1234))))=>(![X1235:$i, X1236:$i > $o]:((in @ (dsetconstr @ X1235 @ (^[Z0/* 3 */:$i]:((X1236 @ Z0)))) @ (powerset @ X1235)))=>(![X1950:$i, X1951:$i > $o]:((subset @ (dsetconstr @ X1950 @ (^[Z0/* 3 */:$i]:((X1951 @ Z0)))) @ X1950))=>(![X1237:$i, X1238:$i, X1239:$i]:(((in @ X1239 @ X1237)=>(in @ X1239 @ (binunion @ X1237 @ X1238))))=>(![X1240:$i, X1241:$i]:((in @ X1241 @ (setadjoin @ X1240 @ (setadjoin @ X1241 @ emptyset))))=>(![X1947:$i, X1948:$i, X1949:$i]:(((in @ X1949 @ X1948)=>(in @ X1949 @ (binunion @ X1947 @ X1948))))=>(![X1943:$i, X1944:$i, X1945:$i, X1946:$o]:(((in @ X1945 @ (binunion @ X1943 @ X1944))=>(((in @ X1945 @ X1943)=>(X1946))=>(((in @ X1945 @ X1944)=>(X1946))=>(X1946)))))=>(![X1242:$i, X1243:$i, X1244:$i]:(((in @ X1244 @ (binunion @ X1242 @ X1243))=>((in @ X1244 @ X1242)|(in @ X1244 @ X1243))))=>(![X1941:$i, X1942:$i]:((subset @ X1941 @ (binunion @ X1941 @ X1942)))=>(![X1245:$i, X1246:$i]:((subset @ X1246 @ (binunion @ X1245 @ X1246)))=>(![X1247:$i, X1248:$i, X1249:$i]:(((in @ X1249 @ X1247)=>((in @ X1249 @ X1248)=>(in @ X1249 @ (binintersect @ X1247 @ X1248)))))=>(![X1250:$i, X1251:$i, X1252:$i]:(((subset @ X1252 @ X1250)=>((subset @ X1252 @ X1251)=>(subset @ X1252 @ (binintersect @ X1250 @ X1251)))))=>(![X1938:$i, X1939:$i, X1940:$i]:(((in @ X1940 @ (binintersect @ X1938 @ X1939))=>(in @ X1940 @ X1938)))=>(![X1253:$i, X1254:$i]:((subset @ (binintersect @ X1253 @ X1254) @ X1253))=>(![X1255:$i, X1256:$i]:(((subset @ X1255 @ X1256)=>((binintersect @ X1255 @ X1256)=(X1255))))=>(![X1257:$i, X1258:$i]:((((binintersect @ X1257 @ 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X1632)=>(X1635)))))=>(X1635))))))))))))=>![X4:$i, X33:$i]:(((subset @ X33 @ (cartprod @ X4 @ X4))=>![X35:$i]:(((subset @ X35 @ (cartprod @ X4 @ X4))=>(subset @ (binunion @ X33 @ X35) @ (cartprod @ X4 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[breln1unionprop]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_323]), foundationAx]), wellorderingAx]), c_0_324]), c_0_325]), c_0_326]), c_0_327]), c_0_328]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_329]), setext]), emptyI]), noeltsimpempty]), c_0_330]), c_0_331]), c_0_332]), c_0_333]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_334]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_335]), c_0_336]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_337]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_338]), c_0_339]), c_0_340]), inCongP]), in__Cong]), c_0_341]), c_0_342]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_343]), c_0_344]), c_0_345]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_346]), c_0_347]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_348]), c_0_349]), c_0_350]), c_0_351]), singletonsuniq]), setukpairinjL1]), c_0_352]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_353]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_354]), c_0_355]), c_0_356]), c_0_357]), c_0_358]), c_0_359]), c_0_360]), c_0_361]), c_0_362]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_363]), c_0_364]), c_0_365]), c_0_366]), c_0_367]), c_0_368]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_369]), c_0_370]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_371]), c_0_372]), c_0_373]), c_0_374]), c_0_375]), c_0_376]), c_0_377]), c_0_378]), c_0_379]), c_0_380]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan1]), demorgan2a]), demorgan2b2]), demorgan2b]), demorgan2]), woz13rule0]), woz13rule1]), woz13rule2]), woz13rule3]), woz13rule4]), woz1_1]), woz1_2]), woz1_3]), woz1_4]), woz1_5]), c_0_321]), c_0_381]), c_0_382]), c_0_383]), c_0_384]), c_0_385]), c_0_386]), c_0_387]), c_0_388]), c_0_389]), c_0_390]), c_0_391]), c_0_392]), c_0_393]), c_0_394])])]), c_0_395])).
85.14/11.36	thf(c_0_397, negated_conjecture, ![X2063:$i, X2064:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2076:$i, X2077:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2085:$i, X2086:$i > $i > $o, X2087:$i, X2089:$i, X2092:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2099:$i, X2100:$i > $o, X2101:$i, X2103:$i, X2104:$i > $o, X2105:$i, X2106:$i, X2107:$i > $o, X2108:$i, X2109:$i, X2110:$i > $o, X2111:$i, X2112:$i > $o, X2113:$i, X2116:$i, X2117:$o, X2118:$i, X2119:$i, X2120:$o, X2121:$i, X2122:$i, X2123:$i > $o, X2124:$i, X2127:$i, X2128:$i, X2131:$i, X2133:$i, X2135:$i, X2136:$i > $o, X2137:$i, X2138:$i, X2140:$i, X2141:$i > $o, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$o, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$o, X2173:$i, X2174:$i, X2175:$i > $o, X2176:$i, X2179:$i, X2180:$i, X2181:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i > $o, X2200:$i, X2201:$i > $o, X2202:$i, X2203:$i, X2204:$i > $o, X2205:$i, X2207:$i, X2208:$i > $o, X2210:$i, X2211:$i, X2212:$i > $o, X2214:$i, X2215:$i, X2216:$i > $o, X2217:$i, X2219:$o, X2220:$o, X2221:$i, X2222:$i > $o, X2224:$i, X2225:$i, X2226:$i > $o, X2227:$i, X2229:$i > $o, X2230:$i, X2233:$i, X2234:$i > $o, X2235:$i, X2239:$i, X2240:$i > $o, X2241:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i > $o, X2254:$i, X2256:$i, X2257:$i, X2258:$i > $o, X2259:$i > $o, X2262:$i, X2265:$i, X2266:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i > $o, X2279:$i, X2281:$i, X2282:$i, X2283:$i > $o, X2284:$i > $o, X2287:$i, X2289:$i, X2291:$i, X2292:$i, X2293:$i > $o, X2294:$i > $o, X2297:$i, X2298:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2327:$i, X2328:$i, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i > $o, X2345:$i, X2346:$i > $o, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$o, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$i, X2364:$i, X2365:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$i, X2372:$i, X2373:$i, X2374:$i, X2375:$i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2383:$i, X2384:$i, X2385:$i, X2387:$i, X2388:$i, X2389:$i, X2390:$i, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$i, X2404:$i, X2405:$i, X2406:$i, X2407:$i, X2408:$i, X2409:$i, X2410:$i, X2411:$i, X2412:$i, X2413:$i, X2414:$i, X2415:$i, X2416:$i, X2417:$i, X2418:$i, X2419:$i, X2420:$i, X2421:$i, X2422:$i, X2423:$i, X2424:$i, X2425:$i, X2426:$o, X2427:$i, X2428:$i, X2429:$i, X2430:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2435:$i, X2436:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, X2442:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$i, X2455:$i, X2456:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i, X2463:$i, X2464:$i, X2465:$i, X2466:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2471:$i, X2472:$i, X2473:$i, X2474:$i, X2475:$i, X2476:$i, X2477:$i, X2478:$i, X2479:$i, X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2494:$i, X2495:$i, X2496:$i, X2497:$i, X2498:$i > $o, X2501:$i, X2502:$i, X2503:$i > $o, X2505:$i, X2506:$i > $o, X2507:$i, X2509:$i, X2510:$i > $o, X2513:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i, X2546:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i, X2551:$i, X2552:$i, X2553:$i, X2554:$i, X2555:$i, X2556:$i, X2557:$i, X2558:$i, X2559:$i, X2560:$i, X2561:$i, X2562:$i, X2563:$i, X2564:$i, X2565:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2570:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i, X2576:$i, X2577:$i, X2578:$i, X2579:$i, X2580:$i, X2581:$i, X2582:$i, X2583:$i, X2584:$i, X2585:$i > $i > $o, X2586:$i, X2587:$i, X2588:$i, X2589:$i, X2590:$i > $i > $o, X2591:$i, X2592:$i, X2593:$i > $i > $o, X2594:$i, X2595:$i, X2596:$i > $i > $o, X2597:$i, X2598:$i, 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X3009)))&(((in @ (esk91_3 @ X3009 @ X3010 @ X3011) @ X3009)|(~(in @ X3014 @ X3010)|(X3011 @ X3014))|~(subset @ X3010 @ (cartprod @ X3009 @ X3009)))&(((in @ (kpair @ (esk90_3 @ X3009 @ X3010 @ X3011) @ (esk91_3 @ X3009 @ X3010 @ X3011)) @ X3010)|(~(in @ X3014 @ X3010)|(X3011 @ X3014))|~(subset @ X3010 @ (cartprod @ X3009 @ X3009)))&(~(X3011 @ (kpair @ (esk90_3 @ X3009 @ X3010 @ X3011) @ (esk91_3 @ X3009 @ X3010 @ X3011)))|(~(in @ X3014 @ X3010)|(X3011 @ X3014))|~(subset @ X3010 @ (cartprod @ X3009 @ X3009))))))&((((in @ (esk92_3 @ X3015 @ X3016 @ X3017) @ X3015)|(subset @ X3016 @ X3017)|~(subset @ X3017 @ (cartprod @ X3015 @ X3015))|~(subset @ X3016 @ (cartprod @ X3015 @ X3015)))&(((in @ (esk93_3 @ X3015 @ X3016 @ X3017) @ X3015)|(subset @ X3016 @ X3017)|~(subset @ X3017 @ (cartprod @ X3015 @ X3015))|~(subset @ X3016 @ (cartprod @ X3015 @ X3015)))&(((in @ (kpair @ (esk92_3 @ X3015 @ X3016 @ X3017) @ (esk93_3 @ X3015 @ X3016 @ X3017)) @ X3016)|(subset @ X3016 @ X3017)|~(subset @ X3017 @ (cartprod @ X3015 @ X3015))|~(subset @ X3016 @ (cartprod @ X3015 @ X3015)))&(~(in @ (kpair @ (esk92_3 @ X3015 @ X3016 @ X3017) @ (esk93_3 @ X3015 @ X3016 @ X3017)) @ X3017)|(subset @ X3016 @ X3017)|~(subset @ X3017 @ (cartprod @ X3015 @ X3015))|~(subset @ X3016 @ (cartprod @ X3015 @ X3015))))))&(((((in @ (esk96_3 @ X3020 @ X3021 @ X3022) @ X3020)|((X3021)=(X3022))|(in @ (esk94_3 @ X3020 @ X3021 @ X3022) @ X3020)|~(subset @ X3022 @ (cartprod @ X3020 @ X3020))|~(subset @ X3021 @ (cartprod @ X3020 @ X3020)))&(((in @ (esk97_3 @ X3020 @ X3021 @ X3022) @ X3020)|((X3021)=(X3022))|(in @ (esk94_3 @ X3020 @ X3021 @ X3022) @ X3020)|~(subset @ X3022 @ (cartprod @ X3020 @ X3020))|~(subset @ X3021 @ (cartprod @ X3020 @ X3020)))&(((in @ (kpair @ (esk96_3 @ X3020 @ X3021 @ X3022) @ (esk97_3 @ X3020 @ X3021 @ X3022)) @ X3022)|((X3021)=(X3022))|(in @ (esk94_3 @ X3020 @ X3021 @ X3022) @ X3020)|~(subset @ X3022 @ (cartprod @ X3020 @ X3020))|~(subset @ X3021 @ (cartprod @ X3020 @ X3020)))&(~(in @ (kpair @ (esk96_3 @ X3020 @ X3021 @ X3022) @ (esk97_3 @ X3020 @ X3021 @ X3022)) @ X3021)|((X3021)=(X3022))|(in @ (esk94_3 @ X3020 @ X3021 @ X3022) @ X3020)|~(subset @ X3022 @ (cartprod @ X3020 @ X3020))|~(subset @ X3021 @ (cartprod @ X3020 @ X3020))))))&((((in @ (esk96_3 @ X3020 @ X3021 @ X3022) @ X3020)|((X3021)=(X3022))|(in @ (esk95_3 @ X3020 @ X3021 @ X3022) @ X3020)|~(subset @ X3022 @ (cartprod @ X3020 @ X3020))|~(subset @ X3021 @ (cartprod @ X3020 @ X3020)))&(((in @ (esk97_3 @ X3020 @ X3021 @ X3022) @ X3020)|((X3021)=(X3022))|(in @ (esk95_3 @ X3020 @ X3021 @ X3022) @ X3020)|~(subset @ X3022 @ (cartprod @ X3020 @ X3020))|~(subset @ X3021 @ (cartprod @ X3020 @ X3020)))&(((in @ (kpair @ (esk96_3 @ X3020 @ X3021 @ X3022) @ (esk97_3 @ X3020 @ X3021 @ X3022)) @ X3022)|((X3021)=(X3022))|(in @ (esk95_3 @ X3020 @ X3021 @ X3022) @ X3020)|~(subset @ X3022 @ (cartprod @ X3020 @ X3020))|~(subset @ X3021 @ (cartprod @ X3020 @ X3020)))&(~(in @ (kpair @ (esk96_3 @ X3020 @ X3021 @ X3022) @ (esk97_3 @ X3020 @ X3021 @ X3022)) @ X3021)|((X3021)=(X3022))|(in @ (esk95_3 @ X3020 @ X3021 @ X3022) @ X3020)|~(subset @ X3022 @ (cartprod @ X3020 @ X3020))|~(subset @ X3021 @ (cartprod @ X3020 @ X3020))))))&((((in @ (esk96_3 @ X3020 @ X3021 @ X3022) @ X3020)|((X3021)=(X3022))|(in @ (kpair @ (esk94_3 @ X3020 @ X3021 @ X3022) @ (esk95_3 @ X3020 @ X3021 @ X3022)) @ X3021)|~(subset @ X3022 @ (cartprod @ X3020 @ X3020))|~(subset @ X3021 @ (cartprod @ X3020 @ X3020)))&(((in @ (esk97_3 @ X3020 @ X3021 @ X3022) @ X3020)|((X3021)=(X3022))|(in @ (kpair @ (esk94_3 @ X3020 @ X3021 @ X3022) @ (esk95_3 @ X3020 @ X3021 @ X3022)) @ X3021)|~(subset @ X3022 @ (cartprod @ X3020 @ X3020))|~(subset @ X3021 @ (cartprod @ X3020 @ X3020)))&(((in @ (kpair @ (esk96_3 @ X3020 @ X3021 @ X3022) @ (esk97_3 @ X3020 @ X3021 @ X3022)) @ X3022)|((X3021)=(X3022))|(in @ (kpair @ (esk94_3 @ X3020 @ X3021 @ X3022) @ (esk95_3 @ X3020 @ X3021 @ X3022)) @ X3021)|~(subset @ X3022 @ (cartprod @ X3020 @ X3020))|~(subset @ X3021 @ (cartprod @ X3020 @ X3020)))&(~(in @ (kpair @ (esk96_3 @ X3020 @ X3021 @ X3022) @ (esk97_3 @ X3020 @ X3021 @ X3022)) @ X3021)|((X3021)=(X3022))|(in @ (kpair @ (esk94_3 @ X3020 @ X3021 @ X3022) @ (esk95_3 @ X3020 @ X3021 @ X3022)) @ X3021)|~(subset @ X3022 @ (cartprod @ X3020 @ X3020))|~(subset @ X3021 @ (cartprod @ X3020 @ X3020))))))&(((in @ (esk96_3 @ X3020 @ X3021 @ X3022) @ X3020)|((X3021)=(X3022))|~(in @ (kpair @ (esk94_3 @ X3020 @ X3021 @ X3022) @ (esk95_3 @ X3020 @ X3021 @ X3022)) @ X3022)|~(subset @ X3022 @ (cartprod @ X3020 @ X3020))|~(subset @ X3021 @ (cartprod @ X3020 @ X3020)))&(((in @ (esk97_3 @ X3020 @ X3021 @ X3022) @ X3020)|((X3021)=(X3022))|~(in @ (kpair @ (esk94_3 @ X3020 @ X3021 @ X3022) @ (esk95_3 @ X3020 @ X3021 @ X3022)) @ X3022)|~(subset @ X3022 @ (cartprod @ X3020 @ X3020))|~(subset @ X3021 @ (cartprod @ X3020 @ X3020)))&(((in @ (kpair @ (esk96_3 @ X3020 @ X3021 @ X3022) @ (esk97_3 @ X3020 @ X3021 @ X3022)) @ X3022)|((X3021)=(X3022))|~(in @ (kpair @ (esk94_3 @ X3020 @ X3021 @ X3022) @ (esk95_3 @ X3020 @ X3021 @ X3022)) @ X3022)|~(subset @ X3022 @ (cartprod @ X3020 @ X3020))|~(subset @ X3021 @ (cartprod @ X3020 @ X3020)))&(~(in @ (kpair @ (esk96_3 @ X3020 @ X3021 @ X3022) @ (esk97_3 @ X3020 @ X3021 @ X3022)) @ X3021)|((X3021)=(X3022))|~(in @ (kpair @ (esk94_3 @ X3020 @ X3021 @ X3022) @ (esk95_3 @ X3020 @ X3021 @ X3022)) @ X3022)|~(subset @ X3022 @ (cartprod @ X3020 @ X3020))|~(subset @ X3021 @ (cartprod @ X3020 @ X3020)))))))))&((~(subset @ X3028 @ (cartprod @ X3027 @ X3027))|(subset @ (breln1invset @ X3027 @ X3028) @ (cartprod @ X3027 @ X3027)))&((~(subset @ X3030 @ (cartprod @ X3029 @ X3029))|(~(in @ X3031 @ X3029)|(~(in @ X3032 @ X3029)|(~(in @ (kpair @ X3031 @ X3032) @ X3030)|(in @ (kpair @ X3032 @ X3031) @ (breln1invset @ X3029 @ X3030))))))&((~(subset @ X3034 @ (cartprod @ X3033 @ X3033))|(~(in @ X3035 @ X3033)|(~(in @ X3036 @ X3033)|(~(in @ (kpair @ X3036 @ X3035) @ (breln1invset @ X3033 @ X3034))|(in @ (kpair @ X3035 @ X3036) @ X3034)))))&((~(subset @ X3038 @ (cartprod @ X3037 @ X3037))|(~(subset @ X3039 @ (cartprod @ X3037 @ X3037))|(subset @ (breln1compset @ X3037 @ X3038 @ X3039) @ (cartprod @ X3037 @ X3037))))&((~(subset @ X3041 @ (cartprod @ X3040 @ X3040))|(~(subset @ X3042 @ (cartprod @ X3040 @ X3040))|(~(in @ X3043 @ X3040)|(~(in @ X3044 @ X3040)|(~(in @ X3045 @ X3040)|(~(in @ (kpair @ X3043 @ X3045) @ X3041)|(~(in @ (kpair @ X3045 @ X3044) @ X3042)|(in @ (kpair @ X3043 @ X3044) @ (breln1compset @ X3040 @ X3041 @ X3042)))))))))&(((((in @ (esk98_5 @ X3046 @ X3047 @ X3048 @ X3049 @ X3050) @ X3046)|~(in @ (kpair @ X3049 @ X3050) @ (breln1compset @ X3046 @ X3047 @ X3048))|~(in @ X3050 @ X3046)|~(in @ X3049 @ X3046)|~(subset @ X3048 @ (cartprod @ X3046 @ X3046))|~(subset @ X3047 @ (cartprod @ X3046 @ X3046)))&((in @ (kpair @ X3049 @ (esk98_5 @ X3046 @ X3047 @ X3048 @ X3049 @ X3050)) @ X3047)|~(in @ (kpair @ X3049 @ X3050) @ (breln1compset @ X3046 @ X3047 @ X3048))|~(in @ X3050 @ X3046)|~(in @ X3049 @ X3046)|~(subset @ X3048 @ (cartprod @ X3046 @ X3046))|~(subset @ X3047 @ (cartprod @ X3046 @ X3046))))&((in @ (kpair @ (esk98_5 @ X3046 @ X3047 @ X3048 @ X3049 @ X3050) @ X3050) @ X3048)|~(in @ (kpair @ X3049 @ X3050) @ (breln1compset @ X3046 @ X3047 @ X3048))|~(in @ X3050 @ X3046)|~(in @ X3049 @ X3046)|~(subset @ X3048 @ (cartprod @ X3046 @ X3046))|~(subset @ X3047 @ (cartprod @ X3046 @ X3046))))&((((in @ (esk99_6 @ X3052 @ X3053 @ X3054 @ X3055 @ X3056 @ X3057) @ X3052)|(X3057)|~(in @ (kpair @ X3055 @ X3056) @ (breln1compset @ X3052 @ X3053 @ X3054))|~(in @ X3056 @ X3052)|~(in @ X3055 @ X3052)|~(subset @ X3054 @ (cartprod @ X3052 @ X3052))|~(subset @ X3053 @ (cartprod @ X3052 @ X3052)))&(((in @ (kpair @ X3055 @ (esk99_6 @ X3052 @ X3053 @ X3054 @ X3055 @ X3056 @ X3057)) @ X3053)|(X3057)|~(in @ (kpair @ X3055 @ X3056) @ (breln1compset @ X3052 @ X3053 @ X3054))|~(in @ X3056 @ X3052)|~(in @ X3055 @ X3052)|~(subset @ X3054 @ (cartprod @ X3052 @ X3052))|~(subset @ X3053 @ (cartprod @ X3052 @ X3052)))&(((in @ (kpair @ (esk99_6 @ X3052 @ X3053 @ X3054 @ X3055 @ X3056 @ X3057) @ X3056) @ X3054)|(X3057)|~(in @ (kpair @ X3055 @ X3056) @ (breln1compset @ X3052 @ X3053 @ X3054))|~(in @ X3056 @ X3052)|~(in @ X3055 @ X3052)|~(subset @ X3054 @ (cartprod @ X3052 @ X3052))|~(subset @ X3053 @ (cartprod @ X3052 @ X3052)))&(~(X3057)|(X3057)|~(in @ (kpair @ X3055 @ X3056) @ (breln1compset @ X3052 @ X3053 @ X3054))|~(in @ X3056 @ X3052)|~(in @ X3055 @ X3052)|~(subset @ X3054 @ (cartprod @ X3052 @ X3052))|~(subset @ X3053 @ (cartprod @ X3052 @ X3052))))))&((subset @ esk101_0 @ (cartprod @ esk100_0 @ esk100_0))&((subset @ esk102_0 @ (cartprod @ esk100_0 @ esk100_0))&~(subset @ (binunion @ esk101_0 @ esk102_0) @ (cartprod @ esk100_0 @ esk100_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_396])])])])])])).
85.14/11.36	thf(c_0_398, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ X2 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_397])).
85.14/11.36	thf(c_0_399, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ (binunion @ X2 @ X4) @ (powerset @ X3))|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_397])).
85.14/11.36	thf(c_0_400, negated_conjecture, ~((subset @ (binunion @ esk101_0 @ esk102_0) @ (cartprod @ esk100_0 @ esk100_0))), inference(split_conjunct,[status(thm)],[c_0_397])).
85.14/11.36	thf(c_0_401, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((subset @ (binunion @ X2 @ X3) @ X4)|~((in @ X3 @ (powerset @ X4)))|~((in @ X2 @ (powerset @ X4))))), inference(spm,[status(thm)],[c_0_398, c_0_399])).
85.14/11.36	thf(c_0_402, negated_conjecture, (~((in @ esk102_0 @ (powerset @ (cartprod @ esk100_0 @ esk100_0))))|~((in @ esk101_0 @ (powerset @ (cartprod @ esk100_0 @ esk100_0))))), inference(spm,[status(thm)],[c_0_400, c_0_401])).
85.14/11.36	thf(c_0_403, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ X3))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_397])).
85.14/11.36	thf(c_0_404, negated_conjecture, (subset @ esk102_0 @ (cartprod @ esk100_0 @ esk100_0)), inference(split_conjunct,[status(thm)],[c_0_397])).
85.14/11.36	thf(c_0_405, negated_conjecture, ~((in @ esk101_0 @ (powerset @ (cartprod @ esk100_0 @ esk100_0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_402, c_0_403]), c_0_404])])).
85.14/11.36	thf(c_0_406, negated_conjecture, (subset @ esk101_0 @ (cartprod @ esk100_0 @ esk100_0)), inference(split_conjunct,[status(thm)],[c_0_397])).
85.14/11.36	thf(c_0_407, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_405, c_0_403]), c_0_406])]), ['proof']).
85.14/11.36	# SZS output end CNFRefutation
85.14/11.36	# Parsed axioms                        : 649
85.14/11.36	# Removed by relevancy pruning/SinE    : 0
85.14/11.36	# Initial clauses                      : 881
85.14/11.36	# Removed in clause preprocessing      : 379
85.14/11.36	# Initial clauses in saturation        : 502
85.14/11.36	# Processed clauses                    : 7171
85.14/11.36	# ...of these trivial                  : 51
85.14/11.36	# ...subsumed                          : 3957
85.14/11.36	# ...remaining for further processing  : 3163
85.14/11.36	# Other redundant clauses eliminated   : 111
85.14/11.36	# Clauses deleted for lack of memory   : 0
85.14/11.36	# Backward-subsumed                    : 152
85.14/11.36	# Backward-rewritten                   : 17
85.14/11.36	# Generated clauses                    : 318732
85.14/11.36	# ...of the previous two non-redundant : 314425
85.14/11.36	# ...aggressively subsumed             : 0
85.14/11.36	# Contextual simplify-reflections      : 97
85.14/11.36	# Paramodulations                      : 318504
85.14/11.36	# Factorizations                       : 74
85.14/11.36	# NegExts                              : 2
85.14/11.36	# Equation resolutions                 : 120
85.14/11.36	# Total rewrite steps                  : 27888
85.14/11.36	# Propositional unsat checks           : 0
85.14/11.36	#    Propositional check models        : 0
85.14/11.36	#    Propositional check unsatisfiable : 0
85.14/11.36	#    Propositional clauses             : 0
85.14/11.36	#    Propositional clauses after purity: 0
85.14/11.36	#    Propositional unsat core size     : 0
85.14/11.36	#    Propositional preprocessing time  : 0.000
85.14/11.36	#    Propositional encoding time       : 0.000
85.14/11.36	#    Propositional solver time         : 0.000
85.14/11.36	#    Success case prop preproc time    : 0.000
85.14/11.36	#    Success case prop encoding time   : 0.000
85.14/11.36	#    Success case prop solver time     : 0.000
85.14/11.36	# Current number of processed clauses  : 2533
85.14/11.36	#    Positive orientable unit clauses  : 63
85.14/11.36	#    Positive unorientable unit clauses: 0
85.14/11.36	#    Negative unit clauses             : 69
85.14/11.36	#    Non-unit-clauses                  : 2401
85.14/11.36	# Current number of unprocessed clauses: 307818
85.14/11.36	# ...number of literals in the above   : 1283407
85.14/11.36	# Current number of archived formulas  : 0
85.14/11.36	# Current number of archived clauses   : 612
85.14/11.36	# Clause-clause subsumption calls (NU) : 657959
85.14/11.36	# Rec. Clause-clause subsumption calls : 322136
85.14/11.36	# Non-unit clause-clause subsumptions  : 2606
85.14/11.36	# Unit Clause-clause subsumption calls : 5116
85.14/11.36	# Rewrite failures with RHS unbound    : 0
85.14/11.36	# BW rewrite match attempts            : 68
85.14/11.36	# BW rewrite match successes           : 15
85.14/11.36	# Condensation attempts                : 0
85.14/11.36	# Condensation successes               : 0
85.14/11.36	# Termbank termtop insertions          : 7034831
85.14/11.36	
85.14/11.36	# -------------------------------------------------
85.14/11.36	# User time                : 10.492 s
85.14/11.36	# System time              : 0.291 s
85.14/11.36	# Total time               : 10.783 s
85.14/11.36	# Maximum resident set size: 9516 pages
86.70/11.59	
86.70/11.59	# -------------------------------------------------
86.70/11.59	# User time                : 10.501 s
86.70/11.59	# System time              : 0.295 s
86.70/11.59	# Total time               : 10.796 s
86.70/11.59	# Maximum resident set size: 2820 pages
86.70/11.59	% E---3.1 exiting
86.70/11.60	EOF