0.10/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.12	% Command    : run_E %s %d THM
0.12/0.32	% Computer : n008.cluster.edu
0.12/0.32	% Model    : x86_64 x86_64
0.12/0.32	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.32	% Memory   : 8042.1875MB
0.12/0.32	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.32	% CPULimit   : 1440
0.12/0.32	% WCLimit    : 180
0.12/0.32	% DateTime   : Thu Jul  4 08:50:54 EDT 2024
0.12/0.33	% CPUTime    : 
0.20/0.47	Running higher-order theorem proving
0.20/0.52	Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p
2.12/0.94	# Version: 3.2.0-ho
2.12/0.94	# Preprocessing class: HSLMSLSSLLLCHFA.
2.12/0.94	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
2.12/0.94	# Starting ehoh_best5 with 180s (1) cores
2.12/0.94	# Starting almost_fo_3_lam with 180s (1) cores
2.12/0.94	# Starting new_bool_5 with 180s (1) cores
2.12/0.94	# Starting pre_casc_3 with 180s (1) cores
2.12/0.94	# Starting ho_unfolding_8 with 180s (1) cores
2.12/0.94	# Starting new_ho_10_cnf2 with 180s (1) cores
2.12/0.94	# Starting new_bool_3 with 180s (1) cores
2.12/0.94	# Starting new_ho_5 with 180s (1) cores
2.12/0.94	# new_bool_3 with pid 10492 completed with status 0
2.12/0.94	# Result found by new_bool_3
2.12/0.94	# Preprocessing class: HSLMSLSSLLLCHFA.
2.12/0.94	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
2.12/0.94	# Starting ehoh_best5 with 180s (1) cores
2.12/0.94	# Starting almost_fo_3_lam with 180s (1) cores
2.12/0.94	# Starting new_bool_5 with 180s (1) cores
2.12/0.94	# Starting pre_casc_3 with 180s (1) cores
2.12/0.94	# Starting ho_unfolding_8 with 180s (1) cores
2.12/0.94	# Starting new_ho_10_cnf2 with 180s (1) cores
2.12/0.94	# Starting new_bool_3 with 180s (1) cores
2.12/0.94	# SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
2.12/0.94	# Search class: HGHSM-FSLM32-MHFMMSBN
2.12/0.94	# Scheduled 9 strats onto 1 cores with 180 seconds (180 total)
2.12/0.94	# Starting ho_unfolding_8 with 37s (1) cores
2.12/0.94	# ho_unfolding_8 with pid 10494 completed with status 0
2.12/0.94	# Result found by ho_unfolding_8
2.12/0.94	# Preprocessing class: HSLMSLSSLLLCHFA.
2.12/0.94	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
2.12/0.94	# Starting ehoh_best5 with 180s (1) cores
2.12/0.94	# Starting almost_fo_3_lam with 180s (1) cores
2.12/0.94	# Starting new_bool_5 with 180s (1) cores
2.12/0.94	# Starting pre_casc_3 with 180s (1) cores
2.12/0.94	# Starting ho_unfolding_8 with 180s (1) cores
2.12/0.94	# Starting new_ho_10_cnf2 with 180s (1) cores
2.12/0.94	# Starting new_bool_3 with 180s (1) cores
2.12/0.94	# SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
2.12/0.94	# Search class: HGHSM-FSLM32-MHFMMSBN
2.12/0.94	# Scheduled 9 strats onto 1 cores with 180 seconds (180 total)
2.12/0.94	# Starting ho_unfolding_8 with 37s (1) cores
2.12/0.94	# Preprocessing time       : 0.075 s
2.12/0.94	# Presaturation interreduction done
2.12/0.94	
2.12/0.94	# Proof found!
2.12/0.94	# SZS status Theorem
2.12/0.94	# SZS output start CNFRefutation
2.12/0.94	thf(decl_22, type, in: $i > $i > $o).
2.12/0.94	thf(decl_23, type, exu: ($i > $o) > $o).
2.12/0.94	thf(decl_24, type, setextAx: $o).
2.12/0.94	thf(decl_25, type, emptyset: $i).
2.12/0.94	thf(decl_26, type, emptysetAx: $o).
2.12/0.94	thf(decl_27, type, setadjoin: $i > $i > $i).
2.12/0.94	thf(decl_28, type, setadjoinAx: $o).
2.12/0.94	thf(decl_29, type, powerset: $i > $i).
2.12/0.94	thf(decl_30, type, powersetAx: $o).
2.12/0.94	thf(decl_31, type, setunion: $i > $i).
2.12/0.94	thf(decl_32, type, setunionAx: $o).
2.12/0.94	thf(decl_33, type, omega: $i).
2.12/0.94	thf(decl_34, type, omega0Ax: $o).
2.12/0.94	thf(decl_35, type, omegaSAx: $o).
2.12/0.94	thf(decl_36, type, omegaIndAx: $o).
2.12/0.94	thf(decl_37, type, replAx: $o).
2.12/0.94	thf(decl_38, type, foundationAx: $o).
2.12/0.94	thf(decl_39, type, wellorderingAx: $o).
2.12/0.94	thf(decl_40, type, descr: ($i > $o) > $i).
2.12/0.94	thf(decl_41, type, descrp: $o).
2.12/0.94	thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
2.12/0.94	thf(decl_43, type, dsetconstrI: $o).
2.12/0.94	thf(decl_44, type, dsetconstrEL: $o).
2.12/0.94	thf(decl_45, type, dsetconstrER: $o).
2.12/0.94	thf(decl_46, type, exuE1: $o).
2.12/0.94	thf(decl_47, type, prop2set: $o > $i).
2.12/0.94	thf(decl_48, type, prop2setE: $o).
2.12/0.94	thf(decl_49, type, emptysetE: $o).
2.12/0.94	thf(decl_50, type, emptysetimpfalse: $o).
2.12/0.94	thf(decl_51, type, notinemptyset: $o).
2.12/0.94	thf(decl_52, type, exuE3e: $o).
2.12/0.94	thf(decl_53, type, setext: $o).
2.12/0.94	thf(decl_54, type, emptyI: $o).
2.12/0.94	thf(decl_55, type, noeltsimpempty: $o).
2.12/0.94	thf(decl_56, type, setbeta: $o).
2.12/0.94	thf(decl_57, type, nonempty: $i > $o).
2.12/0.94	thf(decl_58, type, nonemptyE1: $o).
2.12/0.94	thf(decl_59, type, nonemptyI: $o).
2.12/0.94	thf(decl_60, type, nonemptyI1: $o).
2.12/0.94	thf(decl_61, type, setadjoinIL: $o).
2.12/0.94	thf(decl_62, type, emptyinunitempty: $o).
2.12/0.94	thf(decl_63, type, setadjoinIR: $o).
2.12/0.94	thf(decl_64, type, setadjoinE: $o).
2.12/0.94	thf(decl_65, type, setadjoinOr: $o).
2.12/0.94	thf(decl_66, type, setoftrueEq: $o).
2.12/0.94	thf(decl_67, type, powersetI: $o).
2.12/0.94	thf(decl_68, type, emptyinPowerset: $o).
2.12/0.94	thf(decl_69, type, emptyInPowerset: $o).
2.12/0.94	thf(decl_70, type, powersetE: $o).
2.12/0.94	thf(decl_71, type, setunionI: $o).
2.12/0.94	thf(decl_72, type, setunionE: $o).
2.12/0.94	thf(decl_73, type, subPowSU: $o).
2.12/0.94	thf(decl_74, type, exuE2: $o).
2.12/0.94	thf(decl_75, type, nonemptyImpWitness: $o).
2.12/0.94	thf(decl_76, type, uniqinunit: $o).
2.12/0.94	thf(decl_77, type, notinsingleton: $o).
2.12/0.94	thf(decl_78, type, eqinunit: $o).
2.12/0.94	thf(decl_79, type, singletonsswitch: $o).
2.12/0.94	thf(decl_80, type, upairsetE: $o).
2.12/0.94	thf(decl_81, type, upairsetIL: $o).
2.12/0.94	thf(decl_82, type, upairsetIR: $o).
2.12/0.94	thf(decl_83, type, emptyE1: $o).
2.12/0.94	thf(decl_84, type, vacuousDall: $o).
2.12/0.94	thf(decl_85, type, quantDeMorgan1: $o).
2.12/0.94	thf(decl_86, type, quantDeMorgan2: $o).
2.12/0.94	thf(decl_87, type, quantDeMorgan3: $o).
2.12/0.94	thf(decl_88, type, quantDeMorgan4: $o).
2.12/0.94	thf(decl_89, type, prop2setI: $o).
2.12/0.94	thf(decl_91, type, prop2set2propI: $o).
2.12/0.94	thf(decl_92, type, notdexE: $o).
2.12/0.94	thf(decl_93, type, notdallE: $o).
2.12/0.94	thf(decl_94, type, exuI1: $o).
2.12/0.94	thf(decl_95, type, exuI3: $o).
2.12/0.94	thf(decl_96, type, exuI2: $o).
2.12/0.94	thf(decl_97, type, inCongP: $o).
2.12/0.94	thf(decl_98, type, in__Cong: $o).
2.12/0.94	thf(decl_99, type, exuE3u: $o).
2.12/0.94	thf(decl_100, type, exu__Cong: $o).
2.12/0.94	thf(decl_101, type, emptyset__Cong: $o).
2.12/0.94	thf(decl_102, type, setadjoin__Cong: $o).
2.12/0.94	thf(decl_103, type, powerset__Cong: $o).
2.12/0.94	thf(decl_104, type, setunion__Cong: $o).
2.12/0.94	thf(decl_105, type, omega__Cong: $o).
2.12/0.94	thf(decl_106, type, exuEu: $o).
2.12/0.94	thf(decl_107, type, descr__Cong: $o).
2.12/0.94	thf(decl_108, type, dsetconstr__Cong: $o).
2.12/0.94	thf(decl_109, type, subset: $i > $i > $o).
2.12/0.94	thf(decl_112, type, subsetI1: $o).
2.12/0.94	thf(decl_113, type, eqimpsubset2: $o).
2.12/0.94	thf(decl_114, type, eqimpsubset1: $o).
2.12/0.94	thf(decl_115, type, subsetI2: $o).
2.12/0.94	thf(decl_116, type, emptysetsubset: $o).
2.12/0.94	thf(decl_117, type, subsetE: $o).
2.12/0.94	thf(decl_118, type, subsetE2: $o).
2.12/0.94	thf(decl_119, type, notsubsetI: $o).
2.12/0.94	thf(decl_120, type, notequalI1: $o).
2.12/0.94	thf(decl_121, type, notequalI2: $o).
2.12/0.94	thf(decl_122, type, subsetRefl: $o).
2.12/0.94	thf(decl_123, type, subsetTrans: $o).
2.12/0.94	thf(decl_124, type, setadjoinSub: $o).
2.12/0.94	thf(decl_125, type, setadjoinSub2: $o).
2.12/0.94	thf(decl_126, type, subset2powerset: $o).
2.12/0.94	thf(decl_127, type, setextsub: $o).
2.12/0.94	thf(decl_128, type, subsetemptysetimpeq: $o).
2.12/0.94	thf(decl_129, type, powersetI1: $o).
2.12/0.94	thf(decl_130, type, powersetE1: $o).
2.12/0.94	thf(decl_131, type, inPowerset: $o).
2.12/0.94	thf(decl_132, type, powersetsubset: $o).
2.12/0.94	thf(decl_133, type, sepInPowerset: $o).
2.12/0.94	thf(decl_134, type, sepSubset: $o).
2.12/0.94	thf(decl_135, type, binunion: $i > $i > $i).
2.12/0.94	thf(decl_136, type, binunionIL: $o).
2.12/0.94	thf(decl_137, type, upairset2IR: $o).
2.12/0.94	thf(decl_138, type, binunionIR: $o).
2.12/0.94	thf(decl_139, type, binunionEcases: $o).
2.12/0.94	thf(decl_140, type, binunionE: $o).
2.12/0.94	thf(decl_141, type, binunionLsub: $o).
2.12/0.94	thf(decl_142, type, binunionRsub: $o).
2.12/0.94	thf(decl_143, type, binintersect: $i > $i > $i).
2.12/0.94	thf(decl_144, type, binintersectI: $o).
2.12/0.94	thf(decl_145, type, binintersectSubset5: $o).
2.12/0.94	thf(decl_146, type, binintersectEL: $o).
2.12/0.94	thf(decl_147, type, binintersectLsub: $o).
2.12/0.94	thf(decl_148, type, binintersectSubset2: $o).
2.12/0.94	thf(decl_149, type, binintersectSubset3: $o).
2.12/0.94	thf(decl_150, type, binintersectER: $o).
2.12/0.94	thf(decl_151, type, disjointsetsI1: $o).
2.12/0.94	thf(decl_152, type, binintersectRsub: $o).
2.12/0.94	thf(decl_153, type, binintersectSubset4: $o).
2.12/0.94	thf(decl_154, type, binintersectSubset1: $o).
2.12/0.94	thf(decl_155, type, bs114d: $o).
2.12/0.94	thf(decl_157, type, setminus: $i > $i > $i).
2.12/0.94	thf(decl_158, type, setminusI: $o).
2.12/0.94	thf(decl_159, type, setminusEL: $o).
2.12/0.94	thf(decl_160, type, setminusER: $o).
2.12/0.94	thf(decl_161, type, setminusSubset2: $o).
2.12/0.94	thf(decl_162, type, setminusERneg: $o).
2.12/0.94	thf(decl_163, type, setminusELneg: $o).
2.12/0.94	thf(decl_164, type, setminusILneg: $o).
2.12/0.94	thf(decl_165, type, setminusIRneg: $o).
2.12/0.94	thf(decl_166, type, setminusLsub: $o).
2.12/0.94	thf(decl_167, type, setminusSubset1: $o).
2.12/0.94	thf(decl_168, type, symdiff: $i > $i > $i).
2.12/0.94	thf(decl_169, type, symdiffE: $o).
2.12/0.94	thf(decl_170, type, symdiffI1: $o).
2.12/0.94	thf(decl_171, type, symdiffI2: $o).
2.12/0.94	thf(decl_172, type, symdiffIneg1: $o).
2.12/0.94	thf(decl_173, type, symdiffIneg2: $o).
2.12/0.94	thf(decl_174, type, iskpair: $i > $o).
2.12/0.94	thf(decl_175, type, secondinupair: $o).
2.12/0.94	thf(decl_176, type, setukpairIL: $o).
2.12/0.94	thf(decl_177, type, setukpairIR: $o).
2.12/0.94	thf(decl_178, type, kpairiskpair: $o).
2.12/0.94	thf(decl_179, type, kpair: $i > $i > $i).
2.12/0.94	thf(decl_180, type, kpairp: $o).
2.12/0.94	thf(decl_181, type, cartprod: $i > $i > $i).
2.12/0.94	thf(decl_182, type, singletonsubset: $o).
2.12/0.94	thf(decl_183, type, singletoninpowerset: $o).
2.12/0.94	thf(decl_184, type, singletoninpowunion: $o).
2.12/0.94	thf(decl_185, type, upairset2E: $o).
2.12/0.94	thf(decl_186, type, upairsubunion: $o).
2.12/0.94	thf(decl_187, type, upairinpowunion: $o).
2.12/0.94	thf(decl_188, type, ubforcartprodlem1: $o).
2.12/0.94	thf(decl_189, type, ubforcartprodlem2: $o).
2.12/0.94	thf(decl_190, type, ubforcartprodlem3: $o).
2.12/0.94	thf(decl_191, type, cartprodpairin: $o).
2.12/0.94	thf(decl_192, type, cartprodmempair1: $o).
2.12/0.94	thf(decl_193, type, cartprodmempair: $o).
2.12/0.94	thf(decl_194, type, setunionE2: $o).
2.12/0.94	thf(decl_195, type, setunionsingleton1: $o).
2.12/0.94	thf(decl_196, type, setunionsingleton2: $o).
2.12/0.94	thf(decl_197, type, setunionsingleton: $o).
2.12/0.94	thf(decl_198, type, singleton: $i > $o).
2.12/0.94	thf(decl_199, type, singletonprop: $o).
2.12/0.94	thf(decl_200, type, ex1: $i > ($i > $o) > $o).
2.12/0.94	thf(decl_201, type, ex1E1: $o).
2.12/0.94	thf(decl_202, type, ex1I: $o).
2.12/0.94	thf(decl_203, type, ex1I2: $o).
2.12/0.94	thf(decl_204, type, singletonsuniq: $o).
2.12/0.94	thf(decl_209, type, setukpairinjL1: $o).
2.12/0.94	thf(decl_210, type, kfstsingleton: $o).
2.12/0.94	thf(decl_211, type, theprop: $o).
2.12/0.94	thf(decl_212, type, kfst: $i > $i).
2.12/0.94	thf(decl_213, type, kfstpairEq: $o).
2.12/0.94	thf(decl_214, type, cartprodfstin: $o).
2.12/0.94	thf(decl_215, type, setukpairinjL2: $o).
2.12/0.94	thf(decl_216, type, setukpairinjL: $o).
2.12/0.94	thf(decl_217, type, setukpairinjR11: $o).
2.12/0.94	thf(decl_218, type, setukpairinjR12: $o).
2.12/0.94	thf(decl_219, type, setukpairinjR1: $o).
2.12/0.94	thf(decl_220, type, upairequniteq: $o).
2.12/0.94	thf(decl_221, type, setukpairinjR2: $o).
2.12/0.94	thf(decl_222, type, setukpairinjR: $o).
2.12/0.94	thf(decl_223, type, ksndsingleton: $o).
2.12/0.94	thf(decl_224, type, ksnd: $i > $i).
2.12/0.94	thf(decl_225, type, ksndpairEq: $o).
2.12/0.94	thf(decl_226, type, kpairsurjEq: $o).
2.12/0.94	thf(decl_227, type, cartprodsndin: $o).
2.12/0.94	thf(decl_228, type, cartprodpairmemEL: $o).
2.12/0.94	thf(decl_229, type, cartprodpairmemER: $o).
2.12/0.94	thf(decl_230, type, cartprodmempaircEq: $o).
2.12/0.94	thf(decl_231, type, cartprodfstpairEq: $o).
2.12/0.94	thf(decl_232, type, cartprodsndpairEq: $o).
2.12/0.94	thf(decl_233, type, cartprodpairsurjEq: $o).
2.12/0.94	thf(decl_234, type, breln: $i > $i > $i > $o).
2.12/0.94	thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
2.12/0.94	thf(decl_236, type, dpsetconstrI: $o).
2.12/0.94	thf(decl_237, type, dpsetconstrSub: $o).
2.12/0.94	thf(decl_238, type, setOfPairsIsBReln: $o).
2.12/0.94	thf(decl_239, type, dpsetconstrERa: $o).
2.12/0.94	thf(decl_240, type, dpsetconstrEL1: $o).
2.12/0.94	thf(decl_241, type, dpsetconstrEL2: $o).
2.12/0.94	thf(decl_242, type, dpsetconstrER: $o).
2.12/0.94	thf(decl_243, type, func: $i > $i > $i > $o).
2.12/0.94	thf(decl_244, type, funcSet: $i > $i > $i).
2.12/0.94	thf(decl_245, type, funcImageSingleton: $o).
2.12/0.94	thf(decl_246, type, apProp: $o).
2.12/0.94	thf(decl_247, type, ap: $i > $i > $i > $i > $i).
2.12/0.94	thf(decl_248, type, app: $o).
2.12/0.94	thf(decl_249, type, infuncsetfunc: $o).
2.12/0.94	thf(decl_250, type, ap2p: $o).
2.12/0.94	thf(decl_251, type, funcinfuncset: $o).
2.12/0.94	thf(decl_252, type, lamProp: $o).
2.12/0.94	thf(decl_253, type, lam: $i > $i > ($i > $i) > $i).
2.12/0.94	thf(decl_254, type, lamp: $o).
2.12/0.94	thf(decl_255, type, lam2p: $o).
2.12/0.94	thf(decl_256, type, brelnall1: $o).
2.12/0.94	thf(decl_257, type, brelnall2: $o).
2.12/0.94	thf(decl_258, type, ex1E2: $o).
2.12/0.94	thf(decl_259, type, funcGraphProp1: $o).
2.12/0.94	thf(decl_260, type, funcGraphProp3: $o).
2.12/0.94	thf(decl_261, type, funcGraphProp2: $o).
2.12/0.94	thf(decl_262, type, funcextLem: $o).
2.12/0.94	thf(decl_263, type, funcGraphProp4: $o).
2.12/0.94	thf(decl_264, type, subbreln: $o).
2.12/0.94	thf(decl_265, type, eqbreln: $o).
2.12/0.94	thf(decl_266, type, funcext: $o).
2.12/0.94	thf(decl_267, type, funcext2: $o).
2.12/0.94	thf(decl_268, type, ap2apEq1: $o).
2.12/0.94	thf(decl_269, type, ap2apEq2: $o).
2.12/0.94	thf(decl_270, type, beta1: $o).
2.12/0.94	thf(decl_271, type, eta1: $o).
2.12/0.94	thf(decl_272, type, lam2lamEq: $o).
2.12/0.94	thf(decl_273, type, beta2: $o).
2.12/0.94	thf(decl_274, type, eta2: $o).
2.12/0.94	thf(decl_275, type, iffalseProp1: $o).
2.12/0.94	thf(decl_276, type, iffalseProp2: $o).
2.12/0.94	thf(decl_277, type, iftrueProp1: $o).
2.12/0.94	thf(decl_278, type, iftrueProp2: $o).
2.12/0.94	thf(decl_279, type, ifSingleton: $o).
2.12/0.94	thf(decl_280, type, if: $i > $o > $i > $i > $i).
2.12/0.94	thf(decl_281, type, ifp: $o).
2.12/0.94	thf(decl_282, type, theeq: $o).
2.12/0.94	thf(decl_283, type, iftrue: $o).
2.12/0.94	thf(decl_284, type, iffalse: $o).
2.12/0.94	thf(decl_285, type, iftrueorfalse: $o).
2.12/0.94	thf(decl_286, type, binintersectT_lem: $o).
2.12/0.94	thf(decl_287, type, binunionT_lem: $o).
2.12/0.94	thf(decl_288, type, powersetT_lem: $o).
2.12/0.94	thf(decl_289, type, setminusT_lem: $o).
2.12/0.94	thf(decl_290, type, complementT_lem: $o).
2.12/0.94	thf(decl_291, type, setextT: $o).
2.12/0.94	thf(decl_292, type, subsetTI: $o).
2.12/0.94	thf(decl_293, type, powersetTI1: $o).
2.12/0.94	thf(decl_294, type, powersetTE1: $o).
2.12/0.94	thf(decl_295, type, complementTI1: $o).
2.12/0.94	thf(decl_296, type, complementTE1: $o).
2.12/0.94	thf(decl_297, type, binintersectTELcontra: $o).
2.12/0.94	thf(decl_298, type, binintersectTERcontra: $o).
2.12/0.94	thf(decl_299, type, contrasubsetT: $o).
2.12/0.94	thf(decl_300, type, contrasubsetT1: $o).
2.12/0.94	thf(decl_301, type, contrasubsetT2: $o).
2.12/0.94	thf(decl_302, type, contrasubsetT3: $o).
2.12/0.94	thf(decl_303, type, doubleComplementI1: $o).
2.12/0.94	thf(decl_304, type, doubleComplementE1: $o).
2.12/0.94	thf(decl_305, type, doubleComplementSub1: $o).
2.12/0.94	thf(decl_306, type, doubleComplementSub2: $o).
2.12/0.94	thf(decl_307, type, doubleComplementEq: $o).
2.12/0.94	thf(decl_308, type, complementTnotintersectT: $o).
2.12/0.94	thf(decl_309, type, complementImpComplementIntersect: $o).
2.12/0.94	thf(decl_310, type, complementSubsetComplementIntersect: $o).
2.12/0.94	thf(decl_311, type, complementInPowersetComplementIntersect: $o).
2.12/0.94	thf(decl_312, type, contraSubsetComplement: $o).
2.12/0.94	thf(decl_313, type, complementTcontraSubset: $o).
2.12/0.94	thf(decl_314, type, binunionTILcontra: $o).
2.12/0.94	thf(decl_315, type, binunionTIRcontra: $o).
2.12/0.94	thf(decl_316, type, inIntersectImpInUnion: $o).
2.12/0.94	thf(decl_317, type, inIntersectImpInUnion2: $o).
2.12/0.94	thf(decl_318, type, inIntersectImpInIntersectUnions: $o).
2.12/0.94	thf(decl_319, type, intersectInPowersetIntersectUnions: $o).
2.12/0.94	thf(decl_320, type, inComplementUnionImpNotIn1: $o).
2.12/0.94	thf(decl_321, type, inComplementUnionImpInComplement1: $o).
2.12/0.94	thf(decl_322, type, binunionTE: $o).
2.12/0.94	thf(decl_323, type, binunionTEcontra: $o).
2.12/0.94	thf(decl_324, type, demorgan2a1: $o).
2.12/0.94	thf(decl_325, type, complementUnionInPowersetComplement: $o).
2.12/0.94	thf(decl_326, type, demorgan2a2: $o).
2.12/0.94	thf(decl_327, type, demorgan1a: $o).
2.12/0.94	thf(decl_328, type, demorgan1b: $o).
2.12/0.94	thf(decl_329, type, demorgan1: $o).
2.12/0.94	thf(decl_330, type, demorgan2a: $o).
2.12/0.94	thf(decl_331, type, demorgan2b2: $o).
2.12/0.94	thf(decl_332, type, demorgan2b: $o).
2.12/0.94	thf(decl_333, type, demorgan2: $o).
2.12/0.94	thf(decl_334, type, woz13rule0: $o).
2.12/0.94	thf(decl_335, type, woz13rule1: $o).
2.12/0.94	thf(decl_336, type, woz13rule2: $o).
2.12/0.94	thf(decl_337, type, woz13rule3: $o).
2.12/0.94	thf(decl_338, type, woz13rule4: $o).
2.12/0.94	thf(decl_339, type, woz1_1: $o).
2.12/0.94	thf(decl_340, type, woz1_2: $o).
2.12/0.94	thf(decl_341, type, woz1_3: $o).
2.12/0.94	thf(decl_342, type, woz1_4: $o).
2.12/0.94	thf(decl_343, type, woz1_5: $o).
2.12/0.94	thf(decl_344, type, breln1: $i > $i > $o).
2.12/0.94	thf(decl_345, type, breln1all2: $o).
2.12/0.94	thf(decl_346, type, breln1Set: $i > $i).
2.12/0.94	thf(decl_347, type, breln1SetBreln1: $o).
2.12/0.94	thf(decl_354, type, choice2fnsingleton: $o).
2.12/0.94	thf(decl_355, type, setOfPairsIsBReln1: $o).
2.12/0.94	thf(decl_356, type, breln1all1: $o).
2.12/0.94	thf(decl_357, type, subbreln1: $o).
2.12/0.94	thf(decl_358, type, eqbreln1: $o).
2.12/0.94	thf(decl_359, type, breln1invset: $i > $i > $i).
2.12/0.94	thf(decl_360, type, breln1invprop: $o).
2.12/0.94	thf(decl_361, type, epred1_0: $o).
2.12/0.94	thf(decl_362, type, esk1_2: $i > $i > $i).
2.12/0.94	thf(decl_363, type, esk2_2: $i > $i > $i).
2.12/0.94	thf(decl_364, type, esk3_2: $i > $i > $i).
2.12/0.94	thf(decl_365, type, esk4_1: $i > $i).
2.12/0.94	thf(decl_366, type, esk5_2: ($i > $i > $o) > $i > $i).
2.12/0.94	thf(decl_367, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
2.12/0.94	thf(decl_368, type, esk7_2: ($i > $i > $o) > $i > $i).
2.12/0.94	thf(decl_369, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
2.12/0.94	thf(decl_370, type, esk9_1: $i > $i).
2.12/0.94	thf(decl_371, type, esk10_2: ($i > $o) > $i > $i).
2.12/0.94	thf(decl_372, type, esk11_2: ($i > $o) > $i > $i).
2.12/0.94	thf(decl_373, type, esk12_1: ($i > $o) > $i).
2.12/0.94	thf(decl_374, type, esk13_2: ($i > $o) > $i > $i).
2.12/0.94	thf(decl_375, type, esk14_1: ($i > $o) > $i).
2.12/0.94	thf(decl_376, type, esk15_2: $i > $i > $i).
2.12/0.94	thf(decl_377, type, esk16_2: $i > $i > $i).
2.12/0.94	thf(decl_378, type, esk17_1: $i > $i).
2.12/0.94	thf(decl_379, type, esk18_1: $i > $i).
2.12/0.94	thf(decl_380, type, esk19_1: $i > $i).
2.12/0.94	thf(decl_381, type, esk20_2: $i > $i > $i).
2.12/0.94	thf(decl_382, type, esk21_3: $i > $i > $o > $i).
2.12/0.94	thf(decl_383, type, esk22_2: ($i > $o) > $i > $i).
2.12/0.94	thf(decl_384, type, esk23_1: ($i > $o) > $i).
2.12/0.94	thf(decl_385, type, esk24_1: $i > $i).
2.12/0.94	thf(decl_386, type, esk25_2: $i > ($i > $o) > $i).
2.12/0.94	thf(decl_387, type, esk26_2: $i > ($i > $o) > $i).
2.12/0.94	thf(decl_388, type, esk27_2: $i > ($i > $o) > $i).
2.12/0.94	thf(decl_389, type, esk28_2: $i > ($i > $o) > $i).
2.12/0.94	thf(decl_390, type, esk29_2: $i > ($i > $o) > $i).
2.12/0.94	thf(decl_391, type, esk30_2: $i > ($i > $o) > $i).
2.12/0.94	thf(decl_392, type, esk31_2: ($i > $o) > $i > $i).
2.12/0.94	thf(decl_393, type, esk32_1: ($i > $o) > $i).
2.12/0.94	thf(decl_394, type, esk33_1: ($i > $o) > $i).
2.12/0.94	thf(decl_395, type, esk34_1: ($i > $o) > $i).
2.12/0.94	thf(decl_396, type, esk35_1: ($i > $o) > $i).
2.12/0.94	thf(decl_397, type, esk36_2: ($i > $o) > $i > $i).
2.12/0.94	thf(decl_398, type, esk37_1: ($i > $o) > $i).
2.12/0.94	thf(decl_399, type, esk38_2: ($i > $o) > $i > $i).
2.12/0.94	thf(decl_400, type, esk39_2: ($i > $o) > ($i > $o) > $i).
2.12/0.94	thf(decl_401, type, esk40_2: ($i > $o) > ($i > $o) > $i).
2.12/0.94	thf(decl_402, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
2.12/0.94	thf(decl_403, type, esk42_2: ($i > $o) > ($i > $o) > $i).
2.12/0.94	thf(decl_404, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
2.12/0.94	thf(decl_405, type, esk44_2: ($i > $o) > ($i > $o) > $i).
2.12/0.94	thf(decl_406, type, esk45_2: ($i > $o) > $i > $i).
2.12/0.94	thf(decl_407, type, esk46_2: ($i > $o) > ($i > $o) > $i).
2.12/0.94	thf(decl_408, type, esk47_2: ($i > $o) > ($i > $o) > $i).
2.12/0.94	thf(decl_409, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
2.12/0.94	thf(decl_410, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
2.12/0.94	thf(decl_411, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
2.12/0.94	thf(decl_412, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
2.12/0.94	thf(decl_413, type, esk52_2: $i > $i > $i).
2.12/0.94	thf(decl_414, type, esk53_2: $i > $i > $i).
2.12/0.94	thf(decl_415, type, esk54_2: $i > $i > $i).
2.12/0.94	thf(decl_416, type, esk55_3: $i > $i > $i > $i).
2.12/0.94	thf(decl_417, type, esk56_3: $i > $i > $i > $i).
2.12/0.94	thf(decl_418, type, esk57_2: $i > $i > $i).
2.12/0.94	thf(decl_419, type, esk58_2: $i > ($i > $o) > $i).
2.12/0.94	thf(decl_420, type, esk59_2: $i > ($i > $o) > $i).
2.12/0.94	thf(decl_421, type, esk60_2: $i > ($i > $o) > $i).
2.12/0.94	thf(decl_422, type, esk61_3: $i > ($i > $o) > $i > $i).
2.12/0.94	thf(decl_423, type, esk62_2: $i > ($i > $o) > $i).
2.12/0.94	thf(decl_424, type, esk63_2: $i > ($i > $o) > $i).
2.12/0.94	thf(decl_425, type, esk64_3: $i > $i > ($i > $i) > $i).
2.12/0.94	thf(decl_426, type, esk65_3: $i > $i > ($i > $i) > $i).
2.12/0.94	thf(decl_427, type, esk66_3: $i > $i > ($i > $i) > $i).
2.12/0.94	thf(decl_428, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
2.12/0.94	thf(decl_429, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
2.12/0.94	thf(decl_430, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
2.12/0.94	thf(decl_431, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
2.12/0.94	thf(decl_432, type, esk71_4: $i > $i > $i > $i > $i).
2.12/0.94	thf(decl_433, type, esk72_4: $i > $i > $i > $i > $i).
2.12/0.94	thf(decl_434, type, esk73_4: $i > $i > $i > $i > $i).
2.12/0.94	thf(decl_435, type, esk74_4: $i > $i > $i > $i > $i).
2.12/0.94	thf(decl_436, type, esk75_4: $i > $i > $i > $i > $i).
2.12/0.94	thf(decl_437, type, esk76_4: $i > $i > $i > $i > $i).
2.12/0.94	thf(decl_438, type, esk77_4: $i > $i > $i > $i > $i).
2.12/0.94	thf(decl_439, type, esk78_4: $i > $i > $i > $i > $i).
2.12/0.94	thf(decl_440, type, esk79_4: $i > $i > $i > $i > $i).
2.12/0.94	thf(decl_441, type, esk80_3: $i > $i > ($i > $i) > $i).
2.12/0.94	thf(decl_442, type, esk81_3: $i > $i > ($i > $i) > $i).
2.12/0.94	thf(decl_443, type, esk82_3: $i > $i > ($i > $i) > $i).
2.12/0.94	thf(decl_444, type, esk83_3: $i > $i > $i > $i).
2.12/0.94	thf(decl_445, type, esk84_3: $i > $i > $i > $i).
2.12/0.94	thf(decl_446, type, esk85_3: $i > $i > $i > $i).
2.12/0.94	thf(decl_447, type, esk86_3: $i > $i > $i > $i).
2.12/0.94	thf(decl_448, type, esk87_3: $i > $i > ($i > $o) > $i).
2.12/0.94	thf(decl_449, type, esk88_3: $i > $i > ($i > $o) > $i).
2.12/0.94	thf(decl_450, type, esk89_3: $i > $i > ($i > $o) > $i).
2.12/0.94	thf(decl_451, type, esk90_3: $i > $i > ($i > $o) > $i).
2.12/0.94	thf(decl_452, type, esk91_3: $i > $i > $i > $i).
2.12/0.94	thf(decl_453, type, esk92_3: $i > $i > $i > $i).
2.12/0.94	thf(decl_454, type, esk93_3: $i > $i > $i > $i).
2.12/0.94	thf(decl_455, type, esk94_3: $i > $i > $i > $i).
2.12/0.94	thf(decl_456, type, esk95_3: $i > $i > $i > $i).
2.12/0.94	thf(decl_457, type, esk96_3: $i > $i > $i > $i).
2.12/0.94	thf(decl_458, type, esk97_0: $i).
2.12/0.94	thf(decl_459, type, esk98_0: $i).
2.12/0.94	thf(decl_460, type, esk99_0: $i).
2.12/0.94	thf(decl_461, type, esk100_0: $i).
2.12/0.94	thf(breln1, axiom, ((breln1)=(^[X4:$i, X33:$i]:((breln @ X4 @ X4 @ X33)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', breln1)).
2.12/0.94	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', breln)).
2.12/0.94	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', exuEu)).
2.12/0.94	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', exu)).
2.12/0.94	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', exuE3u)).
2.12/0.94	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', nonempty)).
2.12/0.94	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', replAx)).
2.12/0.94	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setOfPairsIsBReln)).
2.12/0.94	thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setOfPairsIsBReln1)).
2.12/0.94	thf(breln1invset, axiom, ((breln1invset)=(^[X4:$i, X33:$i]:(dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((in @ (kpair @ X3 @ X2) @ X33)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', breln1invset)).
2.12/0.94	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', descr__Cong)).
2.12/0.94	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', exu__Cong)).
2.12/0.94	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', exuI2)).
2.12/0.94	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', exuI3)).
2.12/0.94	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', exuI1)).
2.12/0.94	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', exuE2)).
2.12/0.94	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', nonemptyI)).
2.12/0.94	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', exuE3e)).
2.12/0.94	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', exuE1)).
2.12/0.94	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', descrp)).
2.12/0.94	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', sepSubset)).
2.12/0.94	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', sepInPowerset)).
2.12/0.94	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', dsetconstr__Cong)).
2.12/0.94	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', ksndsingleton)).
2.12/0.94	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setoftrueEq)).
2.12/0.94	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', nonemptyI1)).
2.12/0.94	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', nonemptyE1)).
2.12/0.94	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', singletonprop)).
2.12/0.94	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', ex1E1)).
2.12/0.94	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', dsetconstrER)).
2.12/0.94	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', dsetconstrI)).
2.12/0.94	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', ex1I2)).
2.12/0.94	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', dpsetconstrI)).
2.12/0.94	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', dpsetconstrSub)).
2.12/0.94	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', dpsetconstrERa)).
2.12/0.94	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', dpsetconstrEL2)).
2.12/0.94	thf(lamProp, axiom, ((lamProp)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', lamProp)).
2.12/0.94	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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', lamp)).
2.12/0.94	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', lam2p)).
2.12/0.94	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', brelnall1)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', brelnall2)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', ex1E2)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', beta1)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', eta1)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', beta2)).
2.12/0.94	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', iffalseProp2)).
2.12/0.94	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', iftrueProp2)).
2.12/0.94	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', dpsetconstrER)).
2.12/0.94	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', dpsetconstrEL1)).
2.12/0.94	thf(breln1all2, axiom, ((breln1all2)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', breln1all2)).
2.12/0.94	thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', breln1invprop)).
2.12/0.94	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:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', eqbreln1)).
2.12/0.94	thf(subbreln1, axiom, ((subbreln1)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', subbreln1)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', breln1all1)).
2.12/0.94	thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', breln1SetBreln1)).
2.12/0.94	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', ifSingleton)).
2.12/0.94	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', iftrueProp1)).
2.12/0.94	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', iffalseProp1)).
2.12/0.94	thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', eta2)).
2.12/0.94	thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', lam2lamEq)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', eqbreln)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', subbreln)).
2.12/0.94	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', apProp)).
2.12/0.94	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', funcImageSingleton)).
2.12/0.94	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', kfstsingleton)).
2.12/0.94	thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', ex1I)).
2.12/0.94	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', emptyE1)).
2.12/0.94	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', nonemptyImpWitness)).
2.12/0.94	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setbeta)).
2.12/0.94	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', dsetconstrEL)).
2.12/0.94	thf(breln1invI, conjecture, ((setextAx)=>((emptysetAx)=>(((((omega0Ax)=>(((omegaIndAx)=>(((foundationAx)=>((wellorderingAx)=>((descrp)=>(((dsetconstrEL)=>(((exuE1)=>((((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>(((((setbeta)=>(((nonemptyI)=>(((setadjoinIL)=>((((setadjoinE)=>((setadjoinOr)=>(((powersetI)=>(((((((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((((eqinunit)=>((singletonsswitch)=>(((((emptyE1)=>((((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>(((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>(((in__Cong)=>(((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>(((setunion__Cong)=>((((descr__Cong)=>(((subsetI1)=>((eqimpsubset2)=>(((subsetI2)=>((emptysetsubset)=>(((subsetE2)=>((notsubsetI)=>(((notequalI2)=>(((subsetTrans)=>((setadjoinSub)=>((((setextsub)=>(((powersetI1)=>((powersetE1)=>(((powersetsubset)=>(((((((binunionEcases)=>((binunionE)=>(((binunionRsub)=>((binintersectI)=>(((binintersectEL)=>(((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>(((binintersectSubset4)=>(((bs114d)=>(((setminusEL)=>(((((setminusELneg)=>((setminusILneg)=>(((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>(((singletoninpowerset)=>(((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>(((((cartprodmempair1)=>((cartprodmempair)=>((((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>(((ex1I2)=>((((((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>(((setukpairinjR12)=>(((upairequniteq)=>((((ksndsingleton)=>(((kpairsurjEq)=>(((((cartprodmempaircEq)=>(((((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>(((dpsetconstrEL2)=>(((((((ap2p)=>(((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>(((((funcext)=>(((((beta1)=>((eta1)=>(((beta2)=>((((iffalseProp2)=>(((iftrueProp2)=>(((ifp)=>((((iffalse)=>(((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((((powersetTE1)=>(((complementTE1)=>((binintersectTELcontra)=>(((contrasubsetT)=>((contrasubsetT1)=>(((contrasubsetT3)=>(((doubleComplementE1)=>((doubleComplementSub1)=>((((((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>(((binunionTIRcontra)=>(((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>(((inComplementUnionImpNotIn1)=>(((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>(((demorgan2a)=>((((demorgan2)=>((woz13rule0)=>((woz13rule1)=>(((woz13rule3)=>(((((woz1_3)=>((woz1_4)=>(((breln1all2)=>(((choice2fnsingleton)=>((setOfPairsIsBReln1)=>(((((breln1invprop)=>![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))))))))))<=(eqbreln1))<=(subbreln1))<=(breln1all1))))<=(breln1SetBreln1)))<=(woz1_5))))<=(woz1_2))<=(woz1_1))<=(woz13rule4)))<=(woz13rule2)))))<=(demorgan2b))<=(demorgan2b2)))<=(demorgan1)))))))))<=(inComplementUnionImpInComplement1)))<=(intersectInPowersetIntersectUnions))))<=(inIntersectImpInUnion)))<=(binunionTILcontra))))))<=(complementImpComplementIntersect))<=(complementTnotintersectT))<=(doubleComplementEq))<=(doubleComplementSub2))))<=(doubleComplementI1)))<=(contrasubsetT2))))<=(binintersectTERcontra))))<=(complementTI1)))<=(powersetTI1))<=(subsetTI))))))))<=(iftrueorfalse)))<=(iftrue))<=(theeq)))<=(ifSingleton)))<=(iftrueProp1)))<=(iffalseProp1))<=(eta2)))<=(lam2lamEq))))<=(ap2apEq2))<=(ap2apEq1))<=(funcext2)))<=(eqbreln))<=(subbreln))<=(funcGraphProp4))))))))))))<=(funcinfuncset)))<=(infuncsetfunc))<=(app))<=(apProp))<=(funcImageSingleton))<=(dpsetconstrER)))<=(dpsetconstrEL1))))))<=(cartprodpairsurjEq))<=(cartprodsndpairEq))<=(cartprodfstpairEq)))<=(cartprodpairmemER))<=(cartprodpairmemEL))<=(cartprodsndin)))<=(ksndpairEq)))<=(setukpairinjR))<=(setukpairinjR2)))<=(setukpairinjR1)))<=(setukpairinjR11))))))<=(theprop))<=(kfstsingleton))<=(setukpairinjL1))<=(singletonsuniq)))<=(ex1I))))))<=(setunionsingleton1))<=(setunionE2))))<=(cartprodpairin))<=(ubforcartprodlem3))<=(ubforcartprodlem2))))))<=(singletoninpowunion)))<=(singletonsubset)))))))))<=(symdiffI2))<=(symdiffI1)))))<=(setminusIRneg))))<=(setminusERneg))<=(setminusSubset2))<=(setminusER)))<=(setminusI)))<=(binintersectSubset1)))<=(binintersectRsub))))))<=(binintersectLsub)))<=(binintersectSubset5))))<=(binunionLsub))))<=(binunionIR))<=(upairset2IR))<=(binunionIL))<=(sepSubset))<=(sepInPowerset)))<=(inPowerset))))<=(subsetemptysetimpeq)))<=(subset2powerset))<=(setadjoinSub2))))<=(subsetRefl)))<=(notequalI1))))<=(subsetE))))<=(eqimpsubset1))))<=(dsetconstr__Cong)))<=(exuEu))<=(omega__Cong)))<=(powerset__Cong)))))<=(exuE3u)))<=(inCongP)))))))<=(prop2set2propI))))))<=(quantDeMorgan1))<=(vacuousDall)))<=(upairsetIR))<=(upairsetIL))<=(upairsetE))))<=(notinsingleton))<=(uniqinunit)))))<=(setunionE))<=(setunionI))<=(powersetE))<=(emptyInPowerset))<=(emptyinPowerset)))<=(setoftrueEq))))<=(setadjoinIR))<=(emptyinunitempty)))<=(nonemptyI1)))<=(nonemptyE1)))<=(noeltsimpempty))<=(emptyI))<=(setext)))))<=(emptysetE))<=(prop2setE)))<=(dsetconstrER)))<=(dsetconstrI)))))<=(replAx)))<=(omegaSAx)))<=(setunionAx))<=(powersetAx))<=(setadjoinAx)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', breln1invI)).
2.12/0.94	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', symdiffE)).
2.12/0.94	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', upairsetIR)).
2.12/0.94	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setadjoinAx)).
2.12/0.94	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', upairset2IR)).
2.12/0.94	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setminusSubset1)).
2.12/0.94	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binunionIL)).
2.12/0.94	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setukpairIL)).
2.12/0.94	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', inPowerset)).
2.12/0.94	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setukpairIR)).
2.12/0.94	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', subsetemptysetimpeq)).
2.12/0.94	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', subset2powerset)).
2.12/0.94	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setadjoinSub2)).
2.12/0.94	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', kpairiskpair)).
2.12/0.94	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', subsetRefl)).
2.12/0.94	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', notequalI1)).
2.12/0.94	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', kpairp)).
2.12/0.94	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', subsetE)).
2.12/0.94	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', eqimpsubset1)).
2.12/0.94	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', singletoninpowerset)).
2.12/0.94	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', omega__Cong)).
2.12/0.94	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', powerset__Cong)).
2.12/0.94	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', upairset2E)).
2.12/0.94	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', inCongP)).
2.12/0.94	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', quantDeMorgan1)).
2.12/0.94	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', upairsubunion)).
2.12/0.94	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', vacuousDall)).
2.12/0.94	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', upairsetIL)).
2.12/0.94	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', upairinpowunion)).
2.12/0.94	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', upairsetE)).
2.12/0.94	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', notinsingleton)).
2.12/0.94	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', uniqinunit)).
2.12/0.94	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', ubforcartprodlem1)).
2.12/0.94	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setunionE)).
2.12/0.94	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setunionI)).
2.12/0.94	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', cartprodmempair1)).
2.12/0.94	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', powersetE)).
2.12/0.94	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', emptyInPowerset)).
2.12/0.94	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', emptyinPowerset)).
2.12/0.94	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', cartprodmempair)).
2.12/0.94	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setadjoinIR)).
2.12/0.94	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setunionsingleton2)).
2.12/0.94	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', emptyinunitempty)).
2.12/0.94	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setunionsingleton)).
2.12/0.94	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', noeltsimpempty)).
2.12/0.94	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', emptyI)).
2.12/0.94	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setext)).
2.12/0.94	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', emptysetE)).
2.12/0.94	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', prop2setE)).
2.12/0.94	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', omegaSAx)).
2.12/0.94	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setunionAx)).
2.12/0.94	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', powersetAx)).
2.12/0.94	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', kfstpairEq)).
2.12/0.94	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', cartprodfstin)).
2.12/0.94	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setukpairinjL2)).
2.12/0.94	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setukpairinjL)).
2.12/0.94	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setukpairinjR12)).
2.12/0.94	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', upairequniteq)).
2.12/0.94	thf(setextT, axiom, ((setextT)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setextT)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', powersetTE1)).
2.12/0.94	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', kpairsurjEq)).
2.12/0.94	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', cartprodmempaircEq)).
2.12/0.94	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', ap2p)).
2.12/0.94	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', symdiffIneg1)).
2.12/0.94	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', symdiffIneg2)).
2.12/0.94	thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', funcGraphProp1)).
2.12/0.94	thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', funcGraphProp3)).
2.12/0.94	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', funcGraphProp2)).
2.12/0.94	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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', funcextLem)).
2.12/0.94	thf(funcext, axiom, ((funcext)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', funcext)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', ifp)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', iffalse)).
2.12/0.94	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binintersectT_lem)).
2.12/0.94	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binunionT_lem)).
2.12/0.94	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', powersetT_lem)).
2.12/0.94	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setminusT_lem)).
2.12/0.94	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', complementT_lem)).
2.12/0.94	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', cartprodpairsurjEq)).
2.12/0.94	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', cartprodsndpairEq)).
2.12/0.94	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', cartprodfstpairEq)).
2.12/0.94	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', cartprodpairmemER)).
2.12/0.94	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', cartprodpairmemEL)).
2.12/0.94	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', complementTE1)).
2.12/0.94	thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binintersectTELcontra)).
2.12/0.94	thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', contrasubsetT)).
2.12/0.94	thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', contrasubsetT1)).
2.12/0.94	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', contrasubsetT3)).
2.12/0.94	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', doubleComplementE1)).
2.12/0.94	thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', doubleComplementSub1)).
2.12/0.94	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', complementSubsetComplementIntersect)).
2.12/0.94	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', complementInPowersetComplementIntersect)).
2.12/0.94	thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', contraSubsetComplement)).
2.12/0.94	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', complementTcontraSubset)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binunionTIRcontra)).
2.12/0.94	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', inIntersectImpInUnion2)).
2.12/0.94	thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', inIntersectImpInIntersectUnions)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', inComplementUnionImpNotIn1)).
2.12/0.94	thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binunionTE)).
2.12/0.94	thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binunionTEcontra)).
2.12/0.94	thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', demorgan2a1)).
2.12/0.94	thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', complementUnionInPowersetComplement)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', demorgan2a2)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', demorgan1a)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', demorgan1b)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', demorgan2a)).
2.12/0.94	thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', demorgan2)).
2.12/0.94	thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', woz13rule0)).
2.12/0.94	thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', woz13rule1)).
2.12/0.94	thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', woz13rule3)).
2.12/0.94	thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', woz1_3)).
2.12/0.94	thf(woz1_4, axiom, ((woz1_4)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', woz1_4)).
2.12/0.94	thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', woz1_5)).
2.12/0.94	thf(woz1_2, axiom, ((woz1_2)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', woz1_2)).
2.12/0.94	thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', woz1_1)).
2.12/0.94	thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', woz13rule4)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', woz13rule2)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', demorgan2b)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', demorgan2b2)).
2.12/0.94	thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', demorgan1)).
2.12/0.94	thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', inComplementUnionImpInComplement1)).
2.12/0.94	thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', intersectInPowersetIntersectUnions)).
2.12/0.94	thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', inIntersectImpInUnion)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binunionTILcontra)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', complementImpComplementIntersect)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', complementTnotintersectT)).
2.12/0.94	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', doubleComplementEq)).
2.12/0.94	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', doubleComplementSub2)).
2.12/0.94	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', doubleComplementI1)).
2.12/0.94	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', contrasubsetT2)).
2.12/0.94	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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binintersectTERcontra)).
2.12/0.94	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', complementTI1)).
2.12/0.94	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', powersetTI1)).
2.12/0.94	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', subsetTI)).
2.12/0.94	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', iftrueorfalse)).
2.12/0.94	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', iftrue)).
2.12/0.94	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', theeq)).
2.12/0.94	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', ap2apEq2)).
2.12/0.94	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', ap2apEq1)).
2.12/0.94	thf(funcext2, axiom, ((funcext2)<=>![X4:$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/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', funcext2)).
2.12/0.94	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', funcGraphProp4)).
2.12/0.94	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', funcinfuncset)).
2.12/0.94	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', infuncsetfunc)).
2.12/0.94	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', app)).
2.12/0.94	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', cartprodsndin)).
2.12/0.94	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', ksndpairEq)).
2.12/0.94	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setukpairinjR)).
2.12/0.94	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setukpairinjR2)).
2.12/0.94	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setukpairinjR1)).
2.12/0.94	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setukpairinjR11)).
2.12/0.94	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', theprop)).
2.12/0.94	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setukpairinjL1)).
2.12/0.94	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', singletonsuniq)).
2.12/0.94	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setunionsingleton1)).
2.12/0.94	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setunionE2)).
2.12/0.94	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', cartprodpairin)).
2.12/0.94	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', ubforcartprodlem3)).
2.12/0.94	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', ubforcartprodlem2)).
2.12/0.94	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', singletoninpowunion)).
2.12/0.94	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', singletonsubset)).
2.12/0.94	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', symdiffI2)).
2.12/0.94	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', symdiffI1)).
2.12/0.94	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setminusIRneg)).
2.12/0.94	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setminusERneg)).
2.12/0.94	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setminusSubset2)).
2.12/0.94	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setminusER)).
2.12/0.94	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setminusI)).
2.12/0.94	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binintersectSubset1)).
2.12/0.94	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binintersectRsub)).
2.12/0.94	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binintersectLsub)).
2.12/0.94	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binintersectSubset5)).
2.12/0.94	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binunionLsub)).
2.12/0.94	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binunionIR)).
2.12/0.94	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', secondinupair)).
2.12/0.94	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setminusLsub)).
2.12/0.94	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setminusILneg)).
2.12/0.94	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setminusELneg)).
2.12/0.94	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setminusEL)).
2.12/0.94	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', bs114d)).
2.12/0.94	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binintersectSubset4)).
2.12/0.94	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', disjointsetsI1)).
2.12/0.94	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binintersectER)).
2.12/0.94	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binintersectSubset3)).
2.12/0.94	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binintersectSubset2)).
2.12/0.94	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binintersectEL)).
2.12/0.94	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binintersectI)).
2.12/0.94	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binunionRsub)).
2.12/0.94	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binunionE)).
2.12/0.94	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', binunionEcases)).
2.12/0.94	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', powersetsubset)).
2.12/0.94	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', powersetE1)).
2.12/0.94	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', powersetI1)).
2.12/0.94	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setextsub)).
2.12/0.94	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setadjoinSub)).
2.12/0.94	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', subsetTrans)).
2.12/0.94	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', notequalI2)).
2.12/0.94	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', notsubsetI)).
2.12/0.94	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', subsetE2)).
2.12/0.94	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', emptysetsubset)).
2.12/0.94	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', subsetI2)).
2.12/0.94	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', eqimpsubset2)).
2.12/0.94	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', subsetI1)).
2.12/0.94	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setunion__Cong)).
2.12/0.94	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setadjoin__Cong)).
2.12/0.94	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', emptyset__Cong)).
2.12/0.94	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', in__Cong)).
2.12/0.94	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', notdallE)).
2.12/0.94	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', notdexE)).
2.12/0.94	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', prop2setI)).
2.12/0.94	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', quantDeMorgan4)).
2.12/0.94	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', quantDeMorgan3)).
2.12/0.94	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', quantDeMorgan2)).
2.12/0.94	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', singletonsswitch)).
2.12/0.94	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', eqinunit)).
2.12/0.94	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', subPowSU)).
2.12/0.94	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', powersetI)).
2.12/0.94	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setadjoinOr)).
2.12/0.94	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setadjoinE)).
2.12/0.94	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setadjoinIL)).
2.12/0.94	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', notinemptyset)).
2.12/0.94	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', emptysetimpfalse)).
2.12/0.94	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', wellorderingAx)).
2.12/0.94	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', foundationAx)).
2.12/0.94	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', omegaIndAx)).
2.12/0.94	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', omega0Ax)).
2.12/0.94	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', emptysetAx)).
2.12/0.94	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.raLesNwpak/E---3.1_10408.p', setextAx)).
2.12/0.94	thf(c_0_296, plain, ((breln1)=(^[Z0/* 19 */:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(fof_simplification,[status(thm)],[breln1])).
2.12/0.94	thf(c_0_297, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
2.12/0.94	thf(c_0_298, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
2.12/0.94	thf(c_0_299, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
2.12/0.94	thf(c_0_300, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
2.12/0.94	thf(c_0_301, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
2.12/0.94	thf(c_0_302, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
2.12/0.94	thf(c_0_303, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
2.12/0.94	thf(c_0_304, plain, ((breln1)=(^[Z0/* 19 */:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(apply_def,[status(thm)],[c_0_296, c_0_297])).
2.12/0.94	thf(c_0_305, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
2.12/0.94	thf(c_0_306, plain, ((breln1invset)=(^[Z0/* 19 */:$i, Z1:$i]:(dpsetconstr @ Z0 @ Z0 @ (^[Z2/* 19 */:$i, Z3:$i]:((in @ (kpair @ Z3 @ Z2) @ Z1)))))), inference(fof_simplification,[status(thm)],[breln1invset])).
2.12/0.94	thf(c_0_307, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
2.12/0.94	thf(c_0_308, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
2.12/0.94	thf(c_0_309, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
2.12/0.94	thf(c_0_310, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
2.12/0.94	thf(c_0_311, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
2.12/0.94	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])).
2.12/0.94	thf(c_0_313, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
2.12/0.94	thf(c_0_314, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
2.12/0.94	thf(c_0_315, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
2.12/0.94	thf(c_0_316, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
2.12/0.94	thf(c_0_317, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
2.12/0.94	thf(c_0_318, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
2.12/0.94	thf(c_0_319, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
2.12/0.94	thf(c_0_320, plain, ((exuEu)=(![X1:$i > $o]:(((?[X1016:$i]:((((X1 @ X1016))&![X1017:$i]:((((X1 @ X1017))=>((X1016)=(X1017)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_298, c_0_299])).
2.12/0.94	thf(c_0_321, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X1010:$i]:((((X1 @ X1010))&![X1011:$i]:((((X1 @ X1011))=>((X1010)=(X1011)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_300, c_0_299])).
2.12/0.94	thf(c_0_322, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
2.12/0.94	thf(c_0_323, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
2.12/0.94	thf(c_0_324, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_301])).
2.12/0.94	thf(c_0_325, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_301])).
2.12/0.94	thf(c_0_326, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
2.12/0.94	thf(c_0_327, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
2.12/0.94	thf(c_0_328, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
2.12/0.94	thf(c_0_329, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
2.12/0.94	thf(c_0_330, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X994:$i]:((((X6 @ X2 @ X994))&![X995:$i]:((((X6 @ X2 @ X995))=>((X994)=(X995)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_302, c_0_299])).
2.12/0.94	thf(c_0_331, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
2.12/0.94	thf(c_0_332, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
2.12/0.94	thf(c_0_333, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
2.12/0.94	thf(c_0_334, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_303, c_0_297])).
2.12/0.94	thf(c_0_335, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
2.12/0.94	thf(c_0_336, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
2.12/0.94	thf(c_0_337, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
2.12/0.94	thf(c_0_338, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
2.12/0.94	thf(c_0_339, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
2.12/0.94	thf(c_0_340, axiom, ((brelnall1)=(![X4:$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_297])).
2.12/0.94	thf(c_0_341, 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_297])).
2.12/0.94	thf(c_0_342, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
2.12/0.94	thf(c_0_343, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
2.12/0.94	thf(c_0_344, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
2.12/0.94	thf(c_0_345, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
2.12/0.94	thf(c_0_346, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
2.12/0.94	thf(c_0_347, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
2.12/0.94	thf(c_0_348, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
2.12/0.94	thf(c_0_349, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
2.12/0.94	thf(c_0_350, axiom, ((breln1all2)=(![X4:$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_304])).
2.12/0.94	thf(c_0_351, plain, ((setOfPairsIsBReln1)=(![X4:$i, X53:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X4)))))), inference(apply_def,[status(thm)],[c_0_305, c_0_304])).
2.12/0.94	thf(c_0_352, axiom, ((breln1invprop)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>((subset @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ X33)))) @ (cartprod @ X4 @ X4))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[breln1invprop, c_0_304]), c_0_306])).
2.12/0.94	thf(c_0_353, axiom, ((eqbreln1)=(![X4:$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_304])).
2.12/0.94	thf(c_0_354, axiom, ((subbreln1)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X4)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln1, c_0_304])).
2.12/0.94	thf(c_0_355, axiom, ((breln1all1)=(![X4:$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_304])).
2.12/0.94	thf(c_0_356, axiom, ((breln1SetBreln1)=(![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>((subset @ X33 @ (cartprod @ X4 @ X4))))))), inference(apply_def,[status(thm)],[breln1SetBreln1, c_0_304])).
2.12/0.94	thf(c_0_357, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
2.12/0.94	thf(c_0_358, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
2.12/0.94	thf(c_0_359, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
2.12/0.94	thf(c_0_360, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
2.12/0.94	thf(c_0_361, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
2.12/0.94	thf(c_0_362, 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_297])).
2.12/0.94	thf(c_0_363, 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_297])).
2.12/0.94	thf(c_0_364, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
2.12/0.94	thf(c_0_365, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
2.12/0.94	thf(c_0_366, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
2.12/0.94	thf(c_0_367, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
2.12/0.94	thf(c_0_368, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1018:$i]:((((X1 @ X1018))&![X1019:$i]:((((X1 @ X1019))=>((X1018)=(X1019)))))))=>((?[X1020:$i]:((((X17 @ X1020))&![X1021:$i]:((((X17 @ X1021))=>((X1020)=(X1021)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_307, c_0_299])).
2.12/0.94	thf(c_0_369, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1012:$i]:((((X1 @ X1012))&![X1013:$i]:((((X1 @ X1013))=>((X1012)=(X1013)))))))<=>(?[X1014:$i]:((((X17 @ X1014))&![X1015:$i]:((((X17 @ X1015))=>((X1014)=(X1015)))))))))))), inference(apply_def,[status(thm)],[c_0_308, c_0_299])).
2.12/0.94	thf(c_0_370, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X1008:$i]:((((X1 @ X1008))&![X1009:$i]:((((X1 @ X1009))=>((X1008)=(X1009))))))))))), inference(apply_def,[status(thm)],[c_0_309, c_0_299])).
2.12/0.94	thf(c_0_371, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X1006:$i]:((((X1 @ X1006))&![X1007:$i]:((((X1 @ X1007))=>((X1006)=(X1007)))))))))))), inference(apply_def,[status(thm)],[c_0_310, c_0_299])).
2.12/0.94	thf(c_0_372, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X1004:$i]:((((X1 @ X1004))&![X1005:$i]:((((X1 @ X1005))=>((X1004)=(X1005))))))))))), inference(apply_def,[status(thm)],[c_0_311, c_0_299])).
2.12/0.94	thf(c_0_373, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
2.12/0.94	thf(c_0_374, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_301])).
2.12/0.94	thf(c_0_375, plain, ((exuE2)=(![X1:$i > $o]:(((?[X1002:$i]:((((X1 @ X1002))&![X1003:$i]:((((X1 @ X1003))=>((X1002)=(X1003)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_312, c_0_299])).
2.12/0.94	thf(c_0_376, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_313, c_0_301])).
2.12/0.94	thf(c_0_377, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
2.12/0.94	thf(c_0_378, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X1000:$i]:((((X1 @ X1000))&![X1001:$i]:((((X1 @ X1001))=>((X1000)=(X1001)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_314, c_0_299])).
2.12/0.94	thf(c_0_379, plain, ((exuE1)=(![X1:$i > $o]:(((?[X998:$i]:((((X1 @ X998))&![X999:$i]:((((X1 @ X999))=>((X998)=(X999)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_315, c_0_299])).
2.12/0.94	thf(c_0_380, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
2.12/0.94	thf(c_0_381, plain, ((descrp)=(![X1:$i > $o]:(((?[X996:$i]:((((X1 @ X996))&![X997:$i]:((((X1 @ X997))=>((X996)=(X997)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_316, c_0_299])).
2.12/0.94	thf(c_0_382, plain, ((epred1_0)<=>![X1033:$i]:(?[X1034:$i]:((((![X1035:$i]:(((in @ X1035 @ X1034)=>![X1036:$i]:(((in @ X1036 @ X1035)=>(in @ X1036 @ X1033)))))&![X1037:$i, X1038:$i]:((((in @ X1037 @ X1033)&(in @ X1038 @ X1033))=>(![X1039:$i]:(((in @ X1039 @ X1034)=>((in @ X1037 @ X1039)<=>(in @ X1038 @ X1039))))=>((X1037)=(X1038))))))&![X1040:$i, X1041:$i]:((((in @ X1040 @ X1034)&(in @ X1041 @ X1034))=>(![X1042:$i]:(((in @ X1042 @ X1040)=>(in @ X1042 @ X1041)))|![X1043:$i]:(((in @ X1043 @ X1041)=>(in @ X1043 @ X1040)))))))&![X1044:$i]:(((![X1045:$i]:(((in @ X1045 @ X1044)=>(in @ X1045 @ X1033)))&?[X1046:$i]:((in @ X1046 @ X1044)))=>?[X1047:$i, X1048:$i]:(((((in @ X1047 @ X1034)&(in @ X1048 @ X1044))&~(?[X1049:$i]:(((in @ X1049 @ X1047)&(in @ X1049 @ X1044)))))&![X1050:$i]:(((in @ X1050 @ X1034)=>(![X1051:$i]:(((in @ X1051 @ X1050)=>(in @ X1051 @ X1047)))|(in @ X1048 @ X1050)))))))))))), introduced(definition)).
2.12/0.94	thf(c_0_383, negated_conjecture, ~((![X1022:$i, X1023:$i]:((![X1024:$i]:(((in @ X1024 @ X1022)<=>(in @ X1024 @ X1023)))=>((X1022)=(X1023))))=>(![X1025:$i]:(~(in @ X1025 @ emptyset))=>(![X1983:$i, X1984:$i, X1985:$i]:(((in @ X1985 @ (setadjoin @ X1983 @ X1984))<=>(((X1985)=(X1983))|(in @ X1985 @ X1984))))=>(![X1980:$i, X1981:$i]:(((in @ X1981 @ (powerset @ X1980))<=>![X1982:$i]:(((in @ X1982 @ X1981)=>(in @ X1982 @ X1980)))))=>(![X1977:$i, X1978:$i]:(((in @ X1978 @ (setunion @ X1977))<=>?[X1979:$i]:(((in @ X1978 @ X1979)&(in @ X1979 @ X1977)))))=>((in @ emptyset @ omega)=>(![X1976:$i]:(((in @ X1976 @ omega)=>(in @ (setadjoin @ X1976 @ X1976) @ omega)))=>(![X1026:$i]:((((in @ emptyset @ X1026)&![X1027:$i]:((((in @ X1027 @ omega)&(in @ X1027 @ X1026))=>(in @ (setadjoin @ X1027 @ X1027) @ X1026))))=>![X1028:$i]:(((in @ X1028 @ omega)=>(in @ X1028 @ X1026)))))=>(![X1968:$i > $i > $o, X1969:$i]:((![X1970:$i]:(((in @ X1970 @ X1969)=>?[X1971:$i]:(((X1968 @ X1970 @ X1971)&![X1972:$i]:(((X1968 @ X1970 @ X1972)=>((X1971)=(X1972))))))))=>?[X1973:$i]:(![X1974:$i]:(((in @ X1974 @ X1973)<=>?[X1975:$i]:(((in @ X1975 @ X1969)&(X1968 @ X1975 @ X1974))))))))=>(![X1029:$i]:((?[X1030:$i]:((in @ X1030 @ X1029))=>?[X1031:$i]:(((in @ X1031 @ X1029)&~(?[X1032:$i]:(((in @ X1032 @ X1031)&(in @ X1032 @ X1029))))))))=>((epred1_0)=>(![X1052:$i > $o]:((?[X1053:$i]:(((X1052 @ X1053)&![X1054:$i]:(((X1052 @ X1054)=>((X1053)=(X1054))))))=>(X1052 @ (descr @ (^[Z0/* 17 */:$i]:(X1052 @ Z0))))))=>(![X1965:$i, X1966:$i > $o, X1967:$i]:(((in @ X1967 @ X1965)=>((X1966 @ X1967)=>(in @ X1967 @ (dsetconstr @ X1965 @ X1966)))))=>(![X1055:$i, X1056:$i > $o, X1057:$i]:(((in @ X1057 @ (dsetconstr @ X1055 @ X1056))=>(in @ X1057 @ X1055)))=>(![X1962:$i, X1963:$i > $o, X1964:$i]:(((in @ X1964 @ (dsetconstr @ X1962 @ X1963))=>(X1963 @ X1964)))=>(![X1058:$i > $o]:((?[X1059:$i]:(((X1058 @ X1059)&![X1060:$i]:(((X1058 @ X1060)=>((X1059)=(X1060))))))=>?[X1061:$i]:(((X1058 @ X1061)&![X1062:$i]:(((X1058 @ X1062)=>((X1061)=(X1062))))))))=>(![X1960:$o, X1961:$i]:(((in @ X1961 @ (prop2set @ ((X1960))))=>(X1960)))=>(![X1958:$i]:(((in @ X1958 @ emptyset)=>![X1959:$o]:((X1959))))=>(![X1063:$i]:(((in @ X1063 @ emptyset)=>~($true)))=>(![X1064:$i]:(~(in @ X1064 @ emptyset))=>(![X1065:$i > $o]:((?[X1066:$i]:(((X1065 @ X1066)&![X1067:$i]:(((X1065 @ X1067)=>((X1066)=(X1067))))))=>?[X1068:$i]:((X1065 @ X1068))))=>(![X1954:$i, X1955:$i]:((![X1956:$i]:(((in @ X1956 @ X1954)=>(in @ X1956 @ X1955)))=>(![X1957:$i]:(((in @ X1957 @ X1955)=>(in @ X1957 @ X1954)))=>((X1954)=(X1955)))))=>(![X1952:$i]:((![X1953:$i]:(~(in @ X1953 @ X1952))=>((X1952)=(emptyset))))=>(![X1950:$i]:((![X1951:$i]:(~(in @ X1951 @ X1950))=>((X1950)=(emptyset))))=>(![X1069:$i, X1070:$i > $o, X1071:$i]:(((in @ X1071 @ X1069)=>((in @ X1071 @ (dsetconstr @ X1069 @ X1070))<=>(X1070 @ X1071))))=>(![X1948:$i]:((((X1948)!=(emptyset))=>?[X1949:$i]:((in @ X1949 @ X1948))))=>(![X1072:$i, X1073:$i > $o, X1074:$i]:(((in @ X1074 @ X1072)=>((X1073 @ X1074)=>((dsetconstr @ X1072 @ X1073)!=(emptyset)))))=>(![X1946:$i]:((?[X1947:$i]:((in @ X1947 @ X1946))=>((X1946)!=(emptyset))))=>(![X1075:$i, X1076:$i]:((in @ X1075 @ (setadjoin @ X1075 @ X1076)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1943:$i, X1944:$i, X1945:$i]:(((in @ X1945 @ X1944)=>(in @ X1945 @ (setadjoin @ X1943 @ X1944))))=>(![X1077:$i, X1078:$i, X1079:$i]:(((in @ X1079 @ (setadjoin @ X1077 @ X1078))=>![X1080:$o]:(((((X1079)=(X1077))=>(X1080))=>(((in @ X1079 @ X1078)=>(X1080))=>(X1080))))))=>(![X1081:$i, X1082:$i, X1083:$i]:(((in @ X1083 @ (setadjoin @ X1081 @ X1082))=>(((X1083)=(X1081))|(in @ X1083 @ X1082))))=>(![X1942:$i]:(((dsetconstr @ X1942 @ (^[Z0/* 1 */:$i]:($true)))=(X1942)))=>(![X1084:$i, X1085:$i]:((![X1086:$i]:(((in @ X1086 @ X1085)=>(in @ X1086 @ X1084)))=>(in @ X1085 @ (powerset @ X1084))))=>(![X1941:$i]:((in @ emptyset @ (powerset @ X1941)))=>(![X1940:$i]:((in @ emptyset @ (powerset @ 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inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def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y_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[breln1invI]), symdiffE]), upairsetIR]), setadjoinAx]), upairset2IR]), setminusSubset1]), binunionIL]), c_0_317]), setukpairIL]), c_0_318]), inPowerset]), setukpairIR]), subsetemptysetimpeq]), subset2powerset]), setadjoinSub2]), kpairiskpair]), subsetRefl]), notequalI1]), kpairp]), subsetE]), eqimpsubset1]), c_0_319]), singletoninpowerset]), c_0_320]), omega__Cong]), powerset__Cong]), upairset2E]), c_0_321]), inCongP]), quantDeMorgan1]), upairsubunion]), vacuousDall]), c_0_322]), upairsetIL]), upairinpowunion]), upairsetE]), notinsingleton]), uniqinunit]), ubforcartprodlem1]), setunionE]), setunionI]), cartprodmempair1]), powersetE]), emptyInPowerset]), emptyinPowerset]), cartprodmempair]), c_0_323]), setadjoinIR]), setunionsingleton2]), emptyinunitempty]), c_0_324]), c_0_325]), setunionsingleton]), noeltsimpempty]), emptyI]), c_0_326]), setext]), emptysetE]), prop2setE]), c_0_327]), c_0_328]), c_0_329]), c_0_330]), c_0_331]), omegaSAx]), setunionAx]), powersetAx]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR12]), upairequniteq]), setextT]), powersetTE1]), kpairsurjEq]), cartprodmempaircEq]), c_0_332]), c_0_333]), c_0_334]), c_0_335]), c_0_336]), ap2p]), symdiffIneg1]), c_0_337]), symdiffIneg2]), c_0_338]), c_0_339]), c_0_340]), c_0_341]), c_0_342]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcext]), c_0_343]), c_0_344]), c_0_345]), c_0_346]), c_0_347]), ifp]), iffalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), c_0_348]), c_0_349]), cartprodpairsurjEq]), cartprodsndpairEq]), cartprodfstpairEq]), cartprodpairmemER]), cartprodpairmemEL]), complementTE1]), binintersectTELcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT3]), doubleComplementE1]), doubleComplementSub1]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTIRcontra]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), inComplementUnionImpNotIn1]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan2a]), demorgan2]), woz13rule0]), woz13rule1]), woz13rule3]), woz1_3]), woz1_4]), c_0_350]), c_0_351]), c_0_304]), c_0_352]), c_0_306]), c_0_353]), c_0_354]), c_0_355]), c_0_356]), woz1_5]), woz1_2]), woz1_1]), woz13rule4]), woz13rule2]), demorgan2b]), demorgan2b2]), demorgan1]), inComplementUnionImpInComplement1]), intersectInPowersetIntersectUnions]), inIntersectImpInUnion]), binunionTILcontra]), complementImpComplementIntersect]), complementTnotintersectT]), doubleComplementEq]), doubleComplementSub2]), doubleComplementI1]), contrasubsetT2]), binintersectTERcontra]), complementTI1]), powersetTI1]), subsetTI]), iftrueorfalse]), iftrue]), theeq]), c_0_357]), c_0_358]), c_0_359]), c_0_360]), c_0_361]), ap2apEq2]), ap2apEq1]), funcext2]), c_0_362]), c_0_363]), funcGraphProp4]), funcinfuncset]), infuncsetfunc]), app]), c_0_364]), c_0_365]), cartprodsndin]), ksndpairEq]), setukpairinjR]), setukpairinjR2]), setukpairinjR1]), setukpairinjR11]), theprop]), c_0_366]), setukpairinjL1]), singletonsuniq]), c_0_367]), setunionsingleton1]), setunionE2]), cartprodpairin]), ubforcartprodlem3]), ubforcartprodlem2]), singletoninpowunion]), singletonsubset]), symdiffI2]), symdiffI1]), setminusIRneg]), setminusERneg]), setminusSubset2]), setminusER]), setminusI]), binintersectSubset1]), binintersectRsub]), binintersectLsub]), binintersectSubset5]), binunionLsub]), binunionIR]), secondinupair]), setminusLsub]), setminusILneg]), setminusELneg]), setminusEL]), bs114d]), binintersectSubset4]), disjointsetsI1]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectEL]), binintersectI]), binunionRsub]), binunionE]), binunionEcases]), powersetsubset]), powersetE1]), powersetI1]), setextsub]), setadjoinSub]), subsetTrans]), notequalI2]), notsubsetI]), subsetE2]), emptysetsubset]), subsetI2]), eqimpsubset2]), subsetI1]), c_0_368]), setunion__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_369]), in__Cong]), c_0_370]), c_0_371]), c_0_372]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), c_0_373]), singletonsswitch]), eqinunit]), c_0_374]), c_0_375]), subPowSU]), powersetI]), setadjoinOr]), setadjoinE]), setadjoinIL]), c_0_376]), c_0_377]), c_0_378]), notinemptyset]), emptysetimpfalse]), c_0_379]), c_0_380]), c_0_381]), wellorderingAx]), foundationAx]), omegaIndAx]), omega0Ax]), emptysetAx]), setextAx])])]), c_0_382])).
2.12/0.94	thf(c_0_384, negated_conjecture, ![X1986:$i, X1987:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1999:$i, X2000:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2008:$i, X2009:$i > $i > $o, X2010:$i, X2012:$i, X2015:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2022:$i, X2023:$i > $o, X2024:$i, X2026:$i, X2027:$i > $o, X2028:$i, X2029:$i, X2030:$i > $o, X2031:$i, X2032:$i, X2033:$i > $o, X2034:$i, X2035:$i > $o, X2036:$i, X2039:$i, X2040:$o, X2041:$i, X2042:$i, X2043:$o, X2044:$i, X2045:$i, X2046:$i > $o, X2047:$i, X2050:$i, X2051:$i, X2054:$i, X2056:$i, X2058:$i, X2059:$i > $o, X2060:$i, X2061:$i, X2063:$i, X2064:$i > $o, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$o, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$o, X2096:$i, X2097:$i, X2098:$i > $o, X2099:$i, X2102:$i, X2103:$i, X2104:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i > $o, X2123:$i, X2124:$i > $o, X2125:$i, X2126:$i, X2127:$i > $o, X2128:$i, X2130:$i, X2131:$i > $o, X2133:$i, X2134:$i, X2135:$i > $o, X2137:$i, X2138:$i, X2139:$i > $o, X2140:$i, X2142:$o, X2143:$i, X2144:$i > $o, X2146:$i, X2147:$i, X2148:$i > $o, X2149:$i, X2151:$i > $o, X2152:$i, X2155:$i, X2156:$i > $o, X2157:$i, X2161:$i, X2162:$i > $o, X2163:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i > $o, X2176:$i, X2178:$i, X2179:$i, X2180:$i > $o, X2181:$i > $o, X2184:$i, X2187:$i, X2188:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i > $o, X2201:$i, X2203:$i, X2204:$i, X2205:$i > $o, X2206:$i > $o, X2209:$i, X2211:$i, X2213:$i, X2214:$i, X2215:$i > $o, X2216:$i > $o, X2219:$i, X2220:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2229:$i, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i > $o, X2267:$i, X2268:$i > $o, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$o, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$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, X2345:$i, X2346:$i, X2347:$i, X2348:$o, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, 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:$i, X2386:$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:$i, X2410:$i, X2411:$i, X2412:$i, X2413:$i, X2414:$i, X2416:$i, X2417:$i, X2418:$i, X2419:$i, X2420:$i > $o, X2423:$i, X2424:$i, X2425:$i > $o, X2427:$i, X2428:$i > $o, X2429:$i, X2431:$i, X2432:$i > $o, X2435:$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, X2486:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2493:$i, X2494:$i, X2495:$i, X2496:$i, X2497:$i, X2498:$i, X2499:$i, X2500:$i, X2501:$i, X2502:$i, X2503:$i, X2504:$i, X2505:$i, X2506:$i, X2507:$i > $i > $o, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i > $i > $o, X2513:$i, X2514:$i, X2515:$i > $i > $o, X2516:$i, X2517:$i, X2518:$i > $i > $o, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i > $i > $o, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i > $i > $o, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i > $i > $o, X2534:$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 > $i, X2562:$i, X2563:$i, X2564:$i > $i, X2566:$i, X2567:$i, X2568:$i > $i, X2570:$i, X2571:$i, X2572:$i, X2573:$i > $o, X2576:$i, X2577:$i, X2578:$i, X2579:$i, X2580:$i > $o, X2583:$i, X2584:$i, X2585:$i > $o, X2586:$i, X2587:$i, X2588:$i, X2589:$i, X2590:$i, X2591:$i, X2592:$i, X2593:$i, X2594:$i, X2595:$i, X2596:$i, X2597:$i, X2598:$i, X2599:$i, X2600:$i, X2601:$i, X2602:$i, X2603:$i, X2604:$i, X2606:$i, X2607:$i, X2608:$i, X2609:$i, X2610:$i, X2611:$i, X2612:$i, X2613:$i, X2614:$i, X2615:$i, X2616:$i, X2619:$i, X2620:$i, X2621:$i, X2622:$i, X2627:$i, X2628:$i, 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@ X2936 @ X2937)) @ X2937)|((X2936)=(X2937))|~(in @ (kpair @ (esk93_3 @ X2935 @ X2936 @ X2937) @ (esk94_3 @ X2935 @ X2936 @ X2937)) @ X2937)|~(subset @ X2937 @ (cartprod @ X2935 @ X2935))|~(subset @ X2936 @ (cartprod @ X2935 @ X2935)))&(~(in @ (kpair @ (esk95_3 @ X2935 @ X2936 @ X2937) @ (esk96_3 @ X2935 @ X2936 @ X2937)) @ X2936)|((X2936)=(X2937))|~(in @ (kpair @ (esk93_3 @ X2935 @ X2936 @ X2937) @ (esk94_3 @ X2935 @ X2936 @ X2937)) @ X2937)|~(subset @ X2937 @ (cartprod @ X2935 @ X2935))|~(subset @ X2936 @ (cartprod @ X2935 @ X2935)))))))))&((~(subset @ X2943 @ (cartprod @ X2942 @ X2942))|(subset @ (dpsetconstr @ X2942 @ X2942 @ (^[Z0/* 19 */:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ X2943)))) @ (cartprod @ X2942 @ X2942)))&((subset @ esk98_0 @ (cartprod @ esk97_0 @ esk97_0))&((in @ esk99_0 @ esk97_0)&((in @ esk100_0 @ esk97_0)&((in @ (kpair @ esk99_0 @ esk100_0) @ esk98_0)&~(in @ (kpair @ esk100_0 @ esk99_0) @ (dpsetconstr @ esk97_0 @ esk97_0 @ (^[Z0/* 19 */:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ esk98_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_383])])])])])])])).
2.12/0.94	thf(c_0_385, negated_conjecture, ~((in @ (kpair @ esk100_0 @ esk99_0) @ (dpsetconstr @ esk97_0 @ esk97_0 @ (^[Z0/* 19 */:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ esk98_0)))))), inference(split_conjunct,[status(thm)],[c_0_384])).
2.12/0.94	thf(c_0_386, negated_conjecture, ![X3:$i, X2:$i, X6:$i > $i > $o, X5:$i, X4:$i]:(((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X5 @ X6))|~((in @ X2 @ X3))|~((in @ X4 @ X5))|~((X6 @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_384])).
2.12/0.94	thf(c_0_387, negated_conjecture, (in @ esk99_0 @ esk97_0), inference(split_conjunct,[status(thm)],[c_0_384])).
2.12/0.94	thf(c_0_388, negated_conjecture, (in @ esk100_0 @ esk97_0), inference(split_conjunct,[status(thm)],[c_0_384])).
2.12/0.94	thf(c_0_389, negated_conjecture, (in @ (kpair @ esk99_0 @ esk100_0) @ esk98_0), inference(split_conjunct,[status(thm)],[c_0_384])).
2.12/0.94	thf(c_0_390, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_385, c_0_386]), c_0_387]), c_0_388]), c_0_389])]), ['proof']).
2.12/0.94	# SZS output end CNFRefutation
2.12/0.94	# Parsed axioms                        : 637
2.12/0.94	# Removed by relevancy pruning/SinE    : 341
2.12/0.94	# Initial clauses                      : 505
2.12/0.94	# Removed in clause preprocessing      : 32
2.12/0.94	# Initial clauses in saturation        : 473
2.12/0.94	# Processed clauses                    : 785
2.12/0.94	# ...of these trivial                  : 11
2.12/0.94	# ...subsumed                          : 43
2.12/0.94	# ...remaining for further processing  : 731
2.12/0.94	# Other redundant clauses eliminated   : 35
2.12/0.94	# Clauses deleted for lack of memory   : 0
2.12/0.94	# Backward-subsumed                    : 2
2.12/0.94	# Backward-rewritten                   : 1
2.12/0.94	# Generated clauses                    : 6202
2.12/0.94	# ...of the previous two non-redundant : 6023
2.12/0.94	# ...aggressively subsumed             : 0
2.12/0.94	# Contextual simplify-reflections      : 14
2.12/0.94	# Paramodulations                      : 6144
2.12/0.94	# Factorizations                       : 2
2.12/0.94	# NegExts                              : 0
2.12/0.94	# Equation resolutions                 : 42
2.12/0.94	# Disequality decompositions           : 0
2.12/0.94	# Total rewrite steps                  : 173
2.12/0.94	# ...of those cached                   : 113
2.12/0.94	# Propositional unsat checks           : 0
2.12/0.94	#    Propositional check models        : 0
2.12/0.94	#    Propositional check unsatisfiable : 0
2.12/0.94	#    Propositional clauses             : 0
2.12/0.94	#    Propositional clauses after purity: 0
2.12/0.94	#    Propositional unsat core size     : 0
2.12/0.94	#    Propositional preprocessing time  : 0.000
2.12/0.94	#    Propositional encoding time       : 0.000
2.12/0.94	#    Propositional solver time         : 0.000
2.12/0.94	#    Success case prop preproc time    : 0.000
2.12/0.94	#    Success case prop encoding time   : 0.000
2.12/0.94	#    Success case prop solver time     : 0.000
2.12/0.94	# Current number of processed clauses  : 302
2.12/0.94	#    Positive orientable unit clauses  : 34
2.12/0.94	#    Positive unorientable unit clauses: 0
2.12/0.94	#    Negative unit clauses             : 3
2.12/0.94	#    Non-unit-clauses                  : 265
2.12/0.94	# Current number of unprocessed clauses: 6078
2.12/0.94	# ...number of literals in the above   : 24358
2.12/0.94	# Current number of archived formulas  : 0
2.12/0.94	# Current number of archived clauses   : 414
2.12/0.94	# Clause-clause subsumption calls (NU) : 52904
2.12/0.94	# Rec. Clause-clause subsumption calls : 18892
2.12/0.94	# Non-unit clause-clause subsumptions  : 54
2.12/0.94	# Unit Clause-clause subsumption calls : 65
2.12/0.94	# Rewrite failures with RHS unbound    : 0
2.12/0.94	# BW rewrite match attempts            : 23
2.12/0.94	# BW rewrite match successes           : 1
2.12/0.94	# Condensation attempts                : 0
2.12/0.94	# Condensation successes               : 0
2.12/0.94	# Termbank termtop insertions          : 203137
2.12/0.94	# Search garbage collected termcells   : 31829
2.12/0.94	
2.12/0.94	# -------------------------------------------------
2.12/0.94	# User time                : 0.328 s
2.12/0.94	# System time              : 0.029 s
2.12/0.94	# Total time               : 0.357 s
2.12/0.94	# Maximum resident set size: 9832 pages
2.12/0.94	
2.12/0.94	# -------------------------------------------------
2.12/0.94	# User time                : 0.340 s
2.12/0.94	# System time              : 0.033 s
2.12/0.94	# Total time               : 0.373 s
2.12/0.94	# Maximum resident set size: 2748 pages
2.12/0.94	% E---3.1 exiting
3.40/0.94	% E exiting
3.40/0.94	EOF