0.00/0.09	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.09	% Command    : run_E %s %d THM
0.09/0.29	% Computer : n010.cluster.edu
0.09/0.29	% Model    : x86_64 x86_64
0.09/0.29	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.09/0.29	% Memory   : 8042.1875MB
0.09/0.29	% OS       : Linux 3.10.0-693.el7.x86_64
0.09/0.29	% CPULimit   : 1440
0.09/0.29	% WCLimit    : 180
0.09/0.29	% DateTime   : Thu Jul  4 10:11:53 EDT 2024
0.09/0.29	% CPUTime    : 
0.16/0.40	Running higher-order theorem proving
0.16/0.47	Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p
34.96/4.93	# Version: 3.2.0-ho
34.96/4.93	# Preprocessing class: HSLMSLSSLLLCHFA.
34.96/4.93	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
34.96/4.93	# Starting ehoh_best5 with 180s (1) cores
34.96/4.93	# Starting almost_fo_3_lam with 180s (1) cores
34.96/4.93	# Starting new_bool_5 with 180s (1) cores
34.96/4.93	# Starting pre_casc_3 with 180s (1) cores
34.96/4.93	# Starting ho_unfolding_8 with 180s (1) cores
34.96/4.93	# Starting new_ho_10_cnf2 with 180s (1) cores
34.96/4.93	# Starting new_bool_3 with 180s (1) cores
34.96/4.93	# Starting new_ho_5 with 180s (1) cores
34.96/4.93	# new_bool_3 with pid 22685 completed with status 0
34.96/4.93	# Result found by new_bool_3
34.96/4.93	# Preprocessing class: HSLMSLSSLLLCHFA.
34.96/4.93	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
34.96/4.93	# Starting ehoh_best5 with 180s (1) cores
34.96/4.93	# Starting almost_fo_3_lam with 180s (1) cores
34.96/4.93	# Starting new_bool_5 with 180s (1) cores
34.96/4.93	# Starting pre_casc_3 with 180s (1) cores
34.96/4.93	# Starting ho_unfolding_8 with 180s (1) cores
34.96/4.93	# Starting new_ho_10_cnf2 with 180s (1) cores
34.96/4.93	# Starting new_bool_3 with 180s (1) cores
34.96/4.93	# SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
34.96/4.93	# Search class: HGHSM-FSLM32-DHFMMSBN
34.96/4.93	# partial match(1): HGHSM-FSLM32-MHFMMSBN
34.96/4.93	# Scheduled 9 strats onto 1 cores with 180 seconds (180 total)
34.96/4.93	# Starting ho_unfolding_8 with 37s (1) cores
34.96/4.93	# ho_unfolding_8 with pid 22688 completed with status 0
34.96/4.93	# Result found by ho_unfolding_8
34.96/4.93	# Preprocessing class: HSLMSLSSLLLCHFA.
34.96/4.93	# Scheduled 8 strats onto 8 cores with 180 seconds (1440 total)
34.96/4.93	# Starting ehoh_best5 with 180s (1) cores
34.96/4.93	# Starting almost_fo_3_lam with 180s (1) cores
34.96/4.93	# Starting new_bool_5 with 180s (1) cores
34.96/4.93	# Starting pre_casc_3 with 180s (1) cores
34.96/4.93	# Starting ho_unfolding_8 with 180s (1) cores
34.96/4.93	# Starting new_ho_10_cnf2 with 180s (1) cores
34.96/4.93	# Starting new_bool_3 with 180s (1) cores
34.96/4.93	# SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
34.96/4.93	# Search class: HGHSM-FSLM32-DHFMMSBN
34.96/4.93	# partial match(1): HGHSM-FSLM32-MHFMMSBN
34.96/4.93	# Scheduled 9 strats onto 1 cores with 180 seconds (180 total)
34.96/4.93	# Starting ho_unfolding_8 with 37s (1) cores
34.96/4.93	# Preprocessing time       : 0.331 s
34.96/4.93	# Presaturation interreduction done
34.96/4.93	
34.96/4.93	# Proof found!
34.96/4.93	# SZS status Theorem
34.96/4.93	# SZS output start CNFRefutation
34.96/4.93	thf(decl_22, type, in: $i > $i > $o).
34.96/4.93	thf(decl_23, type, exu: ($i > $o) > $o).
34.96/4.93	thf(decl_24, type, setextAx: $o).
34.96/4.93	thf(decl_25, type, emptyset: $i).
34.96/4.93	thf(decl_26, type, emptysetAx: $o).
34.96/4.93	thf(decl_27, type, setadjoin: $i > $i > $i).
34.96/4.93	thf(decl_28, type, setadjoinAx: $o).
34.96/4.93	thf(decl_29, type, powerset: $i > $i).
34.96/4.93	thf(decl_30, type, powersetAx: $o).
34.96/4.93	thf(decl_31, type, setunion: $i > $i).
34.96/4.93	thf(decl_32, type, setunionAx: $o).
34.96/4.93	thf(decl_33, type, omega: $i).
34.96/4.93	thf(decl_34, type, omega0Ax: $o).
34.96/4.93	thf(decl_35, type, omegaSAx: $o).
34.96/4.93	thf(decl_36, type, omegaIndAx: $o).
34.96/4.93	thf(decl_37, type, replAx: $o).
34.96/4.93	thf(decl_38, type, foundationAx: $o).
34.96/4.93	thf(decl_39, type, wellorderingAx: $o).
34.96/4.93	thf(decl_40, type, descr: ($i > $o) > $i).
34.96/4.93	thf(decl_41, type, descrp: $o).
34.96/4.93	thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
34.96/4.93	thf(decl_43, type, dsetconstrI: $o).
34.96/4.93	thf(decl_44, type, dsetconstrEL: $o).
34.96/4.93	thf(decl_45, type, dsetconstrER: $o).
34.96/4.93	thf(decl_46, type, exuE1: $o).
34.96/4.93	thf(decl_47, type, prop2set: $o > $i).
34.96/4.93	thf(decl_48, type, prop2setE: $o).
34.96/4.93	thf(decl_49, type, emptysetE: $o).
34.96/4.93	thf(decl_50, type, emptysetimpfalse: $o).
34.96/4.93	thf(decl_51, type, notinemptyset: $o).
34.96/4.93	thf(decl_52, type, exuE3e: $o).
34.96/4.93	thf(decl_53, type, setext: $o).
34.96/4.93	thf(decl_54, type, emptyI: $o).
34.96/4.93	thf(decl_55, type, noeltsimpempty: $o).
34.96/4.93	thf(decl_56, type, setbeta: $o).
34.96/4.93	thf(decl_57, type, nonempty: $i > $o).
34.96/4.93	thf(decl_58, type, nonemptyE1: $o).
34.96/4.93	thf(decl_59, type, nonemptyI: $o).
34.96/4.93	thf(decl_60, type, nonemptyI1: $o).
34.96/4.93	thf(decl_61, type, setadjoinIL: $o).
34.96/4.93	thf(decl_62, type, emptyinunitempty: $o).
34.96/4.93	thf(decl_63, type, setadjoinIR: $o).
34.96/4.93	thf(decl_64, type, setadjoinE: $o).
34.96/4.93	thf(decl_65, type, setadjoinOr: $o).
34.96/4.93	thf(decl_66, type, setoftrueEq: $o).
34.96/4.93	thf(decl_67, type, powersetI: $o).
34.96/4.93	thf(decl_68, type, emptyinPowerset: $o).
34.96/4.93	thf(decl_69, type, emptyInPowerset: $o).
34.96/4.93	thf(decl_70, type, powersetE: $o).
34.96/4.93	thf(decl_71, type, setunionI: $o).
34.96/4.93	thf(decl_72, type, setunionE: $o).
34.96/4.93	thf(decl_73, type, subPowSU: $o).
34.96/4.93	thf(decl_74, type, exuE2: $o).
34.96/4.93	thf(decl_75, type, nonemptyImpWitness: $o).
34.96/4.93	thf(decl_76, type, uniqinunit: $o).
34.96/4.93	thf(decl_77, type, notinsingleton: $o).
34.96/4.93	thf(decl_78, type, eqinunit: $o).
34.96/4.93	thf(decl_79, type, singletonsswitch: $o).
34.96/4.93	thf(decl_80, type, upairsetE: $o).
34.96/4.93	thf(decl_81, type, upairsetIL: $o).
34.96/4.93	thf(decl_82, type, upairsetIR: $o).
34.96/4.93	thf(decl_83, type, emptyE1: $o).
34.96/4.93	thf(decl_84, type, vacuousDall: $o).
34.96/4.93	thf(decl_85, type, quantDeMorgan1: $o).
34.96/4.93	thf(decl_86, type, quantDeMorgan2: $o).
34.96/4.93	thf(decl_87, type, quantDeMorgan3: $o).
34.96/4.93	thf(decl_88, type, quantDeMorgan4: $o).
34.96/4.93	thf(decl_89, type, prop2setI: $o).
34.96/4.93	thf(decl_91, type, prop2set2propI: $o).
34.96/4.93	thf(decl_92, type, notdexE: $o).
34.96/4.93	thf(decl_93, type, notdallE: $o).
34.96/4.93	thf(decl_94, type, exuI1: $o).
34.96/4.93	thf(decl_95, type, exuI3: $o).
34.96/4.93	thf(decl_96, type, exuI2: $o).
34.96/4.93	thf(decl_97, type, inCongP: $o).
34.96/4.93	thf(decl_98, type, in__Cong: $o).
34.96/4.93	thf(decl_99, type, exuE3u: $o).
34.96/4.93	thf(decl_100, type, exu__Cong: $o).
34.96/4.93	thf(decl_101, type, emptyset__Cong: $o).
34.96/4.93	thf(decl_102, type, setadjoin__Cong: $o).
34.96/4.93	thf(decl_103, type, powerset__Cong: $o).
34.96/4.93	thf(decl_104, type, setunion__Cong: $o).
34.96/4.93	thf(decl_105, type, omega__Cong: $o).
34.96/4.93	thf(decl_106, type, exuEu: $o).
34.96/4.93	thf(decl_107, type, descr__Cong: $o).
34.96/4.93	thf(decl_108, type, dsetconstr__Cong: $o).
34.96/4.93	thf(decl_109, type, subset: $i > $i > $o).
34.96/4.93	thf(decl_112, type, subsetI1: $o).
34.96/4.93	thf(decl_113, type, eqimpsubset2: $o).
34.96/4.93	thf(decl_114, type, eqimpsubset1: $o).
34.96/4.93	thf(decl_115, type, subsetI2: $o).
34.96/4.93	thf(decl_116, type, emptysetsubset: $o).
34.96/4.93	thf(decl_117, type, subsetE: $o).
34.96/4.93	thf(decl_118, type, subsetE2: $o).
34.96/4.93	thf(decl_119, type, notsubsetI: $o).
34.96/4.93	thf(decl_120, type, notequalI1: $o).
34.96/4.93	thf(decl_121, type, notequalI2: $o).
34.96/4.93	thf(decl_122, type, subsetRefl: $o).
34.96/4.93	thf(decl_123, type, subsetTrans: $o).
34.96/4.93	thf(decl_124, type, setadjoinSub: $o).
34.96/4.93	thf(decl_125, type, setadjoinSub2: $o).
34.96/4.93	thf(decl_126, type, subset2powerset: $o).
34.96/4.93	thf(decl_127, type, setextsub: $o).
34.96/4.93	thf(decl_128, type, subsetemptysetimpeq: $o).
34.96/4.93	thf(decl_129, type, powersetI1: $o).
34.96/4.93	thf(decl_130, type, powersetE1: $o).
34.96/4.93	thf(decl_131, type, inPowerset: $o).
34.96/4.93	thf(decl_132, type, powersetsubset: $o).
34.96/4.93	thf(decl_133, type, sepInPowerset: $o).
34.96/4.93	thf(decl_134, type, sepSubset: $o).
34.96/4.93	thf(decl_135, type, binunion: $i > $i > $i).
34.96/4.93	thf(decl_136, type, binunionIL: $o).
34.96/4.93	thf(decl_137, type, upairset2IR: $o).
34.96/4.93	thf(decl_138, type, binunionIR: $o).
34.96/4.93	thf(decl_139, type, binunionEcases: $o).
34.96/4.93	thf(decl_140, type, binunionE: $o).
34.96/4.93	thf(decl_141, type, binunionLsub: $o).
34.96/4.93	thf(decl_142, type, binunionRsub: $o).
34.96/4.93	thf(decl_143, type, binintersect: $i > $i > $i).
34.96/4.93	thf(decl_144, type, binintersectI: $o).
34.96/4.93	thf(decl_145, type, binintersectSubset5: $o).
34.96/4.93	thf(decl_146, type, binintersectEL: $o).
34.96/4.93	thf(decl_147, type, binintersectLsub: $o).
34.96/4.93	thf(decl_148, type, binintersectSubset2: $o).
34.96/4.93	thf(decl_149, type, binintersectSubset3: $o).
34.96/4.93	thf(decl_150, type, binintersectER: $o).
34.96/4.93	thf(decl_151, type, disjointsetsI1: $o).
34.96/4.93	thf(decl_152, type, binintersectRsub: $o).
34.96/4.93	thf(decl_153, type, binintersectSubset4: $o).
34.96/4.93	thf(decl_154, type, binintersectSubset1: $o).
34.96/4.93	thf(decl_155, type, bs114d: $o).
34.96/4.93	thf(decl_157, type, setminus: $i > $i > $i).
34.96/4.93	thf(decl_158, type, setminusI: $o).
34.96/4.93	thf(decl_159, type, setminusEL: $o).
34.96/4.93	thf(decl_160, type, setminusER: $o).
34.96/4.93	thf(decl_161, type, setminusSubset2: $o).
34.96/4.93	thf(decl_162, type, setminusERneg: $o).
34.96/4.93	thf(decl_163, type, setminusELneg: $o).
34.96/4.93	thf(decl_164, type, setminusILneg: $o).
34.96/4.93	thf(decl_165, type, setminusIRneg: $o).
34.96/4.93	thf(decl_166, type, setminusLsub: $o).
34.96/4.93	thf(decl_167, type, setminusSubset1: $o).
34.96/4.93	thf(decl_168, type, symdiff: $i > $i > $i).
34.96/4.93	thf(decl_169, type, symdiffE: $o).
34.96/4.93	thf(decl_170, type, symdiffI1: $o).
34.96/4.93	thf(decl_171, type, symdiffI2: $o).
34.96/4.93	thf(decl_172, type, symdiffIneg1: $o).
34.96/4.93	thf(decl_173, type, symdiffIneg2: $o).
34.96/4.93	thf(decl_174, type, iskpair: $i > $o).
34.96/4.93	thf(decl_175, type, secondinupair: $o).
34.96/4.93	thf(decl_176, type, setukpairIL: $o).
34.96/4.93	thf(decl_177, type, setukpairIR: $o).
34.96/4.93	thf(decl_178, type, kpairiskpair: $o).
34.96/4.93	thf(decl_179, type, kpair: $i > $i > $i).
34.96/4.93	thf(decl_180, type, kpairp: $o).
34.96/4.93	thf(decl_181, type, cartprod: $i > $i > $i).
34.96/4.93	thf(decl_182, type, singletonsubset: $o).
34.96/4.93	thf(decl_183, type, singletoninpowerset: $o).
34.96/4.93	thf(decl_184, type, singletoninpowunion: $o).
34.96/4.93	thf(decl_185, type, upairset2E: $o).
34.96/4.93	thf(decl_186, type, upairsubunion: $o).
34.96/4.93	thf(decl_187, type, upairinpowunion: $o).
34.96/4.93	thf(decl_188, type, ubforcartprodlem1: $o).
34.96/4.93	thf(decl_189, type, ubforcartprodlem2: $o).
34.96/4.93	thf(decl_190, type, ubforcartprodlem3: $o).
34.96/4.93	thf(decl_191, type, cartprodpairin: $o).
34.96/4.93	thf(decl_192, type, cartprodmempair1: $o).
34.96/4.93	thf(decl_193, type, cartprodmempair: $o).
34.96/4.93	thf(decl_194, type, setunionE2: $o).
34.96/4.93	thf(decl_195, type, setunionsingleton1: $o).
34.96/4.93	thf(decl_196, type, setunionsingleton2: $o).
34.96/4.93	thf(decl_197, type, setunionsingleton: $o).
34.96/4.93	thf(decl_198, type, singleton: $i > $o).
34.96/4.93	thf(decl_199, type, singletonprop: $o).
34.96/4.93	thf(decl_200, type, ex1: $i > ($i > $o) > $o).
34.96/4.93	thf(decl_201, type, ex1E1: $o).
34.96/4.93	thf(decl_202, type, ex1I: $o).
34.96/4.93	thf(decl_203, type, ex1I2: $o).
34.96/4.93	thf(decl_204, type, singletonsuniq: $o).
34.96/4.93	thf(decl_209, type, setukpairinjL1: $o).
34.96/4.93	thf(decl_210, type, kfstsingleton: $o).
34.96/4.93	thf(decl_211, type, theprop: $o).
34.96/4.93	thf(decl_212, type, kfst: $i > $i).
34.96/4.93	thf(decl_213, type, kfstpairEq: $o).
34.96/4.93	thf(decl_214, type, cartprodfstin: $o).
34.96/4.93	thf(decl_215, type, setukpairinjL2: $o).
34.96/4.93	thf(decl_216, type, setukpairinjL: $o).
34.96/4.93	thf(decl_217, type, setukpairinjR11: $o).
34.96/4.93	thf(decl_218, type, setukpairinjR12: $o).
34.96/4.93	thf(decl_219, type, setukpairinjR1: $o).
34.96/4.93	thf(decl_220, type, upairequniteq: $o).
34.96/4.93	thf(decl_221, type, setukpairinjR2: $o).
34.96/4.93	thf(decl_222, type, setukpairinjR: $o).
34.96/4.93	thf(decl_223, type, ksndsingleton: $o).
34.96/4.93	thf(decl_224, type, ksnd: $i > $i).
34.96/4.93	thf(decl_225, type, ksndpairEq: $o).
34.96/4.93	thf(decl_226, type, kpairsurjEq: $o).
34.96/4.93	thf(decl_227, type, cartprodsndin: $o).
34.96/4.93	thf(decl_228, type, cartprodpairmemEL: $o).
34.96/4.93	thf(decl_229, type, cartprodpairmemER: $o).
34.96/4.93	thf(decl_230, type, cartprodmempaircEq: $o).
34.96/4.93	thf(decl_231, type, cartprodfstpairEq: $o).
34.96/4.93	thf(decl_232, type, cartprodsndpairEq: $o).
34.96/4.93	thf(decl_233, type, cartprodpairsurjEq: $o).
34.96/4.93	thf(decl_234, type, breln: $i > $i > $i > $o).
34.96/4.93	thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
34.96/4.93	thf(decl_236, type, dpsetconstrI: $o).
34.96/4.93	thf(decl_237, type, dpsetconstrSub: $o).
34.96/4.93	thf(decl_238, type, setOfPairsIsBReln: $o).
34.96/4.93	thf(decl_239, type, dpsetconstrERa: $o).
34.96/4.93	thf(decl_240, type, dpsetconstrEL1: $o).
34.96/4.93	thf(decl_241, type, dpsetconstrEL2: $o).
34.96/4.93	thf(decl_242, type, dpsetconstrER: $o).
34.96/4.93	thf(decl_243, type, func: $i > $i > $i > $o).
34.96/4.93	thf(decl_244, type, funcSet: $i > $i > $i).
34.96/4.93	thf(decl_245, type, funcImageSingleton: $o).
34.96/4.93	thf(decl_246, type, apProp: $o).
34.96/4.93	thf(decl_247, type, ap: $i > $i > $i > $i > $i).
34.96/4.93	thf(decl_248, type, app: $o).
34.96/4.93	thf(decl_249, type, infuncsetfunc: $o).
34.96/4.93	thf(decl_250, type, ap2p: $o).
34.96/4.93	thf(decl_251, type, funcinfuncset: $o).
34.96/4.93	thf(decl_252, type, lamProp: $o).
34.96/4.93	thf(decl_253, type, lam: $i > $i > ($i > $i) > $i).
34.96/4.93	thf(decl_254, type, lamp: $o).
34.96/4.93	thf(decl_255, type, lam2p: $o).
34.96/4.93	thf(decl_256, type, brelnall1: $o).
34.96/4.93	thf(decl_257, type, brelnall2: $o).
34.96/4.93	thf(decl_258, type, ex1E2: $o).
34.96/4.93	thf(decl_259, type, funcGraphProp1: $o).
34.96/4.93	thf(decl_260, type, funcGraphProp3: $o).
34.96/4.93	thf(decl_261, type, funcGraphProp2: $o).
34.96/4.93	thf(decl_262, type, funcextLem: $o).
34.96/4.93	thf(decl_263, type, funcGraphProp4: $o).
34.96/4.93	thf(decl_264, type, subbreln: $o).
34.96/4.93	thf(decl_265, type, eqbreln: $o).
34.96/4.93	thf(decl_266, type, funcext: $o).
34.96/4.93	thf(decl_267, type, funcext2: $o).
34.96/4.93	thf(decl_268, type, ap2apEq1: $o).
34.96/4.93	thf(decl_269, type, ap2apEq2: $o).
34.96/4.93	thf(decl_270, type, beta1: $o).
34.96/4.93	thf(decl_271, type, eta1: $o).
34.96/4.93	thf(decl_272, type, lam2lamEq: $o).
34.96/4.93	thf(decl_273, type, beta2: $o).
34.96/4.93	thf(decl_274, type, eta2: $o).
34.96/4.93	thf(decl_275, type, iffalseProp1: $o).
34.96/4.93	thf(decl_276, type, iffalseProp2: $o).
34.96/4.93	thf(decl_277, type, iftrueProp1: $o).
34.96/4.93	thf(decl_278, type, iftrueProp2: $o).
34.96/4.93	thf(decl_279, type, ifSingleton: $o).
34.96/4.93	thf(decl_280, type, if: $i > $o > $i > $i > $i).
34.96/4.93	thf(decl_281, type, ifp: $o).
34.96/4.93	thf(decl_282, type, theeq: $o).
34.96/4.93	thf(decl_283, type, iftrue: $o).
34.96/4.93	thf(decl_284, type, iffalse: $o).
34.96/4.93	thf(decl_285, type, iftrueorfalse: $o).
34.96/4.93	thf(decl_286, type, binintersectT_lem: $o).
34.96/4.93	thf(decl_287, type, binunionT_lem: $o).
34.96/4.93	thf(decl_288, type, powersetT_lem: $o).
34.96/4.93	thf(decl_289, type, setminusT_lem: $o).
34.96/4.93	thf(decl_290, type, complementT_lem: $o).
34.96/4.93	thf(decl_291, type, setextT: $o).
34.96/4.93	thf(decl_292, type, subsetTI: $o).
34.96/4.93	thf(decl_293, type, powersetTI1: $o).
34.96/4.93	thf(decl_294, type, powersetTE1: $o).
34.96/4.93	thf(decl_295, type, complementTI1: $o).
34.96/4.93	thf(decl_296, type, complementTE1: $o).
34.96/4.93	thf(decl_297, type, binintersectTELcontra: $o).
34.96/4.93	thf(decl_298, type, binintersectTERcontra: $o).
34.96/4.93	thf(decl_299, type, contrasubsetT: $o).
34.96/4.93	thf(decl_300, type, contrasubsetT1: $o).
34.96/4.93	thf(decl_301, type, contrasubsetT2: $o).
34.96/4.93	thf(decl_302, type, contrasubsetT3: $o).
34.96/4.93	thf(decl_303, type, doubleComplementI1: $o).
34.96/4.93	thf(decl_304, type, doubleComplementE1: $o).
34.96/4.93	thf(decl_305, type, doubleComplementSub1: $o).
34.96/4.93	thf(decl_306, type, doubleComplementSub2: $o).
34.96/4.93	thf(decl_307, type, doubleComplementEq: $o).
34.96/4.93	thf(decl_308, type, complementTnotintersectT: $o).
34.96/4.93	thf(decl_309, type, complementImpComplementIntersect: $o).
34.96/4.93	thf(decl_310, type, complementSubsetComplementIntersect: $o).
34.96/4.93	thf(decl_311, type, complementInPowersetComplementIntersect: $o).
34.96/4.93	thf(decl_312, type, contraSubsetComplement: $o).
34.96/4.93	thf(decl_313, type, complementTcontraSubset: $o).
34.96/4.93	thf(decl_314, type, binunionTILcontra: $o).
34.96/4.93	thf(decl_315, type, binunionTIRcontra: $o).
34.96/4.93	thf(decl_316, type, inIntersectImpInUnion: $o).
34.96/4.93	thf(decl_317, type, inIntersectImpInUnion2: $o).
34.96/4.93	thf(decl_318, type, inIntersectImpInIntersectUnions: $o).
34.96/4.93	thf(decl_319, type, intersectInPowersetIntersectUnions: $o).
34.96/4.93	thf(decl_320, type, inComplementUnionImpNotIn1: $o).
34.96/4.93	thf(decl_321, type, inComplementUnionImpInComplement1: $o).
34.96/4.93	thf(decl_322, type, binunionTE: $o).
34.96/4.93	thf(decl_323, type, binunionTEcontra: $o).
34.96/4.93	thf(decl_324, type, demorgan2a1: $o).
34.96/4.93	thf(decl_325, type, complementUnionInPowersetComplement: $o).
34.96/4.93	thf(decl_326, type, demorgan2a2: $o).
34.96/4.93	thf(decl_327, type, demorgan1a: $o).
34.96/4.93	thf(decl_328, type, demorgan1b: $o).
34.96/4.93	thf(decl_329, type, demorgan1: $o).
34.96/4.93	thf(decl_330, type, demorgan2a: $o).
34.96/4.93	thf(decl_331, type, demorgan2b2: $o).
34.96/4.93	thf(decl_332, type, demorgan2b: $o).
34.96/4.93	thf(decl_333, type, demorgan2: $o).
34.96/4.93	thf(decl_334, type, woz13rule0: $o).
34.96/4.93	thf(decl_335, type, woz13rule1: $o).
34.96/4.93	thf(decl_336, type, woz13rule2: $o).
34.96/4.93	thf(decl_337, type, woz13rule3: $o).
34.96/4.93	thf(decl_338, type, woz13rule4: $o).
34.96/4.93	thf(decl_339, type, woz1_1: $o).
34.96/4.93	thf(decl_340, type, woz1_2: $o).
34.96/4.93	thf(decl_341, type, woz1_3: $o).
34.96/4.93	thf(decl_342, type, woz1_4: $o).
34.96/4.93	thf(decl_343, type, woz1_5: $o).
34.96/4.93	thf(decl_344, type, breln1: $i > $i > $o).
34.96/4.93	thf(decl_345, type, breln1all2: $o).
34.96/4.93	thf(decl_346, type, breln1Set: $i > $i).
34.96/4.93	thf(decl_347, type, breln1SetBreln1: $o).
34.96/4.93	thf(decl_354, type, choice2fnsingleton: $o).
34.96/4.93	thf(decl_355, type, setOfPairsIsBReln1: $o).
34.96/4.93	thf(decl_356, type, breln1all1: $o).
34.96/4.93	thf(decl_357, type, subbreln1: $o).
34.96/4.93	thf(decl_358, type, eqbreln1: $o).
34.96/4.93	thf(decl_359, type, breln1invset: $i > $i > $i).
34.96/4.93	thf(decl_360, type, breln1invprop: $o).
34.96/4.93	thf(decl_361, type, breln1invI: $o).
34.96/4.93	thf(decl_362, type, breln1invE: $o).
34.96/4.93	thf(decl_363, type, breln1compset: $i > $i > $i > $i).
34.96/4.93	thf(decl_364, type, breln1compprop: $o).
34.96/4.93	thf(decl_365, type, breln1compI: $o).
34.96/4.93	thf(decl_366, type, epred1_0: $o).
34.96/4.93	thf(decl_367, type, esk1_2: $i > $i > $i).
34.96/4.93	thf(decl_368, type, esk2_2: $i > $i > $i).
34.96/4.93	thf(decl_369, type, esk3_2: $i > $i > $i).
34.96/4.93	thf(decl_370, type, esk4_1: $i > $i).
34.96/4.93	thf(decl_371, type, esk5_2: ($i > $i > $o) > $i > $i).
34.96/4.93	thf(decl_372, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
34.96/4.93	thf(decl_373, type, esk7_2: ($i > $i > $o) > $i > $i).
34.96/4.93	thf(decl_374, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
34.96/4.93	thf(decl_375, type, esk9_1: $i > $i).
34.96/4.93	thf(decl_376, type, esk10_2: ($i > $o) > $i > $i).
34.96/4.93	thf(decl_377, type, esk11_2: ($i > $o) > $i > $i).
34.96/4.93	thf(decl_378, type, esk12_1: ($i > $o) > $i).
34.96/4.93	thf(decl_379, type, esk13_2: ($i > $o) > $i > $i).
34.96/4.93	thf(decl_380, type, esk14_1: ($i > $o) > $i).
34.96/4.93	thf(decl_381, type, esk15_2: $i > $i > $i).
34.96/4.93	thf(decl_382, type, esk16_2: $i > $i > $i).
34.96/4.93	thf(decl_383, type, esk17_1: $i > $i).
34.96/4.93	thf(decl_384, type, esk18_1: $i > $i).
34.96/4.93	thf(decl_385, type, esk19_1: $i > $i).
34.96/4.93	thf(decl_386, type, esk20_2: $i > $i > $i).
34.96/4.93	thf(decl_387, type, esk21_3: $i > $i > $o > $i).
34.96/4.93	thf(decl_388, type, esk22_2: ($i > $o) > $i > $i).
34.96/4.93	thf(decl_389, type, esk23_1: ($i > $o) > $i).
34.96/4.93	thf(decl_390, type, esk24_1: $i > $i).
34.96/4.93	thf(decl_391, type, esk25_2: $i > ($i > $o) > $i).
34.96/4.93	thf(decl_392, type, esk26_2: $i > ($i > $o) > $i).
34.96/4.93	thf(decl_393, type, esk27_2: $i > ($i > $o) > $i).
34.96/4.93	thf(decl_394, type, esk28_2: $i > ($i > $o) > $i).
34.96/4.93	thf(decl_395, type, esk29_2: $i > ($i > $o) > $i).
34.96/4.93	thf(decl_396, type, esk30_2: $i > ($i > $o) > $i).
34.96/4.93	thf(decl_397, type, esk31_2: ($i > $o) > $i > $i).
34.96/4.93	thf(decl_398, type, esk32_1: ($i > $o) > $i).
34.96/4.93	thf(decl_399, type, esk33_1: ($i > $o) > $i).
34.96/4.93	thf(decl_400, type, esk34_1: ($i > $o) > $i).
34.96/4.93	thf(decl_401, type, esk35_1: ($i > $o) > $i).
34.96/4.93	thf(decl_402, type, esk36_2: ($i > $o) > $i > $i).
34.96/4.93	thf(decl_403, type, esk37_1: ($i > $o) > $i).
34.96/4.93	thf(decl_404, type, esk38_2: ($i > $o) > $i > $i).
34.96/4.93	thf(decl_405, type, esk39_2: ($i > $o) > ($i > $o) > $i).
34.96/4.93	thf(decl_406, type, esk40_2: ($i > $o) > ($i > $o) > $i).
34.96/4.93	thf(decl_407, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
34.96/4.93	thf(decl_408, type, esk42_2: ($i > $o) > ($i > $o) > $i).
34.96/4.93	thf(decl_409, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
34.96/4.93	thf(decl_410, type, esk44_2: ($i > $o) > ($i > $o) > $i).
34.96/4.93	thf(decl_411, type, esk45_2: ($i > $o) > $i > $i).
34.96/4.93	thf(decl_412, type, esk46_2: ($i > $o) > ($i > $o) > $i).
34.96/4.93	thf(decl_413, type, esk47_2: ($i > $o) > ($i > $o) > $i).
34.96/4.93	thf(decl_414, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
34.96/4.93	thf(decl_415, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
34.96/4.93	thf(decl_416, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
34.96/4.93	thf(decl_417, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
34.96/4.93	thf(decl_418, type, esk52_2: $i > $i > $i).
34.96/4.93	thf(decl_419, type, esk53_2: $i > $i > $i).
34.96/4.93	thf(decl_420, type, esk54_2: $i > $i > $i).
34.96/4.93	thf(decl_421, type, esk55_3: $i > $i > $i > $i).
34.96/4.93	thf(decl_422, type, esk56_3: $i > $i > $i > $i).
34.96/4.93	thf(decl_423, type, esk57_2: $i > $i > $i).
34.96/4.93	thf(decl_424, type, esk58_2: $i > ($i > $o) > $i).
34.96/4.93	thf(decl_425, type, esk59_2: $i > ($i > $o) > $i).
34.96/4.93	thf(decl_426, type, esk60_2: $i > ($i > $o) > $i).
34.96/4.93	thf(decl_427, type, esk61_3: $i > ($i > $o) > $i > $i).
34.96/4.93	thf(decl_428, type, esk62_2: $i > ($i > $o) > $i).
34.96/4.93	thf(decl_429, type, esk63_2: $i > ($i > $o) > $i).
34.96/4.93	thf(decl_430, type, esk64_3: $i > $i > ($i > $i) > $i).
34.96/4.93	thf(decl_431, type, esk65_3: $i > $i > ($i > $i) > $i).
34.96/4.93	thf(decl_432, type, esk66_3: $i > $i > ($i > $i) > $i).
34.96/4.93	thf(decl_433, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
34.96/4.93	thf(decl_434, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
34.96/4.93	thf(decl_435, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
34.96/4.93	thf(decl_436, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
34.96/4.93	thf(decl_437, type, esk71_4: $i > $i > $i > $i > $i).
34.96/4.93	thf(decl_438, type, esk72_4: $i > $i > $i > $i > $i).
34.96/4.93	thf(decl_439, type, esk73_4: $i > $i > $i > $i > $i).
34.96/4.93	thf(decl_440, type, esk74_4: $i > $i > $i > $i > $i).
34.96/4.93	thf(decl_441, type, esk75_4: $i > $i > $i > $i > $i).
34.96/4.93	thf(decl_442, type, esk76_4: $i > $i > $i > $i > $i).
34.96/4.93	thf(decl_443, type, esk77_4: $i > $i > $i > $i > $i).
34.96/4.93	thf(decl_444, type, esk78_4: $i > $i > $i > $i > $i).
34.96/4.93	thf(decl_445, type, esk79_4: $i > $i > $i > $i > $i).
34.96/4.93	thf(decl_446, type, esk80_3: $i > $i > ($i > $i) > $i).
34.96/4.93	thf(decl_447, type, esk81_3: $i > $i > ($i > $i) > $i).
34.96/4.93	thf(decl_448, type, esk82_3: $i > $i > ($i > $i) > $i).
34.96/4.93	thf(decl_449, type, esk83_3: $i > $i > $i > $i).
34.96/4.93	thf(decl_450, type, esk84_3: $i > $i > $i > $i).
34.96/4.93	thf(decl_451, type, esk85_3: $i > $i > $i > $i).
34.96/4.93	thf(decl_452, type, esk86_3: $i > $i > $i > $i).
34.96/4.93	thf(decl_453, type, esk87_3: $i > $i > ($i > $o) > $i).
34.96/4.93	thf(decl_454, type, esk88_3: $i > $i > ($i > $o) > $i).
34.96/4.93	thf(decl_455, type, esk89_3: $i > $i > ($i > $o) > $i).
34.96/4.93	thf(decl_456, type, esk90_3: $i > $i > ($i > $o) > $i).
34.96/4.93	thf(decl_457, type, esk91_3: $i > $i > $i > $i).
34.96/4.93	thf(decl_458, type, esk92_3: $i > $i > $i > $i).
34.96/4.93	thf(decl_459, type, esk93_3: $i > $i > $i > $i).
34.96/4.93	thf(decl_460, type, esk94_3: $i > $i > $i > $i).
34.96/4.93	thf(decl_461, type, esk95_3: $i > $i > $i > $i).
34.96/4.93	thf(decl_462, type, esk96_3: $i > $i > $i > $i).
34.96/4.93	thf(decl_463, type, esk97_0: $i).
34.96/4.93	thf(decl_464, type, esk98_0: $i).
34.96/4.93	thf(decl_465, type, esk99_0: $i).
34.96/4.93	thf(decl_466, type, esk100_0: $i).
34.96/4.93	thf(decl_467, type, esk101_0: $i).
34.96/4.93	thf(decl_493, type, esk127_0: $i).
34.96/4.93	thf(breln1, axiom, ((breln1)=(^[X4:$i, X33:$i]:((breln @ X4 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', breln1)).
34.96/4.93	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', breln)).
34.96/4.93	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', exuEu)).
34.96/4.93	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', exu)).
34.96/4.93	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', exuE3u)).
34.96/4.93	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', exuI2)).
34.96/4.93	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', exuI3)).
34.96/4.93	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', exuI1)).
34.96/4.93	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', nonempty)).
34.96/4.93	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', exuE3e)).
34.96/4.93	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', descrp)).
34.96/4.93	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', replAx)).
34.96/4.93	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setOfPairsIsBReln)).
34.96/4.93	thf(breln1compset, axiom, ((breln1compset)=(^[X4:$i, X33:$i, X35:$i]:(dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:(?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', breln1compset)).
34.96/4.93	thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setOfPairsIsBReln1)).
34.96/4.93	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', descr__Cong)).
34.96/4.93	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', exu__Cong)).
34.96/4.93	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', exuE2)).
34.96/4.93	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', nonemptyI)).
34.96/4.93	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', exuE1)).
34.96/4.93	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', emptyE1)).
34.96/4.93	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', dpsetconstrI)).
34.96/4.93	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', nonemptyImpWitness)).
34.96/4.93	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', singletonprop)).
34.96/4.93	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', ex1E1)).
34.96/4.93	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setoftrueEq)).
34.96/4.93	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', nonemptyI1)).
34.96/4.93	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', kfstsingleton)).
34.96/4.93	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', nonemptyE1)).
34.96/4.93	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', dsetconstrEL)).
34.96/4.93	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', ksndsingleton)).
34.96/4.93	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', dpsetconstrSub)).
34.96/4.93	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', dpsetconstrEL1)).
34.96/4.93	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', funcImageSingleton)).
34.96/4.93	thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', lamProp)).
34.96/4.93	thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', lamp)).
34.96/4.93	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', brelnall1)).
34.96/4.93	thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', subbreln)).
34.96/4.93	thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', beta2)).
34.96/4.93	thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', eta2)).
34.96/4.93	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', iffalseProp1)).
34.96/4.93	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', iffalseProp2)).
34.96/4.93	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', iftrueProp1)).
34.96/4.93	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', iftrueProp2)).
34.96/4.93	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', apProp)).
34.96/4.93	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', dpsetconstrER)).
34.96/4.93	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', dpsetconstrEL2)).
34.96/4.93	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', dpsetconstrERa)).
34.96/4.93	thf(breln1all2, axiom, ((breln1all2)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', breln1all2)).
34.96/4.93	thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', breln1SetBreln1)).
34.96/4.93	thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', subbreln1)).
34.96/4.93	thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', eqbreln1)).
34.96/4.93	thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', breln1invprop)).
34.96/4.93	thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', breln1compI)).
34.96/4.93	thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', breln1compprop)).
34.96/4.93	thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', breln1invE)).
34.96/4.93	thf(breln1invI, axiom, ((breln1invI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', breln1invI)).
34.96/4.93	thf(breln1all1, axiom, ((breln1all1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', breln1all1)).
34.96/4.93	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', ifSingleton)).
34.96/4.93	thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', lam2lamEq)).
34.96/4.93	thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', eta1)).
34.96/4.93	thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', beta1)).
34.96/4.93	thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', eqbreln)).
34.96/4.93	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', ex1E2)).
34.96/4.93	thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', brelnall2)).
34.96/4.93	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', lam2p)).
34.96/4.93	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', ex1I2)).
34.96/4.93	thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', ex1I)).
34.96/4.93	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', sepSubset)).
34.96/4.93	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', sepInPowerset)).
34.96/4.93	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', dsetconstr__Cong)).
34.96/4.93	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setbeta)).
34.96/4.93	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', dsetconstrER)).
34.96/4.93	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', dsetconstrI)).
34.96/4.93	thf(breln1compE, conjecture, ((((setadjoinAx)=>(((setunionAx)=>((omega0Ax)=>(((omegaIndAx)=>((((((dsetconstrI)=>(((dsetconstrER)=>((exuE1)=>((((emptysetimpfalse)=>((notinemptyset)=>(((setext)=>((emptyI)=>(((setbeta)=>(((nonemptyI)=>((((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>(((((((powersetE)=>(((setunionE)=>(((exuE2)=>(((uniqinunit)=>(((eqinunit)=>((singletonsswitch)=>(((upairsetIL)=>((((vacuousDall)=>((quantDeMorgan1)=>(((quantDeMorgan3)=>(((prop2setI)=>((prop2set2propI)=>(((notdallE)=>(((((inCongP)=>((in__Cong)=>(((exu__Cong)=>((((powerset__Cong)=>(((omega__Cong)=>(((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((((subsetE2)=>((notsubsetI)=>(((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>(((subset2powerset)=>(((((((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>(((binunionEcases)=>((binunionE)=>(((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((((((binintersectER)=>((disjointsetsI1)=>((((binintersectSubset1)=>(((setminusI)=>((setminusEL)=>((setminusER)=>(((setminusERneg)=>(((setminusILneg)=>((((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>(((((singletonsubset)=>(((singletoninpowunion)=>(((upairsubunion)=>((((ubforcartprodlem2)=>(((cartprodpairin)=>((((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>(((singletonprop)=>((ex1E1)=>((((singletonsuniq)=>(((kfstsingleton)=>(((kfstpairEq)=>(((((setukpairinjR11)=>(((setukpairinjR1)=>(((((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>(((cartprodpairmemEL)=>((cartprodpairmemER)=>((((cartprodsndpairEq)=>(((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>(((dpsetconstrEL1)=>((((funcImageSingleton)=>(((app)=>((infuncsetfunc)=>((((lamProp)=>((lamp)=>(((brelnall1)=>(((((funcGraphProp3)=>((funcGraphProp2)=>(((funcGraphProp4)=>((subbreln)=>((((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>(((((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((((theeq)=>((((iftrueorfalse)=>(((binunionT_lem)=>((powersetT_lem)=>(((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>(((complementTE1)=>((((contrasubsetT)=>(((((((doubleComplementSub1)=>((((((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>(((inComplementUnionImpInComplement1)=>((binunionTE)=>(((demorgan2a1)=>(((demorgan2a2)=>(((demorgan1b)=>((demorgan1)=>((((((woz13rule0)=>((woz13rule1)=>(((woz13rule3)=>(((woz1_1)=>(((woz1_3)=>((woz1_4)=>(((breln1all2)=>((breln1SetBreln1)=>(((((subbreln1)=>((eqbreln1)=>((breln1invprop)=>((((![X4:$i, X33:$i]:((![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X14 @ X3) @ X35))&(in @ (kpair @ X2 @ X14) @ X33))))))))))<=(breln1 @ X4 @ X33)))<=(breln1compI))<=(breln1compprop))<=(breln1invE))<=(breln1invI)))))<=(breln1all1))<=(setOfPairsIsBReln1))<=(choice2fnsingleton))))<=(woz1_5))))<=(woz1_2)))<=(woz13rule4)))<=(woz13rule2))))<=(demorgan2))<=(demorgan2b))<=(demorgan2b2))<=(demorgan2a))))<=(demorgan1a)))<=(complementUnionInPowersetComplement)))<=(binunionTEcontra))))<=(inComplementUnionImpNotIn1)))))<=(inIntersectImpInUnion))<=(binunionTIRcontra)))))))<=(complementImpComplementIntersect))<=(complementTnotintersectT))<=(doubleComplementEq))<=(doubleComplementSub2)))<=(doubleComplementE1))<=(doubleComplementI1))<=(contrasubsetT3))<=(contrasubsetT2))<=(contrasubsetT1)))<=(binintersectTERcontra))<=(binintersectTELcontra)))<=(complementTI1)))))))<=(setminusT_lem))))<=(binintersectT_lem)))<=(iffalse))<=(iftrue)))<=(ifp))<=(ifSingleton))))))))<=(lam2lamEq))<=(eta1))<=(beta1)))))<=(funcext))<=(eqbreln))))<=(funcextLem))))<=(funcGraphProp1))<=(ex1E2))<=(brelnall2)))<=(lam2p))))<=(funcinfuncset))<=(ap2p))))<=(apProp)))<=(dpsetconstrER))<=(dpsetconstrEL2)))<=(dpsetconstrERa)))))<=(cartprodpairsurjEq)))<=(cartprodfstpairEq))<=(cartprodmempaircEq))))<=(cartprodsndin)))))<=(setukpairinjR))<=(setukpairinjR2))<=(upairequniteq)))<=(setukpairinjR12)))<=(setukpairinjL))<=(setukpairinjL2))<=(cartprodfstin)))<=(theprop)))<=(setukpairinjL1)))<=(ex1I2))<=(ex1I))))<=(setunionsingleton)))))<=(cartprodmempair))<=(cartprodmempair1)))<=(ubforcartprodlem3)))<=(ubforcartprodlem1))<=(upairinpowunion)))<=(upairset2E)))<=(singletoninpowerset)))<=(kpairp))<=(kpairiskpair))<=(setukpairIR))))))))))<=(setminusLsub))<=(setminusIRneg)))<=(setminusELneg)))<=(setminusSubset2)))))<=(bs114d)))<=(binintersectSubset4))<=(binintersectRsub))))<=(binintersectSubset3))<=(binintersectSubset2))<=(binintersectLsub))<=(binintersectEL)))))<=(binunionLsub))))<=(binunionIR)))))))<=(inPowerset))<=(powersetE1))<=(powersetI1))<=(subsetemptysetimpeq))<=(setextsub)))<=(setadjoinSub2))))))<=(notequalI1))))<=(subsetE))<=(emptysetsubset))))))))<=(exuEu)))<=(setunion__Cong)))<=(setadjoin__Cong))<=(emptyset__Cong)))<=(exuE3u))))<=(exuI2))<=(exuI3))<=(exuI1)))<=(notdexE))))<=(quantDeMorgan4)))<=(quantDeMorgan2))))<=(emptyE1))<=(upairsetIR)))<=(upairsetE))))<=(notinsingleton)))<=(nonemptyImpWitness)))<=(subPowSU)))<=(setunionI)))<=(emptyInPowerset))<=(emptyinPowerset))<=(powersetI))<=(setoftrueEq))<=(setadjoinOr)))))<=(setadjoinIL))<=(nonemptyI1)))<=(nonemptyE1)))<=(noeltsimpempty))))<=(exuE3e))))<=(emptysetE))<=(prop2setE))))<=(dsetconstrEL)))<=(descrp))<=(wellorderingAx))<=(foundationAx))<=(replAx)))<=(omegaSAx))))<=(powersetAx)))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', breln1compE)).
34.96/4.93	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', symdiffIneg1)).
34.96/4.93	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setextAx)).
34.96/4.93	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', inPowerset)).
34.96/4.93	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', symdiffI2)).
34.96/4.93	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', powersetE1)).
34.96/4.93	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setukpairIL)).
34.96/4.93	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', powersetI1)).
34.96/4.93	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', subsetemptysetimpeq)).
34.96/4.93	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', singletonsubset)).
34.96/4.93	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setextsub)).
34.96/4.93	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setadjoinSub2)).
34.96/4.93	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', notequalI1)).
34.96/4.93	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', singletoninpowunion)).
34.96/4.93	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', subsetE)).
34.96/4.93	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', emptysetsubset)).
34.96/4.93	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', upairsubunion)).
34.96/4.93	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setunion__Cong)).
34.96/4.93	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setadjoin__Cong)).
34.96/4.93	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', ubforcartprodlem2)).
34.96/4.93	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', emptyset__Cong)).
34.96/4.93	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', cartprodpairin)).
34.96/4.93	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', notdexE)).
34.96/4.93	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setunionE2)).
34.96/4.93	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', quantDeMorgan4)).
34.96/4.93	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', quantDeMorgan2)).
34.96/4.93	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setunionsingleton1)).
34.96/4.93	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', upairsetIR)).
34.96/4.93	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', upairsetE)).
34.96/4.93	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', notinsingleton)).
34.96/4.93	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setunionsingleton2)).
34.96/4.93	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', subPowSU)).
34.96/4.93	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setunionI)).
34.96/4.93	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', emptyInPowerset)).
34.96/4.93	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', emptyinPowerset)).
34.96/4.93	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', powersetI)).
34.96/4.93	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', singletonsuniq)).
34.96/4.93	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setadjoinOr)).
34.96/4.93	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setadjoinIL)).
34.96/4.93	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', noeltsimpempty)).
34.96/4.93	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', kfstpairEq)).
34.96/4.93	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', emptysetE)).
34.96/4.93	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', prop2setE)).
34.96/4.93	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setukpairinjR11)).
34.96/4.93	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setukpairinjR1)).
34.96/4.93	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', wellorderingAx)).
34.96/4.93	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', symdiffIneg2)).
34.96/4.93	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', foundationAx)).
34.96/4.93	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', omegaSAx)).
34.96/4.93	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', powersetAx)).
34.96/4.93	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', emptysetAx)).
34.96/4.93	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', ksndpairEq)).
34.96/4.93	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', kpairsurjEq)).
34.96/4.93	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', cartprodpairmemEL)).
34.96/4.93	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', cartprodpairmemER)).
34.96/4.93	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', cartprodsndpairEq)).
34.96/4.93	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', complementTE1)).
34.96/4.93	thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', contrasubsetT)).
34.96/4.93	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', app)).
34.96/4.93	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', infuncsetfunc)).
34.96/4.93	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', secondinupair)).
34.96/4.93	thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', funcGraphProp3)).
34.96/4.93	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', funcGraphProp2)).
34.96/4.93	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', funcGraphProp4)).
34.96/4.93	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', funcext2)).
34.96/4.93	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', ap2apEq1)).
34.96/4.93	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', ap2apEq2)).
34.96/4.93	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', theeq)).
34.96/4.93	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', iftrueorfalse)).
34.96/4.93	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binunionT_lem)).
34.96/4.93	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', powersetT_lem)).
34.96/4.93	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', complementT_lem)).
34.96/4.93	thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setextT)).
34.96/4.93	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', subsetTI)).
34.96/4.93	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', powersetTI1)).
34.96/4.93	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', powersetTE1)).
34.96/4.93	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', cartprodpairsurjEq)).
34.96/4.93	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', cartprodfstpairEq)).
34.96/4.93	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', cartprodmempaircEq)).
34.96/4.93	thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', doubleComplementSub1)).
34.96/4.93	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', complementSubsetComplementIntersect)).
34.96/4.93	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', complementInPowersetComplementIntersect)).
34.96/4.93	thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', contraSubsetComplement)).
34.96/4.93	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', complementTcontraSubset)).
34.96/4.93	thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binunionTILcontra)).
34.96/4.93	thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', inIntersectImpInUnion2)).
34.96/4.93	thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', inIntersectImpInIntersectUnions)).
34.96/4.93	thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', intersectInPowersetIntersectUnions)).
34.96/4.93	thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', inComplementUnionImpInComplement1)).
34.96/4.93	thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binunionTE)).
34.96/4.93	thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', demorgan2a1)).
34.96/4.93	thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', demorgan2a2)).
34.96/4.93	thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', demorgan1b)).
34.96/4.93	thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', demorgan1)).
34.96/4.93	thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', woz13rule0)).
34.96/4.93	thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', woz13rule1)).
34.96/4.93	thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', woz13rule3)).
34.96/4.93	thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', woz1_1)).
34.96/4.93	thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', woz1_3)).
34.96/4.93	thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', woz1_4)).
34.96/4.93	thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', woz1_5)).
34.96/4.93	thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', woz1_2)).
34.96/4.93	thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', woz13rule4)).
34.96/4.93	thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', woz13rule2)).
34.96/4.93	thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', demorgan2)).
34.96/4.93	thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', demorgan2b)).
34.96/4.93	thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', demorgan2b2)).
34.96/4.93	thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', demorgan2a)).
34.96/4.93	thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', demorgan1a)).
34.96/4.93	thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', complementUnionInPowersetComplement)).
34.96/4.93	thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binunionTEcontra)).
34.96/4.93	thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', inComplementUnionImpNotIn1)).
34.96/4.93	thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', inIntersectImpInUnion)).
34.96/4.93	thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binunionTIRcontra)).
34.96/4.93	thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', complementImpComplementIntersect)).
34.96/4.93	thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', complementTnotintersectT)).
34.96/4.93	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', doubleComplementEq)).
34.96/4.93	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', doubleComplementSub2)).
34.96/4.93	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', doubleComplementE1)).
34.96/4.93	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', doubleComplementI1)).
34.96/4.93	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', contrasubsetT3)).
34.96/4.93	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', contrasubsetT2)).
34.96/4.93	thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', contrasubsetT1)).
34.96/4.93	thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binintersectTERcontra)).
34.96/4.93	thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binintersectTELcontra)).
34.96/4.93	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', complementTI1)).
34.96/4.93	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setminusT_lem)).
34.96/4.93	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binintersectT_lem)).
34.96/4.93	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', iffalse)).
34.96/4.93	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', iftrue)).
34.96/4.93	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', ifp)).
34.96/4.93	thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', funcext)).
34.96/4.93	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', funcextLem)).
34.96/4.93	thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', funcGraphProp1)).
34.96/4.93	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', funcinfuncset)).
34.96/4.93	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', ap2p)).
34.96/4.93	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', cartprodsndin)).
34.96/4.93	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setukpairinjR)).
34.96/4.93	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setukpairinjR2)).
34.96/4.93	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', upairequniteq)).
34.96/4.93	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setukpairinjR12)).
34.96/4.93	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setukpairinjL)).
34.96/4.93	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setukpairinjL2)).
34.96/4.93	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', cartprodfstin)).
34.96/4.93	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', theprop)).
34.96/4.93	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setukpairinjL1)).
34.96/4.93	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setunionsingleton)).
34.96/4.93	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', cartprodmempair)).
34.96/4.93	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', cartprodmempair1)).
34.96/4.93	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', ubforcartprodlem3)).
34.96/4.93	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', ubforcartprodlem1)).
34.96/4.93	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', upairinpowunion)).
34.96/4.93	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', upairset2E)).
34.96/4.93	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', singletoninpowerset)).
34.96/4.93	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', kpairp)).
34.96/4.93	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', kpairiskpair)).
34.96/4.93	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setukpairIR)).
34.96/4.93	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setminusLsub)).
34.96/4.93	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setminusIRneg)).
34.96/4.93	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setminusELneg)).
34.96/4.93	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setminusSubset2)).
34.96/4.93	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', bs114d)).
34.96/4.93	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binintersectSubset4)).
34.96/4.93	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binintersectRsub)).
34.96/4.93	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binintersectSubset3)).
34.96/4.93	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binintersectSubset2)).
34.96/4.93	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binintersectLsub)).
34.96/4.93	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binintersectEL)).
34.96/4.93	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binunionLsub)).
34.96/4.93	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binunionIR)).
34.96/4.93	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', symdiffI1)).
34.96/4.93	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', symdiffE)).
34.96/4.93	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setminusSubset1)).
34.96/4.93	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setminusILneg)).
34.96/4.93	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setminusERneg)).
34.96/4.93	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setminusER)).
34.96/4.93	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setminusEL)).
34.96/4.93	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setminusI)).
34.96/4.93	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binintersectSubset1)).
34.96/4.93	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', disjointsetsI1)).
34.96/4.93	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binintersectER)).
34.96/4.93	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binintersectSubset5)).
34.96/4.93	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binintersectI)).
34.96/4.93	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binunionRsub)).
34.96/4.93	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binunionE)).
34.96/4.93	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binunionEcases)).
34.96/4.93	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', upairset2IR)).
34.96/4.93	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', binunionIL)).
34.96/4.93	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', powersetsubset)).
34.96/4.93	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', subset2powerset)).
34.96/4.93	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setadjoinSub)).
34.96/4.93	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', subsetTrans)).
34.96/4.93	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', subsetRefl)).
34.96/4.93	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', notequalI2)).
34.96/4.93	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', notsubsetI)).
34.96/4.93	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', subsetE2)).
34.96/4.93	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', subsetI2)).
34.96/4.93	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', eqimpsubset1)).
34.96/4.93	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', eqimpsubset2)).
34.96/4.93	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', subsetI1)).
34.96/4.93	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', omega__Cong)).
34.96/4.93	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', powerset__Cong)).
34.96/4.93	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', in__Cong)).
34.96/4.93	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', inCongP)).
34.96/4.93	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', notdallE)).
34.96/4.93	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', prop2setI)).
34.96/4.93	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', quantDeMorgan3)).
34.96/4.93	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', quantDeMorgan1)).
34.96/4.93	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', vacuousDall)).
34.96/4.93	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', upairsetIL)).
34.96/4.93	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', singletonsswitch)).
34.96/4.93	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', eqinunit)).
34.96/4.93	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', uniqinunit)).
34.96/4.93	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setunionE)).
34.96/4.93	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', powersetE)).
34.96/4.93	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setadjoinE)).
34.96/4.93	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setadjoinIR)).
34.96/4.93	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', emptyinunitempty)).
34.96/4.93	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', emptyI)).
34.96/4.93	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setext)).
34.96/4.93	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', notinemptyset)).
34.96/4.93	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', emptysetimpfalse)).
34.96/4.93	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', omegaIndAx)).
34.96/4.93	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', omega0Ax)).
34.96/4.93	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setunionAx)).
34.96/4.93	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.I3snLeOA0O/E---3.1_22601.p', setadjoinAx)).
34.96/4.93	thf(c_0_300, plain, ((breln1)=(^[Z0/* 19 */:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(fof_simplification,[status(thm)],[breln1])).
34.96/4.93	thf(c_0_301, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
34.96/4.93	thf(c_0_302, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
34.96/4.93	thf(c_0_303, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
34.96/4.93	thf(c_0_304, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
34.96/4.93	thf(c_0_305, 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])).
34.96/4.93	thf(c_0_306, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
34.96/4.93	thf(c_0_307, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
34.96/4.93	thf(c_0_308, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
34.96/4.93	thf(c_0_309, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
34.96/4.93	thf(c_0_310, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
34.96/4.93	thf(c_0_311, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
34.96/4.93	thf(c_0_312, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
34.96/4.93	thf(c_0_313, plain, ((breln1)=(^[Z0/* 19 */:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(apply_def,[status(thm)],[c_0_300, c_0_301])).
34.96/4.93	thf(c_0_314, plain, ((breln1compset)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:(dpsetconstr @ Z0 @ Z0 @ (^[Z3/* 19 */:$i, Z4:$i]:(?[X14:$i]:((((in @ X14 @ Z0)&(in @ (kpair @ Z3 @ X14) @ Z1))&(in @ (kpair @ X14 @ Z4) @ Z2)))))))), inference(fof_simplification,[status(thm)],[breln1compset])).
34.96/4.93	thf(c_0_315, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
34.96/4.93	thf(c_0_316, plain, ((descr__Cong)<=>![X1:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
34.96/4.93	thf(c_0_317, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
34.96/4.93	thf(c_0_318, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
34.96/4.93	thf(c_0_319, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
34.96/4.93	thf(c_0_320, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
34.96/4.93	thf(c_0_321, 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])).
34.96/4.93	thf(c_0_322, plain, ((exuEu)=(![X1:$i > $o]:(((?[X1035:$i]:((((X1 @ X1035))&![X1036:$i]:((((X1 @ X1036))=>((X1035)=(X1036)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_302, c_0_303])).
34.96/4.93	thf(c_0_323, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X1029:$i]:((((X1 @ X1029))&![X1030:$i]:((((X1 @ X1030))=>((X1029)=(X1030)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_304, c_0_303])).
34.96/4.93	thf(c_0_324, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X1027:$i]:((((X1 @ X1027))&![X1028:$i]:((((X1 @ X1028))=>((X1027)=(X1028))))))))))), inference(apply_def,[status(thm)],[c_0_305, c_0_303])).
34.96/4.93	thf(c_0_325, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X1025:$i]:((((X1 @ X1025))&![X1026:$i]:((((X1 @ X1026))=>((X1025)=(X1026)))))))))))), inference(apply_def,[status(thm)],[c_0_306, c_0_303])).
34.96/4.93	thf(c_0_326, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X1023:$i]:((((X1 @ X1023))&![X1024:$i]:((((X1 @ X1024))=>((X1023)=(X1024))))))))))), inference(apply_def,[status(thm)],[c_0_307, c_0_303])).
34.96/4.93	thf(c_0_327, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
34.96/4.93	thf(c_0_328, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_308])).
34.96/4.93	thf(c_0_329, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
34.96/4.93	thf(c_0_330, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
34.96/4.93	thf(c_0_331, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
34.96/4.93	thf(c_0_332, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_308])).
34.96/4.93	thf(c_0_333, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
34.96/4.93	thf(c_0_334, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_308])).
34.96/4.93	thf(c_0_335, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X1019:$i]:((((X1 @ X1019))&![X1020:$i]:((((X1 @ X1020))=>((X1019)=(X1020)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_309, c_0_303])).
34.96/4.93	thf(c_0_336, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
34.96/4.93	thf(c_0_337, plain, ((descrp)=(![X1:$i > $o]:(((?[X1015:$i]:((((X1 @ X1015))&![X1016:$i]:((((X1 @ X1016))=>((X1015)=(X1016)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_310, c_0_303])).
34.96/4.93	thf(c_0_338, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X1013:$i]:((((X6 @ X2 @ X1013))&![X1014:$i]:((((X6 @ X2 @ X1014))=>((X1013)=(X1014)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_311, c_0_303])).
34.96/4.93	thf(c_0_339, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
34.96/4.93	thf(c_0_340, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
34.96/4.93	thf(c_0_341, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_312, c_0_301])).
34.96/4.93	thf(c_0_342, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
34.96/4.93	thf(c_0_343, plain, ((funcImageSingleton)<=>![X4:$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])).
34.96/4.93	thf(c_0_344, 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])).
34.96/4.93	thf(c_0_345, 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 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
34.96/4.93	thf(c_0_346, axiom, ((brelnall1)=(![X4:$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_301])).
34.96/4.93	thf(c_0_347, 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_301])).
34.96/4.93	thf(c_0_348, 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])).
34.96/4.93	thf(c_0_349, 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])).
34.96/4.93	thf(c_0_350, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
34.96/4.93	thf(c_0_351, plain, ((iffalseProp2)<=>![X4:$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])).
34.96/4.93	thf(c_0_352, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
34.96/4.93	thf(c_0_353, plain, ((iftrueProp2)<=>![X4:$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])).
34.96/4.93	thf(c_0_354, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
34.96/4.93	thf(c_0_355, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
34.96/4.93	thf(c_0_356, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
34.96/4.93	thf(c_0_357, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
34.96/4.93	thf(c_0_358, axiom, ((breln1all2)=(![X4:$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_313])).
34.96/4.93	thf(c_0_359, axiom, ((breln1SetBreln1)=(![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>((subset @ X33 @ (cartprod @ X4 @ X4))))))), inference(apply_def,[status(thm)],[breln1SetBreln1, c_0_313])).
34.96/4.93	thf(c_0_360, axiom, ((subbreln1)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X4)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln1, c_0_313])).
34.96/4.93	thf(c_0_361, axiom, ((eqbreln1)=(![X4:$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_313])).
34.96/4.93	thf(c_0_362, axiom, ((breln1invprop)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>((subset @ (breln1invset @ X4 @ X33) @ (cartprod @ X4 @ X4))))))), inference(apply_def,[status(thm)],[breln1invprop, c_0_313])).
34.96/4.93	thf(c_0_363, axiom, ((breln1compI)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X4)))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:(?[X1042:$i]:((((in @ X1042 @ X4)&(in @ (kpair @ Z0 @ X1042) @ X33))&(in @ (kpair @ X1042 @ Z1) @ X35))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[breln1compI, c_0_314]), c_0_313])).
34.96/4.93	thf(c_0_364, axiom, ((breln1compprop)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X4)))=>((subset @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:(?[X1041:$i]:((((in @ X1041 @ X4)&(in @ (kpair @ Z0 @ X1041) @ X33))&(in @ (kpair @ X1041 @ Z1) @ X35)))))) @ (cartprod @ X4 @ X4))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[breln1compprop, c_0_314]), c_0_313])).
34.96/4.93	thf(c_0_365, axiom, ((breln1invE)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33)))))))))), inference(apply_def,[status(thm)],[breln1invE, c_0_313])).
34.96/4.93	thf(c_0_366, axiom, ((breln1invI)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))))))))))), inference(apply_def,[status(thm)],[breln1invI, c_0_313])).
34.96/4.93	thf(c_0_367, axiom, ((breln1all1)=(![X4:$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_313])).
34.96/4.93	thf(c_0_368, plain, ((setOfPairsIsBReln1)=(![X4:$i, X53:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X4)))))), inference(apply_def,[status(thm)],[c_0_315, c_0_313])).
34.96/4.93	thf(c_0_369, plain, ((ifSingleton)<=>![X4:$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])).
34.96/4.93	thf(c_0_370, 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])).
34.96/4.93	thf(c_0_371, 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])).
34.96/4.93	thf(c_0_372, 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])).
34.96/4.93	thf(c_0_373, 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_301])).
34.96/4.93	thf(c_0_374, 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])).
34.96/4.93	thf(c_0_375, 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_301])).
34.96/4.93	thf(c_0_376, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
34.96/4.93	thf(c_0_377, plain, ((ex1I2)<=>![X4:$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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
34.96/4.93	thf(c_0_378, plain, ((ex1I)<=>![X4:$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])).
34.96/4.93	thf(c_0_379, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
34.96/4.93	thf(c_0_380, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
34.96/4.93	thf(c_0_381, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
34.96/4.93	thf(c_0_382, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1037:$i]:((((X1 @ X1037))&![X1038:$i]:((((X1 @ X1038))=>((X1037)=(X1038)))))))=>((?[X1039:$i]:((((X17 @ X1039))&![X1040:$i]:((((X17 @ X1040))=>((X1039)=(X1040)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_316, c_0_303])).
34.96/4.93	thf(c_0_383, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1031:$i]:((((X1 @ X1031))&![X1032:$i]:((((X1 @ X1032))=>((X1031)=(X1032)))))))<=>(?[X1033:$i]:((((X17 @ X1033))&![X1034:$i]:((((X17 @ X1034))=>((X1033)=(X1034)))))))))))), inference(apply_def,[status(thm)],[c_0_317, c_0_303])).
34.96/4.93	thf(c_0_384, plain, ((exuE2)=(![X1:$i > $o]:(((?[X1021:$i]:((((X1 @ X1021))&![X1022:$i]:((((X1 @ X1022))=>((X1021)=(X1022)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_318, c_0_303])).
34.96/4.93	thf(c_0_385, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_319, c_0_308])).
34.96/4.93	thf(c_0_386, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
34.96/4.93	thf(c_0_387, plain, ((exuE1)=(![X1:$i > $o]:(((?[X1017:$i]:((((X1 @ X1017))&![X1018:$i]:((((X1 @ X1018))=>((X1017)=(X1018)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_320, c_0_303])).
34.96/4.93	thf(c_0_388, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
34.96/4.93	thf(c_0_389, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
34.96/4.93	thf(c_0_390, plain, ((epred1_0)<=>![X1988:$i]:(?[X1989:$i]:((((![X1990:$i]:(((in @ X1990 @ X1989)=>![X1991:$i]:(((in @ X1991 @ X1990)=>(in @ X1991 @ X1988)))))&![X1992:$i, X1993:$i]:((((in @ X1992 @ X1988)&(in @ X1993 @ X1988))=>(![X1994:$i]:(((in @ X1994 @ X1989)=>((in @ X1992 @ X1994)<=>(in @ X1993 @ X1994))))=>((X1992)=(X1993))))))&![X1995:$i, X1996:$i]:((((in @ X1995 @ X1989)&(in @ X1996 @ X1989))=>(![X1997:$i]:(((in @ X1997 @ X1995)=>(in @ X1997 @ X1996)))|![X1998:$i]:(((in @ X1998 @ X1996)=>(in @ X1998 @ X1995)))))))&![X1999:$i]:(((![X2000:$i]:(((in @ X2000 @ X1999)=>(in @ X2000 @ X1988)))&?[X2001:$i]:((in @ X2001 @ X1999)))=>?[X2002:$i, X2003:$i]:(((((in @ X2002 @ X1989)&(in @ X2003 @ X1999))&~(?[X2004:$i]:(((in @ X2004 @ X2002)&(in @ X2004 @ X1999)))))&![X2005:$i]:(((in @ X2005 @ X1989)=>(![X2006:$i]:(((in @ X2006 @ X2005)=>(in @ X2006 @ X2002)))|(in @ X2003 @ X2005)))))))))))), introduced(definition)).
34.96/4.93	thf(c_0_391, negated_conjecture, ~((![X2024:$i, X2025:$i]:((![X2026:$i]:(((in @ X2026 @ X2024)<=>(in @ X2026 @ X2025)))=>((X2024)=(X2025))))=>(![X2023:$i]:(~(in @ X2023 @ emptyset))=>(![X1043:$i, X1044:$i, X1045:$i]:(((in @ X1045 @ (setadjoin @ X1043 @ X1044))<=>(((X1045)=(X1043))|(in @ X1045 @ X1044))))=>(![X2020:$i, X2021:$i]:(((in @ X2021 @ (powerset @ X2020))<=>![X2022:$i]:(((in @ X2022 @ X2021)=>(in @ X2022 @ X2020)))))=>(![X1046:$i, X1047:$i]:(((in @ X1047 @ (setunion @ X1046))<=>?[X1048:$i]:(((in @ X1047 @ X1048)&(in @ X1048 @ X1046)))))=>((in @ emptyset @ omega)=>(![X2019:$i]:(((in @ X2019 @ omega)=>(in @ (setadjoin @ X2019 @ X2019) @ omega)))=>(![X1049:$i]:((((in @ emptyset @ X1049)&![X1050:$i]:((((in @ X1050 @ omega)&(in @ X1050 @ X1049))=>(in @ (setadjoin @ X1050 @ X1050) @ X1049))))=>![X1051:$i]:(((in @ X1051 @ omega)=>(in @ X1051 @ X1049)))))=>(![X2011:$i > $i > $o, X2012:$i]:((![X2013:$i]:(((in @ X2013 @ X2012)=>?[X2014:$i]:(((X2011 @ X2013 @ X2014)&![X2015:$i]:(((X2011 @ X2013 @ X2015)=>((X2014)=(X2015))))))))=>?[X2016:$i]:(![X2017:$i]:(((in @ X2017 @ X2016)<=>?[X2018:$i]:(((in @ X2018 @ X2012)&(X2011 @ X2018 @ X2017))))))))=>(![X2007:$i]:((?[X2008:$i]:((in @ X2008 @ X2007))=>?[X2009:$i]:(((in @ X2009 @ X2007)&~(?[X2010:$i]:(((in @ X2010 @ X2009)&(in @ X2010 @ X2007))))))))=>((epred1_0)=>(![X1985:$i > $o]:((?[X1986:$i]:(((X1985 @ X1986)&![X1987:$i]:(((X1985 @ X1987)=>((X1986)=(X1987))))))=>(X1985 @ (descr @ (^[Z0/* 17 */:$i]:(X1985 @ Z0))))))=>(![X1052:$i, X1053:$i > $o, X1054:$i]:(((in @ X1054 @ X1052)=>((X1053 @ X1054)=>(in @ X1054 @ (dsetconstr @ X1052 @ X1053)))))=>(![X1982:$i, X1983:$i > $o, X1984:$i]:(((in @ X1984 @ (dsetconstr @ X1982 @ X1983))=>(in @ X1984 @ X1982)))=>(![X1055:$i, X1056:$i > $o, X1057:$i]:(((in @ X1057 @ (dsetconstr @ X1055 @ X1056))=>(X1056 @ X1057)))=>(![X1058:$i > $o]:((?[X1059:$i]:(((X1058 @ X1059)&![X1060:$i]:(((X1058 @ X1060)=>((X1059)=(X1060))))))=>?[X1061:$i]:(((X1058 @ X1061)&![X1062:$i]:(((X1058 @ X1062)=>((X1061)=(X1062))))))))=>(![X1980:$o, X1981:$i]:(((in @ X1981 @ (prop2set @ ((X1980))))=>(X1980)))=>(![X1978:$i]:(((in @ X1978 @ emptyset)=>![X1979:$o]:((X1979))))=>(![X1063:$i]:(((in @ X1063 @ emptyset)=>~($true)))=>(![X1064:$i]:(~(in @ X1064 @ emptyset))=>(![X1974:$i > $o]:((?[X1975:$i]:(((X1974 @ X1975)&![X1976:$i]:(((X1974 @ X1976)=>((X1975)=(X1976))))))=>?[X1977:$i]:((X1974 @ X1977))))=>(![X1065:$i, X1066:$i]:((![X1067:$i]:(((in @ X1067 @ X1065)=>(in @ X1067 @ X1066)))=>(![X1068:$i]:(((in @ X1068 @ X1066)=>(in @ X1068 @ X1065)))=>((X1065)=(X1066)))))=>(![X1069:$i]:((![X1070:$i]:(~(in @ X1070 @ X1069))=>((X1069)=(emptyset))))=>(![X1972:$i]:((![X1973:$i]:(~(in @ X1973 @ X1972))=>((X1972)=(emptyset))))=>(![X1071:$i, X1072:$i > $o, X1073:$i]:(((in @ X1073 @ X1071)=>((in @ X1073 @ (dsetconstr @ X1071 @ X1072))<=>(X1072 @ X1073))))=>(![X1970:$i]:((((X1970)!=(emptyset))=>?[X1971:$i]:((in @ X1971 @ X1970))))=>(![X1074:$i, X1075:$i > $o, X1076:$i]:(((in @ X1076 @ X1074)=>((X1075 @ X1076)=>((dsetconstr @ X1074 @ X1075)!=(emptyset)))))=>(![X1968:$i]:((?[X1969:$i]:((in @ X1969 @ X1968))=>((X1968)!=(emptyset))))=>(![X1966:$i, X1967:$i]:((in @ X1966 @ (setadjoin @ X1966 @ X1967)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1077:$i, X1078:$i, X1079:$i]:(((in @ X1079 @ X1078)=>(in @ X1079 @ (setadjoin @ X1077 @ X1078))))=>(![X1080:$i, X1081:$i, X1082:$i]:(((in @ X1082 @ (setadjoin @ X1080 @ X1081))=>![X1083:$o]:(((((X1082)=(X1080))=>(X1083))=>(((in @ X1082 @ X1081)=>(X1083))=>(X1083))))))=>(![X1963:$i, X1964:$i, X1965:$i]:(((in @ X1965 @ (setadjoin @ X1963 @ X1964))=>(((X1965)=(X1963))|(in @ X1965 @ X1964))))=>(![X1962:$i]:(((dsetconstr @ X1962 @ (^[Z0/* 1 */:$i]:($true)))=(X1962)))=>(![X1959:$i, X1960:$i]:((![X1961:$i]:(((in @ X1961 @ X1960)=>(in @ X1961 @ X1959)))=>(in @ X1960 @ (powerset @ X1959))))=>(![X1958:$i]:((in @ emptyset @ (powerset @ X1958)))=>(![X1957:$i]:((in @ emptyset @ (powerset @ X1957)))=>(![X1084:$i, X1085:$i, X1086:$i]:(((in @ X1085 @ (powerset @ X1084))=>((in @ X1086 @ X1085)=>(in @ X1086 @ X1084))))=>(![X1954:$i, X1955:$i, X1956:$i]:(((in @ X1955 @ X1956)=>((in @ X1956 @ X1954)=>(in @ X1955 @ (setunion @ X1954)))))=>(![X1087:$i, X1088:$i]:(((in @ X1088 @ (setunion @ X1087))=>![X1089:$o]:((![X1090:$i]:(((in @ X1088 @ X1090)=>((in @ X1090 @ X1087)=>(X1089))))=>(X1089)))))=>(![X1952:$i, X1953:$i]:(((in @ X1953 @ X1952)=>(in @ X1953 @ (powerset @ (setunion @ X1952)))))=>(![X1091:$i > $o]:((?[X1092:$i]:(((X1091 @ X1092)&![X1093:$i]:(((X1091 @ X1093)=>((X1092)=(X1093))))))=>?[X1094:$i]:(![X1095:$i]:(((X1091 @ X1095)<=>((X1095)=(X1094)))))))=>(![X1950:$i]:((((X1950)!=(emptyset))=>?[X1951:$i]:(((in @ X1951 @ X1950)&$true))))=>(![X1096:$i, X1097:$i]:(((in @ X1096 @ (setadjoin @ X1097 @ emptyset))=>((X1096)=(X1097))))=>(![X1948:$i, X1949:$i]:((((X1948)!=(X1949))=>~(in @ X1949 @ (setadjoin @ X1948 @ emptyset))))=>(![X1098:$i, X1099:$i]:((((X1098)=(X1099))=>(in @ X1098 @ (setadjoin @ X1099 @ emptyset))))=>(![X1100:$i, X1101:$i]:(((in @ X1100 @ (setadjoin @ X1101 @ emptyset))=>(in @ X1101 @ (setadjoin @ X1100 @ emptyset))))=>(![X1945:$i, X1946:$i, X1947:$i]:(((in @ X1947 @ (setadjoin @ X1945 @ (setadjoin @ X1946 @ emptyset)))=>(((X1947)=(X1945))|((X1947)=(X1946)))))=>(![X1102:$i, X1103:$i]:((in @ X1102 @ (setadjoin @ X1102 @ (setadjoin @ X1103 @ emptyset))))=>(![X1943:$i, X1944:$i]:((in @ X1944 @ (setadjoin @ X1943 @ (setadjoin @ X1944 @ emptyset))))=>(![X1940:$i, X1941:$i > $o]:((?[X1942:$i]:(((in @ X1942 @ X1940)&(X1941 @ X1942)))=>(((dsetconstr @ X1940 @ X1941)=(emptyset))=>~($true))))=>(![X1104:$i > $o, X1105:$i]:(((in @ X1105 @ emptyset)=>(X1104 @ X1105)))=>(![X1106:$i, X1107:$i > $o]:((~(![X1108:$i]:(((in @ X1108 @ X1106)=>(X1107 @ X1108))))=>?[X1109:$i]:(((in @ X1109 @ X1106)&~((X1107 @ X1109))))))=>(![X1936:$i, X1937:$i > $o]:((![X1938:$i]:(((in @ X1938 @ X1936)=>~((X1937 @ X1938))))=>~(?[X1939:$i]:(((in @ X1939 @ X1936)&(X1937 @ X1939))))))=>(![X1110:$i, X1111:$i > $o]:((~(?[X1112:$i]:(((in @ X1112 @ X1110)&(X1111 @ X1112))))=>![X1113:$i]:(((in @ X1113 @ X1110)=>~((X1111 @ X1113))))))=>(![X1932:$i, X1933:$i > $o]:((?[X1934:$i]:(((in @ X1934 @ X1932)&~((X1933 @ X1934))))=>~(![X1935:$i]:(((in @ X1935 @ X1932)=>(X1933 @ X1935))))))=>(![X1114:$o]:(((X1114)=>(in @ emptyset @ (prop2set @ ((X1114))))))=>((prop2set2propI)=>(![X1928:$i, X1929:$i > $o]:((~(?[X1930:$i]:(((in @ X1930 @ X1928)&(X1929 @ X1930))))=>![X1931:$i]:(((in @ X1931 @ X1928)=>~((X1929 @ X1931))))))=>(![X1115:$i, X1116:$i > $o]:((~(![X1117:$i]:(((in @ X1117 @ X1115)=>(X1116 @ X1117))))=>?[X1118:$i]:(((in @ X1118 @ X1115)&~((X1116 @ X1118))))))=>(![X1923:$i > $o]:((?[X1924:$i]:(((X1923 @ X1924)&![X1925:$i]:(((X1923 @ X1925)=>((X1924)=(X1925))))))=>?[X1926:$i]:(((X1923 @ X1926)&![X1927:$i]:(((X1923 @ X1927)=>((X1926)=(X1927))))))))=>(![X1917:$i > $o]:((?[X1918:$i]:((X1917 @ X1918))=>(![X1919:$i, X1920:$i]:(((X1917 @ X1919)=>((X1917 @ X1920)=>((X1919)=(X1920)))))=>?[X1921:$i]:(((X1917 @ X1921)&![X1922:$i]:(((X1917 @ X1922)=>((X1921)=(X1922)))))))))=>(![X1912:$i > $o]:((?[X1913:$i]:(![X1914:$i]:(((X1912 @ X1914)<=>((X1914)=(X1913)))))=>?[X1915:$i]:(((X1912 @ X1915)&![X1916:$i]:(((X1912 @ X1916)=>((X1915)=(X1916))))))))=>(![X1119:$i, X1120:$i]:((((X1119)=(X1120))=>![X1121:$i, X1122:$i]:((((X1121)=(X1122))=>((in @ X1121 @ X1119)=>(in @ X1122 @ X1120))))))=>(![X1123:$i, X1124:$i]:((((X1123)=(X1124))=>![X1125:$i, X1126:$i]:((((X1125)=(X1126))=>((in @ X1125 @ X1123)<=>(in @ X1126 @ X1124))))))=>(![X1907:$i > $o]:((?[X1908:$i]:(((X1907 @ X1908)&![X1909:$i]:(((X1907 @ X1909)=>((X1908)=(X1909))))))=>![X1910:$i, X1911:$i]:(((X1907 @ X1910)=>((X1907 @ X1911)=>((X1910)=(X1911)))))))=>(![X1127:$i > $o, X1128:$i > $o]:((![X1129:$i, X1130:$i]:((((X1129)=(X1130))=>((X1127 @ X1129)<=>(X1128 @ X1130))))=>(?[X1131:$i]:(((X1127 @ X1131)&![X1132:$i]:(((X1127 @ X1132)=>((X1131)=(X1132))))))<=>?[X1133:$i]:(((X1128 @ X1133)&![X1134:$i]:(((X1128 @ X1134)=>((X1133)=(X1134)))))))))=>(((emptyset)=(emptyset))=>(![X1903:$i, X1904:$i]:((((X1903)=(X1904))=>![X1905:$i, X1906:$i]:((((X1905)=(X1906))=>((setadjoin @ X1903 @ X1905)=(setadjoin @ X1904 @ X1906))))))=>(![X1135:$i, X1136:$i]:((((X1135)=(X1136))=>((powerset @ X1135)=(powerset @ X1136))))=>(![X1901:$i, X1902:$i]:((((X1901)=(X1902))=>((setunion @ X1901)=(setunion @ X1902))))=>(((omega)=(omega))=>(![X1896:$i > $o]:((?[X1897:$i]:(((X1896 @ X1897)&![X1898:$i]:(((X1896 @ X1898)=>((X1897)=(X1898))))))=>![X1899:$i, X1900:$i]:(((X1896 @ X1899)=>((X1896 @ X1900)=>((X1899)=(X1900)))))))=>(![X1137:$i > $o, X1138:$i > $o]:((![X1139:$i, X1140:$i]:((((X1139)=(X1140))=>((X1137 @ X1139)<=>(X1138 @ X1140))))=>(?[X1141:$i]:(((X1137 @ X1141)&![X1142:$i]:(((X1137 @ X1142)=>((X1141)=(X1142))))))=>(?[X1143:$i]:(((X1138 @ X1143)&![X1144:$i]:(((X1138 @ X1144)=>((X1143)=(X1144))))))=>((descr @ X1137)=(descr @ X1138))))))=>(![X1145:$i, X1146:$i]:((((X1145)=(X1146))=>![X1147:$i > $o, X1148:$i > $o]:((![X1149:$i]:(((in @ X1149 @ X1145)=>![X1150:$i]:(((in @ X1150 @ X1146)=>(((X1149)=(X1150))=>((X1147 @ X1149)<=>(X1148 @ X1150)))))))=>((dsetconstr @ X1145 @ X1147)=(dsetconstr @ X1146 @ X1148))))))=>(![X1151:$i, X1152:$i]:((![X1153:$i]:(((in @ X1153 @ X1151)=>(in @ X1153 @ X1152)))=>(subset @ X1151 @ X1152)))=>(![X1154:$i, X1155:$i]:((((X1154)=(X1155))=>(subset @ X1155 @ X1154)))=>(![X1156:$i, X1157:$i]:((((X1156)=(X1157))=>(subset @ X1156 @ X1157)))=>(![X1158:$i, X1159:$i]:((![X1160:$i]:(((in @ X1160 @ X1158)=>(in @ X1160 @ X1159)))=>(subset @ X1158 @ X1159)))=>(![X1895:$i]:((subset @ emptyset @ X1895))=>(![X1892:$i, X1893:$i, X1894:$i]:(((subset @ X1892 @ X1893)=>((in @ X1894 @ X1892)=>(in @ X1894 @ X1893))))=>(![X1161:$i, X1162:$i, X1163:$i]:(((subset @ X1161 @ X1162)=>(~(in @ X1163 @ X1162)=>~(in @ X1163 @ X1161))))=>(![X1164:$i, X1165:$i, X1166:$i]:(((in @ X1166 @ X1164)=>(~(in @ X1166 @ X1165)=>~(subset @ X1164 @ X1165))))=>(![X1890:$i, X1891:$i]:((~(subset @ X1890 @ X1891)=>((X1890)!=(X1891))))=>(![X1167:$i, X1168:$i, X1169:$i]:(((in @ X1169 @ X1167)=>(~(in @ X1169 @ X1168)=>((X1167)!=(X1168)))))=>(![X1170:$i]:((subset @ X1170 @ X1170))=>(![X1171:$i, X1172:$i, X1173:$i]:(((subset @ X1171 @ X1172)=>((subset @ X1172 @ X1173)=>(subset @ X1171 @ X1173))))=>(![X1174:$i, X1175:$i]:((subset @ X1175 @ (setadjoin @ X1174 @ X1175)))=>(![X1887:$i, X1888:$i, X1889:$i]:(((subset @ X1887 @ X1889)=>(subset @ X1887 @ (setadjoin @ X1888 @ X1889))))=>(![X1176:$i, X1177:$i]:(((subset @ X1176 @ X1177)=>(in @ X1176 @ (powerset @ X1177))))=>(![X1885:$i, X1886:$i]:(((subset @ X1885 @ X1886)=>((subset @ X1886 @ X1885)=>((X1885)=(X1886)))))=>(![X1884:$i]:(((subset @ X1884 @ emptyset)=>((X1884)=(emptyset))))=>(![X1882:$i, X1883:$i]:(((subset @ X1883 @ X1882)=>(in @ X1883 @ (powerset @ X1882))))=>(![X1880:$i, X1881:$i]:(((in @ X1881 @ (powerset @ X1880))=>(subset @ X1881 @ X1880)))=>(![X1879:$i]:((in @ X1879 @ (powerset @ X1879)))=>(![X1178:$i, X1179:$i]:(((subset @ X1178 @ X1179)=>(subset @ (powerset @ X1178) @ (powerset @ X1179))))=>(![X1180:$i, X1181:$i > $o]:((in @ (dsetconstr @ X1180 @ X1181) @ (powerset @ X1180)))=>(![X1182:$i, X1183:$i > $o]:((subset @ (dsetconstr @ X1182 @ X1183) @ X1182))=>(![X1184:$i, X1185:$i, X1186:$i]:(((in @ X1186 @ X1184)=>(in @ X1186 @ (binunion @ X1184 @ X1185))))=>(![X1187:$i, X1188:$i]:((in @ X1188 @ (setadjoin @ X1187 @ (setadjoin @ X1188 @ emptyset))))=>(![X1876:$i, X1877:$i, X1878:$i]:(((in @ X1878 @ X1877)=>(in @ X1878 @ (binunion @ X1876 @ X1877))))=>(![X1189:$i, X1190:$i, X1191:$i, X1192:$o]:(((in @ X1191 @ (binunion @ X1189 @ X1190))=>(((in @ X1191 @ X1189)=>(X1192))=>(((in @ X1191 @ X1190)=>(X1192))=>(X1192)))))=>(![X1193:$i, X1194:$i, X1195:$i]:(((in @ X1195 @ (binunion @ X1193 @ X1194))=>((in @ X1195 @ X1193)|(in @ X1195 @ X1194))))=>(![X1874:$i, X1875:$i]:((subset @ X1874 @ (binunion @ X1874 @ X1875)))=>(![X1196:$i, X1197:$i]:((subset @ X1197 @ (binunion @ X1196 @ X1197)))=>(![X1198:$i, X1199:$i, X1200:$i]:(((in @ X1200 @ X1198)=>((in @ X1200 @ X1199)=>(in @ X1200 @ (binintersect @ X1198 @ X1199)))))=>(![X1201:$i, X1202:$i, X1203:$i]:(((subset @ X1203 @ X1201)=>((subset @ X1203 @ X1202)=>(subset @ X1203 @ (binintersect @ X1201 @ X1202)))))=>(![X1871:$i, X1872:$i, X1873:$i]:(((in @ X1873 @ (binintersect @ X1871 @ X1872))=>(in @ X1873 @ X1871)))=>(![X1869:$i, X1870:$i]:((subset @ (binintersect @ X1869 @ X1870) @ X1869))=>(![X1867:$i, X1868:$i]:(((subset @ X1867 @ X1868)=>((binintersect @ X1867 @ X1868)=(X1867))))=>(![X1865:$i, X1866:$i]:((((binintersect @ X1865 @ X1866)=(X1866))=>(subset @ X1866 @ X1865)))=>(![X1204:$i, X1205:$i, X1206:$i]:(((in @ X1206 @ (binintersect @ X1204 @ X1205))=>(in @ X1206 @ X1205)))=>(![X1207:$i, X1208:$i]:((~(?[X1209:$i]:(((in @ X1209 @ X1207)&(in @ X1209 @ X1208))))=>((binintersect @ X1207 @ X1208)=(emptyset))))=>(![X1863:$i, X1864:$i]:((subset @ (binintersect @ X1863 @ X1864) @ X1864))=>(![X1861:$i, X1862:$i]:(((subset @ X1862 @ X1861)=>((binintersect @ X1861 @ X1862)=(X1862))))=>(![X1210:$i, X1211:$i]:((((binintersect @ X1210 @ X1211)=(X1210))=>(subset @ X1210 @ X1211)))=>(![X1858:$i, X1859:$i, X1860:$i]:(((binintersect @ X1858 @ (binunion @ X1859 @ X1860))=(binunion @ (binintersect @ X1858 @ X1859) @ (binintersect @ X1858 @ X1860))))=>(![X1212:$i, X1213:$i, X1214:$i]:(((in @ X1214 @ X1212)=>(~(in @ X1214 @ X1213)=>(in @ X1214 @ (setminus @ X1212 @ X1213)))))=>(![X1215:$i, X1216:$i, X1217:$i]:(((in @ X1217 @ (setminus @ X1215 @ X1216))=>(in @ X1217 @ X1215)))=>(![X1218:$i, X1219:$i, X1220:$i]:(((in @ X1220 @ (setminus @ X1218 @ X1219))=>~(in @ X1220 @ X1219)))=>(![X1856:$i, X1857:$i]:(((subset @ X1856 @ X1857)=>((setminus @ X1856 @ X1857)=(emptyset))))=>(![X1221:$i, X1222:$i, X1223:$i]:((~(in @ X1223 @ (setminus @ X1221 @ X1222))=>((in @ X1223 @ X1221)=>(in @ X1223 @ X1222))))=>(![X1853:$i, X1854:$i, X1855:$i]:((~(in @ X1855 @ (setminus @ X1853 @ X1854))=>(~(in @ X1855 @ 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symdiffIneg1]), c_0_321]), setextAx]), inPowerset]), symdiffI2]), powersetE1]), setukpairIL]), powersetI1]), subsetemptysetimpeq]), singletonsubset]), setextsub]), setadjoinSub2]), notequalI1]), singletoninpowunion]), subsetE]), emptysetsubset]), upairsubunion]), c_0_322]), setunion__Cong]), setadjoin__Cong]), ubforcartprodlem2]), emptyset__Cong]), c_0_323]), c_0_324]), cartprodpairin]), c_0_325]), c_0_326]), notdexE]), setunionE2]), quantDeMorgan4]), quantDeMorgan2]), c_0_327]), setunionsingleton1]), upairsetIR]), upairsetE]), notinsingleton]), setunionsingleton2]), c_0_328]), subPowSU]), c_0_329]), setunionI]), emptyInPowerset]), emptyinPowerset]), c_0_330]), powersetI]), c_0_331]), singletonsuniq]), setadjoinOr]), setadjoinIL]), c_0_332]), c_0_333]), c_0_334]), noeltsimpempty]), kfstpairEq]), c_0_335]), emptysetE]), prop2setE]), setukpairinjR11]), c_0_336]), c_0_337]), setukpairinjR1]), wellorderingAx]), symdiffIneg2]), foundationAx]), c_0_338]), omegaSAx]), c_0_339]), powersetAx]), emptysetAx]), ksndpairEq]), kpairsurjEq]), cartprodpairmemEL]), cartprodpairmemER]), cartprodsndpairEq]), complementTE1]), contrasubsetT]), c_0_340]), c_0_341]), c_0_342]), c_0_343]), app]), infuncsetfunc]), c_0_344]), c_0_345]), c_0_346]), secondinupair]), funcGraphProp3]), funcGraphProp2]), funcGraphProp4]), c_0_347]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_348]), c_0_349]), c_0_350]), c_0_351]), c_0_352]), c_0_353]), theeq]), iftrueorfalse]), binunionT_lem]), powersetT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), c_0_354]), c_0_355]), c_0_356]), c_0_357]), cartprodpairsurjEq]), cartprodfstpairEq]), cartprodmempaircEq]), doubleComplementSub1]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpInComplement1]), binunionTE]), demorgan2a1]), demorgan2a2]), demorgan1b]), demorgan1]), woz13rule0]), woz13rule1]), woz13rule3]), woz1_1]), woz1_3]), woz1_4]), c_0_358]), c_0_359]), c_0_360]), c_0_361]), c_0_362]), c_0_314]), c_0_363]), c_0_364]), c_0_365]), c_0_366]), c_0_367]), c_0_368]), woz1_5]), woz1_2]), woz13rule4]), woz13rule2]), demorgan2]), demorgan2b]), demorgan2b2]), demorgan2a]), demorgan1a]), complementUnionInPowersetComplement]), binunionTEcontra]), inComplementUnionImpNotIn1]), inIntersectImpInUnion]), binunionTIRcontra]), complementImpComplementIntersect]), complementTnotintersectT]), doubleComplementEq]), doubleComplementSub2]), doubleComplementE1]), doubleComplementI1]), contrasubsetT3]), contrasubsetT2]), contrasubsetT1]), binintersectTERcontra]), binintersectTELcontra]), complementTI1]), setminusT_lem]), binintersectT_lem]), iffalse]), iftrue]), ifp]), c_0_369]), c_0_370]), c_0_371]), c_0_372]), funcext]), c_0_373]), funcextLem]), funcGraphProp1]), c_0_374]), c_0_375]), c_0_376]), funcinfuncset]), ap2p]), cartprodsndin]), setukpairinjR]), setukpairinjR2]), upairequniteq]), setukpairinjR12]), setukpairinjL]), setukpairinjL2]), cartprodfstin]), theprop]), setukpairinjL1]), c_0_377]), c_0_378]), setunionsingleton]), cartprodmempair]), cartprodmempair1]), ubforcartprodlem3]), ubforcartprodlem1]), upairinpowunion]), upairset2E]), singletoninpowerset]), kpairp]), kpairiskpair]), setukpairIR]), setminusLsub]), setminusIRneg]), setminusELneg]), setminusSubset2]), bs114d]), binintersectSubset4]), binintersectRsub]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binunionLsub]), binunionIR]), symdiffI1]), symdiffE]), setminusSubset1]), setminusILneg]), setminusERneg]), setminusER]), setminusEL]), setminusI]), binintersectSubset1]), disjointsetsI1]), binintersectER]), binintersectSubset5]), binintersectI]), binunionRsub]), binunionE]), binunionEcases]), upairset2IR]), binunionIL]), c_0_379]), c_0_380]), powersetsubset]), subset2powerset]), setadjoinSub]), subsetTrans]), subsetRefl]), notequalI2]), notsubsetI]), subsetE2]), subsetI2]), eqimpsubset1]), eqimpsubset2]), subsetI1]), c_0_381]), c_0_382]), omega__Cong]), powerset__Cong]), c_0_383]), in__Cong]), inCongP]), notdallE]), prop2setI]), quantDeMorgan3]), quantDeMorgan1]), vacuousDall]), upairsetIL]), singletonsswitch]), eqinunit]), uniqinunit]), c_0_384]), setunionE]), powersetE]), setadjoinE]), setadjoinIR]), emptyinunitempty]), c_0_385]), c_0_386]), emptyI]), setext]), notinemptyset]), emptysetimpfalse]), c_0_387]), c_0_388]), c_0_389]), omegaIndAx]), omega0Ax]), setunionAx]), setadjoinAx]), c_0_313])])]), c_0_390])).
34.96/4.93	thf(c_0_392, negated_conjecture, ![X2027:$i, X2028:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2040:$i, X2041:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2049:$i, X2050:$i > $i > $o, X2051:$i, X2053:$i, X2056:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2063:$i, X2064:$i > $o, X2065:$i, X2067:$i, X2068:$i > $o, X2069:$i, X2070:$i, X2071:$i > $o, X2072:$i, X2073:$i, X2074:$i > $o, X2075:$i, X2076:$i > $o, X2077:$i, X2080:$i, X2081:$o, X2082:$i, X2083:$i, X2084:$o, X2085:$i, X2086:$i, X2087:$i > $o, X2088:$i, X2091:$i, X2092:$i, X2095:$i, X2097:$i, X2099:$i, X2100:$i > $o, X2101:$i, X2102:$i, X2104:$i, X2105:$i > $o, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$o, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$o, X2137:$i, X2138:$i, X2139:$i > $o, X2140:$i, X2143:$i, X2144:$i, X2145:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i > $o, X2164:$i, X2165:$i > $o, X2166:$i, X2167:$i, X2168:$i > $o, X2169:$i, X2171:$i, X2172:$i > $o, X2174:$i, X2175:$i, X2176:$i > $o, X2178:$i, X2179:$i, X2180:$i > $o, X2181:$i, X2183:$o, X2184:$i, X2185:$i > $o, X2187:$i, X2188:$i, X2189:$i > $o, X2190:$i, X2192:$i > $o, X2193:$i, X2196:$i, X2197:$i > $o, X2198:$i, X2202:$i, X2203:$i > $o, X2204:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i > $o, X2217:$i, X2219:$i, X2220:$i, X2221:$i > $o, X2222:$i > $o, X2225:$i, X2228:$i, X2229:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i > $o, X2242:$i, X2244:$i, X2245:$i, X2246:$i > $o, X2247:$i > $o, X2250:$i, X2252:$i, X2254:$i, X2255:$i, X2256:$i > $o, X2257:$i > $o, X2260:$i, X2261:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, 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 > $o, X2308:$i, X2309:$i > $o, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$o, X2322:$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:$i, X2348:$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:$i, X2389:$o, X2390:$i, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$i, X2404:$i, X2405:$i, X2406:$i, X2407:$i, X2408:$i, X2409:$i, X2410:$i, X2411:$i, X2412:$i, X2413:$i, X2414:$i, X2415:$i, X2416:$i, X2417:$i, X2418:$i, X2419:$i, X2420:$i, X2421:$i, X2422:$i, X2423:$i, X2424:$i, X2425:$i, X2426:$i, X2427:$i, X2428:$i, X2429:$i, X2430:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2435:$i, X2436:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, X2442:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$i, X2455:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i > $o, X2464:$i, X2465:$i, X2466:$i > $o, X2468:$i, X2469:$i > $o, X2470:$i, X2472:$i, X2473:$i > $o, X2476:$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:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i, X2546:$i, X2547:$i, X2548:$i > $i > $o, X2549:$i, X2550:$i, X2551:$i, X2552:$i, X2553:$i > $i > $o, X2554:$i, X2555:$i, X2556:$i > $i > $o, X2557:$i, X2558:$i, X2559:$i > $i > $o, X2560:$i, X2561:$i, X2562:$i, X2563:$i, X2564:$i > $i > $o, X2565:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i > $i > $o, X2570:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i > $i > $o, X2575:$i, X2576:$i, X2577:$i, X2578:$i, X2579:$i, X2580:$i, X2581:$i, X2582:$i, X2583:$i, X2584:$i, X2585:$i, 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 > $i, X2603:$i, X2604:$i, X2605:$i > $i, X2607:$i, X2608:$i, X2609:$i > $i, X2611:$i, X2612:$i, X2613:$i, X2614:$i > $o, X2617:$i, X2618:$i, X2619:$i, X2620:$i, X2621:$i > $o, X2624:$i, X2625:$i, X2626:$i > $o, X2627:$i, X2628:$i, X2629:$i, X2630:$i, X2631:$i, X2632:$i, X2633:$i, X2634:$i, X2635:$i, X2636:$i, X2637:$i, X2638:$i, X2639:$i, X2640:$i, X2641:$i, X2642:$i, X2643:$i, X2644:$i, X2645:$i, X2647:$i, X2648:$i, X2649:$i, X2650:$i, X2651:$i, X2652:$i, X2653:$i, X2654:$i, X2655:$i, X2656:$i, X2657:$i, X2660:$i, X2661:$i, X2662:$i, X2663:$i, X2668:$i, X2669:$i, X2670:$i, X2671:$i, X2673:$i, X2674:$i, X2675:$i, X2676:$i, X2678:$i, X2679:$i, X2680:$i, X2681:$i, X2682:$i, X2683:$i, X2684:$i, X2685:$i, X2686:$i, X2687:$i, X2688:$i > $i, X2690:$i, X2691:$i, X2692:$i, X2693:$i, X2694:$i, X2695:$i, X2696:$i > $i, X2698:$i, X2699:$i, X2700:$i > $i, X2702:$i, X2703:$i, X2704:$i, X2705:$i, X2706:$i, X2707:$o, X2708:$i, X2709:$i, X2710:$i, X2711:$o, X2712:$i, X2713:$i, X2714:$i, X2715:$o, X2716:$i, X2717:$i, X2718:$i, X2719:$o, X2720:$i, X2721:$i, X2722:$i, X2723:$o, X2724:$i, X2725:$i, X2726:$i, X2727:$o, X2728:$i, X2729:$i, X2730:$i, X2731:$i, X2732:$i, X2733:$o, X2734:$i, X2735:$i, X2736:$i, X2737:$o, X2738:$i, X2739:$i, X2740:$i, X2741:$o, X2742:$i, X2743:$i, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i, X2749:$i, X2750:$i, X2751:$i, X2752:$i, X2753:$i, X2754:$i, X2755:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2762:$i, X2763:$i, X2764:$i, X2766:$i, X2767:$i, X2768:$i, X2770:$i, X2771:$i, X2772:$i, X2773:$i, X2774:$i, X2775:$i, X2776:$i, X2777:$i, X2778:$i, X2779:$i, X2780:$i, X2781:$i, X2782:$i, X2783:$i, X2784:$i, X2785:$i, X2786:$i, X2787:$i, X2788:$i, X2789:$i, X2790:$i, X2791:$i, X2792:$i, X2793:$i, X2794:$i, X2795:$i, X2796:$i, X2797:$i, X2798:$i, X2799:$i, X2800:$i, X2801:$i, X2802:$i, X2803:$i, X2804:$i, X2805:$i, X2806:$i, X2807:$i, X2808:$i, X2809:$i, X2810:$i, X2811:$i, X2812:$i, X2813:$i, X2814:$i, X2815:$i, X2816:$i, X2817:$i, X2818:$i, X2819:$i, X2820:$i, X2821:$i, X2822:$i, X2823:$i, X2824:$i, X2825:$i, X2826:$i, X2827:$i, X2828:$i, X2829:$i, X2830:$i, X2831:$i, X2832:$i, X2833:$i, X2834:$i, X2835:$i, X2836:$i, X2837:$i, X2838:$i, X2839:$i, X2840:$i, X2841:$i, X2842:$i, X2843:$i, X2844:$i, X2845:$i, X2846:$i, X2847:$i, X2848:$i, X2849:$i, X2850:$i, X2851:$i, X2852:$i, X2853:$i, X2854:$i, X2855:$i, X2856:$i, X2857:$i, X2858:$i, X2859:$i, X2860:$i, X2861:$i, X2862:$i, X2863:$i, X2864:$i, X2865:$i, X2866:$i, X2867:$i, X2868:$i, X2869:$i, X2870:$i, X2871:$i, X2872:$i, X2873:$o, X2874:$i, X2875:$i, X2876:$i, X2877:$i, X2878:$i, X2879:$i, X2880:$i, X2881:$i, X2882:$i, X2883:$i, X2884:$i, X2885:$i, X2886:$i, X2887:$i, X2888:$i, X2889:$i, X2890:$i, X2891:$i, X2892:$i, X2893:$i, X2894:$i, X2895:$i, X2896:$i, X2897:$i, X2898:$i, X2899:$i, X2900:$i, X2901:$i, X2902:$i, X2903:$i, X2904:$i, X2905:$i, X2906:$i, X2907:$i, X2908:$i, X2909:$i, X2910:$i, X2911:$i, X2912:$i, X2913:$i, X2914:$i, X2915:$i, X2916:$i, X2917:$i, X2918:$i, X2919:$i, X2920:$i, X2921:$i, X2922:$i, X2923:$i, X2924:$i, X2925:$i, X2926:$i, X2927:$i, X2928:$i, X2929:$i, X2930:$i, X2931:$i, X2932:$i, X2933:$i, X2934:$i, X2935:$i, X2936:$i, X2937:$i, X2938:$i, X2939:$i, X2940:$i, X2941:$i, X2942:$i, X2943:$i, X2944:$i, X2945:$i, X2946:$i, X2947:$i, X2948:$i, X2949:$i, X2950:$i, X2951:$i, X2952:$i, X2953:$i, X2954:$i, X2955:$i, X2956:$i, X2957:$i > $o, X2960:$i, X2961:$i, X2962:$i, X2963:$i, X2964:$i > $i > $o, X2965:$i, X2966:$i, X2967:$i > $o, X2970:$i, X2971:$i, X2972:$i, X2973:$i, X2976:$i, X2977:$i, X2978:$i, X2983:$i, X2984:$i, X2985:$i, X2986:$i, X2987:$i, X2988:$i, X2989:$i, X2990:$i, X2991:$i, X2992:$i, X2993:$i, X2994:$i, X2995:$i, X2996:$i, X2997:$i, X2998:$i, X2999:$i, X3000:$i, X3001:$i, X3007:$i]:((((~(in @ (esk1_2 @ X2027 @ X2028) @ X2027)|~(in @ (esk1_2 @ X2027 @ X2028) @ X2028)|((X2027)=(X2028)))&((in @ (esk1_2 @ X2027 @ X2028) @ X2027)|(in @ (esk1_2 @ X2027 @ X2028) @ X2028)|((X2027)=(X2028))))&(~(in @ X2030 @ emptyset)&(((~(in @ X2033 @ (setadjoin @ X2031 @ X2032))|(((X2033)=(X2031))|(in @ X2033 @ X2032)))&((((X2033)!=(X2031))|(in @ X2033 @ (setadjoin @ X2031 @ X2032)))&(~(in @ X2033 @ X2032)|(in @ X2033 @ (setadjoin @ X2031 @ X2032)))))&(((~(in @ X2035 @ (powerset @ X2034))|(~(in @ X2036 @ X2035)|(in @ X2036 @ X2034)))&(((in @ (esk2_2 @ X2037 @ X2038) @ X2038)|(in @ X2038 @ (powerset @ X2037)))&(~(in @ (esk2_2 @ X2037 @ X2038) @ X2037)|(in @ X2038 @ (powerset @ X2037)))))&(((((in @ X2041 @ (esk3_2 @ X2040 @ X2041))|~(in @ X2041 @ (setunion @ X2040)))&((in @ (esk3_2 @ X2040 @ X2041) @ X2040)|~(in @ X2041 @ (setunion @ X2040))))&(~(in @ X2044 @ X2045)|~(in @ X2045 @ X2043)|(in @ X2044 @ (setunion @ X2043))))&((in @ emptyset @ omega)&((~(in @ X2046 @ omega)|(in @ (setadjoin @ X2046 @ X2046) @ omega))&(((((in @ (esk4_1 @ X2047) @ omega)|~(in @ emptyset @ X2047)|(~(in @ X2049 @ omega)|(in @ X2049 @ X2047)))&((in @ (esk4_1 @ X2047) @ X2047)|~(in @ emptyset @ X2047)|(~(in @ X2049 @ omega)|(in @ X2049 @ X2047))))&(~(in @ (setadjoin @ (esk4_1 @ X2047) @ (esk4_1 @ X2047)) @ X2047)|~(in @ emptyset @ X2047)|(~(in @ X2049 @ omega)|(in @ X2049 @ X2047))))&((((((in @ (esk8_3 @ X2050 @ X2051 @ X2056) @ X2051)|~(in @ X2056 @ (esk7_2 @ X2050 @ X2051))|(in @ (esk5_2 @ X2050 @ X2051) @ X2051))&((X2050 @ (esk8_3 @ X2050 @ X2051 @ X2056) @ X2056)|~(in @ X2056 @ (esk7_2 @ X2050 @ X2051))|(in @ (esk5_2 @ X2050 @ X2051) @ X2051)))&(~(in @ X2059 @ X2051)|~(X2050 @ X2059 @ X2058)|(in @ X2058 @ (esk7_2 @ X2050 @ X2051))|(in @ (esk5_2 @ X2050 @ X2051) @ X2051)))&(((((in @ (esk8_3 @ X2050 @ X2051 @ X2056) 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X2937))|(in @ (setminus @ X2937 @ X2938) @ (powerset @ (setminus @ X2937 @ (binintersect @ X2938 @ X2939))))))&((~(in @ X2941 @ (powerset @ X2940))|(~(in @ X2942 @ (powerset @ X2940))|(~(in @ X2943 @ (powerset @ X2940))|(~(in @ X2944 @ (powerset @ X2940))|((setminus @ X2940 @ (binintersect @ (binunion @ X2941 @ X2942) @ (binunion @ X2943 @ X2944)))=(binunion @ (binintersect @ (setminus @ X2940 @ X2941) @ (setminus @ X2940 @ X2942)) @ (binintersect @ (setminus @ X2940 @ X2943) @ (setminus @ X2940 @ X2944))))))))&((~(in @ X2946 @ (powerset @ X2945))|(~(in @ X2947 @ (powerset @ X2945))|(~(in @ X2948 @ (powerset @ X2945))|(in @ (binintersect @ X2946 @ X2947) @ (powerset @ (binintersect @ (binunion @ X2946 @ X2948) @ (binunion @ X2947 @ X2948)))))))&((~(in @ X2950 @ (powerset @ X2949))|(~(in @ X2951 @ (powerset @ X2949))|(~(subset @ X2950 @ (setminus @ X2949 @ X2951))|(subset @ X2951 @ (setminus @ X2949 @ X2950)))))&((~(in @ X2953 @ (powerset @ X2952))|(~(in @ X2954 @ (powerset @ X2952))|(in @ (setminus @ X2952 @ (binunion @ X2953 @ X2954)) @ (powerset @ (setminus @ X2952 @ X2953)))))&((((in @ (esk87_3 @ X2955 @ X2956 @ X2957) @ X2955)|(~(in @ X2960 @ X2956)|(X2957 @ X2960))|~(subset @ X2956 @ (cartprod @ X2955 @ X2955)))&(((in @ (esk88_3 @ X2955 @ X2956 @ X2957) @ X2955)|(~(in @ X2960 @ X2956)|(X2957 @ X2960))|~(subset @ X2956 @ (cartprod @ X2955 @ X2955)))&(((in @ (kpair @ (esk87_3 @ X2955 @ X2956 @ X2957) @ (esk88_3 @ X2955 @ X2956 @ X2957)) @ X2956)|(~(in @ X2960 @ X2956)|(X2957 @ X2960))|~(subset @ X2956 @ (cartprod @ X2955 @ X2955)))&(~(X2957 @ (kpair @ (esk87_3 @ X2955 @ X2956 @ X2957) @ (esk88_3 @ X2955 @ X2956 @ X2957)))|(~(in @ X2960 @ X2956)|(X2957 @ X2960))|~(subset @ X2956 @ (cartprod @ X2955 @ X2955))))))&((~(in @ X2962 @ (breln1Set @ X2961))|(subset @ X2962 @ (cartprod @ X2961 @ X2961)))&((choice2fnsingleton)&((subset @ (dpsetconstr @ X2963 @ X2963 @ X2964) @ (cartprod @ X2963 @ X2963))&((((in @ (esk89_3 @ X2965 @ X2966 @ X2967) @ X2965)|(~(in @ X2970 @ X2966)|(X2967 @ X2970))|~(subset @ X2966 @ (cartprod @ X2965 @ X2965)))&(((in @ (esk90_3 @ X2965 @ X2966 @ X2967) @ X2965)|(~(in @ X2970 @ X2966)|(X2967 @ X2970))|~(subset @ X2966 @ (cartprod @ X2965 @ X2965)))&(((in @ (kpair @ (esk89_3 @ X2965 @ X2966 @ X2967) @ (esk90_3 @ X2965 @ X2966 @ X2967)) @ X2966)|(~(in @ X2970 @ X2966)|(X2967 @ X2970))|~(subset @ X2966 @ (cartprod @ X2965 @ X2965)))&(~(X2967 @ (kpair @ (esk89_3 @ X2965 @ X2966 @ X2967) @ (esk90_3 @ X2965 @ X2966 @ X2967)))|(~(in @ X2970 @ X2966)|(X2967 @ X2970))|~(subset @ X2966 @ (cartprod @ X2965 @ X2965))))))&((((in @ (esk91_3 @ X2971 @ X2972 @ X2973) @ X2971)|(subset @ X2972 @ X2973)|~(subset @ X2973 @ (cartprod @ X2971 @ X2971))|~(subset @ X2972 @ (cartprod @ X2971 @ X2971)))&(((in @ (esk92_3 @ X2971 @ X2972 @ X2973) @ X2971)|(subset @ X2972 @ X2973)|~(subset @ X2973 @ (cartprod @ X2971 @ X2971))|~(subset @ X2972 @ (cartprod @ X2971 @ X2971)))&(((in @ (kpair @ (esk91_3 @ X2971 @ X2972 @ X2973) @ (esk92_3 @ X2971 @ X2972 @ X2973)) @ X2972)|(subset @ X2972 @ X2973)|~(subset @ X2973 @ (cartprod @ X2971 @ X2971))|~(subset @ X2972 @ (cartprod @ X2971 @ X2971)))&(~(in @ (kpair @ (esk91_3 @ X2971 @ X2972 @ X2973) @ (esk92_3 @ X2971 @ X2972 @ X2973)) @ X2973)|(subset @ X2972 @ X2973)|~(subset @ X2973 @ (cartprod @ X2971 @ X2971))|~(subset @ X2972 @ (cartprod @ X2971 @ X2971))))))&(((((in @ (esk95_3 @ X2976 @ X2977 @ X2978) @ X2976)|((X2977)=(X2978))|(in @ (esk93_3 @ X2976 @ X2977 @ X2978) @ X2976)|~(subset @ X2978 @ (cartprod @ X2976 @ X2976))|~(subset @ X2977 @ (cartprod @ X2976 @ X2976)))&(((in @ (esk96_3 @ X2976 @ X2977 @ X2978) @ X2976)|((X2977)=(X2978))|(in @ (esk93_3 @ X2976 @ X2977 @ X2978) @ X2976)|~(subset @ X2978 @ (cartprod @ X2976 @ X2976))|~(subset @ X2977 @ (cartprod @ X2976 @ X2976)))&(((in @ (kpair @ (esk95_3 @ X2976 @ X2977 @ X2978) @ (esk96_3 @ X2976 @ X2977 @ X2978)) @ X2978)|((X2977)=(X2978))|(in @ (esk93_3 @ X2976 @ X2977 @ X2978) @ X2976)|~(subset @ X2978 @ (cartprod @ X2976 @ X2976))|~(subset @ X2977 @ (cartprod @ X2976 @ X2976)))&(~(in @ (kpair @ (esk95_3 @ X2976 @ X2977 @ X2978) @ (esk96_3 @ X2976 @ X2977 @ X2978)) @ X2977)|((X2977)=(X2978))|(in @ (esk93_3 @ X2976 @ X2977 @ X2978) @ X2976)|~(subset @ X2978 @ (cartprod @ X2976 @ X2976))|~(subset @ X2977 @ (cartprod @ X2976 @ X2976))))))&((((in @ (esk95_3 @ X2976 @ X2977 @ X2978) @ X2976)|((X2977)=(X2978))|(in @ (esk94_3 @ X2976 @ X2977 @ X2978) @ X2976)|~(subset @ X2978 @ (cartprod @ X2976 @ X2976))|~(subset @ X2977 @ (cartprod @ X2976 @ X2976)))&(((in @ (esk96_3 @ X2976 @ X2977 @ X2978) @ X2976)|((X2977)=(X2978))|(in @ (esk94_3 @ X2976 @ X2977 @ X2978) @ X2976)|~(subset @ X2978 @ (cartprod @ X2976 @ X2976))|~(subset @ X2977 @ (cartprod @ X2976 @ X2976)))&(((in @ (kpair @ (esk95_3 @ X2976 @ X2977 @ X2978) @ (esk96_3 @ X2976 @ X2977 @ X2978)) @ X2978)|((X2977)=(X2978))|(in @ (esk94_3 @ X2976 @ X2977 @ X2978) @ X2976)|~(subset @ X2978 @ (cartprod @ X2976 @ X2976))|~(subset @ X2977 @ (cartprod @ X2976 @ X2976)))&(~(in @ (kpair @ (esk95_3 @ X2976 @ X2977 @ X2978) @ (esk96_3 @ X2976 @ X2977 @ X2978)) @ X2977)|((X2977)=(X2978))|(in @ (esk94_3 @ X2976 @ X2977 @ X2978) @ X2976)|~(subset @ X2978 @ (cartprod @ X2976 @ X2976))|~(subset @ X2977 @ (cartprod @ X2976 @ X2976))))))&((((in @ (esk95_3 @ X2976 @ X2977 @ X2978) @ X2976)|((X2977)=(X2978))|(in @ (kpair @ (esk93_3 @ X2976 @ X2977 @ X2978) @ (esk94_3 @ X2976 @ X2977 @ X2978)) @ X2977)|~(subset @ X2978 @ (cartprod @ X2976 @ X2976))|~(subset @ X2977 @ (cartprod @ X2976 @ X2976)))&(((in @ (esk96_3 @ X2976 @ X2977 @ X2978) @ X2976)|((X2977)=(X2978))|(in @ (kpair @ (esk93_3 @ X2976 @ X2977 @ X2978) @ (esk94_3 @ X2976 @ X2977 @ X2978)) @ X2977)|~(subset @ X2978 @ (cartprod @ X2976 @ X2976))|~(subset @ X2977 @ (cartprod @ X2976 @ X2976)))&(((in @ (kpair @ (esk95_3 @ X2976 @ X2977 @ X2978) @ (esk96_3 @ X2976 @ X2977 @ X2978)) @ X2978)|((X2977)=(X2978))|(in @ (kpair @ (esk93_3 @ X2976 @ X2977 @ X2978) @ (esk94_3 @ X2976 @ X2977 @ X2978)) @ X2977)|~(subset @ X2978 @ (cartprod @ X2976 @ X2976))|~(subset @ X2977 @ (cartprod @ X2976 @ X2976)))&(~(in @ (kpair @ (esk95_3 @ X2976 @ X2977 @ X2978) @ (esk96_3 @ X2976 @ X2977 @ X2978)) @ X2977)|((X2977)=(X2978))|(in @ (kpair @ (esk93_3 @ X2976 @ X2977 @ X2978) @ (esk94_3 @ X2976 @ X2977 @ X2978)) @ X2977)|~(subset @ X2978 @ (cartprod @ X2976 @ X2976))|~(subset @ X2977 @ (cartprod @ X2976 @ X2976))))))&(((in @ (esk95_3 @ X2976 @ X2977 @ X2978) @ X2976)|((X2977)=(X2978))|~(in @ (kpair @ (esk93_3 @ X2976 @ X2977 @ X2978) @ (esk94_3 @ X2976 @ X2977 @ X2978)) @ X2978)|~(subset @ X2978 @ (cartprod @ X2976 @ X2976))|~(subset @ X2977 @ (cartprod @ X2976 @ X2976)))&(((in @ (esk96_3 @ X2976 @ X2977 @ X2978) @ X2976)|((X2977)=(X2978))|~(in @ (kpair @ (esk93_3 @ X2976 @ X2977 @ X2978) @ (esk94_3 @ X2976 @ X2977 @ X2978)) @ X2978)|~(subset @ X2978 @ (cartprod @ X2976 @ X2976))|~(subset @ X2977 @ (cartprod @ X2976 @ X2976)))&(((in @ (kpair @ (esk95_3 @ X2976 @ X2977 @ X2978) @ (esk96_3 @ X2976 @ X2977 @ X2978)) @ X2978)|((X2977)=(X2978))|~(in @ (kpair @ (esk93_3 @ X2976 @ X2977 @ X2978) @ (esk94_3 @ X2976 @ X2977 @ X2978)) @ X2978)|~(subset @ X2978 @ (cartprod @ X2976 @ X2976))|~(subset @ X2977 @ (cartprod @ X2976 @ X2976)))&(~(in @ (kpair @ (esk95_3 @ X2976 @ X2977 @ X2978) @ (esk96_3 @ X2976 @ X2977 @ X2978)) @ X2977)|((X2977)=(X2978))|~(in @ (kpair @ (esk93_3 @ X2976 @ X2977 @ X2978) @ (esk94_3 @ X2976 @ X2977 @ X2978)) @ X2978)|~(subset @ X2978 @ (cartprod @ X2976 @ X2976))|~(subset @ X2977 @ (cartprod @ X2976 @ X2976)))))))))&((~(subset @ X2984 @ (cartprod @ X2983 @ X2983))|(subset @ (breln1invset @ X2983 @ X2984) @ (cartprod @ X2983 @ X2983)))&((~(subset @ X2986 @ (cartprod @ X2985 @ X2985))|(~(in @ X2987 @ X2985)|(~(in @ X2988 @ X2985)|(~(in @ (kpair @ X2987 @ X2988) @ X2986)|(in @ (kpair @ X2988 @ X2987) @ (breln1invset @ X2985 @ X2986))))))&((~(subset @ X2990 @ (cartprod @ X2989 @ X2989))|(~(in @ X2991 @ X2989)|(~(in @ X2992 @ X2989)|(~(in @ (kpair @ X2992 @ X2991) @ (breln1invset @ X2989 @ X2990))|(in @ (kpair @ X2991 @ X2992) @ X2990)))))&((~(subset @ X2994 @ (cartprod @ X2993 @ X2993))|(~(subset @ X2995 @ (cartprod @ X2993 @ X2993))|(subset @ (dpsetconstr @ X2993 @ X2993 @ (^[Z0/* 19 */:$i, Z1:$i]:(?[X1554:$i]:((((in @ X1554 @ X2993)&(in @ (kpair @ Z0 @ X1554) @ X2994))&(in @ (kpair @ X1554 @ Z1) @ X2995)))))) @ (cartprod @ X2993 @ X2993))))&((~(subset @ X2997 @ (cartprod @ X2996 @ X2996))|(~(subset @ X2998 @ (cartprod @ X2996 @ X2996))|(~(in @ X2999 @ X2996)|(~(in @ X3000 @ X2996)|(~(in @ X3001 @ X2996)|(~(in @ (kpair @ X2999 @ X3001) @ X2997)|(~(in @ (kpair @ X3001 @ X3000) @ X2998)|(in @ (kpair @ X2999 @ X3000) @ (dpsetconstr @ X2996 @ X2996 @ (^[Z0/* 19 */:$i, Z1:$i]:(?[X1550:$i]:((((in @ X1550 @ X2996)&(in @ (kpair @ Z0 @ X1550) @ X2997))&(in @ (kpair @ X1550 @ Z1) @ X2998))))))))))))))&((subset @ esk98_0 @ (cartprod @ esk97_0 @ esk97_0))&((subset @ esk99_0 @ (cartprod @ esk97_0 @ esk97_0))&((in @ esk100_0 @ esk97_0)&((in @ esk101_0 @ esk97_0)&((in @ (kpair @ esk100_0 @ esk101_0) @ (dpsetconstr @ esk97_0 @ esk97_0 @ (^[Z0/* 19 */:$i, Z1:$i]:(?[X1543:$i]:((((in @ X1543 @ esk97_0)&(in @ (kpair @ Z0 @ X1543) @ esk98_0))&(in @ (kpair @ X1543 @ Z1) @ esk99_0)))))))&(~(in @ X3007 @ esk97_0)|~(in @ (kpair @ X3007 @ esk101_0) @ esk99_0)|~(in @ (kpair @ esk100_0 @ X3007) @ esk98_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_391])])])])])])])).
34.96/4.93	thf(c_0_393, negated_conjecture, ![X2:$i, X3:$i, X4:$i, X5:$i, X6:$i > $i > $o]:(((X6 @ X2 @ X3)|~((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ X6))))), inference(split_conjunct,[status(thm)],[c_0_392])).
34.96/4.93	thf(c_0_394, negated_conjecture, (in @ (kpair @ esk100_0 @ esk101_0) @ (dpsetconstr @ esk97_0 @ esk97_0 @ (^[Z0/* 19 */:$i, Z1:$i]:(?[X3029:$i]:((((in @ X3029 @ esk97_0)&(in @ (kpair @ Z0 @ X3029) @ esk98_0))&(in @ (kpair @ X3029 @ Z1) @ esk99_0))))))), inference(split_conjunct,[status(thm)],[c_0_392])).
34.96/4.93	thf(c_0_395, negated_conjecture, ?[X3030:$i]:((((in @ X3030 @ esk97_0)&(in @ (kpair @ esk100_0 @ X3030) @ esk98_0))&(in @ (kpair @ X3030 @ esk101_0) @ esk99_0))), inference(spm,[status(thm)],[c_0_393, c_0_394])).
34.96/4.93	thf(c_0_396, negated_conjecture, ![X2:$i]:((~((in @ X2 @ esk97_0))|~((in @ (kpair @ X2 @ esk101_0) @ esk99_0))|~((in @ (kpair @ esk100_0 @ X2) @ esk98_0)))), inference(split_conjunct,[status(thm)],[c_0_392])).
34.96/4.93	thf(c_0_397, negated_conjecture, (in @ (kpair @ esk127_0 @ esk101_0) @ esk99_0), inference(dynamic_cnf,[status(thm)],[c_0_395])).
34.96/4.93	thf(c_0_398, negated_conjecture, (in @ esk127_0 @ esk97_0), inference(dynamic_cnf,[status(thm)],[c_0_395])).
34.96/4.93	thf(c_0_399, negated_conjecture, ~((in @ (kpair @ esk100_0 @ esk127_0) @ esk98_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_396, c_0_397]), c_0_398])])).
34.96/4.93	thf(c_0_400, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_395]), c_0_399]), ['proof']).
34.96/4.93	# SZS output end CNFRefutation
34.96/4.93	# Parsed axioms                        : 646
34.96/4.93	# Removed by relevancy pruning/SinE    : 346
34.96/4.93	# Initial clauses                      : 510
34.96/4.93	# Removed in clause preprocessing      : 32
34.96/4.93	# Initial clauses in saturation        : 478
34.96/4.93	# Processed clauses                    : 4131
34.96/4.93	# ...of these trivial                  : 33
34.96/4.93	# ...subsumed                          : 1955
34.96/4.93	# ...remaining for further processing  : 2142
34.96/4.93	# Other redundant clauses eliminated   : 68
34.96/4.93	# Clauses deleted for lack of memory   : 0
34.96/4.93	# Backward-subsumed                    : 82
34.96/4.93	# Backward-rewritten                   : 13
34.96/4.93	# Generated clauses                    : 120686
34.96/4.93	# ...of the previous two non-redundant : 118371
34.96/4.93	# ...aggressively subsumed             : 0
34.96/4.93	# Contextual simplify-reflections      : 48
34.96/4.93	# Paramodulations                      : 120529
34.96/4.93	# Factorizations                       : 42
34.96/4.93	# NegExts                              : 20
34.96/4.93	# Equation resolutions                 : 76
34.96/4.93	# Disequality decompositions           : 0
34.96/4.93	# Total rewrite steps                  : 10969
34.96/4.93	# ...of those cached                   : 10686
34.96/4.93	# Propositional unsat checks           : 0
34.96/4.93	#    Propositional check models        : 0
34.96/4.93	#    Propositional check unsatisfiable : 0
34.96/4.93	#    Propositional clauses             : 0
34.96/4.93	#    Propositional clauses after purity: 0
34.96/4.93	#    Propositional unsat core size     : 0
34.96/4.93	#    Propositional preprocessing time  : 0.000
34.96/4.93	#    Propositional encoding time       : 0.000
34.96/4.93	#    Propositional solver time         : 0.000
34.96/4.93	#    Success case prop preproc time    : 0.000
34.96/4.93	#    Success case prop encoding time   : 0.000
34.96/4.93	#    Success case prop solver time     : 0.000
34.96/4.93	# Current number of processed clauses  : 1615
34.96/4.93	#    Positive orientable unit clauses  : 71
34.96/4.93	#    Positive unorientable unit clauses: 0
34.96/4.93	#    Negative unit clauses             : 46
34.96/4.93	#    Non-unit-clauses                  : 1498
34.96/4.93	# Current number of unprocessed clauses: 114934
34.96/4.93	# ...number of literals in the above   : 455242
34.96/4.93	# Current number of archived formulas  : 0
34.96/4.93	# Current number of archived clauses   : 512
34.96/4.93	# Clause-clause subsumption calls (NU) : 238986
34.96/4.93	# Rec. Clause-clause subsumption calls : 114879
34.96/4.93	# Non-unit clause-clause subsumptions  : 1373
34.96/4.93	# Unit Clause-clause subsumption calls : 4573
34.96/4.93	# Rewrite failures with RHS unbound    : 0
34.96/4.93	# BW rewrite match attempts            : 60
34.96/4.93	# BW rewrite match successes           : 11
34.96/4.93	# Condensation attempts                : 0
34.96/4.93	# Condensation successes               : 0
34.96/4.93	# Termbank termtop insertions          : 2567273
34.96/4.93	# Search garbage collected termcells   : 32586
34.96/4.93	
34.96/4.93	# -------------------------------------------------
34.96/4.93	# User time                : 4.129 s
34.96/4.93	# System time              : 0.151 s
34.96/4.93	# Total time               : 4.280 s
34.96/4.93	# Maximum resident set size: 10032 pages
34.96/4.93	
34.96/4.93	# -------------------------------------------------
34.96/4.93	# User time                : 4.147 s
34.96/4.93	# System time              : 0.156 s
34.96/4.93	# Total time               : 4.303 s
34.96/4.93	# Maximum resident set size: 2748 pages
34.96/4.93	% E---3.1 exiting
34.96/4.93	% E exiting
34.96/4.93	EOF