0.04/0.08	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.08	% Command    : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 240 THM
0.08/0.28	% Computer : n013.cluster.edu
0.08/0.28	% Model    : x86_64 x86_64
0.08/0.28	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.08/0.28	% Memory   : 8042.1875MB
0.08/0.28	% OS       : Linux 3.10.0-693.el7.x86_64
0.08/0.28	% CPULimit   : 1920
0.08/0.28	% WCLimit    : 240
0.08/0.28	% DateTime   : Wed Jul 30 02:58:49 EDT 2025
0.08/0.28	% CPUTime    : 
0.13/0.38	Running higher-order theorem proving
0.13/0.44	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=240 /export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p
2.58/0.99	# Version: 3.0.0-ho
2.58/0.99	# Preprocessing class: HSLMSLSSLLLCHFA.
2.58/0.99	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
2.58/0.99	# Starting ehoh_best5 with 240s (1) cores
2.58/0.99	# Starting almost_fo_3_lam with 240s (1) cores
2.58/0.99	# Starting new_bool_5 with 240s (1) cores
2.58/0.99	# Starting pre_casc_3 with 240s (1) cores
2.58/0.99	# Starting ho_unfolding_8 with 240s (1) cores
2.58/0.99	# Starting new_ho_10_cnf2 with 240s (1) cores
2.58/0.99	# Starting new_bool_3 with 240s (1) cores
2.58/0.99	# Starting new_ho_5 with 240s (1) cores
2.58/0.99	# new_bool_5 with pid 14864 completed with status 0
2.58/0.99	# Result found by new_bool_5
2.58/0.99	# Preprocessing class: HSLMSLSSLLLCHFA.
2.58/0.99	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
2.58/0.99	# Starting ehoh_best5 with 240s (1) cores
2.58/0.99	# Starting almost_fo_3_lam with 240s (1) cores
2.58/0.99	# Starting new_bool_5 with 240s (1) cores
2.58/0.99	# SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
2.58/0.99	# Search class: HGHSM-FSLM32-MHFMMSBN
2.58/0.99	# Scheduled 10 strats onto 1 cores with 240 seconds (240 total)
2.58/0.99	# Starting ho_unfolding_8 with 44s (1) cores
2.58/0.99	# ho_unfolding_8 with pid 14870 completed with status 0
2.58/0.99	# Result found by ho_unfolding_8
2.58/0.99	# Preprocessing class: HSLMSLSSLLLCHFA.
2.58/0.99	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
2.58/0.99	# Starting ehoh_best5 with 240s (1) cores
2.58/0.99	# Starting almost_fo_3_lam with 240s (1) cores
2.58/0.99	# Starting new_bool_5 with 240s (1) cores
2.58/0.99	# SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
2.58/0.99	# Search class: HGHSM-FSLM32-MHFMMSBN
2.58/0.99	# Scheduled 10 strats onto 1 cores with 240 seconds (240 total)
2.58/0.99	# Starting ho_unfolding_8 with 44s (1) cores
2.58/0.99	# Preprocessing time       : 0.074 s
2.58/0.99	# Presaturation interreduction done
2.58/0.99	
2.58/0.99	# Proof found!
2.58/0.99	# SZS status Theorem
2.58/0.99	# SZS output start CNFRefutation
2.58/0.99	thf(decl_23, type, in: $i > $i > $o).
2.58/0.99	thf(decl_24, type, exu: ($i > $o) > $o).
2.58/0.99	thf(decl_25, type, setextAx: $o).
2.58/0.99	thf(decl_26, type, emptyset: $i).
2.58/0.99	thf(decl_27, type, emptysetAx: $o).
2.58/0.99	thf(decl_28, type, setadjoin: $i > $i > $i).
2.58/0.99	thf(decl_29, type, setadjoinAx: $o).
2.58/0.99	thf(decl_30, type, powerset: $i > $i).
2.58/0.99	thf(decl_31, type, powersetAx: $o).
2.58/0.99	thf(decl_32, type, setunion: $i > $i).
2.58/0.99	thf(decl_33, type, setunionAx: $o).
2.58/0.99	thf(decl_34, type, omega: $i).
2.58/0.99	thf(decl_35, type, omega0Ax: $o).
2.58/0.99	thf(decl_36, type, omegaSAx: $o).
2.58/0.99	thf(decl_37, type, omegaIndAx: $o).
2.58/0.99	thf(decl_38, type, replAx: $o).
2.58/0.99	thf(decl_39, type, foundationAx: $o).
2.58/0.99	thf(decl_40, type, wellorderingAx: $o).
2.58/0.99	thf(decl_41, type, descr: ($i > $o) > $i).
2.58/0.99	thf(decl_42, type, descrp: $o).
2.58/0.99	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
2.58/0.99	thf(decl_44, type, dsetconstrI: $o).
2.58/0.99	thf(decl_45, type, dsetconstrEL: $o).
2.58/0.99	thf(decl_46, type, dsetconstrER: $o).
2.58/0.99	thf(decl_47, type, exuE1: $o).
2.58/0.99	thf(decl_48, type, prop2set: $o > $i).
2.58/0.99	thf(decl_49, type, prop2setE: $o).
2.58/0.99	thf(decl_50, type, emptysetE: $o).
2.58/0.99	thf(decl_51, type, emptysetimpfalse: $o).
2.58/0.99	thf(decl_52, type, notinemptyset: $o).
2.58/0.99	thf(decl_53, type, exuE3e: $o).
2.58/0.99	thf(decl_54, type, setext: $o).
2.58/0.99	thf(decl_55, type, emptyI: $o).
2.58/0.99	thf(decl_56, type, noeltsimpempty: $o).
2.58/0.99	thf(decl_57, type, setbeta: $o).
2.58/0.99	thf(decl_58, type, nonempty: $i > $o).
2.58/0.99	thf(decl_59, type, nonemptyE1: $o).
2.58/0.99	thf(decl_60, type, nonemptyI: $o).
2.58/0.99	thf(decl_61, type, nonemptyI1: $o).
2.58/0.99	thf(decl_62, type, setadjoinIL: $o).
2.58/0.99	thf(decl_63, type, emptyinunitempty: $o).
2.58/0.99	thf(decl_64, type, setadjoinIR: $o).
2.58/0.99	thf(decl_65, type, setadjoinE: $o).
2.58/0.99	thf(decl_66, type, setadjoinOr: $o).
2.58/0.99	thf(decl_67, type, setoftrueEq: $o).
2.58/0.99	thf(decl_68, type, powersetI: $o).
2.58/0.99	thf(decl_69, type, emptyinPowerset: $o).
2.58/0.99	thf(decl_70, type, emptyInPowerset: $o).
2.58/0.99	thf(decl_71, type, powersetE: $o).
2.58/0.99	thf(decl_72, type, setunionI: $o).
2.58/0.99	thf(decl_73, type, setunionE: $o).
2.58/0.99	thf(decl_74, type, subPowSU: $o).
2.58/0.99	thf(decl_75, type, exuE2: $o).
2.58/0.99	thf(decl_76, type, nonemptyImpWitness: $o).
2.58/0.99	thf(decl_77, type, uniqinunit: $o).
2.58/0.99	thf(decl_78, type, notinsingleton: $o).
2.58/0.99	thf(decl_79, type, eqinunit: $o).
2.58/0.99	thf(decl_80, type, singletonsswitch: $o).
2.58/0.99	thf(decl_81, type, upairsetE: $o).
2.58/0.99	thf(decl_82, type, upairsetIL: $o).
2.58/0.99	thf(decl_83, type, upairsetIR: $o).
2.58/0.99	thf(decl_84, type, emptyE1: $o).
2.58/0.99	thf(decl_85, type, vacuousDall: $o).
2.58/0.99	thf(decl_86, type, quantDeMorgan1: $o).
2.58/0.99	thf(decl_87, type, quantDeMorgan2: $o).
2.58/0.99	thf(decl_88, type, quantDeMorgan3: $o).
2.58/0.99	thf(decl_89, type, quantDeMorgan4: $o).
2.58/0.99	thf(decl_90, type, prop2setI: $o).
2.58/0.99	thf(decl_92, type, prop2set2propI: $o).
2.58/0.99	thf(decl_93, type, notdexE: $o).
2.58/0.99	thf(decl_94, type, notdallE: $o).
2.58/0.99	thf(decl_95, type, exuI1: $o).
2.58/0.99	thf(decl_96, type, exuI3: $o).
2.58/0.99	thf(decl_97, type, exuI2: $o).
2.58/0.99	thf(decl_98, type, inCongP: $o).
2.58/0.99	thf(decl_99, type, in__Cong: $o).
2.58/0.99	thf(decl_100, type, exuE3u: $o).
2.58/0.99	thf(decl_101, type, exu__Cong: $o).
2.58/0.99	thf(decl_102, type, emptyset__Cong: $o).
2.58/0.99	thf(decl_103, type, setadjoin__Cong: $o).
2.58/0.99	thf(decl_104, type, powerset__Cong: $o).
2.58/0.99	thf(decl_105, type, setunion__Cong: $o).
2.58/0.99	thf(decl_106, type, omega__Cong: $o).
2.58/0.99	thf(decl_107, type, exuEu: $o).
2.58/0.99	thf(decl_108, type, descr__Cong: $o).
2.58/0.99	thf(decl_109, type, dsetconstr__Cong: $o).
2.58/0.99	thf(decl_110, type, subset: $i > $i > $o).
2.58/0.99	thf(decl_113, type, subsetI1: $o).
2.58/0.99	thf(decl_114, type, eqimpsubset2: $o).
2.58/0.99	thf(decl_115, type, eqimpsubset1: $o).
2.58/0.99	thf(decl_116, type, subsetI2: $o).
2.58/0.99	thf(decl_117, type, emptysetsubset: $o).
2.58/0.99	thf(decl_118, type, subsetE: $o).
2.58/0.99	thf(decl_119, type, subsetE2: $o).
2.58/0.99	thf(decl_120, type, notsubsetI: $o).
2.58/0.99	thf(decl_121, type, notequalI1: $o).
2.58/0.99	thf(decl_122, type, notequalI2: $o).
2.58/0.99	thf(decl_123, type, subsetRefl: $o).
2.58/0.99	thf(decl_124, type, subsetTrans: $o).
2.58/0.99	thf(decl_125, type, setadjoinSub: $o).
2.58/0.99	thf(decl_126, type, setadjoinSub2: $o).
2.58/0.99	thf(decl_127, type, subset2powerset: $o).
2.58/0.99	thf(decl_128, type, setextsub: $o).
2.58/0.99	thf(decl_129, type, subsetemptysetimpeq: $o).
2.58/0.99	thf(decl_130, type, powersetI1: $o).
2.58/0.99	thf(decl_131, type, powersetE1: $o).
2.58/0.99	thf(decl_132, type, inPowerset: $o).
2.58/0.99	thf(decl_133, type, powersetsubset: $o).
2.58/0.99	thf(decl_134, type, sepInPowerset: $o).
2.58/0.99	thf(decl_135, type, sepSubset: $o).
2.58/0.99	thf(decl_136, type, binunion: $i > $i > $i).
2.58/0.99	thf(decl_137, type, binunionIL: $o).
2.58/0.99	thf(decl_138, type, upairset2IR: $o).
2.58/0.99	thf(decl_139, type, binunionIR: $o).
2.58/0.99	thf(decl_140, type, binunionEcases: $o).
2.58/0.99	thf(decl_141, type, binunionE: $o).
2.58/0.99	thf(decl_142, type, binunionLsub: $o).
2.58/0.99	thf(decl_143, type, binunionRsub: $o).
2.58/0.99	thf(decl_144, type, binintersect: $i > $i > $i).
2.58/0.99	thf(decl_145, type, binintersectI: $o).
2.58/0.99	thf(decl_146, type, binintersectSubset5: $o).
2.58/0.99	thf(decl_147, type, binintersectEL: $o).
2.58/0.99	thf(decl_148, type, binintersectLsub: $o).
2.58/0.99	thf(decl_149, type, binintersectSubset2: $o).
2.58/0.99	thf(decl_150, type, binintersectSubset3: $o).
2.58/0.99	thf(decl_151, type, binintersectER: $o).
2.58/0.99	thf(decl_152, type, disjointsetsI1: $o).
2.58/0.99	thf(decl_153, type, binintersectRsub: $o).
2.58/0.99	thf(decl_154, type, binintersectSubset4: $o).
2.58/0.99	thf(decl_155, type, binintersectSubset1: $o).
2.58/0.99	thf(decl_156, type, bs114d: $o).
2.58/0.99	thf(decl_158, type, setminus: $i > $i > $i).
2.58/0.99	thf(decl_159, type, setminusI: $o).
2.58/0.99	thf(decl_160, type, setminusEL: $o).
2.58/0.99	thf(decl_161, type, setminusER: $o).
2.58/0.99	thf(decl_162, type, setminusSubset2: $o).
2.58/0.99	thf(decl_163, type, setminusERneg: $o).
2.58/0.99	thf(decl_164, type, setminusELneg: $o).
2.58/0.99	thf(decl_165, type, setminusILneg: $o).
2.58/0.99	thf(decl_166, type, setminusIRneg: $o).
2.58/0.99	thf(decl_167, type, setminusLsub: $o).
2.58/0.99	thf(decl_168, type, setminusSubset1: $o).
2.58/0.99	thf(decl_169, type, symdiff: $i > $i > $i).
2.58/0.99	thf(decl_170, type, symdiffE: $o).
2.58/0.99	thf(decl_171, type, symdiffI1: $o).
2.58/0.99	thf(decl_172, type, symdiffI2: $o).
2.58/0.99	thf(decl_173, type, symdiffIneg1: $o).
2.58/0.99	thf(decl_174, type, symdiffIneg2: $o).
2.58/0.99	thf(decl_175, type, iskpair: $i > $o).
2.58/0.99	thf(decl_176, type, secondinupair: $o).
2.58/0.99	thf(decl_177, type, setukpairIL: $o).
2.58/0.99	thf(decl_178, type, setukpairIR: $o).
2.58/0.99	thf(decl_179, type, kpairiskpair: $o).
2.58/0.99	thf(decl_180, type, kpair: $i > $i > $i).
2.58/0.99	thf(decl_181, type, kpairp: $o).
2.58/0.99	thf(decl_182, type, cartprod: $i > $i > $i).
2.58/0.99	thf(decl_183, type, singletonsubset: $o).
2.58/0.99	thf(decl_184, type, singletoninpowerset: $o).
2.58/0.99	thf(decl_185, type, singletoninpowunion: $o).
2.58/0.99	thf(decl_186, type, upairset2E: $o).
2.58/0.99	thf(decl_187, type, upairsubunion: $o).
2.58/0.99	thf(decl_188, type, upairinpowunion: $o).
2.58/0.99	thf(decl_189, type, ubforcartprodlem1: $o).
2.58/0.99	thf(decl_190, type, ubforcartprodlem2: $o).
2.58/0.99	thf(decl_191, type, ubforcartprodlem3: $o).
2.58/0.99	thf(decl_192, type, cartprodpairin: $o).
2.58/0.99	thf(decl_193, type, cartprodmempair1: $o).
2.58/0.99	thf(decl_194, type, cartprodmempair: $o).
2.58/0.99	thf(decl_195, type, setunionE2: $o).
2.58/0.99	thf(decl_196, type, setunionsingleton1: $o).
2.58/0.99	thf(decl_197, type, setunionsingleton2: $o).
2.58/0.99	thf(decl_198, type, setunionsingleton: $o).
2.58/0.99	thf(decl_199, type, singleton: $i > $o).
2.58/0.99	thf(decl_200, type, singletonprop: $o).
2.58/0.99	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
2.58/0.99	thf(decl_202, type, ex1E1: $o).
2.58/0.99	thf(decl_203, type, ex1I: $o).
2.58/0.99	thf(decl_204, type, ex1I2: $o).
2.58/0.99	thf(decl_205, type, singletonsuniq: $o).
2.58/0.99	thf(decl_210, type, setukpairinjL1: $o).
2.58/0.99	thf(decl_211, type, kfstsingleton: $o).
2.58/0.99	thf(decl_212, type, theprop: $o).
2.58/0.99	thf(decl_213, type, kfst: $i > $i).
2.58/0.99	thf(decl_214, type, kfstpairEq: $o).
2.58/0.99	thf(decl_215, type, cartprodfstin: $o).
2.58/0.99	thf(decl_216, type, setukpairinjL2: $o).
2.58/0.99	thf(decl_217, type, setukpairinjL: $o).
2.58/0.99	thf(decl_218, type, setukpairinjR11: $o).
2.58/0.99	thf(decl_219, type, setukpairinjR12: $o).
2.58/0.99	thf(decl_220, type, setukpairinjR1: $o).
2.58/0.99	thf(decl_221, type, upairequniteq: $o).
2.58/0.99	thf(decl_222, type, setukpairinjR2: $o).
2.58/0.99	thf(decl_223, type, setukpairinjR: $o).
2.58/0.99	thf(decl_224, type, ksndsingleton: $o).
2.58/0.99	thf(decl_225, type, ksnd: $i > $i).
2.58/0.99	thf(decl_226, type, ksndpairEq: $o).
2.58/0.99	thf(decl_227, type, kpairsurjEq: $o).
2.58/0.99	thf(decl_228, type, cartprodsndin: $o).
2.58/0.99	thf(decl_229, type, cartprodpairmemEL: $o).
2.58/0.99	thf(decl_230, type, cartprodpairmemER: $o).
2.58/0.99	thf(decl_231, type, cartprodmempaircEq: $o).
2.58/0.99	thf(decl_232, type, cartprodfstpairEq: $o).
2.58/0.99	thf(decl_233, type, cartprodsndpairEq: $o).
2.58/0.99	thf(decl_234, type, cartprodpairsurjEq: $o).
2.58/0.99	thf(decl_235, type, breln: $i > $i > $i > $o).
2.58/0.99	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
2.58/0.99	thf(decl_237, type, dpsetconstrI: $o).
2.58/0.99	thf(decl_238, type, dpsetconstrSub: $o).
2.58/0.99	thf(decl_239, type, setOfPairsIsBReln: $o).
2.58/0.99	thf(decl_240, type, dpsetconstrERa: $o).
2.58/0.99	thf(decl_241, type, dpsetconstrEL1: $o).
2.58/0.99	thf(decl_242, type, dpsetconstrEL2: $o).
2.58/0.99	thf(decl_243, type, dpsetconstrER: $o).
2.58/0.99	thf(decl_244, type, func: $i > $i > $i > $o).
2.58/0.99	thf(decl_245, type, funcSet: $i > $i > $i).
2.58/0.99	thf(decl_246, type, funcImageSingleton: $o).
2.58/0.99	thf(decl_247, type, apProp: $o).
2.58/0.99	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
2.58/0.99	thf(decl_249, type, app: $o).
2.58/0.99	thf(decl_250, type, infuncsetfunc: $o).
2.58/0.99	thf(decl_251, type, ap2p: $o).
2.58/0.99	thf(decl_252, type, funcinfuncset: $o).
2.58/0.99	thf(decl_253, type, lamProp: $o).
2.58/0.99	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
2.58/0.99	thf(decl_255, type, lamp: $o).
2.58/0.99	thf(decl_256, type, lam2p: $o).
2.58/0.99	thf(decl_257, type, brelnall1: $o).
2.58/0.99	thf(decl_258, type, brelnall2: $o).
2.58/0.99	thf(decl_259, type, ex1E2: $o).
2.58/0.99	thf(decl_260, type, funcGraphProp1: $o).
2.58/0.99	thf(decl_261, type, funcGraphProp3: $o).
2.58/0.99	thf(decl_262, type, funcGraphProp2: $o).
2.58/0.99	thf(decl_263, type, funcextLem: $o).
2.58/0.99	thf(decl_264, type, funcGraphProp4: $o).
2.58/0.99	thf(decl_265, type, subbreln: $o).
2.58/0.99	thf(decl_266, type, eqbreln: $o).
2.58/0.99	thf(decl_267, type, funcext: $o).
2.58/0.99	thf(decl_268, type, funcext2: $o).
2.58/0.99	thf(decl_269, type, ap2apEq1: $o).
2.58/0.99	thf(decl_270, type, ap2apEq2: $o).
2.58/0.99	thf(decl_271, type, beta1: $o).
2.58/0.99	thf(decl_272, type, eta1: $o).
2.58/0.99	thf(decl_273, type, lam2lamEq: $o).
2.58/0.99	thf(decl_274, type, beta2: $o).
2.58/0.99	thf(decl_275, type, eta2: $o).
2.58/0.99	thf(decl_276, type, iffalseProp1: $o).
2.58/0.99	thf(decl_277, type, iffalseProp2: $o).
2.58/0.99	thf(decl_278, type, iftrueProp1: $o).
2.58/0.99	thf(decl_279, type, iftrueProp2: $o).
2.58/0.99	thf(decl_280, type, ifSingleton: $o).
2.58/0.99	thf(decl_281, type, if: $i > $o > $i > $i > $i).
2.58/0.99	thf(decl_282, type, ifp: $o).
2.58/0.99	thf(decl_283, type, theeq: $o).
2.58/0.99	thf(decl_284, type, iftrue: $o).
2.58/0.99	thf(decl_285, type, iffalse: $o).
2.58/0.99	thf(decl_286, type, iftrueorfalse: $o).
2.58/0.99	thf(decl_287, type, binintersectT_lem: $o).
2.58/0.99	thf(decl_288, type, binunionT_lem: $o).
2.58/0.99	thf(decl_289, type, powersetT_lem: $o).
2.58/0.99	thf(decl_290, type, setminusT_lem: $o).
2.58/0.99	thf(decl_291, type, complementT_lem: $o).
2.58/0.99	thf(decl_292, type, setextT: $o).
2.58/0.99	thf(decl_293, type, subsetTI: $o).
2.58/0.99	thf(decl_294, type, powersetTI1: $o).
2.58/0.99	thf(decl_295, type, powersetTE1: $o).
2.58/0.99	thf(decl_296, type, complementTI1: $o).
2.58/0.99	thf(decl_297, type, complementTE1: $o).
2.58/0.99	thf(decl_298, type, binintersectTELcontra: $o).
2.58/0.99	thf(decl_299, type, binintersectTERcontra: $o).
2.58/0.99	thf(decl_300, type, contrasubsetT: $o).
2.58/0.99	thf(decl_301, type, contrasubsetT1: $o).
2.58/0.99	thf(decl_302, type, contrasubsetT2: $o).
2.58/0.99	thf(decl_303, type, contrasubsetT3: $o).
2.58/0.99	thf(decl_304, type, doubleComplementI1: $o).
2.58/0.99	thf(decl_305, type, doubleComplementE1: $o).
2.58/0.99	thf(decl_306, type, doubleComplementSub1: $o).
2.58/0.99	thf(decl_307, type, doubleComplementSub2: $o).
2.58/0.99	thf(decl_308, type, doubleComplementEq: $o).
2.58/0.99	thf(decl_309, type, complementTnotintersectT: $o).
2.58/0.99	thf(decl_310, type, complementImpComplementIntersect: $o).
2.58/0.99	thf(decl_311, type, complementSubsetComplementIntersect: $o).
2.58/0.99	thf(decl_312, type, complementInPowersetComplementIntersect: $o).
2.58/0.99	thf(decl_313, type, contraSubsetComplement: $o).
2.58/0.99	thf(decl_314, type, complementTcontraSubset: $o).
2.58/0.99	thf(decl_315, type, binunionTILcontra: $o).
2.58/0.99	thf(decl_316, type, binunionTIRcontra: $o).
2.58/0.99	thf(decl_317, type, inIntersectImpInUnion: $o).
2.58/0.99	thf(decl_318, type, inIntersectImpInUnion2: $o).
2.58/0.99	thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
2.58/0.99	thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
2.58/0.99	thf(decl_321, type, inComplementUnionImpNotIn1: $o).
2.58/0.99	thf(decl_322, type, inComplementUnionImpInComplement1: $o).
2.58/0.99	thf(decl_323, type, binunionTE: $o).
2.58/0.99	thf(decl_324, type, binunionTEcontra: $o).
2.58/0.99	thf(decl_325, type, demorgan2a1: $o).
2.58/0.99	thf(decl_326, type, complementUnionInPowersetComplement: $o).
2.58/0.99	thf(decl_327, type, epred1_0: $o).
2.58/0.99	thf(decl_328, type, esk1_2: $i > $i > $i).
2.58/0.99	thf(decl_329, type, esk2_2: $i > $i > $i).
2.58/0.99	thf(decl_330, type, esk3_2: $i > $i > $i).
2.58/0.99	thf(decl_331, type, esk4_1: $i > $i).
2.58/0.99	thf(decl_332, type, esk5_2: ($i > $i > $o) > $i > $i).
2.58/0.99	thf(decl_333, type, esk6_2: ($i > $i > $o) > $i > $i).
2.58/0.99	thf(decl_334, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
2.58/0.99	thf(decl_335, type, esk8_1: $i > $i).
2.58/0.99	thf(decl_336, type, esk9_1: ($i > $o) > $i).
2.58/0.99	thf(decl_337, type, esk10_1: ($i > $o) > $i).
2.58/0.99	thf(decl_338, type, esk11_2: $i > $i > $i).
2.58/0.99	thf(decl_339, type, esk12_2: $i > $i > $i).
2.58/0.99	thf(decl_340, type, esk13_1: $i > $i).
2.58/0.99	thf(decl_341, type, esk14_1: $i > $i).
2.58/0.99	thf(decl_342, type, esk15_1: $i > $i).
2.58/0.99	thf(decl_343, type, esk16_2: $i > $i > $i).
2.58/0.99	thf(decl_344, type, esk17_3: $i > $i > $o > $i).
2.58/0.99	thf(decl_345, type, esk18_1: ($i > $o) > $i).
2.58/0.99	thf(decl_346, type, esk19_1: $i > $i).
2.58/0.99	thf(decl_347, type, esk20_2: $i > ($i > $o) > $i).
2.58/0.99	thf(decl_348, type, esk21_2: $i > ($i > $o) > $i).
2.58/0.99	thf(decl_349, type, esk22_2: $i > ($i > $o) > $i).
2.58/0.99	thf(decl_350, type, esk23_2: $i > ($i > $o) > $i).
2.58/0.99	thf(decl_351, type, esk24_2: $i > ($i > $o) > $i).
2.58/0.99	thf(decl_352, type, esk25_2: $i > ($i > $o) > $i).
2.58/0.99	thf(decl_353, type, esk26_2: ($i > $o) > $i > $i).
2.58/0.99	thf(decl_354, type, esk27_1: ($i > $o) > $i).
2.58/0.99	thf(decl_355, type, esk28_1: ($i > $o) > $i).
2.58/0.99	thf(decl_356, type, esk29_2: ($i > $o) > $i > $i).
2.58/0.99	thf(decl_357, type, esk30_2: ($i > $o) > ($i > $o) > $i).
2.58/0.99	thf(decl_358, type, esk31_2: ($i > $o) > ($i > $o) > $i).
2.58/0.99	thf(decl_359, type, esk32_2: ($i > $o) > ($i > $o) > $i).
2.58/0.99	thf(decl_360, type, esk33_2: ($i > $o) > ($i > $o) > $i).
2.58/0.99	thf(decl_361, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
2.58/0.99	thf(decl_362, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
2.58/0.99	thf(decl_363, type, esk36_2: $i > $i > $i).
2.58/0.99	thf(decl_364, type, esk37_2: $i > $i > $i).
2.58/0.99	thf(decl_365, type, esk38_2: $i > $i > $i).
2.58/0.99	thf(decl_366, type, esk39_3: $i > $i > $i > $i).
2.58/0.99	thf(decl_367, type, esk40_3: $i > $i > $i > $i).
2.58/0.99	thf(decl_368, type, esk41_2: $i > $i > $i).
2.58/0.99	thf(decl_369, type, esk42_2: $i > ($i > $o) > $i).
2.58/0.99	thf(decl_370, type, esk43_2: $i > ($i > $o) > $i).
2.58/0.99	thf(decl_371, type, esk44_2: $i > ($i > $o) > $i).
2.58/0.99	thf(decl_372, type, esk45_3: $i > ($i > $o) > $i > $i).
2.58/0.99	thf(decl_373, type, esk46_2: $i > ($i > $o) > $i).
2.58/0.99	thf(decl_374, type, esk47_2: $i > ($i > $o) > $i).
2.58/0.99	thf(decl_375, type, esk48_3: $i > $i > ($i > $i) > $i).
2.58/0.99	thf(decl_376, type, esk49_3: $i > $i > ($i > $i) > $i).
2.58/0.99	thf(decl_377, type, esk50_3: $i > $i > ($i > $i) > $i).
2.58/0.99	thf(decl_378, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
2.58/0.99	thf(decl_379, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
2.58/0.99	thf(decl_380, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
2.58/0.99	thf(decl_381, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
2.58/0.99	thf(decl_382, type, esk55_4: $i > $i > $i > $i > $i).
2.58/0.99	thf(decl_383, type, esk56_4: $i > $i > $i > $i > $i).
2.58/0.99	thf(decl_384, type, esk57_4: $i > $i > $i > $i > $i).
2.58/0.99	thf(decl_385, type, esk58_4: $i > $i > $i > $i > $i).
2.58/0.99	thf(decl_386, type, esk59_4: $i > $i > $i > $i > $i).
2.58/0.99	thf(decl_387, type, esk60_4: $i > $i > $i > $i > $i).
2.58/0.99	thf(decl_388, type, esk61_4: $i > $i > $i > $i > $i).
2.58/0.99	thf(decl_389, type, esk62_4: $i > $i > $i > $i > $i).
2.58/0.99	thf(decl_390, type, esk63_4: $i > $i > $i > $i > $i).
2.58/0.99	thf(decl_391, type, esk64_3: $i > $i > ($i > $i) > $i).
2.58/0.99	thf(decl_392, type, esk65_3: $i > $i > ($i > $i) > $i).
2.58/0.99	thf(decl_393, type, esk66_3: $i > $i > ($i > $i) > $i).
2.58/0.99	thf(decl_394, type, esk67_3: $i > $i > $i > $i).
2.58/0.99	thf(decl_395, type, esk68_3: $i > $i > $i > $i).
2.58/0.99	thf(decl_396, type, esk69_3: $i > $i > $i > $i).
2.58/0.99	thf(decl_397, type, esk70_3: $i > $i > $i > $i).
2.58/0.99	thf(decl_398, type, esk71_0: $i).
2.58/0.99	thf(decl_399, type, esk72_0: $i).
2.58/0.99	thf(decl_400, type, esk73_0: $i).
2.58/0.99	thf(decl_401, type, esk74_0: $i).
2.58/0.99	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', sepSubset)).
2.58/0.99	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', sepInPowerset)).
2.58/0.99	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', descr__Cong)).
2.58/0.99	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', exuEu)).
2.58/0.99	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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', exu__Cong)).
2.58/0.99	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', exuE3u)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', exuI2)).
2.58/0.99	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', exuI3)).
2.58/0.99	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', exuE2)).
2.58/0.99	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setoftrueEq)).
2.58/0.99	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', nonemptyI)).
2.58/0.99	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', dsetconstrER)).
2.58/0.99	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', dsetconstrEL)).
2.58/0.99	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', ex1E1)).
2.58/0.99	thf(ex1I, axiom, ((ex1I)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', ex1I)).
2.58/0.99	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', ifSingleton)).
2.58/0.99	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', dpsetconstrSub)).
2.58/0.99	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', dpsetconstrERa)).
2.58/0.99	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', dpsetconstrEL2)).
2.58/0.99	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', funcImageSingleton)).
2.58/0.99	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', apProp)).
2.58/0.99	thf(lamProp, axiom, ((lamProp)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', lamProp)).
2.58/0.99	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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', lam2p)).
2.58/0.99	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', ex1E2)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', beta1)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', lam2lamEq)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', eta2)).
2.58/0.99	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', iffalseProp2)).
2.58/0.99	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', iftrueProp1)).
2.58/0.99	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', iftrueProp2)).
2.58/0.99	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', iffalseProp1)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', beta2)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', eta1)).
2.58/0.99	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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', lamp)).
2.58/0.99	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', dpsetconstrER)).
2.58/0.99	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', dpsetconstrEL1)).
2.58/0.99	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setOfPairsIsBReln)).
2.58/0.99	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', dpsetconstrI)).
2.58/0.99	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', ksndsingleton)).
2.58/0.99	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', kfstsingleton)).
2.58/0.99	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', ex1I2)).
2.58/0.99	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', singletonprop)).
2.58/0.99	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', dsetconstr__Cong)).
2.58/0.99	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', exuI1)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', emptyE1)).
2.58/0.99	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setbeta)).
2.58/0.99	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', exuE3e)).
2.58/0.99	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', exuE1)).
2.58/0.99	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', dsetconstrI)).
2.58/0.99	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', descrp)).
2.58/0.99	thf(replAx, axiom, ((replAx)<=>![X6:$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.gyPNU6FcMF/E---3.1_14783.p', replAx)).
2.58/0.99	thf(demorgan2a2, conjecture, (((emptysetAx)=>(((powersetAx)=>((setunionAx)=>((omega0Ax)=>(((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((((exuE1)=>((((emptysetimpfalse)=>(((exuE3e)=>(((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>(((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>(((setadjoinOr)=>(((powersetI)=>((emptyinPowerset)=>(((((setunionE)=>((subPowSU)=>((((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((((emptyE1)=>((vacuousDall)=>(((quantDeMorgan2)=>((((prop2setI)=>((prop2set2propI)=>((notdexE)=>(((exuI1)=>((((((((((powerset__Cong)=>(((omega__Cong)=>((((dsetconstr__Cong)=>((subsetI1)=>(((((emptysetsubset)=>((subsetE)=>((subsetE2)=>((((notequalI2)=>((subsetRefl)=>((((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>(((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((((binunionIL)=>(((binunionIR)=>((binunionEcases)=>((binunionE)=>(((binunionRsub)=>(((binintersectSubset5)=>((binintersectEL)=>(((((binintersectER)=>((disjointsetsI1)=>(((binintersectSubset4)=>(((bs114d)=>(((((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((((secondinupair)=>(((((kpairp)=>((((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>(((ubforcartprodlem2)=>(((cartprodpairin)=>(((cartprodmempair)=>(((setunionsingleton1)=>((setunionsingleton2)=>((((ex1E1)=>((ex1I)=>((((setukpairinjL1)=>(((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((((setukpairinjR12)=>(((((setukpairinjR)=>(((((((cartprodpairmemER)=>((((cartprodsndpairEq)=>((((dpsetconstrSub)=>(((dpsetconstrERa)=>(((dpsetconstrEL2)=>(((funcImageSingleton)=>((apProp)=>(((infuncsetfunc)=>(((funcinfuncset)=>((lamProp)=>(((lam2p)=>((brelnall1)=>(((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>(((funcextLem)=>(((subbreln)=>((eqbreln)=>((funcext)=>((((ap2apEq2)=>((beta1)=>(((lam2lamEq)=>(((eta2)=>(((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>(((complementT_lem)=>(((((powersetTE1)=>((complementTI1)=>(((binintersectTELcontra)=>((binintersectTERcontra)=>(((contrasubsetT1)=>(((((((doubleComplementSub2)=>((doubleComplementEq)=>(((((complementInPowersetComplementIntersect)=>((((binunionTILcontra)=>(((((inIntersectImpInIntersectUnions)=>(((((((demorgan2a1)=>((complementUnionInPowersetComplement)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X48))<=(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))))<=(binunionTEcontra))<=(binunionTE))<=(inComplementUnionImpInComplement1))<=(inComplementUnionImpNotIn1))<=(intersectInPowersetIntersectUnions)))<=(inIntersectImpInUnion2))<=(inIntersectImpInUnion))<=(binunionTIRcontra)))<=(complementTcontraSubset))<=(contraSubsetComplement)))<=(complementSubsetComplementIntersect))<=(complementImpComplementIntersect))<=(complementTnotintersectT))))<=(doubleComplementSub1))<=(doubleComplementE1))<=(doubleComplementI1))<=(contrasubsetT3))<=(contrasubsetT2)))<=(contrasubsetT))))<=(complementTE1))))<=(powersetTI1))<=(subsetTI))<=(setextT)))<=(setminusT_lem))))))))<=(theeq))<=(ifp))))))<=(iffalseProp1)))<=(beta2)))<=(eta1))))<=(ap2apEq1))<=(funcext2)))))<=(funcGraphProp4)))<=(funcGraphProp2)))))<=(brelnall2))))<=(lamp))))<=(ap2p)))<=(app))))<=(dpsetconstrER)))<=(dpsetconstrEL1)))<=(setOfPairsIsBReln)))<=(dpsetconstrI))<=(cartprodpairsurjEq)))<=(cartprodfstpairEq))<=(cartprodmempaircEq)))<=(cartprodpairmemEL))<=(cartprodsndin))<=(kpairsurjEq))<=(ksndpairEq))<=(ksndsingleton)))<=(setukpairinjR2))<=(upairequniteq))<=(setukpairinjR1)))<=(setukpairinjR11))<=(setukpairinjL))))))<=(kfstsingleton)))<=(singletonsuniq))<=(ex1I2))))<=(singletonprop))<=(setunionsingleton))))<=(setunionE2)))<=(cartprodmempair1)))<=(ubforcartprodlem3)))<=(ubforcartprodlem1))))))<=(singletoninpowerset))<=(singletonsubset)))<=(kpairiskpair))<=(setukpairIR))<=(setukpairIL)))<=(symdiffIneg2))<=(symdiffIneg1)))))<=(setminusSubset1))<=(setminusLsub)))))))<=(setminusER))<=(setminusEL))<=(setminusI)))<=(binintersectSubset1)))<=(binintersectRsub))))<=(binintersectSubset3))<=(binintersectSubset2))<=(binintersectLsub))))<=(binintersectI)))<=(binunionLsub)))))<=(upairset2IR)))<=(sepSubset))<=(sepInPowerset))))))<=(subsetemptysetimpeq)))))<=(setadjoinSub))<=(subsetTrans))))<=(notequalI1))<=(notsubsetI)))))<=(subsetI2))<=(eqimpsubset1))<=(eqimpsubset2))))<=(descr__Cong))<=(exuEu)))<=(setunion__Cong)))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong))<=(exuE3u))<=(in__Cong))<=(inCongP))<=(exuI2))<=(exuI3)))<=(notdallE)))))<=(quantDeMorgan4))<=(quantDeMorgan3)))<=(quantDeMorgan1))))<=(upairsetIR))<=(upairsetIL)))))))<=(nonemptyImpWitness))<=(exuE2))))<=(setunionI))<=(powersetE))<=(emptyInPowerset))))<=(setoftrueEq)))<=(setadjoinE))))))<=(nonemptyI))))))<=(setext)))<=(notinemptyset)))<=(emptysetE))<=(prop2setE)))<=(dsetconstrER))<=(dsetconstrEL))))))))<=(omegaSAx)))))<=(setadjoinAx)))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', demorgan2a2)).
2.58/0.99	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setextAx)).
2.58/0.99	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', upairset2IR)).
2.58/0.99	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binintersectER)).
2.58/0.99	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setminusERneg)).
2.58/0.99	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', subsetemptysetimpeq)).
2.58/0.99	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setadjoinSub)).
2.58/0.99	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', subsetTrans)).
2.58/0.99	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setminusELneg)).
2.58/0.99	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', notequalI1)).
2.58/0.99	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', notsubsetI)).
2.58/0.99	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setminusILneg)).
2.58/0.99	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', subsetI2)).
2.58/0.99	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', eqimpsubset1)).
2.58/0.99	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', eqimpsubset2)).
2.58/0.99	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setminusIRneg)).
2.58/0.99	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', symdiffE)).
2.58/0.99	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setunion__Cong)).
2.58/0.99	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setadjoin__Cong)).
2.58/0.99	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', emptyset__Cong)).
2.58/0.99	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', symdiffI1)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', in__Cong)).
2.58/0.99	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', symdiffI2)).
2.58/0.99	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', inCongP)).
2.58/0.99	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', kfstpairEq)).
2.58/0.99	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', disjointsetsI1)).
2.58/0.99	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', notdallE)).
2.58/0.99	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', secondinupair)).
2.58/0.99	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', quantDeMorgan4)).
2.58/0.99	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', quantDeMorgan3)).
2.58/0.99	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', kpairp)).
2.58/0.99	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', quantDeMorgan1)).
2.58/0.99	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binintersectSubset4)).
2.58/0.99	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', upairsetIR)).
2.58/0.99	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', upairsetIL)).
2.58/0.99	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', nonemptyImpWitness)).
2.58/0.99	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', singletoninpowunion)).
2.58/0.99	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setunionI)).
2.58/0.99	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', upairset2E)).
2.58/0.99	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', powersetE)).
2.58/0.99	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', emptyInPowerset)).
2.58/0.99	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', upairsubunion)).
2.58/0.99	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setadjoinE)).
2.58/0.99	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', upairinpowunion)).
2.58/0.99	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setext)).
2.58/0.99	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', notinemptyset)).
2.58/0.99	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', emptysetE)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', ubforcartprodlem2)).
2.58/0.99	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', prop2setE)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', cartprodpairin)).
2.58/0.99	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', omegaSAx)).
2.58/0.99	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setadjoinAx)).
2.58/0.99	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', cartprodmempair)).
2.58/0.99	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setunionsingleton1)).
2.58/0.99	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setunionsingleton2)).
2.58/0.99	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.gyPNU6FcMF/E---3.1_14783.p', setukpairinjL1)).
2.58/0.99	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', theprop)).
2.58/0.99	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', iftrue)).
2.58/0.99	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', iffalse)).
2.58/0.99	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', cartprodfstin)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', setukpairinjL2)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', setukpairinjR12)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', setukpairinjR)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', cartprodpairmemER)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', cartprodsndpairEq)).
2.58/0.99	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', bs114d)).
2.58/0.99	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', infuncsetfunc)).
2.58/0.99	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', funcinfuncset)).
2.58/0.99	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', brelnall1)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', funcGraphProp1)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', funcGraphProp3)).
2.58/0.99	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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', funcextLem)).
2.58/0.99	thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', subbreln)).
2.58/0.99	thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', eqbreln)).
2.58/0.99	thf(funcext, axiom, ((funcext)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', funcext)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', ap2apEq2)).
2.58/0.99	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binintersectSubset2)).
2.58/0.99	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binintersectLsub)).
2.58/0.99	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binintersectI)).
2.58/0.99	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binunionLsub)).
2.58/0.99	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', iftrueorfalse)).
2.58/0.99	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', binintersectT_lem)).
2.58/0.99	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binunionT_lem)).
2.58/0.99	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', powersetT_lem)).
2.58/0.99	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', complementT_lem)).
2.58/0.99	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', powersetTE1)).
2.58/0.99	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', complementTI1)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', binintersectTELcontra)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', binintersectTERcontra)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', contrasubsetT1)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', doubleComplementSub2)).
2.58/0.99	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', doubleComplementEq)).
2.58/0.99	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', complementInPowersetComplementIntersect)).
2.58/0.99	thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binunionTILcontra)).
2.58/0.99	thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', inIntersectImpInIntersectUnions)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', demorgan2a1)).
2.58/0.99	thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', complementUnionInPowersetComplement)).
2.58/0.99	thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binunionTEcontra)).
2.58/0.99	thf(binunionTE, axiom, ((binunionTE)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', binunionTE)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', inComplementUnionImpInComplement1)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', inComplementUnionImpNotIn1)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', intersectInPowersetIntersectUnions)).
2.58/0.99	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', inIntersectImpInUnion2)).
2.58/0.99	thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', inIntersectImpInUnion)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', binunionTIRcontra)).
2.58/0.99	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', complementTcontraSubset)).
2.58/0.99	thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', contraSubsetComplement)).
2.58/0.99	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', complementSubsetComplementIntersect)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', complementImpComplementIntersect)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', complementTnotintersectT)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', doubleComplementSub1)).
2.58/0.99	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', doubleComplementE1)).
2.58/0.99	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', doubleComplementI1)).
2.58/0.99	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', contrasubsetT3)).
2.58/0.99	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', contrasubsetT2)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', contrasubsetT)).
2.58/0.99	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', complementTE1)).
2.58/0.99	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', powersetTI1)).
2.58/0.99	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', subsetTI)).
2.58/0.99	thf(setextT, axiom, ((setextT)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', setextT)).
2.58/0.99	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setminusT_lem)).
2.58/0.99	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', theeq)).
2.58/0.99	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', ifp)).
2.58/0.99	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', ap2apEq1)).
2.58/0.99	thf(funcext2, axiom, ((funcext2)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', funcext2)).
2.58/0.99	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', funcGraphProp4)).
2.58/0.99	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', funcGraphProp2)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', brelnall2)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', ap2p)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', app)).
2.58/0.99	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', cartprodpairsurjEq)).
2.58/0.99	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', cartprodfstpairEq)).
2.58/0.99	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', cartprodmempaircEq)).
2.58/0.99	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', cartprodpairmemEL)).
2.58/0.99	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', cartprodsndin)).
2.58/0.99	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', kpairsurjEq)).
2.58/0.99	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', ksndpairEq)).
2.58/0.99	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setukpairinjR2)).
2.58/0.99	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', upairequniteq)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', setukpairinjR1)).
2.58/0.99	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setukpairinjR11)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', setukpairinjL)).
2.58/0.99	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', singletonsuniq)).
2.58/0.99	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setunionsingleton)).
2.58/0.99	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setunionE2)).
2.58/0.99	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', cartprodmempair1)).
2.58/0.99	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', ubforcartprodlem3)).
2.58/0.99	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', ubforcartprodlem1)).
2.58/0.99	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', singletoninpowerset)).
2.58/0.99	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', singletonsubset)).
2.58/0.99	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', kpairiskpair)).
2.58/0.99	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setukpairIR)).
2.58/0.99	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setukpairIL)).
2.58/0.99	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', symdiffIneg2)).
2.58/0.99	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', symdiffIneg1)).
2.58/0.99	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setminusSubset1)).
2.58/0.99	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setminusLsub)).
2.58/0.99	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setminusER)).
2.58/0.99	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setminusEL)).
2.58/0.99	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setminusI)).
2.58/0.99	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binintersectSubset1)).
2.58/0.99	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binintersectRsub)).
2.58/0.99	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binintersectSubset3)).
2.58/0.99	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setminusSubset2)).
2.58/0.99	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binintersectEL)).
2.58/0.99	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binintersectSubset5)).
2.58/0.99	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binunionRsub)).
2.58/0.99	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binunionE)).
2.58/0.99	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binunionEcases)).
2.58/0.99	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binunionIR)).
2.58/0.99	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', binunionIL)).
2.58/0.99	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', powersetsubset)).
2.58/0.99	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', inPowerset)).
2.58/0.99	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', powersetE1)).
2.58/0.99	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', powersetI1)).
2.58/0.99	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setextsub)).
2.58/0.99	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', subset2powerset)).
2.58/0.99	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setadjoinSub2)).
2.58/0.99	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', subsetRefl)).
2.58/0.99	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', notequalI2)).
2.58/0.99	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', subsetE2)).
2.58/0.99	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', subsetE)).
2.58/0.99	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', emptysetsubset)).
2.58/0.99	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', subsetI1)).
2.58/0.99	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', omega__Cong)).
2.58/0.99	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', powerset__Cong)).
2.58/0.99	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', notdexE)).
2.58/0.99	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', prop2setI)).
2.58/0.99	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', quantDeMorgan2)).
2.58/0.99	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', vacuousDall)).
2.58/0.99	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', upairsetE)).
2.58/0.99	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', singletonsswitch)).
2.58/0.99	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', eqinunit)).
2.58/0.99	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', notinsingleton)).
2.58/0.99	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', uniqinunit)).
2.58/0.99	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', subPowSU)).
2.58/0.99	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setunionE)).
2.58/0.99	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', emptyinPowerset)).
2.58/0.99	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', powersetI)).
2.58/0.99	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setadjoinOr)).
2.58/0.99	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setadjoinIR)).
2.58/0.99	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', emptyinunitempty)).
2.58/0.99	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setadjoinIL)).
2.58/0.99	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', nonemptyI1)).
2.58/0.99	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', nonemptyE1)).
2.58/0.99	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', noeltsimpempty)).
2.58/0.99	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', emptyI)).
2.58/0.99	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', emptysetimpfalse)).
2.58/0.99	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.gyPNU6FcMF/E---3.1_14783.p', wellorderingAx)).
2.58/0.99	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.gyPNU6FcMF/E---3.1_14783.p', foundationAx)).
2.58/0.99	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', omegaIndAx)).
2.58/0.99	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', omega0Ax)).
2.58/0.99	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', setunionAx)).
2.58/0.99	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', powersetAx)).
2.58/0.99	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.gyPNU6FcMF/E---3.1_14783.p', emptysetAx)).
2.58/0.99	thf(c_0_266, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
2.58/0.99	thf(c_0_267, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
2.58/0.99	thf(c_0_268, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
2.58/0.99	thf(c_0_269, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
2.58/0.99	thf(c_0_270, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
2.58/0.99	thf(c_0_271, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
2.58/0.99	thf(c_0_272, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
2.58/0.99	thf(c_0_273, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
2.58/0.99	thf(c_0_274, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
2.58/0.99	thf(c_0_275, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
2.58/0.99	thf(c_0_276, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
2.58/0.99	thf(c_0_277, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
2.58/0.99	thf(c_0_278, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
2.58/0.99	thf(c_0_279, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
2.58/0.99	thf(c_0_280, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
2.58/0.99	thf(c_0_281, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
2.58/0.99	thf(c_0_282, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
2.58/0.99	thf(c_0_283, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
2.58/0.99	thf(c_0_284, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
2.58/0.99	thf(c_0_285, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
2.58/0.99	thf(c_0_286, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
2.58/0.99	thf(c_0_287, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
2.58/0.99	thf(c_0_288, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
2.58/0.99	thf(c_0_289, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
2.58/0.99	thf(c_0_290, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
2.58/0.99	thf(c_0_291, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
2.58/0.99	thf(c_0_292, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 248 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
2.58/0.99	thf(c_0_293, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
2.58/0.99	thf(c_0_294, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
2.58/0.99	thf(c_0_295, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
2.58/0.99	thf(c_0_296, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
2.58/0.99	thf(c_0_297, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
2.58/0.99	thf(c_0_298, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 248 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
2.58/0.99	thf(c_0_299, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
2.58/0.99	thf(c_0_300, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
2.58/0.99	thf(c_0_301, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
2.58/0.99	thf(c_0_302, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
2.58/0.99	thf(c_0_303, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
2.58/0.99	thf(c_0_304, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
2.58/0.99	thf(c_0_305, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
2.58/0.99	thf(c_0_306, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
2.58/0.99	thf(c_0_307, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
2.58/0.99	thf(c_0_308, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
2.58/0.99	thf(c_0_309, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
2.58/0.99	thf(c_0_310, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
2.58/0.99	thf(c_0_311, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
2.58/0.99	thf(c_0_312, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
2.58/0.99	thf(c_0_313, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
2.58/0.99	thf(c_0_314, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
2.58/0.99	thf(c_0_315, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
2.58/0.99	thf(c_0_316, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
2.58/0.99	thf(c_0_317, plain, ((epred1_0)<=>![X912:$i]:(?[X913:$i]:((((![X914:$i]:(((in @ X914 @ X913)=>![X915:$i]:(((in @ X915 @ X914)=>(in @ X915 @ X912)))))&![X916:$i, X917:$i]:((((in @ X916 @ X912)&(in @ X917 @ X912))=>(![X918:$i]:(((in @ X918 @ X913)=>((in @ X916 @ X918)<=>(in @ X917 @ X918))))=>((X916)=(X917))))))&![X919:$i, X920:$i]:((((in @ X919 @ X913)&(in @ X920 @ X913))=>(![X921:$i]:(((in @ X921 @ X919)=>(in @ X921 @ X920)))|![X922:$i]:(((in @ X922 @ X920)=>(in @ X922 @ X919)))))))&![X923:$i]:(((![X924:$i]:(((in @ X924 @ X923)=>(in @ X924 @ X912)))&?[X925:$i]:((in @ X925 @ X923)))=>?[X926:$i, X927:$i]:(((((in @ X926 @ X913)&(in @ X927 @ X923))&~(?[X928:$i]:(((in @ X928 @ X926)&(in @ X928 @ X923)))))&![X929:$i]:(((in @ X929 @ X913)=>(![X930:$i]:(((in @ X930 @ X929)=>(in @ X930 @ X926)))|(in @ X927 @ X929)))))))))))), introduced(definition)).
2.58/0.99	thf(c_0_318, negated_conjecture, ~((![X1726:$i, X1727:$i]:((![X1728:$i]:(((in @ X1728 @ X1726)<=>(in @ X1728 @ X1727)))=>((X1726)=(X1727))))=>(![X892:$i]:(~(in @ X892 @ emptyset))=>(![X1723:$i, X1724:$i, X1725:$i]:(((in @ X1725 @ (setadjoin @ X1723 @ X1724))<=>(((X1725)=(X1723))|(in @ X1725 @ X1724))))=>(![X893:$i, X894:$i]:(((in @ X894 @ (powerset @ X893))<=>![X895:$i]:(((in @ X895 @ X894)=>(in @ X895 @ X893)))))=>(![X896:$i, X897:$i]:(((in @ X897 @ (setunion @ X896))<=>?[X898:$i]:(((in @ X897 @ X898)&(in @ X898 @ X896)))))=>((in @ emptyset @ omega)=>(![X1722:$i]:(((in @ X1722 @ omega)=>(in @ (setadjoin @ X1722 @ X1722) @ omega)))=>(![X899:$i]:((((in @ emptyset @ X899)&![X900:$i]:((((in @ X900 @ omega)&(in @ X900 @ X899))=>(in @ (setadjoin @ X900 @ X900) @ X899))))=>![X901:$i]:(((in @ X901 @ omega)=>(in @ X901 @ X899)))))=>(![X902:$i > $i > $o, X903:$i]:((![X904:$i]:(((in @ X904 @ X903)=>(exu @ (X902 @ X904))))=>?[X905:$i]:(![X906:$i]:(((in @ X906 @ X905)<=>?[X907:$i]:(((in @ X907 @ X903)&(X902 @ X907 @ X906))))))))=>(![X908:$i]:((?[X909:$i]:((in @ X909 @ X908))=>?[X910:$i]:(((in @ X910 @ X908)&~(?[X911:$i]:(((in @ X911 @ X910)&(in @ X911 @ X908))))))))=>((epred1_0)=>(![X931:$i > $o]:(((exu @ X931)=>(X931 @ (descr @ (^[Z0/* 17 */:$i]:(X931 @ Z0))))))=>(![X932:$i, X933:$i > $o, X934:$i]:(((in @ X934 @ X932)=>((X933 @ X934)=>(in @ X934 @ (dsetconstr @ X932 @ X933)))))=>(![X1719:$i, X1720:$i > $o, X1721:$i]:(((in @ X1721 @ (dsetconstr @ X1719 @ X1720))=>(in @ X1721 @ X1719)))=>(![X1716:$i, X1717:$i > $o, X1718:$i]:(((in @ X1718 @ (dsetconstr @ X1716 @ X1717))=>(X1717 @ X1718)))=>(![X935:$i > $o]:(((exu @ X935)=>?[X936:$i]:(((X935 @ X936)&![X937:$i]:(((X935 @ X937)=>((X936)=(X937))))))))=>(![X1714:$o, X1715:$i]:(((in @ X1715 @ (prop2set @ ((X1714))))=>(X1714)))=>(![X1712:$i]:(((in @ X1712 @ emptyset)=>![X1713:$o]:((X1713))))=>(![X938:$i]:(((in @ X938 @ emptyset)=>~($true)))=>(![X1711:$i]:(~(in @ X1711 @ emptyset))=>(![X939:$i > $o]:(((exu @ X939)=>?[X940:$i]:((X939 @ X940))))=>(![X1707:$i, X1708:$i]:((![X1709:$i]:(((in @ X1709 @ X1707)=>(in @ X1709 @ X1708)))=>(![X1710:$i]:(((in @ X1710 @ X1708)=>(in @ X1710 @ X1707)))=>((X1707)=(X1708)))))=>(![X941:$i]:((![X942:$i]:(~(in @ X942 @ X941))=>((X941)=(emptyset))))=>(![X943:$i]:((![X944:$i]:(~(in @ X944 @ X943))=>((X943)=(emptyset))))=>(![X945:$i, X946:$i > $o, X947:$i]:(((in @ X947 @ X945)=>((in @ X947 @ (dsetconstr @ X945 @ X946))<=>(X946 @ X947))))=>(![X948:$i]:(((nonempty @ X948)=>?[X949:$i]:((in @ X949 @ X948))))=>(![X1704:$i, X1705:$i > $o, X1706:$i]:(((in @ X1706 @ X1704)=>((X1705 @ X1706)=>(nonempty @ (dsetconstr @ X1704 @ X1705)))))=>(![X950:$i]:((?[X951:$i]:((in @ X951 @ X950))=>(nonempty @ X950)))=>(![X952:$i, X953:$i]:((in @ X952 @ (setadjoin @ X952 @ X953)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X954:$i, X955:$i, X956:$i]:(((in @ X956 @ X955)=>(in @ X956 @ (setadjoin @ X954 @ X955))))=>(![X1700:$i, X1701:$i, X1702:$i]:(((in @ X1702 @ (setadjoin @ X1700 @ X1701))=>![X1703:$o]:(((((X1702)=(X1700))=>(X1703))=>(((in @ X1702 @ X1701)=>(X1703))=>(X1703))))))=>(![X957:$i, X958:$i, X959:$i]:(((in @ X959 @ (setadjoin @ X957 @ X958))=>(((X959)=(X957))|(in @ X959 @ X958))))=>(![X1699:$i]:(((dsetconstr @ X1699 @ (^[Z0/* 1 */:$i]:($true)))=(X1699)))=>(![X960:$i, X961:$i]:((![X962:$i]:(((in @ X962 @ X961)=>(in @ X962 @ X960)))=>(in @ X961 @ (powerset @ X960))))=>(![X963:$i]:((in @ emptyset @ (powerset @ X963)))=>(![X1698:$i]:((in @ emptyset @ (powerset @ X1698)))=>(![X1695:$i, X1696:$i, X1697:$i]:(((in @ X1696 @ (powerset @ X1695))=>((in @ X1697 @ X1696)=>(in @ X1697 @ X1695))))=>(![X1692:$i, X1693:$i, X1694:$i]:(((in @ X1693 @ X1694)=>((in @ X1694 @ X1692)=>(in @ X1693 @ (setunion @ X1692)))))=>(![X964:$i, X965:$i]:(((in @ X965 @ (setunion @ X964))=>![X966:$o]:((![X967:$i]:(((in @ X965 @ X967)=>((in @ X967 @ X964)=>(X966))))=>(X966)))))=>(![X968:$i, X969:$i]:(((in @ X969 @ X968)=>(in @ X969 @ (powerset @ (setunion @ X968)))))=>(![X1689:$i > $o]:(((exu @ X1689)=>?[X1690:$i]:(![X1691:$i]:(((X1689 @ X1691)<=>((X1691)=(X1690)))))))=>(![X1687:$i]:(((nonempty @ X1687)=>?[X1688:$i]:(((in @ X1688 @ X1687)&$true))))=>(![X970:$i, X971:$i]:(((in @ X970 @ (setadjoin @ X971 @ emptyset))=>((X970)=(X971))))=>(![X972:$i, X973:$i]:((((X972)!=(X973))=>~(in @ X973 @ (setadjoin @ X972 @ emptyset))))=>(![X974:$i, X975:$i]:((((X974)=(X975))=>(in @ X974 @ (setadjoin @ X975 @ emptyset))))=>(![X976:$i, X977:$i]:(((in @ X976 @ (setadjoin @ X977 @ emptyset))=>(in @ X977 @ (setadjoin @ X976 @ emptyset))))=>(![X978:$i, X979:$i, X980:$i]:(((in @ X980 @ (setadjoin @ X978 @ (setadjoin @ X979 @ emptyset)))=>(((X980)=(X978))|((X980)=(X979)))))=>(![X1685:$i, X1686:$i]:((in @ X1685 @ (setadjoin @ X1685 @ (setadjoin @ X1686 @ emptyset))))=>(![X1683:$i, X1684:$i]:((in @ X1684 @ (setadjoin @ X1683 @ (setadjoin @ X1684 @ emptyset))))=>(![X981:$i, X982:$i > $o]:((?[X983:$i]:(((in @ X983 @ X981)&(X982 @ X983)))=>(((dsetconstr @ X981 @ X982)=(emptyset))=>~($true))))=>(![X984:$i > $o, X985:$i]:(((in @ X985 @ emptyset)=>(X984 @ X985)))=>(![X1679:$i, X1680:$i > $o]:((~(![X1681:$i]:(((in @ X1681 @ X1679)=>(X1680 @ X1681))))=>?[X1682:$i]:(((in @ X1682 @ X1679)&~((X1680 @ X1682))))))=>(![X986:$i, X987:$i > $o]:((![X988:$i]:(((in @ X988 @ X986)=>~((X987 @ X988))))=>~(?[X989:$i]:(((in @ X989 @ X986)&(X987 @ X989))))))=>(![X1675:$i, X1676:$i > $o]:((~(?[X1677:$i]:(((in @ X1677 @ X1675)&(X1676 @ X1677))))=>![X1678:$i]:(((in @ X1678 @ X1675)=>~((X1676 @ X1678))))))=>(![X1671:$i, X1672:$i > $o]:((?[X1673:$i]:(((in @ X1673 @ X1671)&~((X1672 @ X1673))))=>~(![X1674:$i]:(((in @ X1674 @ X1671)=>(X1672 @ X1674))))))=>(![X990:$o]:(((X990)=>(in @ emptyset @ (prop2set @ ((X990))))))=>((prop2set2propI)=>(![X991:$i, X992:$i > $o]:((~(?[X993:$i]:(((in @ X993 @ X991)&(X992 @ X993))))=>![X994:$i]:(((in @ X994 @ X991)=>~((X992 @ X994))))))=>(![X1667:$i, X1668:$i > $o]:((~(![X1669:$i]:(((in @ X1669 @ X1667)=>(X1668 @ X1669))))=>?[X1670:$i]:(((in @ X1670 @ X1667)&~((X1668 @ X1670))))))=>(![X995:$i > $o]:((?[X996:$i]:(((X995 @ X996)&![X997:$i]:(((X995 @ X997)=>((X996)=(X997))))))=>(exu @ X995)))=>(![X1663:$i > $o]:((?[X1664:$i]:((X1663 @ X1664))=>(![X1665:$i, X1666:$i]:(((X1663 @ X1665)=>((X1663 @ X1666)=>((X1665)=(X1666)))))=>(exu @ X1663))))=>(![X1660:$i > $o]:((?[X1661:$i]:(![X1662:$i]:(((X1660 @ X1662)<=>((X1662)=(X1661)))))=>(exu @ X1660)))=>(![X1656:$i, X1657:$i]:((((X1656)=(X1657))=>![X1658:$i, X1659:$i]:((((X1658)=(X1659))=>((in @ X1658 @ X1656)=>(in @ X1659 @ X1657))))))=>(![X1652:$i, X1653:$i]:((((X1652)=(X1653))=>![X1654:$i, X1655:$i]:((((X1654)=(X1655))=>((in @ X1654 @ X1652)<=>(in @ X1655 @ X1653))))))=>(![X1649:$i > $o]:(((exu @ X1649)=>![X1650:$i, X1651:$i]:(((X1649 @ X1650)=>((X1649 @ X1651)=>((X1650)=(X1651)))))))=>(![X1645:$i > $o, X1646:$i > $o]:((![X1647:$i, X1648:$i]:((((X1647)=(X1648))=>((X1645 @ X1647)<=>(X1646 @ X1648))))=>((exu @ X1645)<=>(exu @ X1646))))=>(((emptyset)=(emptyset))=>(![X1641:$i, X1642:$i]:((((X1641)=(X1642))=>![X1643:$i, X1644:$i]:((((X1643)=(X1644))=>((setadjoin @ X1641 @ X1643)=(setadjoin @ X1642 @ X1644))))))=>(![X998:$i, X999:$i]:((((X998)=(X999))=>((powerset @ X998)=(powerset @ X999))))=>(![X1639:$i, X1640:$i]:((((X1639)=(X1640))=>((setunion @ X1639)=(setunion @ X1640))))=>(((omega)=(omega))=>(![X1636:$i > $o]:(((exu @ X1636)=>![X1637:$i, X1638:$i]:(((X1636 @ X1637)=>((X1636 @ X1638)=>((X1637)=(X1638)))))))=>(![X1632:$i > $o, X1633:$i > $o]:((![X1634:$i, X1635:$i]:((((X1634)=(X1635))=>((X1632 @ X1634)<=>(X1633 @ X1635))))=>((exu @ X1632)=>((exu @ X1633)=>((descr @ X1632)=(descr @ X1633))))))=>(![X1000:$i, X1001:$i]:((((X1000)=(X1001))=>![X1002:$i > $o, X1003:$i > $o]:((![X1004:$i]:(((in @ X1004 @ X1000)=>![X1005:$i]:(((in @ X1005 @ X1001)=>(((X1004)=(X1005))=>((X1002 @ X1004)<=>(X1003 @ X1005)))))))=>((dsetconstr @ X1000 @ X1002)=(dsetconstr @ X1001 @ X1003))))))=>(![X1006:$i, X1007:$i]:((![X1008:$i]:(((in @ X1008 @ X1006)=>(in @ X1008 @ X1007)))=>(subset @ X1006 @ X1007)))=>(![X1630:$i, X1631:$i]:((((X1630)=(X1631))=>(subset @ X1631 @ X1630)))=>(![X1628:$i, X1629:$i]:((((X1628)=(X1629))=>(subset @ X1628 @ X1629)))=>(![X1625:$i, X1626:$i]:((![X1627:$i]:(((in @ X1627 @ X1625)=>(in @ X1627 @ X1626)))=>(subset @ X1625 @ X1626)))=>(![X1009:$i]:((subset @ emptyset @ X1009))=>(![X1010:$i, X1011:$i, X1012:$i]:(((subset @ X1010 @ X1011)=>((in @ X1012 @ X1010)=>(in @ X1012 @ X1011))))=>(![X1013:$i, X1014:$i, X1015:$i]:(((subset @ X1013 @ X1014)=>(~(in @ X1015 @ X1014)=>~(in @ X1015 @ X1013))))=>(![X1622:$i, X1623:$i, X1624:$i]:(((in @ X1624 @ X1622)=>(~(in @ X1624 @ X1623)=>~(subset @ X1622 @ X1623))))=>(![X1620:$i, X1621:$i]:((~(subset @ X1620 @ X1621)=>((X1620)!=(X1621))))=>(![X1016:$i, X1017:$i, X1018:$i]:(((in @ X1018 @ X1016)=>(~(in @ X1018 @ X1017)=>((X1016)!=(X1017)))))=>(![X1019:$i]:((subset @ X1019 @ X1019))=>(![X1617:$i, X1618:$i, X1619:$i]:(((subset @ X1617 @ X1618)=>((subset @ X1618 @ X1619)=>(subset @ X1617 @ X1619))))=>(![X1615:$i, X1616:$i]:((subset @ X1616 @ (setadjoin @ X1615 @ X1616)))=>(![X1020:$i, X1021:$i, X1022:$i]:(((subset @ X1020 @ X1022)=>(subset @ X1020 @ (setadjoin @ X1021 @ X1022))))=>(![X1023:$i, X1024:$i]:(((subset @ X1023 @ X1024)=>(in @ X1023 @ (powerset @ X1024))))=>(![X1025:$i, X1026:$i]:(((subset @ X1025 @ X1026)=>((subset @ X1026 @ X1025)=>((X1025)=(X1026)))))=>(![X1614:$i]:(((subset @ X1614 @ emptyset)=>((X1614)=(emptyset))))=>(![X1027:$i, X1028:$i]:(((subset @ X1028 @ X1027)=>(in @ X1028 @ (powerset @ X1027))))=>(![X1029:$i, X1030:$i]:(((in @ X1030 @ (powerset @ X1029))=>(subset @ X1030 @ X1029)))=>(![X1031:$i]:((in @ X1031 @ (powerset @ X1031)))=>(![X1032:$i, X1033:$i]:(((subset @ X1032 @ X1033)=>(subset @ (powerset @ X1032) @ (powerset @ X1033))))=>(![X1612:$i, X1613:$i > $o]:((in @ (dsetconstr @ X1612 @ X1613) @ (powerset @ X1612)))=>(![X1610:$i, X1611:$i > $o]:((subset @ (dsetconstr @ X1610 @ X1611) @ X1610))=>(![X1034:$i, X1035:$i, X1036:$i]:(((in @ X1036 @ X1034)=>(in @ X1036 @ (binunion @ X1034 @ X1035))))=>(![X1608:$i, X1609:$i]:((in @ X1609 @ (setadjoin @ X1608 @ (setadjoin @ X1609 @ emptyset))))=>(![X1037:$i, X1038:$i, X1039:$i]:(((in @ X1039 @ X1038)=>(in @ X1039 @ (binunion @ X1037 @ X1038))))=>(![X1040:$i, X1041:$i, X1042:$i, X1043:$o]:(((in @ X1042 @ (binunion @ X1040 @ X1041))=>(((in @ X1042 @ X1040)=>(X1043))=>(((in @ X1042 @ X1041)=>(X1043))=>(X1043)))))=>(![X1044:$i, X1045:$i, X1046:$i]:(((in @ X1046 @ (binunion @ X1044 @ X1045))=>((in @ X1046 @ X1044)|(in @ X1046 @ X1045))))=>(![X1606:$i, X1607:$i]:((subset @ X1606 @ (binunion @ X1606 @ X1607)))=>(![X1047:$i, X1048:$i]:((subset @ X1048 @ (binunion @ X1047 @ X1048)))=>(![X1603:$i, X1604:$i, X1605:$i]:(((in @ X1605 @ X1603)=>((in @ X1605 @ X1604)=>(in @ X1605 @ (binintersect @ X1603 @ X1604)))))=>(![X1049:$i, X1050:$i, X1051:$i]:(((subset @ X1051 @ X1049)=>((subset @ X1051 @ X1050)=>(subset @ X1051 @ (binintersect @ X1049 @ X1050)))))=>(![X1052:$i, X1053:$i, X1054:$i]:(((in @ X1054 @ (binintersect @ X1052 @ X1053))=>(in @ X1054 @ X1052)))=>(![X1601:$i, X1602:$i]:((subset @ (binintersect @ X1601 @ X1602) @ X1601))=>(![X1599:$i, X1600:$i]:(((subset @ X1599 @ X1600)=>((binintersect @ X1599 @ X1600)=(X1599))))=>(![X1597:$i, X1598:$i]:((((binintersect @ X1597 @ X1598)=(X1598))=>(subset @ X1598 @ X1597)))=>(![X1055:$i, X1056:$i, X1057:$i]:(((in @ X1057 @ (binintersect @ X1055 @ X1056))=>(in @ X1057 @ X1056)))=>(![X1058:$i, X1059:$i]:((~(?[X1060:$i]:(((in @ X1060 @ X1058)&(in @ X1060 @ X1059))))=>((binintersect @ X1058 @ X1059)=(emptyset))))=>(![X1595:$i, X1596:$i]:((subset @ (binintersect @ X1595 @ X1596) @ X1596))=>(![X1061:$i, X1062:$i]:(((subset @ X1062 @ X1061)=>((binintersect @ X1061 @ X1062)=(X1062))))=>(![X1593:$i, X1594:$i]:((((binintersect @ X1593 @ X1594)=(X1593))=>(subset @ X1593 @ X1594)))=>(![X1063:$i, X1064:$i, X1065:$i]:(((binintersect @ X1063 @ (binunion @ X1064 @ X1065))=(binunion @ (binintersect @ X1063 @ X1064) @ 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X48)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def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setextAx]), upairset2IR]), binintersectER]), c_0_266]), c_0_267]), setminusERneg]), subsetemptysetimpeq]), setadjoinSub]), subsetTrans]), setminusELneg]), notequalI1]), notsubsetI]), setminusILneg]), subsetI2]), eqimpsubset1]), eqimpsubset2]), setminusIRneg]), c_0_268]), c_0_269]), symdiffE]), setunion__Cong]), setadjoin__Cong]), emptyset__Cong]), c_0_270]), symdiffI1]), c_0_271]), in__Cong]), symdiffI2]), inCongP]), kfstpairEq]), c_0_272]), c_0_273]), disjointsetsI1]), notdallE]), secondinupair]), quantDeMorgan4]), quantDeMorgan3]), kpairp]), quantDeMorgan1]), binintersectSubset4]), upairsetIR]), upairsetIL]), nonemptyImpWitness]), singletoninpowunion]), c_0_274]), setunionI]), upairset2E]), powersetE]), emptyInPowerset]), c_0_275]), upairsubunion]), setadjoinE]), c_0_276]), upairinpowunion]), setext]), notinemptyset]), emptysetE]), ubforcartprodlem2]), prop2setE]), c_0_277]), cartprodpairin]), c_0_278]), omegaSAx]), setadjoinAx]), cartprodmempair]), setunionsingleton1]), setunionsingleton2]), c_0_279]), c_0_280]), setukpairinjL1]), theprop]), c_0_281]), iftrue]), iffalse]), cartprodfstin]), setukpairinjL2]), setukpairinjR12]), setukpairinjR]), cartprodpairmemER]), cartprodsndpairEq]), c_0_282]), c_0_283]), bs114d]), c_0_284]), c_0_285]), c_0_286]), infuncsetfunc]), funcinfuncset]), c_0_287]), c_0_288]), brelnall1]), c_0_289]), funcGraphProp1]), funcGraphProp3]), funcextLem]), subbreln]), eqbreln]), funcext]), ap2apEq2]), c_0_290]), c_0_291]), c_0_292]), c_0_293]), c_0_294]), c_0_295]), binintersectSubset2]), binintersectLsub]), binintersectI]), binunionLsub]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), complementT_lem]), powersetTE1]), complementTI1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT1]), doubleComplementSub2]), doubleComplementEq]), complementInPowersetComplementIntersect]), binunionTILcontra]), inIntersectImpInIntersectUnions]), demorgan2a1]), complementUnionInPowersetComplement]), binunionTEcontra]), binunionTE]), inComplementUnionImpInComplement1]), inComplementUnionImpNotIn1]), intersectInPowersetIntersectUnions]), inIntersectImpInUnion2]), inIntersectImpInUnion]), binunionTIRcontra]), complementTcontraSubset]), contraSubsetComplement]), complementSubsetComplementIntersect]), complementImpComplementIntersect]), complementTnotintersectT]), doubleComplementSub1]), doubleComplementE1]), doubleComplementI1]), contrasubsetT3]), contrasubsetT2]), contrasubsetT]), complementTE1]), powersetTI1]), subsetTI]), setextT]), setminusT_lem]), theeq]), ifp]), c_0_296]), c_0_297]), c_0_298]), ap2apEq1]), funcext2]), funcGraphProp4]), funcGraphProp2]), brelnall2]), c_0_299]), ap2p]), app]), c_0_300]), c_0_301]), c_0_302]), c_0_303]), cartprodpairsurjEq]), cartprodfstpairEq]), cartprodmempaircEq]), cartprodpairmemEL]), cartprodsndin]), kpairsurjEq]), ksndpairEq]), c_0_304]), setukpairinjR2]), upairequniteq]), setukpairinjR1]), setukpairinjR11]), setukpairinjL]), c_0_305]), singletonsuniq]), c_0_306]), c_0_307]), setunionsingleton]), setunionE2]), cartprodmempair1]), ubforcartprodlem3]), ubforcartprodlem1]), singletoninpowerset]), singletonsubset]), kpairiskpair]), setukpairIR]), setukpairIL]), symdiffIneg2]), symdiffIneg1]), setminusSubset1]), setminusLsub]), setminusER]), setminusEL]), setminusI]), binintersectSubset1]), binintersectRsub]), binintersectSubset3]), setminusSubset2]), binintersectEL]), binintersectSubset5]), binunionRsub]), binunionE]), binunionEcases]), binunionIR]), binunionIL]), powersetsubset]), inPowerset]), powersetE1]), powersetI1]), setextsub]), subset2powerset]), setadjoinSub2]), subsetRefl]), notequalI2]), subsetE2]), subsetE]), emptysetsubset]), subsetI1]), c_0_308]), omega__Cong]), powerset__Cong]), c_0_309]), notdexE]), prop2setI]), quantDeMorgan2]), vacuousDall]), c_0_310]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), subPowSU]), setunionE]), emptyinPowerset]), powersetI]), setadjoinOr]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), nonemptyI1]), nonemptyE1]), c_0_311]), noeltsimpempty]), emptyI]), c_0_312]), emptysetimpfalse]), c_0_313]), c_0_314]), c_0_315]), wellorderingAx]), foundationAx]), c_0_316]), omegaIndAx]), omega0Ax]), setunionAx]), powersetAx]), emptysetAx])])]), c_0_317])).
2.58/0.99	thf(c_0_319, negated_conjecture, ![X1729:$i, X1730:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1742:$i, X1743:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1751:$i, X1752:$i > $i > $o, X1753:$i, X1756:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1763:$i, X1764:$i > $o, X1765:$i, X1766:$i > $o, X1767:$i, X1768:$i, X1769:$i > $o, X1770:$i, X1771:$i, X1772:$i > $o, X1773:$i, X1774:$i > $o, X1776:$i, X1777:$o, X1778:$i, X1779:$i, X1780:$o, X1781:$i, X1782:$i, X1783:$i > $o, X1785:$i, X1786:$i, X1789:$i, X1791:$i, X1793:$i, X1794:$i > $o, X1795:$i, X1796:$i, X1798:$i, X1799:$i > $o, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$o, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$o, X1831:$i, X1832:$i, X1833:$i > $o, X1835:$i, X1836:$i, X1837:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i > $o, X1856:$i, X1857:$i > $o, X1858:$i, X1859:$i, X1860:$i > $o, X1861:$i, X1863:$i, X1864:$i > $o, X1866:$i, X1867:$i, X1868:$i > $o, X1870:$i, X1871:$i, X1872:$i > $o, X1873:$i, X1875:$o, X1876:$i, X1877:$i > $o, X1879:$i, X1880:$i, X1881:$i > $o, X1882:$i, X1884:$i > $o, X1885:$i, X1887:$i > $o, X1888:$i, X1891:$i > $o, X1892:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i > $o, X1903:$i, X1904:$i, X1905:$i > $o, X1906:$i > $o, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i > $o, X1918:$i, X1919:$i, X1920:$i > $o, X1921:$i > $o, X1924:$i, X1925:$i, X1926:$i > $o, X1927:$i > $o, X1930:$i, X1931:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i > $o, X1978:$i, X1979:$i > $o, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$o, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$o, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i > $o, X2134:$i, X2135:$i, X2136:$i > $o, X2138:$i, X2139:$i > $o, X2140:$i, X2142:$i, X2143:$i > $o, X2146:$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:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i > $i > $o, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i > $i > $o, X2224:$i, X2225:$i, X2226:$i > $i > $o, X2227:$i, X2228:$i, X2229:$i > $i > $o, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i > $i > $o, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i > $i > $o, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i > $i > $o, X2245:$i, 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@ X2428 @ X2429) @ X2429)|~(in @ X2429 @ (powerset @ X2427))|~(in @ X2428 @ (powerset @ X2427)))&(~(in @ (esk68_3 @ X2427 @ X2428 @ X2429) @ X2428)|((X2428)=(X2429))|~(in @ (esk67_3 @ X2427 @ X2428 @ X2429) @ X2429)|~(in @ X2429 @ (powerset @ X2427))|~(in @ X2428 @ (powerset @ X2427)))))))&((((in @ (esk69_3 @ X2432 @ X2433 @ X2434) @ X2432)|(subset @ X2433 @ X2434)|~(in @ X2434 @ (powerset @ X2432))|~(in @ X2433 @ (powerset @ X2432)))&(((in @ (esk69_3 @ X2432 @ X2433 @ X2434) @ X2433)|(subset @ X2433 @ X2434)|~(in @ X2434 @ (powerset @ X2432))|~(in @ X2433 @ (powerset @ X2432)))&(~(in @ (esk69_3 @ X2432 @ X2433 @ X2434) @ X2434)|(subset @ X2433 @ X2434)|~(in @ X2434 @ (powerset @ X2432))|~(in @ X2433 @ (powerset @ X2432)))))&((((in @ (esk70_3 @ X2436 @ X2437 @ X2438) @ X2436)|(in @ X2437 @ (powerset @ X2438))|~(in @ X2438 @ (powerset @ X2436))|~(in @ X2437 @ (powerset @ X2436)))&(((in @ (esk70_3 @ X2436 @ X2437 @ X2438) @ X2437)|(in @ X2437 @ (powerset @ X2438))|~(in @ X2438 @ (powerset @ X2436))|~(in @ X2437 @ (powerset @ X2436)))&(~(in @ (esk70_3 @ X2436 @ X2437 @ X2438) @ X2438)|(in @ X2437 @ (powerset @ X2438))|~(in @ X2438 @ (powerset @ X2436))|~(in @ X2437 @ (powerset @ X2436)))))&((~(in @ X2441 @ (powerset @ X2440))|(~(in @ X2442 @ (powerset @ X2440))|(~(in @ X2443 @ X2440)|(~(in @ X2441 @ (powerset @ X2442))|(~(in @ X2443 @ X2441)|(in @ X2443 @ X2442))))))&((~(in @ X2445 @ (powerset @ X2444))|(~(in @ X2446 @ X2444)|(~(in @ X2446 @ X2445)|~(in @ X2446 @ (setminus @ X2444 @ X2445)))))&((~(in @ X2448 @ (powerset @ X2447))|(~(in @ X2449 @ X2447)|((in @ X2449 @ (setminus @ X2447 @ X2448))|(in @ X2449 @ X2448))))&((~(in @ X2451 @ (powerset @ X2450))|(~(in @ X2452 @ (powerset @ X2450))|(~(in @ X2453 @ X2450)|((in @ X2453 @ X2451)|~(in @ X2453 @ (binintersect @ X2451 @ X2452))))))&((~(in @ X2455 @ (powerset @ X2454))|(~(in @ X2456 @ (powerset @ X2454))|(~(in @ X2457 @ X2454)|((in @ X2457 @ X2456)|~(in @ X2457 @ (binintersect @ X2455 @ X2456))))))&((~(in @ X2459 @ (powerset @ X2458))|(~(in @ X2460 @ (powerset @ X2458))|(~(in @ X2461 @ X2458)|(~(subset @ X2459 @ (setminus @ X2458 @ X2460))|(~(in @ X2461 @ X2460)|~(in @ X2461 @ X2459))))))&((~(in @ X2463 @ (powerset @ X2462))|(~(in @ X2464 @ (powerset @ X2462))|(~(in @ X2465 @ X2462)|(~(subset @ X2463 @ X2464)|((in @ X2465 @ X2464)|~(in @ X2465 @ X2463))))))&((~(in @ X2467 @ (powerset @ X2466))|(~(in @ X2468 @ (powerset @ X2466))|(~(subset @ X2467 @ X2468)|(subset @ (setminus @ X2466 @ X2468) @ (setminus @ X2466 @ X2467)))))&((~(in @ X2470 @ (powerset @ X2469))|(~(in @ X2471 @ (powerset @ X2469))|(~(subset @ (setminus @ X2469 @ X2471) @ (setminus @ X2469 @ X2470))|(subset @ X2470 @ X2471))))&((~(in @ X2473 @ (powerset @ X2472))|(~(in @ X2474 @ X2472)|(~(in @ X2474 @ X2473)|(in @ X2474 @ (setminus @ X2472 @ (setminus @ X2472 @ X2473))))))&((~(in @ X2476 @ (powerset @ X2475))|(~(in @ X2477 @ X2475)|(~(in @ X2477 @ (setminus @ X2475 @ (setminus @ X2475 @ X2476)))|(in @ X2477 @ X2476))))&((~(in @ X2479 @ (powerset @ X2478))|(subset @ X2479 @ (setminus @ X2478 @ (setminus @ X2478 @ X2479))))&((~(in @ X2481 @ (powerset @ X2480))|(subset @ (setminus @ X2480 @ (setminus @ X2480 @ X2481)) @ X2481))&((~(in @ X2483 @ (powerset @ X2482))|((X2483)=(setminus @ X2482 @ (setminus @ X2482 @ X2483))))&((~(in @ X2485 @ (powerset @ X2484))|(~(in @ X2486 @ (powerset @ X2484))|(~(in @ X2487 @ X2484)|(~(in @ X2487 @ (setminus @ X2484 @ X2485))|~(in @ X2487 @ (binintersect @ X2485 @ X2486))))))&((~(in @ X2489 @ (powerset @ X2488))|(~(in @ X2490 @ (powerset @ X2488))|(~(in @ X2491 @ X2488)|(~(in @ X2491 @ (setminus @ X2488 @ X2489))|(in @ X2491 @ (setminus @ X2488 @ (binintersect @ X2489 @ X2490)))))))&((~(in @ X2493 @ (powerset @ X2492))|(~(in @ X2494 @ (powerset @ X2492))|(subset @ (setminus @ X2492 @ X2493) @ (setminus @ X2492 @ (binintersect @ X2493 @ X2494)))))&((~(in @ X2496 @ (powerset @ X2495))|(~(in @ X2497 @ (powerset @ X2495))|(in @ (setminus @ X2495 @ X2496) @ (powerset @ (setminus @ X2495 @ (binintersect @ X2496 @ X2497))))))&((~(in @ X2499 @ (powerset @ X2498))|(~(in @ X2500 @ (powerset @ X2498))|(~(subset @ X2499 @ (setminus @ X2498 @ X2500))|(~(in @ X2501 @ X2498)|(~(in @ X2501 @ X2500)|(in @ X2501 @ (setminus @ X2498 @ X2499)))))))&((~(in @ X2503 @ (powerset @ X2502))|(~(in @ X2504 @ (powerset @ X2502))|(~(subset @ X2503 @ (setminus @ X2502 @ X2504))|(subset @ X2504 @ (setminus @ X2502 @ X2503)))))&((~(in @ X2506 @ (powerset @ X2505))|(~(in @ X2507 @ (powerset @ X2505))|(~(in @ X2508 @ X2505)|((in @ X2508 @ (binunion @ X2506 @ X2507))|~(in @ X2508 @ X2506)))))&((~(in @ X2510 @ (powerset @ X2509))|(~(in @ X2511 @ (powerset @ X2509))|(~(in @ X2512 @ X2509)|((in @ X2512 @ (binunion @ X2510 @ X2511))|~(in @ X2512 @ X2511)))))&((~(in @ X2514 @ (powerset @ X2513))|(~(in @ X2515 @ (powerset @ X2513))|(~(in @ X2516 @ (powerset @ X2513))|(~(in @ X2517 @ X2513)|(~(in @ X2517 @ (binintersect @ X2514 @ X2515))|(in @ X2517 @ (binunion @ X2514 @ X2516)))))))&((~(in @ X2519 @ (powerset @ X2518))|(~(in @ X2520 @ (powerset @ X2518))|(~(in @ X2521 @ (powerset @ X2518))|(~(in @ X2522 @ X2518)|(~(in @ X2522 @ (binintersect @ X2519 @ X2520))|(in @ X2522 @ (binunion @ X2520 @ X2521)))))))&((~(in @ X2524 @ (powerset @ X2523))|(~(in @ X2525 @ (powerset @ X2523))|(~(in @ X2526 @ (powerset @ X2523))|(~(in @ X2527 @ X2523)|(~(in @ X2527 @ (binintersect @ X2524 @ X2525))|(in @ X2527 @ (binintersect @ (binunion @ X2524 @ X2526) @ (binunion @ X2525 @ X2526))))))))&((~(in @ X2529 @ (powerset @ X2528))|(~(in @ X2530 @ (powerset @ X2528))|(~(in @ X2531 @ (powerset @ X2528))|(in @ (binintersect @ X2529 @ X2530) @ (powerset @ (binintersect @ (binunion @ X2529 @ X2531) @ (binunion @ X2530 @ X2531)))))))&((~(in @ X2533 @ (powerset @ X2532))|(~(in @ X2534 @ (powerset @ X2532))|(~(in @ X2535 @ X2532)|(~(in @ X2535 @ (setminus @ X2532 @ (binunion @ X2533 @ X2534)))|~(in @ X2535 @ X2533)))))&((~(in @ X2537 @ (powerset @ X2536))|(~(in @ X2538 @ (powerset @ X2536))|(~(in @ X2539 @ X2536)|(~(in @ X2539 @ (setminus @ X2536 @ (binunion @ X2537 @ X2538)))|(in @ X2539 @ (setminus @ X2536 @ X2537))))))&(((((in @ X2544 @ X2542)|(X2543)|(in @ X2544 @ X2541)|~(in @ X2544 @ (binunion @ X2541 @ X2542))|~(in @ X2544 @ X2540)|~(in @ X2542 @ (powerset @ X2540))|~(in @ X2541 @ (powerset @ X2540)))&(~(X2543)|(X2543)|(in @ X2544 @ X2541)|~(in @ X2544 @ (binunion @ X2541 @ X2542))|~(in @ X2544 @ X2540)|~(in @ X2542 @ (powerset @ X2540))|~(in @ X2541 @ (powerset @ X2540))))&(((in @ X2544 @ X2542)|(X2543)|~(X2543)|~(in @ X2544 @ (binunion @ X2541 @ X2542))|~(in @ X2544 @ X2540)|~(in @ X2542 @ (powerset @ X2540))|~(in @ X2541 @ (powerset @ X2540)))&(~(X2543)|(X2543)|~(X2543)|~(in @ X2544 @ (binunion @ X2541 @ X2542))|~(in @ X2544 @ X2540)|~(in @ X2542 @ (powerset @ X2540))|~(in @ X2541 @ (powerset @ X2540)))))&((~(in @ X2546 @ (powerset @ X2545))|(~(in @ X2547 @ (powerset @ X2545))|(~(in @ X2548 @ X2545)|((in @ X2548 @ X2546)|((in @ X2548 @ X2547)|~(in @ X2548 @ (binunion @ X2546 @ X2547)))))))&((~(in @ X2550 @ (powerset @ X2549))|(~(in @ X2551 @ (powerset @ X2549))|(~(in @ X2552 @ X2549)|(~(in @ X2552 @ (setminus @ X2549 @ (binunion @ X2550 @ X2551)))|(in @ X2552 @ (setminus @ X2549 @ X2550))))))&((~(in @ X2554 @ (powerset @ X2553))|(~(in @ X2555 @ (powerset @ X2553))|(in @ (setminus @ X2553 @ (binunion @ X2554 @ X2555)) @ (powerset @ (setminus @ X2553 @ X2554)))))&((in @ esk72_0 @ (powerset @ esk71_0))&((in @ esk73_0 @ (powerset @ esk71_0))&((in @ esk74_0 @ esk71_0)&((in @ esk74_0 @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0)))&~(in @ esk74_0 @ (setminus @ esk71_0 @ esk73_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_318])])])])])])])).
2.58/0.99	thf(c_0_320, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((~((in @ X2 @ (setminus @ X3 @ X4)))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_319])).
2.58/0.99	thf(c_0_321, negated_conjecture, (in @ esk74_0 @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0))), inference(split_conjunct,[status(thm)],[c_0_319])).
2.58/0.99	thf(c_0_322, negated_conjecture, ~((in @ esk74_0 @ (binunion @ esk72_0 @ esk73_0))), inference(spm,[status(thm)],[c_0_320, c_0_321])).
2.58/0.99	thf(c_0_323, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X4 @ X3))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_319])).
2.58/0.99	thf(c_0_324, negated_conjecture, ~((in @ esk74_0 @ (setminus @ esk71_0 @ esk73_0))), inference(split_conjunct,[status(thm)],[c_0_319])).
2.58/0.99	thf(c_0_325, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setminus @ X3 @ X4))|(in @ X2 @ X4)|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_319])).
2.58/0.99	thf(c_0_326, negated_conjecture, (in @ esk74_0 @ esk71_0), inference(split_conjunct,[status(thm)],[c_0_319])).
2.58/0.99	thf(c_0_327, negated_conjecture, ~((in @ esk74_0 @ esk73_0)), inference(spm,[status(thm)],[c_0_322, c_0_323])).
2.58/0.99	thf(c_0_328, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_324, c_0_325]), c_0_326])]), c_0_327]), ['proof']).
2.58/0.99	# SZS output end CNFRefutation
2.58/0.99	# Parsed axioms                        : 575
2.58/0.99	# Removed by relevancy pruning/SinE    : 309
2.58/0.99	# Initial clauses                      : 431
2.58/0.99	# Removed in clause preprocessing      : 37
2.58/0.99	# Initial clauses in saturation        : 394
2.58/0.99	# Processed clauses                    : 774
2.58/0.99	# ...of these trivial                  : 10
2.58/0.99	# ...subsumed                          : 46
2.58/0.99	# ...remaining for further processing  : 717
2.58/0.99	# Other redundant clauses eliminated   : 54
2.58/0.99	# Clauses deleted for lack of memory   : 0
2.58/0.99	# Backward-subsumed                    : 0
2.58/0.99	# Backward-rewritten                   : 3
2.58/0.99	# Generated clauses                    : 7986
2.58/0.99	# ...of the previous two non-redundant : 7747
2.58/0.99	# ...aggressively subsumed             : 0
2.58/0.99	# Contextual simplify-reflections      : 7
2.58/0.99	# Paramodulations                      : 7897
2.58/0.99	# Factorizations                       : 2
2.58/0.99	# NegExts                              : 0
2.58/0.99	# Equation resolutions                 : 61
2.58/0.99	# Disequality decompositions           : 0
2.58/0.99	# Total rewrite steps                  : 208
2.58/0.99	# ...of those cached                   : 138
2.58/0.99	# Propositional unsat checks           : 0
2.58/0.99	#    Propositional check models        : 0
2.58/0.99	#    Propositional check unsatisfiable : 0
2.58/0.99	#    Propositional clauses             : 0
2.58/0.99	#    Propositional clauses after purity: 0
2.58/0.99	#    Propositional unsat core size     : 0
2.58/0.99	#    Propositional preprocessing time  : 0.000
2.58/0.99	#    Propositional encoding time       : 0.000
2.58/0.99	#    Propositional solver time         : 0.000
2.58/0.99	#    Success case prop preproc time    : 0.000
2.58/0.99	#    Success case prop encoding time   : 0.000
2.58/0.99	#    Success case prop solver time     : 0.000
2.58/0.99	# Current number of processed clauses  : 356
2.58/0.99	#    Positive orientable unit clauses  : 45
2.58/0.99	#    Positive unorientable unit clauses: 0
2.58/0.99	#    Negative unit clauses             : 8
2.58/0.99	#    Non-unit-clauses                  : 303
2.58/0.99	# Current number of unprocessed clauses: 7706
2.58/0.99	# ...number of literals in the above   : 32878
2.58/0.99	# Current number of archived formulas  : 0
2.58/0.99	# Current number of archived clauses   : 345
2.58/0.99	# Clause-clause subsumption calls (NU) : 61465
2.58/0.99	# Rec. Clause-clause subsumption calls : 26248
2.58/0.99	# Non-unit clause-clause subsumptions  : 43
2.58/0.99	# Unit Clause-clause subsumption calls : 1508
2.58/0.99	# Rewrite failures with RHS unbound    : 0
2.58/0.99	# BW rewrite match attempts            : 33
2.58/0.99	# BW rewrite match successes           : 2
2.58/0.99	# Condensation attempts                : 0
2.58/0.99	# Condensation successes               : 0
2.58/0.99	# Termbank termtop insertions          : 212966
2.58/0.99	# Search garbage collected termcells   : 27057
2.58/0.99	
2.58/0.99	# -------------------------------------------------
2.58/0.99	# User time                : 0.450 s
2.58/0.99	# System time              : 0.031 s
2.58/0.99	# Total time               : 0.481 s
2.58/0.99	# Maximum resident set size: 8796 pages
2.58/0.99	
2.58/0.99	# -------------------------------------------------
2.58/0.99	# User time                : 0.465 s
2.58/0.99	# System time              : 0.035 s
2.58/0.99	# Total time               : 0.500 s
2.58/0.99	# Maximum resident set size: 2504 pages
2.58/0.99	% E exiting
2.58/0.99	% E exiting
2.58/0.99	EOF