0.11/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.12	% Command    : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM
0.12/0.33	% Computer : n029.cluster.edu
0.12/0.33	% Model    : x86_64 x86_64
0.12/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory   : 8042.1875MB
0.12/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 1920
0.12/0.33	% WCLimit    : 240
0.12/0.33	% DateTime   : Wed Jul 30 05:54:04 EDT 2025
0.12/0.33	% CPUTime    : 
0.20/0.47	Running higher-order theorem proving
0.20/0.54	Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=240 /export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p
2.09/1.10	# Version: 3.0.0-ho
2.09/1.10	# Preprocessing class: HSLMSLSSLLLCHFA.
2.09/1.10	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
2.09/1.10	# Starting ehoh_best5 with 240s (1) cores
2.09/1.10	# Starting almost_fo_3_lam with 240s (1) cores
2.09/1.10	# Starting new_bool_5 with 240s (1) cores
2.09/1.10	# Starting pre_casc_3 with 240s (1) cores
2.09/1.10	# Starting ho_unfolding_8 with 240s (1) cores
2.09/1.10	# Starting new_ho_10_cnf2 with 240s (1) cores
2.09/1.10	# Starting new_bool_3 with 240s (1) cores
2.09/1.10	# Starting new_ho_5 with 240s (1) cores
2.09/1.10	# new_bool_5 with pid 18297 completed with status 0
2.09/1.10	# Result found by new_bool_5
2.09/1.10	# Preprocessing class: HSLMSLSSLLLCHFA.
2.09/1.10	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
2.09/1.10	# Starting ehoh_best5 with 240s (1) cores
2.09/1.10	# Starting almost_fo_3_lam with 240s (1) cores
2.09/1.10	# Starting new_bool_5 with 240s (1) cores
2.09/1.10	# SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
2.09/1.10	# Search class: HGHSM-FSLM32-MHFMMSBN
2.09/1.10	# Scheduled 10 strats onto 1 cores with 240 seconds (240 total)
2.09/1.10	# Starting ho_unfolding_8 with 44s (1) cores
2.09/1.10	# ho_unfolding_8 with pid 18306 completed with status 0
2.09/1.10	# Result found by ho_unfolding_8
2.09/1.10	# Preprocessing class: HSLMSLSSLLLCHFA.
2.09/1.10	# Scheduled 8 strats onto 8 cores with 240 seconds (1920 total)
2.09/1.10	# Starting ehoh_best5 with 240s (1) cores
2.09/1.10	# Starting almost_fo_3_lam with 240s (1) cores
2.09/1.10	# Starting new_bool_5 with 240s (1) cores
2.09/1.10	# SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
2.09/1.10	# Search class: HGHSM-FSLM32-MHFMMSBN
2.09/1.10	# Scheduled 10 strats onto 1 cores with 240 seconds (240 total)
2.09/1.10	# Starting ho_unfolding_8 with 44s (1) cores
2.09/1.10	# Preprocessing time       : 0.056 s
2.09/1.10	# Presaturation interreduction done
2.09/1.10	
2.09/1.10	# Proof found!
2.09/1.10	# SZS status Theorem
2.09/1.10	# SZS output start CNFRefutation
2.09/1.10	thf(decl_23, type, in: $i > $i > $o).
2.09/1.10	thf(decl_24, type, exu: ($i > $o) > $o).
2.09/1.10	thf(decl_25, type, setextAx: $o).
2.09/1.10	thf(decl_26, type, emptyset: $i).
2.09/1.10	thf(decl_27, type, emptysetAx: $o).
2.09/1.10	thf(decl_28, type, setadjoin: $i > $i > $i).
2.09/1.10	thf(decl_29, type, setadjoinAx: $o).
2.09/1.10	thf(decl_30, type, powerset: $i > $i).
2.09/1.10	thf(decl_31, type, powersetAx: $o).
2.09/1.10	thf(decl_32, type, setunion: $i > $i).
2.09/1.10	thf(decl_33, type, setunionAx: $o).
2.09/1.10	thf(decl_34, type, omega: $i).
2.09/1.10	thf(decl_35, type, omega0Ax: $o).
2.09/1.10	thf(decl_36, type, omegaSAx: $o).
2.09/1.10	thf(decl_37, type, omegaIndAx: $o).
2.09/1.10	thf(decl_38, type, replAx: $o).
2.09/1.10	thf(decl_39, type, foundationAx: $o).
2.09/1.10	thf(decl_40, type, wellorderingAx: $o).
2.09/1.10	thf(decl_41, type, descr: ($i > $o) > $i).
2.09/1.10	thf(decl_42, type, descrp: $o).
2.09/1.10	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
2.09/1.10	thf(decl_44, type, dsetconstrI: $o).
2.09/1.10	thf(decl_45, type, dsetconstrEL: $o).
2.09/1.10	thf(decl_46, type, dsetconstrER: $o).
2.09/1.10	thf(decl_47, type, exuE1: $o).
2.09/1.10	thf(decl_48, type, prop2set: $o > $i).
2.09/1.10	thf(decl_49, type, prop2setE: $o).
2.09/1.10	thf(decl_50, type, emptysetE: $o).
2.09/1.10	thf(decl_51, type, emptysetimpfalse: $o).
2.09/1.10	thf(decl_52, type, notinemptyset: $o).
2.09/1.10	thf(decl_53, type, exuE3e: $o).
2.09/1.10	thf(decl_54, type, setext: $o).
2.09/1.10	thf(decl_55, type, emptyI: $o).
2.09/1.10	thf(decl_56, type, noeltsimpempty: $o).
2.09/1.10	thf(decl_57, type, setbeta: $o).
2.09/1.10	thf(decl_58, type, nonempty: $i > $o).
2.09/1.10	thf(decl_59, type, nonemptyE1: $o).
2.09/1.10	thf(decl_60, type, nonemptyI: $o).
2.09/1.10	thf(decl_61, type, nonemptyI1: $o).
2.09/1.10	thf(decl_62, type, setadjoinIL: $o).
2.09/1.10	thf(decl_63, type, emptyinunitempty: $o).
2.09/1.10	thf(decl_64, type, setadjoinIR: $o).
2.09/1.10	thf(decl_65, type, setadjoinE: $o).
2.09/1.10	thf(decl_66, type, setadjoinOr: $o).
2.09/1.10	thf(decl_67, type, setoftrueEq: $o).
2.09/1.10	thf(decl_68, type, powersetI: $o).
2.09/1.10	thf(decl_69, type, emptyinPowerset: $o).
2.09/1.10	thf(decl_70, type, emptyInPowerset: $o).
2.09/1.10	thf(decl_71, type, powersetE: $o).
2.09/1.10	thf(decl_72, type, setunionI: $o).
2.09/1.10	thf(decl_73, type, setunionE: $o).
2.09/1.10	thf(decl_74, type, subPowSU: $o).
2.09/1.10	thf(decl_75, type, exuE2: $o).
2.09/1.10	thf(decl_76, type, nonemptyImpWitness: $o).
2.09/1.10	thf(decl_77, type, uniqinunit: $o).
2.09/1.10	thf(decl_78, type, notinsingleton: $o).
2.09/1.10	thf(decl_79, type, eqinunit: $o).
2.09/1.10	thf(decl_80, type, singletonsswitch: $o).
2.09/1.10	thf(decl_81, type, upairsetE: $o).
2.09/1.10	thf(decl_82, type, upairsetIL: $o).
2.09/1.10	thf(decl_83, type, upairsetIR: $o).
2.09/1.10	thf(decl_84, type, emptyE1: $o).
2.09/1.10	thf(decl_85, type, vacuousDall: $o).
2.09/1.10	thf(decl_86, type, quantDeMorgan1: $o).
2.09/1.10	thf(decl_87, type, quantDeMorgan2: $o).
2.09/1.10	thf(decl_88, type, quantDeMorgan3: $o).
2.09/1.10	thf(decl_89, type, quantDeMorgan4: $o).
2.09/1.10	thf(decl_90, type, prop2setI: $o).
2.09/1.10	thf(decl_92, type, prop2set2propI: $o).
2.09/1.10	thf(decl_93, type, notdexE: $o).
2.09/1.10	thf(decl_94, type, notdallE: $o).
2.09/1.10	thf(decl_95, type, exuI1: $o).
2.09/1.10	thf(decl_96, type, exuI3: $o).
2.09/1.10	thf(decl_97, type, exuI2: $o).
2.09/1.10	thf(decl_98, type, inCongP: $o).
2.09/1.10	thf(decl_99, type, in__Cong: $o).
2.09/1.10	thf(decl_100, type, exuE3u: $o).
2.09/1.10	thf(decl_101, type, exu__Cong: $o).
2.09/1.10	thf(decl_102, type, emptyset__Cong: $o).
2.09/1.10	thf(decl_103, type, setadjoin__Cong: $o).
2.09/1.10	thf(decl_104, type, powerset__Cong: $o).
2.09/1.10	thf(decl_105, type, setunion__Cong: $o).
2.09/1.10	thf(decl_106, type, omega__Cong: $o).
2.09/1.10	thf(decl_107, type, exuEu: $o).
2.09/1.10	thf(decl_108, type, descr__Cong: $o).
2.09/1.10	thf(decl_109, type, dsetconstr__Cong: $o).
2.09/1.10	thf(decl_110, type, subset: $i > $i > $o).
2.09/1.10	thf(decl_113, type, subsetI1: $o).
2.09/1.10	thf(decl_114, type, eqimpsubset2: $o).
2.09/1.10	thf(decl_115, type, eqimpsubset1: $o).
2.09/1.10	thf(decl_116, type, subsetI2: $o).
2.09/1.10	thf(decl_117, type, emptysetsubset: $o).
2.09/1.10	thf(decl_118, type, subsetE: $o).
2.09/1.10	thf(decl_119, type, subsetE2: $o).
2.09/1.10	thf(decl_120, type, notsubsetI: $o).
2.09/1.10	thf(decl_121, type, notequalI1: $o).
2.09/1.10	thf(decl_122, type, notequalI2: $o).
2.09/1.10	thf(decl_123, type, subsetRefl: $o).
2.09/1.10	thf(decl_124, type, subsetTrans: $o).
2.09/1.10	thf(decl_125, type, setadjoinSub: $o).
2.09/1.10	thf(decl_126, type, setadjoinSub2: $o).
2.09/1.10	thf(decl_127, type, subset2powerset: $o).
2.09/1.10	thf(decl_128, type, setextsub: $o).
2.09/1.10	thf(decl_129, type, subsetemptysetimpeq: $o).
2.09/1.10	thf(decl_130, type, powersetI1: $o).
2.09/1.10	thf(decl_131, type, powersetE1: $o).
2.09/1.10	thf(decl_132, type, inPowerset: $o).
2.09/1.10	thf(decl_133, type, powersetsubset: $o).
2.09/1.10	thf(decl_134, type, sepInPowerset: $o).
2.09/1.10	thf(decl_135, type, sepSubset: $o).
2.09/1.10	thf(decl_136, type, binunion: $i > $i > $i).
2.09/1.10	thf(decl_137, type, binunionIL: $o).
2.09/1.10	thf(decl_138, type, upairset2IR: $o).
2.09/1.10	thf(decl_139, type, binunionIR: $o).
2.09/1.10	thf(decl_140, type, binunionEcases: $o).
2.09/1.10	thf(decl_141, type, binunionE: $o).
2.09/1.10	thf(decl_142, type, binunionLsub: $o).
2.09/1.10	thf(decl_143, type, binunionRsub: $o).
2.09/1.10	thf(decl_144, type, binintersect: $i > $i > $i).
2.09/1.10	thf(decl_145, type, binintersectI: $o).
2.09/1.10	thf(decl_146, type, binintersectSubset5: $o).
2.09/1.10	thf(decl_147, type, binintersectEL: $o).
2.09/1.10	thf(decl_148, type, binintersectLsub: $o).
2.09/1.10	thf(decl_149, type, binintersectSubset2: $o).
2.09/1.10	thf(decl_150, type, binintersectSubset3: $o).
2.09/1.10	thf(decl_151, type, binintersectER: $o).
2.09/1.10	thf(decl_152, type, disjointsetsI1: $o).
2.09/1.10	thf(decl_153, type, binintersectRsub: $o).
2.09/1.10	thf(decl_154, type, binintersectSubset4: $o).
2.09/1.10	thf(decl_155, type, binintersectSubset1: $o).
2.09/1.10	thf(decl_156, type, bs114d: $o).
2.09/1.10	thf(decl_158, type, setminus: $i > $i > $i).
2.09/1.10	thf(decl_159, type, setminusI: $o).
2.09/1.10	thf(decl_160, type, setminusEL: $o).
2.09/1.10	thf(decl_161, type, setminusER: $o).
2.09/1.10	thf(decl_162, type, setminusSubset2: $o).
2.09/1.10	thf(decl_163, type, setminusERneg: $o).
2.09/1.10	thf(decl_164, type, setminusELneg: $o).
2.09/1.10	thf(decl_165, type, setminusILneg: $o).
2.09/1.10	thf(decl_166, type, setminusIRneg: $o).
2.09/1.10	thf(decl_167, type, setminusLsub: $o).
2.09/1.10	thf(decl_168, type, setminusSubset1: $o).
2.09/1.10	thf(decl_169, type, symdiff: $i > $i > $i).
2.09/1.10	thf(decl_170, type, symdiffE: $o).
2.09/1.10	thf(decl_171, type, symdiffI1: $o).
2.09/1.10	thf(decl_172, type, symdiffI2: $o).
2.09/1.10	thf(decl_173, type, symdiffIneg1: $o).
2.09/1.10	thf(decl_174, type, symdiffIneg2: $o).
2.09/1.10	thf(decl_175, type, iskpair: $i > $o).
2.09/1.10	thf(decl_176, type, secondinupair: $o).
2.09/1.10	thf(decl_177, type, setukpairIL: $o).
2.09/1.10	thf(decl_178, type, setukpairIR: $o).
2.09/1.10	thf(decl_179, type, kpairiskpair: $o).
2.09/1.10	thf(decl_180, type, kpair: $i > $i > $i).
2.09/1.10	thf(decl_181, type, kpairp: $o).
2.09/1.10	thf(decl_182, type, cartprod: $i > $i > $i).
2.09/1.10	thf(decl_183, type, singletonsubset: $o).
2.09/1.10	thf(decl_184, type, singletoninpowerset: $o).
2.09/1.10	thf(decl_185, type, singletoninpowunion: $o).
2.09/1.10	thf(decl_186, type, upairset2E: $o).
2.09/1.10	thf(decl_187, type, upairsubunion: $o).
2.09/1.10	thf(decl_188, type, upairinpowunion: $o).
2.09/1.10	thf(decl_189, type, ubforcartprodlem1: $o).
2.09/1.10	thf(decl_190, type, ubforcartprodlem2: $o).
2.09/1.10	thf(decl_191, type, ubforcartprodlem3: $o).
2.09/1.10	thf(decl_192, type, cartprodpairin: $o).
2.09/1.10	thf(decl_193, type, cartprodmempair1: $o).
2.09/1.10	thf(decl_194, type, cartprodmempair: $o).
2.09/1.10	thf(decl_195, type, setunionE2: $o).
2.09/1.10	thf(decl_196, type, setunionsingleton1: $o).
2.09/1.10	thf(decl_197, type, setunionsingleton2: $o).
2.09/1.10	thf(decl_198, type, setunionsingleton: $o).
2.09/1.10	thf(decl_199, type, singleton: $i > $o).
2.09/1.10	thf(decl_200, type, singletonprop: $o).
2.09/1.10	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
2.09/1.10	thf(decl_202, type, ex1E1: $o).
2.09/1.10	thf(decl_203, type, ex1I: $o).
2.09/1.10	thf(decl_204, type, ex1I2: $o).
2.09/1.10	thf(decl_205, type, singletonsuniq: $o).
2.09/1.10	thf(decl_210, type, setukpairinjL1: $o).
2.09/1.10	thf(decl_211, type, kfstsingleton: $o).
2.09/1.10	thf(decl_212, type, theprop: $o).
2.09/1.10	thf(decl_213, type, kfst: $i > $i).
2.09/1.10	thf(decl_214, type, kfstpairEq: $o).
2.09/1.10	thf(decl_215, type, cartprodfstin: $o).
2.09/1.10	thf(decl_216, type, setukpairinjL2: $o).
2.09/1.10	thf(decl_217, type, setukpairinjL: $o).
2.09/1.10	thf(decl_218, type, setukpairinjR11: $o).
2.09/1.10	thf(decl_219, type, setukpairinjR12: $o).
2.09/1.10	thf(decl_220, type, setukpairinjR1: $o).
2.09/1.10	thf(decl_221, type, upairequniteq: $o).
2.09/1.10	thf(decl_222, type, setukpairinjR2: $o).
2.09/1.10	thf(decl_223, type, setukpairinjR: $o).
2.09/1.10	thf(decl_224, type, ksndsingleton: $o).
2.09/1.10	thf(decl_225, type, ksnd: $i > $i).
2.09/1.10	thf(decl_226, type, ksndpairEq: $o).
2.09/1.10	thf(decl_227, type, kpairsurjEq: $o).
2.09/1.10	thf(decl_228, type, cartprodsndin: $o).
2.09/1.10	thf(decl_229, type, cartprodpairmemEL: $o).
2.09/1.10	thf(decl_230, type, cartprodpairmemER: $o).
2.09/1.10	thf(decl_231, type, cartprodmempaircEq: $o).
2.09/1.10	thf(decl_232, type, cartprodfstpairEq: $o).
2.09/1.10	thf(decl_233, type, cartprodsndpairEq: $o).
2.09/1.10	thf(decl_234, type, cartprodpairsurjEq: $o).
2.09/1.10	thf(decl_235, type, breln: $i > $i > $i > $o).
2.09/1.10	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
2.09/1.10	thf(decl_237, type, dpsetconstrI: $o).
2.09/1.10	thf(decl_238, type, dpsetconstrSub: $o).
2.09/1.10	thf(decl_239, type, setOfPairsIsBReln: $o).
2.09/1.10	thf(decl_240, type, dpsetconstrERa: $o).
2.09/1.10	thf(decl_241, type, dpsetconstrEL1: $o).
2.09/1.10	thf(decl_242, type, dpsetconstrEL2: $o).
2.09/1.10	thf(decl_243, type, dpsetconstrER: $o).
2.09/1.10	thf(decl_244, type, func: $i > $i > $i > $o).
2.09/1.10	thf(decl_245, type, funcSet: $i > $i > $i).
2.09/1.10	thf(decl_246, type, funcImageSingleton: $o).
2.09/1.10	thf(decl_247, type, apProp: $o).
2.09/1.10	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
2.09/1.10	thf(decl_249, type, app: $o).
2.09/1.10	thf(decl_250, type, infuncsetfunc: $o).
2.09/1.10	thf(decl_251, type, ap2p: $o).
2.09/1.10	thf(decl_252, type, funcinfuncset: $o).
2.09/1.10	thf(decl_253, type, lamProp: $o).
2.09/1.10	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
2.09/1.10	thf(decl_255, type, lamp: $o).
2.09/1.10	thf(decl_256, type, lam2p: $o).
2.09/1.10	thf(decl_257, type, brelnall1: $o).
2.09/1.10	thf(decl_258, type, brelnall2: $o).
2.09/1.10	thf(decl_259, type, ex1E2: $o).
2.09/1.10	thf(decl_260, type, funcGraphProp1: $o).
2.09/1.10	thf(decl_261, type, funcGraphProp3: $o).
2.09/1.10	thf(decl_262, type, funcGraphProp2: $o).
2.09/1.10	thf(decl_263, type, funcextLem: $o).
2.09/1.10	thf(decl_264, type, funcGraphProp4: $o).
2.09/1.10	thf(decl_265, type, subbreln: $o).
2.09/1.10	thf(decl_266, type, eqbreln: $o).
2.09/1.10	thf(decl_267, type, funcext: $o).
2.09/1.10	thf(decl_268, type, funcext2: $o).
2.09/1.10	thf(decl_269, type, ap2apEq1: $o).
2.09/1.10	thf(decl_270, type, ap2apEq2: $o).
2.09/1.10	thf(decl_271, type, beta1: $o).
2.09/1.10	thf(decl_272, type, eta1: $o).
2.09/1.10	thf(decl_273, type, lam2lamEq: $o).
2.09/1.10	thf(decl_274, type, beta2: $o).
2.09/1.10	thf(decl_275, type, eta2: $o).
2.09/1.10	thf(decl_276, type, iffalseProp1: $o).
2.09/1.10	thf(decl_277, type, iffalseProp2: $o).
2.09/1.10	thf(decl_278, type, iftrueProp1: $o).
2.09/1.10	thf(decl_279, type, iftrueProp2: $o).
2.09/1.10	thf(decl_280, type, ifSingleton: $o).
2.09/1.10	thf(decl_281, type, if: $i > $o > $i > $i > $i).
2.09/1.10	thf(decl_282, type, ifp: $o).
2.09/1.10	thf(decl_283, type, theeq: $o).
2.09/1.10	thf(decl_284, type, iftrue: $o).
2.09/1.10	thf(decl_285, type, iffalse: $o).
2.09/1.10	thf(decl_286, type, iftrueorfalse: $o).
2.09/1.10	thf(decl_287, type, binintersectT_lem: $o).
2.09/1.10	thf(decl_288, type, binunionT_lem: $o).
2.09/1.10	thf(decl_289, type, powersetT_lem: $o).
2.09/1.10	thf(decl_290, type, setminusT_lem: $o).
2.09/1.10	thf(decl_291, type, complementT_lem: $o).
2.09/1.10	thf(decl_292, type, setextT: $o).
2.09/1.10	thf(decl_293, type, subsetTI: $o).
2.09/1.10	thf(decl_294, type, powersetTI1: $o).
2.09/1.10	thf(decl_295, type, powersetTE1: $o).
2.09/1.10	thf(decl_296, type, complementTI1: $o).
2.09/1.10	thf(decl_297, type, complementTE1: $o).
2.09/1.10	thf(decl_298, type, binintersectTELcontra: $o).
2.09/1.10	thf(decl_299, type, binintersectTERcontra: $o).
2.09/1.10	thf(decl_300, type, contrasubsetT: $o).
2.09/1.10	thf(decl_301, type, contrasubsetT1: $o).
2.09/1.10	thf(decl_302, type, contrasubsetT2: $o).
2.09/1.10	thf(decl_303, type, contrasubsetT3: $o).
2.09/1.10	thf(decl_304, type, doubleComplementI1: $o).
2.09/1.10	thf(decl_305, type, doubleComplementE1: $o).
2.09/1.10	thf(decl_306, type, doubleComplementSub1: $o).
2.09/1.10	thf(decl_307, type, doubleComplementSub2: $o).
2.09/1.10	thf(decl_308, type, doubleComplementEq: $o).
2.09/1.10	thf(decl_309, type, complementTnotintersectT: $o).
2.09/1.10	thf(decl_310, type, complementImpComplementIntersect: $o).
2.09/1.10	thf(decl_311, type, complementSubsetComplementIntersect: $o).
2.09/1.10	thf(decl_312, type, complementInPowersetComplementIntersect: $o).
2.09/1.10	thf(decl_313, type, contraSubsetComplement: $o).
2.09/1.10	thf(decl_314, type, complementTcontraSubset: $o).
2.09/1.10	thf(decl_315, type, binunionTILcontra: $o).
2.09/1.10	thf(decl_316, type, binunionTIRcontra: $o).
2.09/1.10	thf(decl_317, type, inIntersectImpInUnion: $o).
2.09/1.10	thf(decl_318, type, inIntersectImpInUnion2: $o).
2.09/1.10	thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
2.09/1.10	thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
2.09/1.10	thf(decl_321, type, inComplementUnionImpNotIn1: $o).
2.09/1.10	thf(decl_322, type, inComplementUnionImpInComplement1: $o).
2.09/1.10	thf(decl_323, type, binunionTE: $o).
2.09/1.10	thf(decl_324, type, binunionTEcontra: $o).
2.09/1.10	thf(decl_325, type, demorgan2a1: $o).
2.09/1.10	thf(decl_326, type, complementUnionInPowersetComplement: $o).
2.09/1.10	thf(decl_327, type, demorgan2a2: $o).
2.09/1.10	thf(decl_328, type, demorgan1a: $o).
2.09/1.10	thf(decl_329, type, demorgan1b: $o).
2.09/1.10	thf(decl_330, type, demorgan1: $o).
2.09/1.10	thf(decl_331, type, demorgan2a: $o).
2.09/1.10	thf(decl_332, type, demorgan2b2: $o).
2.09/1.10	thf(decl_333, type, demorgan2b: $o).
2.09/1.10	thf(decl_334, type, demorgan2: $o).
2.09/1.10	thf(decl_335, type, woz13rule0: $o).
2.09/1.10	thf(decl_336, type, woz13rule1: $o).
2.09/1.10	thf(decl_337, type, woz13rule2: $o).
2.09/1.10	thf(decl_338, type, woz13rule3: $o).
2.09/1.10	thf(decl_339, type, woz13rule4: $o).
2.09/1.10	thf(decl_340, type, woz1_1: $o).
2.09/1.10	thf(decl_341, type, epred1_0: $o).
2.09/1.10	thf(decl_342, type, esk1_2: $i > $i > $i).
2.09/1.10	thf(decl_343, type, esk2_2: $i > $i > $i).
2.09/1.10	thf(decl_344, type, esk3_2: $i > $i > $i).
2.09/1.10	thf(decl_345, type, esk4_1: $i > $i).
2.09/1.10	thf(decl_346, type, esk5_2: ($i > $i > $o) > $i > $i).
2.09/1.10	thf(decl_347, type, esk6_2: ($i > $i > $o) > $i > $i).
2.09/1.10	thf(decl_348, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
2.09/1.10	thf(decl_349, type, esk8_1: $i > $i).
2.09/1.10	thf(decl_350, type, esk9_1: ($i > $o) > $i).
2.09/1.10	thf(decl_351, type, esk10_1: ($i > $o) > $i).
2.09/1.10	thf(decl_352, type, esk11_2: $i > $i > $i).
2.09/1.10	thf(decl_353, type, esk12_2: $i > $i > $i).
2.09/1.10	thf(decl_354, type, esk13_1: $i > $i).
2.09/1.10	thf(decl_355, type, esk14_1: $i > $i).
2.09/1.10	thf(decl_356, type, esk15_1: $i > $i).
2.09/1.10	thf(decl_357, type, esk16_2: $i > $i > $i).
2.09/1.10	thf(decl_358, type, esk17_3: $i > $i > $o > $i).
2.09/1.10	thf(decl_359, type, esk18_1: ($i > $o) > $i).
2.09/1.10	thf(decl_360, type, esk19_1: $i > $i).
2.09/1.10	thf(decl_361, type, esk20_2: $i > ($i > $o) > $i).
2.09/1.10	thf(decl_362, type, esk21_2: $i > ($i > $o) > $i).
2.09/1.10	thf(decl_363, type, esk22_2: $i > ($i > $o) > $i).
2.09/1.10	thf(decl_364, type, esk23_2: $i > ($i > $o) > $i).
2.09/1.10	thf(decl_365, type, esk24_2: $i > ($i > $o) > $i).
2.09/1.10	thf(decl_366, type, esk25_2: $i > ($i > $o) > $i).
2.09/1.10	thf(decl_367, type, esk26_2: ($i > $o) > $i > $i).
2.09/1.10	thf(decl_368, type, esk27_1: ($i > $o) > $i).
2.09/1.10	thf(decl_369, type, esk28_1: ($i > $o) > $i).
2.09/1.10	thf(decl_370, type, esk29_2: ($i > $o) > $i > $i).
2.09/1.10	thf(decl_371, type, esk30_2: ($i > $o) > ($i > $o) > $i).
2.09/1.10	thf(decl_372, type, esk31_2: ($i > $o) > ($i > $o) > $i).
2.09/1.10	thf(decl_373, type, esk32_2: ($i > $o) > ($i > $o) > $i).
2.09/1.10	thf(decl_374, type, esk33_2: ($i > $o) > ($i > $o) > $i).
2.09/1.10	thf(decl_375, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i).
2.09/1.10	thf(decl_376, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i).
2.09/1.10	thf(decl_377, type, esk36_2: $i > $i > $i).
2.09/1.10	thf(decl_378, type, esk37_2: $i > $i > $i).
2.09/1.10	thf(decl_379, type, esk38_2: $i > $i > $i).
2.09/1.10	thf(decl_380, type, esk39_3: $i > $i > $i > $i).
2.09/1.10	thf(decl_381, type, esk40_3: $i > $i > $i > $i).
2.09/1.10	thf(decl_382, type, esk41_2: $i > $i > $i).
2.09/1.10	thf(decl_383, type, esk42_2: $i > ($i > $o) > $i).
2.09/1.10	thf(decl_384, type, esk43_2: $i > ($i > $o) > $i).
2.09/1.10	thf(decl_385, type, esk44_2: $i > ($i > $o) > $i).
2.09/1.10	thf(decl_386, type, esk45_3: $i > ($i > $o) > $i > $i).
2.09/1.10	thf(decl_387, type, esk46_2: $i > ($i > $o) > $i).
2.09/1.10	thf(decl_388, type, esk47_2: $i > ($i > $o) > $i).
2.09/1.10	thf(decl_389, type, esk48_3: $i > $i > ($i > $i) > $i).
2.09/1.10	thf(decl_390, type, esk49_3: $i > $i > ($i > $i) > $i).
2.09/1.10	thf(decl_391, type, esk50_3: $i > $i > ($i > $i) > $i).
2.09/1.10	thf(decl_392, type, esk51_4: $i > $i > $i > ($i > $o) > $i).
2.09/1.10	thf(decl_393, type, esk52_4: $i > $i > $i > ($i > $o) > $i).
2.09/1.10	thf(decl_394, type, esk53_4: $i > $i > $i > ($i > $o) > $i).
2.09/1.10	thf(decl_395, type, esk54_4: $i > $i > $i > ($i > $o) > $i).
2.09/1.10	thf(decl_396, type, esk55_4: $i > $i > $i > $i > $i).
2.09/1.10	thf(decl_397, type, esk56_4: $i > $i > $i > $i > $i).
2.09/1.10	thf(decl_398, type, esk57_4: $i > $i > $i > $i > $i).
2.09/1.10	thf(decl_399, type, esk58_4: $i > $i > $i > $i > $i).
2.09/1.10	thf(decl_400, type, esk59_4: $i > $i > $i > $i > $i).
2.09/1.10	thf(decl_401, type, esk60_4: $i > $i > $i > $i > $i).
2.09/1.10	thf(decl_402, type, esk61_4: $i > $i > $i > $i > $i).
2.09/1.10	thf(decl_403, type, esk62_4: $i > $i > $i > $i > $i).
2.09/1.10	thf(decl_404, type, esk63_4: $i > $i > $i > $i > $i).
2.09/1.10	thf(decl_405, type, esk64_3: $i > $i > ($i > $i) > $i).
2.09/1.10	thf(decl_406, type, esk65_3: $i > $i > ($i > $i) > $i).
2.09/1.10	thf(decl_407, type, esk66_3: $i > $i > ($i > $i) > $i).
2.09/1.10	thf(decl_408, type, esk67_3: $i > $i > $i > $i).
2.09/1.10	thf(decl_409, type, esk68_3: $i > $i > $i > $i).
2.09/1.10	thf(decl_410, type, esk69_3: $i > $i > $i > $i).
2.09/1.10	thf(decl_411, type, esk70_3: $i > $i > $i > $i).
2.09/1.10	thf(decl_412, type, esk71_0: $i).
2.09/1.10	thf(decl_413, type, esk72_0: $i).
2.09/1.10	thf(decl_414, type, esk73_0: $i).
2.09/1.10	thf(decl_415, type, esk74_0: $i).
2.09/1.10	thf(decl_416, type, esk75_0: $i).
2.09/1.10	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', dsetconstr__Cong)).
2.09/1.10	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', descr__Cong)).
2.09/1.10	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', exu__Cong)).
2.09/1.10	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', exuE3u)).
2.09/1.10	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', ex1E1)).
2.09/1.10	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', exuI2)).
2.09/1.10	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', ex1I2)).
2.09/1.10	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', kfstsingleton)).
2.09/1.10	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', exuE2)).
2.09/1.10	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', exuE3e)).
2.09/1.10	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', dsetconstrER)).
2.09/1.10	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', dsetconstrEL)).
2.09/1.10	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', dsetconstrI)).
2.09/1.10	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', replAx)).
2.09/1.10	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', ksndsingleton)).
2.09/1.10	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', dpsetconstrERa)).
2.09/1.10	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', dpsetconstrEL1)).
2.09/1.10	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', dpsetconstrEL2)).
2.09/1.10	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', dpsetconstrER)).
2.09/1.10	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', funcImageSingleton)).
2.09/1.10	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', apProp)).
2.09/1.10	thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', lamProp)).
2.09/1.10	thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', beta1)).
2.09/1.10	thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', eta1)).
2.09/1.10	thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', lam2lamEq)).
2.09/1.10	thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', beta2)).
2.09/1.10	thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', eta2)).
2.09/1.10	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', iffalseProp1)).
2.09/1.10	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', iffalseProp2)).
2.09/1.10	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', iftrueProp1)).
2.09/1.10	thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', ifSingleton)).
2.09/1.10	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', iftrueProp2)).
2.09/1.10	thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', ex1E2)).
2.09/1.10	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', lam2p)).
2.09/1.10	thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', lamp)).
2.09/1.10	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setOfPairsIsBReln)).
2.09/1.10	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', dpsetconstrSub)).
2.09/1.10	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', dpsetconstrI)).
2.09/1.10	thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', ex1I)).
2.09/1.10	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', singletonprop)).
2.09/1.10	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', sepSubset)).
2.09/1.10	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', sepInPowerset)).
2.09/1.10	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', exuEu)).
2.09/1.10	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', exuI3)).
2.09/1.10	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', exuI1)).
2.09/1.10	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', emptyE1)).
2.09/1.10	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setoftrueEq)).
2.09/1.10	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', nonemptyI)).
2.09/1.10	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setbeta)).
2.09/1.10	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', exuE1)).
2.09/1.10	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', descrp)).
2.09/1.10	thf(woz1_2, conjecture, ((((setadjoinAx)=>(((setunionAx)=>((omega0Ax)=>((((((wellorderingAx)=>((descrp)=>(((((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((((emptyI)=>((noeltsimpempty)=>((setbeta)=>(((nonemptyI)=>((nonemptyI1)=>(((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>(((((powersetE)=>((setunionI)=>((setunionE)=>(((((((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((((emptyE1)=>((((quantDeMorgan2)=>((((prop2setI)=>((prop2set2propI)=>((notdexE)=>(((exuI1)=>((exuI3)=>(((((((emptyset__Cong)=>(((((omega__Cong)=>((exuEu)=>(((((((subsetI2)=>((emptysetsubset)=>((subsetE)=>(((((notequalI2)=>(((((setadjoinSub2)=>(((setextsub)=>((((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((((binunionIR)=>((binunionEcases)=>((binunionE)=>(((binunionRsub)=>((binintersectI)=>(((binintersectEL)=>(((binintersectSubset2)=>(((binintersectER)=>(((binintersectRsub)=>((binintersectSubset4)=>((((setminusI)=>((((setminusSubset2)=>((setminusERneg)=>((((setminusIRneg)=>((setminusLsub)=>((((((symdiffIneg1)=>(((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((((singletonsubset)=>(((singletoninpowunion)=>((((upairinpowunion)=>(((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>(((setunionsingleton1)=>(((setunionsingleton)=>(((ex1E1)=>(((ex1I2)=>(((setukpairinjL1)=>((kfstsingleton)=>(((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>(((cartprodpairmemEL)=>((cartprodpairmemER)=>(((cartprodfstpairEq)=>(((((((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>(((ap2p)=>((funcinfuncset)=>((lamProp)=>(((((((funcGraphProp1)=>((((funcextLem)=>((funcGraphProp4)=>(((((funcext2)=>(((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>(((ifSingleton)=>(((theeq)=>((iftrue)=>((((binintersectT_lem)=>((binunionT_lem)=>((((complementT_lem)=>((((((((binintersectTELcontra)=>(((contrasubsetT)=>(((((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>(((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>(((contraSubsetComplement)=>(((binunionTILcontra)=>(((((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>(((demorgan2a1)=>(((demorgan2a2)=>((demorgan1a)=>(((((((((woz13rule1)=>(((woz13rule3)=>((![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:((![X49:$i]:((![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))<=(in @ X49 @ (powerset @ X4))))<=(in @ X48 @ (powerset @ X4))))))<=(woz1_1))<=(woz13rule4)))<=(woz13rule2)))<=(woz13rule0))<=(demorgan2))<=(demorgan2b))<=(demorgan2b2))<=(demorgan2a))<=(demorgan1))<=(demorgan1b))))<=(complementUnionInPowersetComplement)))<=(binunionTEcontra)))))))<=(inIntersectImpInUnion2))<=(inIntersectImpInUnion))<=(binunionTIRcontra)))<=(complementTcontraSubset)))<=(complementInPowersetComplementIntersect)))))<=(doubleComplementEq))))))<=(contrasubsetT3))<=(contrasubsetT2))<=(contrasubsetT1)))<=(binintersectTERcontra)))<=(complementTE1))<=(complementTI1))<=(powersetTE1))<=(powersetTI1))<=(subsetTI))<=(setextT)))<=(setminusT_lem))<=(powersetT_lem))))<=(iftrueorfalse))<=(iffalse))))<=(ifp)))<=(iftrueProp2)))))))))))<=(ap2apEq1)))<=(funcext))<=(eqbreln))<=(subbreln))))<=(funcGraphProp2))<=(funcGraphProp3)))<=(ex1E2))<=(brelnall2))<=(brelnall1))<=(lam2p))<=(lamp)))))<=(infuncsetfunc)))))))))<=(setOfPairsIsBReln))<=(dpsetconstrSub))<=(dpsetconstrI))<=(cartprodpairsurjEq))<=(cartprodsndpairEq)))<=(cartprodmempaircEq))))<=(cartprodsndin)))))))<=(upairequniteq))<=(setukpairinjR1))))))))<=(theprop))))<=(singletonsuniq)))<=(ex1I)))<=(singletonprop)))<=(setunionsingleton2)))<=(setunionE2)))))))<=(ubforcartprodlem1)))<=(upairsubunion))<=(upairset2E)))<=(singletoninpowerset)))<=(kpairp))<=(kpairiskpair)))))<=(symdiffIneg2)))<=(symdiffI2))<=(symdiffI1))<=(symdiffE))<=(setminusSubset1))))<=(setminusILneg))<=(setminusELneg))))<=(setminusER))<=(setminusEL)))<=(bs114d))<=(binintersectSubset1))))<=(disjointsetsI1)))<=(binintersectSubset3)))<=(binintersectLsub)))<=(binintersectSubset5))))<=(binunionLsub)))))<=(upairset2IR))<=(binunionIL)))))))<=(powersetI1))<=(subsetemptysetimpeq)))<=(subset2powerset)))<=(setadjoinSub))<=(subsetTrans))<=(subsetRefl)))<=(notequalI1))<=(notsubsetI))<=(subsetE2)))))<=(eqimpsubset1))<=(eqimpsubset2))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong))))<=(setunion__Cong))<=(powerset__Cong))<=(setadjoin__Cong)))<=(exu__Cong))<=(exuE3u))<=(in__Cong))<=(inCongP))<=(exuI2))))<=(notdallE)))))<=(quantDeMorgan4))<=(quantDeMorgan3)))<=(quantDeMorgan1))<=(vacuousDall)))<=(upairsetIR))<=(upairsetIL)))))<=(notinsingleton))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU)))))<=(emptyInPowerset))<=(emptyinPowerset))<=(powersetI)))))))<=(setadjoinIL))))<=(nonemptyE1)))))<=(setext))<=(exuE3e)))))))<=(dsetconstrER))<=(dsetconstrEL))<=(dsetconstrI))))<=(foundationAx))<=(replAx))<=(omegaIndAx))<=(omegaSAx))))<=(powersetAx)))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', woz1_2)).
2.09/1.10	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setukpairinjL1)).
2.09/1.10	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setextAx)).
2.09/1.10	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', notequalI1)).
2.09/1.10	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', singletoninpowunion)).
2.09/1.10	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', notsubsetI)).
2.09/1.10	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', cartprodpairin)).
2.09/1.10	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', subsetE2)).
2.09/1.10	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', eqimpsubset1)).
2.09/1.10	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', cartprodmempair1)).
2.09/1.10	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', eqimpsubset2)).
2.09/1.10	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', subsetI1)).
2.09/1.10	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', cartprodmempair)).
2.09/1.10	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setunion__Cong)).
2.09/1.10	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setunionsingleton1)).
2.09/1.10	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', powerset__Cong)).
2.09/1.10	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setadjoin__Cong)).
2.09/1.10	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setunionsingleton)).
2.09/1.10	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', in__Cong)).
2.09/1.10	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', inCongP)).
2.09/1.10	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', notdallE)).
2.09/1.10	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', quantDeMorgan4)).
2.09/1.10	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', quantDeMorgan3)).
2.09/1.10	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', quantDeMorgan1)).
2.09/1.10	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', cartprodfstpairEq)).
2.09/1.10	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', vacuousDall)).
2.09/1.10	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', upairsetIR)).
2.09/1.10	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', upairinpowunion)).
2.09/1.10	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', upairsetIL)).
2.09/1.10	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', notinsingleton)).
2.09/1.10	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', uniqinunit)).
2.09/1.10	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', nonemptyImpWitness)).
2.09/1.10	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', ubforcartprodlem2)).
2.09/1.10	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', kfstpairEq)).
2.09/1.10	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', subPowSU)).
2.09/1.10	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', emptyInPowerset)).
2.09/1.10	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', emptyinPowerset)).
2.09/1.10	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', cartprodfstin)).
2.09/1.10	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', powersetI)).
2.09/1.10	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setadjoinIL)).
2.09/1.10	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setukpairinjL2)).
2.09/1.10	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', nonemptyE1)).
2.09/1.10	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setext)).
2.09/1.10	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setukpairinjL)).
2.09/1.10	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setukpairinjR11)).
2.09/1.10	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', foundationAx)).
2.09/1.10	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setukpairinjR12)).
2.09/1.10	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', omegaIndAx)).
2.09/1.10	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', omegaSAx)).
2.09/1.10	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setukpairinjR2)).
2.09/1.10	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', powersetAx)).
2.09/1.10	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', emptysetAx)).
2.09/1.10	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setukpairinjR)).
2.09/1.10	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', ksndpairEq)).
2.09/1.10	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', kpairsurjEq)).
2.09/1.10	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', cartprodpairmemEL)).
2.09/1.10	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', cartprodpairmemER)).
2.09/1.10	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', doubleComplementI1)).
2.09/1.10	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', doubleComplementE1)).
2.09/1.10	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', app)).
2.09/1.10	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', ap2p)).
2.09/1.10	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', funcinfuncset)).
2.09/1.10	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', ubforcartprodlem3)).
2.09/1.10	thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', funcGraphProp1)).
2.09/1.10	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', funcextLem)).
2.09/1.10	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', funcGraphProp4)).
2.09/1.10	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', funcext2)).
2.09/1.10	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', ap2apEq2)).
2.09/1.10	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', theeq)).
2.09/1.10	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', iftrue)).
2.09/1.10	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binintersectT_lem)).
2.09/1.10	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binunionT_lem)).
2.09/1.10	thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', complementT_lem)).
2.09/1.10	thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binintersectTELcontra)).
2.09/1.10	thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', contrasubsetT)).
2.09/1.10	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setminusELneg)).
2.09/1.10	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setminusER)).
2.09/1.10	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setminusEL)).
2.09/1.10	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', bs114d)).
2.09/1.10	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binintersectSubset1)).
2.09/1.10	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', disjointsetsI1)).
2.09/1.10	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binintersectSubset3)).
2.09/1.10	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binintersectLsub)).
2.09/1.10	thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', doubleComplementSub1)).
2.09/1.10	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', doubleComplementSub2)).
2.09/1.10	thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', complementTnotintersectT)).
2.09/1.10	thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', complementImpComplementIntersect)).
2.09/1.10	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', complementSubsetComplementIntersect)).
2.09/1.10	thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', contraSubsetComplement)).
2.09/1.10	thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binunionTILcontra)).
2.09/1.10	thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', inIntersectImpInIntersectUnions)).
2.09/1.10	thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', intersectInPowersetIntersectUnions)).
2.09/1.10	thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', inComplementUnionImpNotIn1)).
2.09/1.10	thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', inComplementUnionImpInComplement1)).
2.09/1.10	thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binunionTE)).
2.09/1.10	thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', demorgan2a1)).
2.09/1.10	thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', demorgan2a2)).
2.09/1.10	thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', demorgan1a)).
2.09/1.10	thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', woz13rule1)).
2.09/1.10	thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', woz13rule3)).
2.09/1.10	thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', woz1_1)).
2.09/1.10	thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', woz13rule4)).
2.09/1.10	thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', woz13rule2)).
2.09/1.10	thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', woz13rule0)).
2.09/1.10	thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', demorgan2)).
2.09/1.10	thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', demorgan2b)).
2.09/1.10	thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', demorgan2b2)).
2.09/1.10	thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', demorgan2a)).
2.09/1.10	thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', demorgan1)).
2.09/1.10	thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', demorgan1b)).
2.09/1.10	thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', complementUnionInPowersetComplement)).
2.09/1.10	thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binunionTEcontra)).
2.09/1.10	thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', inIntersectImpInUnion2)).
2.09/1.10	thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', inIntersectImpInUnion)).
2.09/1.10	thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binunionTIRcontra)).
2.09/1.10	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', complementTcontraSubset)).
2.09/1.10	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', complementInPowersetComplementIntersect)).
2.09/1.10	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', doubleComplementEq)).
2.09/1.10	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', contrasubsetT3)).
2.09/1.10	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', contrasubsetT2)).
2.09/1.10	thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', contrasubsetT1)).
2.09/1.10	thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binintersectTERcontra)).
2.09/1.10	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', complementTE1)).
2.09/1.10	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', complementTI1)).
2.09/1.10	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', powersetTE1)).
2.09/1.10	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', powersetTI1)).
2.09/1.10	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', subsetTI)).
2.09/1.10	thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setextT)).
2.09/1.10	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setminusT_lem)).
2.09/1.10	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', powersetT_lem)).
2.09/1.10	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', iftrueorfalse)).
2.09/1.10	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', iffalse)).
2.09/1.10	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', ifp)).
2.09/1.10	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', ap2apEq1)).
2.09/1.10	thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', funcext)).
2.09/1.10	thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', eqbreln)).
2.09/1.10	thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', subbreln)).
2.09/1.10	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', funcGraphProp2)).
2.09/1.10	thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', funcGraphProp3)).
2.09/1.10	thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', brelnall2)).
2.09/1.10	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', brelnall1)).
2.09/1.10	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', infuncsetfunc)).
2.09/1.10	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', cartprodpairsurjEq)).
2.09/1.10	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', cartprodsndpairEq)).
2.09/1.10	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', cartprodmempaircEq)).
2.09/1.10	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', cartprodsndin)).
2.09/1.10	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', upairequniteq)).
2.09/1.10	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setukpairinjR1)).
2.09/1.10	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', theprop)).
2.09/1.10	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', singletonsuniq)).
2.09/1.10	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setunionsingleton2)).
2.09/1.10	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setunionE2)).
2.09/1.10	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', ubforcartprodlem1)).
2.09/1.10	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', upairsubunion)).
2.09/1.10	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', upairset2E)).
2.09/1.10	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', singletoninpowerset)).
2.09/1.10	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', kpairp)).
2.09/1.10	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', kpairiskpair)).
2.09/1.10	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', symdiffIneg2)).
2.09/1.10	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', symdiffI2)).
2.09/1.10	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', symdiffI1)).
2.09/1.10	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', symdiffE)).
2.09/1.10	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setminusSubset1)).
2.09/1.10	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setminusILneg)).
2.09/1.10	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binintersectSubset5)).
2.09/1.10	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binunionLsub)).
2.09/1.10	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', upairset2IR)).
2.09/1.10	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binunionIL)).
2.09/1.10	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', powersetI1)).
2.09/1.10	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', subsetemptysetimpeq)).
2.09/1.10	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', subset2powerset)).
2.09/1.10	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setadjoinSub)).
2.09/1.10	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', subsetTrans)).
2.09/1.10	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', subsetRefl)).
2.09/1.10	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', singletonsubset)).
2.09/1.10	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setukpairIR)).
2.09/1.10	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setukpairIL)).
2.09/1.10	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', secondinupair)).
2.09/1.10	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', symdiffIneg1)).
2.09/1.10	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setminusLsub)).
2.09/1.10	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setminusIRneg)).
2.09/1.10	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setminusERneg)).
2.09/1.10	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setminusSubset2)).
2.09/1.10	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setminusI)).
2.09/1.10	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binintersectSubset4)).
2.09/1.10	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binintersectRsub)).
2.09/1.10	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binintersectER)).
2.09/1.10	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binintersectSubset2)).
2.09/1.10	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binintersectEL)).
2.09/1.10	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binintersectI)).
2.09/1.10	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binunionRsub)).
2.09/1.10	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binunionE)).
2.09/1.10	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binunionEcases)).
2.09/1.10	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', binunionIR)).
2.09/1.10	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', powersetsubset)).
2.09/1.10	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', inPowerset)).
2.09/1.10	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', powersetE1)).
2.09/1.10	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setextsub)).
2.09/1.10	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setadjoinSub2)).
2.09/1.10	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', notequalI2)).
2.09/1.10	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', subsetE)).
2.09/1.10	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', emptysetsubset)).
2.09/1.10	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', subsetI2)).
2.09/1.10	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', omega__Cong)).
2.09/1.10	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', emptyset__Cong)).
2.09/1.10	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', notdexE)).
2.09/1.10	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', prop2setI)).
2.09/1.10	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', quantDeMorgan2)).
2.09/1.10	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', upairsetE)).
2.09/1.10	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', singletonsswitch)).
2.09/1.10	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', eqinunit)).
2.09/1.10	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setunionE)).
2.09/1.10	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setunionI)).
2.09/1.10	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', powersetE)).
2.09/1.10	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setadjoinOr)).
2.09/1.10	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setadjoinE)).
2.09/1.10	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setadjoinIR)).
2.09/1.10	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', emptyinunitempty)).
2.09/1.10	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', nonemptyI1)).
2.09/1.10	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', noeltsimpempty)).
2.09/1.10	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', emptyI)).
2.09/1.10	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', notinemptyset)).
2.09/1.10	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', emptysetimpfalse)).
2.09/1.10	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', emptysetE)).
2.09/1.10	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', prop2setE)).
2.09/1.10	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', wellorderingAx)).
2.09/1.10	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', omega0Ax)).
2.09/1.10	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setunionAx)).
2.09/1.10	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ps2JGGfKvd/E---3.1_18217.p', setadjoinAx)).
2.09/1.10	thf(c_0_280, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
2.09/1.10	thf(c_0_281, plain, ((descr__Cong)<=>![X1:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
2.09/1.10	thf(c_0_282, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
2.09/1.10	thf(c_0_283, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
2.09/1.10	thf(c_0_284, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
2.09/1.10	thf(c_0_285, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
2.09/1.10	thf(c_0_286, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
2.09/1.10	thf(c_0_287, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
2.09/1.10	thf(c_0_288, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
2.09/1.10	thf(c_0_289, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
2.09/1.10	thf(c_0_290, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
2.09/1.10	thf(c_0_291, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
2.09/1.10	thf(c_0_292, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
2.09/1.10	thf(c_0_293, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
2.09/1.10	thf(c_0_294, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
2.09/1.10	thf(c_0_295, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
2.09/1.10	thf(c_0_296, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
2.09/1.10	thf(c_0_297, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
2.09/1.10	thf(c_0_298, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
2.09/1.10	thf(c_0_299, plain, ((funcImageSingleton)<=>![X4:$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])).
2.09/1.10	thf(c_0_300, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
2.09/1.10	thf(c_0_301, plain, ((lamProp)<=>![X4:$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])).
2.09/1.10	thf(c_0_302, 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])).
2.09/1.10	thf(c_0_303, 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])).
2.09/1.10	thf(c_0_304, 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])).
2.09/1.10	thf(c_0_305, 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])).
2.09/1.10	thf(c_0_306, 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])).
2.09/1.10	thf(c_0_307, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
2.09/1.10	thf(c_0_308, plain, ((iffalseProp2)<=>![X4:$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])).
2.09/1.10	thf(c_0_309, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
2.09/1.10	thf(c_0_310, plain, ((ifSingleton)<=>![X4:$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])).
2.09/1.10	thf(c_0_311, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
2.09/1.10	thf(c_0_312, plain, ((ex1E2)<=>![X4:$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])).
2.09/1.10	thf(c_0_313, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
2.09/1.10	thf(c_0_314, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
2.09/1.10	thf(c_0_315, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
2.09/1.10	thf(c_0_316, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
2.09/1.10	thf(c_0_317, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
2.09/1.10	thf(c_0_318, plain, ((ex1I)<=>![X4:$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])).
2.09/1.10	thf(c_0_319, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
2.09/1.10	thf(c_0_320, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
2.09/1.10	thf(c_0_321, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
2.09/1.10	thf(c_0_322, 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])).
2.09/1.10	thf(c_0_323, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
2.09/1.10	thf(c_0_324, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
2.09/1.10	thf(c_0_325, 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])).
2.09/1.10	thf(c_0_326, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
2.09/1.10	thf(c_0_327, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
2.09/1.10	thf(c_0_328, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
2.09/1.10	thf(c_0_329, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
2.09/1.10	thf(c_0_330, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
2.09/1.10	thf(c_0_331, plain, ((epred1_0)<=>![X954:$i]:(?[X955:$i]:((((![X956:$i]:(((in @ X956 @ X955)=>![X957:$i]:(((in @ X957 @ X956)=>(in @ X957 @ X954)))))&![X958:$i, X959:$i]:((((in @ X958 @ X954)&(in @ X959 @ X954))=>(![X960:$i]:(((in @ X960 @ X955)=>((in @ X958 @ X960)<=>(in @ X959 @ X960))))=>((X958)=(X959))))))&![X961:$i, X962:$i]:((((in @ X961 @ X955)&(in @ X962 @ X955))=>(![X963:$i]:(((in @ X963 @ X961)=>(in @ X963 @ X962)))|![X964:$i]:(((in @ X964 @ X962)=>(in @ X964 @ X961)))))))&![X965:$i]:(((![X966:$i]:(((in @ X966 @ X965)=>(in @ X966 @ X954)))&?[X967:$i]:((in @ X967 @ X965)))=>?[X968:$i, X969:$i]:(((((in @ X968 @ X955)&(in @ X969 @ X965))&~(?[X970:$i]:(((in @ X970 @ X968)&(in @ X970 @ X965)))))&![X971:$i]:(((in @ X971 @ X955)=>(![X972:$i]:(((in @ X972 @ X971)=>(in @ X972 @ X968)))|(in @ X969 @ X971)))))))))))), introduced(definition)).
2.09/1.10	thf(c_0_332, negated_conjecture, ~((![X1836:$i, X1837:$i]:((![X1838:$i]:(((in @ X1838 @ X1836)<=>(in @ X1838 @ X1837)))=>((X1836)=(X1837))))=>(![X1835:$i]:(~(in @ X1835 @ emptyset))=>(![X948:$i, X949:$i, X950:$i]:(((in @ X950 @ (setadjoin @ X948 @ X949))<=>(((X950)=(X948))|(in @ X950 @ X949))))=>(![X1832:$i, X1833:$i]:(((in @ X1833 @ (powerset @ X1832))<=>![X1834:$i]:(((in @ X1834 @ X1833)=>(in @ X1834 @ X1832)))))=>(![X951:$i, X952:$i]:(((in @ X952 @ (setunion @ X951))<=>?[X953:$i]:(((in @ X952 @ X953)&(in @ X953 @ X951)))))=>((in @ emptyset @ omega)=>(![X1831:$i]:(((in @ X1831 @ omega)=>(in @ (setadjoin @ X1831 @ X1831) @ omega)))=>(![X1828:$i]:((((in @ emptyset @ X1828)&![X1829:$i]:((((in @ X1829 @ omega)&(in @ X1829 @ X1828))=>(in @ (setadjoin @ X1829 @ X1829) @ X1828))))=>![X1830:$i]:(((in @ X1830 @ omega)=>(in @ X1830 @ X1828)))))=>(![X1822:$i > $i > $o, X1823:$i]:((![X1824:$i]:(((in @ X1824 @ X1823)=>(exu @ (X1822 @ X1824))))=>?[X1825:$i]:(![X1826:$i]:(((in @ X1826 @ X1825)<=>?[X1827:$i]:(((in @ X1827 @ X1823)&(X1822 @ X1827 @ X1826))))))))=>(![X1818:$i]:((?[X1819:$i]:((in @ X1819 @ X1818))=>?[X1820:$i]:(((in @ X1820 @ X1818)&~(?[X1821:$i]:(((in @ X1821 @ X1820)&(in @ X1821 @ X1818))))))))=>((epred1_0)=>(![X973:$i > $o]:(((exu @ X973)=>(X973 @ (descr @ (^[Z0/* 17 */:$i]:(X973 @ Z0))))))=>(![X1815:$i, X1816:$i > $o, X1817:$i]:(((in @ X1817 @ X1815)=>((X1816 @ X1817)=>(in @ X1817 @ (dsetconstr @ X1815 @ X1816)))))=>(![X1812:$i, X1813:$i > $o, X1814:$i]:(((in @ X1814 @ (dsetconstr @ X1812 @ X1813))=>(in @ X1814 @ X1812)))=>(![X1809:$i, X1810:$i > $o, X1811:$i]:(((in @ X1811 @ (dsetconstr @ X1809 @ X1810))=>(X1810 @ X1811)))=>(![X974:$i > $o]:(((exu @ X974)=>?[X975:$i]:(((X974 @ X975)&![X976:$i]:(((X974 @ X976)=>((X975)=(X976))))))))=>(![X977:$o, X978:$i]:(((in @ X978 @ (prop2set @ ((X977))))=>(X977)))=>(![X979:$i]:(((in @ X979 @ emptyset)=>![X980:$o]:((X980))))=>(![X981:$i]:(((in @ X981 @ emptyset)=>~($true)))=>(![X982:$i]:(~(in @ X982 @ emptyset))=>(![X1807:$i > $o]:(((exu @ X1807)=>?[X1808:$i]:((X1807 @ X1808))))=>(![X1803:$i, X1804:$i]:((![X1805:$i]:(((in @ X1805 @ X1803)=>(in @ X1805 @ X1804)))=>(![X1806:$i]:(((in @ X1806 @ X1804)=>(in @ X1806 @ X1803)))=>((X1803)=(X1804)))))=>(![X983:$i]:((![X984:$i]:(~(in @ X984 @ X983))=>((X983)=(emptyset))))=>(![X985:$i]:((![X986:$i]:(~(in @ X986 @ X985))=>((X985)=(emptyset))))=>(![X987:$i, X988:$i > $o, X989:$i]:(((in @ X989 @ X987)=>((in @ X989 @ (dsetconstr @ X987 @ X988))<=>(X988 @ X989))))=>(![X1801:$i]:(((nonempty @ X1801)=>?[X1802:$i]:((in @ X1802 @ X1801))))=>(![X990:$i, X991:$i > $o, X992:$i]:(((in @ X992 @ X990)=>((X991 @ X992)=>(nonempty @ (dsetconstr @ X990 @ X991)))))=>(![X993:$i]:((?[X994:$i]:((in @ X994 @ X993))=>(nonempty @ X993)))=>(![X1799:$i, X1800:$i]:((in @ X1799 @ (setadjoin @ X1799 @ X1800)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X995:$i, X996:$i, X997:$i]:(((in @ X997 @ X996)=>(in @ X997 @ (setadjoin @ X995 @ X996))))=>(![X998:$i, X999:$i, X1000:$i]:(((in @ X1000 @ (setadjoin @ X998 @ X999))=>![X1001:$o]:(((((X1000)=(X998))=>(X1001))=>(((in @ X1000 @ X999)=>(X1001))=>(X1001))))))=>(![X1002:$i, X1003:$i, X1004:$i]:(((in @ X1004 @ (setadjoin @ X1002 @ X1003))=>(((X1004)=(X1002))|(in @ X1004 @ X1003))))=>(![X1005:$i]:(((dsetconstr @ X1005 @ (^[Z0/* 1 */:$i]:($true)))=(X1005)))=>(![X1796:$i, X1797:$i]:((![X1798:$i]:(((in @ X1798 @ X1797)=>(in @ X1798 @ X1796)))=>(in @ X1797 @ (powerset @ X1796))))=>(![X1795:$i]:((in @ emptyset @ (powerset @ X1795)))=>(![X1794:$i]:((in @ emptyset @ (powerset @ X1794)))=>(![X1006:$i, X1007:$i, X1008:$i]:(((in @ X1007 @ (powerset @ X1006))=>((in @ X1008 @ X1007)=>(in @ X1008 @ X1006))))=>(![X1009:$i, X1010:$i, X1011:$i]:(((in @ X1010 @ X1011)=>((in @ X1011 @ X1009)=>(in @ X1010 @ (setunion @ X1009)))))=>(![X1012:$i, X1013:$i]:(((in @ X1013 @ (setunion @ X1012))=>![X1014:$o]:((![X1015:$i]:(((in @ X1013 @ X1015)=>((in @ X1015 @ X1012)=>(X1014))))=>(X1014)))))=>(![X1792:$i, X1793:$i]:(((in @ X1793 @ X1792)=>(in @ X1793 @ (powerset @ (setunion @ X1792)))))=>(![X1789:$i > $o]:(((exu @ X1789)=>?[X1790:$i]:(![X1791:$i]:(((X1789 @ X1791)<=>((X1791)=(X1790)))))))=>(![X1787:$i]:(((nonempty @ X1787)=>?[X1788:$i]:(((in @ X1788 @ X1787)&$true))))=>(![X1785:$i, X1786:$i]:(((in @ X1785 @ (setadjoin @ X1786 @ emptyset))=>((X1785)=(X1786))))=>(![X1783:$i, X1784:$i]:((((X1783)!=(X1784))=>~(in @ X1784 @ (setadjoin @ X1783 @ emptyset))))=>(![X1016:$i, X1017:$i]:((((X1016)=(X1017))=>(in @ X1016 @ (setadjoin @ X1017 @ emptyset))))=>(![X1018:$i, X1019:$i]:(((in @ X1018 @ (setadjoin @ X1019 @ emptyset))=>(in @ X1019 @ (setadjoin @ X1018 @ emptyset))))=>(![X1020:$i, X1021:$i, X1022:$i]:(((in @ X1022 @ (setadjoin @ X1020 @ (setadjoin @ X1021 @ emptyset)))=>(((X1022)=(X1020))|((X1022)=(X1021)))))=>(![X1781:$i, X1782:$i]:((in @ X1781 @ (setadjoin @ X1781 @ (setadjoin @ X1782 @ emptyset))))=>(![X1779:$i, X1780:$i]:((in @ X1780 @ (setadjoin @ X1779 @ (setadjoin @ X1780 @ 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X51))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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setukpairinjL1]), setextAx]), notequalI1]), singletoninpowunion]), notsubsetI]), cartprodpairin]), subsetE2]), eqimpsubset1]), cartprodmempair1]), eqimpsubset2]), subsetI1]), c_0_280]), cartprodmempair]), c_0_281]), setunion__Cong]), setunionsingleton1]), powerset__Cong]), setadjoin__Cong]), c_0_282]), setunionsingleton]), c_0_283]), in__Cong]), c_0_284]), inCongP]), c_0_285]), notdallE]), quantDeMorgan4]), c_0_286]), quantDeMorgan3]), quantDeMorgan1]), cartprodfstpairEq]), vacuousDall]), upairsetIR]), upairinpowunion]), upairsetIL]), notinsingleton]), c_0_287]), uniqinunit]), nonemptyImpWitness]), ubforcartprodlem2]), c_0_288]), kfstpairEq]), subPowSU]), emptyInPowerset]), emptyinPowerset]), cartprodfstin]), powersetI]), setadjoinIL]), setukpairinjL2]), nonemptyE1]), setext]), c_0_289]), setukpairinjL]), c_0_290]), c_0_291]), setukpairinjR11]), c_0_292]), foundationAx]), c_0_293]), setukpairinjR12]), omegaIndAx]), omegaSAx]), setukpairinjR2]), powersetAx]), emptysetAx]), setukpairinjR]), c_0_294]), ksndpairEq]), kpairsurjEq]), cartprodpairmemEL]), cartprodpairmemER]), doubleComplementI1]), doubleComplementE1]), c_0_295]), c_0_296]), c_0_297]), c_0_298]), c_0_299]), c_0_300]), app]), ap2p]), funcinfuncset]), ubforcartprodlem3]), c_0_301]), funcGraphProp1]), funcextLem]), funcGraphProp4]), funcext2]), ap2apEq2]), c_0_302]), c_0_303]), c_0_304]), c_0_305]), c_0_306]), c_0_307]), c_0_308]), c_0_309]), c_0_310]), theeq]), iftrue]), binintersectT_lem]), binunionT_lem]), complementT_lem]), binintersectTELcontra]), contrasubsetT]), setminusELneg]), setminusER]), setminusEL]), bs114d]), binintersectSubset1]), disjointsetsI1]), binintersectSubset3]), binintersectLsub]), doubleComplementSub1]), doubleComplementSub2]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), contraSubsetComplement]), binunionTILcontra]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), demorgan2a1]), demorgan2a2]), demorgan1a]), woz13rule1]), woz13rule3]), woz1_1]), woz13rule4]), woz13rule2]), woz13rule0]), demorgan2]), demorgan2b]), demorgan2b2]), demorgan2a]), demorgan1]), demorgan1b]), complementUnionInPowersetComplement]), binunionTEcontra]), inIntersectImpInUnion2]), inIntersectImpInUnion]), binunionTIRcontra]), complementTcontraSubset]), complementInPowersetComplementIntersect]), doubleComplementEq]), contrasubsetT3]), contrasubsetT2]), contrasubsetT1]), binintersectTERcontra]), complementTE1]), complementTI1]), powersetTE1]), powersetTI1]), subsetTI]), setextT]), setminusT_lem]), powersetT_lem]), iftrueorfalse]), iffalse]), ifp]), c_0_311]), ap2apEq1]), funcext]), eqbreln]), subbreln]), funcGraphProp2]), funcGraphProp3]), c_0_312]), brelnall2]), brelnall1]), c_0_313]), c_0_314]), infuncsetfunc]), c_0_315]), c_0_316]), c_0_317]), cartprodpairsurjEq]), cartprodsndpairEq]), cartprodmempaircEq]), cartprodsndin]), upairequniteq]), setukpairinjR1]), theprop]), singletonsuniq]), c_0_318]), c_0_319]), setunionsingleton2]), setunionE2]), ubforcartprodlem1]), upairsubunion]), upairset2E]), singletoninpowerset]), kpairp]), kpairiskpair]), symdiffIneg2]), symdiffI2]), symdiffI1]), symdiffE]), setminusSubset1]), setminusILneg]), binintersectSubset5]), binunionLsub]), upairset2IR]), binunionIL]), powersetI1]), subsetemptysetimpeq]), subset2powerset]), setadjoinSub]), subsetTrans]), subsetRefl]), singletonsubset]), setukpairIR]), setukpairIL]), secondinupair]), symdiffIneg1]), setminusLsub]), setminusIRneg]), setminusERneg]), setminusSubset2]), setminusI]), binintersectSubset4]), binintersectRsub]), binintersectER]), binintersectSubset2]), binintersectEL]), binintersectI]), binunionRsub]), binunionE]), binunionEcases]), binunionIR]), c_0_320]), c_0_321]), powersetsubset]), inPowerset]), powersetE1]), setextsub]), setadjoinSub2]), notequalI2]), subsetE]), emptysetsubset]), subsetI2]), c_0_322]), omega__Cong]), emptyset__Cong]), c_0_323]), c_0_324]), notdexE]), prop2setI]), quantDeMorgan2]), c_0_325]), upairsetE]), singletonsswitch]), eqinunit]), setunionE]), setunionI]), powersetE]), c_0_326]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), nonemptyI1]), c_0_327]), c_0_328]), noeltsimpempty]), emptyI]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_329]), c_0_330]), wellorderingAx]), omega0Ax]), setunionAx]), setadjoinAx])])]), c_0_331])).
2.09/1.10	thf(c_0_333, negated_conjecture, ![X1839:$i, X1840:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1852:$i, X1853:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1861:$i, X1862:$i > $i > $o, X1863:$i, X1866:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1873:$i, X1874:$i > $o, X1875:$i, X1876:$i > $o, X1877:$i, X1878:$i, X1879:$i > $o, X1880:$i, X1881:$i, X1882:$i > $o, X1883:$i, X1884:$i > $o, X1886:$i, X1887:$o, X1888:$i, X1889:$i, X1890:$o, X1891:$i, X1892:$i, X1893:$i > $o, X1895:$i, X1896:$i, X1899:$i, X1901:$i, X1903:$i, X1904:$i > $o, X1905:$i, X1906:$i, X1908:$i, X1909:$i > $o, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$o, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$o, X1941:$i, X1942:$i, X1943:$i > $o, X1945:$i, X1946:$i, X1947:$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 > $o, X1966:$i, X1967:$i > $o, X1968:$i, X1969:$i, X1970:$i > $o, X1971:$i, X1973:$i, X1974:$i > $o, X1976:$i, X1977:$i, X1978:$i > $o, X1980:$i, X1981:$i, X1982:$i > $o, X1983:$i, X1985:$o, X1986:$i, X1987:$i > $o, X1989:$i, X1990:$i, X1991:$i > $o, X1992:$i, X1994:$i > $o, X1995:$i, X1997:$i > $o, X1998:$i, X2001:$i > $o, X2002:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i > $o, X2013:$i, X2014:$i, X2015:$i > $o, X2016:$i > $o, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i > $o, X2028:$i, X2029:$i, X2030:$i > $o, X2031:$i > $o, X2034:$i, X2035:$i, X2036:$i > $o, X2037:$i > $o, X2040:$i, X2041:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$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 > $o, X2088:$i, X2089:$i > $o, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$o, X2102:$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, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, 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:$i, X2169:$o, 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:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i > $o, X2244:$i, X2245:$i, X2246:$i > $o, X2248:$i, X2249:$i > $o, X2250:$i, X2252:$i, X2253:$i > $o, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2327:$i, X2328:$i > $i > $o, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2333:$i > $i > $o, X2334:$i, X2335:$i, X2336:$i > $i > $o, X2337:$i, X2338:$i, X2339:$i > $i > $o, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i > $i > $o, X2345:$i, X2346:$i, X2347:$i, X2348:$i, X2349:$i > $i > $o, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i > $i > $o, X2355:$i, 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X2537)|((X2538)=(X2539))|(in @ (esk67_3 @ X2537 @ X2538 @ X2539) @ X2537)|~(in @ X2539 @ (powerset @ X2537))|~(in @ X2538 @ (powerset @ X2537)))&(((in @ (esk68_3 @ X2537 @ X2538 @ X2539) @ X2539)|((X2538)=(X2539))|(in @ (esk67_3 @ X2537 @ X2538 @ X2539) @ X2537)|~(in @ X2539 @ (powerset @ X2537))|~(in @ X2538 @ (powerset @ X2537)))&(~(in @ (esk68_3 @ X2537 @ X2538 @ X2539) @ X2538)|((X2538)=(X2539))|(in @ (esk67_3 @ X2537 @ X2538 @ X2539) @ X2537)|~(in @ X2539 @ (powerset @ X2537))|~(in @ X2538 @ (powerset @ X2537)))))&((((in @ (esk68_3 @ X2537 @ X2538 @ X2539) @ X2537)|((X2538)=(X2539))|(in @ (esk67_3 @ X2537 @ X2538 @ X2539) @ X2538)|~(in @ X2539 @ (powerset @ X2537))|~(in @ X2538 @ (powerset @ X2537)))&(((in @ (esk68_3 @ X2537 @ X2538 @ X2539) @ X2539)|((X2538)=(X2539))|(in @ (esk67_3 @ X2537 @ X2538 @ X2539) @ X2538)|~(in @ X2539 @ (powerset @ X2537))|~(in @ X2538 @ (powerset @ X2537)))&(~(in @ (esk68_3 @ X2537 @ X2538 @ X2539) @ X2538)|((X2538)=(X2539))|(in @ (esk67_3 @ X2537 @ X2538 @ X2539) @ X2538)|~(in @ X2539 @ (powerset @ X2537))|~(in @ X2538 @ (powerset @ X2537)))))&(((in @ (esk68_3 @ X2537 @ X2538 @ X2539) @ X2537)|((X2538)=(X2539))|~(in @ (esk67_3 @ X2537 @ X2538 @ X2539) @ X2539)|~(in @ X2539 @ (powerset @ X2537))|~(in @ X2538 @ (powerset @ X2537)))&(((in @ (esk68_3 @ X2537 @ X2538 @ X2539) @ X2539)|((X2538)=(X2539))|~(in @ (esk67_3 @ X2537 @ X2538 @ X2539) @ X2539)|~(in @ X2539 @ (powerset @ X2537))|~(in @ X2538 @ (powerset @ X2537)))&(~(in @ (esk68_3 @ X2537 @ X2538 @ X2539) @ X2538)|((X2538)=(X2539))|~(in @ (esk67_3 @ X2537 @ X2538 @ X2539) @ X2539)|~(in @ X2539 @ (powerset @ X2537))|~(in @ X2538 @ (powerset @ X2537)))))))&((((in @ (esk69_3 @ X2542 @ X2543 @ X2544) @ X2542)|(subset @ X2543 @ X2544)|~(in @ X2544 @ (powerset @ X2542))|~(in @ X2543 @ (powerset @ X2542)))&(((in @ (esk69_3 @ X2542 @ X2543 @ X2544) @ X2543)|(subset @ X2543 @ X2544)|~(in @ X2544 @ (powerset @ X2542))|~(in @ X2543 @ (powerset @ X2542)))&(~(in @ (esk69_3 @ X2542 @ X2543 @ X2544) @ X2544)|(subset @ X2543 @ X2544)|~(in @ X2544 @ (powerset @ X2542))|~(in @ X2543 @ (powerset @ X2542)))))&((((in @ (esk70_3 @ X2546 @ X2547 @ X2548) @ X2546)|(in @ X2547 @ (powerset @ X2548))|~(in @ X2548 @ (powerset @ X2546))|~(in @ X2547 @ (powerset @ X2546)))&(((in @ (esk70_3 @ X2546 @ X2547 @ X2548) @ X2547)|(in @ X2547 @ (powerset @ X2548))|~(in @ X2548 @ (powerset @ X2546))|~(in @ X2547 @ (powerset @ X2546)))&(~(in @ (esk70_3 @ X2546 @ X2547 @ X2548) @ X2548)|(in @ X2547 @ (powerset @ X2548))|~(in @ X2548 @ (powerset @ X2546))|~(in @ X2547 @ (powerset @ X2546)))))&((~(in @ X2551 @ (powerset @ X2550))|(~(in @ X2552 @ (powerset @ X2550))|(~(in @ X2553 @ X2550)|(~(in @ X2551 @ (powerset @ X2552))|(~(in @ X2553 @ X2551)|(in @ X2553 @ X2552))))))&((~(in @ X2555 @ (powerset @ X2554))|(~(in @ X2556 @ X2554)|(~(in @ X2556 @ X2555)|~(in @ X2556 @ (setminus @ X2554 @ X2555)))))&((~(in @ X2558 @ (powerset @ X2557))|(~(in @ X2559 @ X2557)|((in @ X2559 @ (setminus @ X2557 @ X2558))|(in @ X2559 @ X2558))))&((~(in @ X2561 @ (powerset @ X2560))|(~(in @ X2562 @ (powerset @ X2560))|(~(in @ X2563 @ X2560)|((in @ X2563 @ X2561)|~(in @ X2563 @ (binintersect @ X2561 @ X2562))))))&((~(in @ X2565 @ (powerset @ X2564))|(~(in @ X2566 @ (powerset @ X2564))|(~(in @ X2567 @ X2564)|((in @ X2567 @ X2566)|~(in @ X2567 @ (binintersect @ X2565 @ X2566))))))&((~(in @ X2569 @ (powerset @ X2568))|(~(in @ X2570 @ (powerset @ X2568))|(~(in @ X2571 @ X2568)|(~(subset @ X2569 @ (setminus @ X2568 @ X2570))|(~(in @ X2571 @ X2570)|~(in @ X2571 @ X2569))))))&((~(in @ X2573 @ (powerset @ X2572))|(~(in @ X2574 @ (powerset @ X2572))|(~(in @ X2575 @ X2572)|(~(subset @ X2573 @ X2574)|((in @ X2575 @ X2574)|~(in @ X2575 @ X2573))))))&((~(in @ X2577 @ (powerset @ X2576))|(~(in @ X2578 @ (powerset @ X2576))|(~(subset @ X2577 @ X2578)|(subset @ (setminus @ X2576 @ X2578) @ (setminus @ X2576 @ X2577)))))&((~(in @ X2580 @ (powerset @ X2579))|(~(in @ X2581 @ (powerset @ X2579))|(~(subset @ (setminus @ X2579 @ X2581) @ (setminus @ X2579 @ X2580))|(subset @ X2580 @ X2581))))&((~(in @ X2583 @ (powerset @ X2582))|(~(in @ X2584 @ X2582)|(~(in @ X2584 @ X2583)|(in @ X2584 @ (setminus @ X2582 @ (setminus @ X2582 @ X2583))))))&((~(in @ X2586 @ (powerset @ X2585))|(~(in @ X2587 @ X2585)|(~(in @ X2587 @ (setminus @ X2585 @ (setminus @ X2585 @ X2586)))|(in @ X2587 @ X2586))))&((~(in @ X2589 @ (powerset @ X2588))|(subset @ X2589 @ (setminus @ X2588 @ (setminus @ X2588 @ X2589))))&((~(in @ X2591 @ (powerset @ X2590))|(subset @ (setminus @ X2590 @ (setminus @ X2590 @ X2591)) @ X2591))&((~(in @ X2593 @ (powerset @ X2592))|((X2593)=(setminus @ X2592 @ (setminus @ X2592 @ X2593))))&((~(in @ X2595 @ (powerset @ X2594))|(~(in @ X2596 @ (powerset @ X2594))|(~(in @ X2597 @ X2594)|(~(in @ X2597 @ (setminus @ X2594 @ X2595))|~(in @ X2597 @ (binintersect @ X2595 @ X2596))))))&((~(in @ X2599 @ (powerset @ X2598))|(~(in @ X2600 @ (powerset @ X2598))|(~(in @ X2601 @ X2598)|(~(in @ X2601 @ (setminus @ X2598 @ X2599))|(in @ X2601 @ (setminus @ X2598 @ (binintersect @ X2599 @ X2600)))))))&((~(in @ X2603 @ (powerset @ X2602))|(~(in @ X2604 @ (powerset @ X2602))|(subset @ (setminus @ X2602 @ X2603) @ (setminus @ X2602 @ (binintersect @ X2603 @ X2604)))))&((~(in @ X2606 @ (powerset @ X2605))|(~(in @ X2607 @ (powerset @ X2605))|(in @ (setminus @ X2605 @ X2606) @ (powerset @ (setminus @ X2605 @ (binintersect @ X2606 @ X2607))))))&((~(in @ X2609 @ (powerset @ X2608))|(~(in @ X2610 @ (powerset @ X2608))|(~(subset @ X2609 @ (setminus @ X2608 @ X2610))|(~(in @ X2611 @ X2608)|(~(in @ X2611 @ X2610)|(in @ X2611 @ (setminus @ X2608 @ X2609)))))))&((~(in @ X2613 @ (powerset @ X2612))|(~(in @ X2614 @ (powerset @ X2612))|(~(subset @ X2613 @ (setminus @ X2612 @ X2614))|(subset @ X2614 @ (setminus @ X2612 @ X2613)))))&((~(in @ X2616 @ (powerset @ X2615))|(~(in @ X2617 @ (powerset @ X2615))|(~(in @ X2618 @ X2615)|((in @ X2618 @ (binunion @ X2616 @ X2617))|~(in @ X2618 @ X2616)))))&((~(in @ X2620 @ (powerset @ X2619))|(~(in @ X2621 @ (powerset @ X2619))|(~(in @ X2622 @ X2619)|((in @ X2622 @ (binunion @ X2620 @ X2621))|~(in @ X2622 @ X2621)))))&((~(in @ X2624 @ (powerset @ X2623))|(~(in @ X2625 @ (powerset @ X2623))|(~(in @ X2626 @ (powerset @ X2623))|(~(in @ X2627 @ X2623)|(~(in @ X2627 @ (binintersect @ X2624 @ X2625))|(in @ X2627 @ (binunion @ X2624 @ X2626)))))))&((~(in @ X2629 @ (powerset @ X2628))|(~(in @ X2630 @ (powerset @ X2628))|(~(in @ X2631 @ (powerset @ X2628))|(~(in @ X2632 @ X2628)|(~(in @ X2632 @ (binintersect @ X2629 @ X2630))|(in @ X2632 @ (binunion @ X2630 @ X2631)))))))&((~(in @ X2634 @ (powerset @ X2633))|(~(in @ X2635 @ (powerset @ X2633))|(~(in @ X2636 @ (powerset @ X2633))|(~(in @ X2637 @ X2633)|(~(in @ X2637 @ (binintersect @ X2634 @ X2635))|(in @ X2637 @ (binintersect @ (binunion @ X2634 @ X2636) @ (binunion @ X2635 @ X2636))))))))&((~(in @ X2639 @ (powerset @ X2638))|(~(in @ X2640 @ (powerset @ X2638))|(~(in @ X2641 @ (powerset @ X2638))|(in @ (binintersect @ X2639 @ X2640) @ (powerset @ (binintersect @ (binunion @ X2639 @ X2641) @ (binunion @ X2640 @ X2641)))))))&((~(in @ X2643 @ (powerset @ X2642))|(~(in @ X2644 @ (powerset @ X2642))|(~(in @ X2645 @ X2642)|(~(in @ X2645 @ (setminus @ X2642 @ (binunion @ X2643 @ X2644)))|~(in @ X2645 @ X2643)))))&((~(in @ X2647 @ (powerset @ X2646))|(~(in @ X2648 @ (powerset @ X2646))|(~(in @ X2649 @ X2646)|(~(in @ X2649 @ (setminus @ X2646 @ (binunion @ X2647 @ X2648)))|(in @ X2649 @ (setminus @ X2646 @ X2647))))))&(((((in @ X2654 @ X2652)|(X2653)|(in @ X2654 @ X2651)|~(in @ X2654 @ (binunion @ X2651 @ X2652))|~(in @ X2654 @ X2650)|~(in @ X2652 @ (powerset @ X2650))|~(in @ X2651 @ (powerset @ X2650)))&(~(X2653)|(X2653)|(in @ X2654 @ X2651)|~(in @ X2654 @ (binunion @ X2651 @ X2652))|~(in @ X2654 @ X2650)|~(in @ X2652 @ (powerset @ X2650))|~(in @ X2651 @ (powerset @ X2650))))&(((in @ X2654 @ X2652)|(X2653)|~(X2653)|~(in @ X2654 @ (binunion @ X2651 @ X2652))|~(in @ X2654 @ X2650)|~(in @ X2652 @ (powerset @ X2650))|~(in @ X2651 @ (powerset @ X2650)))&(~(X2653)|(X2653)|~(X2653)|~(in @ X2654 @ (binunion @ X2651 @ X2652))|~(in @ X2654 @ X2650)|~(in @ X2652 @ (powerset @ X2650))|~(in @ X2651 @ (powerset @ X2650)))))&((~(in @ X2656 @ (powerset @ X2655))|(~(in @ X2657 @ (powerset @ X2655))|(~(in @ X2658 @ X2655)|((in @ X2658 @ X2656)|((in @ X2658 @ X2657)|~(in @ X2658 @ (binunion @ X2656 @ X2657)))))))&((~(in @ X2660 @ (powerset @ X2659))|(~(in @ X2661 @ (powerset @ X2659))|(~(in @ X2662 @ X2659)|(~(in @ X2662 @ (setminus @ X2659 @ (binunion @ X2660 @ X2661)))|(in @ X2662 @ (setminus @ X2659 @ X2660))))))&((~(in @ X2664 @ (powerset @ X2663))|(~(in @ X2665 @ (powerset @ X2663))|(in @ (setminus @ X2663 @ (binunion @ X2664 @ X2665)) @ (powerset @ (setminus @ X2663 @ X2664)))))&((~(in @ X2667 @ (powerset @ X2666))|(~(in @ X2668 @ (powerset @ X2666))|(~(in @ X2669 @ X2666)|(~(in @ X2669 @ (setminus @ X2666 @ (binunion @ X2667 @ X2668)))|(in @ X2669 @ (setminus @ X2666 @ X2668))))))&((~(in @ X2671 @ (powerset @ X2670))|(~(in @ X2672 @ (powerset @ X2670))|(~(in @ X2673 @ X2670)|(~(in @ X2673 @ (setminus @ X2670 @ (binintersect @ X2671 @ X2672)))|(in @ X2673 @ (binunion @ (setminus @ X2670 @ X2671) @ (setminus @ X2670 @ X2672)))))))&((~(in @ X2675 @ (powerset @ X2674))|(~(in @ X2676 @ (powerset @ X2674))|(~(in @ X2677 @ X2674)|(~(in @ X2677 @ (binunion @ (setminus @ X2674 @ X2675) @ (setminus @ X2674 @ X2676)))|(in @ X2677 @ (setminus @ X2674 @ (binintersect @ X2675 @ X2676)))))))&((~(in @ X2679 @ (powerset @ X2678))|(~(in @ X2680 @ (powerset @ X2678))|((setminus @ X2678 @ (binintersect @ X2679 @ X2680))=(binunion @ (setminus @ X2678 @ X2679) @ (setminus @ X2678 @ X2680)))))&((~(in @ X2682 @ (powerset @ X2681))|(~(in @ X2683 @ (powerset @ X2681))|(~(in @ X2684 @ X2681)|(~(in @ X2684 @ (setminus @ X2681 @ (binunion @ X2682 @ X2683)))|(in @ X2684 @ (binintersect @ (setminus @ X2681 @ X2682) @ (setminus @ X2681 @ X2683)))))))&((~(in @ X2686 @ (powerset @ X2685))|(~(in @ X2687 @ (powerset @ X2685))|(~(in @ X2688 @ X2685)|(~(in @ X2688 @ (setminus @ X2685 @ X2686))|(~(in @ X2688 @ (setminus @ X2685 @ X2687))|(in @ X2688 @ (setminus @ X2685 @ (binunion @ X2686 @ X2687))))))))&((~(in @ X2690 @ (powerset @ X2689))|(~(in @ X2691 @ (powerset @ X2689))|(~(in @ X2692 @ X2689)|(~(in @ X2692 @ (binintersect @ (setminus @ X2689 @ X2690) @ (setminus @ X2689 @ X2691)))|(in @ X2692 @ (setminus @ X2689 @ (binunion @ X2690 @ X2691)))))))&((~(in @ X2694 @ (powerset @ X2693))|(~(in @ X2695 @ (powerset @ X2693))|((setminus @ X2693 @ (binunion @ X2694 @ X2695))=(binintersect @ (setminus @ X2693 @ X2694) @ (setminus @ X2693 @ X2695)))))&((~(in @ X2697 @ (powerset @ X2696))|(~(in @ X2698 @ (powerset @ X2696))|(~(in @ X2699 @ (binintersect @ X2697 @ X2698))|(in @ X2699 @ X2696))))&((~(in @ X2701 @ (powerset @ X2700))|(~(in @ X2702 @ (powerset @ X2700))|(~(in @ X2703 @ (powerset @ X2700))|(~(subset @ X2701 @ X2703)|(subset @ (binintersect @ X2701 @ X2702) @ X2703)))))&((~(in @ X2705 @ (powerset @ X2704))|(~(in @ X2706 @ (powerset @ X2704))|(~(in @ X2707 @ (powerset @ X2704))|(~(subset @ X2706 @ X2707)|(subset @ (binintersect @ X2705 @ X2706) @ X2707)))))&((~(in @ X2709 @ (powerset @ X2708))|(~(in @ X2710 @ (powerset @ X2708))|(~(in @ X2711 @ (powerset @ X2708))|(~(subset @ X2709 @ X2710)|(~(subset @ X2709 @ X2711)|(subset @ X2709 @ (binintersect @ X2710 @ X2711)))))))&((~(in @ X2713 @ (powerset @ X2712))|(~(in @ X2714 @ (powerset @ X2712))|(~(in @ X2715 @ (powerset @ X2712))|(~(in @ X2716 @ (powerset @ X2712))|(~(subset @ X2713 @ X2715)|(~(subset @ X2714 @ X2716)|(subset @ (binintersect @ X2713 @ X2714) @ (binintersect @ X2715 @ X2716))))))))&((~(in @ X2718 @ (powerset @ X2717))|(~(in @ X2719 @ (powerset @ X2717))|(in @ (setminus @ X2717 @ X2718) @ (powerset @ (setminus @ X2717 @ (binintersect @ X2718 @ X2719))))))&((in @ esk72_0 @ (powerset @ esk71_0))&((in @ esk73_0 @ (powerset @ esk71_0))&((in @ esk74_0 @ (powerset @ esk71_0))&((in @ esk75_0 @ (powerset @ esk71_0))&((setminus @ esk71_0 @ (binintersect @ (binunion @ esk72_0 @ esk73_0) @ (binunion @ esk74_0 @ esk75_0)))!=(binunion @ (binintersect @ (setminus @ esk71_0 @ esk72_0) @ (setminus @ esk71_0 @ esk73_0)) @ (binintersect @ (setminus @ esk71_0 @ esk74_0) @ (setminus @ esk71_0 @ esk75_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_332])])])])])])])).
2.09/1.10	thf(c_0_334, negated_conjecture, ((setminus @ esk71_0 @ (binintersect @ (binunion @ esk72_0 @ esk73_0) @ (binunion @ esk74_0 @ esk75_0)))!=(binunion @ (binintersect @ (setminus @ esk71_0 @ esk72_0) @ (setminus @ esk71_0 @ esk73_0)) @ (binintersect @ (setminus @ esk71_0 @ esk74_0) @ (setminus @ esk71_0 @ esk75_0)))), inference(split_conjunct,[status(thm)],[c_0_333])).
2.09/1.10	thf(c_0_335, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:((((setminus @ X3 @ (binunion @ X2 @ X4))=(binintersect @ (setminus @ X3 @ X2) @ (setminus @ X3 @ X4)))|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_333])).
2.09/1.10	thf(c_0_336, negated_conjecture, (in @ esk75_0 @ (powerset @ esk71_0)), inference(split_conjunct,[status(thm)],[c_0_333])).
2.09/1.10	thf(c_0_337, negated_conjecture, (in @ esk74_0 @ (powerset @ esk71_0)), inference(split_conjunct,[status(thm)],[c_0_333])).
2.09/1.10	thf(c_0_338, negated_conjecture, ((binunion @ (binintersect @ (setminus @ esk71_0 @ esk72_0) @ (setminus @ esk71_0 @ esk73_0)) @ (setminus @ esk71_0 @ (binunion @ esk74_0 @ esk75_0)))!=(setminus @ esk71_0 @ (binintersect @ (binunion @ esk72_0 @ esk73_0) @ (binunion @ esk74_0 @ esk75_0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_334, c_0_335]), c_0_336]), c_0_337])])).
2.09/1.10	thf(c_0_339, negated_conjecture, (in @ esk73_0 @ (powerset @ esk71_0)), inference(split_conjunct,[status(thm)],[c_0_333])).
2.09/1.10	thf(c_0_340, negated_conjecture, (in @ esk72_0 @ (powerset @ esk71_0)), inference(split_conjunct,[status(thm)],[c_0_333])).
2.09/1.10	thf(c_0_341, negated_conjecture, ((binunion @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0)) @ (setminus @ esk71_0 @ (binunion @ esk74_0 @ esk75_0)))!=(setminus @ esk71_0 @ (binintersect @ (binunion @ esk72_0 @ esk73_0) @ (binunion @ esk74_0 @ esk75_0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_338, c_0_335]), c_0_339]), c_0_340])])).
2.09/1.10	thf(c_0_342, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:((((setminus @ X3 @ (binintersect @ X2 @ X4))=(binunion @ (setminus @ X3 @ X2) @ (setminus @ X3 @ X4)))|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_333])).
2.09/1.10	thf(c_0_343, negated_conjecture, (~((in @ (binunion @ esk74_0 @ esk75_0) @ (powerset @ esk71_0)))|~((in @ (binunion @ esk72_0 @ esk73_0) @ (powerset @ esk71_0)))), inference(spm,[status(thm)],[c_0_341, c_0_342])).
2.09/1.10	thf(c_0_344, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ (binunion @ X2 @ X4) @ (powerset @ X3))|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_333])).
2.09/1.10	thf(c_0_345, negated_conjecture, ~((in @ (binunion @ esk72_0 @ esk73_0) @ (powerset @ esk71_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_343, c_0_344]), c_0_336]), c_0_337])])).
2.09/1.10	thf(c_0_346, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_345, c_0_344]), c_0_339]), c_0_340])]), ['proof']).
2.09/1.10	# SZS output end CNFRefutation
2.09/1.10	# Parsed axioms                        : 603
2.09/1.10	# Removed by relevancy pruning/SinE    : 323
2.09/1.10	# Initial clauses                      : 445
2.09/1.10	# Removed in clause preprocessing      : 37
2.09/1.10	# Initial clauses in saturation        : 408
2.09/1.10	# Processed clauses                    : 1112
2.09/1.10	# ...of these trivial                  : 16
2.09/1.10	# ...subsumed                          : 161
2.09/1.10	# ...remaining for further processing  : 935
2.09/1.10	# Other redundant clauses eliminated   : 62
2.09/1.10	# Clauses deleted for lack of memory   : 0
2.09/1.10	# Backward-subsumed                    : 6
2.09/1.10	# Backward-rewritten                   : 5
2.09/1.10	# Generated clauses                    : 13452
2.09/1.10	# ...of the previous two non-redundant : 13094
2.09/1.10	# ...aggressively subsumed             : 0
2.09/1.10	# Contextual simplify-reflections      : 14
2.09/1.10	# Paramodulations                      : 13355
2.09/1.10	# Factorizations                       : 2
2.09/1.10	# NegExts                              : 0
2.09/1.10	# Equation resolutions                 : 69
2.09/1.10	# Disequality decompositions           : 0
2.09/1.10	# Total rewrite steps                  : 393
2.09/1.10	# ...of those cached                   : 294
2.09/1.10	# Propositional unsat checks           : 0
2.09/1.10	#    Propositional check models        : 0
2.09/1.10	#    Propositional check unsatisfiable : 0
2.09/1.10	#    Propositional clauses             : 0
2.09/1.10	#    Propositional clauses after purity: 0
2.09/1.10	#    Propositional unsat core size     : 0
2.09/1.10	#    Propositional preprocessing time  : 0.000
2.09/1.10	#    Propositional encoding time       : 0.000
2.09/1.10	#    Propositional solver time         : 0.000
2.09/1.10	#    Success case prop preproc time    : 0.000
2.09/1.10	#    Success case prop encoding time   : 0.000
2.09/1.10	#    Success case prop solver time     : 0.000
2.09/1.10	# Current number of processed clauses  : 554
2.09/1.10	#    Positive orientable unit clauses  : 53
2.09/1.10	#    Positive unorientable unit clauses: 0
2.09/1.10	#    Negative unit clauses             : 32
2.09/1.10	#    Non-unit-clauses                  : 469
2.09/1.10	# Current number of unprocessed clauses: 12590
2.09/1.10	# ...number of literals in the above   : 51833
2.09/1.10	# Current number of archived formulas  : 0
2.09/1.10	# Current number of archived clauses   : 365
2.09/1.10	# Clause-clause subsumption calls (NU) : 94786
2.09/1.10	# Rec. Clause-clause subsumption calls : 44202
2.09/1.10	# Non-unit clause-clause subsumptions  : 144
2.09/1.10	# Unit Clause-clause subsumption calls : 3550
2.09/1.10	# Rewrite failures with RHS unbound    : 0
2.09/1.10	# BW rewrite match attempts            : 41
2.09/1.10	# BW rewrite match successes           : 4
2.09/1.10	# Condensation attempts                : 0
2.09/1.10	# Condensation successes               : 0
2.09/1.10	# Termbank termtop insertions          : 309577
2.09/1.10	# Search garbage collected termcells   : 28827
2.09/1.10	
2.09/1.10	# -------------------------------------------------
2.09/1.10	# User time                : 0.472 s
2.09/1.10	# System time              : 0.037 s
2.09/1.10	# Total time               : 0.508 s
2.09/1.10	# Maximum resident set size: 9016 pages
2.09/1.10	
2.09/1.10	# -------------------------------------------------
2.09/1.10	# User time                : 0.488 s
2.09/1.10	# System time              : 0.041 s
2.09/1.10	# Total time               : 0.530 s
2.09/1.10	# Maximum resident set size: 2764 pages
2.09/1.10	% E exiting
2.09/1.10	% E exiting
2.09/1.10	EOF