0.01/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.01/0.11	% Command    : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM
0.09/0.32	% Computer : n020.cluster.edu
0.09/0.32	% Model    : x86_64 x86_64
0.09/0.32	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.09/0.32	% Memory   : 8042.1875MB
0.09/0.32	% OS       : Linux 3.10.0-693.el7.x86_64
0.09/0.32	% CPULimit   : 1920
0.09/0.32	% WCLimit    : 240
0.09/0.32	% DateTime   : Wed Jul 30 02:24:19 EDT 2025
0.09/0.32	% CPUTime    : 
0.16/0.45	Running higher-order theorem proving
0.16/0.51	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.N6TN1y9XWN/E---3.1_29775.p
1.29/1.02	# Version: 3.0.0-ho
1.29/1.02	# Preprocessing class: HSLMSLSSLLLCHSA.
1.29/1.02	# Scheduled 5 strats onto 8 cores with 240 seconds (1920 total)
1.29/1.02	# Starting ho_unfolding_5 with 960s (4) cores
1.29/1.02	# Starting pre_casc_3 with 240s (1) cores
1.29/1.02	# Starting new_ho_10_cnf2 with 240s (1) cores
1.29/1.02	# Starting full_lambda_10 with 240s (1) cores
1.29/1.02	# Starting ehoh_best_nonlift_rwall with 240s (1) cores
1.29/1.02	# ho_unfolding_5 with pid 29853 completed with status 0
1.29/1.02	# Result found by ho_unfolding_5
1.29/1.02	# Preprocessing class: HSLMSLSSLLLCHSA.
1.29/1.02	# Scheduled 5 strats onto 8 cores with 240 seconds (1920 total)
1.29/1.02	# Starting ho_unfolding_5 with 960s (4) cores
1.29/1.02	# No SInE strategy applied
1.29/1.02	# Search class: HGHSM-FSLM32-MHSMMSBN
1.29/1.02	# Scheduled 12 strats onto 4 cores with 960 seconds (960 total)
1.29/1.02	# Starting full_lambda_5 with 79s (1) cores
1.29/1.02	# Starting ho_unfolding_5 with 97s (1) cores
1.29/1.02	# Starting pre_casc_4 with 79s (1) cores
1.29/1.02	# Starting pre_casc_3 with 79s (1) cores
1.29/1.02	# ho_unfolding_5 with pid 29863 completed with status 0
1.29/1.02	# Result found by ho_unfolding_5
1.29/1.02	# Preprocessing class: HSLMSLSSLLLCHSA.
1.29/1.02	# Scheduled 5 strats onto 8 cores with 240 seconds (1920 total)
1.29/1.02	# Starting ho_unfolding_5 with 960s (4) cores
1.29/1.02	# No SInE strategy applied
1.29/1.02	# Search class: HGHSM-FSLM32-MHSMMSBN
1.29/1.02	# Scheduled 12 strats onto 4 cores with 960 seconds (960 total)
1.29/1.02	# Starting full_lambda_5 with 79s (1) cores
1.29/1.02	# Starting ho_unfolding_5 with 97s (1) cores
1.29/1.02	# Preprocessing time       : 0.009 s
1.29/1.02	# Presaturation interreduction done
1.29/1.02	
1.29/1.02	# Proof found!
1.29/1.02	# SZS status Theorem
1.29/1.02	# SZS output start CNFRefutation
1.29/1.02	thf(decl_23, type, in: $i > $i > $o).
1.29/1.02	thf(decl_24, type, exu: ($i > $o) > $o).
1.29/1.02	thf(decl_25, type, setextAx: $o).
1.29/1.02	thf(decl_26, type, emptyset: $i).
1.29/1.02	thf(decl_27, type, emptysetAx: $o).
1.29/1.02	thf(decl_28, type, setadjoin: $i > $i > $i).
1.29/1.02	thf(decl_29, type, setadjoinAx: $o).
1.29/1.02	thf(decl_30, type, powerset: $i > $i).
1.29/1.02	thf(decl_31, type, powersetAx: $o).
1.29/1.02	thf(decl_32, type, setunion: $i > $i).
1.29/1.02	thf(decl_33, type, setunionAx: $o).
1.29/1.02	thf(decl_34, type, omega: $i).
1.29/1.02	thf(decl_35, type, omega0Ax: $o).
1.29/1.02	thf(decl_36, type, omegaSAx: $o).
1.29/1.02	thf(decl_37, type, omegaIndAx: $o).
1.29/1.02	thf(decl_38, type, replAx: $o).
1.29/1.02	thf(decl_39, type, foundationAx: $o).
1.29/1.02	thf(decl_40, type, wellorderingAx: $o).
1.29/1.02	thf(decl_41, type, descr: ($i > $o) > $i).
1.29/1.02	thf(decl_42, type, descrp: $o).
1.29/1.02	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
1.29/1.02	thf(decl_44, type, dsetconstrI: $o).
1.29/1.02	thf(decl_45, type, dsetconstrEL: $o).
1.29/1.02	thf(decl_46, type, dsetconstrER: $o).
1.29/1.02	thf(decl_47, type, exuE1: $o).
1.29/1.02	thf(decl_48, type, prop2set: $o > $i).
1.29/1.02	thf(decl_49, type, prop2setE: $o).
1.29/1.02	thf(decl_50, type, emptysetE: $o).
1.29/1.02	thf(decl_51, type, emptysetimpfalse: $o).
1.29/1.02	thf(decl_52, type, notinemptyset: $o).
1.29/1.02	thf(decl_53, type, exuE3e: $o).
1.29/1.02	thf(decl_54, type, setext: $o).
1.29/1.02	thf(decl_55, type, emptyI: $o).
1.29/1.02	thf(decl_56, type, noeltsimpempty: $o).
1.29/1.02	thf(decl_57, type, setbeta: $o).
1.29/1.02	thf(decl_58, type, nonempty: $i > $o).
1.29/1.02	thf(decl_59, type, nonemptyE1: $o).
1.29/1.02	thf(decl_60, type, nonemptyI: $o).
1.29/1.02	thf(decl_61, type, nonemptyI1: $o).
1.29/1.02	thf(decl_62, type, setadjoinIL: $o).
1.29/1.02	thf(decl_63, type, emptyinunitempty: $o).
1.29/1.02	thf(decl_64, type, setadjoinIR: $o).
1.29/1.02	thf(decl_65, type, setadjoinE: $o).
1.29/1.02	thf(decl_66, type, setadjoinOr: $o).
1.29/1.02	thf(decl_67, type, setoftrueEq: $o).
1.29/1.02	thf(decl_68, type, powersetI: $o).
1.29/1.02	thf(decl_69, type, emptyinPowerset: $o).
1.29/1.02	thf(decl_70, type, emptyInPowerset: $o).
1.29/1.02	thf(decl_71, type, powersetE: $o).
1.29/1.02	thf(decl_72, type, setunionI: $o).
1.29/1.02	thf(decl_73, type, setunionE: $o).
1.29/1.02	thf(decl_74, type, subPowSU: $o).
1.29/1.02	thf(decl_75, type, exuE2: $o).
1.29/1.02	thf(decl_76, type, nonemptyImpWitness: $o).
1.29/1.02	thf(decl_77, type, uniqinunit: $o).
1.29/1.02	thf(decl_78, type, notinsingleton: $o).
1.29/1.02	thf(decl_79, type, eqinunit: $o).
1.29/1.02	thf(decl_80, type, singletonsswitch: $o).
1.29/1.02	thf(decl_81, type, upairsetE: $o).
1.29/1.02	thf(decl_82, type, upairsetIL: $o).
1.29/1.02	thf(decl_83, type, upairsetIR: $o).
1.29/1.02	thf(decl_84, type, emptyE1: $o).
1.29/1.02	thf(decl_85, type, vacuousDall: $o).
1.29/1.02	thf(decl_86, type, quantDeMorgan1: $o).
1.29/1.02	thf(decl_87, type, quantDeMorgan2: $o).
1.29/1.02	thf(decl_88, type, quantDeMorgan3: $o).
1.29/1.02	thf(decl_89, type, quantDeMorgan4: $o).
1.29/1.02	thf(decl_90, type, prop2setI: $o).
1.29/1.02	thf(decl_91, type, set2prop: $i > $o).
1.29/1.02	thf(decl_92, type, prop2set2propI: $o).
1.29/1.02	thf(decl_93, type, notdexE: $o).
1.29/1.02	thf(decl_94, type, notdallE: $o).
1.29/1.02	thf(decl_95, type, exuI1: $o).
1.29/1.02	thf(decl_96, type, exuI3: $o).
1.29/1.02	thf(decl_97, type, exuI2: $o).
1.29/1.02	thf(decl_98, type, inCongP: $o).
1.29/1.02	thf(decl_99, type, in__Cong: $o).
1.29/1.02	thf(decl_100, type, exuE3u: $o).
1.29/1.02	thf(decl_101, type, exu__Cong: $o).
1.29/1.02	thf(decl_102, type, emptyset__Cong: $o).
1.29/1.02	thf(decl_103, type, setadjoin__Cong: $o).
1.29/1.02	thf(decl_104, type, powerset__Cong: $o).
1.29/1.02	thf(decl_105, type, setunion__Cong: $o).
1.29/1.02	thf(decl_106, type, omega__Cong: $o).
1.29/1.02	thf(decl_107, type, exuEu: $o).
1.29/1.02	thf(decl_108, type, descr__Cong: $o).
1.29/1.02	thf(decl_109, type, dsetconstr__Cong: $o).
1.29/1.02	thf(decl_110, type, subset: $i > $i > $o).
1.29/1.02	thf(decl_113, type, subsetI1: $o).
1.29/1.02	thf(decl_114, type, eqimpsubset2: $o).
1.29/1.02	thf(decl_115, type, eqimpsubset1: $o).
1.29/1.02	thf(decl_116, type, subsetI2: $o).
1.29/1.02	thf(decl_117, type, emptysetsubset: $o).
1.29/1.02	thf(decl_118, type, subsetE: $o).
1.29/1.02	thf(decl_119, type, subsetE2: $o).
1.29/1.02	thf(decl_120, type, notsubsetI: $o).
1.29/1.02	thf(decl_121, type, notequalI1: $o).
1.29/1.02	thf(decl_122, type, notequalI2: $o).
1.29/1.02	thf(decl_123, type, subsetRefl: $o).
1.29/1.02	thf(decl_124, type, subsetTrans: $o).
1.29/1.02	thf(decl_125, type, setadjoinSub: $o).
1.29/1.02	thf(decl_126, type, setadjoinSub2: $o).
1.29/1.02	thf(decl_127, type, subset2powerset: $o).
1.29/1.02	thf(decl_128, type, setextsub: $o).
1.29/1.02	thf(decl_129, type, subsetemptysetimpeq: $o).
1.29/1.02	thf(decl_130, type, powersetI1: $o).
1.29/1.02	thf(decl_131, type, powersetE1: $o).
1.29/1.02	thf(decl_132, type, inPowerset: $o).
1.29/1.02	thf(decl_133, type, powersetsubset: $o).
1.29/1.02	thf(decl_134, type, sepInPowerset: $o).
1.29/1.02	thf(decl_135, type, sepSubset: $o).
1.29/1.02	thf(decl_136, type, binunion: $i > $i > $i).
1.29/1.02	thf(decl_137, type, binunionIL: $o).
1.29/1.02	thf(decl_138, type, upairset2IR: $o).
1.29/1.02	thf(decl_139, type, binunionIR: $o).
1.29/1.02	thf(decl_140, type, binunionEcases: $o).
1.29/1.02	thf(decl_141, type, binunionE: $o).
1.29/1.02	thf(decl_142, type, binunionLsub: $o).
1.29/1.02	thf(decl_143, type, binunionRsub: $o).
1.29/1.02	thf(decl_144, type, binintersect: $i > $i > $i).
1.29/1.02	thf(decl_145, type, binintersectI: $o).
1.29/1.02	thf(decl_146, type, binintersectSubset5: $o).
1.29/1.02	thf(decl_147, type, binintersectEL: $o).
1.29/1.02	thf(decl_148, type, binintersectLsub: $o).
1.29/1.02	thf(decl_149, type, binintersectSubset2: $o).
1.29/1.02	thf(decl_150, type, binintersectSubset3: $o).
1.29/1.02	thf(decl_151, type, binintersectER: $o).
1.29/1.02	thf(decl_152, type, disjointsetsI1: $o).
1.29/1.02	thf(decl_153, type, binintersectRsub: $o).
1.29/1.02	thf(decl_154, type, binintersectSubset4: $o).
1.29/1.02	thf(decl_155, type, binintersectSubset1: $o).
1.29/1.02	thf(decl_156, type, bs114d: $o).
1.29/1.02	thf(decl_158, type, setminus: $i > $i > $i).
1.29/1.02	thf(decl_159, type, setminusI: $o).
1.29/1.02	thf(decl_160, type, setminusEL: $o).
1.29/1.02	thf(decl_161, type, setminusER: $o).
1.29/1.02	thf(decl_162, type, setminusSubset2: $o).
1.29/1.02	thf(decl_163, type, setminusERneg: $o).
1.29/1.02	thf(decl_164, type, setminusELneg: $o).
1.29/1.02	thf(decl_165, type, setminusILneg: $o).
1.29/1.02	thf(decl_166, type, setminusIRneg: $o).
1.29/1.02	thf(decl_167, type, setminusLsub: $o).
1.29/1.02	thf(decl_168, type, setminusSubset1: $o).
1.29/1.02	thf(decl_169, type, symdiff: $i > $i > $i).
1.29/1.02	thf(decl_170, type, symdiffE: $o).
1.29/1.02	thf(decl_171, type, symdiffI1: $o).
1.29/1.02	thf(decl_172, type, symdiffI2: $o).
1.29/1.02	thf(decl_173, type, symdiffIneg1: $o).
1.29/1.02	thf(decl_174, type, symdiffIneg2: $o).
1.29/1.02	thf(decl_175, type, iskpair: $i > $o).
1.29/1.02	thf(decl_176, type, secondinupair: $o).
1.29/1.02	thf(decl_177, type, setukpairIL: $o).
1.29/1.02	thf(decl_178, type, setukpairIR: $o).
1.29/1.02	thf(decl_179, type, kpairiskpair: $o).
1.29/1.02	thf(decl_180, type, kpair: $i > $i > $i).
1.29/1.02	thf(decl_181, type, kpairp: $o).
1.29/1.02	thf(decl_182, type, cartprod: $i > $i > $i).
1.29/1.02	thf(decl_183, type, singletonsubset: $o).
1.29/1.02	thf(decl_184, type, singletoninpowerset: $o).
1.29/1.02	thf(decl_185, type, singletoninpowunion: $o).
1.29/1.02	thf(decl_186, type, upairset2E: $o).
1.29/1.02	thf(decl_187, type, upairsubunion: $o).
1.29/1.02	thf(decl_188, type, upairinpowunion: $o).
1.29/1.02	thf(decl_189, type, ubforcartprodlem1: $o).
1.29/1.02	thf(decl_190, type, ubforcartprodlem2: $o).
1.29/1.02	thf(decl_191, type, ubforcartprodlem3: $o).
1.29/1.02	thf(decl_192, type, cartprodpairin: $o).
1.29/1.02	thf(decl_193, type, cartprodmempair1: $o).
1.29/1.02	thf(decl_194, type, cartprodmempair: $o).
1.29/1.02	thf(decl_195, type, setunionE2: $o).
1.29/1.02	thf(decl_196, type, setunionsingleton1: $o).
1.29/1.02	thf(decl_197, type, setunionsingleton2: $o).
1.29/1.02	thf(decl_198, type, setunionsingleton: $o).
1.29/1.02	thf(decl_199, type, singleton: $i > $o).
1.29/1.02	thf(decl_200, type, singletonprop: $o).
1.29/1.02	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
1.29/1.02	thf(decl_202, type, ex1E1: $o).
1.29/1.02	thf(decl_203, type, ex1I: $o).
1.29/1.02	thf(decl_204, type, ex1I2: $o).
1.29/1.02	thf(decl_205, type, singletonsuniq: $o).
1.29/1.02	thf(decl_210, type, setukpairinjL1: $o).
1.29/1.02	thf(decl_211, type, kfstsingleton: $o).
1.29/1.02	thf(decl_212, type, theprop: $o).
1.29/1.02	thf(decl_213, type, kfst: $i > $i).
1.29/1.02	thf(decl_214, type, kfstpairEq: $o).
1.29/1.02	thf(decl_215, type, cartprodfstin: $o).
1.29/1.02	thf(decl_216, type, setukpairinjL2: $o).
1.29/1.02	thf(decl_217, type, setukpairinjL: $o).
1.29/1.02	thf(decl_218, type, setukpairinjR11: $o).
1.29/1.02	thf(decl_219, type, setukpairinjR12: $o).
1.29/1.02	thf(decl_220, type, setukpairinjR1: $o).
1.29/1.02	thf(decl_221, type, upairequniteq: $o).
1.29/1.02	thf(decl_222, type, setukpairinjR2: $o).
1.29/1.02	thf(decl_223, type, setukpairinjR: $o).
1.29/1.02	thf(decl_224, type, ksndsingleton: $o).
1.29/1.02	thf(decl_225, type, ksnd: $i > $i).
1.29/1.02	thf(decl_226, type, ksndpairEq: $o).
1.29/1.02	thf(decl_227, type, kpairsurjEq: $o).
1.29/1.02	thf(decl_228, type, cartprodsndin: $o).
1.29/1.02	thf(decl_229, type, cartprodpairmemEL: $o).
1.29/1.02	thf(decl_230, type, cartprodpairmemER: $o).
1.29/1.02	thf(decl_231, type, cartprodmempaircEq: $o).
1.29/1.02	thf(decl_232, type, cartprodfstpairEq: $o).
1.29/1.02	thf(decl_233, type, cartprodsndpairEq: $o).
1.29/1.02	thf(decl_234, type, cartprodpairsurjEq: $o).
1.29/1.02	thf(decl_235, type, breln: $i > $i > $i > $o).
1.29/1.02	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
1.29/1.02	thf(decl_237, type, dpsetconstrI: $o).
1.29/1.02	thf(decl_238, type, dpsetconstrSub: $o).
1.29/1.02	thf(decl_239, type, setOfPairsIsBReln: $o).
1.29/1.02	thf(decl_240, type, dpsetconstrERa: $o).
1.29/1.02	thf(decl_241, type, dpsetconstrEL1: $o).
1.29/1.02	thf(decl_242, type, dpsetconstrEL2: $o).
1.29/1.02	thf(decl_243, type, dpsetconstrER: $o).
1.29/1.02	thf(decl_244, type, func: $i > $i > $i > $o).
1.29/1.02	thf(decl_245, type, funcSet: $i > $i > $i).
1.29/1.02	thf(decl_246, type, funcImageSingleton: $o).
1.29/1.02	thf(decl_247, type, apProp: $o).
1.29/1.02	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
1.29/1.02	thf(decl_249, type, app: $o).
1.29/1.02	thf(decl_250, type, infuncsetfunc: $o).
1.29/1.02	thf(decl_251, type, ap2p: $o).
1.29/1.02	thf(decl_252, type, funcinfuncset: $o).
1.29/1.02	thf(decl_253, type, lamProp: $o).
1.29/1.02	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
1.29/1.02	thf(decl_255, type, lamp: $o).
1.29/1.02	thf(decl_256, type, lam2p: $o).
1.29/1.02	thf(decl_257, type, brelnall1: $o).
1.29/1.02	thf(decl_258, type, brelnall2: $o).
1.29/1.02	thf(decl_259, type, ex1E2: $o).
1.29/1.02	thf(decl_260, type, funcGraphProp1: $o).
1.29/1.02	thf(decl_261, type, funcGraphProp3: $o).
1.29/1.02	thf(decl_262, type, funcGraphProp2: $o).
1.29/1.02	thf(decl_263, type, funcextLem: $o).
1.29/1.02	thf(decl_264, type, funcGraphProp4: $o).
1.29/1.02	thf(decl_265, type, subbreln: $o).
1.29/1.02	thf(decl_266, type, eqbreln: $o).
1.29/1.02	thf(decl_267, type, funcext: $o).
1.29/1.02	thf(decl_268, type, funcext2: $o).
1.29/1.02	thf(decl_269, type, ap2apEq1: $o).
1.29/1.02	thf(decl_270, type, ap2apEq2: $o).
1.29/1.02	thf(decl_271, type, beta1: $o).
1.29/1.02	thf(decl_272, type, eta1: $o).
1.29/1.02	thf(decl_273, type, lam2lamEq: $o).
1.29/1.02	thf(decl_274, type, beta2: $o).
1.29/1.02	thf(decl_275, type, eta2: $o).
1.29/1.02	thf(decl_276, type, iffalseProp1: $o).
1.29/1.02	thf(decl_277, type, iffalseProp2: $o).
1.29/1.02	thf(decl_278, type, iftrueProp1: $o).
1.29/1.02	thf(decl_279, type, iftrueProp2: $o).
1.29/1.02	thf(decl_280, type, ifSingleton: $o).
1.29/1.02	thf(decl_281, type, if: $i > $o > $i > $i > $i).
1.29/1.02	thf(decl_282, type, ifp: $o).
1.29/1.02	thf(decl_283, type, theeq: $o).
1.29/1.02	thf(decl_284, type, iftrue: $o).
1.29/1.02	thf(decl_285, type, iffalse: $o).
1.29/1.02	thf(decl_286, type, iftrueorfalse: $o).
1.29/1.02	thf(decl_287, type, binintersectT_lem: $o).
1.29/1.02	thf(decl_288, type, binunionT_lem: $o).
1.29/1.02	thf(decl_289, type, powersetT_lem: $o).
1.29/1.02	thf(decl_290, type, setminusT_lem: $o).
1.29/1.02	thf(decl_291, type, complementT_lem: $o).
1.29/1.02	thf(decl_292, type, setextT: $o).
1.29/1.02	thf(decl_293, type, subsetTI: $o).
1.29/1.02	thf(decl_294, type, powersetTI1: $o).
1.29/1.02	thf(decl_295, type, powersetTE1: $o).
1.29/1.02	thf(decl_296, type, complementTI1: $o).
1.29/1.02	thf(decl_297, type, complementTE1: $o).
1.29/1.02	thf(decl_298, type, binintersectTELcontra: $o).
1.29/1.02	thf(decl_299, type, binintersectTERcontra: $o).
1.29/1.02	thf(decl_300, type, contrasubsetT: $o).
1.29/1.02	thf(decl_301, type, contrasubsetT1: $o).
1.29/1.02	thf(decl_302, type, contrasubsetT2: $o).
1.29/1.02	thf(decl_303, type, contrasubsetT3: $o).
1.29/1.02	thf(decl_304, type, doubleComplementI1: $o).
1.29/1.02	thf(decl_305, type, doubleComplementE1: $o).
1.29/1.02	thf(decl_306, type, doubleComplementSub1: $o).
1.29/1.02	thf(decl_307, type, doubleComplementSub2: $o).
1.29/1.02	thf(decl_308, type, doubleComplementEq: $o).
1.29/1.02	thf(decl_309, type, complementTnotintersectT: $o).
1.29/1.02	thf(decl_310, type, complementImpComplementIntersect: $o).
1.29/1.02	thf(decl_311, type, complementSubsetComplementIntersect: $o).
1.29/1.02	thf(decl_312, type, complementInPowersetComplementIntersect: $o).
1.29/1.02	thf(decl_313, type, contraSubsetComplement: $o).
1.29/1.02	thf(decl_314, type, complementTcontraSubset: $o).
1.29/1.02	thf(decl_315, type, binunionTILcontra: $o).
1.29/1.02	thf(decl_316, type, binunionTIRcontra: $o).
1.29/1.02	thf(decl_317, type, inIntersectImpInUnion: $o).
1.29/1.02	thf(decl_318, type, inIntersectImpInUnion2: $o).
1.29/1.02	thf(decl_319, type, inIntersectImpInIntersectUnions: $o).
1.29/1.02	thf(decl_320, type, intersectInPowersetIntersectUnions: $o).
1.29/1.02	thf(decl_321, type, inComplementUnionImpNotIn1: $o).
1.29/1.02	thf(decl_322, type, inComplementUnionImpInComplement1: $o).
1.29/1.02	thf(decl_323, type, binunionTE: $o).
1.29/1.02	thf(decl_324, type, binunionTEcontra: $o).
1.29/1.02	thf(decl_325, type, demorgan2a1: $o).
1.29/1.02	thf(decl_326, type, complementUnionInPowersetComplement: $o).
1.29/1.02	thf(decl_327, type, demorgan2a2: $o).
1.29/1.02	thf(decl_328, type, demorgan1a: $o).
1.29/1.02	thf(decl_329, type, demorgan1b: $o).
1.29/1.02	thf(decl_330, type, demorgan1: $o).
1.29/1.02	thf(decl_331, type, demorgan2a: $o).
1.29/1.02	thf(decl_332, type, demorgan2b2: $o).
1.29/1.02	thf(decl_333, type, demorgan2b: $o).
1.29/1.02	thf(decl_334, type, demorgan2: $o).
1.29/1.02	thf(decl_335, type, woz13rule0: $o).
1.29/1.02	thf(decl_336, type, woz13rule1: $o).
1.29/1.02	thf(decl_337, type, woz13rule2: $o).
1.29/1.02	thf(decl_338, type, woz13rule3: $o).
1.29/1.02	thf(decl_339, type, woz13rule4: $o).
1.29/1.02	thf(decl_340, type, woz1_1: $o).
1.29/1.02	thf(decl_341, type, woz1_2: $o).
1.29/1.02	thf(decl_342, type, woz1_3: $o).
1.29/1.02	thf(decl_343, type, woz1_4: $o).
1.29/1.02	thf(decl_344, type, woz1_5: $o).
1.29/1.02	thf(decl_345, type, breln1: $i > $i > $o).
1.29/1.02	thf(decl_346, type, epred1_0: $o).
1.29/1.02	thf(decl_347, type, esk1_2: $i > $i > $i).
1.29/1.02	thf(decl_348, type, esk2_2: $i > $i > $i).
1.29/1.02	thf(decl_349, type, esk3_2: $i > $i > $i).
1.29/1.02	thf(decl_350, type, esk4_1: $i > $i).
1.29/1.02	thf(decl_351, type, esk5_2: ($i > $i > $o) > $i > $i).
1.29/1.02	thf(decl_352, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
1.29/1.02	thf(decl_353, type, esk7_2: ($i > $i > $o) > $i > $i).
1.29/1.02	thf(decl_354, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
1.29/1.02	thf(decl_355, type, esk9_1: $i > $i).
1.29/1.02	thf(decl_356, type, esk10_2: ($i > $o) > $i > $i).
1.29/1.02	thf(decl_357, type, esk11_2: ($i > $o) > $i > $i).
1.29/1.02	thf(decl_358, type, esk12_1: ($i > $o) > $i).
1.29/1.02	thf(decl_359, type, esk13_2: ($i > $o) > $i > $i).
1.29/1.02	thf(decl_360, type, esk14_1: ($i > $o) > $i).
1.29/1.02	thf(decl_361, type, esk15_2: $i > $i > $i).
1.29/1.02	thf(decl_362, type, esk16_2: $i > $i > $i).
1.29/1.02	thf(decl_363, type, esk17_1: $i > $i).
1.29/1.02	thf(decl_364, type, esk18_1: $i > $i).
1.29/1.02	thf(decl_365, type, esk19_1: $i > $i).
1.29/1.02	thf(decl_366, type, esk20_2: $i > $i > $i).
1.29/1.02	thf(decl_367, type, esk21_3: $i > $i > $o > $i).
1.29/1.02	thf(decl_368, type, esk22_2: ($i > $o) > $i > $i).
1.29/1.02	thf(decl_369, type, esk23_1: ($i > $o) > $i).
1.29/1.02	thf(decl_370, type, esk24_1: $i > $i).
1.29/1.02	thf(decl_371, type, esk25_2: $i > ($i > $o) > $i).
1.29/1.02	thf(decl_372, type, esk26_2: $i > ($i > $o) > $i).
1.29/1.02	thf(decl_373, type, esk27_2: $i > ($i > $o) > $i).
1.29/1.02	thf(decl_374, type, esk28_2: $i > ($i > $o) > $i).
1.29/1.02	thf(decl_375, type, esk29_2: $i > ($i > $o) > $i).
1.29/1.02	thf(decl_376, type, esk30_2: $i > ($i > $o) > $i).
1.29/1.02	thf(decl_377, type, esk31_2: ($i > $o) > $i > $i).
1.29/1.02	thf(decl_378, type, esk32_1: ($i > $o) > $i).
1.29/1.02	thf(decl_379, type, esk33_1: ($i > $o) > $i).
1.29/1.02	thf(decl_380, type, esk34_1: ($i > $o) > $i).
1.29/1.02	thf(decl_381, type, esk35_1: ($i > $o) > $i).
1.29/1.02	thf(decl_382, type, esk36_2: ($i > $o) > $i > $i).
1.29/1.02	thf(decl_383, type, esk37_1: ($i > $o) > $i).
1.29/1.02	thf(decl_384, type, esk38_2: ($i > $o) > $i > $i).
1.29/1.02	thf(decl_385, type, esk39_2: ($i > $o) > ($i > $o) > $i).
1.29/1.02	thf(decl_386, type, esk40_2: ($i > $o) > ($i > $o) > $i).
1.29/1.02	thf(decl_387, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
1.29/1.02	thf(decl_388, type, esk42_2: ($i > $o) > ($i > $o) > $i).
1.29/1.02	thf(decl_389, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
1.29/1.02	thf(decl_390, type, esk44_2: ($i > $o) > ($i > $o) > $i).
1.29/1.02	thf(decl_391, type, esk45_2: ($i > $o) > $i > $i).
1.29/1.02	thf(decl_392, type, esk46_2: ($i > $o) > ($i > $o) > $i).
1.29/1.02	thf(decl_393, type, esk47_2: ($i > $o) > ($i > $o) > $i).
1.29/1.02	thf(decl_394, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
1.29/1.02	thf(decl_395, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
1.29/1.02	thf(decl_396, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
1.29/1.02	thf(decl_397, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
1.29/1.02	thf(decl_398, type, esk52_2: $i > $i > $i).
1.29/1.02	thf(decl_399, type, esk53_2: $i > $i > $i).
1.29/1.02	thf(decl_400, type, esk54_2: $i > $i > $i).
1.29/1.02	thf(decl_401, type, esk55_3: $i > $i > $i > $i).
1.29/1.02	thf(decl_402, type, esk56_3: $i > $i > $i > $i).
1.29/1.02	thf(decl_403, type, esk57_2: $i > $i > $i).
1.29/1.02	thf(decl_404, type, esk58_2: $i > ($i > $o) > $i).
1.29/1.02	thf(decl_405, type, esk59_2: $i > ($i > $o) > $i).
1.29/1.02	thf(decl_406, type, esk60_2: $i > ($i > $o) > $i).
1.29/1.02	thf(decl_407, type, esk61_3: $i > ($i > $o) > $i > $i).
1.29/1.02	thf(decl_408, type, esk62_2: $i > ($i > $o) > $i).
1.29/1.02	thf(decl_409, type, esk63_2: $i > ($i > $o) > $i).
1.29/1.02	thf(decl_410, type, esk64_3: $i > $i > ($i > $i) > $i).
1.29/1.02	thf(decl_411, type, esk65_3: $i > $i > ($i > $i) > $i).
1.29/1.02	thf(decl_412, type, esk66_3: $i > $i > ($i > $i) > $i).
1.29/1.02	thf(decl_413, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
1.29/1.02	thf(decl_414, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
1.29/1.02	thf(decl_415, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
1.29/1.02	thf(decl_416, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
1.29/1.02	thf(decl_417, type, esk71_4: $i > $i > $i > $i > $i).
1.29/1.02	thf(decl_418, type, esk72_4: $i > $i > $i > $i > $i).
1.29/1.02	thf(decl_419, type, esk73_4: $i > $i > $i > $i > $i).
1.29/1.02	thf(decl_420, type, esk74_4: $i > $i > $i > $i > $i).
1.29/1.02	thf(decl_421, type, esk75_4: $i > $i > $i > $i > $i).
1.29/1.02	thf(decl_422, type, esk76_4: $i > $i > $i > $i > $i).
1.29/1.02	thf(decl_423, type, esk77_4: $i > $i > $i > $i > $i).
1.29/1.02	thf(decl_424, type, esk78_4: $i > $i > $i > $i > $i).
1.29/1.02	thf(decl_425, type, esk79_4: $i > $i > $i > $i > $i).
1.29/1.02	thf(decl_426, type, esk80_3: $i > $i > ($i > $i) > $i).
1.29/1.02	thf(decl_427, type, esk81_3: $i > $i > ($i > $i) > $i).
1.29/1.02	thf(decl_428, type, esk82_3: $i > $i > ($i > $i) > $i).
1.29/1.02	thf(decl_429, type, esk83_3: $i > $i > $i > $i).
1.29/1.02	thf(decl_430, type, esk84_3: $i > $i > $i > $i).
1.29/1.02	thf(decl_431, type, esk85_3: $i > $i > $i > $i).
1.29/1.02	thf(decl_432, type, esk86_3: $i > $i > $i > $i).
1.29/1.02	thf(decl_433, type, esk87_0: $i).
1.29/1.02	thf(decl_434, type, esk88_0: $i).
1.29/1.02	thf(decl_435, type, epred2_0: $i > $o).
1.29/1.02	thf(decl_436, type, esk89_0: $i).
1.29/1.02	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', replAx)).
1.29/1.02	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', exu)).
1.29/1.02	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', descrp)).
1.29/1.02	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', exuE1)).
1.29/1.02	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', exuE3e)).
1.29/1.02	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', nonempty)).
1.29/1.02	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', nonemptyI)).
1.29/1.02	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', exuE2)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', exuI1)).
1.29/1.02	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', exuI3)).
1.29/1.02	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', exuI2)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', exuE3u)).
1.29/1.02	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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', exu__Cong)).
1.29/1.02	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', exuEu)).
1.29/1.02	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', descr__Cong)).
1.29/1.02	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', ex1E1)).
1.29/1.02	thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', ex1)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', ex1I)).
1.29/1.02	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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', ex1I2)).
1.29/1.02	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setOfPairsIsBReln)).
1.29/1.02	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', breln)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', ex1E2)).
1.29/1.02	thf(breln1, axiom, ((breln1)=(^[X4:$i, X33:$i]:((breln @ X4 @ X4 @ X33)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', breln1)).
1.29/1.02	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', dsetconstrI)).
1.29/1.02	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', dsetconstrEL)).
1.29/1.02	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', dsetconstrER)).
1.29/1.02	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setbeta)).
1.29/1.02	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', nonemptyE1)).
1.29/1.02	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', nonemptyI1)).
1.29/1.02	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setoftrueEq)).
1.29/1.02	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', nonemptyImpWitness)).
1.29/1.02	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', emptyE1)).
1.29/1.02	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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', dsetconstr__Cong)).
1.29/1.02	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', sepInPowerset)).
1.29/1.02	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', sepSubset)).
1.29/1.02	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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', singletonprop)).
1.29/1.02	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', kfstsingleton)).
1.29/1.02	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', ksndsingleton)).
1.29/1.02	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', dpsetconstrI)).
1.29/1.02	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', dpsetconstrSub)).
1.29/1.02	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', dpsetconstrERa)).
1.29/1.02	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', dpsetconstrEL1)).
1.29/1.02	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', dpsetconstrEL2)).
1.29/1.02	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', dpsetconstrER)).
1.29/1.02	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', funcImageSingleton)).
1.29/1.02	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', apProp)).
1.29/1.02	thf(lamProp, axiom, ((lamProp)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', lamProp)).
1.29/1.02	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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', lamp)).
1.29/1.02	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', lam2p)).
1.29/1.02	thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', brelnall1)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', brelnall2)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', subbreln)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', eqbreln)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', beta1)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', eta1)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', lam2lamEq)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', beta2)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', eta2)).
1.29/1.02	thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', iffalseProp1)).
1.29/1.02	thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', iffalseProp2)).
1.29/1.02	thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', iftrueProp1)).
1.29/1.02	thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', iftrueProp2)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', ifSingleton)).
1.29/1.02	thf(breln1all2, conjecture, ((((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((((omegaIndAx)=>(((((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((((prop2setE)=>((emptysetE)=>(((((setext)=>((((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>(((emptyinunitempty)=>((setadjoinIR)=>((((((emptyinPowerset)=>((emptyInPowerset)=>((((((exuE2)=>((nonemptyImpWitness)=>(((notinsingleton)=>(((singletonsswitch)=>(((upairsetIL)=>(((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>(((((prop2setI)=>(((notdexE)=>((notdallE)=>((((exuI2)=>(((((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>(((((exuEu)=>((((subsetI1)=>(((((emptysetsubset)=>((((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>(((setadjoinSub)=>((setadjoinSub2)=>(((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((((((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>(((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>(((binintersectSubset1)=>((bs114d)=>((((((setminusERneg)=>((setminusELneg)=>((((((symdiffE)=>(((((symdiffIneg2)=>((secondinupair)=>(((((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>(((upairset2E)=>((((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>(((cartprodmempair1)=>((cartprodmempair)=>((((setunionsingleton2)=>((setunionsingleton)=>(((ex1E1)=>(((ex1I2)=>((((kfstsingleton)=>(((((setukpairinjL2)=>(((setukpairinjR11)=>((((upairequniteq)=>(((setukpairinjR)=>((ksndsingleton)=>(((((cartprodpairmemEL)=>((cartprodpairmemER)=>((((cartprodsndpairEq)=>(((dpsetconstrI)=>((((((dpsetconstrEL2)=>(((funcImageSingleton)=>(((((ap2p)=>((((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((((((((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>(((lam2lamEq)=>((beta2)=>(((((iftrueProp1)=>((((ifp)=>(((iftrue)=>((((((powersetT_lem)=>(((((subsetTI)=>(((powersetTE1)=>((((binintersectTELcontra)=>(((contrasubsetT)=>(((contrasubsetT2)=>(((doubleComplementI1)=>(((((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>(((complementInPowersetComplementIntersect)=>(((complementTcontraSubset)=>(((((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>(((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((((demorgan2a1)=>((((demorgan1a)=>((((((demorgan2b)=>((demorgan2)=>(((((woz13rule3)=>((woz13rule4)=>(((((![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((X1 @ X2)<=(in @ X2 @ X33)))))))<=(woz1_5))<=(woz1_4))<=(woz1_3))<=(woz1_2))<=(woz1_1))))<=(woz13rule2))<=(woz13rule1))<=(woz13rule0))))<=(demorgan2b2))<=(demorgan2a))<=(demorgan1))<=(demorgan1b)))<=(demorgan2a2))<=(complementUnionInPowersetComplement)))<=(binunionTEcontra))<=(binunionTE))))<=(intersectInPowersetIntersectUnions))))<=(inIntersectImpInUnion))<=(binunionTIRcontra))<=(binunionTILcontra)))<=(contraSubsetComplement)))<=(complementSubsetComplementIntersect)))))<=(doubleComplementSub2))<=(doubleComplementSub1))<=(doubleComplementE1)))<=(contrasubsetT3)))<=(contrasubsetT1)))<=(binintersectTERcontra)))<=(complementTE1))<=(complementTI1)))<=(powersetTI1)))<=(setextT))<=(complementT_lem))<=(setminusT_lem)))<=(binunionT_lem))<=(binintersectT_lem))<=(iftrueorfalse))<=(iffalse)))<=(theeq)))<=(ifSingleton))<=(iftrueProp2)))<=(iffalseProp2))<=(iffalseProp1))<=(eta2))))<=(eta1)))))))<=(eqbreln))<=(subbreln))<=(funcGraphProp4))<=(funcextLem))<=(funcGraphProp2))<=(funcGraphProp3))))))))<=(lamProp))<=(funcinfuncset)))<=(infuncsetfunc))<=(app))<=(apProp)))<=(dpsetconstrER)))<=(dpsetconstrEL1))<=(dpsetconstrERa))<=(setOfPairsIsBReln))<=(dpsetconstrSub)))<=(cartprodpairsurjEq)))<=(cartprodfstpairEq))<=(cartprodmempaircEq))))<=(cartprodsndin))<=(kpairsurjEq))<=(ksndpairEq))))<=(setukpairinjR2)))<=(setukpairinjR1))<=(setukpairinjR12)))<=(setukpairinjL)))<=(cartprodfstin))<=(kfstpairEq))<=(theprop)))<=(setukpairinjL1))<=(singletonsuniq)))<=(ex1I)))<=(singletonprop))))<=(setunionsingleton1))<=(setunionE2))))<=(cartprodpairin)))))<=(upairinpowunion))<=(upairsubunion)))<=(singletoninpowunion)))))<=(kpairiskpair))<=(setukpairIR))<=(setukpairIL))))<=(symdiffIneg1))<=(symdiffI2))<=(symdiffI1)))<=(setminusSubset1))<=(setminusLsub))<=(setminusIRneg))<=(setminusILneg))))<=(setminusSubset2))<=(setminusER))<=(setminusEL))<=(setminusI))))<=(binintersectSubset4)))))))))<=(binintersectSubset5))))))))<=(upairset2IR))<=(binunionIL))<=(sepSubset))<=(sepInPowerset))))))))<=(subset2powerset))))<=(subsetTrans))))))<=(subsetE2))<=(subsetE)))<=(subsetI2))<=(eqimpsubset1))<=(eqimpsubset2)))<=(dsetconstr__Cong))<=(descr__Cong)))<=(omega__Cong))<=(setunion__Cong))<=(powerset__Cong)))))<=(exuE3u))<=(in__Cong))<=(inCongP)))<=(exuI3))<=(exuI1))))<=(prop2set2propI)))<=(quantDeMorgan4))<=(quantDeMorgan3))<=(quantDeMorgan2)))))<=(upairsetIR)))<=(upairsetE)))<=(eqinunit)))<=(uniqinunit))))<=(subPowSU))<=(setunionE))<=(setunionI))<=(powersetE))))<=(powersetI))<=(setoftrueEq))<=(setadjoinOr))<=(setadjoinE))))<=(setadjoinIL))))))<=(noeltsimpempty))<=(emptyI)))<=(exuE3e))<=(notinemptyset))<=(emptysetimpfalse))))<=(exuE1))<=(dsetconstrER)))))<=(wellorderingAx))<=(foundationAx))<=(replAx)))<=(omegaSAx))<=(omega0Ax)))))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', breln1all2)).
1.29/1.02	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setextAx)).
1.29/1.02	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', emptysetAx)).
1.29/1.02	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setadjoinAx)).
1.29/1.02	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', powersetAx)).
1.29/1.02	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setunionAx)).
1.29/1.02	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', omega0Ax)).
1.29/1.02	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', omegaSAx)).
1.29/1.02	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', omegaIndAx)).
1.29/1.02	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', foundationAx)).
1.29/1.02	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', wellorderingAx)).
1.29/1.02	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', prop2setE)).
1.29/1.02	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', emptysetE)).
1.29/1.02	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', emptysetimpfalse)).
1.29/1.02	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', notinemptyset)).
1.29/1.02	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setext)).
1.29/1.02	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', emptyI)).
1.29/1.02	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', noeltsimpempty)).
1.29/1.02	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setadjoinIL)).
1.29/1.02	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', emptyinunitempty)).
1.29/1.02	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setadjoinIR)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', setadjoinE)).
1.29/1.02	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setadjoinOr)).
1.29/1.02	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', powersetI)).
1.29/1.02	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', emptyinPowerset)).
1.29/1.02	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', emptyInPowerset)).
1.29/1.02	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', powersetE)).
1.29/1.02	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setunionI)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', setunionE)).
1.29/1.02	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', subPowSU)).
1.29/1.02	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', uniqinunit)).
1.29/1.02	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', notinsingleton)).
1.29/1.02	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', eqinunit)).
1.29/1.02	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', singletonsswitch)).
1.29/1.02	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', upairsetE)).
1.29/1.02	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', upairsetIL)).
1.29/1.02	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', upairsetIR)).
1.29/1.02	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', vacuousDall)).
1.29/1.02	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', quantDeMorgan1)).
1.29/1.02	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', quantDeMorgan2)).
1.29/1.02	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', quantDeMorgan3)).
1.29/1.02	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', quantDeMorgan4)).
1.29/1.02	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', prop2setI)).
1.29/1.02	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', prop2set2propI)).
1.29/1.02	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', notdexE)).
1.29/1.02	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', notdallE)).
1.29/1.02	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', inCongP)).
1.29/1.02	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', in__Cong)).
1.29/1.02	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', emptyset__Cong)).
1.29/1.02	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setadjoin__Cong)).
1.29/1.02	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', powerset__Cong)).
1.29/1.02	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setunion__Cong)).
1.29/1.02	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', omega__Cong)).
1.29/1.02	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', subsetI1)).
1.29/1.02	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', eqimpsubset2)).
1.29/1.02	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', eqimpsubset1)).
1.29/1.02	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', subsetI2)).
1.29/1.02	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', emptysetsubset)).
1.29/1.02	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', subsetE)).
1.29/1.02	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', subsetE2)).
1.29/1.02	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', notsubsetI)).
1.29/1.02	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', notequalI1)).
1.29/1.02	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', notequalI2)).
1.29/1.02	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', subsetRefl)).
1.29/1.02	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', subsetTrans)).
1.29/1.02	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setadjoinSub)).
1.29/1.02	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setadjoinSub2)).
1.29/1.02	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', subset2powerset)).
1.29/1.02	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setextsub)).
1.29/1.02	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', subsetemptysetimpeq)).
1.29/1.02	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', powersetI1)).
1.29/1.02	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', powersetE1)).
1.29/1.02	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', inPowerset)).
1.29/1.02	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', powersetsubset)).
1.29/1.02	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binunionIL)).
1.29/1.02	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', upairset2IR)).
1.29/1.02	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binunionIR)).
1.29/1.02	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binunionEcases)).
1.29/1.02	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binunionE)).
1.29/1.02	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binunionLsub)).
1.29/1.02	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binunionRsub)).
1.29/1.02	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binintersectI)).
1.29/1.02	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binintersectSubset5)).
1.29/1.02	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binintersectEL)).
1.29/1.02	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binintersectLsub)).
1.29/1.02	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binintersectSubset2)).
1.29/1.02	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binintersectSubset3)).
1.29/1.02	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binintersectER)).
1.29/1.02	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', disjointsetsI1)).
1.29/1.02	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binintersectRsub)).
1.29/1.02	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binintersectSubset4)).
1.29/1.02	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binintersectSubset1)).
1.29/1.02	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', bs114d)).
1.29/1.02	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setminusI)).
1.29/1.02	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setminusEL)).
1.29/1.02	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setminusER)).
1.29/1.02	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setminusSubset2)).
1.29/1.02	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setminusERneg)).
1.29/1.02	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setminusELneg)).
1.29/1.02	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setminusILneg)).
1.29/1.02	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setminusIRneg)).
1.29/1.02	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setminusLsub)).
1.29/1.02	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setminusSubset1)).
1.29/1.02	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', symdiffE)).
1.29/1.02	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', symdiffI1)).
1.29/1.02	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', symdiffI2)).
1.29/1.02	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', symdiffIneg1)).
1.29/1.02	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', symdiffIneg2)).
1.29/1.02	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', secondinupair)).
1.29/1.02	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setukpairIL)).
1.29/1.02	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setukpairIR)).
1.29/1.02	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', kpairiskpair)).
1.29/1.02	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', kpairp)).
1.29/1.02	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', singletonsubset)).
1.29/1.02	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', singletoninpowerset)).
1.29/1.02	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', singletoninpowunion)).
1.29/1.02	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', upairset2E)).
1.29/1.02	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', upairsubunion)).
1.29/1.02	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', upairinpowunion)).
1.29/1.02	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', ubforcartprodlem1)).
1.29/1.02	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', ubforcartprodlem2)).
1.29/1.02	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', ubforcartprodlem3)).
1.29/1.02	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', cartprodpairin)).
1.29/1.02	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', cartprodmempair1)).
1.29/1.02	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', cartprodmempair)).
1.29/1.02	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setunionE2)).
1.29/1.02	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setunionsingleton1)).
1.29/1.02	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setunionsingleton2)).
1.29/1.02	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setunionsingleton)).
1.29/1.02	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', singletonsuniq)).
1.29/1.02	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.N6TN1y9XWN/E---3.1_29775.p', setukpairinjL1)).
1.29/1.02	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', theprop)).
1.29/1.02	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', kfstpairEq)).
1.29/1.02	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', cartprodfstin)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', setukpairinjL2)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', setukpairinjL)).
1.29/1.02	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setukpairinjR11)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', setukpairinjR12)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', setukpairinjR1)).
1.29/1.02	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', upairequniteq)).
1.29/1.02	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setukpairinjR2)).
1.29/1.02	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setukpairinjR)).
1.29/1.02	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', ksndpairEq)).
1.29/1.02	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', kpairsurjEq)).
1.29/1.02	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', cartprodsndin)).
1.29/1.02	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', cartprodpairmemEL)).
1.29/1.02	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', cartprodpairmemER)).
1.29/1.02	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', cartprodmempaircEq)).
1.29/1.02	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', cartprodfstpairEq)).
1.29/1.02	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', cartprodsndpairEq)).
1.29/1.02	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', cartprodpairsurjEq)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', app)).
1.29/1.02	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', infuncsetfunc)).
1.29/1.02	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', ap2p)).
1.29/1.02	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', funcinfuncset)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', funcGraphProp1)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', funcGraphProp3)).
1.29/1.02	thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', funcGraphProp2)).
1.29/1.02	thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', funcextLem)).
1.29/1.02	thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', funcGraphProp4)).
1.29/1.02	thf(funcext, axiom, ((funcext)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', funcext)).
1.29/1.02	thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', funcext2)).
1.29/1.02	thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', ap2apEq1)).
1.29/1.02	thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', ap2apEq2)).
1.29/1.02	thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', ifp)).
1.29/1.02	thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', theeq)).
1.29/1.02	thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', iftrue)).
1.29/1.02	thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', iffalse)).
1.29/1.02	thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', iftrueorfalse)).
1.29/1.02	thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', binintersectT_lem)).
1.29/1.02	thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binunionT_lem)).
1.29/1.02	thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', powersetT_lem)).
1.29/1.02	thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', setminusT_lem)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', complementT_lem)).
1.29/1.02	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', setextT)).
1.29/1.02	thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', subsetTI)).
1.29/1.02	thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', powersetTI1)).
1.29/1.02	thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', powersetTE1)).
1.29/1.02	thf(complementTI1, axiom, ((complementTI1)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', complementTI1)).
1.29/1.02	thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', complementTE1)).
1.29/1.02	thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binintersectTELcontra)).
1.29/1.02	thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', binintersectTERcontra)).
1.29/1.02	thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', contrasubsetT)).
1.29/1.02	thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', contrasubsetT1)).
1.29/1.02	thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', contrasubsetT2)).
1.29/1.02	thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', contrasubsetT3)).
1.29/1.02	thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', doubleComplementI1)).
1.29/1.02	thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', doubleComplementE1)).
1.29/1.02	thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', doubleComplementSub1)).
1.29/1.02	thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', doubleComplementSub2)).
1.29/1.02	thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', doubleComplementEq)).
1.29/1.02	thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', complementTnotintersectT)).
1.29/1.02	thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', complementImpComplementIntersect)).
1.29/1.02	thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', complementSubsetComplementIntersect)).
1.29/1.02	thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', complementInPowersetComplementIntersect)).
1.29/1.02	thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', contraSubsetComplement)).
1.29/1.02	thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', complementTcontraSubset)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', binunionTILcontra)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', binunionTIRcontra)).
1.29/1.02	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', inIntersectImpInUnion)).
1.29/1.02	thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', inIntersectImpInUnion2)).
1.29/1.02	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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', inIntersectImpInIntersectUnions)).
1.29/1.02	thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', intersectInPowersetIntersectUnions)).
1.29/1.02	thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', inComplementUnionImpNotIn1)).
1.29/1.02	thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', inComplementUnionImpInComplement1)).
1.29/1.02	thf(binunionTE, axiom, ((binunionTE)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', binunionTE)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', binunionTEcontra)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', demorgan2a1)).
1.29/1.02	thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', complementUnionInPowersetComplement)).
1.29/1.02	thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', demorgan2a2)).
1.29/1.02	thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', demorgan1a)).
1.29/1.02	thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', demorgan1b)).
1.29/1.02	thf(demorgan1, axiom, ((demorgan1)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', demorgan1)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', demorgan2a)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', demorgan2b2)).
1.29/1.02	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.N6TN1y9XWN/E---3.1_29775.p', demorgan2b)).
1.29/1.02	thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', demorgan2)).
1.29/1.02	thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', woz13rule0)).
1.29/1.02	thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', woz13rule1)).
1.29/1.02	thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', woz13rule2)).
1.29/1.02	thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', woz13rule3)).
1.29/1.02	thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$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.N6TN1y9XWN/E---3.1_29775.p', woz13rule4)).
1.29/1.02	thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', woz1_1)).
1.29/1.02	thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', woz1_2)).
1.29/1.02	thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', woz1_3)).
1.29/1.02	thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', woz1_4)).
1.29/1.02	thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.N6TN1y9XWN/E---3.1_29775.p', woz1_5)).
1.29/1.02	thf(c_0_290, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
1.29/1.02	thf(c_0_291, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
1.29/1.02	thf(c_0_292, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
1.29/1.02	thf(c_0_293, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
1.29/1.02	thf(c_0_294, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
1.29/1.02	thf(c_0_295, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
1.29/1.02	thf(c_0_296, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
1.29/1.02	thf(c_0_297, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
1.29/1.02	thf(c_0_298, 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])).
1.29/1.02	thf(c_0_299, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
1.29/1.02	thf(c_0_300, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
1.29/1.02	thf(c_0_301, 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])).
1.29/1.02	thf(c_0_302, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
1.29/1.02	thf(c_0_303, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
1.29/1.02	thf(c_0_304, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
1.29/1.02	thf(c_0_305, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
1.29/1.02	thf(c_0_306, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])).
1.29/1.02	thf(c_0_307, 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])).
1.29/1.02	thf(c_0_308, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
1.29/1.02	thf(c_0_309, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
1.29/1.02	thf(c_0_310, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
1.29/1.02	thf(c_0_311, 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])).
1.29/1.02	thf(c_0_312, plain, ((breln1)=(^[Z0/* 19 */:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(fof_simplification,[status(thm)],[breln1])).
1.29/1.02	thf(c_0_313, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X965:$i]:((((X6 @ X2 @ X965))&![X966:$i]:((((X6 @ X2 @ X966))=>((X965)=(X966)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_290, c_0_291])).
1.29/1.02	thf(c_0_314, plain, ((descrp)=(![X1:$i > $o]:(((?[X967:$i]:((((X1 @ X967))&![X968:$i]:((((X1 @ X968))=>((X967)=(X968)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_292, c_0_291])).
1.29/1.02	thf(c_0_315, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
1.29/1.02	thf(c_0_316, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
1.29/1.02	thf(c_0_317, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
1.29/1.02	thf(c_0_318, plain, ((exuE1)=(![X1:$i > $o]:(((?[X969:$i]:((((X1 @ X969))&![X970:$i]:((((X1 @ X970))=>((X969)=(X970)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_293, c_0_291])).
1.29/1.02	thf(c_0_319, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X971:$i]:((((X1 @ X971))&![X972:$i]:((((X1 @ X972))=>((X971)=(X972)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_294, c_0_291])).
1.29/1.02	thf(c_0_320, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
1.29/1.02	thf(c_0_321, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_295])).
1.29/1.02	thf(c_0_322, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_296, c_0_295])).
1.29/1.02	thf(c_0_323, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_295])).
1.29/1.02	thf(c_0_324, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
1.29/1.02	thf(c_0_325, plain, ((exuE2)=(![X1:$i > $o]:(((?[X973:$i]:((((X1 @ X973))&![X974:$i]:((((X1 @ X974))=>((X973)=(X974)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_297, c_0_291])).
1.29/1.02	thf(c_0_326, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_295])).
1.29/1.02	thf(c_0_327, 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])).
1.29/1.02	thf(c_0_328, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X975:$i]:((((X1 @ X975))&![X976:$i]:((((X1 @ X976))=>((X975)=(X976))))))))))), inference(apply_def,[status(thm)],[c_0_298, c_0_291])).
1.29/1.02	thf(c_0_329, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X977:$i]:((((X1 @ X977))&![X978:$i]:((((X1 @ X978))=>((X977)=(X978)))))))))))), inference(apply_def,[status(thm)],[c_0_299, c_0_291])).
1.29/1.02	thf(c_0_330, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X979:$i]:((((X1 @ X979))&![X980:$i]:((((X1 @ X980))=>((X979)=(X980))))))))))), inference(apply_def,[status(thm)],[c_0_300, c_0_291])).
1.29/1.02	thf(c_0_331, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X981:$i]:((((X1 @ X981))&![X982:$i]:((((X1 @ X982))=>((X981)=(X982)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_301, c_0_291])).
1.29/1.02	thf(c_0_332, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X983:$i]:((((X1 @ X983))&![X984:$i]:((((X1 @ X984))=>((X983)=(X984)))))))<=>(?[X985:$i]:((((X17 @ X985))&![X986:$i]:((((X17 @ X986))=>((X985)=(X986)))))))))))), inference(apply_def,[status(thm)],[c_0_302, c_0_291])).
1.29/1.02	thf(c_0_333, plain, ((exuEu)=(![X1:$i > $o]:(((?[X987:$i]:((((X1 @ X987))&![X988:$i]:((((X1 @ X988))=>((X987)=(X988)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_303, c_0_291])).
1.29/1.02	thf(c_0_334, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X989:$i]:((((X1 @ X989))&![X990:$i]:((((X1 @ X990))=>((X989)=(X990)))))))=>((?[X991:$i]:((((X17 @ X991))&![X992:$i]:((((X17 @ X992))=>((X991)=(X992)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_304, c_0_291])).
1.29/1.02	thf(c_0_335, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
1.29/1.02	thf(c_0_336, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
1.29/1.02	thf(c_0_337, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
1.29/1.02	thf(c_0_338, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
1.29/1.02	thf(c_0_339, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_305, c_0_306])).
1.29/1.02	thf(c_0_340, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))))))))), inference(apply_def,[status(thm)],[c_0_307, c_0_306])).
1.29/1.02	thf(c_0_341, 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)))=>((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))))))), inference(apply_def,[status(thm)],[c_0_308, c_0_306])).
1.29/1.02	thf(c_0_342, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
1.29/1.02	thf(c_0_343, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
1.29/1.02	thf(c_0_344, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
1.29/1.02	thf(c_0_345, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
1.29/1.02	thf(c_0_346, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_309, c_0_310])).
1.29/1.02	thf(c_0_347, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
1.29/1.02	thf(c_0_348, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
1.29/1.02	thf(c_0_349, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
1.29/1.02	thf(c_0_350, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
1.29/1.02	thf(c_0_351, plain, ((funcImageSingleton)<=>![X4:$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])).
1.29/1.02	thf(c_0_352, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
1.29/1.02	thf(c_0_353, plain, ((lamProp)<=>![X4:$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])).
1.29/1.02	thf(c_0_354, 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 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
1.29/1.02	thf(c_0_355, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
1.29/1.02	thf(c_0_356, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_310])).
1.29/1.02	thf(c_0_357, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_310])).
1.29/1.02	thf(c_0_358, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_311, c_0_306])).
1.29/1.02	thf(c_0_359, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln, c_0_310])).
1.29/1.02	thf(c_0_360, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_310])).
1.29/1.02	thf(c_0_361, 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])).
1.29/1.02	thf(c_0_362, 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])).
1.29/1.02	thf(c_0_363, 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])).
1.29/1.02	thf(c_0_364, 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])).
1.29/1.02	thf(c_0_365, 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])).
1.29/1.02	thf(c_0_366, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
1.29/1.02	thf(c_0_367, plain, ((iffalseProp2)<=>![X4:$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])).
1.29/1.02	thf(c_0_368, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
1.29/1.02	thf(c_0_369, plain, ((iftrueProp2)<=>![X4:$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])).
1.29/1.02	thf(c_0_370, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
1.29/1.02	thf(c_0_371, plain, ((breln1)=(^[Z0/* 19 */:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(apply_def,[status(thm)],[c_0_312, c_0_310])).
1.29/1.02	thf(c_0_372, plain, ((epred1_0)<=>![X1892:$i]:(?[X1893:$i]:((((![X1894:$i]:(((in @ X1894 @ X1893)=>![X1895:$i]:(((in @ X1895 @ X1894)=>(in @ X1895 @ X1892)))))&![X1896:$i, X1897:$i]:((((in @ X1896 @ X1892)&(in @ X1897 @ X1892))=>(![X1898:$i]:(((in @ X1898 @ X1893)=>((in @ X1896 @ X1898)<=>(in @ X1897 @ X1898))))=>((X1896)=(X1897))))))&![X1899:$i, X1900:$i]:((((in @ X1899 @ X1893)&(in @ X1900 @ X1893))=>(![X1901:$i]:(((in @ X1901 @ X1899)=>(in @ X1901 @ X1900)))|![X1902:$i]:(((in @ X1902 @ X1900)=>(in @ X1902 @ X1899)))))))&![X1903:$i]:(((![X1904:$i]:(((in @ X1904 @ X1903)=>(in @ X1904 @ X1892)))&?[X1905:$i]:((in @ X1905 @ X1903)))=>?[X1906:$i, X1907:$i]:(((((in @ X1906 @ X1893)&(in @ X1907 @ X1903))&~(?[X1908:$i]:(((in @ X1908 @ X1906)&(in @ X1908 @ X1903)))))&![X1909:$i]:(((in @ X1909 @ X1893)=>(![X1910:$i]:(((in @ X1910 @ X1909)=>(in @ X1910 @ X1906)))|(in @ X1907 @ X1909)))))))))))), introduced(definition)).
1.29/1.02	thf(c_0_373, negated_conjecture, ~((![X1925:$i, X1926:$i]:((![X1927:$i]:(((in @ X1927 @ X1925)<=>(in @ X1927 @ X1926)))=>((X1925)=(X1926))))=>(![X1924:$i]:(~(in @ X1924 @ emptyset))=>(![X993:$i, X994:$i, X995:$i]:(((in @ X995 @ (setadjoin @ X993 @ X994))<=>(((X995)=(X993))|(in @ X995 @ X994))))=>(![X996:$i, X997:$i]:(((in @ X997 @ (powerset @ X996))<=>![X998:$i]:(((in @ X998 @ X997)=>(in @ X998 @ X996)))))=>(![X999:$i, X1000:$i]:(((in @ X1000 @ (setunion @ X999))<=>?[X1001:$i]:(((in @ X1000 @ X1001)&(in @ X1001 @ X999)))))=>((in @ emptyset @ omega)=>(![X1923:$i]:(((in @ X1923 @ omega)=>(in @ (setadjoin @ X1923 @ X1923) @ omega)))=>(![X1002:$i]:((((in @ emptyset @ X1002)&![X1003:$i]:((((in @ X1003 @ omega)&(in @ X1003 @ X1002))=>(in @ (setadjoin @ X1003 @ X1003) @ X1002))))=>![X1004:$i]:(((in @ X1004 @ omega)=>(in @ X1004 @ X1002)))))=>(![X1915:$i > $i > $o, X1916:$i]:((![X1917:$i]:(((in @ X1917 @ X1916)=>?[X1918:$i]:(((X1915 @ X1917 @ X1918)&![X1919:$i]:(((X1915 @ X1917 @ X1919)=>((X1918)=(X1919))))))))=>?[X1920:$i]:(![X1921:$i]:(((in @ X1921 @ X1920)<=>?[X1922:$i]:(((in @ X1922 @ X1916)&(X1915 @ X1922 @ X1921))))))))=>(![X1911:$i]:((?[X1912:$i]:((in @ X1912 @ X1911))=>?[X1913:$i]:(((in @ X1913 @ X1911)&~(?[X1914:$i]:(((in @ X1914 @ X1913)&(in @ X1914 @ X1911))))))))=>((epred1_0)=>(![X1005:$i > $o]:((?[X1006:$i]:(((X1005 @ X1006)&![X1007:$i]:(((X1005 @ X1007)=>((X1006)=(X1007))))))=>(X1005 @ (descr @ (^[Z0/* 17 */:$i]:(X1005 @ Z0))))))=>(![X1008:$i, X1009:$i > $o, X1010:$i]:(((in @ X1010 @ X1008)=>((X1009 @ X1010)=>(in @ X1010 @ (dsetconstr @ X1008 @ X1009)))))=>(![X1011:$i, X1012:$i > $o, X1013:$i]:(((in @ X1013 @ (dsetconstr @ X1011 @ X1012))=>(in @ X1013 @ X1011)))=>(![X1889:$i, X1890:$i > $o, X1891:$i]:(((in @ X1891 @ (dsetconstr @ X1889 @ X1890))=>(X1890 @ X1891)))=>(![X1884:$i > $o]:((?[X1885:$i]:(((X1884 @ X1885)&![X1886:$i]:(((X1884 @ X1886)=>((X1885)=(X1886))))))=>?[X1887:$i]:(((X1884 @ X1887)&![X1888:$i]:(((X1884 @ X1888)=>((X1887)=(X1888))))))))=>(![X1014:$o, X1015:$i]:(((in @ X1015 @ (prop2set @ ((X1014))))=>(X1014)))=>(![X1016:$i]:(((in @ X1016 @ emptyset)=>![X1017:$o]:((X1017))))=>(![X1883:$i]:(((in @ X1883 @ emptyset)=>~($true)))=>(![X1882:$i]:(~(in @ X1882 @ emptyset))=>(![X1878:$i > $o]:((?[X1879:$i]:(((X1878 @ X1879)&![X1880:$i]:(((X1878 @ X1880)=>((X1879)=(X1880))))))=>?[X1881:$i]:((X1878 @ X1881))))=>(![X1018:$i, X1019:$i]:((![X1020:$i]:(((in @ X1020 @ X1018)=>(in @ X1020 @ X1019)))=>(![X1021:$i]:(((in @ X1021 @ X1019)=>(in @ X1021 @ X1018)))=>((X1018)=(X1019)))))=>(![X1876:$i]:((![X1877:$i]:(~(in @ X1877 @ X1876))=>((X1876)=(emptyset))))=>(![X1874:$i]:((![X1875:$i]:(~(in @ X1875 @ X1874))=>((X1874)=(emptyset))))=>(![X1022:$i, X1023:$i > $o, X1024:$i]:(((in @ X1024 @ X1022)=>((in @ X1024 @ (dsetconstr @ X1022 @ X1023))<=>(X1023 @ X1024))))=>(![X1025:$i]:((((X1025)!=(emptyset))=>?[X1026:$i]:((in @ X1026 @ X1025))))=>(![X1027:$i, X1028:$i > $o, X1029:$i]:(((in @ X1029 @ X1027)=>((X1028 @ X1029)=>((dsetconstr @ X1027 @ X1028)!=(emptyset)))))=>(![X1030:$i]:((?[X1031:$i]:((in @ X1031 @ X1030))=>((X1030)!=(emptyset))))=>(![X1872:$i, X1873:$i]:((in @ X1872 @ (setadjoin @ X1872 @ X1873)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1032:$i, X1033:$i, X1034:$i]:(((in @ X1034 @ X1033)=>(in @ X1034 @ (setadjoin @ X1032 @ X1033))))=>(![X1868:$i, X1869:$i, X1870:$i]:(((in @ X1870 @ (setadjoin @ X1868 @ X1869))=>![X1871:$o]:(((((X1870)=(X1868))=>(X1871))=>(((in @ X1870 @ X1869)=>(X1871))=>(X1871))))))=>(![X1865:$i, X1866:$i, X1867:$i]:(((in @ X1867 @ (setadjoin @ X1865 @ X1866))=>(((X1867)=(X1865))|(in @ X1867 @ X1866))))=>(![X1864:$i]:(((dsetconstr @ X1864 @ (^[Z0/* 1 */:$i]:($true)))=(X1864)))=>(![X1861:$i, X1862:$i]:((![X1863:$i]:(((in @ X1863 @ X1862)=>(in @ X1863 @ X1861)))=>(in @ X1862 @ (powerset @ X1861))))=>(![X1035:$i]:((in @ emptyset @ (powerset @ X1035)))=>(![X1036:$i]:((in @ emptyset @ (powerset @ X1036)))=>(![X1858:$i, X1859:$i, X1860:$i]:(((in @ X1859 @ (powerset @ X1858))=>((in @ X1860 @ X1859)=>(in @ X1860 @ X1858))))=>(![X1855:$i, X1856:$i, X1857:$i]:(((in @ X1856 @ X1857)=>((in @ X1857 @ X1855)=>(in @ X1856 @ (setunion @ X1855)))))=>(![X1851:$i, X1852:$i]:(((in @ X1852 @ (setunion @ X1851))=>![X1853:$o]:((![X1854:$i]:(((in @ X1852 @ X1854)=>((in @ X1854 @ X1851)=>(X1853))))=>(X1853)))))=>(![X1849:$i, X1850:$i]:(((in @ X1850 @ X1849)=>(in @ X1850 @ (powerset @ (setunion @ X1849)))))=>(![X1037:$i > $o]:((?[X1038:$i]:(((X1037 @ X1038)&![X1039:$i]:(((X1037 @ X1039)=>((X1038)=(X1039))))))=>?[X1040:$i]:(![X1041:$i]:(((X1037 @ X1041)<=>((X1041)=(X1040)))))))=>(![X1042:$i]:((((X1042)!=(emptyset))=>?[X1043:$i]:(((in @ X1043 @ X1042)&$true))))=>(![X1847:$i, X1848:$i]:(((in @ X1847 @ (setadjoin @ X1848 @ emptyset))=>((X1847)=(X1848))))=>(![X1044:$i, X1045:$i]:((((X1044)!=(X1045))=>~(in @ X1045 @ (setadjoin @ X1044 @ emptyset))))=>(![X1845:$i, X1846:$i]:((((X1845)=(X1846))=>(in @ X1845 @ (setadjoin @ X1846 @ emptyset))))=>(![X1046:$i, X1047:$i]:(((in @ X1046 @ (setadjoin @ X1047 @ emptyset))=>(in @ X1047 @ (setadjoin @ X1046 @ emptyset))))=>(![X1842:$i, X1843:$i, X1844:$i]:(((in @ X1844 @ (setadjoin @ X1842 @ (setadjoin @ X1843 @ emptyset)))=>(((X1844)=(X1842))|((X1844)=(X1843)))))=>(![X1048:$i, X1049:$i]:((in @ X1048 @ (setadjoin @ X1048 @ (setadjoin @ X1049 @ emptyset))))=>(![X1840:$i, X1841:$i]:((in @ X1841 @ (setadjoin @ X1840 @ (setadjoin @ X1841 @ emptyset))))=>(![X1050:$i, X1051:$i > $o]:((?[X1052:$i]:(((in @ X1052 @ X1050)&(X1051 @ X1052)))=>(((dsetconstr @ X1050 @ X1051)=(emptyset))=>~($true))))=>(![X1053:$i > $o, X1054:$i]:(((in @ X1054 @ emptyset)=>(X1053 @ X1054)))=>(![X1055:$i, X1056:$i > $o]:((~(![X1057:$i]:(((in @ X1057 @ X1055)=>(X1056 @ X1057))))=>?[X1058:$i]:(((in @ X1058 @ X1055)&~((X1056 @ X1058))))))=>(![X1836:$i, X1837:$i > $o]:((![X1838:$i]:(((in @ X1838 @ X1836)=>~((X1837 @ X1838))))=>~(?[X1839:$i]:(((in @ X1839 @ X1836)&(X1837 @ X1839))))))=>(![X1832:$i, X1833:$i > $o]:((~(?[X1834:$i]:(((in 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y_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[breln1all2]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_313]), foundationAx]), wellorderingAx]), c_0_314]), c_0_315]), c_0_316]), c_0_317]), c_0_318]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_319]), setext]), emptyI]), noeltsimpempty]), c_0_320]), c_0_321]), c_0_322]), c_0_323]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_324]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_325]), c_0_326]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_327]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_328]), c_0_329]), c_0_330]), inCongP]), in__Cong]), c_0_331]), c_0_332]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_333]), c_0_334]), c_0_335]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_336]), c_0_337]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_338]), c_0_339]), c_0_340]), c_0_341]), singletonsuniq]), setukpairinjL1]), c_0_342]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_343]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_344]), c_0_345]), c_0_346]), c_0_347]), c_0_348]), c_0_349]), c_0_350]), c_0_351]), c_0_352]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_353]), c_0_354]), c_0_355]), c_0_356]), c_0_357]), c_0_358]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_359]), c_0_360]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_361]), c_0_362]), c_0_363]), c_0_364]), c_0_365]), c_0_366]), c_0_367]), c_0_368]), c_0_369]), c_0_370]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan1]), demorgan2a]), demorgan2b2]), demorgan2b]), demorgan2]), woz13rule0]), woz13rule1]), woz13rule2]), woz13rule3]), woz13rule4]), woz1_1]), woz1_2]), woz1_3]), woz1_4]), woz1_5]), c_0_371])])]), c_0_372])).
1.29/1.02	thf(c_0_374, negated_conjecture, ![X1928:$i, X1929:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1941:$i, X1942:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1950:$i, X1951:$i > $i > $o, X1952:$i, X1954:$i, X1957:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1964:$i, X1965:$i > $o, X1966:$i, X1968:$i, X1969:$i > $o, X1970:$i, X1971:$i, X1972:$i > $o, X1973:$i, X1974:$i, X1975:$i > $o, X1976:$i, X1977:$i > $o, X1978:$i, X1981:$i, X1982:$o, X1983:$i, X1984:$i, X1985:$o, X1986:$i, X1987:$i, X1988:$i > $o, X1989:$i, X1992:$i, X1993:$i, X1996:$i, X1998:$i, X2000:$i, X2001:$i > $o, X2002:$i, X2003:$i, X2005:$i, X2006:$i > $o, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$o, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$o, X2038:$i, X2039:$i, X2040:$i > $o, X2041:$i, X2044:$i, X2045:$i, X2046:$i, X2048:$i, X2049:$i, X2050:$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 > $o, X2065:$i, X2066:$i > $o, X2067:$i, X2068:$i, X2069:$i > $o, X2070:$i, X2072:$i, X2073:$i > $o, X2075:$i, X2076:$i, X2077:$i > $o, X2079:$i, X2080:$i, X2081:$i > $o, X2082:$i, X2084:$o, X2085:$o, X2086:$i, X2087:$i > $o, X2089:$i, X2090:$i, X2091:$i > $o, X2092:$i, X2094:$i > $o, X2095:$i, X2098:$i, X2099:$i > $o, X2100:$i, X2104:$i, X2105:$i > $o, X2106:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i > $o, X2119:$i, X2121:$i, X2122:$i, X2123:$i > $o, X2124:$i > $o, X2127:$i, X2130:$i, X2131:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i > $o, X2144:$i, X2146:$i, X2147:$i, X2148:$i > $o, X2149:$i > $o, X2152:$i, X2154:$i, X2156:$i, X2157:$i, X2158:$i > $o, X2159:$i > $o, X2162:$i, X2163:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2172:$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 > $o, X2210:$i, X2211:$i > $o, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$o, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$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:$i, X2291:$o, 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:$i, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$i > 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X2674))|(~(in @ X2675 @ X2673)|(in @ X2675 @ X2674))))))&((~(in @ X2677 @ (powerset @ X2676))|(~(in @ X2678 @ X2676)|(~(in @ X2678 @ X2677)|~(in @ X2678 @ (setminus @ X2676 @ X2677)))))&((~(in @ X2680 @ (powerset @ X2679))|(~(in @ X2681 @ X2679)|((in @ X2681 @ (setminus @ X2679 @ X2680))|(in @ X2681 @ X2680))))&((~(in @ X2683 @ (powerset @ X2682))|(~(in @ X2684 @ (powerset @ X2682))|(~(in @ X2685 @ X2682)|((in @ X2685 @ X2683)|~(in @ X2685 @ (binintersect @ X2683 @ X2684))))))&((~(in @ X2687 @ (powerset @ X2686))|(~(in @ X2688 @ (powerset @ X2686))|(~(in @ X2689 @ X2686)|((in @ X2689 @ X2688)|~(in @ X2689 @ (binintersect @ X2687 @ X2688))))))&((~(in @ X2691 @ (powerset @ X2690))|(~(in @ X2692 @ (powerset @ X2690))|(~(in @ X2693 @ X2690)|(~(subset @ X2691 @ (setminus @ X2690 @ X2692))|(~(in @ X2693 @ X2692)|~(in @ X2693 @ X2691))))))&((~(in @ X2695 @ (powerset @ X2694))|(~(in @ X2696 @ (powerset @ X2694))|(~(in @ X2697 @ X2694)|(~(subset @ X2695 @ X2696)|((in @ X2697 @ X2696)|~(in @ X2697 @ X2695))))))&((~(in @ X2699 @ (powerset @ X2698))|(~(in @ X2700 @ (powerset @ X2698))|(~(subset @ X2699 @ X2700)|(subset @ (setminus @ X2698 @ X2700) @ (setminus @ X2698 @ X2699)))))&((~(in @ X2702 @ (powerset @ X2701))|(~(in @ X2703 @ (powerset @ X2701))|(~(subset @ (setminus @ X2701 @ X2703) @ (setminus @ X2701 @ X2702))|(subset @ X2702 @ X2703))))&((~(in @ X2705 @ (powerset @ X2704))|(~(in @ X2706 @ X2704)|(~(in @ X2706 @ X2705)|(in @ X2706 @ (setminus @ X2704 @ (setminus @ X2704 @ X2705))))))&((~(in @ X2708 @ (powerset @ X2707))|(~(in @ X2709 @ X2707)|(~(in @ X2709 @ (setminus @ X2707 @ (setminus @ X2707 @ X2708)))|(in @ X2709 @ X2708))))&((~(in @ X2711 @ (powerset @ X2710))|(subset @ X2711 @ (setminus @ X2710 @ (setminus @ X2710 @ X2711))))&((~(in @ X2713 @ (powerset @ X2712))|(subset @ (setminus @ X2712 @ (setminus @ X2712 @ X2713)) @ X2713))&((~(in @ X2715 @ (powerset @ X2714))|((X2715)=(setminus @ X2714 @ (setminus @ X2714 @ X2715))))&((~(in @ X2717 @ (powerset @ X2716))|(~(in @ X2718 @ (powerset @ X2716))|(~(in @ X2719 @ X2716)|(~(in @ X2719 @ (setminus @ X2716 @ X2717))|~(in @ X2719 @ (binintersect @ X2717 @ X2718))))))&((~(in @ X2721 @ (powerset @ X2720))|(~(in @ X2722 @ (powerset @ X2720))|(~(in @ X2723 @ X2720)|(~(in @ X2723 @ (setminus @ X2720 @ X2721))|(in @ X2723 @ (setminus @ X2720 @ (binintersect @ X2721 @ X2722)))))))&((~(in @ X2725 @ (powerset @ X2724))|(~(in @ X2726 @ (powerset @ X2724))|(subset @ (setminus @ X2724 @ X2725) @ (setminus @ X2724 @ (binintersect @ X2725 @ X2726)))))&((~(in @ X2728 @ (powerset @ X2727))|(~(in @ X2729 @ (powerset @ X2727))|(in @ (setminus @ X2727 @ X2728) @ (powerset @ (setminus @ X2727 @ (binintersect @ X2728 @ X2729))))))&((~(in @ X2731 @ (powerset @ X2730))|(~(in @ X2732 @ (powerset @ X2730))|(~(subset @ X2731 @ (setminus @ X2730 @ X2732))|(~(in @ X2733 @ X2730)|(~(in @ X2733 @ X2732)|(in @ X2733 @ (setminus @ X2730 @ X2731)))))))&((~(in @ X2735 @ (powerset @ X2734))|(~(in @ X2736 @ (powerset @ X2734))|(~(subset @ X2735 @ (setminus @ X2734 @ X2736))|(subset @ X2736 @ (setminus @ X2734 @ X2735)))))&((~(in @ X2738 @ (powerset @ X2737))|(~(in @ X2739 @ (powerset @ X2737))|(~(in @ X2740 @ X2737)|((in @ X2740 @ (binunion @ X2738 @ X2739))|~(in @ X2740 @ X2738)))))&((~(in @ X2742 @ (powerset @ X2741))|(~(in @ X2743 @ (powerset @ X2741))|(~(in @ X2744 @ X2741)|((in @ X2744 @ (binunion @ X2742 @ X2743))|~(in @ X2744 @ X2743)))))&((~(in @ X2746 @ (powerset @ X2745))|(~(in @ X2747 @ (powerset @ X2745))|(~(in @ X2748 @ (powerset @ X2745))|(~(in @ X2749 @ X2745)|(~(in @ X2749 @ (binintersect @ X2746 @ X2747))|(in @ X2749 @ (binunion @ X2746 @ X2748)))))))&((~(in @ X2751 @ (powerset @ X2750))|(~(in @ X2752 @ (powerset @ X2750))|(~(in @ X2753 @ (powerset @ X2750))|(~(in @ X2754 @ X2750)|(~(in @ X2754 @ (binintersect @ X2751 @ X2752))|(in @ X2754 @ (binunion @ X2752 @ X2753)))))))&((~(in @ X2756 @ (powerset @ X2755))|(~(in @ X2757 @ (powerset @ X2755))|(~(in @ X2758 @ (powerset @ X2755))|(~(in @ X2759 @ X2755)|(~(in @ X2759 @ (binintersect @ X2756 @ X2757))|(in @ X2759 @ (binintersect @ (binunion @ X2756 @ X2758) @ (binunion @ X2757 @ X2758))))))))&((~(in @ X2761 @ (powerset @ X2760))|(~(in @ X2762 @ (powerset @ X2760))|(~(in @ X2763 @ (powerset @ X2760))|(in @ (binintersect @ X2761 @ X2762) @ (powerset @ (binintersect @ (binunion @ X2761 @ X2763) @ (binunion @ X2762 @ X2763)))))))&((~(in @ X2765 @ (powerset @ X2764))|(~(in @ X2766 @ (powerset @ X2764))|(~(in @ X2767 @ X2764)|(~(in @ X2767 @ (setminus @ X2764 @ (binunion @ X2765 @ X2766)))|~(in @ X2767 @ X2765)))))&((~(in @ X2769 @ (powerset @ X2768))|(~(in @ X2770 @ (powerset @ X2768))|(~(in @ X2771 @ X2768)|(~(in @ X2771 @ (setminus @ X2768 @ (binunion @ X2769 @ X2770)))|(in @ X2771 @ (setminus @ X2768 @ X2769))))))&(((((in @ X2776 @ X2774)|(X2775)|(in @ X2776 @ X2773)|~(in @ X2776 @ (binunion @ X2773 @ X2774))|~(in @ X2776 @ X2772)|~(in @ X2774 @ (powerset @ X2772))|~(in @ X2773 @ (powerset @ X2772)))&(~(X2775)|(X2775)|(in @ X2776 @ X2773)|~(in @ X2776 @ (binunion @ X2773 @ X2774))|~(in @ X2776 @ X2772)|~(in @ X2774 @ (powerset @ X2772))|~(in @ X2773 @ (powerset @ X2772))))&(((in @ X2776 @ X2774)|(X2775)|~(X2775)|~(in @ X2776 @ (binunion @ X2773 @ X2774))|~(in @ X2776 @ X2772)|~(in @ X2774 @ (powerset @ X2772))|~(in @ X2773 @ (powerset @ X2772)))&(~(X2775)|(X2775)|~(X2775)|~(in @ X2776 @ (binunion @ X2773 @ X2774))|~(in @ X2776 @ X2772)|~(in @ X2774 @ (powerset @ X2772))|~(in @ X2773 @ (powerset @ X2772)))))&((~(in @ X2778 @ (powerset @ X2777))|(~(in @ X2779 @ (powerset @ X2777))|(~(in @ X2780 @ X2777)|((in @ X2780 @ X2778)|((in @ X2780 @ X2779)|~(in @ X2780 @ (binunion @ X2778 @ X2779)))))))&((~(in @ X2782 @ (powerset @ X2781))|(~(in @ X2783 @ (powerset @ X2781))|(~(in @ X2784 @ X2781)|(~(in @ X2784 @ (setminus @ X2781 @ (binunion @ X2782 @ X2783)))|(in @ X2784 @ (setminus @ X2781 @ X2782))))))&((~(in @ X2786 @ (powerset @ X2785))|(~(in @ X2787 @ (powerset @ X2785))|(in @ (setminus @ X2785 @ (binunion @ X2786 @ X2787)) @ (powerset @ (setminus @ X2785 @ X2786)))))&((~(in @ X2789 @ (powerset @ X2788))|(~(in @ X2790 @ (powerset @ X2788))|(~(in @ X2791 @ X2788)|(~(in @ X2791 @ (setminus @ X2788 @ (binunion @ X2789 @ X2790)))|(in @ X2791 @ (setminus @ X2788 @ X2790))))))&((~(in @ X2793 @ (powerset @ X2792))|(~(in @ X2794 @ (powerset @ X2792))|(~(in @ X2795 @ X2792)|(~(in @ X2795 @ (setminus @ X2792 @ (binintersect @ X2793 @ X2794)))|(in @ X2795 @ (binunion @ (setminus @ X2792 @ X2793) @ (setminus @ X2792 @ X2794)))))))&((~(in @ X2797 @ (powerset @ X2796))|(~(in @ X2798 @ (powerset @ X2796))|(~(in @ X2799 @ X2796)|(~(in @ X2799 @ (binunion @ (setminus @ X2796 @ X2797) @ (setminus @ X2796 @ X2798)))|(in @ X2799 @ (setminus @ X2796 @ (binintersect @ X2797 @ X2798)))))))&((~(in @ X2801 @ (powerset @ X2800))|(~(in @ X2802 @ (powerset @ X2800))|((setminus @ X2800 @ (binintersect @ X2801 @ X2802))=(binunion @ (setminus @ X2800 @ X2801) @ (setminus @ X2800 @ X2802)))))&((~(in @ X2804 @ (powerset @ X2803))|(~(in @ X2805 @ (powerset @ X2803))|(~(in @ X2806 @ X2803)|(~(in @ X2806 @ (setminus @ X2803 @ (binunion @ X2804 @ X2805)))|(in @ X2806 @ (binintersect @ (setminus @ X2803 @ X2804) @ (setminus @ X2803 @ X2805)))))))&((~(in @ X2808 @ (powerset @ X2807))|(~(in @ X2809 @ (powerset @ X2807))|(~(in @ X2810 @ X2807)|(~(in @ X2810 @ (setminus @ X2807 @ X2808))|(~(in @ X2810 @ (setminus @ X2807 @ X2809))|(in @ X2810 @ (setminus @ X2807 @ (binunion @ X2808 @ X2809))))))))&((~(in @ X2812 @ (powerset @ X2811))|(~(in @ X2813 @ (powerset @ X2811))|(~(in @ X2814 @ X2811)|(~(in @ X2814 @ (binintersect @ (setminus @ X2811 @ X2812) @ (setminus @ X2811 @ X2813)))|(in @ X2814 @ (setminus @ X2811 @ (binunion @ X2812 @ X2813)))))))&((~(in @ X2816 @ (powerset @ X2815))|(~(in @ X2817 @ (powerset @ X2815))|((setminus @ X2815 @ (binunion @ X2816 @ X2817))=(binintersect @ (setminus @ X2815 @ X2816) @ (setminus @ X2815 @ X2817)))))&((~(in @ X2819 @ (powerset @ X2818))|(~(in @ X2820 @ (powerset @ X2818))|(~(in @ X2821 @ (binintersect @ X2819 @ X2820))|(in @ X2821 @ X2818))))&((~(in @ X2823 @ (powerset @ X2822))|(~(in @ X2824 @ (powerset @ X2822))|(~(in @ X2825 @ (powerset @ X2822))|(~(subset @ X2823 @ X2825)|(subset @ (binintersect @ X2823 @ X2824) @ X2825)))))&((~(in @ X2827 @ (powerset @ X2826))|(~(in @ X2828 @ (powerset @ X2826))|(~(in @ X2829 @ (powerset @ X2826))|(~(subset @ X2828 @ X2829)|(subset @ (binintersect @ X2827 @ X2828) @ X2829)))))&((~(in @ X2831 @ (powerset @ X2830))|(~(in @ X2832 @ (powerset @ X2830))|(~(in @ X2833 @ (powerset @ X2830))|(~(subset @ X2831 @ X2832)|(~(subset @ X2831 @ X2833)|(subset @ X2831 @ (binintersect @ X2832 @ X2833)))))))&((~(in @ X2835 @ (powerset @ X2834))|(~(in @ X2836 @ (powerset @ X2834))|(~(in @ X2837 @ (powerset @ X2834))|(~(in @ X2838 @ (powerset @ X2834))|(~(subset @ X2835 @ X2837)|(~(subset @ X2836 @ X2838)|(subset @ (binintersect @ X2835 @ X2836) @ (binintersect @ X2837 @ X2838))))))))&((~(in @ X2840 @ (powerset @ X2839))|(~(in @ X2841 @ (powerset @ X2839))|(in @ (setminus @ X2839 @ X2840) @ (powerset @ (setminus @ X2839 @ (binintersect @ X2840 @ X2841))))))&((~(in @ X2843 @ (powerset @ X2842))|(~(in @ X2844 @ (powerset @ X2842))|(~(in @ X2845 @ (powerset @ X2842))|(~(in @ X2846 @ (powerset @ X2842))|((setminus @ X2842 @ (binintersect @ (binunion @ X2843 @ X2844) @ (binunion @ X2845 @ X2846)))=(binunion @ (binintersect @ (setminus @ X2842 @ X2843) @ (setminus @ X2842 @ X2844)) @ (binintersect @ (setminus @ X2842 @ X2845) @ (setminus @ X2842 @ X2846))))))))&((~(in @ X2848 @ (powerset @ X2847))|(~(in @ X2849 @ (powerset @ X2847))|(~(in @ X2850 @ (powerset @ X2847))|(in @ (binintersect @ X2848 @ X2849) @ (powerset @ (binintersect @ (binunion @ X2848 @ X2850) @ (binunion @ X2849 @ X2850)))))))&((~(in @ X2852 @ (powerset @ X2851))|(~(in @ X2853 @ (powerset @ X2851))|(~(subset @ X2852 @ (setminus @ X2851 @ X2853))|(subset @ X2853 @ (setminus @ X2851 @ X2852)))))&((~(in @ X2855 @ (powerset @ X2854))|(~(in @ X2856 @ (powerset @ X2854))|(in @ (setminus @ X2854 @ (binunion @ X2855 @ X2856)) @ (powerset @ (setminus @ X2854 @ X2855)))))&((subset @ esk88_0 @ (cartprod @ esk87_0 @ esk87_0))&((~(in @ X2860 @ esk87_0)|(~(in @ X2861 @ esk87_0)|(~(in @ (kpair @ X2860 @ X2861) @ esk88_0)|(epred2_0 @ (kpair @ X2860 @ X2861)))))&((in @ esk89_0 @ esk88_0)&~(epred2_0 @ esk89_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_373])])])])])])])).
1.29/1.02	thf(c_0_375, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((subset @ X2 @ X3))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_374])).
1.29/1.02	thf(c_0_376, negated_conjecture, (in @ esk89_0 @ esk88_0), inference(split_conjunct,[status(thm)],[c_0_374])).
1.29/1.02	thf(c_0_377, negated_conjecture, ![X2:$i]:(((in @ esk89_0 @ X2)|~((subset @ esk88_0 @ X2)))), inference(spm,[status(thm)],[c_0_375, c_0_376])).
1.29/1.02	thf(c_0_378, negated_conjecture, (subset @ esk88_0 @ (cartprod @ esk87_0 @ esk87_0)), inference(split_conjunct,[status(thm)],[c_0_374])).
1.29/1.02	thf(c_0_379, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((((kpair @ (kfst @ X2) @ (ksnd @ X2))=(X2))|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_374])).
1.29/1.02	thf(c_0_380, negated_conjecture, (in @ esk89_0 @ (cartprod @ esk87_0 @ esk87_0)), inference(spm,[status(thm)],[c_0_377, c_0_378])).
1.29/1.02	thf(c_0_381, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ (ksnd @ X2) @ X4)|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_374])).
1.29/1.02	thf(c_0_382, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ (kfst @ X2) @ X3)|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_374])).
1.29/1.02	thf(c_0_383, negated_conjecture, ![X2:$i, X3:$i]:(((epred2_0 @ (kpair @ X2 @ X3))|~((in @ X2 @ esk87_0))|~((in @ X3 @ esk87_0))|~((in @ (kpair @ X2 @ X3) @ esk88_0)))), inference(split_conjunct,[status(thm)],[c_0_374])).
1.29/1.02	thf(c_0_384, negated_conjecture, ((kpair @ (kfst @ esk89_0) @ (ksnd @ esk89_0))=(esk89_0)), inference(spm,[status(thm)],[c_0_379, c_0_380])).
1.29/1.02	thf(c_0_385, negated_conjecture, (in @ (ksnd @ esk89_0) @ esk87_0), inference(spm,[status(thm)],[c_0_381, c_0_380])).
1.29/1.02	thf(c_0_386, negated_conjecture, (in @ (kfst @ esk89_0) @ esk87_0), inference(spm,[status(thm)],[c_0_382, c_0_380])).
1.29/1.02	thf(c_0_387, negated_conjecture, ~((epred2_0 @ esk89_0)), inference(split_conjunct,[status(thm)],[c_0_374])).
1.29/1.02	thf(c_0_388, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_383, c_0_384]), c_0_376]), c_0_385]), c_0_386])]), c_0_387]), ['proof']).
1.29/1.02	# SZS output end CNFRefutation
1.29/1.02	# Parsed axioms                        : 613
1.29/1.02	# Removed by relevancy pruning/SinE    : 0
1.29/1.02	# Initial clauses                      : 816
1.29/1.02	# Removed in clause preprocessing      : 362
1.29/1.02	# Initial clauses in saturation        : 454
1.29/1.02	# Processed clauses                    : 986
1.29/1.02	# ...of these trivial                  : 11
1.29/1.02	# ...subsumed                          : 238
1.29/1.02	# ...remaining for further processing  : 737
1.29/1.02	# Other redundant clauses eliminated   : 37
1.29/1.02	# Clauses deleted for lack of memory   : 0
1.29/1.02	# Backward-subsumed                    : 11
1.29/1.02	# Backward-rewritten                   : 7
1.29/1.02	# Generated clauses                    : 2449
1.29/1.02	# ...of the previous two non-redundant : 2244
1.29/1.02	# ...aggressively subsumed             : 0
1.29/1.02	# Contextual simplify-reflections      : 16
1.29/1.02	# Paramodulations                      : 2388
1.29/1.02	# Factorizations                       : 0
1.29/1.02	# NegExts                              : 4
1.29/1.02	# Equation resolutions                 : 40
1.29/1.02	# Disequality decompositions           : 0
1.29/1.02	# Total rewrite steps                  : 250
1.29/1.02	# ...of those cached                   : 170
1.29/1.02	# Propositional unsat checks           : 0
1.29/1.02	#    Propositional check models        : 0
1.29/1.02	#    Propositional check unsatisfiable : 0
1.29/1.02	#    Propositional clauses             : 0
1.29/1.02	#    Propositional clauses after purity: 0
1.29/1.02	#    Propositional unsat core size     : 0
1.29/1.02	#    Propositional preprocessing time  : 0.000
1.29/1.02	#    Propositional encoding time       : 0.000
1.29/1.02	#    Propositional solver time         : 0.000
1.29/1.02	#    Success case prop preproc time    : 0.000
1.29/1.02	#    Success case prop encoding time   : 0.000
1.29/1.02	#    Success case prop solver time     : 0.000
1.29/1.02	# Current number of processed clauses  : 307
1.29/1.02	#    Positive orientable unit clauses  : 65
1.29/1.02	#    Positive unorientable unit clauses: 0
1.29/1.02	#    Negative unit clauses             : 8
1.29/1.02	#    Non-unit-clauses                  : 234
1.29/1.02	# Current number of unprocessed clauses: 2082
1.29/1.02	# ...number of literals in the above   : 5713
1.29/1.02	# Current number of archived formulas  : 0
1.29/1.02	# Current number of archived clauses   : 414
1.29/1.02	# Clause-clause subsumption calls (NU) : 48996
1.29/1.02	# Rec. Clause-clause subsumption calls : 20061
1.29/1.02	# Non-unit clause-clause subsumptions  : 153
1.29/1.02	# Unit Clause-clause subsumption calls : 255
1.29/1.02	# Rewrite failures with RHS unbound    : 0
1.29/1.02	# BW rewrite match attempts            : 42
1.29/1.02	# BW rewrite match successes           : 6
1.29/1.02	# Condensation attempts                : 0
1.29/1.02	# Condensation successes               : 0
1.29/1.02	# Termbank termtop insertions          : 133510
1.29/1.02	# Search garbage collected termcells   : 30911
1.29/1.02	
1.29/1.02	# -------------------------------------------------
1.29/1.02	# User time                : 0.270 s
1.29/1.02	# System time              : 0.025 s
1.29/1.02	# Total time               : 0.295 s
1.29/1.02	# Maximum resident set size: 9348 pages
1.29/1.02	
1.29/1.02	# -------------------------------------------------
1.29/1.02	# User time                : 0.433 s
1.29/1.02	# System time              : 0.043 s
1.29/1.02	# Total time               : 0.475 s
1.29/1.02	# Maximum resident set size: 2764 pages
1.29/1.02	% E exiting
1.29/1.02	% E exiting
1.29/1.02	EOF