0.10/0.19	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.19	% Command    : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 240 THM
0.10/0.39	% Computer : n027.cluster.edu
0.10/0.39	% Model    : x86_64 x86_64
0.10/0.39	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.39	% Memory   : 8042.1875MB
0.10/0.39	% OS       : Linux 3.10.0-693.el7.x86_64
0.10/0.39	% CPULimit   : 1920
0.10/0.39	% WCLimit    : 240
0.10/0.39	% DateTime   : Wed Jul 30 03:41:19 EDT 2025
0.10/0.39	% CPUTime    : 
0.20/0.59	Running higher-order theorem proving
0.25/0.63	Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=240 /export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p
0.27/0.92	# Version: 3.0.0-ho
0.27/0.92	# Preprocessing class: HSLMSLSSLLLCHSA.
0.27/0.92	# Scheduled 5 strats onto 8 cores with 240 seconds (1920 total)
0.27/0.92	# Starting ho_unfolding_5 with 960s (4) cores
0.27/0.92	# Starting pre_casc_3 with 240s (1) cores
0.27/0.92	# Starting new_ho_10_cnf2 with 240s (1) cores
0.27/0.92	# Starting full_lambda_10 with 240s (1) cores
0.27/0.92	# Starting ehoh_best_nonlift_rwall with 240s (1) cores
0.27/0.92	# ho_unfolding_5 with pid 32517 completed with status 0
0.27/0.92	# Result found by ho_unfolding_5
0.27/0.92	# Preprocessing class: HSLMSLSSLLLCHSA.
0.27/0.92	# Scheduled 5 strats onto 8 cores with 240 seconds (1920 total)
0.27/0.92	# Starting ho_unfolding_5 with 960s (4) cores
0.27/0.92	# No SInE strategy applied
0.27/0.92	# Search class: HGHSM-FSLM32-DHSMMSBN
0.27/0.92	# partial match(1): HGHSM-FSLM32-MHSMMSBN
0.27/0.92	# Scheduled 12 strats onto 4 cores with 960 seconds (960 total)
0.27/0.92	# Starting full_lambda_5 with 79s (1) cores
0.27/0.92	# Starting ho_unfolding_5 with 97s (1) cores
0.27/0.92	# Starting pre_casc_4 with 79s (1) cores
0.27/0.92	# Starting pre_casc_3 with 79s (1) cores
0.27/0.92	# ho_unfolding_5 with pid 32526 completed with status 0
0.27/0.92	# Result found by ho_unfolding_5
0.27/0.92	# Preprocessing class: HSLMSLSSLLLCHSA.
0.27/0.92	# Scheduled 5 strats onto 8 cores with 240 seconds (1920 total)
0.27/0.92	# Starting ho_unfolding_5 with 960s (4) cores
0.27/0.92	# No SInE strategy applied
0.27/0.92	# Search class: HGHSM-FSLM32-DHSMMSBN
0.27/0.92	# partial match(1): HGHSM-FSLM32-MHSMMSBN
0.27/0.92	# Scheduled 12 strats onto 4 cores with 960 seconds (960 total)
0.27/0.92	# Starting full_lambda_5 with 79s (1) cores
0.27/0.92	# Starting ho_unfolding_5 with 97s (1) cores
0.27/0.92	# Preprocessing time       : 0.005 s
0.27/0.92	# Presaturation interreduction done
0.27/0.92	
0.27/0.92	# Proof found!
0.27/0.92	# SZS status Theorem
0.27/0.92	# SZS output start CNFRefutation
0.27/0.92	thf(decl_23, type, in: $i > $i > $o).
0.27/0.92	thf(decl_24, type, exu: ($i > $o) > $o).
0.27/0.92	thf(decl_25, type, setextAx: $o).
0.27/0.92	thf(decl_26, type, emptyset: $i).
0.27/0.92	thf(decl_27, type, emptysetAx: $o).
0.27/0.92	thf(decl_28, type, setadjoin: $i > $i > $i).
0.27/0.92	thf(decl_29, type, setadjoinAx: $o).
0.27/0.92	thf(decl_30, type, powerset: $i > $i).
0.27/0.92	thf(decl_31, type, powersetAx: $o).
0.27/0.92	thf(decl_32, type, setunion: $i > $i).
0.27/0.92	thf(decl_33, type, setunionAx: $o).
0.27/0.92	thf(decl_34, type, omega: $i).
0.27/0.92	thf(decl_35, type, omega0Ax: $o).
0.27/0.92	thf(decl_36, type, omegaSAx: $o).
0.27/0.92	thf(decl_37, type, omegaIndAx: $o).
0.27/0.92	thf(decl_38, type, replAx: $o).
0.27/0.92	thf(decl_39, type, foundationAx: $o).
0.27/0.92	thf(decl_40, type, wellorderingAx: $o).
0.27/0.92	thf(decl_41, type, descr: ($i > $o) > $i).
0.27/0.92	thf(decl_42, type, descrp: $o).
0.27/0.92	thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
0.27/0.92	thf(decl_44, type, dsetconstrI: $o).
0.27/0.92	thf(decl_45, type, dsetconstrEL: $o).
0.27/0.92	thf(decl_46, type, dsetconstrER: $o).
0.27/0.92	thf(decl_47, type, exuE1: $o).
0.27/0.92	thf(decl_48, type, prop2set: $o > $i).
0.27/0.92	thf(decl_49, type, prop2setE: $o).
0.27/0.92	thf(decl_50, type, emptysetE: $o).
0.27/0.92	thf(decl_51, type, emptysetimpfalse: $o).
0.27/0.92	thf(decl_52, type, notinemptyset: $o).
0.27/0.92	thf(decl_53, type, exuE3e: $o).
0.27/0.92	thf(decl_54, type, setext: $o).
0.27/0.92	thf(decl_55, type, emptyI: $o).
0.27/0.92	thf(decl_56, type, noeltsimpempty: $o).
0.27/0.92	thf(decl_57, type, setbeta: $o).
0.27/0.92	thf(decl_58, type, nonempty: $i > $o).
0.27/0.92	thf(decl_59, type, nonemptyE1: $o).
0.27/0.92	thf(decl_60, type, nonemptyI: $o).
0.27/0.92	thf(decl_61, type, nonemptyI1: $o).
0.27/0.92	thf(decl_62, type, setadjoinIL: $o).
0.27/0.92	thf(decl_63, type, emptyinunitempty: $o).
0.27/0.92	thf(decl_64, type, setadjoinIR: $o).
0.27/0.92	thf(decl_65, type, setadjoinE: $o).
0.27/0.92	thf(decl_66, type, setadjoinOr: $o).
0.27/0.92	thf(decl_67, type, setoftrueEq: $o).
0.27/0.92	thf(decl_68, type, powersetI: $o).
0.27/0.92	thf(decl_69, type, emptyinPowerset: $o).
0.27/0.92	thf(decl_70, type, emptyInPowerset: $o).
0.27/0.92	thf(decl_71, type, powersetE: $o).
0.27/0.92	thf(decl_72, type, setunionI: $o).
0.27/0.92	thf(decl_73, type, setunionE: $o).
0.27/0.92	thf(decl_74, type, subPowSU: $o).
0.27/0.92	thf(decl_75, type, exuE2: $o).
0.27/0.92	thf(decl_76, type, nonemptyImpWitness: $o).
0.27/0.92	thf(decl_77, type, uniqinunit: $o).
0.27/0.92	thf(decl_78, type, notinsingleton: $o).
0.27/0.92	thf(decl_79, type, eqinunit: $o).
0.27/0.92	thf(decl_80, type, singletonsswitch: $o).
0.27/0.92	thf(decl_81, type, upairsetE: $o).
0.27/0.92	thf(decl_82, type, upairsetIL: $o).
0.27/0.92	thf(decl_83, type, upairsetIR: $o).
0.27/0.92	thf(decl_84, type, emptyE1: $o).
0.27/0.92	thf(decl_85, type, vacuousDall: $o).
0.27/0.92	thf(decl_86, type, quantDeMorgan1: $o).
0.27/0.92	thf(decl_87, type, quantDeMorgan2: $o).
0.27/0.92	thf(decl_88, type, quantDeMorgan3: $o).
0.27/0.92	thf(decl_89, type, quantDeMorgan4: $o).
0.27/0.92	thf(decl_90, type, prop2setI: $o).
0.27/0.92	thf(decl_91, type, set2prop: $i > $o).
0.27/0.92	thf(decl_92, type, prop2set2propI: $o).
0.27/0.92	thf(decl_93, type, notdexE: $o).
0.27/0.92	thf(decl_94, type, notdallE: $o).
0.27/0.92	thf(decl_95, type, exuI1: $o).
0.27/0.92	thf(decl_96, type, exuI3: $o).
0.27/0.92	thf(decl_97, type, exuI2: $o).
0.27/0.92	thf(decl_98, type, inCongP: $o).
0.27/0.92	thf(decl_99, type, in__Cong: $o).
0.27/0.92	thf(decl_100, type, exuE3u: $o).
0.27/0.92	thf(decl_101, type, exu__Cong: $o).
0.27/0.92	thf(decl_102, type, emptyset__Cong: $o).
0.27/0.92	thf(decl_103, type, setadjoin__Cong: $o).
0.27/0.92	thf(decl_104, type, powerset__Cong: $o).
0.27/0.92	thf(decl_105, type, setunion__Cong: $o).
0.27/0.92	thf(decl_106, type, omega__Cong: $o).
0.27/0.92	thf(decl_107, type, exuEu: $o).
0.27/0.92	thf(decl_108, type, descr__Cong: $o).
0.27/0.92	thf(decl_109, type, dsetconstr__Cong: $o).
0.27/0.92	thf(decl_110, type, subset: $i > $i > $o).
0.27/0.92	thf(decl_113, type, subsetI1: $o).
0.27/0.92	thf(decl_114, type, eqimpsubset2: $o).
0.27/0.92	thf(decl_115, type, eqimpsubset1: $o).
0.27/0.92	thf(decl_116, type, subsetI2: $o).
0.27/0.92	thf(decl_117, type, emptysetsubset: $o).
0.27/0.92	thf(decl_118, type, subsetE: $o).
0.27/0.92	thf(decl_119, type, subsetE2: $o).
0.27/0.92	thf(decl_120, type, notsubsetI: $o).
0.27/0.92	thf(decl_121, type, notequalI1: $o).
0.27/0.92	thf(decl_122, type, notequalI2: $o).
0.27/0.92	thf(decl_123, type, subsetRefl: $o).
0.27/0.92	thf(decl_124, type, subsetTrans: $o).
0.27/0.92	thf(decl_125, type, setadjoinSub: $o).
0.27/0.92	thf(decl_126, type, setadjoinSub2: $o).
0.27/0.92	thf(decl_127, type, subset2powerset: $o).
0.27/0.92	thf(decl_128, type, setextsub: $o).
0.27/0.92	thf(decl_129, type, subsetemptysetimpeq: $o).
0.27/0.92	thf(decl_130, type, powersetI1: $o).
0.27/0.92	thf(decl_131, type, powersetE1: $o).
0.27/0.92	thf(decl_132, type, inPowerset: $o).
0.27/0.92	thf(decl_133, type, powersetsubset: $o).
0.27/0.92	thf(decl_134, type, sepInPowerset: $o).
0.27/0.92	thf(decl_135, type, sepSubset: $o).
0.27/0.92	thf(decl_136, type, binunion: $i > $i > $i).
0.27/0.92	thf(decl_137, type, binunionIL: $o).
0.27/0.92	thf(decl_138, type, upairset2IR: $o).
0.27/0.92	thf(decl_139, type, binunionIR: $o).
0.27/0.92	thf(decl_140, type, binunionEcases: $o).
0.27/0.92	thf(decl_141, type, binunionE: $o).
0.27/0.92	thf(decl_142, type, binunionLsub: $o).
0.27/0.92	thf(decl_143, type, binunionRsub: $o).
0.27/0.92	thf(decl_144, type, binintersect: $i > $i > $i).
0.27/0.92	thf(decl_145, type, binintersectI: $o).
0.27/0.92	thf(decl_146, type, binintersectSubset5: $o).
0.27/0.92	thf(decl_147, type, binintersectEL: $o).
0.27/0.92	thf(decl_148, type, binintersectLsub: $o).
0.27/0.92	thf(decl_149, type, binintersectSubset2: $o).
0.27/0.92	thf(decl_150, type, binintersectSubset3: $o).
0.27/0.92	thf(decl_151, type, binintersectER: $o).
0.27/0.92	thf(decl_152, type, disjointsetsI1: $o).
0.27/0.92	thf(decl_153, type, binintersectRsub: $o).
0.27/0.92	thf(decl_154, type, binintersectSubset4: $o).
0.27/0.92	thf(decl_155, type, binintersectSubset1: $o).
0.27/0.92	thf(decl_156, type, bs114d: $o).
0.27/0.92	thf(decl_158, type, setminus: $i > $i > $i).
0.27/0.92	thf(decl_159, type, setminusI: $o).
0.27/0.92	thf(decl_160, type, setminusEL: $o).
0.27/0.92	thf(decl_161, type, setminusER: $o).
0.27/0.92	thf(decl_162, type, setminusSubset2: $o).
0.27/0.92	thf(decl_163, type, setminusERneg: $o).
0.27/0.92	thf(decl_164, type, setminusELneg: $o).
0.27/0.92	thf(decl_165, type, setminusILneg: $o).
0.27/0.92	thf(decl_166, type, setminusIRneg: $o).
0.27/0.92	thf(decl_167, type, setminusLsub: $o).
0.27/0.92	thf(decl_168, type, setminusSubset1: $o).
0.27/0.92	thf(decl_169, type, symdiff: $i > $i > $i).
0.27/0.92	thf(decl_170, type, symdiffE: $o).
0.27/0.92	thf(decl_171, type, symdiffI1: $o).
0.27/0.92	thf(decl_172, type, symdiffI2: $o).
0.27/0.92	thf(decl_173, type, symdiffIneg1: $o).
0.27/0.92	thf(decl_174, type, symdiffIneg2: $o).
0.27/0.92	thf(decl_175, type, iskpair: $i > $o).
0.27/0.92	thf(decl_176, type, secondinupair: $o).
0.27/0.92	thf(decl_177, type, setukpairIL: $o).
0.27/0.92	thf(decl_178, type, setukpairIR: $o).
0.27/0.92	thf(decl_179, type, kpairiskpair: $o).
0.27/0.92	thf(decl_180, type, kpair: $i > $i > $i).
0.27/0.92	thf(decl_181, type, kpairp: $o).
0.27/0.92	thf(decl_182, type, cartprod: $i > $i > $i).
0.27/0.92	thf(decl_183, type, singletonsubset: $o).
0.27/0.92	thf(decl_184, type, singletoninpowerset: $o).
0.27/0.92	thf(decl_185, type, singletoninpowunion: $o).
0.27/0.92	thf(decl_186, type, upairset2E: $o).
0.27/0.92	thf(decl_187, type, upairsubunion: $o).
0.27/0.92	thf(decl_188, type, upairinpowunion: $o).
0.27/0.92	thf(decl_189, type, ubforcartprodlem1: $o).
0.27/0.92	thf(decl_190, type, ubforcartprodlem2: $o).
0.27/0.92	thf(decl_191, type, ubforcartprodlem3: $o).
0.27/0.92	thf(decl_192, type, cartprodpairin: $o).
0.27/0.92	thf(decl_193, type, cartprodmempair1: $o).
0.27/0.92	thf(decl_194, type, cartprodmempair: $o).
0.27/0.92	thf(decl_195, type, setunionE2: $o).
0.27/0.92	thf(decl_196, type, setunionsingleton1: $o).
0.27/0.92	thf(decl_197, type, setunionsingleton2: $o).
0.27/0.92	thf(decl_198, type, setunionsingleton: $o).
0.27/0.92	thf(decl_199, type, singleton: $i > $o).
0.27/0.92	thf(decl_200, type, singletonprop: $o).
0.27/0.92	thf(decl_201, type, ex1: $i > ($i > $o) > $o).
0.27/0.92	thf(decl_202, type, ex1E1: $o).
0.27/0.92	thf(decl_203, type, ex1I: $o).
0.27/0.92	thf(decl_204, type, ex1I2: $o).
0.27/0.92	thf(decl_205, type, singletonsuniq: $o).
0.27/0.92	thf(decl_210, type, setukpairinjL1: $o).
0.27/0.92	thf(decl_211, type, kfstsingleton: $o).
0.27/0.92	thf(decl_212, type, theprop: $o).
0.27/0.92	thf(decl_213, type, kfst: $i > $i).
0.27/0.92	thf(decl_214, type, kfstpairEq: $o).
0.27/0.92	thf(decl_215, type, cartprodfstin: $o).
0.27/0.92	thf(decl_216, type, setukpairinjL2: $o).
0.27/0.92	thf(decl_217, type, setukpairinjL: $o).
0.27/0.92	thf(decl_218, type, setukpairinjR11: $o).
0.27/0.92	thf(decl_219, type, setukpairinjR12: $o).
0.27/0.92	thf(decl_220, type, setukpairinjR1: $o).
0.27/0.92	thf(decl_221, type, upairequniteq: $o).
0.27/0.92	thf(decl_222, type, setukpairinjR2: $o).
0.27/0.92	thf(decl_223, type, setukpairinjR: $o).
0.27/0.92	thf(decl_224, type, ksndsingleton: $o).
0.27/0.92	thf(decl_225, type, ksnd: $i > $i).
0.27/0.92	thf(decl_226, type, ksndpairEq: $o).
0.27/0.92	thf(decl_227, type, kpairsurjEq: $o).
0.27/0.92	thf(decl_228, type, cartprodsndin: $o).
0.27/0.92	thf(decl_229, type, cartprodpairmemEL: $o).
0.27/0.92	thf(decl_230, type, cartprodpairmemER: $o).
0.27/0.92	thf(decl_231, type, cartprodmempaircEq: $o).
0.27/0.92	thf(decl_232, type, cartprodfstpairEq: $o).
0.27/0.92	thf(decl_233, type, cartprodsndpairEq: $o).
0.27/0.92	thf(decl_234, type, cartprodpairsurjEq: $o).
0.27/0.92	thf(decl_235, type, breln: $i > $i > $i > $o).
0.27/0.92	thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
0.27/0.92	thf(decl_237, type, dpsetconstrI: $o).
0.27/0.92	thf(decl_238, type, dpsetconstrSub: $o).
0.27/0.92	thf(decl_239, type, setOfPairsIsBReln: $o).
0.27/0.92	thf(decl_240, type, dpsetconstrERa: $o).
0.27/0.92	thf(decl_241, type, dpsetconstrEL1: $o).
0.27/0.92	thf(decl_242, type, dpsetconstrEL2: $o).
0.27/0.92	thf(decl_243, type, dpsetconstrER: $o).
0.27/0.92	thf(decl_244, type, func: $i > $i > $i > $o).
0.27/0.92	thf(decl_245, type, funcSet: $i > $i > $i).
0.27/0.92	thf(decl_246, type, funcImageSingleton: $o).
0.27/0.92	thf(decl_247, type, apProp: $o).
0.27/0.92	thf(decl_248, type, ap: $i > $i > $i > $i > $i).
0.27/0.92	thf(decl_249, type, app: $o).
0.27/0.92	thf(decl_250, type, infuncsetfunc: $o).
0.27/0.92	thf(decl_251, type, ap2p: $o).
0.27/0.92	thf(decl_252, type, funcinfuncset: $o).
0.27/0.92	thf(decl_253, type, lamProp: $o).
0.27/0.92	thf(decl_254, type, lam: $i > $i > ($i > $i) > $i).
0.27/0.92	thf(decl_255, type, lamp: $o).
0.27/0.92	thf(decl_256, type, lam2p: $o).
0.27/0.92	thf(decl_257, type, epred1_0: $o).
0.27/0.92	thf(decl_258, type, esk1_2: $i > $i > $i).
0.27/0.92	thf(decl_259, type, esk2_2: $i > $i > $i).
0.27/0.92	thf(decl_260, type, esk3_2: $i > $i > $i).
0.27/0.92	thf(decl_261, type, esk4_1: $i > $i).
0.27/0.92	thf(decl_262, type, esk5_2: ($i > $i > $o) > $i > $i).
0.27/0.92	thf(decl_263, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
0.27/0.92	thf(decl_264, type, esk7_2: ($i > $i > $o) > $i > $i).
0.27/0.92	thf(decl_265, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
0.27/0.92	thf(decl_266, type, esk9_1: $i > $i).
0.27/0.92	thf(decl_267, type, esk10_2: ($i > $o) > $i > $i).
0.27/0.92	thf(decl_268, type, esk11_2: ($i > $o) > $i > $i).
0.27/0.92	thf(decl_269, type, esk12_1: ($i > $o) > $i).
0.27/0.92	thf(decl_270, type, esk13_2: ($i > $o) > $i > $i).
0.27/0.92	thf(decl_271, type, esk14_1: ($i > $o) > $i).
0.27/0.92	thf(decl_272, type, esk15_2: $i > $i > $i).
0.27/0.92	thf(decl_273, type, esk16_2: $i > $i > $i).
0.27/0.92	thf(decl_274, type, esk17_1: $i > $i).
0.27/0.92	thf(decl_275, type, esk18_1: $i > $i).
0.27/0.92	thf(decl_276, type, esk19_1: $i > $i).
0.27/0.92	thf(decl_277, type, esk20_2: $i > $i > $i).
0.27/0.92	thf(decl_278, type, esk21_3: $i > $i > $o > $i).
0.27/0.92	thf(decl_279, type, esk22_2: ($i > $o) > $i > $i).
0.27/0.92	thf(decl_280, type, esk23_1: ($i > $o) > $i).
0.27/0.92	thf(decl_281, type, esk24_1: $i > $i).
0.27/0.92	thf(decl_282, type, esk25_2: $i > ($i > $o) > $i).
0.27/0.92	thf(decl_283, type, esk26_2: $i > ($i > $o) > $i).
0.27/0.92	thf(decl_284, type, esk27_2: $i > ($i > $o) > $i).
0.27/0.92	thf(decl_285, type, esk28_2: $i > ($i > $o) > $i).
0.27/0.92	thf(decl_286, type, esk29_2: $i > ($i > $o) > $i).
0.27/0.92	thf(decl_287, type, esk30_2: $i > ($i > $o) > $i).
0.27/0.92	thf(decl_288, type, esk31_2: ($i > $o) > $i > $i).
0.27/0.92	thf(decl_289, type, esk32_1: ($i > $o) > $i).
0.27/0.92	thf(decl_290, type, esk33_1: ($i > $o) > $i).
0.27/0.92	thf(decl_291, type, esk34_1: ($i > $o) > $i).
0.27/0.92	thf(decl_292, type, esk35_1: ($i > $o) > $i).
0.27/0.92	thf(decl_293, type, esk36_2: ($i > $o) > $i > $i).
0.27/0.92	thf(decl_294, type, esk37_1: ($i > $o) > $i).
0.27/0.92	thf(decl_295, type, esk38_2: ($i > $o) > $i > $i).
0.27/0.92	thf(decl_296, type, esk39_2: ($i > $o) > ($i > $o) > $i).
0.27/0.92	thf(decl_297, type, esk40_2: ($i > $o) > ($i > $o) > $i).
0.27/0.92	thf(decl_298, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
0.27/0.92	thf(decl_299, type, esk42_2: ($i > $o) > ($i > $o) > $i).
0.27/0.92	thf(decl_300, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
0.27/0.92	thf(decl_301, type, esk44_2: ($i > $o) > ($i > $o) > $i).
0.27/0.92	thf(decl_302, type, esk45_2: ($i > $o) > $i > $i).
0.27/0.92	thf(decl_303, type, esk46_2: ($i > $o) > ($i > $o) > $i).
0.27/0.92	thf(decl_304, type, esk47_2: ($i > $o) > ($i > $o) > $i).
0.27/0.92	thf(decl_305, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
0.27/0.92	thf(decl_306, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
0.27/0.92	thf(decl_307, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
0.27/0.92	thf(decl_308, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
0.27/0.92	thf(decl_309, type, esk52_2: $i > $i > $i).
0.27/0.92	thf(decl_310, type, esk53_2: $i > $i > $i).
0.27/0.92	thf(decl_311, type, esk54_2: $i > $i > $i).
0.27/0.92	thf(decl_312, type, esk55_3: $i > $i > $i > $i).
0.27/0.92	thf(decl_313, type, esk56_3: $i > $i > $i > $i).
0.27/0.92	thf(decl_314, type, esk57_2: $i > $i > $i).
0.27/0.92	thf(decl_315, type, esk58_2: $i > ($i > $o) > $i).
0.27/0.92	thf(decl_316, type, esk59_2: $i > ($i > $o) > $i).
0.27/0.92	thf(decl_317, type, esk60_2: $i > ($i > $o) > $i).
0.27/0.92	thf(decl_318, type, esk61_2: $i > ($i > $o) > $i).
0.27/0.92	thf(decl_319, type, esk62_3: $i > ($i > $o) > $i > $i).
0.27/0.92	thf(decl_320, type, esk63_3: $i > ($i > $o) > $i > $i).
0.27/0.92	thf(decl_321, type, esk64_2: $i > ($i > $o) > $i).
0.27/0.92	thf(decl_322, type, esk65_2: $i > ($i > $o) > $i).
0.27/0.92	thf(decl_323, type, esk66_2: $i > ($i > $o) > $i).
0.27/0.92	thf(decl_324, type, esk67_1: $i > $i).
0.27/0.92	thf(decl_325, type, esk68_1: $i > $i).
0.27/0.92	thf(decl_326, type, esk69_3: $i > $i > $i > $i).
0.27/0.92	thf(decl_327, type, esk70_4: $i > $i > $i > $i > $i).
0.27/0.92	thf(decl_328, type, esk71_3: $i > $i > $i > $i).
0.27/0.92	thf(decl_329, type, esk72_3: $i > $i > $i > $i).
0.27/0.92	thf(decl_330, type, esk73_4: $i > $i > $i > $i > $i).
0.27/0.92	thf(decl_331, type, esk74_3: $i > $i > $i > $i).
0.27/0.92	thf(decl_332, type, esk75_3: $i > $i > ($i > $i) > $i).
0.27/0.92	thf(decl_333, type, esk76_4: $i > $i > ($i > $i) > $i > $i).
0.27/0.92	thf(decl_334, type, esk77_3: $i > $i > ($i > $i) > $i).
0.27/0.92	thf(decl_335, type, esk78_4: $i > $i > ($i > $i) > $i > $i).
0.27/0.92	thf(decl_336, type, esk79_3: $i > $i > ($i > $i) > $i).
0.27/0.92	thf(decl_337, type, esk80_0: $i).
0.27/0.92	thf(decl_338, type, esk81_0: $i).
0.27/0.92	thf(decl_339, type, esk82_0: $i).
0.27/0.92	thf(decl_340, type, epred2_0: $i > $o).
0.27/0.92	thf(decl_341, type, esk83_0: $i).
0.27/0.92	thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', ex1)).
0.27/0.92	thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', singleton)).
0.27/0.92	thf(func, axiom, ((func)=(^[X4:$i, X5:$i, X29:$i]:(((breln @ X4 @ X5 @ X29)&![X2:$i]:(((in @ X2 @ X4)=>(ex1 @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', func)).
0.27/0.92	thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', breln)).
0.27/0.92	thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', replAx)).
0.27/0.92	thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', exu)).
0.27/0.92	thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', descrp)).
0.27/0.92	thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', exuE1)).
0.27/0.92	thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', exuE3e)).
0.27/0.92	thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', nonempty)).
0.27/0.92	thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', nonemptyI)).
0.27/0.92	thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', exuE2)).
0.27/0.92	thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', exuI1)).
0.27/0.92	thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', exuI3)).
0.27/0.92	thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', exuI2)).
0.27/0.92	thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', exuE3u)).
0.27/0.92	thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', exu__Cong)).
0.27/0.92	thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', exuEu)).
0.27/0.92	thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', descr__Cong)).
0.27/0.92	thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', singletonprop)).
0.27/0.92	thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', ex1E1)).
0.27/0.92	thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', ex1I)).
0.27/0.92	thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', ex1I2)).
0.27/0.92	thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', kfstsingleton)).
0.27/0.92	thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', ksndsingleton)).
0.27/0.92	thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setOfPairsIsBReln)).
0.27/0.92	thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30)))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', funcImageSingleton)).
0.27/0.92	thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', apProp)).
0.27/0.92	thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X31 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', lamProp)).
0.27/0.92	thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X33 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', lamp)).
0.27/0.92	thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', dsetconstrI)).
0.27/0.92	thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', dsetconstrEL)).
0.27/0.92	thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', dsetconstrER)).
0.27/0.92	thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setbeta)).
0.27/0.92	thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', nonemptyE1)).
0.27/0.92	thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', nonemptyI1)).
0.27/0.92	thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setoftrueEq)).
0.27/0.92	thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', nonemptyImpWitness)).
0.27/0.92	thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', emptyE1)).
0.27/0.92	thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', dsetconstr__Cong)).
0.27/0.92	thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', sepInPowerset)).
0.27/0.92	thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', sepSubset)).
0.27/0.92	thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', theprop)).
0.27/0.92	thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', dpsetconstrI)).
0.27/0.92	thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', dpsetconstrSub)).
0.27/0.92	thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', dpsetconstrERa)).
0.27/0.92	thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', dpsetconstrEL1)).
0.27/0.92	thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', dpsetconstrEL2)).
0.27/0.92	thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', dpsetconstrER)).
0.27/0.92	thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', app)).
0.27/0.92	thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X30)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', infuncsetfunc)).
0.27/0.92	thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>(in @ X30 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', funcinfuncset)).
0.27/0.92	thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X34:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X34 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X34 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', lam2p)).
0.27/0.92	thf(brelnall1, conjecture, ((setextAx)=>(((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((((omegaIndAx)=>(((foundationAx)=>(((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((((((notinemptyset)=>(((((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>(((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((((emptyinPowerset)=>((emptyInPowerset)=>(((setunionI)=>((setunionE)=>((subPowSU)=>(((nonemptyImpWitness)=>(((((singletonsswitch)=>(((upairsetIL)=>((upairsetIR)=>((((quantDeMorgan1)=>((quantDeMorgan2)=>(((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>(((inCongP)=>(((exuE3u)=>((exu__Cong)=>(((((setunion__Cong)=>(((exuEu)=>(((((((subsetI2)=>(((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>(((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>(((subsetemptysetimpeq)=>((((inPowerset)=>((powersetsubset)=>(((sepSubset)=>(((upairset2IR)=>(((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((((binintersectEL)=>(((binintersectSubset2)=>((((disjointsetsI1)=>(((((bs114d)=>((((setminusER)=>(((setminusERneg)=>((setminusELneg)=>(((setminusIRneg)=>(((setminusSubset1)=>(((((symdiffIneg1)=>(((secondinupair)=>((setukpairIL)=>(((kpairiskpair)=>((kpairp)=>((((singletoninpowunion)=>((((upairinpowunion)=>(((((cartprodpairin)=>(((cartprodmempair)=>(((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>(((ex1I2)=>((((kfstsingleton)=>((((((setukpairinjL)=>((setukpairinjR11)=>(((setukpairinjR1)=>(((((ksndsingleton)=>((ksndpairEq)=>((((cartprodpairmemEL)=>(((cartprodmempaircEq)=>(((cartprodsndpairEq)=>(((dpsetconstrI)=>((((dpsetconstrERa)=>(((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>(((app)=>(((((lamProp)=>((lamp)=>(![X4:$i, X5:$i, X29:$i]:(((breln @ X4 @ X5 @ X29)=>![X1:$i > $o]:((![X2:$i]:((![X3:$i]:(((in @ X3 @ X5)=>((X1 @ (kpair @ X2 @ X3))<=(in @ (kpair @ X2 @ X3) @ X29))))<=(in @ X2 @ X4)))=>![X2:$i]:(((X1 @ X2)<=(in @ X2 @ X29)))))))<=(lam2p))))<=(funcinfuncset))<=(ap2p))<=(infuncsetfunc)))<=(apProp)))))<=(dpsetconstrEL1)))<=(setOfPairsIsBReln))<=(dpsetconstrSub)))<=(cartprodpairsurjEq)))<=(cartprodfstpairEq)))<=(cartprodpairmemER)))<=(cartprodsndin))<=(kpairsurjEq))))<=(setukpairinjR))<=(setukpairinjR2))<=(upairequniteq)))<=(setukpairinjR12))))<=(setukpairinjL2))<=(cartprodfstin))<=(kfstpairEq))<=(theprop)))<=(setukpairinjL1))<=(singletonsuniq)))<=(ex1I)))))))<=(setunionE2)))<=(cartprodmempair1)))<=(ubforcartprodlem3))<=(ubforcartprodlem2))<=(ubforcartprodlem1)))<=(upairsubunion))<=(upairset2E)))<=(singletoninpowerset))<=(singletonsubset))))<=(setukpairIR))))<=(symdiffIneg2)))<=(symdiffI2))<=(symdiffI1))<=(symdiffE)))<=(setminusLsub)))<=(setminusILneg))))<=(setminusSubset2)))<=(setminusEL))<=(setminusI)))<=(binintersectSubset1))<=(binintersectSubset4))<=(binintersectRsub)))<=(binintersectER))<=(binintersectSubset3)))<=(binintersectLsub)))<=(binintersectSubset5))<=(binintersectI))))))<=(binunionIR)))<=(binunionIL)))<=(sepInPowerset))))<=(powersetE1))<=(powersetI1)))<=(setextsub)))))<=(subsetTrans))))))))<=(emptysetsubset)))<=(eqimpsubset1))<=(eqimpsubset2))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong)))<=(omega__Cong)))<=(powerset__Cong))<=(setadjoin__Cong))<=(emptyset__Cong))))<=(in__Cong)))<=(exuI2)))))))))<=(quantDeMorgan3))))<=(vacuousDall))<=(emptyE1))))<=(upairsetE)))<=(eqinunit))<=(notinsingleton))<=(uniqinunit)))<=(exuE2)))))<=(powersetE))))<=(powersetI))<=(setoftrueEq))))))))<=(nonemptyI)))))<=(emptyI))<=(setext))<=(exuE3e)))<=(emptysetimpfalse))<=(emptysetE))<=(prop2setE))<=(exuE1))))))<=(wellorderingAx)))<=(replAx)))<=(omegaSAx))<=(omega0Ax)))))<=(emptysetAx))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', brelnall1)).
0.27/0.92	thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setextAx)).
0.27/0.92	thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', emptysetAx)).
0.27/0.92	thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setadjoinAx)).
0.27/0.92	thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', powersetAx)).
0.27/0.92	thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setunionAx)).
0.27/0.92	thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', omega0Ax)).
0.27/0.92	thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', omegaSAx)).
0.27/0.92	thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', omegaIndAx)).
0.27/0.92	thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', foundationAx)).
0.27/0.92	thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', wellorderingAx)).
0.27/0.92	thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', prop2setE)).
0.27/0.92	thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', emptysetE)).
0.27/0.92	thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', emptysetimpfalse)).
0.27/0.92	thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', notinemptyset)).
0.27/0.92	thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setext)).
0.27/0.92	thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', emptyI)).
0.27/0.92	thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', noeltsimpempty)).
0.27/0.92	thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setadjoinIL)).
0.27/0.92	thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', emptyinunitempty)).
0.27/0.92	thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setadjoinIR)).
0.27/0.92	thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setadjoinE)).
0.27/0.92	thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setadjoinOr)).
0.27/0.92	thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', powersetI)).
0.27/0.92	thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', emptyinPowerset)).
0.27/0.92	thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', emptyInPowerset)).
0.27/0.92	thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', powersetE)).
0.27/0.92	thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setunionI)).
0.27/0.92	thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setunionE)).
0.27/0.92	thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', subPowSU)).
0.27/0.92	thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', uniqinunit)).
0.27/0.92	thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', notinsingleton)).
0.27/0.92	thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', eqinunit)).
0.27/0.92	thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', singletonsswitch)).
0.27/0.92	thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', upairsetE)).
0.27/0.92	thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', upairsetIL)).
0.27/0.92	thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', upairsetIR)).
0.27/0.92	thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', vacuousDall)).
0.27/0.92	thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', quantDeMorgan1)).
0.27/0.92	thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', quantDeMorgan2)).
0.27/0.92	thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', quantDeMorgan3)).
0.27/0.92	thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', quantDeMorgan4)).
0.27/0.92	thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', prop2setI)).
0.27/0.92	thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', prop2set2propI)).
0.27/0.92	thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', notdexE)).
0.27/0.92	thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', notdallE)).
0.27/0.92	thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', inCongP)).
0.27/0.92	thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', in__Cong)).
0.27/0.92	thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', emptyset__Cong)).
0.27/0.92	thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setadjoin__Cong)).
0.27/0.92	thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', powerset__Cong)).
0.27/0.92	thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setunion__Cong)).
0.27/0.92	thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', omega__Cong)).
0.27/0.92	thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', subsetI1)).
0.27/0.92	thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', eqimpsubset2)).
0.27/0.92	thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', eqimpsubset1)).
0.27/0.92	thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', subsetI2)).
0.27/0.92	thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', emptysetsubset)).
0.27/0.92	thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', subsetE)).
0.27/0.92	thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', subsetE2)).
0.27/0.92	thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', notsubsetI)).
0.27/0.92	thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', notequalI1)).
0.27/0.92	thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', notequalI2)).
0.27/0.92	thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', subsetRefl)).
0.27/0.92	thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', subsetTrans)).
0.27/0.92	thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setadjoinSub)).
0.27/0.92	thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setadjoinSub2)).
0.27/0.92	thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', subset2powerset)).
0.27/0.92	thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setextsub)).
0.27/0.92	thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', subsetemptysetimpeq)).
0.27/0.92	thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', powersetI1)).
0.27/0.92	thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', powersetE1)).
0.27/0.92	thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', inPowerset)).
0.27/0.92	thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', powersetsubset)).
0.27/0.92	thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', binunionIL)).
0.27/0.92	thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', upairset2IR)).
0.27/0.92	thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', binunionIR)).
0.27/0.92	thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', binunionEcases)).
0.27/0.92	thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', binunionE)).
0.27/0.92	thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', binunionLsub)).
0.27/0.92	thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', binunionRsub)).
0.27/0.92	thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', binintersectI)).
0.27/0.92	thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', binintersectSubset5)).
0.27/0.92	thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', binintersectEL)).
0.27/0.92	thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', binintersectLsub)).
0.27/0.92	thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', binintersectSubset2)).
0.27/0.92	thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', binintersectSubset3)).
0.27/0.92	thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', binintersectER)).
0.27/0.92	thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', disjointsetsI1)).
0.27/0.92	thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', binintersectRsub)).
0.27/0.92	thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', binintersectSubset4)).
0.27/0.92	thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', binintersectSubset1)).
0.27/0.92	thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', bs114d)).
0.27/0.92	thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setminusI)).
0.27/0.92	thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setminusEL)).
0.27/0.92	thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setminusER)).
0.27/0.92	thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setminusSubset2)).
0.27/0.92	thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setminusERneg)).
0.27/0.92	thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setminusELneg)).
0.27/0.92	thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setminusILneg)).
0.27/0.92	thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setminusIRneg)).
0.27/0.92	thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setminusLsub)).
0.27/0.92	thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setminusSubset1)).
0.27/0.92	thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', symdiffE)).
0.27/0.92	thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', symdiffI1)).
0.27/0.92	thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', symdiffI2)).
0.27/0.92	thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', symdiffIneg1)).
0.27/0.92	thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', symdiffIneg2)).
0.27/0.92	thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', secondinupair)).
0.27/0.92	thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setukpairIL)).
0.27/0.92	thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setukpairIR)).
0.27/0.92	thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', kpairiskpair)).
0.27/0.92	thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', kpairp)).
0.27/0.92	thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', singletonsubset)).
0.27/0.92	thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', singletoninpowerset)).
0.27/0.92	thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', singletoninpowunion)).
0.27/0.92	thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', upairset2E)).
0.27/0.92	thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', upairsubunion)).
0.27/0.92	thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', upairinpowunion)).
0.27/0.92	thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', ubforcartprodlem1)).
0.27/0.92	thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', ubforcartprodlem2)).
0.27/0.92	thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', ubforcartprodlem3)).
0.27/0.92	thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', cartprodpairin)).
0.27/0.92	thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', cartprodmempair1)).
0.27/0.92	thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', cartprodmempair)).
0.27/0.92	thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setunionE2)).
0.27/0.92	thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setunionsingleton1)).
0.27/0.92	thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setunionsingleton2)).
0.27/0.92	thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setunionsingleton)).
0.27/0.92	thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', singletonsuniq)).
0.27/0.92	thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setukpairinjL1)).
0.27/0.92	thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', kfstpairEq)).
0.27/0.92	thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', cartprodfstin)).
0.27/0.92	thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setukpairinjL2)).
0.27/0.92	thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setukpairinjL)).
0.27/0.92	thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setukpairinjR11)).
0.27/0.92	thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setukpairinjR12)).
0.27/0.92	thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setukpairinjR1)).
0.27/0.92	thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', upairequniteq)).
0.27/0.92	thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setukpairinjR2)).
0.27/0.92	thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', setukpairinjR)).
0.27/0.92	thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', ksndpairEq)).
0.27/0.92	thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', kpairsurjEq)).
0.27/0.92	thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', cartprodsndin)).
0.27/0.92	thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', cartprodpairmemEL)).
0.27/0.92	thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', cartprodpairmemER)).
0.27/0.92	thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', cartprodmempaircEq)).
0.27/0.92	thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', cartprodfstpairEq)).
0.27/0.92	thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', cartprodsndpairEq)).
0.27/0.92	thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', cartprodpairsurjEq)).
0.27/0.92	thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.8I1R685QuK/E---3.1_32439.p', ap2p)).
0.27/0.92	thf(c_0_204, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X634:$i]:(((in @ X634 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X634 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])).
0.27/0.92	thf(c_0_205, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])).
0.27/0.92	thf(c_0_206, plain, ((func)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((((subset @ Z2 @ (cartprod @ Z0 @ Z1)))&![X2:$i]:(((in @ X2 @ Z0)=>(?[X641:$i]:(((in @ X641 @ (dsetconstr @ Z1 @ (^[Z3/* 3 */:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2))))))&((dsetconstr @ Z1 @ (^[Z3/* 3 */:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))=(setadjoin @ X641 @ emptyset))))))))))), inference(fof_simplification,[status(thm)],[func])).
0.27/0.92	thf(c_0_207, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X634:$i]:(((in @ X634 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X634 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_204, c_0_205])).
0.27/0.92	thf(c_0_208, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
0.27/0.92	thf(c_0_209, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
0.27/0.92	thf(c_0_210, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
0.27/0.92	thf(c_0_211, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
0.27/0.92	thf(c_0_212, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
0.27/0.92	thf(c_0_213, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
0.27/0.92	thf(c_0_214, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
0.27/0.92	thf(c_0_215, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
0.27/0.92	thf(c_0_216, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
0.27/0.92	thf(c_0_217, 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])).
0.27/0.92	thf(c_0_218, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
0.27/0.92	thf(c_0_219, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
0.27/0.92	thf(c_0_220, 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])).
0.27/0.92	thf(c_0_221, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
0.27/0.92	thf(c_0_222, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
0.27/0.92	thf(c_0_223, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
0.27/0.92	thf(c_0_224, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
0.27/0.92	thf(c_0_225, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
0.27/0.92	thf(c_0_226, plain, ((ex1I)<=>![X4:$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])).
0.27/0.92	thf(c_0_227, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
0.27/0.92	thf(c_0_228, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
0.27/0.92	thf(c_0_229, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
0.27/0.92	thf(c_0_230, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
0.27/0.92	thf(c_0_231, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
0.27/0.92	thf(c_0_232, plain, ((func)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((((subset @ Z2 @ (cartprod @ Z0 @ Z1)))&![X2:$i]:(((in @ X2 @ Z0)=>(?[X641:$i]:(((in @ X641 @ (dsetconstr @ Z1 @ (^[Z3/* 3 */:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2))))))&((dsetconstr @ Z1 @ (^[Z3/* 3 */:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))=(setadjoin @ X641 @ emptyset))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_206, c_0_207]), c_0_208])).
0.27/0.92	thf(c_0_233, plain, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
0.27/0.92	thf(c_0_234, plain, ((lamProp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X31 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
0.27/0.92	thf(c_0_235, plain, ((lamp)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X33 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
0.27/0.92	thf(c_0_236, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X605:$i]:((((X6 @ X2 @ X605))&![X606:$i]:((((X6 @ X2 @ X606))=>((X605)=(X606)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_209, c_0_210])).
0.27/0.92	thf(c_0_237, plain, ((descrp)=(![X1:$i > $o]:(((?[X607:$i]:((((X1 @ X607))&![X608:$i]:((((X1 @ X608))=>((X607)=(X608)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_211, c_0_210])).
0.27/0.92	thf(c_0_238, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
0.27/0.92	thf(c_0_239, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
0.27/0.92	thf(c_0_240, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
0.27/0.92	thf(c_0_241, plain, ((exuE1)=(![X1:$i > $o]:(((?[X609:$i]:((((X1 @ X609))&![X610:$i]:((((X1 @ X610))=>((X609)=(X610)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_212, c_0_210])).
0.27/0.92	thf(c_0_242, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X611:$i]:((((X1 @ X611))&![X612:$i]:((((X1 @ X612))=>((X611)=(X612)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_213, c_0_210])).
0.27/0.92	thf(c_0_243, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
0.27/0.92	thf(c_0_244, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_214])).
0.27/0.92	thf(c_0_245, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_215, c_0_214])).
0.27/0.92	thf(c_0_246, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_214])).
0.27/0.92	thf(c_0_247, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
0.27/0.92	thf(c_0_248, plain, ((exuE2)=(![X1:$i > $o]:(((?[X613:$i]:((((X1 @ X613))&![X614:$i]:((((X1 @ X614))=>((X613)=(X614)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_216, c_0_210])).
0.27/0.92	thf(c_0_249, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_214])).
0.27/0.92	thf(c_0_250, 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])).
0.27/0.92	thf(c_0_251, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X615:$i]:((((X1 @ X615))&![X616:$i]:((((X1 @ X616))=>((X615)=(X616))))))))))), inference(apply_def,[status(thm)],[c_0_217, c_0_210])).
0.27/0.92	thf(c_0_252, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X617:$i]:((((X1 @ X617))&![X618:$i]:((((X1 @ X618))=>((X617)=(X618)))))))))))), inference(apply_def,[status(thm)],[c_0_218, c_0_210])).
0.27/0.92	thf(c_0_253, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X619:$i]:((((X1 @ X619))&![X620:$i]:((((X1 @ X620))=>((X619)=(X620))))))))))), inference(apply_def,[status(thm)],[c_0_219, c_0_210])).
0.27/0.92	thf(c_0_254, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X621:$i]:((((X1 @ X621))&![X622:$i]:((((X1 @ X622))=>((X621)=(X622)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_220, c_0_210])).
0.27/0.92	thf(c_0_255, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X623:$i]:((((X1 @ X623))&![X624:$i]:((((X1 @ X624))=>((X623)=(X624)))))))<=>(?[X625:$i]:((((X17 @ X625))&![X626:$i]:((((X17 @ X626))=>((X625)=(X626)))))))))))), inference(apply_def,[status(thm)],[c_0_221, c_0_210])).
0.27/0.92	thf(c_0_256, plain, ((exuEu)=(![X1:$i > $o]:(((?[X627:$i]:((((X1 @ X627))&![X628:$i]:((((X1 @ X628))=>((X627)=(X628)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_222, c_0_210])).
0.27/0.92	thf(c_0_257, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X629:$i]:((((X1 @ X629))&![X630:$i]:((((X1 @ X630))=>((X629)=(X630)))))))=>((?[X631:$i]:((((X17 @ X631))&![X632:$i]:((((X17 @ X632))=>((X631)=(X632)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_223, c_0_210])).
0.27/0.92	thf(c_0_258, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
0.27/0.92	thf(c_0_259, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
0.27/0.92	thf(c_0_260, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
0.27/0.92	thf(c_0_261, 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)))=>(?[X633:$i]:(((in @ X633 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X633 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_224, c_0_205])).
0.27/0.92	thf(c_0_262, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X635:$i]:(((in @ X635 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X635 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_225, c_0_207])).
0.27/0.92	thf(c_0_263, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X636:$i]:(((in @ X636 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X636 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_226, c_0_207])).
0.27/0.92	thf(c_0_264, 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)))=>(?[X637:$i]:(((in @ X637 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X637 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_227, c_0_207])).
0.27/0.92	thf(c_0_265, plain, ((kfstsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X638:$i]:(((in @ X638 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X638 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_228, c_0_205])).
0.27/0.92	thf(c_0_266, axiom, ((theprop)=(![X21:$i]:(((?[X639:$i]:(((in @ X639 @ X21)&((X21)=(setadjoin @ X639 @ emptyset)))))=>(in @ (setunion @ X21) @ X21))))), inference(apply_def,[status(thm)],[theprop, c_0_205])).
0.27/0.92	thf(c_0_267, plain, ((ksndsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X640:$i]:(((in @ X640 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X640 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_229, c_0_205])).
0.27/0.92	thf(c_0_268, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
0.27/0.92	thf(c_0_269, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
0.27/0.92	thf(c_0_270, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_230, c_0_208])).
0.27/0.92	thf(c_0_271, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
0.27/0.92	thf(c_0_272, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
0.27/0.92	thf(c_0_273, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
0.27/0.92	thf(c_0_274, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
0.27/0.92	thf(c_0_275, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X30:$i]:((((((subset @ X30 @ (cartprod @ X4 @ X5)))&![X642:$i]:(((in @ X642 @ X4)=>(?[X643:$i]:(((in @ X643 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X642 @ Z0) @ X30))))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X642 @ Z0) @ X30)))))=(setadjoin @ X643 @ emptyset)))))))))=>![X2:$i]:(((in @ X2 @ X4)=>(?[X644:$i]:(((in @ X644 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30)))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))=(setadjoin @ X644 @ emptyset))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_231, c_0_205]), c_0_232])).
0.27/0.92	thf(c_0_276, plain, ((apProp)=(![X4:$i, X5:$i, X30:$i]:((((((subset @ X30 @ (cartprod @ X4 @ X5)))&![X645:$i]:(((in @ X645 @ X4)=>(?[X646:$i]:(((in @ X646 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X645 @ Z0) @ X30))))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X645 @ Z0) @ X30)))))=(setadjoin @ X646 @ emptyset)))))))))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5))))))), inference(apply_def,[status(thm)],[c_0_233, c_0_232])).
0.27/0.92	thf(c_0_277, axiom, ((app)=(![X4:$i, X5:$i, X30:$i]:((((((subset @ X30 @ (cartprod @ X4 @ X5)))&![X647:$i]:(((in @ X647 @ X4)=>(?[X648:$i]:(((in @ X648 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X647 @ Z0) @ X30))))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X647 @ Z0) @ X30)))))=(setadjoin @ X648 @ emptyset)))))))))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5))))))), inference(apply_def,[status(thm)],[app, c_0_232])).
0.27/0.92	thf(c_0_278, axiom, ((infuncsetfunc)=(![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>((((subset @ X30 @ (cartprod @ X4 @ X5)))&![X649:$i]:(((in @ X649 @ X4)=>(?[X650:$i]:(((in @ X650 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X649 @ Z0) @ X30))))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X649 @ Z0) @ X30)))))=(setadjoin @ X650 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[infuncsetfunc, c_0_232])).
0.27/0.92	thf(c_0_279, axiom, ((funcinfuncset)=(![X4:$i, X5:$i, X30:$i]:((((((subset @ X30 @ (cartprod @ X4 @ X5)))&![X651:$i]:(((in @ X651 @ X4)=>(?[X652:$i]:(((in @ X652 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X651 @ Z0) @ X30))))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X651 @ Z0) @ X30)))))=(setadjoin @ X652 @ emptyset)))))))))=>(in @ X30 @ (funcSet @ X4 @ X5)))))), inference(apply_def,[status(thm)],[funcinfuncset, c_0_232])).
0.27/0.92	thf(c_0_280, plain, ((lamProp)=(![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>((((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X31 @ Z0)=(Z1))))) @ (cartprod @ X4 @ X5)))&![X653:$i]:(((in @ X653 @ X4)=>(?[X654:$i]:(((in @ X654 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X653 @ Z0) @ (dpsetconstr @ X4 @ X5 @ (^[Z1/* 19 */:$i, Z2:$i]:(((X31 @ Z1)=(Z2)))))))))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X653 @ Z0) @ (dpsetconstr @ X4 @ X5 @ (^[Z1/* 19 */:$i, Z2:$i]:(((X31 @ Z1)=(Z2))))))))))=(setadjoin @ X654 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_234, c_0_232])).
0.27/0.92	thf(c_0_281, plain, ((lamp)=(![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>((((subset @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X33 @ Z0))) @ (cartprod @ X4 @ X5)))&![X655:$i]:(((in @ X655 @ X4)=>(?[X656:$i]:(((in @ X656 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X655 @ Z0) @ (lam @ X4 @ X5 @ (^[Z1/* 17 */:$i]:(X33 @ Z1)))))))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X655 @ Z0) @ (lam @ X4 @ X5 @ (^[Z1/* 17 */:$i]:(X33 @ Z1))))))))=(setadjoin @ X656 @ emptyset))))))))))))), inference(apply_def,[status(thm)],[c_0_235, c_0_232])).
0.27/0.92	thf(c_0_282, plain, ((lam2p)<=>![X4:$i, X5:$i, X34:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X34 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X34 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
0.27/0.92	thf(c_0_283, plain, ((epred1_0)<=>![X1241:$i]:(?[X1242:$i]:((((![X1243:$i]:(((in @ X1243 @ X1242)=>![X1244:$i]:(((in @ X1244 @ X1243)=>(in @ X1244 @ X1241)))))&![X1245:$i, X1246:$i]:((((in @ X1245 @ X1241)&(in @ X1246 @ X1241))=>(![X1247:$i]:(((in @ X1247 @ X1242)=>((in @ X1245 @ X1247)<=>(in @ X1246 @ X1247))))=>((X1245)=(X1246))))))&![X1248:$i, X1249:$i]:((((in @ X1248 @ X1242)&(in @ X1249 @ X1242))=>(![X1250:$i]:(((in @ X1250 @ X1248)=>(in @ X1250 @ X1249)))|![X1251:$i]:(((in @ X1251 @ X1249)=>(in @ X1251 @ X1248)))))))&![X1252:$i]:(((![X1253:$i]:(((in @ X1253 @ X1252)=>(in @ X1253 @ X1241)))&?[X1254:$i]:((in @ X1254 @ X1252)))=>?[X1255:$i, X1256:$i]:(((((in @ X1255 @ X1242)&(in @ X1256 @ X1252))&~(?[X1257:$i]:(((in @ X1257 @ X1255)&(in @ X1257 @ X1252)))))&![X1258:$i]:(((in @ X1258 @ X1242)=>(![X1259:$i]:(((in @ X1259 @ X1258)=>(in @ X1259 @ X1255)))|(in @ X1256 @ X1258)))))))))))), introduced(definition)).
0.27/0.92	thf(c_0_284, negated_conjecture, ~((![X657:$i, X658:$i]:((![X659:$i]:(((in @ X659 @ X657)<=>(in @ X659 @ X658)))=>((X657)=(X658))))=>(![X1269:$i]:(~(in @ X1269 @ emptyset))=>(![X660:$i, X661:$i, X662:$i]:(((in @ X662 @ (setadjoin @ X660 @ X661))<=>(((X662)=(X660))|(in @ X662 @ X661))))=>(![X663:$i, X664:$i]:(((in @ X664 @ (powerset @ X663))<=>![X665:$i]:(((in @ X665 @ X664)=>(in @ X665 @ X663)))))=>(![X666:$i, X667:$i]:(((in @ X667 @ (setunion @ X666))<=>?[X668:$i]:(((in @ X667 @ X668)&(in @ X668 @ X666)))))=>((in @ emptyset @ omega)=>(![X1268:$i]:(((in @ X1268 @ omega)=>(in @ (setadjoin @ X1268 @ X1268) @ omega)))=>(![X669:$i]:((((in @ emptyset @ X669)&![X670:$i]:((((in @ X670 @ omega)&(in @ X670 @ X669))=>(in @ (setadjoin @ X670 @ X670) @ X669))))=>![X671:$i]:(((in @ X671 @ omega)=>(in @ X671 @ X669)))))=>(![X1260:$i > $i > $o, X1261:$i]:((![X1262:$i]:(((in @ X1262 @ X1261)=>?[X1263:$i]:(((X1260 @ X1262 @ X1263)&![X1264:$i]:(((X1260 @ X1262 @ X1264)=>((X1263)=(X1264))))))))=>?[X1265:$i]:(![X1266:$i]:(((in @ X1266 @ X1265)<=>?[X1267:$i]:(((in @ X1267 @ X1261)&(X1260 @ X1267 @ X1266))))))))=>(![X672:$i]:((?[X673:$i]:((in @ X673 @ X672))=>?[X674:$i]:(((in @ X674 @ X672)&~(?[X675:$i]:(((in @ X675 @ X674)&(in @ X675 @ X672))))))))=>((epred1_0)=>(![X676:$i > $o]:((?[X677:$i]:(((X676 @ X677)&![X678:$i]:(((X676 @ X678)=>((X677)=(X678))))))=>(X676 @ (descr @ (^[Z0/* 17 */:$i]:(X676 @ Z0))))))=>(![X679:$i, X680:$i > $o, X681:$i]:(((in @ X681 @ X679)=>((X680 @ X681)=>(in @ X681 @ (dsetconstr @ X679 @ X680)))))=>(![X682:$i, X683:$i > $o, X684:$i]:(((in @ X684 @ (dsetconstr @ X682 @ X683))=>(in @ X684 @ X682)))=>(![X685:$i, X686:$i > $o, X687:$i]:(((in @ X687 @ (dsetconstr @ X685 @ X686))=>(X686 @ X687)))=>(![X1236:$i > $o]:((?[X1237:$i]:(((X1236 @ X1237)&![X1238:$i]:(((X1236 @ X1238)=>((X1237)=(X1238))))))=>?[X1239:$i]:(((X1236 @ X1239)&![X1240:$i]:(((X1236 @ X1240)=>((X1239)=(X1240))))))))=>(![X1234:$o, X1235:$i]:(((in @ X1235 @ (prop2set @ ((X1234))))=>(X1234)))=>(![X1232:$i]:(((in @ X1232 @ emptyset)=>![X1233:$o]:((X1233))))=>(![X1231:$i]:(((in @ X1231 @ emptyset)=>~($true)))=>(![X688:$i]:(~(in @ X688 @ emptyset))=>(![X1227:$i > $o]:((?[X1228:$i]:(((X1227 @ X1228)&![X1229:$i]:(((X1227 @ X1229)=>((X1228)=(X1229))))))=>?[X1230:$i]:((X1227 @ X1230))))=>(![X1223:$i, X1224:$i]:((![X1225:$i]:(((in @ X1225 @ X1223)=>(in @ X1225 @ X1224)))=>(![X1226:$i]:(((in @ X1226 @ X1224)=>(in @ X1226 @ X1223)))=>((X1223)=(X1224)))))=>(![X1221:$i]:((![X1222:$i]:(~(in @ X1222 @ X1221))=>((X1221)=(emptyset))))=>(![X689:$i]:((![X690:$i]:(~(in @ X690 @ X689))=>((X689)=(emptyset))))=>(![X691:$i, X692:$i > $o, X693:$i]:(((in @ X693 @ X691)=>((in @ X693 @ (dsetconstr @ X691 @ X692))<=>(X692 @ X693))))=>(![X694:$i]:((((X694)!=(emptyset))=>?[X695:$i]:((in @ X695 @ X694))))=>(![X1218:$i, X1219:$i > $o, X1220:$i]:(((in @ X1220 @ X1218)=>((X1219 @ X1220)=>((dsetconstr @ X1218 @ X1219)!=(emptyset)))))=>(![X696:$i]:((?[X697:$i]:((in @ X697 @ X696))=>((X696)!=(emptyset))))=>(![X698:$i, X699:$i]:((in @ X698 @ (setadjoin @ X698 @ X699)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X700:$i, X701:$i, X702:$i]:(((in @ X702 @ X701)=>(in @ X702 @ (setadjoin @ X700 @ X701))))=>(![X703:$i, X704:$i, X705:$i]:(((in @ X705 @ (setadjoin @ X703 @ X704))=>![X706:$o]:(((((X705)=(X703))=>(X706))=>(((in @ X705 @ X704)=>(X706))=>(X706))))))=>(![X707:$i, X708:$i, X709:$i]:(((in @ X709 @ (setadjoin @ X707 @ X708))=>(((X709)=(X707))|(in @ X709 @ X708))))=>(![X1217:$i]:(((dsetconstr @ X1217 @ (^[Z0/* 1 */:$i]:($true)))=(X1217)))=>(![X1214:$i, X1215:$i]:((![X1216:$i]:(((in @ X1216 @ X1215)=>(in @ X1216 @ X1214)))=>(in @ X1215 @ (powerset @ X1214))))=>(![X710:$i]:((in @ emptyset @ (powerset @ X710)))=>(![X711:$i]:((in @ emptyset @ (powerset @ X711)))=>(![X1211:$i, X1212:$i, X1213:$i]:(((in @ X1212 @ (powerset @ X1211))=>((in @ X1213 @ X1212)=>(in @ X1213 @ X1211))))=>(![X712:$i, X713:$i, X714:$i]:(((in @ X713 @ X714)=>((in @ X714 @ X712)=>(in @ X713 @ (setunion @ X712)))))=>(![X715:$i, X716:$i]:(((in @ X716 @ (setunion @ X715))=>![X717:$o]:((![X718:$i]:(((in @ X716 @ X718)=>((in @ X718 @ X715)=>(X717))))=>(X717)))))=>(![X719:$i, X720:$i]:(((in @ X720 @ X719)=>(in @ X720 @ (powerset @ (setunion @ X719)))))=>(![X1206:$i > $o]:((?[X1207:$i]:(((X1206 @ X1207)&![X1208:$i]:(((X1206 @ X1208)=>((X1207)=(X1208))))))=>?[X1209:$i]:(![X1210:$i]:(((X1206 @ X1210)<=>((X1210)=(X1209)))))))=>(![X721:$i]:((((X721)!=(emptyset))=>?[X722:$i]:(((in @ X722 @ X721)&$true))))=>(![X1204:$i, X1205:$i]:(((in @ X1204 @ (setadjoin @ X1205 @ emptyset))=>((X1204)=(X1205))))=>(![X1202:$i, X1203:$i]:((((X1202)!=(X1203))=>~(in @ X1203 @ (setadjoin @ X1202 @ emptyset))))=>(![X1200:$i, X1201:$i]:((((X1200)=(X1201))=>(in @ X1200 @ (setadjoin @ X1201 @ emptyset))))=>(![X723:$i, X724:$i]:(((in @ X723 @ (setadjoin @ X724 @ emptyset))=>(in @ X724 @ (setadjoin @ X723 @ emptyset))))=>(![X1197:$i, X1198:$i, X1199:$i]:(((in @ X1199 @ (setadjoin @ X1197 @ (setadjoin @ X1198 @ emptyset)))=>(((X1199)=(X1197))|((X1199)=(X1198)))))=>(![X725:$i, X726:$i]:((in @ X725 @ (setadjoin @ X725 @ (setadjoin @ X726 @ emptyset))))=>(![X727:$i, X728:$i]:((in @ X728 @ (setadjoin @ X727 @ (setadjoin @ X728 @ emptyset))))=>(![X1194:$i, X1195:$i > $o]:((?[X1196:$i]:(((in @ X1196 @ X1194)&(X1195 @ X1196)))=>(((dsetconstr @ X1194 @ X1195)=(emptyset))=>~($true))))=>(![X1192:$i > $o, X1193:$i]:(((in @ X1193 @ emptyset)=>(X1192 @ X1193)))=>(![X729:$i, X730:$i > $o]:((~(![X731:$i]:(((in @ X731 @ X729)=>(X730 @ X731))))=>?[X732:$i]:(((in @ X732 @ X729)&~((X730 @ X732))))))=>(![X733:$i, X734:$i > $o]:((![X735:$i]:(((in @ X735 @ X733)=>~((X734 @ X735))))=>~(?[X736:$i]:(((in @ X736 @ X733)&(X734 @ X736))))))=>(![X1188:$i, X1189:$i > $o]:((~(?[X1190:$i]:(((in @ X1190 @ X1188)&(X1189 @ X1190))))=>![X1191:$i]:(((in @ X1191 @ X1188)=>~((X1189 @ X1191))))))=>(![X737:$i, X738:$i > $o]:((?[X739:$i]:(((in @ X739 @ X737)&~((X738 @ X739))))=>~(![X740:$i]:(((in @ X740 @ X737)=>(X738 @ X740))))))=>(![X741:$o]:(((X741)=>(in @ emptyset @ (prop2set @ ((X741))))))=>(![X742:$o]:(((X742)=>(set2prop @ (prop2set @ ((X742))))))=>(![X743:$i, X744:$i > $o]:((~(?[X745:$i]:(((in @ X745 @ X743)&(X744 @ X745))))=>![X746:$i]:(((in @ X746 @ X743)=>~((X744 @ X746))))))=>(![X747:$i, X748:$i > $o]:((~(![X749:$i]:(((in @ X749 @ X747)=>(X748 @ X749))))=>?[X750:$i]:(((in @ X750 @ X747)&~((X748 @ X750))))))=>(![X751:$i > $o]:((?[X752:$i]:(((X751 @ X752)&![X753:$i]:(((X751 @ X753)=>((X752)=(X753))))))=>?[X754:$i]:(((X751 @ X754)&![X755:$i]:(((X751 @ X755)=>((X754)=(X755))))))))=>(![X756:$i > $o]:((?[X757:$i]:((X756 @ X757))=>(![X758:$i, X759:$i]:(((X756 @ X758)=>((X756 @ X759)=>((X758)=(X759)))))=>?[X760:$i]:(((X756 @ X760)&![X761:$i]:(((X756 @ X761)=>((X760)=(X761)))))))))=>(![X1183:$i > $o]:((?[X1184:$i]:(![X1185:$i]:(((X1183 @ X1185)<=>((X1185)=(X1184)))))=>?[X1186:$i]:(((X1183 @ X1186)&![X1187:$i]:(((X1183 @ X1187)=>((X1186)=(X1187))))))))=>(![X762:$i, X763:$i]:((((X762)=(X763))=>![X764:$i, X765:$i]:((((X764)=(X765))=>((in @ X764 @ X762)=>(in @ X765 @ X763))))))=>(![X1179:$i, X1180:$i]:((((X1179)=(X1180))=>![X1181:$i, X1182:$i]:((((X1181)=(X1182))=>((in @ X1181 @ X1179)<=>(in @ X1182 @ X1180))))))=>(![X766:$i > $o]:((?[X767:$i]:(((X766 @ X767)&![X768:$i]:(((X766 @ X768)=>((X767)=(X768))))))=>![X769:$i, X770:$i]:(((X766 @ X769)=>((X766 @ X770)=>((X769)=(X770)))))))=>(![X771:$i > $o, X772:$i > $o]:((![X773:$i, X774:$i]:((((X773)=(X774))=>((X771 @ X773)<=>(X772 @ X774))))=>(?[X775:$i]:(((X771 @ X775)&![X776:$i]:(((X771 @ X776)=>((X775)=(X776))))))<=>?[X777:$i]:(((X772 @ X777)&![X778:$i]:(((X772 @ X778)=>((X777)=(X778)))))))))=>(((emptyset)=(emptyset))=>(![X1175:$i, X1176:$i]:((((X1175)=(X1176))=>![X1177:$i, X1178:$i]:((((X1177)=(X1178))=>((setadjoin @ X1175 @ X1177)=(setadjoin @ X1176 @ X1178))))))=>(![X1173:$i, X1174:$i]:((((X1173)=(X1174))=>((powerset @ X1173)=(powerset @ X1174))))=>(![X779:$i, X780:$i]:((((X779)=(X780))=>((setunion @ X779)=(setunion @ X780))))=>(((omega)=(omega))=>(![X781:$i > $o]:((?[X782:$i]:(((X781 @ X782)&![X783:$i]:(((X781 @ X783)=>((X782)=(X783))))))=>![X784:$i, X785:$i]:(((X781 @ X784)=>((X781 @ X785)=>((X784)=(X785)))))))=>(![X1165:$i > $o, X1166:$i > $o]:((![X1167:$i, X1168:$i]:((((X1167)=(X1168))=>((X1165 @ X1167)<=>(X1166 @ X1168))))=>(?[X1169:$i]:(((X1165 @ X1169)&![X1170:$i]:(((X1165 @ X1170)=>((X1169)=(X1170))))))=>(?[X1171:$i]:(((X1166 @ X1171)&![X1172:$i]:(((X1166 @ X1172)=>((X1171)=(X1172))))))=>((descr @ X1165)=(descr @ X1166))))))=>(![X1159:$i, X1160:$i]:((((X1159)=(X1160))=>![X1161:$i > $o, X1162:$i > $o]:((![X1163:$i]:(((in @ X1163 @ X1159)=>![X1164:$i]:(((in @ X1164 @ X1160)=>(((X1163)=(X1164))=>((X1161 @ X1163)<=>(X1162 @ X1164)))))))=>((dsetconstr @ X1159 @ X1161)=(dsetconstr @ X1160 @ X1162))))))=>(![X1156:$i, X1157:$i]:((![X1158:$i]:(((in @ X1158 @ X1156)=>(in @ X1158 @ X1157)))=>(subset @ X1156 @ X1157)))=>(![X1154:$i, X1155:$i]:((((X1154)=(X1155))=>(subset @ X1155 @ X1154)))=>(![X1152:$i, X1153:$i]:((((X1152)=(X1153))=>(subset @ X1152 @ X1153)))=>(![X786:$i, X787:$i]:((![X788:$i]:(((in @ X788 @ X786)=>(in @ X788 @ X787)))=>(subset @ X786 @ X787)))=>(![X1151:$i]:((subset @ emptyset @ X1151))=>(![X789:$i, X790:$i, X791:$i]:(((subset @ X789 @ X790)=>((in @ X791 @ X789)=>(in @ X791 @ X790))))=>(![X792:$i, X793:$i, X794:$i]:(((subset @ X792 @ X793)=>(~(in @ X794 @ X793)=>~(in @ X794 @ X792))))=>(![X795:$i, X796:$i, X797:$i]:(((in @ X797 @ X795)=>(~(in @ X797 @ X796)=>~(subset @ X795 @ X796))))=>(![X798:$i, X799:$i]:((~(subset @ X798 @ X799)=>((X798)!=(X799))))=>(![X800:$i, X801:$i, X802:$i]:(((in @ X802 @ X800)=>(~(in @ X802 @ X801)=>((X800)!=(X801)))))=>(![X803:$i]:((subset @ X803 @ X803))=>(![X1148:$i, X1149:$i, X1150:$i]:(((subset @ X1148 @ X1149)=>((subset @ X1149 @ X1150)=>(subset @ X1148 @ X1150))))=>(![X804:$i, X805:$i]:((subset @ X805 @ (setadjoin @ X804 @ X805)))=>(![X806:$i, X807:$i, X808:$i]:(((subset @ X806 @ X808)=>(subset @ X806 @ 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X978)))))&((dsetconstr @ X977 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X979 @ Z0) @ X978))))=(setadjoin @ X980 @ emptyset)))))))=>(in @ X978 @ (funcSet @ X976 @ X977))))=>(![X960:$i, X961:$i, X962:$i > $i]:((![X963:$i]:(((in @ X963 @ X960)=>(in @ (X962 @ X963) @ X961)))=>((subset @ (dpsetconstr @ X960 @ X961 @ (^[Z0/* 3 */:$i]:($eq @ (X962 @ Z0)))) @ (cartprod @ X960 @ X961))&![X964:$i]:(((in @ X964 @ X960)=>?[X965:$i]:(((in @ X965 @ (dsetconstr @ X961 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X964 @ Z0) @ (dpsetconstr @ X960 @ X961 @ (^[Z1/* 3 */:$i]:($eq @ (X962 @ Z1)))))))))&((dsetconstr @ X961 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X964 @ Z0) @ (dpsetconstr @ X960 @ X961 @ (^[Z1/* 3 */:$i]:($eq @ (X962 @ Z1))))))))=(setadjoin @ X965 @ emptyset)))))))))=>(![X966:$i, X967:$i, X968:$i > $i]:((![X969:$i]:(((in @ X969 @ X966)=>(in @ (X968 @ X969) @ X967)))=>((subset @ (lam @ X966 @ X967 @ X968) @ (cartprod @ X966 @ X967))&![X970:$i]:(((in @ X970 @ X966)=>?[X971:$i]:(((in @ X971 @ (dsetconstr @ X967 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X970 @ Z0) @ (lam @ X966 @ X967 @ X968))))))&((dsetconstr @ X967 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X970 @ Z0) @ (lam @ X966 @ X967 @ X968)))))=(setadjoin @ X971 @ emptyset)))))))))=>(![X972:$i, X973:$i, X974:$i > $i]:((![X975:$i]:(((in @ X975 @ X972)=>(in @ (X974 @ X975) @ X973)))=>(in @ (lam @ X972 @ X973 @ X974) @ (funcSet @ X972 @ X973))))=>![X4:$i, X5:$i, X29:$i]:(((subset @ X29 @ (cartprod @ X4 @ X5))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X29)=>(X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[brelnall1]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_236]), foundationAx]), wellorderingAx]), c_0_237]), c_0_238]), c_0_239]), c_0_240]), c_0_241]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_242]), setext]), emptyI]), noeltsimpempty]), c_0_243]), c_0_244]), c_0_245]), c_0_246]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_247]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_248]), c_0_249]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_250]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_251]), c_0_252]), c_0_253]), inCongP]), in__Cong]), c_0_254]), c_0_255]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_256]), c_0_257]), c_0_258]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_259]), c_0_260]), 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_261]), c_0_262]), c_0_263]), c_0_264]), singletonsuniq]), setukpairinjL1]), c_0_265]), c_0_266]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_267]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_208]), c_0_268]), c_0_269]), c_0_270]), c_0_271]), c_0_272]), c_0_273]), c_0_274]), c_0_275]), c_0_276]), c_0_277]), c_0_278]), ap2p]), c_0_279]), c_0_280]), c_0_281]), c_0_282])])]), c_0_283])).
0.27/0.92	thf(c_0_285, negated_conjecture, ![X1284:$i, X1285:$i, X1287:$i, X1288:$i, X1289:$i, X1290:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1297:$i, X1298:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1306:$i, X1307:$i > $i > $o, X1308:$i, X1310:$i, X1313:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1320:$i, X1321:$i > $o, X1322:$i, X1324:$i, X1325:$i > $o, X1326:$i, X1327:$i, X1328:$i > $o, X1329:$i, X1330:$i, X1331:$i > $o, X1332:$i, X1333:$i > $o, X1334:$i, X1337:$i, X1338:$o, X1339:$i, X1340:$i, X1341:$o, X1342:$i, X1343:$i, X1344:$i > $o, X1345:$i, X1348:$i, X1349:$i, X1352:$i, X1354:$i, X1356:$i, X1357:$i > $o, X1358:$i, X1359:$i, X1361:$i, X1362:$i > $o, X1363:$i, X1364:$i, X1365:$i, X1366:$i, X1367:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$o, X1375:$i, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i, X1382:$i, X1383:$i, X1384:$i, X1385:$i, X1386:$i, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$o, X1394:$i, X1395:$i, X1396:$i > $o, X1397:$i, X1400:$i, X1401:$i, X1402:$i, X1404:$i, X1405:$i, X1406:$i, X1407:$i, X1408:$i, X1409:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1417:$i, X1418:$i, X1419:$i, X1420:$i > $o, X1421:$i, X1422:$i > $o, X1423:$i, X1424:$i, X1425:$i > $o, X1426:$i, X1428:$i, X1429:$i > $o, X1431:$i, X1432:$i, X1433:$i > $o, X1435:$i, X1436:$i, X1437:$i > $o, X1438:$i, X1440:$o, X1441:$o, X1442:$i, X1443:$i > $o, X1445:$i, X1446:$i, X1447:$i > $o, X1448:$i, X1450:$i > $o, X1451:$i, X1454:$i, X1455:$i > $o, X1456:$i, X1460:$i, X1461:$i > $o, X1462:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1470:$i, X1471:$i, X1472:$i, X1473:$i, X1474:$i > $o, X1475:$i, X1477:$i, X1478:$i, X1479:$i > $o, X1480:$i > $o, X1483:$i, X1486:$i, X1487:$i, X1490:$i, X1491:$i, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i > $o, X1500:$i, X1502:$i, X1503:$i, X1504:$i > $o, X1505:$i > $o, X1508:$i, X1510:$i, X1512:$i, X1513:$i, X1514:$i > $o, X1515:$i > $o, X1518:$i, X1519:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i > $o, X1566:$i, X1567:$i > $o, X1568:$i, X1569:$i, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$o, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1599:$i, X1600:$i, X1601:$i, X1602:$i, X1603:$i, X1604:$i, X1605:$i, X1606:$i, X1608:$i, X1609:$i, X1610:$i, X1611:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i, X1626:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i, X1633:$i, X1634:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i, X1643:$i, X1644:$i, X1645:$i, X1646:$i, X1647:$o, X1648:$i, X1649:$i, X1650:$i, X1651:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$i, X1685:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$i, X1719:$i > $o, X1722:$i, X1724:$i, X1725:$i > $o, X1726:$i, X1728:$i, X1729:$i > $o, X1730:$i, X1733:$i, X1734:$i > $o, X1737:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i > $i > $o, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i > $i > $o, X1819:$i, X1820:$i, X1821:$i > $i > $o, X1822:$i, X1823:$i, X1824:$i > $i > $o, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i > $i > $o, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i > $i > $o, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i > $i > $o, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1846:$i, X1847:$i, X1849:$i, X1850:$i, X1851:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i > $i, X1879:$i, X1881:$i, X1882:$i, X1883:$i > $i, X1885:$i, X1887:$i, X1888:$i, X1889:$i > $i, X1895:$i, X1896:$i]:((((~(in @ (esk1_2 @ X1284 @ X1285) @ X1284)|~(in @ (esk1_2 @ X1284 @ X1285) @ X1285)|((X1284)=(X1285)))&((in @ (esk1_2 @ X1284 @ X1285) @ X1284)|(in @ (esk1_2 @ X1284 @ X1285) @ X1285)|((X1284)=(X1285))))&(~(in @ X1287 @ emptyset)&(((~(in @ X1290 @ (setadjoin @ X1288 @ X1289))|(((X1290)=(X1288))|(in @ X1290 @ X1289)))&((((X1290)!=(X1288))|(in @ X1290 @ (setadjoin @ X1288 @ 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X1862))|~(in @ X1863 @ (funcSet @ X1861 @ X1862)))&(((in @ (esk73_4 @ X1861 @ X1862 @ X1863 @ X1864) @ (dsetconstr @ X1862 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1864 @ Z0) @ X1863)))))|~(in @ X1864 @ X1861)|~(in @ X1863 @ (funcSet @ X1861 @ X1862)))&(((dsetconstr @ X1862 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1864 @ Z0) @ X1863))))=(setadjoin @ (esk73_4 @ X1861 @ X1862 @ X1863 @ X1864) @ emptyset))|~(in @ X1864 @ X1861)|~(in @ X1863 @ (funcSet @ X1861 @ X1862)))))&((~(in @ X1868 @ (funcSet @ X1866 @ X1867))|(~(in @ X1869 @ X1866)|(in @ (ap @ X1866 @ X1867 @ X1868 @ X1869) @ X1867)))&((((in @ (esk74_3 @ X1870 @ X1871 @ X1872) @ X1870)|~(subset @ X1872 @ (cartprod @ X1870 @ X1871))|(in @ X1872 @ (funcSet @ X1870 @ X1871)))&(~(in @ X1874 @ (dsetconstr @ X1871 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ (esk74_3 @ X1870 @ X1871 @ X1872) @ Z0) @ X1872)))))|((dsetconstr @ X1871 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ (esk74_3 @ X1870 @ X1871 @ X1872) @ Z0) @ X1872))))!=(setadjoin @ X1874 @ emptyset))|~(subset @ X1872 @ (cartprod @ X1870 @ X1871))|(in @ X1872 @ (funcSet @ X1870 @ X1871))))&(((((subset @ (dpsetconstr @ X1875 @ X1876 @ (^[Z0/* 3 */:$i]:($eq @ (X1877 @ Z0)))) @ (cartprod @ X1875 @ X1876))|(in @ (esk75_3 @ X1875 @ X1876 @ X1877) @ X1875))&(((in @ (esk76_4 @ X1875 @ X1876 @ X1877 @ X1879) @ (dsetconstr @ X1876 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1879 @ Z0) @ (dpsetconstr @ X1875 @ X1876 @ (^[Z1/* 3 */:$i]:($eq @ (X1877 @ Z1)))))))))|~(in @ X1879 @ X1875)|(in @ (esk75_3 @ X1875 @ X1876 @ X1877) @ X1875))&(((dsetconstr @ X1876 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1879 @ Z0) @ (dpsetconstr @ X1875 @ X1876 @ (^[Z1/* 3 */:$i]:($eq @ (X1877 @ Z1))))))))=(setadjoin @ (esk76_4 @ X1875 @ X1876 @ X1877 @ X1879) @ emptyset))|~(in @ X1879 @ X1875)|(in @ (esk75_3 @ X1875 @ X1876 @ X1877) @ X1875))))&(((subset @ (dpsetconstr @ X1875 @ X1876 @ (^[Z0/* 3 */:$i]:($eq @ (X1877 @ Z0)))) @ (cartprod @ X1875 @ X1876))|~(in @ (X1877 @ (esk75_3 @ X1875 @ X1876 @ X1877)) @ X1876))&(((in @ (esk76_4 @ X1875 @ X1876 @ X1877 @ X1879) @ (dsetconstr @ X1876 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1879 @ Z0) @ (dpsetconstr @ X1875 @ X1876 @ (^[Z1/* 3 */:$i]:($eq @ (X1877 @ Z1)))))))))|~(in @ X1879 @ X1875)|~(in @ (X1877 @ (esk75_3 @ X1875 @ X1876 @ X1877)) @ X1876))&(((dsetconstr @ X1876 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1879 @ Z0) @ (dpsetconstr @ X1875 @ X1876 @ (^[Z1/* 3 */:$i]:($eq @ (X1877 @ Z1))))))))=(setadjoin @ (esk76_4 @ X1875 @ X1876 @ X1877 @ X1879) @ emptyset))|~(in @ X1879 @ X1875)|~(in @ (X1877 @ (esk75_3 @ X1875 @ X1876 @ X1877)) @ X1876)))))&(((((subset @ (lam @ X1881 @ X1882 @ X1883) @ (cartprod @ X1881 @ X1882))|(in @ (esk77_3 @ X1881 @ X1882 @ X1883) @ X1881))&(((in @ (esk78_4 @ X1881 @ X1882 @ X1883 @ X1885) @ (dsetconstr @ X1882 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1885 @ Z0) @ (lam @ X1881 @ X1882 @ X1883))))))|~(in @ X1885 @ X1881)|(in @ (esk77_3 @ X1881 @ X1882 @ X1883) @ X1881))&(((dsetconstr @ X1882 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1885 @ Z0) @ (lam @ X1881 @ X1882 @ X1883)))))=(setadjoin @ (esk78_4 @ X1881 @ X1882 @ X1883 @ X1885) @ emptyset))|~(in @ X1885 @ X1881)|(in @ (esk77_3 @ X1881 @ X1882 @ X1883) @ X1881))))&(((subset @ (lam @ X1881 @ X1882 @ X1883) @ (cartprod @ X1881 @ X1882))|~(in @ (X1883 @ (esk77_3 @ X1881 @ X1882 @ X1883)) @ X1882))&(((in @ (esk78_4 @ X1881 @ X1882 @ X1883 @ X1885) @ (dsetconstr @ X1882 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1885 @ Z0) @ (lam @ X1881 @ X1882 @ X1883))))))|~(in @ X1885 @ X1881)|~(in @ (X1883 @ (esk77_3 @ X1881 @ X1882 @ X1883)) @ X1882))&(((dsetconstr @ X1882 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1885 @ Z0) @ (lam @ X1881 @ X1882 @ X1883)))))=(setadjoin @ (esk78_4 @ X1881 @ X1882 @ X1883 @ X1885) @ emptyset))|~(in @ X1885 @ X1881)|~(in @ (X1883 @ (esk77_3 @ X1881 @ X1882 @ X1883)) @ X1882)))))&((((in @ (esk79_3 @ X1887 @ X1888 @ X1889) @ X1887)|(in @ (lam @ X1887 @ X1888 @ X1889) @ (funcSet @ X1887 @ X1888)))&(~(in @ (X1889 @ (esk79_3 @ X1887 @ X1888 @ X1889)) @ X1888)|(in @ (lam @ X1887 @ X1888 @ X1889) @ (funcSet @ X1887 @ X1888))))&((subset @ esk82_0 @ (cartprod @ esk80_0 @ esk81_0))&((~(in @ X1895 @ esk80_0)|(~(in @ X1896 @ esk81_0)|(~(in @ (kpair @ X1895 @ X1896) @ esk82_0)|(epred2_0 @ (kpair @ X1895 @ X1896)))))&((in @ esk83_0 @ esk82_0)&~(epred2_0 @ esk83_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_284])])])])])])])).
0.27/0.92	thf(c_0_286, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((subset @ X2 @ X3))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_285])).
0.27/0.92	thf(c_0_287, negated_conjecture, (in @ esk83_0 @ esk82_0), inference(split_conjunct,[status(thm)],[c_0_285])).
0.27/0.92	thf(c_0_288, negated_conjecture, ![X2:$i]:(((in @ esk83_0 @ X2)|~((subset @ esk82_0 @ X2)))), inference(spm,[status(thm)],[c_0_286, c_0_287])).
0.27/0.92	thf(c_0_289, negated_conjecture, (subset @ esk82_0 @ (cartprod @ esk80_0 @ esk81_0)), inference(split_conjunct,[status(thm)],[c_0_285])).
0.27/0.92	thf(c_0_290, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((((kpair @ (kfst @ X2) @ (ksnd @ X2))=(X2))|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_285])).
0.27/0.92	thf(c_0_291, negated_conjecture, (in @ esk83_0 @ (cartprod @ esk80_0 @ esk81_0)), inference(spm,[status(thm)],[c_0_288, c_0_289])).
0.27/0.92	thf(c_0_292, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ (ksnd @ X2) @ X4)|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_285])).
0.27/0.92	thf(c_0_293, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ (kfst @ X2) @ X3)|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_285])).
0.27/0.92	thf(c_0_294, negated_conjecture, ![X2:$i, X3:$i]:(((epred2_0 @ (kpair @ X2 @ X3))|~((in @ X2 @ esk80_0))|~((in @ X3 @ esk81_0))|~((in @ (kpair @ X2 @ X3) @ esk82_0)))), inference(split_conjunct,[status(thm)],[c_0_285])).
0.27/0.92	thf(c_0_295, negated_conjecture, ((kpair @ (kfst @ esk83_0) @ (ksnd @ esk83_0))=(esk83_0)), inference(spm,[status(thm)],[c_0_290, c_0_291])).
0.27/0.92	thf(c_0_296, negated_conjecture, (in @ (ksnd @ esk83_0) @ esk81_0), inference(spm,[status(thm)],[c_0_292, c_0_291])).
0.27/0.92	thf(c_0_297, negated_conjecture, (in @ (kfst @ esk83_0) @ esk80_0), inference(spm,[status(thm)],[c_0_293, c_0_291])).
0.27/0.92	thf(c_0_298, negated_conjecture, ~((epred2_0 @ esk83_0)), inference(split_conjunct,[status(thm)],[c_0_285])).
0.27/0.92	thf(c_0_299, 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_294, c_0_295]), c_0_287]), c_0_296]), c_0_297])]), c_0_298]), ['proof']).
0.27/0.92	# SZS output end CNFRefutation
0.27/0.92	# Parsed axioms                        : 440
0.27/0.92	# Removed by relevancy pruning/SinE    : 0
0.27/0.92	# Initial clauses                      : 616
0.27/0.92	# Removed in clause preprocessing      : 264
0.27/0.92	# Initial clauses in saturation        : 352
0.27/0.92	# Processed clauses                    : 733
0.27/0.92	# ...of these trivial                  : 21
0.27/0.92	# ...subsumed                          : 124
0.27/0.92	# ...remaining for further processing  : 588
0.27/0.92	# Other redundant clauses eliminated   : 36
0.27/0.92	# Clauses deleted for lack of memory   : 0
0.27/0.92	# Backward-subsumed                    : 1
0.27/0.92	# Backward-rewritten                   : 4
0.27/0.92	# Generated clauses                    : 2125
0.27/0.92	# ...of the previous two non-redundant : 1924
0.27/0.92	# ...aggressively subsumed             : 0
0.27/0.92	# Contextual simplify-reflections      : 1
0.27/0.92	# Paramodulations                      : 2070
0.27/0.92	# Factorizations                       : 0
0.27/0.92	# NegExts                              : 0
0.27/0.92	# Equation resolutions                 : 39
0.27/0.92	# Disequality decompositions           : 0
0.27/0.92	# Total rewrite steps                  : 260
0.27/0.92	# ...of those cached                   : 190
0.27/0.92	# Propositional unsat checks           : 0
0.27/0.92	#    Propositional check models        : 0
0.27/0.92	#    Propositional check unsatisfiable : 0
0.27/0.92	#    Propositional clauses             : 0
0.27/0.92	#    Propositional clauses after purity: 0
0.27/0.92	#    Propositional unsat core size     : 0
0.27/0.92	#    Propositional preprocessing time  : 0.000
0.27/0.92	#    Propositional encoding time       : 0.000
0.27/0.92	#    Propositional solver time         : 0.000
0.27/0.92	#    Success case prop preproc time    : 0.000
0.27/0.92	#    Success case prop encoding time   : 0.000
0.27/0.92	#    Success case prop solver time     : 0.000
0.27/0.92	# Current number of processed clauses  : 259
0.27/0.92	#    Positive orientable unit clauses  : 60
0.27/0.92	#    Positive unorientable unit clauses: 0
0.27/0.92	#    Negative unit clauses             : 5
0.27/0.92	#    Non-unit-clauses                  : 194
0.27/0.92	# Current number of unprocessed clauses: 1827
0.27/0.92	# ...number of literals in the above   : 4849
0.27/0.92	# Current number of archived formulas  : 0
0.27/0.92	# Current number of archived clauses   : 317
0.27/0.92	# Clause-clause subsumption calls (NU) : 24314
0.27/0.92	# Rec. Clause-clause subsumption calls : 11984
0.27/0.92	# Non-unit clause-clause subsumptions  : 86
0.27/0.92	# Unit Clause-clause subsumption calls : 236
0.27/0.92	# Rewrite failures with RHS unbound    : 0
0.27/0.92	# BW rewrite match attempts            : 18
0.27/0.92	# BW rewrite match successes           : 3
0.27/0.92	# Condensation attempts                : 0
0.27/0.92	# Condensation successes               : 0
0.27/0.92	# Termbank termtop insertions          : 93337
0.27/0.92	# Search garbage collected termcells   : 20664
0.27/0.92	
0.27/0.92	# -------------------------------------------------
0.27/0.92	# User time                : 0.099 s
0.27/0.92	# System time              : 0.008 s
0.27/0.92	# Total time               : 0.107 s
0.27/0.92	# Maximum resident set size: 6976 pages
0.27/0.92	
0.27/0.92	# -------------------------------------------------
0.27/0.92	# User time                : 0.313 s
0.27/0.92	# System time              : 0.021 s
0.27/0.92	# Total time               : 0.334 s
0.27/0.92	# Maximum resident set size: 2344 pages
0.27/0.92	% E exiting
0.27/0.92	% E exiting
0.27/0.92	EOF