0.00/0.02 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.08/0.35 % Computer : n024.cluster.edu 0.08/0.35 % Model : x86_64 x86_64 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.08/0.35 % Memory : 8046.5625MB 0.08/0.35 % OS : Linux 6.8.0-71-generic 0.08/0.35 % CPULimit : 1440 0.08/0.35 % WCLimit : 180 0.08/0.35 % DateTime : Mon Jul 27 06:58:00 UTC 2026 0.08/0.36 % CPUTime : 0.08/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.12/0.40 Running higher-order theorem proving 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p 126.84/19.39 % Version: 3.5.1-ho 126.84/19.39 % Preprocessing class: HSLMSLSSLLLCHFA. 126.84/19.39 % Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 126.84/19.39 % Starting ehoh_best5 with 180s (1) cores 126.84/19.39 % Starting almost_fo_3_lam with 180s (1) cores 126.84/19.39 % Starting new_bool_5 with 180s (1) cores 126.84/19.39 % Starting pre_casc_3 with 180s (1) cores 126.84/19.39 % Starting ho_unfolding_8 with 180s (1) cores 126.84/19.39 % Starting new_ho_10_cnf2 with 180s (1) cores 126.84/19.39 % Starting new_bool_3 with 180s (1) cores 126.84/19.39 % Starting new_ho_5 with 180s (1) cores 126.84/19.39 % new_ho_5 with pid 2969946 completed with status 0 126.84/19.39 % Result found by new_ho_5 126.84/19.39 % Preprocessing class: HSLMSLSSLLLCHFA. 126.84/19.39 % Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 126.84/19.39 % Starting ehoh_best5 with 180s (1) cores 126.84/19.39 % Starting almost_fo_3_lam with 180s (1) cores 126.84/19.39 % Starting new_bool_5 with 180s (1) cores 126.84/19.39 % Starting pre_casc_3 with 180s (1) cores 126.84/19.39 % Starting ho_unfolding_8 with 180s (1) cores 126.84/19.39 % Starting new_ho_10_cnf2 with 180s (1) cores 126.84/19.39 % Starting new_bool_3 with 180s (1) cores 126.84/19.39 % Starting new_ho_5 with 180s (1) cores 126.84/19.39 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)) 126.84/19.39 % SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true) 126.84/19.39 % Search class: HGHSM-SMLM32-MHFMMSBN 126.84/19.39 % Scheduled 7 strats onto 1 cores with 180 seconds (180 total) 126.84/19.39 % Starting SubtermCWHack with 17s (1) cores 126.84/19.39 % SubtermCWHack with pid 2969949 completed with status 8 126.84/19.39 % Starting new_ho_5 with 19s (1) cores 126.84/19.39 % new_ho_5 with pid 2969956 completed with status 0 126.84/19.39 % Result found by new_ho_5 126.84/19.39 % Preprocessing class: HSLMSLSSLLLCHFA. 126.84/19.39 % Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 126.84/19.39 % Starting ehoh_best5 with 180s (1) cores 126.84/19.39 % Starting almost_fo_3_lam with 180s (1) cores 126.84/19.39 % Starting new_bool_5 with 180s (1) cores 126.84/19.39 % Starting pre_casc_3 with 180s (1) cores 126.84/19.39 % Starting ho_unfolding_8 with 180s (1) cores 126.84/19.39 % Starting new_ho_10_cnf2 with 180s (1) cores 126.84/19.39 % Starting new_bool_3 with 180s (1) cores 126.84/19.39 % Starting new_ho_5 with 180s (1) cores 126.84/19.39 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)) 126.84/19.39 % SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true) 126.84/19.39 % Search class: HGHSM-SMLM32-MHFMMSBN 126.84/19.39 % Scheduled 7 strats onto 1 cores with 180 seconds (180 total) 126.84/19.39 % Starting SubtermCWHack with 17s (1) cores 126.84/19.39 % SubtermCWHack with pid 2969949 completed with status 8 126.84/19.39 % Starting new_ho_5 with 19s (1) cores 126.84/19.39 % Preprocessing time : 0.033 s 126.84/19.39 % Presaturation interreduction done 126.84/19.39 126.84/19.39 % Proof found! 126.84/19.39 % SZS status Theorem 126.84/19.39 % SZS output start CNFRefutation 126.84/19.39 thf(decl_23, type, in: $i > $i > $o). 126.84/19.39 thf(decl_24, type, exu: ($i > $o) > $o). 126.84/19.39 thf(decl_25, type, setextAx: $o). 126.84/19.39 thf(decl_26, type, emptyset: $i). 126.84/19.39 thf(decl_27, type, emptysetAx: $o). 126.84/19.39 thf(decl_28, type, setadjoin: $i > $i > $i). 126.84/19.39 thf(decl_29, type, setadjoinAx: $o). 126.84/19.39 thf(decl_30, type, powerset: $i > $i). 126.84/19.39 thf(decl_31, type, powersetAx: $o). 126.84/19.39 thf(decl_32, type, setunion: $i > $i). 126.84/19.39 thf(decl_33, type, setunionAx: $o). 126.84/19.39 thf(decl_34, type, omega: $i). 126.84/19.39 thf(decl_35, type, omega0Ax: $o). 126.84/19.39 thf(decl_36, type, omegaSAx: $o). 126.84/19.39 thf(decl_37, type, omegaIndAx: $o). 126.84/19.39 thf(decl_38, type, replAx: $o). 126.84/19.39 thf(decl_39, type, foundationAx: $o). 126.84/19.39 thf(decl_40, type, wellorderingAx: $o). 126.84/19.39 thf(decl_41, type, descr: ($i > $o) > $i). 126.84/19.39 thf(decl_42, type, descrp: $o). 126.84/19.39 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i). 126.84/19.39 thf(decl_44, type, dsetconstrI: $o). 126.84/19.39 thf(decl_45, type, dsetconstrEL: $o). 126.84/19.39 thf(decl_46, type, dsetconstrER: $o). 126.84/19.39 thf(decl_47, type, exuE1: $o). 126.84/19.39 thf(decl_48, type, prop2set: $o > $i). 126.84/19.39 thf(decl_49, type, prop2setE: $o). 126.84/19.39 thf(decl_50, type, emptysetE: $o). 126.84/19.39 thf(decl_51, type, emptysetimpfalse: $o). 126.84/19.39 thf(decl_52, type, notinemptyset: $o). 126.84/19.39 thf(decl_53, type, exuE3e: $o). 126.84/19.39 thf(decl_54, type, setext: $o). 126.84/19.39 thf(decl_55, type, emptyI: $o). 126.84/19.39 thf(decl_56, type, noeltsimpempty: $o). 126.84/19.39 thf(decl_57, type, setbeta: $o). 126.84/19.39 thf(decl_58, type, nonempty: $i > $o). 126.84/19.39 thf(decl_59, type, nonemptyE1: $o). 126.84/19.39 thf(decl_60, type, nonemptyI: $o). 126.84/19.39 thf(decl_61, type, nonemptyI1: $o). 126.84/19.39 thf(decl_62, type, setadjoinIL: $o). 126.84/19.39 thf(decl_63, type, emptyinunitempty: $o). 126.84/19.39 thf(decl_64, type, setadjoinIR: $o). 126.84/19.39 thf(decl_65, type, setadjoinE: $o). 126.84/19.39 thf(decl_66, type, setadjoinOr: $o). 126.84/19.39 thf(decl_67, type, setoftrueEq: $o). 126.84/19.39 thf(decl_68, type, powersetI: $o). 126.84/19.39 thf(decl_69, type, emptyinPowerset: $o). 126.84/19.39 thf(decl_70, type, emptyInPowerset: $o). 126.84/19.39 thf(decl_71, type, powersetE: $o). 126.84/19.39 thf(decl_72, type, setunionI: $o). 126.84/19.39 thf(decl_73, type, setunionE: $o). 126.84/19.39 thf(decl_74, type, subPowSU: $o). 126.84/19.39 thf(decl_75, type, exuE2: $o). 126.84/19.39 thf(decl_76, type, nonemptyImpWitness: $o). 126.84/19.39 thf(decl_77, type, uniqinunit: $o). 126.84/19.39 thf(decl_78, type, notinsingleton: $o). 126.84/19.39 thf(decl_79, type, eqinunit: $o). 126.84/19.39 thf(decl_80, type, singletonsswitch: $o). 126.84/19.39 thf(decl_81, type, upairsetE: $o). 126.84/19.39 thf(decl_82, type, upairsetIL: $o). 126.84/19.39 thf(decl_83, type, upairsetIR: $o). 126.84/19.39 thf(decl_84, type, emptyE1: $o). 126.84/19.39 thf(decl_85, type, vacuousDall: $o). 126.84/19.39 thf(decl_86, type, quantDeMorgan1: $o). 126.84/19.39 thf(decl_87, type, quantDeMorgan2: $o). 126.84/19.39 thf(decl_88, type, quantDeMorgan3: $o). 126.84/19.39 thf(decl_89, type, quantDeMorgan4: $o). 126.84/19.39 thf(decl_90, type, prop2setI: $o). 126.84/19.39 thf(decl_91, type, set2prop: $i > $o). 126.84/19.39 thf(decl_92, type, prop2set2propI: $o). 126.84/19.39 thf(decl_93, type, notdexE: $o). 126.84/19.39 thf(decl_94, type, notdallE: $o). 126.84/19.39 thf(decl_95, type, exuI1: $o). 126.84/19.39 thf(decl_96, type, exuI3: $o). 126.84/19.39 thf(decl_97, type, exuI2: $o). 126.84/19.39 thf(decl_98, type, inCongP: $o). 126.84/19.39 thf(decl_99, type, in__Cong: $o). 126.84/19.39 thf(decl_100, type, exuE3u: $o). 126.84/19.39 thf(decl_101, type, exu__Cong: $o). 126.84/19.39 thf(decl_102, type, emptyset__Cong: $o). 126.84/19.39 thf(decl_103, type, setadjoin__Cong: $o). 126.84/19.39 thf(decl_104, type, powerset__Cong: $o). 126.84/19.39 thf(decl_105, type, setunion__Cong: $o). 126.84/19.39 thf(decl_106, type, omega__Cong: $o). 126.84/19.39 thf(decl_107, type, exuEu: $o). 126.84/19.39 thf(decl_108, type, descr__Cong: $o). 126.84/19.39 thf(decl_109, type, dsetconstr__Cong: $o). 126.84/19.39 thf(decl_110, type, subset: $i > $i > $o). 126.84/19.39 thf(decl_113, type, subsetI1: $o). 126.84/19.39 thf(decl_114, type, eqimpsubset2: $o). 126.84/19.39 thf(decl_115, type, eqimpsubset1: $o). 126.84/19.39 thf(decl_116, type, subsetI2: $o). 126.84/19.39 thf(decl_117, type, emptysetsubset: $o). 126.84/19.39 thf(decl_118, type, subsetE: $o). 126.84/19.39 thf(decl_119, type, subsetE2: $o). 126.84/19.39 thf(decl_120, type, notsubsetI: $o). 126.84/19.39 thf(decl_121, type, notequalI1: $o). 126.84/19.39 thf(decl_122, type, notequalI2: $o). 126.84/19.39 thf(decl_123, type, subsetRefl: $o). 126.84/19.39 thf(decl_124, type, subsetTrans: $o). 126.84/19.39 thf(decl_125, type, setadjoinSub: $o). 126.84/19.39 thf(decl_126, type, setadjoinSub2: $o). 126.84/19.39 thf(decl_127, type, subset2powerset: $o). 126.84/19.39 thf(decl_128, type, setextsub: $o). 126.84/19.39 thf(decl_129, type, subsetemptysetimpeq: $o). 126.84/19.39 thf(decl_130, type, powersetI1: $o). 126.84/19.39 thf(decl_131, type, powersetE1: $o). 126.84/19.39 thf(decl_132, type, inPowerset: $o). 126.84/19.39 thf(decl_133, type, powersetsubset: $o). 126.84/19.39 thf(decl_134, type, sepInPowerset: $o). 126.84/19.39 thf(decl_135, type, sepSubset: $o). 126.84/19.39 thf(decl_136, type, binunion: $i > $i > $i). 126.84/19.39 thf(decl_137, type, binunionIL: $o). 126.84/19.39 thf(decl_138, type, upairset2IR: $o). 126.84/19.39 thf(decl_139, type, binunionIR: $o). 126.84/19.39 thf(decl_140, type, binunionEcases: $o). 126.84/19.39 thf(decl_141, type, binunionE: $o). 126.84/19.39 thf(decl_142, type, binunionLsub: $o). 126.84/19.39 thf(decl_143, type, binunionRsub: $o). 126.84/19.39 thf(decl_144, type, binintersect: $i > $i > $i). 126.84/19.39 thf(decl_145, type, binintersectI: $o). 126.84/19.39 thf(decl_146, type, binintersectSubset5: $o). 126.84/19.39 thf(decl_147, type, binintersectEL: $o). 126.84/19.39 thf(decl_148, type, binintersectLsub: $o). 126.84/19.39 thf(decl_149, type, binintersectSubset2: $o). 126.84/19.39 thf(decl_150, type, binintersectSubset3: $o). 126.84/19.39 thf(decl_151, type, binintersectER: $o). 126.84/19.39 thf(decl_152, type, disjointsetsI1: $o). 126.84/19.39 thf(decl_153, type, binintersectRsub: $o). 126.84/19.39 thf(decl_154, type, binintersectSubset4: $o). 126.84/19.39 thf(decl_155, type, binintersectSubset1: $o). 126.84/19.39 thf(decl_156, type, bs114d: $o). 126.84/19.39 thf(decl_158, type, setminus: $i > $i > $i). 126.84/19.39 thf(decl_159, type, setminusI: $o). 126.84/19.39 thf(decl_160, type, setminusEL: $o). 126.84/19.39 thf(decl_161, type, setminusER: $o). 126.84/19.39 thf(decl_162, type, setminusSubset2: $o). 126.84/19.39 thf(decl_163, type, setminusERneg: $o). 126.84/19.39 thf(decl_164, type, setminusELneg: $o). 126.84/19.39 thf(decl_165, type, setminusILneg: $o). 126.84/19.39 thf(decl_166, type, setminusIRneg: $o). 126.84/19.39 thf(decl_167, type, setminusLsub: $o). 126.84/19.39 thf(decl_168, type, setminusSubset1: $o). 126.84/19.39 thf(decl_169, type, symdiff: $i > $i > $i). 126.84/19.39 thf(decl_170, type, symdiffE: $o). 126.84/19.39 thf(decl_171, type, symdiffI1: $o). 126.84/19.39 thf(decl_172, type, symdiffI2: $o). 126.84/19.39 thf(decl_173, type, symdiffIneg1: $o). 126.84/19.39 thf(decl_174, type, symdiffIneg2: $o). 126.84/19.39 thf(decl_175, type, iskpair: $i > $o). 126.84/19.39 thf(decl_176, type, secondinupair: $o). 126.84/19.39 thf(decl_177, type, setukpairIL: $o). 126.84/19.39 thf(decl_178, type, setukpairIR: $o). 126.84/19.39 thf(decl_179, type, kpairiskpair: $o). 126.84/19.39 thf(decl_180, type, kpair: $i > $i > $i). 126.84/19.39 thf(decl_181, type, kpairp: $o). 126.84/19.39 thf(decl_182, type, cartprod: $i > $i > $i). 126.84/19.39 thf(decl_183, type, singletonsubset: $o). 126.84/19.39 thf(decl_184, type, singletoninpowerset: $o). 126.84/19.39 thf(decl_185, type, singletoninpowunion: $o). 126.84/19.39 thf(decl_186, type, upairset2E: $o). 126.84/19.39 thf(decl_187, type, upairsubunion: $o). 126.84/19.39 thf(decl_188, type, upairinpowunion: $o). 126.84/19.39 thf(decl_189, type, ubforcartprodlem1: $o). 126.84/19.39 thf(decl_190, type, ubforcartprodlem2: $o). 126.84/19.39 thf(decl_191, type, ubforcartprodlem3: $o). 126.84/19.39 thf(decl_192, type, cartprodpairin: $o). 126.84/19.39 thf(decl_193, type, cartprodmempair1: $o). 126.84/19.39 thf(decl_194, type, cartprodmempair: $o). 126.84/19.39 thf(decl_195, type, setunionE2: $o). 126.84/19.39 thf(decl_196, type, setunionsingleton1: $o). 126.84/19.39 thf(decl_197, type, setunionsingleton2: $o). 126.84/19.39 thf(decl_198, type, setunionsingleton: $o). 126.84/19.39 thf(decl_199, type, singleton: $i > $o). 126.84/19.39 thf(decl_200, type, singletonprop: $o). 126.84/19.39 thf(decl_201, type, ex1: $i > ($i > $o) > $o). 126.84/19.39 thf(decl_202, type, ex1E1: $o). 126.84/19.39 thf(decl_203, type, ex1I: $o). 126.84/19.39 thf(decl_204, type, ex1I2: $o). 126.84/19.39 thf(decl_205, type, singletonsuniq: $o). 126.84/19.39 thf(decl_210, type, setukpairinjL1: $o). 126.84/19.39 thf(decl_211, type, kfstsingleton: $o). 126.84/19.39 thf(decl_212, type, theprop: $o). 126.84/19.39 thf(decl_213, type, kfst: $i > $i). 126.84/19.39 thf(decl_214, type, kfstpairEq: $o). 126.84/19.39 thf(decl_215, type, cartprodfstin: $o). 126.84/19.39 thf(decl_216, type, setukpairinjL2: $o). 126.84/19.39 thf(decl_217, type, setukpairinjL: $o). 126.84/19.39 thf(decl_218, type, setukpairinjR11: $o). 126.84/19.39 thf(decl_219, type, setukpairinjR12: $o). 126.84/19.39 thf(decl_220, type, setukpairinjR1: $o). 126.84/19.39 thf(decl_221, type, upairequniteq: $o). 126.84/19.39 thf(decl_222, type, setukpairinjR2: $o). 126.84/19.39 thf(decl_223, type, setukpairinjR: $o). 126.84/19.39 thf(decl_224, type, ksndsingleton: $o). 126.84/19.39 thf(decl_225, type, ksnd: $i > $i). 126.84/19.39 thf(decl_226, type, ksndpairEq: $o). 126.84/19.39 thf(decl_227, type, kpairsurjEq: $o). 126.84/19.39 thf(decl_228, type, cartprodsndin: $o). 126.84/19.39 thf(decl_229, type, cartprodpairmemEL: $o). 126.84/19.39 thf(decl_230, type, cartprodpairmemER: $o). 126.84/19.39 thf(decl_231, type, cartprodmempaircEq: $o). 126.84/19.39 thf(decl_232, type, cartprodfstpairEq: $o). 126.84/19.39 thf(decl_233, type, cartprodsndpairEq: $o). 126.84/19.39 thf(decl_234, type, cartprodpairsurjEq: $o). 126.84/19.39 thf(decl_235, type, breln: $i > $i > $i > $o). 126.84/19.39 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 126.84/19.39 thf(decl_237, type, dpsetconstrI: $o). 126.84/19.39 thf(decl_238, type, dpsetconstrSub: $o). 126.84/19.39 thf(decl_239, type, setOfPairsIsBReln: $o). 126.84/19.39 thf(decl_240, type, dpsetconstrERa: $o). 126.84/19.39 thf(decl_241, type, dpsetconstrEL1: $o). 126.84/19.39 thf(decl_242, type, dpsetconstrEL2: $o). 126.84/19.39 thf(decl_243, type, dpsetconstrER: $o). 126.84/19.39 thf(decl_244, type, func: $i > $i > $i > $o). 126.84/19.39 thf(decl_245, type, funcSet: $i > $i > $i). 126.84/19.39 thf(decl_246, type, funcImageSingleton: $o). 126.84/19.39 thf(decl_247, type, apProp: $o). 126.84/19.39 thf(decl_248, type, ap: $i > $i > $i > $i > $i). 126.84/19.39 thf(decl_249, type, app: $o). 126.84/19.39 thf(decl_250, type, infuncsetfunc: $o). 126.84/19.39 thf(decl_251, type, ap2p: $o). 126.84/19.39 thf(decl_252, type, funcinfuncset: $o). 126.84/19.39 thf(decl_253, type, lamProp: $o). 126.84/19.39 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i). 126.84/19.39 thf(decl_255, type, lamp: $o). 126.84/19.39 thf(decl_256, type, lam2p: $o). 126.84/19.39 thf(decl_257, type, brelnall1: $o). 126.84/19.39 thf(decl_258, type, brelnall2: $o). 126.84/19.39 thf(decl_259, type, ex1E2: $o). 126.84/19.39 thf(decl_260, type, funcGraphProp1: $o). 126.84/19.39 thf(decl_261, type, funcGraphProp3: $o). 126.84/19.39 thf(decl_262, type, funcGraphProp2: $o). 126.84/19.39 thf(decl_263, type, funcextLem: $o). 126.84/19.39 thf(decl_264, type, funcGraphProp4: $o). 126.84/19.39 thf(decl_265, type, subbreln: $o). 126.84/19.39 thf(decl_266, type, eqbreln: $o). 126.84/19.39 thf(decl_267, type, funcext: $o). 126.84/19.39 thf(decl_268, type, funcext2: $o). 126.84/19.39 thf(decl_269, type, ap2apEq1: $o). 126.84/19.39 thf(decl_270, type, ap2apEq2: $o). 126.84/19.39 thf(decl_271, type, beta1: $o). 126.84/19.39 thf(decl_272, type, eta1: $o). 126.84/19.39 thf(decl_273, type, lam2lamEq: $o). 126.84/19.39 thf(decl_274, type, beta2: $o). 126.84/19.39 thf(decl_275, type, eta2: $o). 126.84/19.39 thf(decl_276, type, iffalseProp1: $o). 126.84/19.39 thf(decl_277, type, iffalseProp2: $o). 126.84/19.39 thf(decl_278, type, iftrueProp1: $o). 126.84/19.39 thf(decl_279, type, iftrueProp2: $o). 126.84/19.39 thf(decl_280, type, ifSingleton: $o). 126.84/19.39 thf(decl_281, type, if: $i > $o > $i > $i > $i). 126.84/19.39 thf(decl_282, type, ifp: $o). 126.84/19.39 thf(decl_283, type, theeq: $o). 126.84/19.39 thf(decl_284, type, iftrue: $o). 126.84/19.39 thf(decl_285, type, iffalse: $o). 126.84/19.39 thf(decl_286, type, iftrueorfalse: $o). 126.84/19.39 thf(decl_287, type, binintersectT_lem: $o). 126.84/19.39 thf(decl_288, type, binunionT_lem: $o). 126.84/19.39 thf(decl_289, type, powersetT_lem: $o). 126.84/19.39 thf(decl_290, type, setminusT_lem: $o). 126.84/19.39 thf(decl_291, type, complementT_lem: $o). 126.84/19.39 thf(decl_292, type, setextT: $o). 126.84/19.39 thf(decl_293, type, subsetTI: $o). 126.84/19.39 thf(decl_294, type, powersetTI1: $o). 126.84/19.39 thf(decl_295, type, powersetTE1: $o). 126.84/19.39 thf(decl_296, type, complementTI1: $o). 126.84/19.39 thf(decl_297, type, complementTE1: $o). 126.84/19.39 thf(decl_298, type, binintersectTELcontra: $o). 126.84/19.39 thf(decl_299, type, binintersectTERcontra: $o). 126.84/19.39 thf(decl_300, type, contrasubsetT: $o). 126.84/19.39 thf(decl_301, type, contrasubsetT1: $o). 126.84/19.39 thf(decl_302, type, contrasubsetT2: $o). 126.84/19.39 thf(decl_303, type, contrasubsetT3: $o). 126.84/19.39 thf(decl_304, type, doubleComplementI1: $o). 126.84/19.39 thf(decl_305, type, doubleComplementE1: $o). 126.84/19.39 thf(decl_306, type, doubleComplementSub1: $o). 126.84/19.39 thf(decl_307, type, doubleComplementSub2: $o). 126.84/19.39 thf(decl_308, type, doubleComplementEq: $o). 126.84/19.39 thf(decl_309, type, complementTnotintersectT: $o). 126.84/19.39 thf(decl_310, type, complementImpComplementIntersect: $o). 126.84/19.39 thf(decl_311, type, complementSubsetComplementIntersect: $o). 126.84/19.39 thf(decl_312, type, complementInPowersetComplementIntersect: $o). 126.84/19.39 thf(decl_313, type, contraSubsetComplement: $o). 126.84/19.39 thf(decl_314, type, complementTcontraSubset: $o). 126.84/19.39 thf(decl_315, type, binunionTILcontra: $o). 126.84/19.39 thf(decl_316, type, binunionTIRcontra: $o). 126.84/19.39 thf(decl_317, type, inIntersectImpInUnion: $o). 126.84/19.39 thf(decl_318, type, inIntersectImpInUnion2: $o). 126.84/19.39 thf(decl_319, type, inIntersectImpInIntersectUnions: $o). 126.84/19.39 thf(decl_320, type, intersectInPowersetIntersectUnions: $o). 126.84/19.39 thf(decl_321, type, inComplementUnionImpNotIn1: $o). 126.84/19.39 thf(decl_322, type, inComplementUnionImpInComplement1: $o). 126.84/19.39 thf(decl_323, type, binunionTE: $o). 126.84/19.39 thf(decl_324, type, binunionTEcontra: $o). 126.84/19.39 thf(decl_325, type, demorgan2a1: $o). 126.84/19.39 thf(decl_326, type, complementUnionInPowersetComplement: $o). 126.84/19.39 thf(decl_327, type, demorgan2a2: $o). 126.84/19.39 thf(decl_328, type, demorgan1a: $o). 126.84/19.39 thf(decl_329, type, demorgan1b: $o). 126.84/19.39 thf(decl_330, type, demorgan1: $o). 126.84/19.39 thf(decl_331, type, demorgan2a: $o). 126.84/19.39 thf(decl_332, type, demorgan2b2: $o). 126.84/19.39 thf(decl_333, type, demorgan2b: $o). 126.84/19.39 thf(decl_334, type, demorgan2: $o). 126.84/19.39 thf(decl_335, type, woz13rule0: $o). 126.84/19.39 thf(decl_336, type, woz13rule1: $o). 126.84/19.39 thf(decl_337, type, woz13rule2: $o). 126.84/19.39 thf(decl_338, type, woz13rule3: $o). 126.84/19.39 thf(decl_339, type, woz13rule4: $o). 126.84/19.39 thf(decl_340, type, woz1_1: $o). 126.84/19.39 thf(decl_341, type, woz1_2: $o). 126.84/19.39 thf(decl_342, type, woz1_3: $o). 126.84/19.39 thf(decl_343, type, woz1_4: $o). 126.84/19.39 thf(decl_344, type, woz1_5: $o). 126.84/19.39 thf(decl_345, type, breln1: $i > $i > $o). 126.84/19.39 thf(decl_346, type, breln1all2: $o). 126.84/19.39 thf(decl_347, type, breln1Set: $i > $i). 126.84/19.39 thf(decl_348, type, breln1SetBreln1: $o). 126.84/19.39 thf(decl_354, type, reflwellordering: $i > $i > $o). 126.84/19.39 thf(decl_355, type, choice2fnsingleton: $o). 126.84/19.39 thf(decl_356, type, setOfPairsIsBReln1: $o). 126.84/19.39 thf(decl_357, type, breln1all1: $o). 126.84/19.39 thf(decl_358, type, subbreln1: $o). 126.84/19.39 thf(decl_359, type, eqbreln1: $o). 126.84/19.39 thf(decl_360, type, breln1invset: $i > $i > $i). 126.84/19.39 thf(decl_361, type, breln1invprop: $o). 126.84/19.39 thf(decl_362, type, breln1invI: $o). 126.84/19.39 thf(decl_363, type, breln1invE: $o). 126.84/19.39 thf(decl_364, type, breln1compset: $i > $i > $i > $i). 126.84/19.39 thf(decl_365, type, breln1compprop: $o). 126.84/19.39 thf(decl_366, type, breln1compI: $o). 126.84/19.39 thf(decl_367, type, breln1compE: $o). 126.84/19.39 thf(decl_368, type, breln1compEex: $o). 126.84/19.39 thf(decl_369, type, breln1unionprop: $o). 126.84/19.39 thf(decl_370, type, breln1unionIL: $o). 126.84/19.39 thf(decl_371, type, breln1unionIR: $o). 126.84/19.39 thf(decl_372, type, breln1unionI: $o). 126.84/19.39 thf(decl_373, type, breln1unionE: $o). 126.84/19.39 thf(decl_374, type, breln1unionEcases: $o). 126.84/19.39 thf(decl_375, type, breln1unionCommutes: $o). 126.84/19.39 thf(decl_376, type, woz2Ex: $o). 126.84/19.39 thf(decl_377, type, woz2W: $o). 126.84/19.39 thf(decl_378, type, woz2A: $o). 126.84/19.39 thf(decl_379, type, woz2B: $o). 126.84/19.39 thf(decl_380, type, image1Ex: $o). 126.84/19.39 thf(decl_381, type, image1Ex1: $o). 126.84/19.39 thf(decl_382, type, image1: $i > ($i > $i) > $i). 126.84/19.39 thf(decl_383, type, image1Equiv: $o). 126.84/19.39 thf(decl_384, type, image1E: $o). 126.84/19.39 thf(decl_385, type, image1I: $o). 126.84/19.39 thf(decl_386, type, injective: $i > $i > $i > $o). 126.84/19.39 thf(decl_387, type, injFuncSet: $i > $i > $i). 126.84/19.39 thf(decl_388, type, injFuncInInjFuncSet: $o). 126.84/19.39 thf(decl_389, type, injFuncSetFuncIn: $o). 126.84/19.39 thf(decl_390, type, injFuncSetFuncInj: $o). 126.84/19.39 thf(decl_391, type, surjective: $i > $i > $i > $o). 126.84/19.39 thf(decl_392, type, surjFuncSet: $i > $i > $i). 126.84/19.39 thf(decl_393, type, surjFuncSetFuncIn: $o). 126.84/19.39 thf(decl_394, type, surjFuncSetFuncSurj: $o). 126.84/19.39 thf(decl_395, type, leftInvIsSurj: $o). 126.84/19.39 thf(decl_396, type, surjCantorThm: $o). 126.84/19.39 thf(decl_397, type, foundation2: $o). 126.84/19.39 thf(decl_398, type, notinself: $o). 126.84/19.39 thf(decl_399, type, notinself2: $o). 126.84/19.39 thf(decl_400, type, omegaS: $i > $i). 126.84/19.39 thf(decl_401, type, omegaSp: $o). 126.84/19.39 thf(decl_402, type, omegaSclos: $o). 126.84/19.39 thf(decl_403, type, peano0notS: $o). 126.84/19.39 thf(decl_407, type, peanoSinj: $o). 126.84/19.39 thf(decl_409, type, transitiveset: $i > $o). 126.84/19.39 thf(decl_410, type, transitivesetOp1: $o). 126.84/19.39 thf(decl_411, type, binintTransitive: $o). 126.84/19.39 thf(decl_412, type, transitivesetOp2: $o). 126.84/19.39 thf(decl_413, type, setunionTransitive: $o). 126.84/19.39 thf(decl_414, type, stricttotalorderedByIn: $i > $o). 126.84/19.39 thf(decl_415, type, wellorderedByIn: $i > $o). 126.84/19.39 thf(decl_416, type, ordinal: $i > $o). 126.84/19.39 thf(decl_418, type, ordinalMinLem1: $o). 126.84/19.39 thf(decl_419, type, ordinalTransSet: $o). 126.84/19.39 thf(decl_420, type, ordinalTransSet1: $o). 126.84/19.39 thf(decl_421, type, epred1_0: $o). 126.84/19.39 thf(decl_422, type, epred2_1: $i > $o). 126.84/19.39 thf(decl_423, type, epred3_1: $i > $o). 126.84/19.39 thf(decl_424, type, epred4_1: $i > $o). 126.84/19.39 thf(decl_425, type, epred5_1: $i > $o). 126.84/19.39 thf(decl_426, type, epred6_1: $i > $o). 126.84/19.39 thf(decl_427, type, esk1_2: $i > $i > $i). 126.84/19.39 thf(decl_428, type, esk2_2: $i > $i > $i). 126.84/19.39 thf(decl_429, type, esk3_2: $i > $i > $i). 126.84/19.39 thf(decl_430, type, esk4_1: $i > $i). 126.84/19.39 thf(decl_431, type, esk5_2: ($i > $i > $o) > $i > $i). 126.84/19.39 thf(decl_432, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 126.84/19.39 thf(decl_433, type, esk7_2: ($i > $i > $o) > $i > $i). 126.84/19.39 thf(decl_434, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 126.84/19.39 thf(decl_435, type, esk9_1: $i > $i). 126.84/19.39 thf(decl_436, type, esk10_2: ($i > $o) > $i > $i). 126.84/19.39 thf(decl_437, type, esk11_2: ($i > $o) > $i > $i). 126.84/19.39 thf(decl_438, type, esk12_1: ($i > $o) > $i). 126.84/19.39 thf(decl_439, type, esk13_2: ($i > $o) > $i > $i). 126.84/19.39 thf(decl_440, type, esk14_1: ($i > $o) > $i). 126.84/19.39 thf(decl_441, type, esk15_2: $i > $i > $i). 126.84/19.39 thf(decl_442, type, esk16_2: $i > $i > $i). 126.84/19.39 thf(decl_443, type, esk17_1: $i > $i). 126.84/19.39 thf(decl_444, type, esk18_1: $i > $i). 126.84/19.39 thf(decl_445, type, esk19_1: $i > $i). 126.84/19.39 thf(decl_446, type, esk20_2: $i > $i > $i). 126.84/19.39 thf(decl_447, type, esk21_3: $i > $i > $o > $i). 126.84/19.39 thf(decl_448, type, esk22_2: ($i > $o) > $i > $i). 126.84/19.39 thf(decl_449, type, esk23_1: ($i > $o) > $i). 126.84/19.39 thf(decl_450, type, esk24_1: $i > $i). 126.84/19.39 thf(decl_451, type, esk25_2: $i > ($i > $o) > $i). 126.84/19.39 thf(decl_452, type, esk26_2: $i > ($i > $o) > $i). 126.84/19.39 thf(decl_453, type, esk27_2: $i > ($i > $o) > $i). 126.84/19.39 thf(decl_454, type, esk28_2: $i > ($i > $o) > $i). 126.84/19.39 thf(decl_455, type, esk29_2: $i > ($i > $o) > $i). 126.84/19.39 thf(decl_456, type, esk30_2: $i > ($i > $o) > $i). 126.84/19.39 thf(decl_457, type, esk31_2: ($i > $o) > $i > $i). 126.84/19.39 thf(decl_458, type, esk32_1: ($i > $o) > $i). 126.84/19.39 thf(decl_459, type, esk33_1: ($i > $o) > $i). 126.84/19.39 thf(decl_460, type, esk34_1: ($i > $o) > $i). 126.84/19.39 thf(decl_461, type, esk35_1: ($i > $o) > $i). 126.84/19.39 thf(decl_462, type, esk36_2: ($i > $o) > $i > $i). 126.84/19.39 thf(decl_463, type, esk37_1: ($i > $o) > $i). 126.84/19.39 thf(decl_464, type, esk38_2: ($i > $o) > $i > $i). 126.84/19.39 thf(decl_465, type, esk39_2: ($i > $o) > ($i > $o) > $i). 126.84/19.39 thf(decl_466, type, esk40_2: ($i > $o) > ($i > $o) > $i). 126.84/19.39 thf(decl_467, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 126.84/19.39 thf(decl_468, type, esk42_2: ($i > $o) > ($i > $o) > $i). 126.84/19.39 thf(decl_469, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 126.84/19.39 thf(decl_470, type, esk44_2: ($i > $o) > ($i > $o) > $i). 126.84/19.39 thf(decl_471, type, esk45_2: ($i > $o) > $i > $i). 126.84/19.39 thf(decl_472, type, esk46_2: ($i > $o) > ($i > $o) > $i). 126.84/19.39 thf(decl_473, type, esk47_2: ($i > $o) > ($i > $o) > $i). 126.84/19.39 thf(decl_474, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 126.84/19.39 thf(decl_475, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 126.84/19.39 thf(decl_476, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 126.84/19.39 thf(decl_477, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 126.84/19.39 thf(decl_478, type, esk52_2: $i > $i > $i). 126.84/19.39 thf(decl_479, type, esk53_2: $i > $i > $i). 126.84/19.39 thf(decl_480, type, esk54_2: $i > $i > $i). 126.84/19.39 thf(decl_481, type, esk55_3: $i > $i > $i > $i). 126.84/19.39 thf(decl_482, type, esk56_3: $i > $i > $i > $i). 126.84/19.39 thf(decl_483, type, esk57_2: $i > $i > $i). 126.84/19.39 thf(decl_484, type, esk58_2: $i > ($i > $o) > $i). 126.84/19.39 thf(decl_485, type, esk59_2: $i > ($i > $o) > $i). 126.84/19.39 thf(decl_486, type, esk60_2: $i > ($i > $o) > $i). 126.84/19.39 thf(decl_487, type, esk61_3: $i > ($i > $o) > $i > $i). 126.84/19.39 thf(decl_488, type, esk62_2: $i > ($i > $o) > $i). 126.84/19.39 thf(decl_489, type, esk63_2: $i > ($i > $o) > $i). 126.84/19.39 thf(decl_490, type, esk64_3: $i > $i > ($i > $i) > $i). 126.84/19.39 thf(decl_491, type, esk65_3: $i > $i > ($i > $i) > $i). 126.84/19.39 thf(decl_492, type, esk66_3: $i > $i > ($i > $i) > $i). 126.84/19.39 thf(decl_493, type, esk67_4: $i > $i > $i > ($i > $o) > $i). 126.84/19.39 thf(decl_494, type, esk68_4: $i > $i > $i > ($i > $o) > $i). 126.84/19.39 thf(decl_495, type, esk69_4: $i > $i > $i > ($i > $o) > $i). 126.84/19.39 thf(decl_496, type, esk70_4: $i > $i > $i > ($i > $o) > $i). 126.84/19.39 thf(decl_497, type, esk71_4: $i > $i > $i > $i > $i). 126.84/19.39 thf(decl_498, type, esk72_4: $i > $i > $i > $i > $i). 126.84/19.39 thf(decl_499, type, esk73_4: $i > $i > $i > $i > $i). 126.84/19.39 thf(decl_500, type, esk74_4: $i > $i > $i > $i > $i). 126.84/19.39 thf(decl_501, type, esk75_4: $i > $i > $i > $i > $i). 126.84/19.39 thf(decl_502, type, esk76_4: $i > $i > $i > $i > $i). 126.84/19.39 thf(decl_503, type, esk77_4: $i > $i > $i > $i > $i). 126.84/19.39 thf(decl_504, type, esk78_4: $i > $i > $i > $i > $i). 126.84/19.39 thf(decl_505, type, esk79_4: $i > $i > $i > $i > $i). 126.84/19.39 thf(decl_506, type, esk80_3: $i > $i > ($i > $i) > $i). 126.84/19.39 thf(decl_507, type, esk81_3: $i > $i > ($i > $i) > $i). 126.84/19.39 thf(decl_508, type, esk82_3: $i > $i > ($i > $i) > $i). 126.84/19.39 thf(decl_509, type, esk83_3: $i > $i > $i > $i). 126.84/19.39 thf(decl_510, type, esk84_3: $i > $i > $i > $i). 126.84/19.39 thf(decl_511, type, esk85_3: $i > $i > $i > $i). 126.84/19.39 thf(decl_512, type, esk86_3: $i > $i > $i > $i). 126.84/19.39 thf(decl_513, type, esk87_3: $i > $i > ($i > $o) > $i). 126.84/19.39 thf(decl_514, type, esk88_3: $i > $i > ($i > $o) > $i). 126.84/19.39 thf(decl_515, type, esk89_3: $i > $i > ($i > $i > $o) > $i). 126.84/19.39 thf(decl_516, type, esk90_3: $i > $i > ($i > $o) > $i). 126.84/19.39 thf(decl_517, type, esk91_3: $i > $i > ($i > $o) > $i). 126.84/19.39 thf(decl_518, type, esk92_3: $i > $i > $i > $i). 126.84/19.39 thf(decl_519, type, esk93_3: $i > $i > $i > $i). 126.84/19.39 thf(decl_520, type, esk94_3: $i > $i > $i > $i). 126.84/19.39 thf(decl_521, type, esk95_3: $i > $i > $i > $i). 126.84/19.39 thf(decl_522, type, esk96_3: $i > $i > $i > $i). 126.84/19.39 thf(decl_523, type, esk97_3: $i > $i > $i > $i). 126.84/19.39 thf(decl_524, type, esk98_5: $i > $i > $i > $i > $i > $i). 126.84/19.39 thf(decl_525, type, esk99_6: $i > $i > $i > $i > $i > $o > $i). 126.84/19.39 thf(decl_526, type, esk100_2: $i > ($i > $i) > $i). 126.84/19.39 thf(decl_527, type, esk101_3: $i > ($i > $i) > $i > $i). 126.84/19.39 thf(decl_528, type, esk102_2: $i > ($i > $i) > $i). 126.84/19.39 thf(decl_529, type, esk103_3: $i > ($i > $i) > $i > $i). 126.84/19.39 thf(decl_530, type, esk104_3: $i > ($i > $i) > $i > $i). 126.84/19.39 thf(decl_531, type, esk105_3: $i > ($i > $i) > $i > $i). 126.84/19.39 thf(decl_532, type, esk106_3: $i > ($i > $i) > $i > $i). 126.84/19.39 thf(decl_533, type, esk107_3: $i > ($i > $i) > $i > $i). 126.84/19.39 thf(decl_534, type, esk108_3: $i > $i > ($i > $i) > $i). 126.84/19.39 thf(decl_535, type, esk109_4: $i > $i > ($i > $i) > $i > $i). 126.84/19.39 thf(decl_536, type, esk110_1: $i > $i). 126.84/19.39 thf(decl_537, type, esk111_1: $i > $i). 126.84/19.39 thf(decl_538, type, esk112_1: $i > $i). 126.84/19.39 thf(decl_539, type, esk113_2: $i > $i > $i). 126.84/19.39 thf(decl_540, type, esk114_1: $i > $i). 126.84/19.39 thf(decl_541, type, esk115_1: $i > $i). 126.84/19.39 thf(decl_542, type, esk116_1: $i > $i). 126.84/19.39 thf(decl_543, type, esk117_1: $i > $i). 126.84/19.39 thf(decl_544, type, esk118_1: $i > $i). 126.84/19.39 thf(decl_545, type, esk119_1: $i > $i). 126.84/19.39 thf(decl_546, type, esk120_2: $i > $i > $i). 126.84/19.39 thf(decl_547, type, esk121_2: $i > $i > $i). 126.84/19.39 thf(decl_548, type, esk122_2: $i > $i > $i). 126.84/19.39 thf(decl_549, type, esk123_2: $i > $i > $i). 126.84/19.39 thf(decl_550, type, esk124_3: $i > $i > $i > $i). 126.84/19.39 thf(decl_551, type, esk125_1: $i > $i). 126.84/19.39 thf(decl_552, type, esk126_1: $i > $i). 126.84/19.39 thf(decl_553, type, esk127_1: $i > $i). 126.84/19.39 thf(decl_554, type, esk128_2: $i > $i > $i). 126.84/19.39 thf(decl_555, type, esk129_1: $i > $i). 126.84/19.39 thf(decl_556, type, esk130_1: $i > $i). 126.84/19.39 thf(decl_557, type, esk131_1: $i > $i). 126.84/19.39 thf(decl_558, type, esk132_2: $i > $i > $i). 126.84/19.39 thf(decl_559, type, esk133_0: $i). 126.84/19.39 thf(decl_560, type, esk134_0: $i). 126.84/19.39 thf(decl_586, type, esk160_2: $i > $i > $i). 126.84/19.39 thf(wellorderedByIn, axiom, ((wellorderedByIn)=(^[X4:$i]:((((stricttotalorderedByIn @ X4))&(![X21:$i]:((((in @ X21 @ (powerset @ X4)))=>((((nonempty @ X21))=>(?[X2:$i]:((((in @ X2 @ X21))&(![X48:$i]:((((in @ X48 @ X21))=>(((((X2)=(X48)))|((in @ X2 @ X48))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', wellorderedByIn)). 126.84/19.39 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', nonempty)). 126.84/19.39 thf(stricttotalorderedByIn, axiom, ((stricttotalorderedByIn)=(^[X4:$i]:(((((![X2:$i]:((((in @ X2 @ X4))=>(![X21:$i]:((((in @ X21 @ X4))=>(![X48:$i]:((((in @ X48 @ X4))=>((((((in @ X2 @ X21))&((in @ X21 @ X48))))=>((in @ X2 @ X48)))))))))))))&(![X21:$i]:((((in @ X21 @ X4))=>(![X48:$i]:((((in @ X48 @ X4))=>(((((((X21)=(X48)))|((in @ X21 @ X48))))|((in @ X48 @ X21))))))))))))&(![X21:$i]:((((in @ X21 @ X4))=>(~((in @ X21 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', stricttotalorderedByIn)). 126.84/19.39 thf(ordinal, axiom, ((ordinal)=(^[X2:$i]:((((transitiveset @ X2))&((wellorderedByIn @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', ordinal)). 126.84/19.39 thf(transitiveset, axiom, ((transitiveset)=(^[X4:$i]:(![X21:$i]:((((in @ X21 @ X4))=>((subset @ X21 @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', transitiveset)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', exuE3u)). 126.84/19.39 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', exu)). 126.84/19.39 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', exuI3)). 126.84/19.39 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', exuE2)). 126.84/19.39 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', nonemptyI)). 126.84/19.39 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', descrp)). 126.84/19.39 thf(image1Ex1, axiom, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&(((X2)=(X58 @ X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', image1Ex1)). 126.84/19.39 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', descr__Cong)). 126.84/19.39 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', exuEu)). 126.84/19.39 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', exu__Cong)). 126.84/19.39 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', exuI2)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', exuI1)). 126.84/19.39 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', exuE3e)). 126.84/19.39 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', exuE1)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', replAx)). 126.84/19.39 thf(setunionOrdinalLem1, conjecture, ((setextAx)=>(((setadjoinAx)=>((((omega0Ax)=>(((omegaIndAx)=>((replAx)=>(((wellorderingAx)=>(((dsetconstrI)=>(((dsetconstrER)=>((exuE1)=>(((emptysetE)=>((((exuE3e)=>(((emptyI)=>((noeltsimpempty)=>(((((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((((((((emptyInPowerset)=>((powersetE)=>(((setunionE)=>(((((((eqinunit)=>(((upairsetE)=>((upairsetIL)=>((((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>(((((notdallE)=>((exuI1)=>(((exuI2)=>((inCongP)=>((((exu__Cong)=>((emptyset__Cong)=>(((powerset__Cong)=>((((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>(((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>(((((notequalI1)=>(((((((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>(((inPowerset)=>((((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((((binunionLsub)=>((binunionRsub)=>((binintersectI)=>(((binintersectEL)=>((((binintersectSubset3)=>(((disjointsetsI1)=>((binintersectRsub)=>(((binintersectSubset1)=>((bs114d)=>(((setminusEL)=>((setminusER)=>((((setminusELneg)=>((((setminusLsub)=>((setminusSubset1)=>(((symdiffI1)=>(((symdiffIneg1)=>(((((((((singletoninpowerset)=>((singletoninpowunion)=>(((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((((((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>(((ex1I)=>((ex1I2)=>((((kfstsingleton)=>((theprop)=>(((cartprodfstin)=>(((setukpairinjL)=>((setukpairinjR11)=>((((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((((kpairsurjEq)=>((cartprodsndin)=>(((cartprodpairmemER)=>((cartprodmempaircEq)=>(((((((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((((funcImageSingleton)=>((apProp)=>((app)=>(((ap2p)=>((funcinfuncset)=>((lamProp)=>(((lam2p)=>((((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>(((funcextLem)=>(((subbreln)=>(((((ap2apEq1)=>((ap2apEq2)=>((((((((((((ifp)=>((((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((((((setextT)=>((subsetTI)=>((((complementTI1)=>((complementTE1)=>(((binintersectTERcontra)=>((contrasubsetT)=>((((contrasubsetT3)=>((doubleComplementI1)=>(((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>(((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((((inIntersectImpInIntersectUnions)=>(((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>(((binunionTEcontra)=>((demorgan2a1)=>(((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>(((demorgan2a)=>(((demorgan2b)=>((demorgan2)=>((woz13rule0)=>(((woz13rule2)=>(((((woz1_2)=>((woz1_3)=>((woz1_4)=>((woz1_5)=>((((choice2fnsingleton)=>((setOfPairsIsBReln1)=>((((eqbreln1)=>((breln1invprop)=>((breln1invI)=>(((breln1compprop)=>((breln1compI)=>(((((((breln1unionI)=>(((breln1unionEcases)=>(((woz2Ex)=>((woz2W)=>((((((image1Equiv)=>(((((injFuncSetFuncIn)=>((injFuncSetFuncInj)=>(((surjFuncSetFuncSurj)=>((leftInvIsSurj)=>(((foundation2)=>((notinself)=>(((omegaSp)=>(((((transitivesetOp1)=>(((transitivesetOp2)=>((setunionTransitive)=>(((ordinalTransSet)=>((ordinalTransSet1)=>![X21:$i]:((![X2:$i]:(((ordinal @ X2)<=(in @ X2 @ X21)))=>(transitiveset @ (setunion @ X21))))))<=(ordinalMinLem1))))<=(binintTransitive)))<=(peanoSinj))<=(peano0notS))<=(omegaSclos)))<=(notinself2))))<=(surjCantorThm))))<=(surjFuncSetFuncIn))))<=(injFuncInInjFuncSet))<=(image1I))<=(image1E)))<=(image1Ex1))<=(image1Ex))<=(woz2B))<=(woz2A))))<=(breln1unionCommutes)))<=(breln1unionE)))<=(breln1unionIR))<=(breln1unionIL))<=(breln1unionprop))<=(breln1compEex))<=(breln1compE))))<=(breln1invE)))))<=(subbreln1))<=(breln1all1))))<=(breln1SetBreln1))<=(breln1all2))))))<=(woz1_1))<=(woz13rule4))<=(woz13rule3)))<=(woz13rule1)))))<=(demorgan2b2)))<=(demorgan1)))))<=(complementUnionInPowersetComplement))))<=(binunionTE))))<=(intersectInPowersetIntersectUnions)))<=(inIntersectImpInUnion2))<=(inIntersectImpInUnion)))))))))<=(complementTnotintersectT)))))<=(doubleComplementE1))))<=(contrasubsetT2))<=(contrasubsetT1))))<=(binintersectTELcontra))))<=(powersetTE1))<=(powersetTI1))))<=(complementT_lem))<=(setminusT_lem))<=(powersetT_lem))<=(binunionT_lem)))))<=(iftrue))<=(theeq)))<=(ifSingleton))<=(iftrueProp2))<=(iftrueProp1))<=(iffalseProp2))<=(iffalseProp1))<=(eta2))<=(beta2))<=(lam2lamEq))<=(eta1))<=(beta1))))<=(funcext2))<=(funcext))<=(eqbreln)))<=(funcGraphProp4)))<=(funcGraphProp2)))))<=(brelnall2))<=(brelnall1)))<=(lamp)))))<=(infuncsetfunc)))))<=(dpsetconstrER))<=(dpsetconstrEL2)))))<=(dpsetconstrSub))<=(dpsetconstrI))<=(cartprodpairsurjEq))<=(cartprodsndpairEq))<=(cartprodfstpairEq))))<=(cartprodpairmemEL))))<=(ksndpairEq))<=(ksndsingleton)))))<=(setukpairinjR1))<=(setukpairinjR12))))<=(setukpairinjL2)))<=(kfstpairEq))))<=(setukpairinjL1))<=(singletonsuniq))))<=(ex1E1))))))<=(setunionE2))<=(cartprodmempair))<=(cartprodmempair1))<=(cartprodpairin)))))))<=(upairset2E))))<=(singletonsubset))<=(kpairp))<=(kpairiskpair))<=(setukpairIR))<=(setukpairIL))<=(secondinupair))<=(symdiffIneg2)))<=(symdiffI2)))<=(symdiffE))))<=(setminusIRneg))<=(setminusILneg)))<=(setminusERneg))<=(setminusSubset2))))<=(setminusI))))<=(binintersectSubset4))))<=(binintersectER)))<=(binintersectSubset2))<=(binintersectLsub)))<=(binintersectSubset5)))))<=(binunionE))<=(binunionEcases))))))<=(sepInPowerset))<=(powersetsubset)))<=(powersetE1))))))<=(setadjoinSub2))<=(setadjoinSub))<=(subsetTrans))<=(subsetRefl))<=(notequalI2)))<=(notsubsetI))<=(subsetE2))<=(subsetE))))))<=(subsetI1)))))<=(omega__Cong))<=(setunion__Cong)))<=(setadjoin__Cong))))<=(exuE3u))<=(in__Cong))))<=(exuI3))))<=(notdexE))<=(prop2set2propI))<=(prop2setI)))))))<=(emptyE1))<=(upairsetIR))))<=(singletonsswitch)))<=(notinsingleton))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU)))<=(setunionI))))<=(emptyinPowerset))<=(powersetI))<=(setoftrueEq))<=(setadjoinOr))<=(setadjoinE))<=(setadjoinIR)))))<=(nonemptyI))<=(nonemptyE1))<=(setbeta))))<=(setext)))<=(notinemptyset))<=(emptysetimpfalse)))<=(prop2setE))))<=(dsetconstrEL)))<=(descrp)))<=(foundationAx))))<=(omegaSAx)))<=(setunionAx))<=(powersetAx)))<=(emptysetAx))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setunionOrdinalLem1)). 126.84/19.39 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', sepInPowerset)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', emptyE1)). 126.84/19.39 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', nonemptyImpWitness)). 126.84/19.39 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setoftrueEq)). 126.84/19.39 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', nonemptyE1)). 126.84/19.39 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setbeta)). 126.84/19.39 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', kfstsingleton)). 126.84/19.39 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', ex1I2)). 126.84/19.39 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.GyZKKTrfzH/E---3.1_2969926.p', ex1I)). 126.84/19.39 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', dsetconstrEL)). 126.84/19.39 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', singletonprop)). 126.84/19.39 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', apProp)). 126.84/19.39 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', funcImageSingleton)). 126.84/19.39 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', dpsetconstrEL1)). 126.84/19.39 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', dpsetconstrERa)). 126.84/19.39 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setOfPairsIsBReln)). 126.84/19.39 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', ex1E2)). 126.84/19.39 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', lam2p)). 126.84/19.39 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', lamProp)). 126.84/19.39 thf(image1E, axiom, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X60 @ X3))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', image1E)). 126.84/19.39 thf(image1I, axiom, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X61 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', image1I)). 126.84/19.39 thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setOfPairsIsBReln1)). 126.84/19.39 thf(choice2fnsingleton, axiom, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((((X52 @ X2 @ X3))&(![X14:$i]:((((in @ X14 @ X5))=>((((X52 @ X2 @ X14))=>((in @ (kpair @ X3 @ X14) @ X33)))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', choice2fnsingleton)). 126.84/19.39 thf(image1Equiv, axiom, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X59 @ X3))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', image1Equiv)). 126.84/19.39 thf(setunionTransitive, axiom, ((setunionTransitive)<=>![X21:$i]:((![X2:$i]:(((in @ X2 @ X21)=>(transitiveset @ X2)))=>(transitiveset @ (setunion @ X21))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setunionTransitive)). 126.84/19.39 thf(ordinalTransSet, axiom, ((ordinalTransSet)<=>![X21:$i]:(((ordinal @ X21)=>![X2:$i, X4:$i]:(((in @ X4 @ X21)=>((in @ X2 @ X4)=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', ordinalTransSet)). 126.84/19.39 thf(ordinalTransSet1, axiom, ((ordinalTransSet1)<=>![X21:$i]:(((ordinal @ X21)=>![X4:$i]:(((in @ X4 @ X21)=>(subset @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', ordinalTransSet1)). 126.84/19.39 thf(foundation2, axiom, ((foundation2)<=>![X4:$i]:(((nonempty @ X4)=>?[X21:$i]:(((in @ X21 @ X4)&((binintersect @ X21 @ X4)=(emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', foundation2)). 126.84/19.39 thf(transitivesetOp2, axiom, ((transitivesetOp2)<=>![X21:$i]:(((transitiveset @ X21)=>![X4:$i, X2:$i]:(((in @ X4 @ X21)=>((in @ X2 @ X4)=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', transitivesetOp2)). 126.84/19.39 thf(binintTransitive, axiom, ((binintTransitive)<=>![X21:$i]:(((transitiveset @ X21)=>![X48:$i]:(((transitiveset @ X48)=>(transitiveset @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binintTransitive)). 126.84/19.39 thf(ordinalMinLem1, axiom, ((ordinalMinLem1)<=>![X21:$i]:(((ordinal @ X21)=>![X48:$i]:(((ordinal @ X48)=>(transitiveset @ (binintersect @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', ordinalMinLem1)). 126.84/19.39 thf(transitivesetOp1, axiom, ((transitivesetOp1)<=>![X21:$i]:(((transitiveset @ X21)=>![X4:$i]:(((in @ X4 @ X21)=>(subset @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', transitivesetOp1)). 126.84/19.39 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X42))&(((X14)=(X2)))))|(((~((X42)))&(((X14)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', iftrueProp2)). 126.84/19.39 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X43))&(((X14)=(X2)))))|(((~((X43)))&(((X14)=(X3))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', ifSingleton)). 126.84/19.39 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X41))&(((X14)=(X2)))))|(((~((X41)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', iftrueProp1)). 126.84/19.39 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', beta1)). 126.84/19.39 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', eta1)). 126.84/19.39 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', lam2lamEq)). 126.84/19.39 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', beta2)). 126.84/19.39 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', eta2)). 126.84/19.39 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((((X39))&(((X14)=(X2)))))|(((~((X39)))&(((X14)=(X3)))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', iffalseProp1)). 126.84/19.39 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((((X40))&(((X14)=(X2)))))|(((~((X40)))&(((X14)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', iffalseProp2)). 126.84/19.39 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', lamp)). 126.84/19.39 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', dpsetconstrI)). 126.84/19.39 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', dpsetconstrSub)). 126.84/19.39 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', dpsetconstrEL2)). 126.84/19.39 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', dpsetconstrER)). 126.84/19.39 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', ksndsingleton)). 126.84/19.39 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', ex1E1)). 126.84/19.39 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', sepSubset)). 126.84/19.39 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', dsetconstr__Cong)). 126.84/19.39 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', nonemptyI1)). 126.84/19.39 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', dsetconstrER)). 126.84/19.39 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', dsetconstrI)). 126.84/19.39 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binintersectSubset4)). 126.84/19.39 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binintersectER)). 126.84/19.39 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binintersectSubset2)). 126.84/19.39 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binintersectLsub)). 126.84/19.39 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', symdiffIneg1)). 126.84/19.39 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binintersectSubset5)). 126.84/19.39 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', symdiffI1)). 126.84/19.39 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binunionE)). 126.84/19.39 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setminusSubset1)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', binunionEcases)). 126.84/19.39 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setminusLsub)). 126.84/19.39 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setminusELneg)). 126.84/19.39 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', powersetsubset)). 126.84/19.39 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setminusER)). 126.84/19.39 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', powersetE1)). 126.84/19.39 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setminusEL)). 126.84/19.39 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setadjoinSub2)). 126.84/19.39 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', singletoninpowerset)). 126.84/19.39 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setadjoinSub)). 126.84/19.39 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', subsetTrans)). 126.84/19.39 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', subsetRefl)). 126.84/19.39 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', notequalI2)). 126.84/19.39 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', notsubsetI)). 126.84/19.39 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', subsetE2)). 126.84/19.39 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', subsetE)). 126.84/19.39 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', subsetI1)). 126.84/19.39 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', omega__Cong)). 126.84/19.39 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setunion__Cong)). 126.84/19.39 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setadjoin__Cong)). 126.84/19.39 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', in__Cong)). 126.84/19.39 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setunionsingleton1)). 126.84/19.39 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', notdexE)). 126.84/19.39 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', ubforcartprodlem3)). 126.84/19.39 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', prop2set2propI)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', ubforcartprodlem2)). 126.84/19.39 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', prop2setI)). 126.84/19.39 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', ubforcartprodlem1)). 126.84/19.39 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', upairinpowunion)). 126.84/19.39 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', upairsetIR)). 126.84/19.39 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', upairsubunion)). 126.84/19.39 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', singletonsswitch)). 126.84/19.39 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', singletoninpowunion)). 126.84/19.39 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', notinsingleton)). 126.84/19.39 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setunionsingleton2)). 126.84/19.39 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', uniqinunit)). 126.84/19.39 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', subPowSU)). 126.84/19.39 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setunionI)). 126.84/19.39 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', emptyinPowerset)). 126.84/19.39 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', powersetI)). 126.84/19.39 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setadjoinOr)). 126.84/19.39 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setadjoinE)). 126.84/19.39 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setadjoinIR)). 126.84/19.39 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', cartprodfstin)). 126.84/19.39 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setext)). 126.84/19.39 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', theprop)). 126.84/19.39 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', notinemptyset)). 126.84/19.39 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', emptysetimpfalse)). 126.84/19.39 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', prop2setE)). 126.84/19.39 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setunionsingleton)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', foundationAx)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', setukpairinjL)). 126.84/19.39 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', omegaSAx)). 126.84/19.39 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setunionAx)). 126.84/19.39 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', powersetAx)). 126.84/19.39 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', emptysetAx)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', cartprodpairmemER)). 126.84/19.39 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', cartprodsndin)). 126.84/19.39 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', kpairsurjEq)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', setukpairinjR)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', setukpairinjR2)). 126.84/19.39 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', upairequniteq)). 126.84/19.39 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setukpairinjR11)). 126.84/19.39 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', cartprodmempaircEq)). 126.84/19.39 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', ap2p)). 126.84/19.39 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', app)). 126.84/19.39 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', funcinfuncset)). 126.84/19.39 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', subbreln)). 126.84/19.39 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', funcextLem)). 126.84/19.39 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', funcGraphProp3)). 126.84/19.39 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', funcGraphProp1)). 126.84/19.39 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', ap2apEq1)). 126.84/19.39 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', subsetTI)). 126.84/19.39 thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setextT)). 126.84/19.39 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binintersectT_lem)). 126.84/19.39 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', iftrueorfalse)). 126.84/19.39 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', iffalse)). 126.84/19.39 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', ifp)). 126.84/19.39 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', ap2apEq2)). 126.84/19.39 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', complementTI1)). 126.84/19.39 thf(image1Ex, axiom, ((image1Ex)<=>![X4:$i, X57:$i > $i]:(?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X57 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', image1Ex)). 126.84/19.39 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', doubleComplementSub2)). 126.84/19.39 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', doubleComplementSub1)). 126.84/19.39 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', doubleComplementI1)). 126.84/19.39 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', contrasubsetT3)). 126.84/19.39 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', contrasubsetT)). 126.84/19.39 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binintersectTERcontra)). 126.84/19.39 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', complementTE1)). 126.84/19.39 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', doubleComplementEq)). 126.84/19.39 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binunionTIRcontra)). 126.84/19.39 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binunionTILcontra)). 126.84/19.39 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', complementTcontraSubset)). 126.84/19.39 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', contraSubsetComplement)). 126.84/19.39 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', complementInPowersetComplementIntersect)). 126.84/19.39 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', complementSubsetComplementIntersect)). 126.84/19.39 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', complementImpComplementIntersect)). 126.84/19.39 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', inIntersectImpInIntersectUnions)). 126.84/19.39 thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', demorgan1b)). 126.84/19.39 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', demorgan1a)). 126.84/19.39 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', demorgan2a2)). 126.84/19.39 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', demorgan2a1)). 126.84/19.39 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binunionTEcontra)). 126.84/19.39 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', inComplementUnionImpInComplement1)). 126.84/19.39 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', inComplementUnionImpNotIn1)). 126.84/19.39 thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', demorgan2a)). 126.84/19.39 thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', woz1_4)). 126.84/19.39 thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', woz1_3)). 126.84/19.39 thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', woz1_2)). 126.84/19.39 thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', woz13rule2)). 126.84/19.39 thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', woz13rule0)). 126.84/19.39 thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', demorgan2)). 126.84/19.39 thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', demorgan2b)). 126.84/19.39 thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', woz1_5)). 126.84/19.39 thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', breln1compI)). 126.84/19.39 thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', breln1compprop)). 126.84/19.39 thf(breln1invI, axiom, ((breln1invI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', breln1invI)). 126.84/19.39 thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', breln1invprop)). 126.84/19.39 thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', eqbreln1)). 126.84/19.39 thf(breln1unionI, axiom, ((breln1unionI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35))=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', breln1unionI)). 126.84/19.39 thf(surjFuncSetFuncSurj, axiom, ((surjFuncSetFuncSurj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X2 @ X3))=>(surjective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', surjFuncSetFuncSurj)). 126.84/19.39 thf(injFuncSetFuncInj, axiom, ((injFuncSetFuncInj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X2 @ X3))=>(injective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', injFuncSetFuncInj)). 126.84/19.39 thf(injFuncSetFuncIn, axiom, ((injFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', injFuncSetFuncIn)). 126.84/19.39 thf(woz2W, axiom, ((woz2W)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((breln1invset @ X4 @ (breln1compset @ X4 @ X33 @ X35))=(breln1compset @ X4 @ (breln1invset @ X4 @ X35) @ (breln1invset @ X4 @ X33)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', woz2W)). 126.84/19.39 thf(woz2Ex, axiom, ((woz2Ex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>((X33)=(breln1invset @ X4 @ (breln1invset @ X4 @ X33)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', woz2Ex)). 126.84/19.39 thf(breln1unionEcases, axiom, ((breln1unionEcases)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>![X55:$o]:((((in @ (kpair @ X2 @ X3) @ X33)=>(X55))=>(((in @ (kpair @ X2 @ X3) @ X35)=>(X55))=>(X55)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', breln1unionEcases)). 126.84/19.39 thf(leftInvIsSurj, axiom, ((leftInvIsSurj)<=>![X4:$i, X5:$i, X62:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X62 @ X2) @ X5)))=>![X34:$i]:(((in @ X34 @ (funcSet @ X5 @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X5 @ X4 @ X34 @ (X62 @ X2))=(X2))))=>(surjective @ X5 @ X4 @ X34))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', leftInvIsSurj)). 126.84/19.39 thf(omegaSp, axiom, ((omegaSp)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (omegaS @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', omegaSp)). 126.84/19.39 thf(notinself, axiom, ((notinself)<=>![X4:$i]:(~((in @ X4 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', notinself)). 126.84/19.39 thf(omegaSclos, axiom, ((omegaSclos)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', omegaSclos)). 126.84/19.39 thf(peano0notS, axiom, ((peano0notS)<=>![X2:$i]:(((in @ X2 @ omega)=>((omegaS @ X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', peano0notS)). 126.84/19.39 thf(peanoSinj, axiom, ((peanoSinj)<=>![X2:$i]:(((in @ X2 @ omega)=>![X3:$i]:(((in @ X3 @ omega)=>(((omegaS @ X2)=(omegaS @ X3))=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', peanoSinj)). 126.84/19.39 thf(notinself2, axiom, ((notinself2)<=>![X4:$i, X5:$i]:(((in @ X4 @ X5)=>~((in @ X5 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', notinself2)). 126.84/19.39 thf(injFuncInInjFuncSet, axiom, ((injFuncInInjFuncSet)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((injective @ X4 @ X5 @ X29)=>(in @ X29 @ (injFuncSet @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', injFuncInInjFuncSet)). 126.84/19.39 thf(surjFuncSetFuncIn, axiom, ((surjFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', surjFuncSetFuncIn)). 126.84/19.39 thf(surjCantorThm, axiom, ((surjCantorThm)<=>![X4:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ (powerset @ X4)))=>~((surjective @ X4 @ (powerset @ X4) @ X29))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', surjCantorThm)). 126.84/19.39 thf(woz2B, axiom, ((woz2B)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X35))) @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X33)))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', woz2B)). 126.84/19.39 thf(breln1compEex, axiom, ((breln1compEex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>![X54:$o]:((![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(X54)))))=>(X54))))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', breln1compEex)). 126.84/19.39 thf(breln1unionprop, axiom, ((breln1unionprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', breln1unionprop)). 126.84/19.39 thf(breln1unionIL, axiom, ((breln1unionIL)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', breln1unionIL)). 126.84/19.39 thf(breln1unionIR, axiom, ((breln1unionIR)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', breln1unionIR)). 126.84/19.39 thf(breln1unionE, axiom, ((breln1unionE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', breln1unionE)). 126.84/19.39 thf(breln1unionCommutes, axiom, ((breln1unionCommutes)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((binunion @ X33 @ X35)=(binunion @ X35 @ X33))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', breln1unionCommutes)). 126.84/19.39 thf(woz2A, axiom, ((woz2A)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1compset @ X4 @ X33 @ X56) @ (breln1compset @ X4 @ X35 @ X56)))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', woz2A)). 126.84/19.39 thf(breln1compE, axiom, ((breln1compE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35))))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', breln1compE)). 126.84/19.39 thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', woz13rule4)). 126.84/19.39 thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', woz1_1)). 126.84/19.39 thf(breln1all2, axiom, ((breln1all2)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', breln1all2)). 126.84/19.39 thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', breln1SetBreln1)). 126.84/19.39 thf(breln1all1, axiom, ((breln1all1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', breln1all1)). 126.84/19.39 thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', subbreln1)). 126.84/19.39 thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', breln1invE)). 126.84/19.39 thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', woz13rule3)). 126.84/19.39 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', inIntersectImpInUnion2)). 126.84/19.39 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', intersectInPowersetIntersectUnions)). 126.84/19.39 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binunionTE)). 126.84/19.39 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', complementUnionInPowersetComplement)). 126.84/19.39 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', demorgan1)). 126.84/19.39 thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', demorgan2b2)). 126.84/19.39 thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', woz13rule1)). 126.84/19.39 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', inIntersectImpInUnion)). 126.84/19.39 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', powersetTI1)). 126.84/19.39 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', powersetTE1)). 126.84/19.39 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binintersectTELcontra)). 126.84/19.39 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', contrasubsetT1)). 126.84/19.39 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', contrasubsetT2)). 126.84/19.39 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', doubleComplementE1)). 126.84/19.39 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', complementTnotintersectT)). 126.84/19.39 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', complementT_lem)). 126.84/19.39 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', theeq)). 126.84/19.39 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', iftrue)). 126.84/19.39 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binunionT_lem)). 126.84/19.39 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', powersetT_lem)). 126.84/19.39 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setminusT_lem)). 126.84/19.39 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', funcext2)). 126.84/19.39 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', brelnall1)). 126.84/19.39 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', brelnall2)). 126.84/19.39 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', funcGraphProp2)). 126.84/19.39 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', funcGraphProp4)). 126.84/19.39 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', eqbreln)). 126.84/19.39 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', funcext)). 126.84/19.39 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', infuncsetfunc)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', cartprodfstpairEq)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', cartprodsndpairEq)). 126.84/19.39 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', cartprodpairsurjEq)). 126.84/19.39 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', cartprodpairmemEL)). 126.84/19.39 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.GyZKKTrfzH/E---3.1_2969926.p', setukpairinjL1)). 126.84/19.39 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', kfstpairEq)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', setukpairinjL2)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', setukpairinjR12)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', setukpairinjR1)). 126.84/19.39 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', ksndpairEq)). 126.84/19.39 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', singletonsuniq)). 126.84/19.39 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', singletonsubset)). 126.84/19.39 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', upairset2E)). 126.84/19.39 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', cartprodpairin)). 126.84/19.39 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.GyZKKTrfzH/E---3.1_2969926.p', cartprodmempair1)). 126.84/19.39 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', cartprodmempair)). 126.84/19.39 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setunionE2)). 126.84/19.39 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', kpairp)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', symdiffE)). 126.84/19.39 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', symdiffI2)). 126.84/19.39 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', symdiffIneg2)). 126.84/19.39 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', secondinupair)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', setukpairIL)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', setukpairIR)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', kpairiskpair)). 126.84/19.39 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setminusIRneg)). 126.84/19.39 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setminusILneg)). 126.84/19.39 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setminusERneg)). 126.84/19.39 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setminusSubset2)). 126.84/19.39 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setminusI)). 126.84/19.39 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', bs114d)). 126.84/19.39 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binintersectSubset1)). 126.84/19.39 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binintersectRsub)). 126.84/19.39 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', disjointsetsI1)). 126.84/19.39 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binintersectSubset3)). 126.84/19.39 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binintersectEL)). 126.84/19.39 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binintersectI)). 126.84/19.39 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binunionRsub)). 126.84/19.39 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binunionLsub)). 126.84/19.39 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binunionIR)). 126.84/19.39 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', upairset2IR)). 126.84/19.39 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', binunionIL)). 126.84/19.39 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', inPowerset)). 126.84/19.39 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', powersetI1)). 126.84/19.39 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', subsetemptysetimpeq)). 126.84/19.39 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setextsub)). 126.84/19.39 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', subset2powerset)). 126.84/19.39 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', notequalI1)). 126.84/19.39 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', emptysetsubset)). 126.84/19.39 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', subsetI2)). 126.84/19.39 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', eqimpsubset1)). 126.84/19.39 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', eqimpsubset2)). 126.84/19.39 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', powerset__Cong)). 126.84/19.39 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', emptyset__Cong)). 126.84/19.39 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.GyZKKTrfzH/E---3.1_2969926.p', inCongP)). 126.84/19.39 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', notdallE)). 126.84/19.39 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', quantDeMorgan4)). 126.84/19.39 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', quantDeMorgan3)). 126.84/19.39 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', quantDeMorgan2)). 126.84/19.39 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', quantDeMorgan1)). 126.84/19.39 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', vacuousDall)). 126.84/19.39 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', upairsetIL)). 126.84/19.39 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', upairsetE)). 126.84/19.39 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', eqinunit)). 126.84/19.39 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setunionE)). 126.84/19.39 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', powersetE)). 126.84/19.39 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', emptyInPowerset)). 126.84/19.39 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', emptyinunitempty)). 126.84/19.39 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setadjoinIL)). 126.84/19.39 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', noeltsimpempty)). 126.84/19.39 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', emptyI)). 126.84/19.39 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', emptysetE)). 126.84/19.39 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.GyZKKTrfzH/E---3.1_2969926.p', wellorderingAx)). 126.84/19.39 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', omegaIndAx)). 126.84/19.39 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', omega0Ax)). 126.84/19.39 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setadjoinAx)). 126.84/19.39 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.GyZKKTrfzH/E---3.1_2969926.p', setextAx)). 126.84/19.39 thf(c_0_342, plain, ((wellorderedByIn)=(^[Z0:$i]:((((((((![X1189:$i]:((((in @ X1189 @ Z0))=>(![X1190:$i]:((((in @ X1190 @ Z0))=>(![X1191:$i]:((((in @ X1191 @ Z0))=>((((((in @ X1189 @ X1190))&((in @ X1190 @ X1191))))=>((in @ X1189 @ X1191)))))))))))))&(![X1192:$i]:((((in @ X1192 @ Z0))=>(![X1193:$i]:((((in @ X1193 @ Z0))=>(((((((X1192)=(X1193)))|((in @ X1192 @ X1193))))|((in @ X1193 @ X1192))))))))))))&(![X1194:$i]:((((in @ X1194 @ Z0))=>(~((in @ X1194 @ X1194)))))))))&(![X21:$i]:((((in @ X21 @ (powerset @ Z0)))=>((((((X21)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X21))&(![X48:$i]:((((in @ X48 @ X21))=>(((((X2)=(X48)))|((in @ X2 @ X48))))))))))))))))))), inference(fof_simplification,[status(thm)],[wellorderedByIn])). 126.84/19.39 thf(c_0_343, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 126.84/19.39 thf(c_0_344, plain, ((stricttotalorderedByIn)=(^[Z0:$i]:(((((![X2:$i]:((((in @ X2 @ Z0))=>(![X21:$i]:((((in @ X21 @ Z0))=>(![X48:$i]:((((in @ X48 @ Z0))=>((((((in @ X2 @ X21))&((in @ X21 @ X48))))=>((in @ X2 @ X48)))))))))))))&(![X21:$i]:((((in @ X21 @ Z0))=>(![X48:$i]:((((in @ X48 @ Z0))=>(((((((X21)=(X48)))|((in @ X21 @ X48))))|((in @ X48 @ X21))))))))))))&(![X21:$i]:((((in @ X21 @ Z0))=>(~((in @ X21 @ X21)))))))))), inference(fof_simplification,[status(thm)],[stricttotalorderedByIn])). 126.84/19.39 thf(c_0_345, plain, ((ordinal)=(^[Z0:$i]:((((![X1195:$i]:((((in @ X1195 @ Z0))=>((subset @ X1195 @ Z0))))))&(((((((((![X1196:$i]:((((in @ X1196 @ Z0))=>(![X1197:$i]:((((in @ X1197 @ Z0))=>(![X1198:$i]:((((in @ X1198 @ Z0))=>((((((in @ X1196 @ X1197))&((in @ X1197 @ X1198))))=>((in @ X1196 @ X1198)))))))))))))&(![X1199:$i]:((((in @ X1199 @ Z0))=>(![X1200:$i]:((((in @ X1200 @ Z0))=>(((((((X1199)=(X1200)))|((in @ X1199 @ X1200))))|((in @ X1200 @ X1199))))))))))))&(![X1201:$i]:((((in @ X1201 @ Z0))=>(~((in @ X1201 @ X1201)))))))))&(![X1202:$i]:((((in @ X1202 @ (powerset @ Z0)))=>((((((X1202)!=(emptyset))))=>(?[X1203:$i]:((((in @ X1203 @ X1202))&(![X1204:$i]:((((in @ X1204 @ X1202))=>(((((X1203)=(X1204)))|((in @ X1203 @ X1204)))))))))))))))))))))), inference(fof_simplification,[status(thm)],[ordinal])). 126.84/19.39 thf(c_0_346, plain, ((transitiveset)=(^[Z0:$i]:(![X21:$i]:((((in @ X21 @ Z0))=>((subset @ X21 @ Z0))))))), inference(fof_simplification,[status(thm)],[transitiveset])). 126.84/19.39 thf(c_0_347, plain, ((wellorderedByIn)=(^[Z0:$i]:((((((((![X1189:$i]:((((in @ X1189 @ Z0))=>(![X1190:$i]:((((in @ X1190 @ Z0))=>(![X1191:$i]:((((in @ X1191 @ Z0))=>((((((in @ X1189 @ X1190))&((in @ X1190 @ X1191))))=>((in @ X1189 @ X1191)))))))))))))&(![X1192:$i]:((((in @ X1192 @ Z0))=>(![X1193:$i]:((((in @ X1193 @ Z0))=>(((((((X1192)=(X1193)))|((in @ X1192 @ X1193))))|((in @ X1193 @ X1192))))))))))))&(![X1194:$i]:((((in @ X1194 @ Z0))=>(~((in @ X1194 @ X1194)))))))))&(![X21:$i]:((((in @ X21 @ (powerset @ Z0)))=>((((((X21)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X21))&(![X48:$i]:((((in @ X48 @ X21))=>(((((X2)=(X48)))|((in @ X2 @ X48))))))))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_342, c_0_343]), c_0_344])). 126.84/19.39 thf(c_0_348, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 126.84/19.39 thf(c_0_349, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])). 126.84/19.39 thf(c_0_350, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 126.84/19.39 thf(c_0_351, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 126.84/19.39 thf(c_0_352, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 126.84/19.39 thf(c_0_353, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 126.84/19.39 thf(c_0_354, plain, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[Z0:$i]:(![X2:$i]:((((in @ X2 @ Z0))<=>(?[X3:$i]:((((in @ X3 @ X4))&(((X2)=(X58 @ X3))))))))))))), inference(fof_simplification,[status(thm)],[image1Ex1])). 126.84/19.39 thf(c_0_355, plain, ((ordinal)=(^[Z0:$i]:((((![X1195:$i]:((((in @ X1195 @ Z0))=>((subset @ X1195 @ Z0))))))&(((((((((![X1196:$i]:((((in @ X1196 @ Z0))=>(![X1197:$i]:((((in @ X1197 @ Z0))=>(![X1198:$i]:((((in @ X1198 @ Z0))=>((((((in @ X1196 @ X1197))&((in @ X1197 @ X1198))))=>((in @ X1196 @ X1198)))))))))))))&(![X1199:$i]:((((in @ X1199 @ Z0))=>(![X1200:$i]:((((in @ X1200 @ Z0))=>(((((((X1199)=(X1200)))|((in @ X1199 @ X1200))))|((in @ X1200 @ X1199))))))))))))&(![X1201:$i]:((((in @ X1201 @ Z0))=>(~((in @ X1201 @ X1201)))))))))&(![X1202:$i]:((((in @ X1202 @ (powerset @ Z0)))=>((((((X1202)!=(emptyset))))=>(?[X1203:$i]:((((in @ X1203 @ X1202))&(![X1204:$i]:((((in @ X1204 @ X1202))=>(((((X1203)=(X1204)))|((in @ X1203 @ X1204)))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_345, c_0_346]), c_0_347])). 126.84/19.39 thf(c_0_356, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 126.84/19.39 thf(c_0_357, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 126.84/19.39 thf(c_0_358, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 126.84/19.39 thf(c_0_359, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 126.84/19.39 thf(c_0_360, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 126.84/19.39 thf(c_0_361, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 126.84/19.39 thf(c_0_362, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 126.84/19.39 thf(c_0_363, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$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])). 126.84/19.39 thf(c_0_364, negated_conjecture, ~(((setextAx)=>(((setadjoinAx)=>((((omega0Ax)=>(((omegaIndAx)=>((replAx)=>(((wellorderingAx)=>(((dsetconstrI)=>(((dsetconstrER)=>((exuE1)=>(((emptysetE)=>((((exuE3e)=>(((emptyI)=>((noeltsimpempty)=>(((((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((((((((emptyInPowerset)=>((powersetE)=>(((setunionE)=>(((((((eqinunit)=>(((upairsetE)=>((upairsetIL)=>((((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>(((((notdallE)=>((exuI1)=>(((exuI2)=>((inCongP)=>((((exu__Cong)=>((emptyset__Cong)=>(((powerset__Cong)=>((((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>(((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>(((((notequalI1)=>(((((((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>(((inPowerset)=>((((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((((binunionLsub)=>((binunionRsub)=>((binintersectI)=>(((binintersectEL)=>((((binintersectSubset3)=>(((disjointsetsI1)=>((binintersectRsub)=>(((binintersectSubset1)=>((bs114d)=>(((setminusEL)=>((setminusER)=>((((setminusELneg)=>((((setminusLsub)=>((setminusSubset1)=>(((symdiffI1)=>(((symdiffIneg1)=>(((((((((singletoninpowerset)=>((singletoninpowunion)=>(((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((((((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>(((ex1I)=>((ex1I2)=>((((kfstsingleton)=>((theprop)=>(((cartprodfstin)=>(((setukpairinjL)=>((setukpairinjR11)=>((((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((((kpairsurjEq)=>((cartprodsndin)=>(((cartprodpairmemER)=>((cartprodmempaircEq)=>(((((((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((((funcImageSingleton)=>((apProp)=>((app)=>(((ap2p)=>((funcinfuncset)=>((lamProp)=>(((lam2p)=>((((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>(((funcextLem)=>(((subbreln)=>(((((ap2apEq1)=>((ap2apEq2)=>((((((((((((ifp)=>((((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((((((setextT)=>((subsetTI)=>((((complementTI1)=>((complementTE1)=>(((binintersectTERcontra)=>((contrasubsetT)=>((((contrasubsetT3)=>((doubleComplementI1)=>(((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>(((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((((inIntersectImpInIntersectUnions)=>(((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>(((binunionTEcontra)=>((demorgan2a1)=>(((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>(((demorgan2a)=>(((demorgan2b)=>((demorgan2)=>((woz13rule0)=>(((woz13rule2)=>(((((woz1_2)=>((woz1_3)=>((woz1_4)=>((woz1_5)=>((((choice2fnsingleton)=>((setOfPairsIsBReln1)=>((((eqbreln1)=>((breln1invprop)=>((breln1invI)=>(((breln1compprop)=>((breln1compI)=>(((((((breln1unionI)=>(((breln1unionEcases)=>(((woz2Ex)=>((woz2W)=>((((((image1Equiv)=>(((((injFuncSetFuncIn)=>((injFuncSetFuncInj)=>(((surjFuncSetFuncSurj)=>((leftInvIsSurj)=>(((foundation2)=>((notinself)=>(((omegaSp)=>(((((transitivesetOp1)=>(((transitivesetOp2)=>((setunionTransitive)=>(((ordinalTransSet)=>((ordinalTransSet1)=>![X21:$i]:((![X2:$i]:(((ordinal @ X2)<=(in @ X2 @ X21)))=>(transitiveset @ (setunion @ X21))))))<=(ordinalMinLem1))))<=(binintTransitive)))<=(peanoSinj))<=(peano0notS))<=(omegaSclos)))<=(notinself2))))<=(surjCantorThm))))<=(surjFuncSetFuncIn))))<=(injFuncInInjFuncSet))<=(image1I))<=(image1E)))<=(image1Ex1))<=(image1Ex))<=(woz2B))<=(woz2A))))<=(breln1unionCommutes)))<=(breln1unionE)))<=(breln1unionIR))<=(breln1unionIL))<=(breln1unionprop))<=(breln1compEex))<=(breln1compE))))<=(breln1invE)))))<=(subbreln1))<=(breln1all1))))<=(breln1SetBreln1))<=(breln1all2))))))<=(woz1_1))<=(woz13rule4))<=(woz13rule3)))<=(woz13rule1)))))<=(demorgan2b2)))<=(demorgan1)))))<=(complementUnionInPowersetComplement))))<=(binunionTE))))<=(intersectInPowersetIntersectUnions)))<=(inIntersectImpInUnion2))<=(inIntersectImpInUnion)))))))))<=(complementTnotintersectT)))))<=(doubleComplementE1))))<=(contrasubsetT2))<=(contrasubsetT1))))<=(binintersectTELcontra))))<=(powersetTE1))<=(powersetTI1))))<=(complementT_lem))<=(setminusT_lem))<=(powersetT_lem))<=(binunionT_lem)))))<=(iftrue))<=(theeq)))<=(ifSingleton))<=(iftrueProp2))<=(iftrueProp1))<=(iffalseProp2))<=(iffalseProp1))<=(eta2))<=(beta2))<=(lam2lamEq))<=(eta1))<=(beta1))))<=(funcext2))<=(funcext))<=(eqbreln)))<=(funcGraphProp4)))<=(funcGraphProp2)))))<=(brelnall2))<=(brelnall1)))<=(lamp)))))<=(infuncsetfunc)))))<=(dpsetconstrER))<=(dpsetconstrEL2)))))<=(dpsetconstrSub))<=(dpsetconstrI))<=(cartprodpairsurjEq))<=(cartprodsndpairEq))<=(cartprodfstpairEq))))<=(cartprodpairmemEL))))<=(ksndpairEq))<=(ksndsingleton)))))<=(setukpairinjR1))<=(setukpairinjR12))))<=(setukpairinjL2)))<=(kfstpairEq))))<=(setukpairinjL1))<=(singletonsuniq))))<=(ex1E1))))))<=(setunionE2))<=(cartprodmempair))<=(cartprodmempair1))<=(cartprodpairin)))))))<=(upairset2E))))<=(singletonsubset))<=(kpairp))<=(kpairiskpair))<=(setukpairIR))<=(setukpairIL))<=(secondinupair))<=(symdiffIneg2)))<=(symdiffI2)))<=(symdiffE))))<=(setminusIRneg))<=(setminusILneg)))<=(setminusERneg))<=(setminusSubset2))))<=(setminusI))))<=(binintersectSubset4))))<=(binintersectER)))<=(binintersectSubset2))<=(binintersectLsub)))<=(binintersectSubset5)))))<=(binunionE))<=(binunionEcases))))))<=(sepInPowerset))<=(powersetsubset)))<=(powersetE1))))))<=(setadjoinSub2))<=(setadjoinSub))<=(subsetTrans))<=(subsetRefl))<=(notequalI2)))<=(notsubsetI))<=(subsetE2))<=(subsetE))))))<=(subsetI1)))))<=(omega__Cong))<=(setunion__Cong)))<=(setadjoin__Cong))))<=(exuE3u))<=(in__Cong))))<=(exuI3))))<=(notdexE))<=(prop2set2propI))<=(prop2setI)))))))<=(emptyE1))<=(upairsetIR))))<=(singletonsswitch)))<=(notinsingleton))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU)))<=(setunionI))))<=(emptyinPowerset))<=(powersetI))<=(setoftrueEq))<=(setadjoinOr))<=(setadjoinE))<=(setadjoinIR)))))<=(nonemptyI))<=(nonemptyE1))<=(setbeta))))<=(setext)))<=(notinemptyset))<=(emptysetimpfalse)))<=(prop2setE))))<=(dsetconstrEL)))<=(descrp)))<=(foundationAx))))<=(omegaSAx)))<=(setunionAx))<=(powersetAx)))<=(emptysetAx)))), inference(assume_negation,[status(cth)],[setunionOrdinalLem1])). 126.84/19.39 thf(c_0_365, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 126.84/19.39 thf(c_0_366, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X1168:$i]:(((((X1 @ X1168)))&(![X1169:$i]:(((((X1 @ X1169)))=>(((X1168)=(X1169))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_348, c_0_349])). 126.84/19.39 thf(c_0_367, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X1164:$i]:(((((X1 @ X1164)))&(![X1165:$i]:(((((X1 @ X1165)))=>(((X1164)=(X1165)))))))))))))))), inference(apply_def,[status(thm)],[c_0_350, c_0_349])). 126.84/19.39 thf(c_0_368, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 126.84/19.39 thf(c_0_369, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_343])). 126.84/19.39 thf(c_0_370, plain, ((exuE2)=(![X1:$i > $o]:((((?[X1160:$i]:(((((X1 @ X1160)))&(![X1161:$i]:(((((X1 @ X1161)))=>(((X1160)=(X1161))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_351, c_0_349])). 126.84/19.39 thf(c_0_371, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 126.84/19.39 thf(c_0_372, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_352, c_0_343])). 126.84/19.39 thf(c_0_373, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_343])). 126.84/19.39 thf(c_0_374, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 126.84/19.39 thf(c_0_375, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 126.84/19.39 thf(c_0_376, plain, ((ex1I2)<=>![X4:$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:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 126.84/19.39 thf(c_0_377, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])). 126.84/19.39 thf(c_0_378, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 126.84/19.39 thf(c_0_379, plain, ((singletonprop)<=>![X4:$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:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 126.84/19.39 thf(c_0_380, plain, ((descrp)=(![X1:$i > $o]:((((?[X1154:$i]:(((((X1 @ X1154)))&(![X1155:$i]:(((((X1 @ X1155)))=>(((X1154)=(X1155))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_353, c_0_349])). 126.84/19.39 thf(c_0_381, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 126.84/19.39 thf(c_0_382, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])). 126.84/19.39 thf(c_0_383, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 126.84/19.39 thf(c_0_384, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 126.84/19.39 thf(c_0_385, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 126.84/19.39 thf(c_0_386, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])). 126.84/19.39 thf(c_0_387, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 126.84/19.39 thf(c_0_388, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])). 126.84/19.39 thf(c_0_389, plain, ((image1Ex1)=(![X4:$i, X58:$i > $i]:((?[X1180:$i]:((((![X2:$i]:((((in @ X2 @ X1180))<=>(?[X3:$i]:((((in @ X3 @ X4))&(((X2)=(X58 @ X3))))))))))&(![X1181:$i]:((((![X2:$i]:((((in @ X2 @ X1181))<=>(?[X3:$i]:((((in @ X3 @ X4))&(((X2)=(X58 @ X3))))))))))=>(((X1180)=(X1181)))))))))))), inference(apply_def,[status(thm)],[c_0_354, c_0_349])). 126.84/19.39 thf(c_0_390, plain, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0:$i]:(X60 @ Z0))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), inference(fof_simplification,[status(thm)],[image1E])). 126.84/19.39 thf(c_0_391, plain, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[Z0:$i]:(X61 @ Z0))))))), inference(fof_simplification,[status(thm)],[image1I])). 126.84/19.39 thf(c_0_392, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])). 126.84/19.39 thf(c_0_393, plain, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0:$i]:((((X52 @ X2 @ Z0))&(![X14:$i]:((((in @ X14 @ X5))=>((((X52 @ X2 @ X14))=>((in @ (kpair @ Z0 @ X14) @ X33)))))))))))))))))))), inference(fof_simplification,[status(thm)],[choice2fnsingleton])). 126.84/19.39 thf(c_0_394, plain, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0:$i]:(X59 @ Z0))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), inference(fof_simplification,[status(thm)],[image1Equiv])). 126.84/19.39 thf(c_0_395, axiom, ((setunionTransitive)=(![X21:$i]:(((![X2:$i]:((((in @ X2 @ X21))=>((![X1187:$i]:((((in @ X1187 @ X2))=>((subset @ X1187 @ X2)))))))))=>((![X1188:$i]:((((in @ X1188 @ (setunion @ X21)))=>((subset @ X1188 @ (setunion @ X21))))))))))), inference(apply_def,[status(thm)],[setunionTransitive, c_0_346])). 126.84/19.39 thf(c_0_396, axiom, ((ordinalTransSet)=(![X21:$i]:(((((((![X1226:$i]:((((in @ X1226 @ X21))=>((subset @ X1226 @ X21))))))&(((((((((![X1227:$i]:((((in @ X1227 @ X21))=>(![X1228:$i]:((((in @ X1228 @ X21))=>(![X1229:$i]:((((in @ X1229 @ X21))=>((((((in @ X1227 @ X1228))&((in @ X1228 @ X1229))))=>((in @ X1227 @ X1229)))))))))))))&(![X1230:$i]:((((in @ X1230 @ X21))=>(![X1231:$i]:((((in @ X1231 @ X21))=>(((((((X1230)=(X1231)))|((in @ X1230 @ X1231))))|((in @ X1231 @ X1230))))))))))))&(![X1232:$i]:((((in @ X1232 @ X21))=>(~((in @ X1232 @ X1232)))))))))&(![X1233:$i]:((((in @ X1233 @ (powerset @ X21)))=>((((((X1233)!=(emptyset))))=>(?[X1234:$i]:((((in @ X1234 @ X1233))&(![X1235:$i]:((((in @ X1235 @ X1233))=>(((((X1234)=(X1235)))|((in @ X1234 @ X1235)))))))))))))))))))))=>(![X2:$i, X4:$i]:((((in @ X4 @ X21))=>((((in @ X2 @ X4))=>((in @ X2 @ X21))))))))))), inference(apply_def,[status(thm)],[ordinalTransSet, c_0_355])). 126.84/19.39 thf(c_0_397, axiom, ((ordinalTransSet1)=(![X21:$i]:(((((((![X1236:$i]:((((in @ X1236 @ X21))=>((subset @ X1236 @ X21))))))&(((((((((![X1237:$i]:((((in @ X1237 @ X21))=>(![X1238:$i]:((((in @ X1238 @ X21))=>(![X1239:$i]:((((in @ X1239 @ X21))=>((((((in @ X1237 @ X1238))&((in @ X1238 @ X1239))))=>((in @ X1237 @ X1239)))))))))))))&(![X1240:$i]:((((in @ X1240 @ X21))=>(![X1241:$i]:((((in @ X1241 @ X21))=>(((((((X1240)=(X1241)))|((in @ X1240 @ X1241))))|((in @ X1241 @ X1240))))))))))))&(![X1242:$i]:((((in @ X1242 @ X21))=>(~((in @ X1242 @ X1242)))))))))&(![X1243:$i]:((((in @ X1243 @ (powerset @ X21)))=>((((((X1243)!=(emptyset))))=>(?[X1244:$i]:((((in @ X1244 @ X1243))&(![X1245:$i]:((((in @ X1245 @ X1243))=>(((((X1244)=(X1245)))|((in @ X1244 @ X1245)))))))))))))))))))))=>(![X4:$i]:((((in @ X4 @ X21))=>((subset @ X4 @ X21))))))))), inference(apply_def,[status(thm)],[ordinalTransSet1, c_0_355])). 126.84/19.39 thf(c_0_398, axiom, ((foundation2)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X21:$i]:((((in @ X21 @ X4))&(((binintersect @ X21 @ X4)=(emptyset)))))))))), inference(apply_def,[status(thm)],[foundation2, c_0_343])). 126.84/19.39 thf(c_0_399, axiom, ((transitivesetOp2)=(![X21:$i]:((((![X1186:$i]:((((in @ X1186 @ X21))=>((subset @ X1186 @ X21))))))=>(![X4:$i, X2:$i]:((((in @ X4 @ X21))=>((((in @ X2 @ X4))=>((in @ X2 @ X21))))))))))), inference(apply_def,[status(thm)],[transitivesetOp2, c_0_346])). 126.84/19.39 thf(c_0_400, axiom, ((binintTransitive)=(![X21:$i]:((((![X1183:$i]:((((in @ X1183 @ X21))=>((subset @ X1183 @ X21))))))=>(![X48:$i]:((((![X1184:$i]:((((in @ X1184 @ X48))=>((subset @ X1184 @ X48))))))=>((![X1185:$i]:((((in @ X1185 @ (binintersect @ X21 @ X48)))=>((subset @ X1185 @ (binintersect @ X21 @ X48)))))))))))))), inference(apply_def,[status(thm)],[binintTransitive, c_0_346])). 126.84/19.39 thf(c_0_401, axiom, ((ordinalMinLem1)=(![X21:$i]:(((((((![X1205:$i]:((((in @ X1205 @ X21))=>((subset @ X1205 @ X21))))))&(((((((((![X1206:$i]:((((in @ X1206 @ X21))=>(![X1207:$i]:((((in @ X1207 @ X21))=>(![X1208:$i]:((((in @ X1208 @ X21))=>((((((in @ X1206 @ X1207))&((in @ X1207 @ X1208))))=>((in @ X1206 @ X1208)))))))))))))&(![X1209:$i]:((((in @ X1209 @ X21))=>(![X1210:$i]:((((in @ X1210 @ X21))=>(((((((X1209)=(X1210)))|((in @ X1209 @ X1210))))|((in @ X1210 @ X1209))))))))))))&(![X1211:$i]:((((in @ X1211 @ X21))=>(~((in @ X1211 @ X1211)))))))))&(![X1212:$i]:((((in @ X1212 @ (powerset @ X21)))=>((((((X1212)!=(emptyset))))=>(?[X1213:$i]:((((in @ X1213 @ X1212))&(![X1214:$i]:((((in @ X1214 @ X1212))=>(((((X1213)=(X1214)))|((in @ X1213 @ X1214)))))))))))))))))))))=>(![X48:$i]:(((((((![X1215:$i]:((((in @ X1215 @ X48))=>((subset @ X1215 @ X48))))))&(((((((((![X1216:$i]:((((in @ X1216 @ X48))=>(![X1217:$i]:((((in @ X1217 @ X48))=>(![X1218:$i]:((((in @ X1218 @ X48))=>((((((in @ X1216 @ X1217))&((in @ X1217 @ X1218))))=>((in @ X1216 @ X1218)))))))))))))&(![X1219:$i]:((((in @ X1219 @ X48))=>(![X1220:$i]:((((in @ X1220 @ X48))=>(((((((X1219)=(X1220)))|((in @ X1219 @ X1220))))|((in @ X1220 @ X1219))))))))))))&(![X1221:$i]:((((in @ X1221 @ X48))=>(~((in @ X1221 @ X1221)))))))))&(![X1222:$i]:((((in @ X1222 @ (powerset @ X48)))=>((((((X1222)!=(emptyset))))=>(?[X1223:$i]:((((in @ X1223 @ X1222))&(![X1224:$i]:((((in @ X1224 @ X1222))=>(((((X1223)=(X1224)))|((in @ X1223 @ X1224)))))))))))))))))))))=>((![X1225:$i]:((((in @ X1225 @ (binintersect @ X21 @ X48)))=>((subset @ X1225 @ (binintersect @ X21 @ X48)))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[ordinalMinLem1, c_0_355]), c_0_346])). 126.84/19.39 thf(c_0_402, axiom, ((transitivesetOp1)=(![X21:$i]:((((![X1182:$i]:((((in @ X1182 @ X21))=>((subset @ X1182 @ X21))))))=>(![X4:$i]:((((in @ X4 @ X21))=>((subset @ X4 @ X21))))))))), inference(apply_def,[status(thm)],[transitivesetOp1, c_0_346])). 126.84/19.39 thf(c_0_403, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X42))&(((Z0)=(X2)))))|(((~((X42)))&(((Z0)=(X3)))))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])). 126.84/19.39 thf(c_0_404, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X43))&(((Z0)=(X2)))))|(((~((X43)))&(((Z0)=(X3))))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 126.84/19.39 thf(c_0_405, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X41))&(((Z0)=(X2)))))|(((~((X41)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 126.84/19.39 thf(c_0_406, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])). 126.84/19.39 thf(c_0_407, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])). 126.84/19.39 thf(c_0_408, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])). 126.84/19.39 thf(c_0_409, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])). 126.84/19.39 thf(c_0_410, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])). 126.84/19.39 thf(c_0_411, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0:$i]:((((((X39))&(((Z0)=(X2)))))|(((~((X39)))&(((Z0)=(X3)))))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 126.84/19.39 thf(c_0_412, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0:$i]:((((((X40))&(((Z0)=(X2)))))|(((~((X40)))&(((Z0)=(X3)))))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])). 126.84/19.39 thf(c_0_413, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 126.84/19.39 thf(c_0_414, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 126.84/19.39 thf(c_0_415, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 126.84/19.39 thf(c_0_416, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 126.84/19.39 thf(c_0_417, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 126.84/19.39 thf(c_0_418, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 126.84/19.39 thf(c_0_419, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 126.84/19.39 thf(c_0_420, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 126.84/19.39 thf(c_0_421, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 126.84/19.39 thf(c_0_422, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X1176:$i]:(((((X1 @ X1176)))&(![X1177:$i]:(((((X1 @ X1177)))=>(((X1176)=(X1177))))))))))=>((((?[X1178:$i]:(((((X17 @ X1178)))&(![X1179:$i]:(((((X17 @ X1179)))=>(((X1178)=(X1179))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_356, c_0_349])). 126.84/19.39 thf(c_0_423, plain, ((exuEu)=(![X1:$i > $o]:((((?[X1174:$i]:(((((X1 @ X1174)))&(![X1175:$i]:(((((X1 @ X1175)))=>(((X1174)=(X1175))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_357, c_0_349])). 126.84/19.39 thf(c_0_424, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X1170:$i]:(((((X1 @ X1170)))&(![X1171:$i]:(((((X1 @ X1171)))=>(((X1170)=(X1171))))))))))<=>((?[X1172:$i]:(((((X17 @ X1172)))&(![X1173:$i]:(((((X17 @ X1173)))=>(((X1172)=(X1173)))))))))))))))), inference(apply_def,[status(thm)],[c_0_358, c_0_349])). 126.84/19.39 thf(c_0_425, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X1166:$i]:(((((X1 @ X1166)))&(![X1167:$i]:(((((X1 @ X1167)))=>(((X1166)=(X1167)))))))))))))), inference(apply_def,[status(thm)],[c_0_359, c_0_349])). 126.84/19.39 thf(c_0_426, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X1162:$i]:(((((X1 @ X1162)))&(![X1163:$i]:(((((X1 @ X1163)))=>(((X1162)=(X1163)))))))))))))), inference(apply_def,[status(thm)],[c_0_360, c_0_349])). 126.84/19.39 thf(c_0_427, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_343])). 126.84/19.39 thf(c_0_428, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X1158:$i]:(((((X1 @ X1158)))&(![X1159:$i]:(((((X1 @ X1159)))=>(((X1158)=(X1159))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_361, c_0_349])). 126.84/19.39 thf(c_0_429, plain, ((exuE1)=(![X1:$i > $o]:((((?[X1156:$i]:(((((X1 @ X1156)))&(![X1157:$i]:(((((X1 @ X1157)))=>(((X1156)=(X1157))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_362, c_0_349])). 126.84/19.39 thf(c_0_430, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 126.84/19.39 thf(c_0_431, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 126.84/19.39 thf(c_0_432, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X1152:$i]:(((((X6 @ X2 @ X1152)))&(![X1153:$i]:(((((X6 @ X2 @ X1153)))=>(((X1152)=(X1153)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_363, c_0_349])). 126.84/19.39 thf(c_0_433, plain, ((epred1_0)<=>![X1263:$i]:(?[X1264:$i]:((((![X1265:$i]:(((in @ X1265 @ X1264)=>![X1266:$i]:(((in @ X1266 @ X1265)=>(in @ X1266 @ X1263)))))&![X1267:$i, X1268:$i]:((((in @ X1267 @ X1263)&(in @ X1268 @ X1263))=>(![X1269:$i]:(((in @ X1269 @ X1264)=>((in @ X1267 @ X1269)<=>(in @ X1268 @ X1269))))=>((X1267)=(X1268))))))&![X1270:$i, X1271:$i]:((((in @ X1270 @ X1264)&(in @ X1271 @ X1264))=>(![X1272:$i]:(((in @ X1272 @ X1270)=>(in @ X1272 @ X1271)))|![X1273:$i]:(((in @ X1273 @ X1271)=>(in @ X1273 @ X1270)))))))&![X1274:$i]:(((![X1275:$i]:(((in @ X1275 @ X1274)=>(in @ X1275 @ X1263)))&?[X1276:$i]:((in @ X1276 @ X1274)))=>?[X1277:$i, X1278:$i]:(((((in @ X1277 @ X1264)&(in @ X1278 @ X1274))&~(?[X1279:$i]:(((in @ X1279 @ X1277)&(in @ X1279 @ X1274)))))&![X1280:$i]:(((in @ X1280 @ X1264)=>(![X1281:$i]:(((in @ X1281 @ X1280)=>(in @ X1281 @ X1277)))|(in @ X1278 @ X1280)))))))))))), introduced(definition)). 126.84/19.39 thf(c_0_434, plain, ![X1865:$i]:(((epred2_1 @ X1865)<=>(![X1867:$i]:(((in @ X1867 @ X1865)=>![X1868:$i]:(((in @ X1868 @ X1865)=>![X1869:$i]:(((in @ X1869 @ X1865)=>(((in @ X1867 @ X1868)&(in @ X1868 @ X1869))=>(in @ X1867 @ X1869))))))))&![X1870:$i]:(((in @ X1870 @ X1865)=>![X1871:$i]:(((in @ X1871 @ X1865)=>(((X1870)=(X1871))|(in @ X1870 @ X1871)|(in @ X1871 @ X1870))))))))), introduced(definition)). 126.84/19.39 thf(c_0_435, plain, ![X1876:$i]:(((epred3_1 @ X1876)<=>(![X1878:$i]:(((in @ X1878 @ X1876)=>![X1879:$i]:(((in @ X1879 @ X1876)=>![X1880:$i]:(((in @ X1880 @ X1876)=>(((in @ X1878 @ X1879)&(in @ X1879 @ X1880))=>(in @ X1878 @ X1880))))))))&![X1881:$i]:(((in @ X1881 @ X1876)=>![X1882:$i]:(((in @ X1882 @ X1876)=>(((X1881)=(X1882))|(in @ X1881 @ X1882)|(in @ X1882 @ X1881))))))))), introduced(definition)). 126.84/19.39 thf(c_0_436, plain, ![X1829:$i]:(((epred4_1 @ X1829)<=>(![X1831:$i]:(((in @ X1831 @ X1829)=>![X1832:$i]:(((in @ X1832 @ X1829)=>![X1833:$i]:(((in @ X1833 @ X1829)=>(((in @ X1831 @ X1832)&(in @ X1832 @ X1833))=>(in @ X1831 @ X1833))))))))&![X1834:$i]:(((in @ X1834 @ X1829)=>![X1835:$i]:(((in @ X1835 @ X1829)=>(((X1834)=(X1835))|(in @ X1834 @ X1835)|(in @ X1835 @ X1834))))))))), introduced(definition)). 126.84/19.39 thf(c_0_437, plain, ![X1842:$i]:(((epred5_1 @ X1842)<=>(![X1844:$i]:(((in @ X1844 @ X1842)=>![X1845:$i]:(((in @ X1845 @ X1842)=>![X1846:$i]:(((in @ X1846 @ X1842)=>(((in @ X1844 @ X1845)&(in @ X1845 @ X1846))=>(in @ X1844 @ X1846))))))))&![X1847:$i]:(((in @ X1847 @ X1842)=>![X1848:$i]:(((in @ X1848 @ X1842)=>(((X1847)=(X1848))|(in @ X1847 @ X1848)|(in @ X1848 @ X1847))))))))), introduced(definition)). 126.84/19.39 thf(c_0_438, plain, ![X2:$i]:(((epred6_1 @ X2)<=>(![X1854:$i]:(((in @ X1854 @ X2)=>(subset @ X1854 @ X2)))&(((![X1855:$i]:(((in @ X1855 @ X2)=>![X1856:$i]:(((in @ X1856 @ X2)=>![X1857:$i]:(((in @ X1857 @ X2)=>(((in @ X1855 @ X1856)&(in @ X1856 @ X1857))=>(in @ X1855 @ X1857))))))))&![X1858:$i]:(((in @ X1858 @ X2)=>![X1859:$i]:(((in @ X1859 @ X2)=>(((X1858)=(X1859))|(in @ X1858 @ X1859)|(in @ X1859 @ X1858)))))))&![X1860:$i]:(((in @ X1860 @ X2)=>~(in @ X1860 @ X1860))))&![X1861:$i]:(((in @ X1861 @ (powerset @ X2))=>(((X1861)!=(emptyset))=>?[X1862:$i]:(((in @ X1862 @ X1861)&![X1863:$i]:(((in @ X1863 @ X1861)=>(((X1862)=(X1863))|(in @ X1862 @ X1863))))))))))))), introduced(definition)). 126.84/19.39 thf(c_0_439, negated_conjecture, ~((![X1246:$i, X1247:$i]:((![X1248:$i]:(((in @ X1248 @ X1246)<=>(in @ X1248 @ X1247)))=>((X1246)=(X1247))))=>(![X2426:$i]:(~(in @ X2426 @ emptyset))=>(![X1249:$i, X1250:$i, X1251:$i]:(((in @ X1251 @ (setadjoin @ X1249 @ X1250))<=>(((X1251)=(X1249))|(in @ X1251 @ X1250))))=>(![X2423:$i, X2424:$i]:(((in @ X2424 @ (powerset @ X2423))<=>![X2425:$i]:(((in @ X2425 @ X2424)=>(in @ X2425 @ X2423)))))=>(![X2420:$i, X2421:$i]:(((in @ X2421 @ (setunion @ X2420))<=>?[X2422:$i]:(((in @ X2421 @ X2422)&(in @ X2422 @ X2420)))))=>((in @ emptyset @ omega)=>(![X2419:$i]:(((in @ X2419 @ omega)=>(in @ (setadjoin @ X2419 @ X2419) @ omega)))=>(![X1252:$i]:((((in @ emptyset @ X1252)&![X1253:$i]:((((in @ X1253 @ omega)&(in @ X1253 @ X1252))=>(in @ (setadjoin @ X1253 @ X1253) @ X1252))))=>![X1254:$i]:(((in @ X1254 @ omega)=>(in @ X1254 @ X1252)))))=>(![X1255:$i > $i > $o, X1256:$i]:((![X1257:$i]:(((in @ X1257 @ X1256)=>?[X1258:$i]:(((X1255 @ X1257 @ X1258)&![X1259:$i]:(((X1255 @ X1257 @ X1259)=>((X1258)=(X1259))))))))=>?[X1260:$i]:(![X1261:$i]:(((in @ X1261 @ X1260)<=>?[X1262:$i]:(((in @ X1262 @ X1256)&(X1255 @ X1262 @ X1261))))))))=>(![X2415:$i]:((?[X2416:$i]:((in @ X2416 @ X2415))=>?[X2417:$i]:(((in @ X2417 @ X2415)&~(?[X2418:$i]:(((in @ X2418 @ X2417)&(in @ X2418 @ X2415))))))))=>((epred1_0)=>(![X2412:$i > $o]:((?[X2413:$i]:(((X2412 @ X2413)&![X2414:$i]:(((X2412 @ X2414)=>((X2413)=(X2414))))))=>(X2412 @ (descr @ (^[Z0:$i]:(X2412 @ Z0))))))=>(![X1282:$i, X1283:$i > $o, X1284:$i]:(((in @ X1284 @ X1282)=>((X1283 @ X1284)=>(in @ X1284 @ (dsetconstr @ X1282 @ X1283)))))=>(![X2409:$i, X2410:$i > $o, X2411:$i]:(((in @ X2411 @ (dsetconstr @ X2409 @ X2410))=>(in @ X2411 @ X2409)))=>(![X1285:$i, X1286:$i > $o, X1287:$i]:(((in @ X1287 @ (dsetconstr @ X1285 @ X1286))=>(X1286 @ X1287)))=>(![X1288:$i > $o]:((?[X1289:$i]:(((X1288 @ X1289)&![X1290:$i]:(((X1288 @ X1290)=>((X1289)=(X1290))))))=>?[X1291:$i]:(((X1288 @ X1291)&![X1292:$i]:(((X1288 @ X1292)=>((X1291)=(X1292))))))))=>(![X2407:$o, X2408:$i]:(((in @ X2408 @ (prop2set @ ((X2407))))=>(X2407)))=>(![X1293:$i]:(((in @ X1293 @ emptyset)=>![X1294:$o]:((X1294))))=>(![X2406:$i]:(((in @ X2406 @ emptyset)=>~($true)))=>(![X2405:$i]:(~(in @ X2405 @ emptyset))=>(![X1295:$i > $o]:((?[X1296:$i]:(((X1295 @ X1296)&![X1297:$i]:(((X1295 @ X1297)=>((X1296)=(X1297))))))=>?[X1298:$i]:((X1295 @ X1298))))=>(![X2401:$i, X2402:$i]:((![X2403:$i]:(((in @ X2403 @ X2401)=>(in @ X2403 @ X2402)))=>(![X2404:$i]:(((in @ X2404 @ X2402)=>(in @ X2404 @ X2401)))=>((X2401)=(X2402)))))=>(![X1299:$i]:((![X1300:$i]:(~(in @ X1300 @ X1299))=>((X1299)=(emptyset))))=>(![X1301:$i]:((![X1302:$i]:(~(in @ X1302 @ X1301))=>((X1301)=(emptyset))))=>(![X2398:$i, X2399:$i > $o, X2400:$i]:(((in @ X2400 @ X2398)=>((in @ X2400 @ (dsetconstr @ X2398 @ X2399))<=>(X2399 @ X2400))))=>(![X2396:$i]:((((X2396)!=(emptyset))=>?[X2397:$i]:((in @ X2397 @ X2396))))=>(![X2393:$i, X2394:$i > $o, X2395:$i]:(((in @ X2395 @ X2393)=>((X2394 @ X2395)=>((dsetconstr @ X2393 @ X2394)!=(emptyset)))))=>(![X1303:$i]:((?[X1304:$i]:((in @ X1304 @ X1303))=>((X1303)!=(emptyset))))=>(![X1305:$i, X1306:$i]:((in @ X1305 @ (setadjoin @ X1305 @ X1306)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X2390:$i, X2391:$i, X2392:$i]:(((in @ X2392 @ X2391)=>(in @ X2392 @ (setadjoin @ X2390 @ X2391))))=>(![X2386:$i, X2387:$i, X2388:$i]:(((in @ X2388 @ (setadjoin @ X2386 @ X2387))=>![X2389:$o]:(((((X2388)=(X2386))=>(X2389))=>(((in @ X2388 @ X2387)=>(X2389))=>(X2389))))))=>(![X2383:$i, X2384:$i, X2385:$i]:(((in @ X2385 @ (setadjoin @ X2383 @ X2384))=>(((X2385)=(X2383))|(in @ X2385 @ X2384))))=>(![X2382:$i]:(((dsetconstr @ X2382 @ (^[Z0:$i]:($true)))=(X2382)))=>(![X2379:$i, X2380:$i]:((![X2381:$i]:(((in @ X2381 @ X2380)=>(in @ X2381 @ X2379)))=>(in @ X2380 @ (powerset @ X2379))))=>(![X2378:$i]:((in @ emptyset @ (powerset @ X2378)))=>(![X1307:$i]:((in @ emptyset @ (powerset @ X1307)))=>(![X1308:$i, X1309:$i, X1310:$i]:(((in @ X1309 @ (powerset @ X1308))=>((in @ X1310 @ X1309)=>(in @ X1310 @ X1308))))=>(![X2375:$i, X2376:$i, X2377:$i]:(((in @ X2376 @ X2377)=>((in @ X2377 @ X2375)=>(in @ X2376 @ (setunion @ X2375)))))=>(![X1311:$i, X1312:$i]:(((in @ X1312 @ (setunion @ X1311))=>![X1313:$o]:((![X1314:$i]:(((in @ X1312 @ X1314)=>((in @ X1314 @ X1311)=>(X1313))))=>(X1313)))))=>(![X2373:$i, X2374:$i]:(((in @ X2374 @ X2373)=>(in @ X2374 @ (powerset @ (setunion @ X2373)))))=>(![X2368:$i > $o]:((?[X2369:$i]:(((X2368 @ X2369)&![X2370:$i]:(((X2368 @ X2370)=>((X2369)=(X2370))))))=>?[X2371:$i]:(![X2372:$i]:(((X2368 @ X2372)<=>((X2372)=(X2371)))))))=>(![X2366:$i]:((((X2366)!=(emptyset))=>?[X2367:$i]:(((in @ X2367 @ X2366)&$true))))=>(![X2364:$i, X2365:$i]:(((in @ X2364 @ (setadjoin @ X2365 @ emptyset))=>((X2364)=(X2365))))=>(![X2362:$i, X2363:$i]:((((X2362)!=(X2363))=>~(in @ X2363 @ (setadjoin @ X2362 @ emptyset))))=>(![X1315:$i, X1316:$i]:((((X1315)=(X1316))=>(in @ X1315 @ (setadjoin @ X1316 @ emptyset))))=>(![X2360:$i, X2361:$i]:(((in @ X2360 @ (setadjoin @ X2361 @ emptyset))=>(in @ X2361 @ (setadjoin @ X2360 @ emptyset))))=>(![X1317:$i, X1318:$i, X1319:$i]:(((in @ X1319 @ (setadjoin @ X1317 @ (setadjoin @ X1318 @ emptyset)))=>(((X1319)=(X1317))|((X1319)=(X1318)))))=>(![X1320:$i, X1321:$i]:((in @ X1320 @ (setadjoin @ X1320 @ (setadjoin @ X1321 @ emptyset))))=>(![X2358:$i, X2359:$i]:((in @ X2359 @ (setadjoin @ X2358 @ (setadjoin @ X2359 @ emptyset))))=>(![X2355:$i, X2356:$i > $o]:((?[X2357:$i]:(((in @ X2357 @ X2355)&(X2356 @ X2357)))=>(((dsetconstr @ X2355 @ X2356)=(emptyset))=>~($true))))=>(![X1322:$i > $o, X1323:$i]:(((in @ X1323 @ emptyset)=>(X1322 @ X1323)))=>(![X1324:$i, X1325:$i > $o]:((~(![X1326:$i]:(((in @ X1326 @ X1324)=>(X1325 @ X1326))))=>?[X1327:$i]:(((in @ X1327 @ X1324)&~((X1325 @ X1327))))))=>(![X1328:$i, X1329:$i > $o]:((![X1330:$i]:(((in @ X1330 @ X1328)=>~((X1329 @ X1330))))=>~(?[X1331:$i]:(((in @ X1331 @ X1328)&(X1329 @ X1331))))))=>(![X1332:$i, X1333:$i > $o]:((~(?[X1334:$i]:(((in @ X1334 @ X1332)&(X1333 @ X1334))))=>![X1335:$i]:(((in @ X1335 @ X1332)=>~((X1333 @ X1335))))))=>(![X1336:$i, X1337:$i > $o]:((?[X1338:$i]:(((in @ X1338 @ X1336)&~((X1337 @ X1338))))=>~(![X1339:$i]:(((in @ X1339 @ X1336)=>(X1337 @ X1339))))))=>(![X2354:$o]:(((X2354)=>(in @ emptyset @ (prop2set @ ((X2354))))))=>(![X2353:$o]:(((X2353)=>(set2prop @ (prop2set @ ((X2353))))))=>(![X2349:$i, X2350:$i > $o]:((~(?[X2351:$i]:(((in @ X2351 @ X2349)&(X2350 @ X2351))))=>![X2352:$i]:(((in @ X2352 @ X2349)=>~((X2350 @ X2352))))))=>(![X1340:$i, X1341:$i > $o]:((~(![X1342:$i]:(((in @ X1342 @ X1340)=>(X1341 @ X1342))))=>?[X1343:$i]:(((in @ X1343 @ X1340)&~((X1341 @ X1343))))))=>(![X1344:$i > $o]:((?[X1345:$i]:(((X1344 @ X1345)&![X1346:$i]:(((X1344 @ X1346)=>((X1345)=(X1346))))))=>?[X1347:$i]:(((X1344 @ X1347)&![X1348:$i]:(((X1344 @ X1348)=>((X1347)=(X1348))))))))=>(![X2343:$i > $o]:((?[X2344:$i]:((X2343 @ X2344))=>(![X2345:$i, X2346:$i]:(((X2343 @ X2345)=>((X2343 @ X2346)=>((X2345)=(X2346)))))=>?[X2347:$i]:(((X2343 @ X2347)&![X2348:$i]:(((X2343 @ X2348)=>((X2347)=(X2348)))))))))=>(![X1349:$i > $o]:((?[X1350:$i]:(![X1351:$i]:(((X1349 @ X1351)<=>((X1351)=(X1350)))))=>?[X1352:$i]:(((X1349 @ X1352)&![X1353:$i]:(((X1349 @ X1353)=>((X1352)=(X1353))))))))=>(![X1354:$i, X1355:$i]:((((X1354)=(X1355))=>![X1356:$i, X1357:$i]:((((X1356)=(X1357))=>((in @ X1356 @ X1354)=>(in @ X1357 @ X1355))))))=>(![X2339:$i, X2340:$i]:((((X2339)=(X2340))=>![X2341:$i, X2342:$i]:((((X2341)=(X2342))=>((in @ X2341 @ X2339)<=>(in @ X2342 @ X2340))))))=>(![X2334:$i > $o]:((?[X2335:$i]:(((X2334 @ X2335)&![X2336:$i]:(((X2334 @ X2336)=>((X2335)=(X2336))))))=>![X2337:$i, X2338:$i]:(((X2334 @ X2337)=>((X2334 @ X2338)=>((X2337)=(X2338)))))))=>(![X1358:$i > $o, X1359:$i > $o]:((![X1360:$i, X1361:$i]:((((X1360)=(X1361))=>((X1358 @ X1360)<=>(X1359 @ X1361))))=>(?[X1362:$i]:(((X1358 @ X1362)&![X1363:$i]:(((X1358 @ X1363)=>((X1362)=(X1363))))))<=>?[X1364:$i]:(((X1359 @ X1364)&![X1365:$i]:(((X1359 @ X1365)=>((X1364)=(X1365)))))))))=>(((emptyset)=(emptyset))=>(![X2330:$i, X2331:$i]:((((X2330)=(X2331))=>![X2332:$i, X2333:$i]:((((X2332)=(X2333))=>((setadjoin @ X2330 @ X2332)=(setadjoin @ X2331 @ X2333))))))=>(![X1366:$i, X1367:$i]:((((X1366)=(X1367))=>((powerset @ X1366)=(powerset @ X1367))))=>(![X2328:$i, X2329:$i]:((((X2328)=(X2329))=>((setunion @ X2328)=(setunion @ X2329))))=>(((omega)=(omega))=>(![X1368:$i > $o]:((?[X1369:$i]:(((X1368 @ X1369)&![X1370:$i]:(((X1368 @ X1370)=>((X1369)=(X1370))))))=>![X1371:$i, X1372:$i]:(((X1368 @ X1371)=>((X1368 @ X1372)=>((X1371)=(X1372)))))))=>(![X1373:$i > $o, X1374:$i > $o]:((![X1375:$i, X1376:$i]:((((X1375)=(X1376))=>((X1373 @ X1375)<=>(X1374 @ X1376))))=>(?[X1377:$i]:(((X1373 @ X1377)&![X1378:$i]:(((X1373 @ X1378)=>((X1377)=(X1378))))))=>(?[X1379:$i]:(((X1374 @ X1379)&![X1380:$i]:(((X1374 @ X1380)=>((X1379)=(X1380))))))=>((descr @ X1373)=(descr @ X1374))))))=>(![X1381:$i, X1382:$i]:((((X1381)=(X1382))=>![X1383:$i > $o, X1384:$i > $o]:((![X1385:$i]:(((in @ X1385 @ X1381)=>![X1386:$i]:(((in @ X1386 @ X1382)=>(((X1385)=(X1386))=>((X1383 @ X1385)<=>(X1384 @ X1386)))))))=>((dsetconstr @ X1381 @ X1383)=(dsetconstr @ X1382 @ X1384))))))=>(![X2325:$i, X2326:$i]:((![X2327:$i]:(((in @ X2327 @ X2325)=>(in @ X2327 @ X2326)))=>(subset @ X2325 @ X2326)))=>(![X1387:$i, X1388:$i]:((((X1387)=(X1388))=>(subset @ X1388 @ X1387)))=>(![X1389:$i, X1390:$i]:((((X1389)=(X1390))=>(subset @ X1389 @ X1390)))=>(![X1391:$i, X1392:$i]:((![X1393:$i]:(((in @ X1393 @ X1391)=>(in @ X1393 @ X1392)))=>(subset @ X1391 @ X1392)))=>(![X1394:$i]:((subset @ emptyset @ X1394))=>(![X2322:$i, X2323:$i, X2324:$i]:(((subset @ X2322 @ X2323)=>((in @ X2324 @ X2322)=>(in @ X2324 @ X2323))))=>(![X2319:$i, X2320:$i, X2321:$i]:(((subset @ X2319 @ X2320)=>(~(in @ X2321 @ X2320)=>~(in @ X2321 @ X2319))))=>(![X2316:$i, X2317:$i, X2318:$i]:(((in @ X2318 @ 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breln1unionIR]), breln1unionE]), breln1unionCommutes]), woz2A]), breln1compE]), woz13rule4]), woz1_1]), breln1all2]), breln1SetBreln1]), breln1all1]), subbreln1]), breln1invE]), woz13rule3]), inIntersectImpInUnion2]), intersectInPowersetIntersectUnions]), binunionTE]), complementUnionInPowersetComplement]), demorgan1]), demorgan2b2]), woz13rule1]), inIntersectImpInUnion]), powersetTI1]), powersetTE1]), binintersectTELcontra]), contrasubsetT1]), contrasubsetT2]), doubleComplementE1]), complementTnotintersectT]), complementT_lem]), c_0_403]), c_0_404]), theeq]), iftrue]), binunionT_lem]), powersetT_lem]), setminusT_lem]), c_0_405]), c_0_406]), c_0_407]), c_0_408]), c_0_409]), c_0_410]), c_0_411]), c_0_412]), funcext2]), c_0_413]), brelnall1]), brelnall2]), funcGraphProp2]), funcGraphProp4]), eqbreln]), funcext]), infuncsetfunc]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_414]), c_0_415]), c_0_416]), c_0_417]), cartprodpairmemEL]), setukpairinjL1]), kfstpairEq]), setukpairinjL2]), setukpairinjR12]), setukpairinjR1]), c_0_418]), ksndpairEq]), singletonsuniq]), singletonsubset]), upairset2E]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), c_0_419]), kpairp]), symdiffE]), symdiffI2]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), setminusIRneg]), setminusILneg]), setminusERneg]), setminusSubset2]), setminusI]), bs114d]), binintersectSubset1]), binintersectRsub]), disjointsetsI1]), binintersectSubset3]), binintersectEL]), binintersectI]), binunionRsub]), binunionLsub]), binunionIR]), upairset2IR]), binunionIL]), c_0_420]), inPowerset]), powersetI1]), subsetemptysetimpeq]), setextsub]), subset2powerset]), notequalI1]), emptysetsubset]), subsetI2]), eqimpsubset1]), eqimpsubset2]), c_0_421]), c_0_422]), c_0_423]), powerset__Cong]), emptyset__Cong]), c_0_424]), inCongP]), c_0_425]), c_0_426]), notdallE]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), upairsetIL]), upairsetE]), eqinunit]), setunionE]), powersetE]), emptyInPowerset]), emptyinunitempty]), setadjoinIL]), c_0_427]), noeltsimpempty]), emptyI]), c_0_428]), emptysetE]), c_0_429]), c_0_430]), c_0_431]), wellorderingAx]), c_0_432]), omegaIndAx]), omega0Ax]), setadjoinAx]), setextAx])])]), c_0_433]), c_0_434]), c_0_435]), c_0_436]), c_0_437]), c_0_438])). 126.84/19.39 thf(c_0_440, negated_conjecture, ![X2427:$i, X2428:$i, X2430:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2435:$i, X2436:$i, X2437:$i, X2438:$i, X2440:$i, X2441:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i, X2447:$i, X2449:$i, X2450:$i > $i > $o, X2451:$i, X2453:$i, X2456:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2463:$i, X2464:$i > $o, X2465:$i, X2467:$i, X2468:$i > $o, X2469:$i, X2470:$i, X2471:$i > $o, X2472:$i, X2473:$i, X2474:$i > $o, X2475:$i, X2476:$i > $o, X2477:$i, X2480:$i, X2481:$o, X2482:$i, X2483:$i, X2484:$o, X2485:$i, X2486:$i, X2487:$i > $o, X2488:$i, X2491:$i, X2492:$i, X2495:$i, X2497:$i, X2499:$i, X2500:$i > $o, X2501:$i, X2502:$i, X2504:$i, X2505:$i > $o, X2506:$i, X2507:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$o, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$o, X2537:$i, X2538:$i, X2539:$i > $o, X2540:$i, X2543:$i, X2544:$i, X2545:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i, X2551:$i, X2552:$i, X2553:$i, X2554:$i, X2555:$i, X2556:$i, X2557:$i, X2558:$i, X2559:$i, X2560:$i, X2561:$i, X2562:$i, X2563:$i > $o, X2564:$i, X2565:$i > $o, X2566:$i, X2567:$i, X2568:$i > $o, X2569:$i, X2571:$i, X2572:$i > $o, X2574:$i, X2575:$i, X2576:$i > $o, X2578:$i, X2579:$i, X2580:$i > $o, X2581:$i, X2583:$o, X2584:$o, X2585:$i, X2586:$i > $o, X2588:$i, X2589:$i, X2590:$i > $o, X2591:$i, X2593:$i > $o, X2594:$i, X2597:$i, X2598:$i > $o, X2599:$i, X2603:$i, X2604:$i > $o, X2605:$i, X2608:$i, X2609:$i, X2610:$i, X2611:$i, X2612:$i, X2613:$i, X2614:$i, X2615:$i, X2616:$i, X2617:$i > $o, X2618:$i, X2620:$i, X2621:$i, X2622:$i > $o, X2623:$i > $o, X2626:$i, X2629:$i, X2630:$i, X2633:$i, X2634:$i, X2635:$i, X2636:$i, X2637:$i, X2638:$i, X2639:$i, X2640:$i, X2641:$i, X2642:$i > $o, X2643:$i, X2645:$i, X2646:$i, X2647:$i > $o, X2648:$i > $o, X2651:$i, X2653:$i, X2655:$i, X2656:$i, X2657:$i > $o, X2658:$i > $o, X2661:$i, X2662:$i, X2664:$i, X2665:$i, X2666:$i, X2667:$i, X2668:$i, X2669:$i, X2671:$i, X2672:$i, X2673:$i, X2674:$i, X2675:$i, X2676:$i, X2677:$i, X2678:$i, X2679:$i, X2680:$i, X2681:$i, X2682:$i, X2683:$i, X2684:$i, X2685:$i, X2686:$i, X2687:$i, X2688:$i, X2689:$i, X2690:$i, X2691:$i, X2692:$i, X2693:$i, X2694:$i, X2695:$i, X2696:$i, X2697:$i, X2698:$i, X2699:$i, X2700:$i, X2701:$i, X2702:$i, X2703:$i, X2704:$i, X2705:$i, X2706:$i, X2707:$i, X2708:$i > $o, X2709:$i, X2710:$i > $o, X2711:$i, X2712:$i, X2713:$i, X2714:$i, X2715:$i, X2716:$i, X2717:$i, X2718:$i, X2719:$i, X2720:$i, X2721:$i, X2722:$o, X2723:$i, X2724:$i, X2725:$i, X2726:$i, X2727:$i, X2728:$i, X2729:$i, X2730:$i, X2731:$i, X2732:$i, X2733:$i, X2734:$i, X2735:$i, X2736:$i, X2737:$i, X2738:$i, X2739:$i, X2740:$i, X2741:$i, X2742:$i, X2743:$i, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i, X2749:$i, X2751:$i, X2752:$i, X2753:$i, X2754:$i, X2755:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2760:$i, X2761:$i, X2762:$i, X2763:$i, X2764:$i, X2765:$i, X2766:$i, X2767:$i, X2768:$i, X2769:$i, X2770:$i, X2771:$i, X2772:$i, X2773:$i, X2774:$i, X2775:$i, X2776:$i, X2777:$i, X2778:$i, X2779:$i, X2780:$i, X2781:$i, X2782:$i, X2783:$i, X2784:$i, X2785:$i, X2786:$i, X2787:$i, X2788:$i, X2789:$i, X2790:$o, X2791:$i, X2792:$i, X2793:$i, X2794:$i, X2795:$i, X2796:$i, X2797:$i, X2798:$i, X2799:$i, X2800:$i, X2801:$i, X2802:$i, X2803:$i, X2804:$i, X2805:$i, X2806:$i, X2807:$i, X2808:$i, X2809:$i, X2810:$i, X2811:$i, X2812:$i, X2813:$i, X2814:$i, X2815:$i, X2816:$i, X2817:$i, X2818:$i, X2819:$i, X2820:$i, X2821:$i, X2822:$i, X2823:$i, X2824:$i, X2825:$i, X2826:$i, X2827:$i, X2828:$i, X2829:$i, X2830:$i, X2831:$i, X2832:$i, X2833:$i, X2834:$i, X2835:$i, X2836:$i, X2837:$i, X2838:$i, X2839:$i, X2840:$i, X2841:$i, X2842:$i, X2843:$i, X2844:$i, X2845:$i, X2846:$i, X2847:$i, X2848:$i, X2849:$i, X2852:$i, X2853:$i, X2854:$i, X2855:$i, X2856:$i, X2858:$i, X2859:$i, X2860:$i, X2861:$i, X2862:$i > $o, X2865:$i, X2866:$i, X2867:$i > $o, X2869:$i, X2870:$i > $o, X2871:$i, X2873:$i, X2874:$i > $o, X2877:$i, X2878:$i, X2879:$i, X2880:$i, X2881:$i, X2882:$i, X2883:$i, X2884:$i, X2885:$i, X2886:$i, X2887:$i, X2888:$i, X2889:$i, X2890:$i, X2891:$i, X2892:$i, X2893:$i, X2894:$i, X2895:$i, X2896:$i, X2897:$i, X2898:$i, X2899:$i, X2900:$i, X2901:$i, X2902:$i, X2903:$i, X2904:$i, X2905:$i, X2906:$i, X2907:$i, X2908:$i, X2909:$i, X2910:$i, X2911:$i, X2912:$i, X2913:$i, X2914:$i, X2915:$i, X2916:$i, X2917:$i, X2918:$i, X2919:$i, X2920:$i, X2921:$i, X2922:$i, X2923:$i, X2924:$i, X2925:$i, X2926:$i, X2927:$i, X2928:$i, X2929:$i, X2930:$i, X2931:$i, X2932:$i, X2933:$i, X2934:$i, X2935:$i, X2936:$i, X2937:$i, X2938:$i, X2939:$i, X2940:$i, X2941:$i, X2942:$i, X2943:$i, X2944:$i, X2945:$i, X2946:$i, X2947:$i, X2948:$i, X2949:$i > $i > $o, X2950:$i, X2951:$i, X2952:$i, X2953:$i, X2954:$i > $i > $o, X2955:$i, X2956:$i, X2957:$i > $i > $o, X2958:$i, X2959:$i, X2960:$i > $i > $o, X2961:$i, X2962:$i, X2963:$i, X2964:$i, X2965:$i > $i > $o, X2966:$i, X2967:$i, X2968:$i, X2969:$i, X2970:$i > $i > $o, X2971:$i, X2972:$i, X2973:$i, X2974:$i, X2975:$i > $i > $o, X2976:$i, X2977:$i, X2978:$i, X2979:$i, X2980:$i, X2981:$i, X2982:$i, X2983:$i, X2984:$i, X2985:$i, X2986:$i, X2987:$i, X2988:$i, X2989:$i, X2990:$i, X2991:$i, X2992:$i, X2993:$i, X2994:$i, X2995:$i, X2996:$i, X2997:$i, X2998:$i, X2999:$i, X3000:$i, X3001:$i, X3002:$i > $i, X3004:$i, X3005:$i, X3006:$i > $i, X3008:$i, X3009:$i, X3010:$i > $i, X3012:$i, X3013:$i, X3014:$i, X3015:$i > $o, X3018:$i, X3019:$i, X3020:$i, X3021:$i, X3022:$i > $o, X3025:$i, X3026:$i, X3027:$i > $o, X3028:$i, X3029:$i, X3030:$i, X3031:$i, X3032:$i, X3033:$i, X3034:$i, X3035:$i, X3036:$i, X3037:$i, X3038:$i, X3039:$i, X3040:$i, X3041:$i, X3042:$i, X3043:$i, X3044:$i, X3045:$i, X3046:$i, X3048:$i, X3049:$i, X3050:$i, X3051:$i, X3052:$i, X3053:$i, X3054:$i, X3055:$i, X3056:$i, X3057:$i, X3058:$i, X3061:$i, X3062:$i, X3063:$i, X3064:$i, X3069:$i, X3070:$i, X3071:$i, X3072:$i, X3074:$i, X3075:$i, X3076:$i, X3077:$i, X3079:$i, X3080:$i, X3081:$i, X3082:$i, X3083:$i, X3084:$i, X3085:$i, X3086:$i, X3087:$i, X3088:$i, X3089:$i > $i, X3091:$i, X3092:$i, X3093:$i, X3094:$i, X3095:$i, X3096:$i, X3097:$i > $i, X3099:$i, X3100:$i, X3101:$i > $i, X3103:$i, X3104:$i, X3105:$i, X3106:$i, X3107:$i, X3108:$o, X3109:$i, X3110:$i, X3111:$i, X3112:$o, X3113:$i, X3114:$i, X3115:$i, X3116:$o, X3117:$i, X3118:$i, X3119:$i, X3120:$o, X3121:$i, X3122:$i, X3123:$i, X3124:$o, X3125:$i, X3126:$i, X3127:$i, X3128:$o, X3129:$i, X3130:$i, X3131:$i, X3132:$i, X3133:$i, X3134:$o, X3135:$i, X3136:$i, X3137:$i, X3138:$o, X3139:$i, X3140:$i, X3141:$i, X3142:$o, X3143:$i, X3144:$i, X3145:$i, X3146:$i, X3147:$i, X3148:$i, X3149:$i, X3150:$i, X3151:$i, X3152:$i, X3153:$i, X3154:$i, X3155:$i, X3156:$i, X3157:$i, X3158:$i, X3159:$i, X3160:$i, X3163:$i, X3164:$i, X3165:$i, X3167:$i, X3168:$i, X3169:$i, X3171:$i, X3172:$i, X3173:$i, X3174:$i, X3175:$i, X3176:$i, X3177:$i, X3178:$i, X3179:$i, X3180:$i, X3181:$i, X3182:$i, X3183:$i, X3184:$i, X3185:$i, X3186:$i, X3187:$i, X3188:$i, X3189:$i, X3190:$i, X3191:$i, X3192:$i, X3193:$i, X3194:$i, X3195:$i, X3196:$i, X3197:$i, X3198:$i, X3199:$i, X3200:$i, X3201:$i, X3202:$i, X3203:$i, X3204:$i, X3205:$i, X3206:$i, X3207:$i, X3208:$i, X3209:$i, X3210:$i, X3211:$i, X3212:$i, X3213:$i, X3214:$i, X3215:$i, X3216:$i, X3217:$i, X3218:$i, X3219:$i, X3220:$i, X3221:$i, X3222:$i, X3223:$i, X3224:$i, X3225:$i, X3226:$i, X3227:$i, X3228:$i, X3229:$i, X3230:$i, X3231:$i, X3232:$i, X3233:$i, X3234:$i, X3235:$i, X3236:$i, X3237:$i, X3238:$i, X3239:$i, X3240:$i, X3241:$i, X3242:$i, X3243:$i, X3244:$i, X3245:$i, X3246:$i, X3247:$i, X3248:$i, X3249:$i, X3250:$i, X3251:$i, X3252:$i, X3253:$i, X3254:$i, X3255:$i, X3256:$i, X3257:$i, X3258:$i, X3259:$i, X3260:$i, X3261:$i, X3262:$i, X3263:$i, X3264:$i, X3265:$i, X3266:$i, X3267:$i, X3268:$i, X3269:$i, X3270:$i, X3271:$i, X3272:$i, X3273:$i, X3274:$o, X3275:$i, X3276:$i, X3277:$i, X3278:$i, X3279:$i, X3280:$i, X3281:$i, X3282:$i, X3283:$i, X3284:$i, X3285:$i, X3286:$i, X3287:$i, X3288:$i, X3289:$i, X3290:$i, X3291:$i, X3292:$i, X3293:$i, X3294:$i, X3295:$i, X3296:$i, X3297:$i, X3298:$i, X3299:$i, X3300:$i, X3301:$i, X3302:$i, X3303:$i, X3304:$i, X3305:$i, X3306:$i, X3307:$i, X3308:$i, X3309:$i, X3310:$i, X3311:$i, X3312:$i, X3313:$i, X3314:$i, X3315:$i, X3316:$i, X3317:$i, X3318:$i, X3319:$i, X3320:$i, X3321:$i, X3322:$i, X3323:$i, X3324:$i, X3325:$i, X3326:$i, X3327:$i, X3328:$i, X3329:$i, X3330:$i, X3331:$i, X3332:$i, X3333:$i, X3334:$i, X3335:$i, X3336:$i, X3337:$i, X3338:$i, X3339:$i, X3340:$i, X3341:$i, X3342:$i, X3343:$i, X3344:$i, X3345:$i, X3346:$i, X3347:$i, X3348:$i, X3349:$i, X3350:$i, X3351:$i, X3352:$i, X3353:$i, X3354:$i, X3355:$i, X3356:$i, X3357:$i, X3358:$i > $o, X3361:$i, X3362:$i, X3363:$i, X3364:$i, X3365:$i, X3366:$i > $i > $o, X3368:$i, X3369:$i, X3370:$i, X3371:$i, X3372:$i > $i > $o, X3373:$i, X3374:$i, X3375:$i > $o, X3378:$i, X3379:$i, X3380:$i, X3381:$i, X3384:$i, X3385:$i, X3386:$i, X3391:$i, X3392:$i, X3393:$i, X3394:$i, X3395:$i, X3396:$i, X3397:$i, X3398:$i, X3399:$i, X3400:$i, X3401:$i, X3402:$i, X3403:$i, X3404:$i, X3405:$i, X3406:$i, X3407:$i, X3408:$i, X3409:$i, X3410:$i, X3411:$i, X3412:$i, X3413:$i, X3414:$i, X3416:$i, X3417:$i, X3418:$i, X3419:$i, X3420:$i, X3421:$o, X3423:$i, X3424:$i, X3425:$i, X3426:$i, X3427:$i, X3428:$i, X3429:$i, X3430:$i, X3431:$i, X3432:$i, X3433:$i, X3434:$i, X3435:$i, X3436:$i, X3437:$i, X3438:$i, X3439:$i, X3440:$i, X3441:$i, X3442:$i, X3443:$i, X3444:$i, X3445:$i, X3446:$i, X3447:$i, X3448:$i, X3449:$i, X3450:$i, X3451:$o, X3452:$i, X3453:$i, X3454:$i, X3455:$i, X3456:$i, X3457:$i, X3458:$i, X3459:$i, X3460:$i, X3461:$i, X3462:$i, X3463:$i, X3464:$i, X3465:$i, X3466:$i, X3467:$i, X3468:$i, X3469:$i > $i, X3471:$i, X3473:$i, X3474:$i, X3475:$i, X3476:$i > $i, X3478:$i, X3480:$i, X3481:$i, X3482:$i, X3484:$i, X3486:$i, X3487:$i > $i, X3488:$i, X3490:$i, X3491:$i > $i, X3492:$i, X3493:$i, X3494:$i, X3495:$i > $i, X3496:$i, X3498:$i, X3499:$i > $i, X3500:$i, X3501:$i, X3502:$i, X3503:$i, X3504:$i, X3505:$i, X3506:$i, X3507:$i, X3508:$i, X3509:$i, X3510:$i, X3511:$i, X3512:$i, X3513:$i, X3514:$i, X3515:$i, X3516:$i, X3517:$i, X3518:$i, X3519:$i > $i, X3521:$i, X3523:$i, X3524:$i, X3525:$i, X3527:$i, X3528:$i, X3529:$i, X3530:$i, X3531:$i, X3532:$i, X3533:$i, X3534:$i, X3535:$i, X3537:$i, X3538:$i, X3540:$i, X3542:$i, X3543:$i, X3545:$i, X3546:$i, X3547:$i, X3550:$i, X3551:$i, X3555:$i, X3557:$i, X3561:$i, X3563:$i, X3564:$i, X3568:$i, X3570:$i, X3571:$i, X3572:$i, X3576:$i, X3578:$i, X3580:$i]:((((~(in @ (esk1_2 @ X2427 @ X2428) @ X2427)|~(in @ (esk1_2 @ X2427 @ X2428) @ X2428)|((X2427)=(X2428)))&((in @ (esk1_2 @ X2427 @ X2428) @ X2427)|(in @ (esk1_2 @ X2427 @ X2428) @ X2428)|((X2427)=(X2428))))&(~(in @ X2430 @ emptyset)&(((~(in @ X2433 @ (setadjoin @ X2431 @ X2432))|(((X2433)=(X2431))|(in @ X2433 @ X2432)))&((((X2433)!=(X2431))|(in @ X2433 @ (setadjoin @ X2431 @ X2432)))&(~(in @ X2433 @ X2432)|(in @ X2433 @ (setadjoin @ X2431 @ X2432)))))&(((~(in @ X2435 @ (powerset @ X2434))|(~(in @ X2436 @ X2435)|(in @ X2436 @ X2434)))&(((in @ (esk2_2 @ X2437 @ X2438) @ X2438)|(in @ X2438 @ (powerset @ X2437)))&(~(in @ (esk2_2 @ X2437 @ X2438) @ X2437)|(in @ X2438 @ (powerset @ X2437)))))&(((((in @ X2441 @ (esk3_2 @ X2440 @ X2441))|~(in @ X2441 @ (setunion @ X2440)))&((in @ (esk3_2 @ X2440 @ X2441) @ X2440)|~(in @ X2441 @ (setunion @ X2440))))&(~(in @ X2444 @ X2445)|~(in @ X2445 @ X2443)|(in @ X2444 @ (setunion @ X2443))))&((in @ emptyset @ omega)&((~(in @ X2446 @ omega)|(in @ 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(esk125_1 @ X3564) @ X3564)|(~(in @ X3571 @ X3564)|(~(in @ X3570 @ X3571)|(in @ X3570 @ X3564))))&((((esk127_1 @ X3564)!=(emptyset))|((in @ (esk126_1 @ X3564) @ X3564)|~(epred4_1 @ X3564))|~(subset @ (esk125_1 @ X3564) @ X3564)|(~(in @ X3571 @ X3564)|(~(in @ X3570 @ X3571)|(in @ X3570 @ X3564))))&(((in @ (esk128_2 @ X3564 @ X3568) @ (esk127_1 @ X3564))|~(in @ X3568 @ (esk127_1 @ X3564))|((in @ (esk126_1 @ X3564) @ X3564)|~(epred4_1 @ X3564))|~(subset @ (esk125_1 @ X3564) @ X3564)|(~(in @ X3571 @ X3564)|(~(in @ X3570 @ X3571)|(in @ X3570 @ X3564))))&((((X3568)!=(esk128_2 @ X3564 @ X3568))|~(in @ X3568 @ (esk127_1 @ X3564))|((in @ (esk126_1 @ X3564) @ X3564)|~(epred4_1 @ X3564))|~(subset @ (esk125_1 @ X3564) @ X3564)|(~(in @ X3571 @ X3564)|(~(in @ X3570 @ X3571)|(in @ X3570 @ X3564))))&(~(in @ X3568 @ (esk128_2 @ X3564 @ X3568))|~(in @ X3568 @ (esk127_1 @ X3564))|((in @ (esk126_1 @ X3564) @ X3564)|~(epred4_1 @ X3564))|~(subset @ (esk125_1 @ X3564) @ X3564)|(~(in @ X3571 @ X3564)|(~(in @ X3570 @ X3571)|(in @ X3570 @ X3564))))))))&(((in @ (esk127_1 @ X3564) @ (powerset @ X3564))|((in @ (esk126_1 @ X3564) @ (esk126_1 @ X3564))|~(epred4_1 @ X3564))|~(subset @ (esk125_1 @ X3564) @ X3564)|(~(in @ X3571 @ X3564)|(~(in @ X3570 @ X3571)|(in @ X3570 @ X3564))))&((((esk127_1 @ X3564)!=(emptyset))|((in @ (esk126_1 @ X3564) @ (esk126_1 @ X3564))|~(epred4_1 @ X3564))|~(subset @ (esk125_1 @ X3564) @ X3564)|(~(in @ X3571 @ X3564)|(~(in @ X3570 @ X3571)|(in @ X3570 @ X3564))))&(((in @ (esk128_2 @ X3564 @ X3568) @ (esk127_1 @ X3564))|~(in @ X3568 @ (esk127_1 @ X3564))|((in @ (esk126_1 @ X3564) @ (esk126_1 @ X3564))|~(epred4_1 @ X3564))|~(subset @ (esk125_1 @ X3564) @ X3564)|(~(in @ X3571 @ X3564)|(~(in @ X3570 @ X3571)|(in @ X3570 @ X3564))))&((((X3568)!=(esk128_2 @ X3564 @ X3568))|~(in @ X3568 @ (esk127_1 @ X3564))|((in @ (esk126_1 @ X3564) @ (esk126_1 @ X3564))|~(epred4_1 @ X3564))|~(subset @ (esk125_1 @ X3564) @ X3564)|(~(in @ X3571 @ X3564)|(~(in @ X3570 @ X3571)|(in @ X3570 @ X3564))))&(~(in @ X3568 @ (esk128_2 @ X3564 @ X3568))|~(in @ X3568 @ (esk127_1 @ X3564))|((in @ (esk126_1 @ X3564) @ (esk126_1 @ X3564))|~(epred4_1 @ X3564))|~(subset @ (esk125_1 @ X3564) @ X3564)|(~(in @ X3571 @ X3564)|(~(in @ X3570 @ X3571)|(in @ X3570 @ X3564))))))))))&((((((in @ (esk131_1 @ X3572) @ (powerset @ X3572))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&((((esk131_1 @ X3572)!=(emptyset))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&(((in @ (esk132_2 @ X3572 @ X3576) @ (esk131_1 @ X3572))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&((((X3576)!=(esk132_2 @ X3572 @ X3576))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&(~(in @ X3576 @ (esk132_2 @ X3572 @ X3576))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))))))&(((in @ (esk131_1 @ X3572) @ (powerset @ X3572))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&((((esk131_1 @ X3572)!=(emptyset))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&(((in @ (esk132_2 @ X3572 @ X3576) @ (esk131_1 @ X3572))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&((((X3576)!=(esk132_2 @ X3572 @ X3576))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&(~(in @ X3576 @ (esk132_2 @ X3572 @ X3576))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|(in @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572))))))))&((((in @ (esk131_1 @ X3572) @ (powerset @ X3572))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&((((esk131_1 @ X3572)!=(emptyset))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&(((in @ (esk132_2 @ X3572 @ X3576) @ (esk131_1 @ X3572))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&((((X3576)!=(esk132_2 @ X3572 @ X3576))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&(~(in @ X3576 @ (esk132_2 @ X3572 @ X3576))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ X3572)|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))))))&(((in @ (esk131_1 @ X3572) @ (powerset @ X3572))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&((((esk131_1 @ X3572)!=(emptyset))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&(((in @ (esk132_2 @ X3572 @ X3576) @ (esk131_1 @ X3572))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&((((X3576)!=(esk132_2 @ X3572 @ X3576))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))&(~(in @ X3576 @ (esk132_2 @ X3572 @ X3576))|~(in @ X3576 @ (esk131_1 @ X3572))|((in @ (esk130_1 @ X3572) @ (esk130_1 @ X3572))|~(epred5_1 @ X3572))|~(subset @ (esk129_1 @ X3572) @ X3572)|(~(in @ X3578 @ X3572)|(subset @ X3578 @ X3572)))))))))&((~(in @ X3580 @ esk133_0)|(epred6_1 @ X3580))&((in @ esk134_0 @ (setunion @ esk133_0))&~(subset @ esk134_0 @ (setunion @ esk133_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_439])])])])])])])). 126.84/19.40 thf(c_0_441, plain, ![X2:$i]:(((epred6_1 @ X2)=>(![X1854:$i]:(((in @ X1854 @ X2)=>(subset @ X1854 @ X2)))&(((![X1855:$i]:(((in @ X1855 @ X2)=>![X1856:$i]:(((in @ X1856 @ X2)=>![X1857:$i]:(((in @ X1857 @ X2)=>(((in @ X1855 @ X1856)&(in @ X1856 @ X1857))=>(in @ X1855 @ X1857))))))))&![X1858:$i]:(((in @ X1858 @ X2)=>![X1859:$i]:(((in @ X1859 @ X2)=>(((X1858)=(X1859))|(in @ X1858 @ X1859)|(in @ X1859 @ X1858)))))))&![X1860:$i]:(((in @ X1860 @ X2)=>~(in @ X1860 @ X1860))))&![X1861:$i]:(((in @ X1861 @ (powerset @ X2))=>(((X1861)!=(emptyset))=>?[X1862:$i]:(((in @ X1862 @ X1861)&![X1863:$i]:(((in @ X1863 @ X1861)=>(((X1862)=(X1863))|(in @ X1862 @ X1863))))))))))))), inference(split_equiv,[status(thm)],[c_0_438])). 126.84/19.40 thf(c_0_442, negated_conjecture, ![X3:$i, X2:$i]:(((in @ (esk115_1 @ X2) @ X2)|(subset @ X3 @ (setunion @ X2))|~((in @ X3 @ (setunion @ X2))))), inference(split_conjunct,[status(thm)],[c_0_440])). 126.84/19.40 thf(c_0_443, negated_conjecture, (in @ esk134_0 @ (setunion @ esk133_0)), inference(split_conjunct,[status(thm)],[c_0_440])). 126.84/19.40 thf(c_0_444, negated_conjecture, ~((subset @ esk134_0 @ (setunion @ esk133_0))), inference(split_conjunct,[status(thm)],[c_0_440])). 126.84/19.40 thf(c_0_445, plain, ![X3625:$i, X3626:$i, X3627:$i, X3628:$i, X3629:$i, X3630:$i, X3631:$i, X3632:$i, X3633:$i, X3635:$i]:(((~(in @ X3626 @ X3625)|(subset @ X3626 @ X3625)|~(epred6_1 @ X3625))&((((~(in @ X3627 @ X3625)|(~(in @ X3628 @ X3625)|(~(in @ X3629 @ X3625)|(~(in @ X3627 @ X3628)|~(in @ X3628 @ X3629)|(in @ X3627 @ X3629))))|~(epred6_1 @ X3625))&(~(in @ X3630 @ X3625)|(~(in @ X3631 @ X3625)|(((X3630)=(X3631))|(in @ X3630 @ X3631)|(in @ X3631 @ X3630)))|~(epred6_1 @ X3625)))&(~(in @ X3632 @ X3625)|~(in @ X3632 @ X3632)|~(epred6_1 @ X3625)))&(((in @ (esk160_2 @ X3625 @ X3633) @ X3633)|((X3633)=(emptyset))|~(in @ X3633 @ (powerset @ X3625))|~(epred6_1 @ X3625))&(~(in @ X3635 @ X3633)|(((esk160_2 @ X3625 @ X3633)=(X3635))|(in @ (esk160_2 @ X3625 @ X3633) @ X3635))|((X3633)=(emptyset))|~(in @ X3633 @ (powerset @ X3625))|~(epred6_1 @ X3625)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_441])])])])])])). 126.84/19.40 thf(c_0_446, negated_conjecture, ![X3:$i, X2:$i]:(((in @ (esk116_1 @ X2) @ (esk115_1 @ X2))|(subset @ X3 @ (setunion @ X2))|~((in @ X3 @ (setunion @ X2))))), inference(split_conjunct,[status(thm)],[c_0_440])). 126.84/19.40 thf(c_0_447, negated_conjecture, ![X2:$i]:(((epred6_1 @ X2)|~((in @ X2 @ esk133_0)))), inference(split_conjunct,[status(thm)],[c_0_440])). 126.84/19.40 thf(c_0_448, negated_conjecture, (in @ (esk115_1 @ esk133_0) @ esk133_0), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_442, c_0_443]), c_0_444])). 126.84/19.40 thf(c_0_449, negated_conjecture, ![X3:$i, X2:$i]:(((subset @ X3 @ (setunion @ X2))|~((subset @ (esk116_1 @ X2) @ (esk115_1 @ X2)))|~((in @ X3 @ (setunion @ X2))))), inference(split_conjunct,[status(thm)],[c_0_440])). 126.84/19.40 thf(c_0_450, plain, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ X2 @ X3))|~((epred6_1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_445])). 126.84/19.40 thf(c_0_451, negated_conjecture, (in @ (esk116_1 @ esk133_0) @ (esk115_1 @ esk133_0)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_446, c_0_443]), c_0_444])). 126.84/19.40 thf(c_0_452, negated_conjecture, (epred6_1 @ (esk115_1 @ esk133_0)), inference(spm,[status(thm)],[c_0_447, c_0_448])). 126.84/19.40 thf(c_0_453, negated_conjecture, ~((subset @ (esk116_1 @ esk133_0) @ (esk115_1 @ esk133_0))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_449, c_0_443]), c_0_444])). 126.84/19.40 thf(c_0_454, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_450, c_0_451]), c_0_452])]), c_0_453]), ['proof']). 126.84/19.40 % SZS output end CNFRefutation 126.84/19.40 % Parsed axioms : 740 126.84/19.40 % Removed by relevancy pruning/SinE : 398 126.84/19.40 % Initial clauses : 1166 126.84/19.40 % Removed in clause preprocessing : 41 126.84/19.40 % Initial clauses in saturation : 1125 126.84/19.40 % Processed clauses : 3070 126.84/19.40 % ...of these trivial : 60 126.84/19.40 % ...subsumed : 666 126.84/19.40 % ...remaining for further processing : 2344 126.84/19.40 % Other redundant clauses eliminated : 35 126.84/19.40 % Clauses deleted for lack of memory : 0 126.84/19.40 % Backward-subsumed : 330 126.84/19.40 % Backward-rewritten : 8 126.84/19.40 % Generated clauses : 12193 126.84/19.40 % ...of the previous two non-redundant : 11272 126.84/19.40 % ...aggressively subsumed : 0 126.84/19.40 % Contextual simplify-reflections : 15 126.84/19.40 % Paramodulations : 12130 126.84/19.40 % Factorizations : 22 126.84/19.40 % NegExts : 0 126.84/19.40 % Equation resolutions : 38 126.84/19.40 % Disequality decompositions : 0 126.84/19.40 % Total rewrite steps : 975 126.84/19.40 % ...of those cached : 591 126.84/19.40 % Propositional unsat checks : 0 126.84/19.40 % Propositional check models : 0 126.84/19.40 % Propositional check unsatisfiable : 0 126.84/19.40 % Propositional clauses : 0 126.84/19.40 % Propositional clauses after purity: 0 126.84/19.40 % Propositional unsat core size : 0 126.84/19.40 % Propositional preprocessing time : 0.000 126.84/19.40 % Propositional encoding time : 0.000 126.84/19.40 % Propositional solver time : 0.000 126.84/19.40 % Success case prop preproc time : 0.000 126.84/19.40 % Success case prop encoding time : 0.000 126.84/19.40 % Success case prop solver time : 0.000 126.84/19.40 % Current number of processed clauses : 1246 126.84/19.40 % Positive orientable unit clauses : 298 126.84/19.40 % Positive unorientable unit clauses: 0 126.84/19.40 % Negative unit clauses : 275 126.84/19.40 % Non-unit-clauses : 673 126.84/19.40 % Current number of unprocessed clauses: 10029 126.84/19.40 % ...number of literals in the above : 25071 126.84/19.40 % Current number of archived formulas : 0 126.84/19.40 % Current number of archived clauses : 1076 126.84/19.40 % Clause-clause subsumption calls (NU) : 1135256 126.84/19.40 % Rec. Clause-clause subsumption calls : 90624 126.84/19.40 % Non-unit clause-clause subsumptions : 704 126.84/19.40 % Unit Clause-clause subsumption calls : 18802 126.84/19.40 % Rewrite failures with RHS unbound : 0 126.84/19.40 % BW rewrite match attempts : 197 126.84/19.40 % BW rewrite match successes : 8 126.84/19.40 % Condensation attempts : 0 126.84/19.40 % Condensation successes : 0 126.84/19.40 % Termbank termtop insertions : 744580 126.84/19.40 % Search garbage collected termcells : 42271 126.84/19.40 126.84/19.40 % ------------------------------------------------- 126.84/19.40 % User time : 18.166 s 126.84/19.40 % System time : 0.504 s 126.84/19.40 % Total time : 18.670 s 126.84/19.40 % Maximum resident set size: 14460 pages 126.84/19.40 126.84/19.40 % ------------------------------------------------- 126.84/19.40 % User time : 18.186 s 126.84/19.40 % System time : 0.514 s 126.84/19.40 % Total time : 18.700 s 126.84/19.40 % Maximum resident set size: 6400 pages 126.84/19.40 % E exiting 145.83/19.40 EOF