0.10/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.12 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 240 THM 0.12/0.33 % Computer : n009.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 1920 0.12/0.33 % WCLimit : 240 0.12/0.33 % DateTime : Wed Jul 30 09:31:34 EDT 2025 0.12/0.33 % CPUTime : 0.20/0.48 Running higher-order theorem proving 0.20/0.55 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=240 /export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p 361.08/46.39 # Version: 3.0.0-ho 361.08/46.39 # Preprocessing class: HSLMSLSSLLLCHFA. 361.08/46.39 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 361.08/46.39 # Starting ehoh_best5 with 240s (1) cores 361.08/46.39 # Starting almost_fo_3_lam with 240s (1) cores 361.08/46.39 # Starting new_bool_5 with 240s (1) cores 361.08/46.39 # Starting pre_casc_3 with 240s (1) cores 361.08/46.39 # Starting ho_unfolding_8 with 240s (1) cores 361.08/46.39 # Starting new_ho_10_cnf2 with 240s (1) cores 361.08/46.39 # Starting new_bool_3 with 240s (1) cores 361.08/46.39 # Starting new_ho_5 with 240s (1) cores 361.08/46.39 # new_bool_5 with pid 5294 completed with status 0 361.08/46.39 # Result found by new_bool_5 361.08/46.39 # Preprocessing class: HSLMSLSSLLLCHFA. 361.08/46.39 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 361.08/46.39 # Starting ehoh_best5 with 240s (1) cores 361.08/46.39 # Starting almost_fo_3_lam with 240s (1) cores 361.08/46.39 # Starting new_bool_5 with 240s (1) cores 361.08/46.39 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 361.08/46.39 # Search class: HGHSM-FSLM32-MHFMMSBN 361.08/46.39 # Scheduled 10 strats onto 1 cores with 240 seconds (240 total) 361.08/46.39 # Starting ho_unfolding_8 with 44s (1) cores 361.08/46.39 # ho_unfolding_8 with pid 5303 completed with status 8 361.08/46.39 # Starting new_bool_5 with 25s (1) cores 361.08/46.39 # new_bool_5 with pid 5800 completed with status 0 361.08/46.39 # Result found by new_bool_5 361.08/46.39 # Preprocessing class: HSLMSLSSLLLCHFA. 361.08/46.39 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 361.08/46.39 # Starting ehoh_best5 with 240s (1) cores 361.08/46.39 # Starting almost_fo_3_lam with 240s (1) cores 361.08/46.39 # Starting new_bool_5 with 240s (1) cores 361.08/46.39 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 361.08/46.39 # Search class: HGHSM-FSLM32-MHFMMSBN 361.08/46.39 # Scheduled 10 strats onto 1 cores with 240 seconds (240 total) 361.08/46.39 # Starting ho_unfolding_8 with 44s (1) cores 361.08/46.39 # ho_unfolding_8 with pid 5303 completed with status 8 361.08/46.39 # Starting new_bool_5 with 25s (1) cores 361.08/46.39 # Preprocessing time : 0.006 s 361.08/46.39 # Presaturation interreduction done 361.08/46.39 361.08/46.39 # Proof found! 361.08/46.39 # SZS status Theorem 361.08/46.39 # SZS output start CNFRefutation 361.08/46.39 thf(decl_23, type, in: $i > $i > $o). 361.08/46.39 thf(decl_24, type, exu: ($i > $o) > $o). 361.08/46.39 thf(decl_25, type, setextAx: $o). 361.08/46.39 thf(decl_26, type, emptyset: $i). 361.08/46.39 thf(decl_27, type, emptysetAx: $o). 361.08/46.39 thf(decl_28, type, setadjoin: $i > $i > $i). 361.08/46.39 thf(decl_29, type, setadjoinAx: $o). 361.08/46.39 thf(decl_30, type, powerset: $i > $i). 361.08/46.39 thf(decl_31, type, powersetAx: $o). 361.08/46.39 thf(decl_32, type, setunion: $i > $i). 361.08/46.39 thf(decl_33, type, setunionAx: $o). 361.08/46.39 thf(decl_34, type, omega: $i). 361.08/46.39 thf(decl_35, type, omega0Ax: $o). 361.08/46.39 thf(decl_36, type, omegaSAx: $o). 361.08/46.39 thf(decl_37, type, omegaIndAx: $o). 361.08/46.39 thf(decl_38, type, replAx: $o). 361.08/46.39 thf(decl_39, type, foundationAx: $o). 361.08/46.39 thf(decl_40, type, wellorderingAx: $o). 361.08/46.39 thf(decl_41, type, descr: ($i > $o) > $i). 361.08/46.39 thf(decl_42, type, descrp: $o). 361.08/46.39 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i). 361.08/46.39 thf(decl_44, type, dsetconstrI: $o). 361.08/46.39 thf(decl_45, type, dsetconstrEL: $o). 361.08/46.39 thf(decl_46, type, dsetconstrER: $o). 361.08/46.39 thf(decl_47, type, exuE1: $o). 361.08/46.39 thf(decl_48, type, prop2set: $o > $i). 361.08/46.39 thf(decl_49, type, prop2setE: $o). 361.08/46.39 thf(decl_50, type, emptysetE: $o). 361.08/46.39 thf(decl_51, type, emptysetimpfalse: $o). 361.08/46.39 thf(decl_52, type, notinemptyset: $o). 361.08/46.39 thf(decl_53, type, exuE3e: $o). 361.08/46.39 thf(decl_54, type, setext: $o). 361.08/46.39 thf(decl_55, type, emptyI: $o). 361.08/46.39 thf(decl_56, type, noeltsimpempty: $o). 361.08/46.39 thf(decl_57, type, setbeta: $o). 361.08/46.39 thf(decl_58, type, nonempty: $i > $o). 361.08/46.39 thf(decl_59, type, nonemptyE1: $o). 361.08/46.39 thf(decl_60, type, nonemptyI: $o). 361.08/46.39 thf(decl_61, type, nonemptyI1: $o). 361.08/46.39 thf(decl_62, type, setadjoinIL: $o). 361.08/46.39 thf(decl_63, type, emptyinunitempty: $o). 361.08/46.39 thf(decl_64, type, setadjoinIR: $o). 361.08/46.39 thf(decl_65, type, setadjoinE: $o). 361.08/46.39 thf(decl_66, type, setadjoinOr: $o). 361.08/46.39 thf(decl_67, type, setoftrueEq: $o). 361.08/46.39 thf(decl_68, type, powersetI: $o). 361.08/46.39 thf(decl_69, type, emptyinPowerset: $o). 361.08/46.39 thf(decl_70, type, emptyInPowerset: $o). 361.08/46.39 thf(decl_71, type, powersetE: $o). 361.08/46.39 thf(decl_72, type, setunionI: $o). 361.08/46.39 thf(decl_73, type, setunionE: $o). 361.08/46.39 thf(decl_74, type, subPowSU: $o). 361.08/46.39 thf(decl_75, type, exuE2: $o). 361.08/46.39 thf(decl_76, type, nonemptyImpWitness: $o). 361.08/46.39 thf(decl_77, type, uniqinunit: $o). 361.08/46.39 thf(decl_78, type, notinsingleton: $o). 361.08/46.39 thf(decl_79, type, eqinunit: $o). 361.08/46.39 thf(decl_80, type, singletonsswitch: $o). 361.08/46.39 thf(decl_81, type, upairsetE: $o). 361.08/46.39 thf(decl_82, type, upairsetIL: $o). 361.08/46.39 thf(decl_83, type, upairsetIR: $o). 361.08/46.39 thf(decl_84, type, emptyE1: $o). 361.08/46.39 thf(decl_85, type, vacuousDall: $o). 361.08/46.39 thf(decl_86, type, quantDeMorgan1: $o). 361.08/46.39 thf(decl_87, type, quantDeMorgan2: $o). 361.08/46.39 thf(decl_88, type, quantDeMorgan3: $o). 361.08/46.39 thf(decl_89, type, quantDeMorgan4: $o). 361.08/46.39 thf(decl_90, type, prop2setI: $o). 361.08/46.39 thf(decl_92, type, prop2set2propI: $o). 361.08/46.39 thf(decl_93, type, notdexE: $o). 361.08/46.39 thf(decl_94, type, notdallE: $o). 361.08/46.39 thf(decl_95, type, exuI1: $o). 361.08/46.39 thf(decl_96, type, exuI3: $o). 361.08/46.39 thf(decl_97, type, exuI2: $o). 361.08/46.39 thf(decl_98, type, inCongP: $o). 361.08/46.39 thf(decl_99, type, in__Cong: $o). 361.08/46.39 thf(decl_100, type, exuE3u: $o). 361.08/46.39 thf(decl_101, type, exu__Cong: $o). 361.08/46.39 thf(decl_102, type, emptyset__Cong: $o). 361.08/46.39 thf(decl_103, type, setadjoin__Cong: $o). 361.08/46.39 thf(decl_104, type, powerset__Cong: $o). 361.08/46.39 thf(decl_105, type, setunion__Cong: $o). 361.08/46.39 thf(decl_106, type, omega__Cong: $o). 361.08/46.39 thf(decl_107, type, exuEu: $o). 361.08/46.39 thf(decl_108, type, descr__Cong: $o). 361.08/46.39 thf(decl_109, type, dsetconstr__Cong: $o). 361.08/46.39 thf(decl_110, type, subset: $i > $i > $o). 361.08/46.39 thf(decl_113, type, subsetI1: $o). 361.08/46.39 thf(decl_114, type, eqimpsubset2: $o). 361.08/46.39 thf(decl_115, type, eqimpsubset1: $o). 361.08/46.39 thf(decl_116, type, subsetI2: $o). 361.08/46.39 thf(decl_117, type, emptysetsubset: $o). 361.08/46.39 thf(decl_118, type, subsetE: $o). 361.08/46.39 thf(decl_119, type, subsetE2: $o). 361.08/46.39 thf(decl_120, type, notsubsetI: $o). 361.08/46.39 thf(decl_121, type, notequalI1: $o). 361.08/46.39 thf(decl_122, type, notequalI2: $o). 361.08/46.39 thf(decl_123, type, subsetRefl: $o). 361.08/46.39 thf(decl_124, type, subsetTrans: $o). 361.08/46.39 thf(decl_125, type, setadjoinSub: $o). 361.08/46.39 thf(decl_126, type, setadjoinSub2: $o). 361.08/46.39 thf(decl_127, type, subset2powerset: $o). 361.08/46.39 thf(decl_128, type, setextsub: $o). 361.08/46.39 thf(decl_129, type, subsetemptysetimpeq: $o). 361.08/46.39 thf(decl_130, type, powersetI1: $o). 361.08/46.39 thf(decl_131, type, powersetE1: $o). 361.08/46.39 thf(decl_132, type, inPowerset: $o). 361.08/46.39 thf(decl_133, type, powersetsubset: $o). 361.08/46.39 thf(decl_134, type, sepInPowerset: $o). 361.08/46.39 thf(decl_135, type, sepSubset: $o). 361.08/46.39 thf(decl_136, type, binunion: $i > $i > $i). 361.08/46.39 thf(decl_137, type, binunionIL: $o). 361.08/46.39 thf(decl_138, type, upairset2IR: $o). 361.08/46.39 thf(decl_139, type, binunionIR: $o). 361.08/46.39 thf(decl_140, type, binunionEcases: $o). 361.08/46.39 thf(decl_141, type, binunionE: $o). 361.08/46.39 thf(decl_142, type, binunionLsub: $o). 361.08/46.39 thf(decl_143, type, binunionRsub: $o). 361.08/46.39 thf(decl_144, type, binintersect: $i > $i > $i). 361.08/46.39 thf(decl_145, type, binintersectI: $o). 361.08/46.39 thf(decl_146, type, binintersectSubset5: $o). 361.08/46.39 thf(decl_147, type, binintersectEL: $o). 361.08/46.39 thf(decl_148, type, binintersectLsub: $o). 361.08/46.39 thf(decl_149, type, binintersectSubset2: $o). 361.08/46.39 thf(decl_150, type, binintersectSubset3: $o). 361.08/46.39 thf(decl_151, type, binintersectER: $o). 361.08/46.39 thf(decl_152, type, disjointsetsI1: $o). 361.08/46.39 thf(decl_153, type, binintersectRsub: $o). 361.08/46.39 thf(decl_154, type, binintersectSubset4: $o). 361.08/46.39 thf(decl_155, type, binintersectSubset1: $o). 361.08/46.39 thf(decl_156, type, bs114d: $o). 361.08/46.39 thf(decl_158, type, setminus: $i > $i > $i). 361.08/46.39 thf(decl_159, type, setminusI: $o). 361.08/46.39 thf(decl_160, type, setminusEL: $o). 361.08/46.39 thf(decl_161, type, setminusER: $o). 361.08/46.39 thf(decl_162, type, setminusSubset2: $o). 361.08/46.39 thf(decl_163, type, setminusERneg: $o). 361.08/46.39 thf(decl_164, type, setminusELneg: $o). 361.08/46.39 thf(decl_165, type, setminusILneg: $o). 361.08/46.39 thf(decl_166, type, setminusIRneg: $o). 361.08/46.39 thf(decl_167, type, setminusLsub: $o). 361.08/46.39 thf(decl_168, type, setminusSubset1: $o). 361.08/46.39 thf(decl_169, type, symdiff: $i > $i > $i). 361.08/46.39 thf(decl_170, type, symdiffE: $o). 361.08/46.39 thf(decl_171, type, symdiffI1: $o). 361.08/46.39 thf(decl_172, type, symdiffI2: $o). 361.08/46.39 thf(decl_173, type, symdiffIneg1: $o). 361.08/46.39 thf(decl_174, type, symdiffIneg2: $o). 361.08/46.39 thf(decl_175, type, iskpair: $i > $o). 361.08/46.39 thf(decl_176, type, secondinupair: $o). 361.08/46.39 thf(decl_177, type, setukpairIL: $o). 361.08/46.39 thf(decl_178, type, setukpairIR: $o). 361.08/46.39 thf(decl_179, type, kpairiskpair: $o). 361.08/46.39 thf(decl_180, type, kpair: $i > $i > $i). 361.08/46.39 thf(decl_181, type, kpairp: $o). 361.08/46.39 thf(decl_182, type, cartprod: $i > $i > $i). 361.08/46.39 thf(decl_183, type, singletonsubset: $o). 361.08/46.39 thf(decl_184, type, singletoninpowerset: $o). 361.08/46.39 thf(decl_185, type, singletoninpowunion: $o). 361.08/46.39 thf(decl_186, type, upairset2E: $o). 361.08/46.39 thf(decl_187, type, upairsubunion: $o). 361.08/46.39 thf(decl_188, type, upairinpowunion: $o). 361.08/46.39 thf(decl_189, type, ubforcartprodlem1: $o). 361.08/46.39 thf(decl_190, type, ubforcartprodlem2: $o). 361.08/46.39 thf(decl_191, type, ubforcartprodlem3: $o). 361.08/46.39 thf(decl_192, type, cartprodpairin: $o). 361.08/46.39 thf(decl_193, type, cartprodmempair1: $o). 361.08/46.39 thf(decl_194, type, cartprodmempair: $o). 361.08/46.39 thf(decl_195, type, setunionE2: $o). 361.08/46.39 thf(decl_196, type, setunionsingleton1: $o). 361.08/46.39 thf(decl_197, type, setunionsingleton2: $o). 361.08/46.39 thf(decl_198, type, setunionsingleton: $o). 361.08/46.39 thf(decl_199, type, singleton: $i > $o). 361.08/46.39 thf(decl_200, type, singletonprop: $o). 361.08/46.39 thf(decl_201, type, ex1: $i > ($i > $o) > $o). 361.08/46.39 thf(decl_202, type, ex1E1: $o). 361.08/46.39 thf(decl_203, type, ex1I: $o). 361.08/46.39 thf(decl_204, type, ex1I2: $o). 361.08/46.39 thf(decl_205, type, singletonsuniq: $o). 361.08/46.39 thf(decl_210, type, setukpairinjL1: $o). 361.08/46.39 thf(decl_211, type, kfstsingleton: $o). 361.08/46.39 thf(decl_212, type, theprop: $o). 361.08/46.39 thf(decl_213, type, kfst: $i > $i). 361.08/46.39 thf(decl_214, type, kfstpairEq: $o). 361.08/46.39 thf(decl_215, type, cartprodfstin: $o). 361.08/46.39 thf(decl_216, type, setukpairinjL2: $o). 361.08/46.39 thf(decl_217, type, setukpairinjL: $o). 361.08/46.39 thf(decl_218, type, setukpairinjR11: $o). 361.08/46.39 thf(decl_219, type, setukpairinjR12: $o). 361.08/46.39 thf(decl_220, type, setukpairinjR1: $o). 361.08/46.39 thf(decl_221, type, upairequniteq: $o). 361.08/46.39 thf(decl_222, type, setukpairinjR2: $o). 361.08/46.39 thf(decl_223, type, setukpairinjR: $o). 361.08/46.39 thf(decl_224, type, ksndsingleton: $o). 361.08/46.39 thf(decl_225, type, ksnd: $i > $i). 361.08/46.39 thf(decl_226, type, ksndpairEq: $o). 361.08/46.39 thf(decl_227, type, kpairsurjEq: $o). 361.08/46.39 thf(decl_228, type, cartprodsndin: $o). 361.08/46.39 thf(decl_229, type, cartprodpairmemEL: $o). 361.08/46.39 thf(decl_230, type, cartprodpairmemER: $o). 361.08/46.39 thf(decl_231, type, cartprodmempaircEq: $o). 361.08/46.39 thf(decl_232, type, cartprodfstpairEq: $o). 361.08/46.39 thf(decl_233, type, cartprodsndpairEq: $o). 361.08/46.39 thf(decl_234, type, cartprodpairsurjEq: $o). 361.08/46.39 thf(decl_235, type, breln: $i > $i > $i > $o). 361.08/46.39 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 361.08/46.39 thf(decl_237, type, dpsetconstrI: $o). 361.08/46.39 thf(decl_238, type, dpsetconstrSub: $o). 361.08/46.39 thf(decl_239, type, setOfPairsIsBReln: $o). 361.08/46.39 thf(decl_240, type, dpsetconstrERa: $o). 361.08/46.39 thf(decl_241, type, dpsetconstrEL1: $o). 361.08/46.39 thf(decl_242, type, dpsetconstrEL2: $o). 361.08/46.39 thf(decl_243, type, dpsetconstrER: $o). 361.08/46.39 thf(decl_244, type, func: $i > $i > $i > $o). 361.08/46.39 thf(decl_245, type, funcSet: $i > $i > $i). 361.08/46.39 thf(decl_246, type, funcImageSingleton: $o). 361.08/46.39 thf(decl_247, type, apProp: $o). 361.08/46.39 thf(decl_248, type, ap: $i > $i > $i > $i > $i). 361.08/46.39 thf(decl_249, type, app: $o). 361.08/46.39 thf(decl_250, type, infuncsetfunc: $o). 361.08/46.39 thf(decl_251, type, ap2p: $o). 361.08/46.39 thf(decl_252, type, funcinfuncset: $o). 361.08/46.39 thf(decl_253, type, lamProp: $o). 361.08/46.39 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i). 361.08/46.39 thf(decl_255, type, lamp: $o). 361.08/46.39 thf(decl_256, type, lam2p: $o). 361.08/46.39 thf(decl_257, type, brelnall1: $o). 361.08/46.39 thf(decl_258, type, brelnall2: $o). 361.08/46.39 thf(decl_259, type, ex1E2: $o). 361.08/46.39 thf(decl_260, type, funcGraphProp1: $o). 361.08/46.39 thf(decl_261, type, funcGraphProp3: $o). 361.08/46.39 thf(decl_262, type, funcGraphProp2: $o). 361.08/46.39 thf(decl_263, type, funcextLem: $o). 361.08/46.39 thf(decl_264, type, funcGraphProp4: $o). 361.08/46.39 thf(decl_265, type, subbreln: $o). 361.08/46.39 thf(decl_266, type, eqbreln: $o). 361.08/46.39 thf(decl_267, type, funcext: $o). 361.08/46.39 thf(decl_268, type, funcext2: $o). 361.08/46.39 thf(decl_269, type, ap2apEq1: $o). 361.08/46.39 thf(decl_270, type, ap2apEq2: $o). 361.08/46.39 thf(decl_271, type, beta1: $o). 361.08/46.39 thf(decl_272, type, eta1: $o). 361.08/46.39 thf(decl_273, type, lam2lamEq: $o). 361.08/46.39 thf(decl_274, type, beta2: $o). 361.08/46.39 thf(decl_275, type, eta2: $o). 361.08/46.39 thf(decl_276, type, iffalseProp1: $o). 361.08/46.39 thf(decl_277, type, iffalseProp2: $o). 361.08/46.39 thf(decl_278, type, iftrueProp1: $o). 361.08/46.39 thf(decl_279, type, iftrueProp2: $o). 361.08/46.39 thf(decl_280, type, ifSingleton: $o). 361.08/46.39 thf(decl_281, type, if: $i > $o > $i > $i > $i). 361.08/46.39 thf(decl_282, type, ifp: $o). 361.08/46.39 thf(decl_283, type, theeq: $o). 361.08/46.39 thf(decl_284, type, iftrue: $o). 361.08/46.39 thf(decl_285, type, iffalse: $o). 361.08/46.39 thf(decl_286, type, iftrueorfalse: $o). 361.08/46.39 thf(decl_287, type, binintersectT_lem: $o). 361.08/46.39 thf(decl_288, type, binunionT_lem: $o). 361.08/46.39 thf(decl_289, type, powersetT_lem: $o). 361.08/46.39 thf(decl_290, type, setminusT_lem: $o). 361.08/46.39 thf(decl_291, type, complementT_lem: $o). 361.08/46.39 thf(decl_292, type, setextT: $o). 361.08/46.39 thf(decl_293, type, subsetTI: $o). 361.08/46.39 thf(decl_294, type, powersetTI1: $o). 361.08/46.39 thf(decl_295, type, powersetTE1: $o). 361.08/46.39 thf(decl_296, type, complementTI1: $o). 361.08/46.39 thf(decl_297, type, complementTE1: $o). 361.08/46.39 thf(decl_298, type, binintersectTELcontra: $o). 361.08/46.39 thf(decl_299, type, binintersectTERcontra: $o). 361.08/46.39 thf(decl_300, type, contrasubsetT: $o). 361.08/46.39 thf(decl_301, type, contrasubsetT1: $o). 361.08/46.39 thf(decl_302, type, contrasubsetT2: $o). 361.08/46.39 thf(decl_303, type, contrasubsetT3: $o). 361.08/46.39 thf(decl_304, type, doubleComplementI1: $o). 361.08/46.39 thf(decl_305, type, doubleComplementE1: $o). 361.08/46.39 thf(decl_306, type, doubleComplementSub1: $o). 361.08/46.39 thf(decl_307, type, doubleComplementSub2: $o). 361.08/46.39 thf(decl_308, type, doubleComplementEq: $o). 361.08/46.39 thf(decl_309, type, complementTnotintersectT: $o). 361.08/46.39 thf(decl_310, type, complementImpComplementIntersect: $o). 361.08/46.39 thf(decl_311, type, complementSubsetComplementIntersect: $o). 361.08/46.39 thf(decl_312, type, complementInPowersetComplementIntersect: $o). 361.08/46.39 thf(decl_313, type, contraSubsetComplement: $o). 361.08/46.39 thf(decl_314, type, complementTcontraSubset: $o). 361.08/46.39 thf(decl_315, type, binunionTILcontra: $o). 361.08/46.39 thf(decl_316, type, binunionTIRcontra: $o). 361.08/46.39 thf(decl_317, type, inIntersectImpInUnion: $o). 361.08/46.39 thf(decl_318, type, inIntersectImpInUnion2: $o). 361.08/46.39 thf(decl_319, type, inIntersectImpInIntersectUnions: $o). 361.08/46.39 thf(decl_320, type, intersectInPowersetIntersectUnions: $o). 361.08/46.39 thf(decl_321, type, inComplementUnionImpNotIn1: $o). 361.08/46.39 thf(decl_322, type, inComplementUnionImpInComplement1: $o). 361.08/46.39 thf(decl_323, type, binunionTE: $o). 361.08/46.39 thf(decl_324, type, binunionTEcontra: $o). 361.08/46.39 thf(decl_325, type, demorgan2a1: $o). 361.08/46.39 thf(decl_326, type, complementUnionInPowersetComplement: $o). 361.08/46.39 thf(decl_327, type, demorgan2a2: $o). 361.08/46.39 thf(decl_328, type, demorgan1a: $o). 361.08/46.39 thf(decl_329, type, demorgan1b: $o). 361.08/46.39 thf(decl_330, type, demorgan1: $o). 361.08/46.39 thf(decl_331, type, demorgan2a: $o). 361.08/46.39 thf(decl_332, type, demorgan2b2: $o). 361.08/46.39 thf(decl_333, type, demorgan2b: $o). 361.08/46.39 thf(decl_334, type, demorgan2: $o). 361.08/46.39 thf(decl_335, type, woz13rule0: $o). 361.08/46.39 thf(decl_336, type, woz13rule1: $o). 361.08/46.39 thf(decl_337, type, woz13rule2: $o). 361.08/46.39 thf(decl_338, type, woz13rule3: $o). 361.08/46.39 thf(decl_339, type, woz13rule4: $o). 361.08/46.39 thf(decl_340, type, woz1_1: $o). 361.08/46.39 thf(decl_341, type, woz1_2: $o). 361.08/46.39 thf(decl_342, type, woz1_3: $o). 361.08/46.39 thf(decl_343, type, woz1_4: $o). 361.08/46.39 thf(decl_344, type, woz1_5: $o). 361.08/46.39 thf(decl_345, type, breln1: $i > $i > $o). 361.08/46.39 thf(decl_346, type, breln1all2: $o). 361.08/46.39 thf(decl_347, type, breln1Set: $i > $i). 361.08/46.39 thf(decl_348, type, breln1SetBreln1: $o). 361.08/46.39 thf(decl_355, type, choice2fnsingleton: $o). 361.08/46.39 thf(decl_356, type, setOfPairsIsBReln1: $o). 361.08/46.39 thf(decl_357, type, breln1all1: $o). 361.08/46.39 thf(decl_358, type, subbreln1: $o). 361.08/46.39 thf(decl_359, type, eqbreln1: $o). 361.08/46.39 thf(decl_360, type, breln1invset: $i > $i > $i). 361.08/46.39 thf(decl_361, type, breln1invprop: $o). 361.08/46.39 thf(decl_362, type, breln1invI: $o). 361.08/46.39 thf(decl_363, type, breln1invE: $o). 361.08/46.39 thf(decl_364, type, breln1compset: $i > $i > $i > $i). 361.08/46.39 thf(decl_365, type, breln1compprop: $o). 361.08/46.39 thf(decl_366, type, breln1compI: $o). 361.08/46.39 thf(decl_367, type, breln1compE: $o). 361.08/46.39 thf(decl_368, type, breln1compEex: $o). 361.08/46.39 thf(decl_369, type, breln1unionprop: $o). 361.08/46.39 thf(decl_370, type, breln1unionIL: $o). 361.08/46.39 thf(decl_371, type, breln1unionIR: $o). 361.08/46.39 thf(decl_372, type, breln1unionI: $o). 361.08/46.39 thf(decl_373, type, breln1unionE: $o). 361.08/46.39 thf(decl_374, type, breln1unionEcases: $o). 361.08/46.39 thf(decl_375, type, breln1unionCommutes: $o). 361.08/46.39 thf(decl_376, type, woz2Ex: $o). 361.08/46.39 thf(decl_377, type, woz2W: $o). 361.08/46.39 thf(decl_378, type, woz2A: $o). 361.08/46.39 thf(decl_379, type, woz2B: $o). 361.08/46.39 thf(decl_380, type, image1Ex: $o). 361.08/46.39 thf(decl_381, type, image1Ex1: $o). 361.08/46.39 thf(decl_382, type, image1: $i > ($i > $i) > $i). 361.08/46.39 thf(decl_383, type, image1Equiv: $o). 361.08/46.39 thf(decl_384, type, image1E: $o). 361.08/46.39 thf(decl_385, type, image1I: $o). 361.08/46.39 thf(decl_386, type, injective: $i > $i > $i > $o). 361.08/46.39 thf(decl_387, type, injFuncSet: $i > $i > $i). 361.08/46.39 thf(decl_388, type, injFuncInInjFuncSet: $o). 361.08/46.39 thf(decl_389, type, injFuncSetFuncIn: $o). 361.08/46.39 thf(decl_390, type, injFuncSetFuncInj: $o). 361.08/46.39 thf(decl_391, type, surjective: $i > $i > $i > $o). 361.08/46.39 thf(decl_392, type, surjFuncSet: $i > $i > $i). 361.08/46.39 thf(decl_393, type, surjFuncSetFuncIn: $o). 361.08/46.39 thf(decl_394, type, surjFuncSetFuncSurj: $o). 361.08/46.39 thf(decl_395, type, leftInvIsSurj: $o). 361.08/46.39 thf(decl_396, type, surjCantorThm: $o). 361.08/46.39 thf(decl_397, type, epred1_0: $o). 361.08/46.39 thf(decl_398, type, esk1_2: $i > $i > $i). 361.08/46.39 thf(decl_399, type, esk2_2: $i > $i > $i). 361.08/46.39 thf(decl_400, type, esk3_2: $i > $i > $i). 361.08/46.39 thf(decl_401, type, esk4_1: $i > $i). 361.08/46.39 thf(decl_402, type, esk5_2: ($i > $i > $o) > $i > $i). 361.08/46.39 thf(decl_403, type, esk6_2: ($i > $i > $o) > $i > $i). 361.08/46.39 thf(decl_404, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 361.08/46.39 thf(decl_405, type, esk8_1: $i > $i). 361.08/46.39 thf(decl_406, type, esk9_1: ($i > $o) > $i). 361.08/46.39 thf(decl_407, type, esk10_1: ($i > $o) > $i). 361.08/46.39 thf(decl_408, type, esk11_2: $i > $i > $i). 361.08/46.39 thf(decl_409, type, esk12_2: $i > $i > $i). 361.08/46.39 thf(decl_410, type, esk13_1: $i > $i). 361.08/46.39 thf(decl_411, type, esk14_1: $i > $i). 361.08/46.39 thf(decl_412, type, esk15_1: $i > $i). 361.08/46.39 thf(decl_413, type, esk16_2: $i > $i > $i). 361.08/46.39 thf(decl_414, type, esk17_3: $i > $i > $o > $i). 361.08/46.39 thf(decl_415, type, esk18_1: ($i > $o) > $i). 361.08/46.39 thf(decl_416, type, esk19_1: $i > $i). 361.08/46.39 thf(decl_417, type, esk20_2: $i > ($i > $o) > $i). 361.08/46.39 thf(decl_418, type, esk21_2: $i > ($i > $o) > $i). 361.08/46.39 thf(decl_419, type, esk22_2: $i > ($i > $o) > $i). 361.08/46.39 thf(decl_420, type, esk23_2: $i > ($i > $o) > $i). 361.08/46.39 thf(decl_421, type, esk24_2: $i > ($i > $o) > $i). 361.08/46.39 thf(decl_422, type, esk25_2: $i > ($i > $o) > $i). 361.08/46.39 thf(decl_423, type, esk26_2: ($i > $o) > $i > $i). 361.08/46.39 thf(decl_424, type, esk27_1: ($i > $o) > $i). 361.08/46.39 thf(decl_425, type, esk28_1: ($i > $o) > $i). 361.08/46.39 thf(decl_426, type, esk29_2: ($i > $o) > $i > $i). 361.08/46.39 thf(decl_427, type, esk30_2: ($i > $o) > ($i > $o) > $i). 361.08/46.39 thf(decl_428, type, esk31_2: ($i > $o) > ($i > $o) > $i). 361.08/46.39 thf(decl_429, type, esk32_2: ($i > $o) > ($i > $o) > $i). 361.08/46.39 thf(decl_430, type, esk33_2: ($i > $o) > ($i > $o) > $i). 361.08/46.39 thf(decl_431, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i). 361.08/46.39 thf(decl_432, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i). 361.08/46.39 thf(decl_433, type, esk36_2: $i > $i > $i). 361.08/46.39 thf(decl_434, type, esk37_2: $i > $i > $i). 361.08/46.39 thf(decl_435, type, esk38_2: $i > $i > $i). 361.08/46.39 thf(decl_436, type, esk39_3: $i > $i > $i > $i). 361.08/46.39 thf(decl_437, type, esk40_3: $i > $i > $i > $i). 361.08/46.39 thf(decl_438, type, esk41_2: $i > $i > $i). 361.08/46.39 thf(decl_439, type, esk42_2: $i > ($i > $o) > $i). 361.08/46.39 thf(decl_440, type, esk43_2: $i > ($i > $o) > $i). 361.08/46.39 thf(decl_441, type, esk44_2: $i > ($i > $o) > $i). 361.08/46.39 thf(decl_442, type, esk45_3: $i > ($i > $o) > $i > $i). 361.08/46.39 thf(decl_443, type, esk46_2: $i > ($i > $o) > $i). 361.08/46.39 thf(decl_444, type, esk47_2: $i > ($i > $o) > $i). 361.08/46.39 thf(decl_445, type, esk48_3: $i > $i > ($i > $i) > $i). 361.08/46.39 thf(decl_446, type, esk49_3: $i > $i > ($i > $i) > $i). 361.08/46.39 thf(decl_447, type, esk50_3: $i > $i > ($i > $i) > $i). 361.08/46.39 thf(decl_448, type, esk51_4: $i > $i > $i > ($i > $o) > $i). 361.08/46.39 thf(decl_449, type, esk52_4: $i > $i > $i > ($i > $o) > $i). 361.08/46.39 thf(decl_450, type, esk53_4: $i > $i > $i > ($i > $o) > $i). 361.08/46.39 thf(decl_451, type, esk54_4: $i > $i > $i > ($i > $o) > $i). 361.08/46.39 thf(decl_452, type, esk55_4: $i > $i > $i > $i > $i). 361.08/46.39 thf(decl_453, type, esk56_4: $i > $i > $i > $i > $i). 361.08/46.39 thf(decl_454, type, esk57_4: $i > $i > $i > $i > $i). 361.08/46.39 thf(decl_455, type, esk58_4: $i > $i > $i > $i > $i). 361.08/46.39 thf(decl_456, type, esk59_4: $i > $i > $i > $i > $i). 361.08/46.39 thf(decl_457, type, esk60_4: $i > $i > $i > $i > $i). 361.08/46.39 thf(decl_458, type, esk61_4: $i > $i > $i > $i > $i). 361.08/46.39 thf(decl_459, type, esk62_4: $i > $i > $i > $i > $i). 361.08/46.39 thf(decl_460, type, esk63_4: $i > $i > $i > $i > $i). 361.08/46.39 thf(decl_461, type, esk64_3: $i > $i > ($i > $i) > $i). 361.08/46.39 thf(decl_462, type, esk65_3: $i > $i > ($i > $i) > $i). 361.08/46.39 thf(decl_463, type, esk66_3: $i > $i > ($i > $i) > $i). 361.08/46.39 thf(decl_464, type, esk67_3: $i > $i > $i > $i). 361.08/46.39 thf(decl_465, type, esk68_3: $i > $i > $i > $i). 361.08/46.39 thf(decl_466, type, esk69_3: $i > $i > $i > $i). 361.08/46.39 thf(decl_467, type, esk70_3: $i > $i > $i > $i). 361.08/46.39 thf(decl_468, type, esk71_3: $i > $i > ($i > $o) > $i). 361.08/46.39 thf(decl_469, type, esk72_3: $i > $i > ($i > $o) > $i). 361.08/46.39 thf(decl_470, type, esk73_3: $i > $i > ($i > $o) > $i). 361.08/46.39 thf(decl_471, type, esk74_3: $i > $i > ($i > $o) > $i). 361.08/46.39 thf(decl_472, type, esk75_3: $i > $i > $i > $i). 361.08/46.39 thf(decl_473, type, esk76_3: $i > $i > $i > $i). 361.08/46.39 thf(decl_474, type, esk77_3: $i > $i > $i > $i). 361.08/46.39 thf(decl_475, type, esk78_3: $i > $i > $i > $i). 361.08/46.39 thf(decl_476, type, esk79_3: $i > $i > $i > $i). 361.08/46.39 thf(decl_477, type, esk80_3: $i > $i > $i > $i). 361.08/46.39 thf(decl_478, type, esk81_5: $i > $i > $i > $i > $i > $i). 361.08/46.39 thf(decl_479, type, esk82_6: $i > $i > $i > $i > $i > $o > $i). 361.08/46.39 thf(decl_480, type, esk83_2: $i > ($i > $i) > $i). 361.08/46.39 thf(decl_481, type, esk84_3: $i > ($i > $i) > $i > $i). 361.08/46.39 thf(decl_482, type, esk85_3: $i > ($i > $i) > $i > $i). 361.08/46.39 thf(decl_483, type, esk86_3: $i > ($i > $i) > $i > $i). 361.08/46.39 thf(decl_484, type, esk87_3: $i > $i > ($i > $i) > $i). 361.08/46.39 thf(decl_485, type, esk88_4: $i > $i > ($i > $i) > $i > $i). 361.08/46.39 thf(decl_486, type, esk89_0: $i). 361.08/46.39 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', nonempty)). 361.08/46.39 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', nonemptyI)). 361.08/46.39 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', sepInPowerset)). 361.08/46.39 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', singletonprop)). 361.08/46.39 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', kfstsingleton)). 361.08/46.39 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', exu__Cong)). 361.08/46.39 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', exuE3u)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', exuI2)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', ksndsingleton)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', exuI1)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', emptyE1)). 361.08/46.39 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', nonemptyImpWitness)). 361.08/46.39 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', dpsetconstrI)). 361.08/46.39 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', dpsetconstrEL2)). 361.08/46.39 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', funcImageSingleton)). 361.08/46.39 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', nonemptyE1)). 361.08/46.39 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', exuE3e)). 361.08/46.39 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', exuE1)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', lamProp)). 361.08/46.39 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', dsetconstrEL)). 361.08/46.39 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', dsetconstrI)). 361.08/46.39 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', lamp)). 361.08/46.39 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', descrp)). 361.08/46.39 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', replAx)). 361.08/46.39 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', lam2lamEq)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', eta2)). 361.08/46.39 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', iffalseProp1)). 361.08/46.39 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', iftrueProp2)). 361.08/46.39 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', ifSingleton)). 361.08/46.39 thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setOfPairsIsBReln1)). 361.08/46.39 thf(image1Ex1, axiom, ((image1Ex1)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', image1Ex1)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', image1Equiv)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', image1I)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', image1E)). 361.08/46.39 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', iftrueProp1)). 361.08/46.39 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', iffalseProp2)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', beta2)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', eta1)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', beta1)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', ex1E2)). 361.08/46.39 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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', lam2p)). 361.08/46.39 thf(apProp, axiom, ((apProp)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', apProp)). 361.08/46.39 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:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', dpsetconstrER)). 361.08/46.39 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', dpsetconstrEL1)). 361.08/46.39 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', dpsetconstrERa)). 361.08/46.39 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setOfPairsIsBReln)). 361.08/46.39 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', dpsetconstrSub)). 361.08/46.39 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', ex1I2)). 361.08/46.39 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', ex1I)). 361.08/46.39 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', ex1E1)). 361.08/46.39 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', sepSubset)). 361.08/46.39 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', dsetconstr__Cong)). 361.08/46.39 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', descr__Cong)). 361.08/46.39 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', exuEu)). 361.08/46.39 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', exuI3)). 361.08/46.39 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', exuE2)). 361.08/46.39 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setoftrueEq)). 361.08/46.39 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', nonemptyI1)). 361.08/46.39 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setbeta)). 361.08/46.39 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', dsetconstrER)). 361.08/46.39 thf(foundation2, conjecture, ((setextAx)=>(((((setunionAx)=>(((omegaSAx)=>((omegaIndAx)=>((((((((dsetconstrER)=>(((((emptysetimpfalse)=>(((((emptyI)=>(((setbeta)=>((((nonemptyI1)=>(((emptyinunitempty)=>((setadjoinIR)=>((((setoftrueEq)=>(((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((((subPowSU)=>((exuE2)=>((((notinsingleton)=>((((upairsetE)=>((upairsetIL)=>((((vacuousDall)=>((((quantDeMorgan3)=>((quantDeMorgan4)=>((((notdexE)=>((notdallE)=>(((exuI3)=>((((((((setadjoin__Cong)=>(((setunion__Cong)=>(((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>(((eqimpsubset1)=>(((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>(((((subsetTrans)=>(((setadjoinSub2)=>((((subsetemptysetimpeq)=>(((powersetE1)=>((inPowerset)=>((powersetsubset)=>(((sepSubset)=>((((((binunionE)=>((binunionLsub)=>(((binintersectI)=>((((binintersectLsub)=>(((binintersectSubset3)=>(((disjointsetsI1)=>((((binintersectSubset1)=>(((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>(((setminusLsub)=>(((symdiffE)=>((((symdiffIneg1)=>(((secondinupair)=>((setukpairIL)=>(((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((((upairset2E)=>(((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>(((cartprodmempair)=>(((setunionsingleton1)=>((setunionsingleton2)=>(((singletonprop)=>(((((singletonsuniq)=>(((kfstsingleton)=>(((kfstpairEq)=>((cartprodfstin)=>((((((((setukpairinjR2)=>(((ksndsingleton)=>((((((cartprodpairmemER)=>((((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((((((dpsetconstrEL2)=>(((funcImageSingleton)=>(((app)=>((infuncsetfunc)=>((((lamProp)=>((lamp)=>((((brelnall2)=>((((((funcextLem)=>(((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((((((lam2lamEq)=>(((eta2)=>((iffalseProp1)=>((((iftrueProp2)=>((ifSingleton)=>(((theeq)=>((((iftrueorfalse)=>(((binunionT_lem)=>((powersetT_lem)=>(((complementT_lem)=>(((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>(((((contrasubsetT1)=>((((((doubleComplementSub1)=>(((doubleComplementEq)=>(((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>(((((((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>(((inComplementUnionImpNotIn1)=>((((binunionTEcontra)=>((demorgan2a1)=>((((demorgan1a)=>(((demorgan1)=>((demorgan2a)=>(((((woz13rule0)=>((((((woz1_1)=>((woz1_2)=>((((woz1_5)=>((((choice2fnsingleton)=>((setOfPairsIsBReln1)=>((breln1all1)=>(((eqbreln1)=>((breln1invprop)=>(((breln1invE)=>(((breln1compI)=>((breln1compE)=>((breln1compEex)=>((breln1unionprop)=>((breln1unionIL)=>(((((breln1unionEcases)=>((((woz2W)=>(((woz2B)=>((image1Ex)=>((image1Ex1)=>((image1Equiv)=>(((image1I)=>((injFuncInInjFuncSet)=>(((((surjFuncSetFuncSurj)=>(((surjCantorThm)=>![X4:$i]:(((nonempty @ X4)=>?[X21:$i]:((((binintersect @ X21 @ X4)=(emptyset))&(in @ X21 @ X4))))))<=(leftInvIsSurj)))<=(surjFuncSetFuncIn))<=(injFuncSetFuncInj))<=(injFuncSetFuncIn))))<=(image1E))))))<=(woz2A)))<=(woz2Ex))<=(breln1unionCommutes)))<=(breln1unionE))<=(breln1unionI))<=(breln1unionIR)))))))<=(breln1compprop)))<=(breln1invI))))<=(subbreln1)))))<=(breln1SetBreln1))<=(breln1all2)))<=(woz1_4))<=(woz1_3))))<=(woz13rule4))<=(woz13rule3))<=(woz13rule2))<=(woz13rule1)))<=(demorgan2))<=(demorgan2b))<=(demorgan2b2))))<=(demorgan1b)))<=(demorgan2a2))<=(complementUnionInPowersetComplement))))<=(binunionTE))<=(inComplementUnionImpInComplement1)))<=(intersectInPowersetIntersectUnions)))))<=(binunionTIRcontra))<=(binunionTILcontra))<=(complementTcontraSubset))<=(contraSubsetComplement))<=(complementInPowersetComplementIntersect))))<=(complementTnotintersectT)))<=(doubleComplementSub2)))<=(doubleComplementE1))<=(doubleComplementI1))<=(contrasubsetT3))<=(contrasubsetT2)))<=(contrasubsetT))<=(binintersectTERcontra))<=(binintersectTELcontra)))))))<=(setextT)))<=(setminusT_lem))))<=(binintersectT_lem)))<=(iffalse))<=(iftrue)))<=(ifp))))<=(iftrueProp1))<=(iffalseProp2))))<=(beta2)))<=(eta1))<=(beta1))<=(ap2apEq2))<=(ap2apEq1))))))<=(funcGraphProp4)))<=(funcGraphProp2))<=(funcGraphProp3))<=(funcGraphProp1))<=(ex1E2)))<=(brelnall1))<=(lam2p))))<=(funcinfuncset))<=(ap2p))))<=(apProp)))<=(dpsetconstrER)))<=(dpsetconstrEL1))<=(dpsetconstrERa))<=(setOfPairsIsBReln))<=(dpsetconstrSub)))))<=(cartprodfstpairEq))<=(cartprodmempaircEq)))<=(cartprodpairmemEL))<=(cartprodsndin))<=(kpairsurjEq))<=(ksndpairEq)))<=(setukpairinjR)))<=(upairequniteq))<=(setukpairinjR1))<=(setukpairinjR12))<=(setukpairinjR11))<=(setukpairinjL))<=(setukpairinjL2))))<=(theprop)))<=(setukpairinjL1)))<=(ex1I2))<=(ex1I))<=(ex1E1)))<=(setunionsingleton))))<=(setunionE2)))<=(cartprodmempair1)))))))<=(upairsubunion)))<=(singletoninpowunion))<=(singletoninpowerset)))))<=(setukpairIR))))<=(symdiffIneg2)))<=(symdiffI2))<=(symdiffI1)))<=(setminusSubset1)))<=(setminusIRneg)))))))))<=(bs114d)))<=(binintersectSubset4))<=(binintersectRsub)))<=(binintersectER)))<=(binintersectSubset2)))<=(binintersectEL))<=(binintersectSubset5)))<=(binunionRsub))))<=(binunionEcases))<=(binunionIR))<=(upairset2IR))<=(binunionIL)))<=(sepInPowerset)))))<=(powersetI1)))<=(setextsub))<=(subset2powerset)))<=(setadjoinSub)))<=(subsetRefl))<=(notequalI2))<=(notequalI1))))))<=(subsetI2)))<=(eqimpsubset2))))))<=(omega__Cong)))<=(powerset__Cong)))<=(emptyset__Cong))<=(exu__Cong))<=(exuE3u))<=(in__Cong))<=(inCongP))<=(exuI2)))<=(exuI1))))<=(prop2set2propI))<=(prop2setI))))<=(quantDeMorgan2))<=(quantDeMorgan1)))<=(emptyE1))<=(upairsetIR))))<=(singletonsswitch))<=(eqinunit)))<=(uniqinunit))<=(nonemptyImpWitness))))<=(setunionE))<=(setunionI)))))<=(powersetI)))<=(setadjoinOr))<=(setadjoinE))))<=(setadjoinIL)))<=(nonemptyI))<=(nonemptyE1)))<=(noeltsimpempty)))<=(setext))<=(exuE3e))<=(notinemptyset)))<=(emptysetE))<=(prop2setE))<=(exuE1)))<=(dsetconstrEL))<=(dsetconstrI))<=(descrp))<=(wellorderingAx))<=(foundationAx))<=(replAx))))<=(omega0Ax)))<=(powersetAx))<=(setadjoinAx))<=(emptysetAx))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', foundation2)). 361.08/46.39 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setukpairinjR2)). 361.08/46.39 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', emptysetAx)). 361.08/46.39 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binunionRsub)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', ubforcartprodlem1)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', binunionEcases)). 361.08/46.39 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binunionIR)). 361.08/46.39 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', upairset2IR)). 361.08/46.39 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setunionsingleton2)). 361.08/46.39 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binunionIL)). 361.08/46.39 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', powersetI1)). 361.08/46.39 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setextsub)). 361.08/46.39 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', subset2powerset)). 361.08/46.39 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', singletonsuniq)). 361.08/46.39 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setadjoinSub)). 361.08/46.39 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', subsetRefl)). 361.08/46.39 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', notequalI2)). 361.08/46.39 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', notequalI1)). 361.08/46.39 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', subsetI2)). 361.08/46.39 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', kfstpairEq)). 361.08/46.39 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', eqimpsubset2)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', ubforcartprodlem2)). 361.08/46.39 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', omega__Cong)). 361.08/46.39 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', powerset__Cong)). 361.08/46.39 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', cartprodfstin)). 361.08/46.39 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', emptyset__Cong)). 361.08/46.39 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', eqbreln)). 361.08/46.39 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', in__Cong)). 361.08/46.39 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', inCongP)). 361.08/46.39 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', prop2setI)). 361.08/46.39 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', quantDeMorgan2)). 361.08/46.39 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', ubforcartprodlem3)). 361.08/46.39 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', quantDeMorgan1)). 361.08/46.39 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', cartprodpairmemER)). 361.08/46.39 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', upairsetIR)). 361.08/46.39 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', cartprodsndpairEq)). 361.08/46.39 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', singletonsswitch)). 361.08/46.39 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', eqinunit)). 361.08/46.39 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', uniqinunit)). 361.08/46.39 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', cartprodpairsurjEq)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', setunionE)). 361.08/46.39 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setunionI)). 361.08/46.39 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', powersetI)). 361.08/46.39 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setadjoinOr)). 361.08/46.39 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setadjoinE)). 361.08/46.39 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setadjoinIL)). 361.08/46.39 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', noeltsimpempty)). 361.08/46.39 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', app)). 361.08/46.39 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setext)). 361.08/46.39 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', notinemptyset)). 361.08/46.39 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', infuncsetfunc)). 361.08/46.39 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', emptysetE)). 361.08/46.39 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', prop2setE)). 361.08/46.39 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', wellorderingAx)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', foundationAx)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', brelnall2)). 361.08/46.39 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', omega0Ax)). 361.08/46.39 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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', funcextLem)). 361.08/46.39 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', powersetAx)). 361.08/46.39 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setadjoinAx)). 361.08/46.39 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', subbreln)). 361.08/46.39 thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', woz13rule0)). 361.08/46.39 thf(woz1_1, axiom, ((woz1_1)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', woz1_1)). 361.08/46.39 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', funcext)). 361.08/46.39 thf(funcext2, axiom, ((funcext2)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', funcext2)). 361.08/46.39 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', theeq)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', cartprodpairin)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', iftrueorfalse)). 361.08/46.39 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binunionT_lem)). 361.08/46.39 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', cartprodmempair)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', powersetT_lem)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', complementT_lem)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', subsetTI)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', powersetTI1)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', powersetTE1)). 361.08/46.39 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', complementTI1)). 361.08/46.39 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', complementTE1)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', contrasubsetT1)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', doubleComplementSub1)). 361.08/46.39 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', doubleComplementEq)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', complementImpComplementIntersect)). 361.08/46.39 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', complementSubsetComplementIntersect)). 361.08/46.39 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', inIntersectImpInUnion)). 361.08/46.39 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', inIntersectImpInUnion2)). 361.08/46.39 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', inIntersectImpInIntersectUnions)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', inComplementUnionImpNotIn1)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', binunionTEcontra)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', demorgan2a1)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', demorgan1a)). 361.08/46.39 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', demorgan1)). 361.08/46.39 thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', demorgan2a)). 361.08/46.39 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', doubleComplementI1)). 361.08/46.39 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', contrasubsetT3)). 361.08/46.39 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', contrasubsetT2)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', contrasubsetT)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', binintersectTERcontra)). 361.08/46.39 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:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', woz1_2)). 361.08/46.39 thf(woz1_5, axiom, ((woz1_5)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', woz1_5)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', breln1all1)). 361.08/46.39 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:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', eqbreln1)). 361.08/46.39 thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', breln1invprop)). 361.08/46.39 thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', breln1invE)). 361.08/46.39 thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', breln1compI)). 361.08/46.39 thf(breln1compE, axiom, ((breln1compE)<=>![X4:$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:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35))))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', breln1compE)). 361.08/46.39 thf(breln1compEex, axiom, ((breln1compEex)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', breln1compEex)). 361.08/46.39 thf(breln1unionprop, axiom, ((breln1unionprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', breln1unionprop)). 361.08/46.39 thf(breln1unionIL, axiom, ((breln1unionIL)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', breln1unionIL)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', breln1unionEcases)). 361.08/46.39 thf(woz2W, axiom, ((woz2W)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((breln1invset @ X4 @ (breln1compset @ X4 @ X33 @ X35))=(breln1compset @ X4 @ (breln1invset @ X4 @ X35) @ (breln1invset @ X4 @ X33)))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', woz2W)). 361.08/46.39 thf(woz2B, axiom, ((woz2B)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X35))) @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X33)))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', woz2B)). 361.08/46.39 thf(image1Ex, axiom, ((image1Ex)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', image1Ex)). 361.08/46.39 thf(injFuncInInjFuncSet, axiom, ((injFuncInInjFuncSet)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((injective @ X4 @ X5 @ X29)=>(in @ X29 @ (injFuncSet @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', injFuncInInjFuncSet)). 361.08/46.39 thf(surjFuncSetFuncSurj, axiom, ((surjFuncSetFuncSurj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X2 @ X3))=>(surjective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', surjFuncSetFuncSurj)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', surjCantorThm)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', leftInvIsSurj)). 361.08/46.39 thf(surjFuncSetFuncIn, axiom, ((surjFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', surjFuncSetFuncIn)). 361.08/46.39 thf(injFuncSetFuncInj, axiom, ((injFuncSetFuncInj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X2 @ X3))=>(injective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', injFuncSetFuncInj)). 361.08/46.39 thf(injFuncSetFuncIn, axiom, ((injFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', injFuncSetFuncIn)). 361.08/46.39 thf(woz2A, axiom, ((woz2A)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1compset @ X4 @ X33 @ X56) @ (breln1compset @ X4 @ X35 @ X56)))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', woz2A)). 361.08/46.39 thf(woz2Ex, axiom, ((woz2Ex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>((X33)=(breln1invset @ X4 @ (breln1invset @ X4 @ X33)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', woz2Ex)). 361.08/46.39 thf(breln1unionCommutes, axiom, ((breln1unionCommutes)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((binunion @ X33 @ X35)=(binunion @ X35 @ X33))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', breln1unionCommutes)). 361.08/46.39 thf(breln1unionE, axiom, ((breln1unionE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', breln1unionE)). 361.08/46.39 thf(breln1unionI, axiom, ((breln1unionI)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', breln1unionI)). 361.08/46.39 thf(breln1unionIR, axiom, ((breln1unionIR)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', breln1unionIR)). 361.08/46.39 thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', breln1compprop)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', breln1invI)). 361.08/46.39 thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', subbreln1)). 361.08/46.39 thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', breln1SetBreln1)). 361.08/46.39 thf(breln1all2, axiom, ((breln1all2)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', breln1all2)). 361.08/46.39 thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', woz1_4)). 361.08/46.39 thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', woz1_3)). 361.08/46.39 thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', woz13rule4)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', woz13rule3)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', woz13rule2)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', woz13rule1)). 361.08/46.39 thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', demorgan2)). 361.08/46.39 thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', demorgan2b)). 361.08/46.39 thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', demorgan2b2)). 361.08/46.39 thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', demorgan1b)). 361.08/46.39 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', demorgan2a2)). 361.08/46.39 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', complementUnionInPowersetComplement)). 361.08/46.39 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binunionTE)). 361.08/46.39 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', inComplementUnionImpInComplement1)). 361.08/46.39 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', intersectInPowersetIntersectUnions)). 361.08/46.39 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binunionTIRcontra)). 361.08/46.39 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binunionTILcontra)). 361.08/46.39 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', complementTcontraSubset)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', contraSubsetComplement)). 361.08/46.39 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', complementInPowersetComplementIntersect)). 361.08/46.39 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', complementTnotintersectT)). 361.08/46.39 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', doubleComplementSub2)). 361.08/46.39 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', doubleComplementE1)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', binintersectTELcontra)). 361.08/46.39 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setextT)). 361.08/46.39 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', setminusT_lem)). 361.08/46.39 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binintersectT_lem)). 361.08/46.39 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', iffalse)). 361.08/46.39 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', iftrue)). 361.08/46.39 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', ifp)). 361.08/46.39 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', ap2apEq2)). 361.08/46.39 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', ap2apEq1)). 361.08/46.39 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', funcGraphProp4)). 361.08/46.39 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', funcGraphProp2)). 361.08/46.39 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', funcGraphProp3)). 361.08/46.39 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', funcGraphProp1)). 361.08/46.39 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', brelnall1)). 361.08/46.39 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', funcinfuncset)). 361.08/46.39 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', ap2p)). 361.08/46.39 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', cartprodfstpairEq)). 361.08/46.39 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', cartprodmempaircEq)). 361.08/46.39 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', cartprodpairmemEL)). 361.08/46.39 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', cartprodsndin)). 361.08/46.39 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', kpairsurjEq)). 361.08/46.39 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', ksndpairEq)). 361.08/46.39 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setukpairinjR)). 361.08/46.39 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', upairequniteq)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', setukpairinjR1)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', setukpairinjR12)). 361.08/46.39 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setukpairinjR11)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', setukpairinjL)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', setukpairinjL2)). 361.08/46.39 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', theprop)). 361.08/46.39 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.2BgcLvWq1B/E---3.1_5214.p', setukpairinjL1)). 361.08/46.39 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setunionsingleton)). 361.08/46.39 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setunionE2)). 361.08/46.39 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', cartprodmempair1)). 361.08/46.39 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', upairsubunion)). 361.08/46.39 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', singletoninpowunion)). 361.08/46.39 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', singletoninpowerset)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', setukpairIR)). 361.08/46.39 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', symdiffIneg2)). 361.08/46.39 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', symdiffI2)). 361.08/46.39 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', symdiffI1)). 361.08/46.39 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setminusSubset1)). 361.08/46.39 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setminusIRneg)). 361.08/46.39 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', bs114d)). 361.08/46.39 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binintersectSubset4)). 361.08/46.39 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binintersectRsub)). 361.08/46.39 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binintersectER)). 361.08/46.39 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binintersectSubset2)). 361.08/46.39 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binintersectEL)). 361.08/46.39 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binintersectSubset5)). 361.08/46.39 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setunionsingleton1)). 361.08/46.39 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', upairinpowunion)). 361.08/46.39 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', upairset2E)). 361.08/46.39 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', singletonsubset)). 361.08/46.39 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', kpairp)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', kpairiskpair)). 361.08/46.39 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.2BgcLvWq1B/E---3.1_5214.p', setukpairIL)). 361.08/46.39 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', secondinupair)). 361.08/46.39 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', symdiffIneg1)). 361.08/46.39 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', symdiffE)). 361.08/46.39 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setminusLsub)). 361.08/46.39 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setminusILneg)). 361.08/46.39 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setminusELneg)). 361.08/46.39 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setminusERneg)). 361.08/46.39 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setminusSubset2)). 361.08/46.39 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setminusER)). 361.08/46.39 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setminusEL)). 361.08/46.39 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setminusI)). 361.08/46.39 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binintersectSubset1)). 361.08/46.39 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', disjointsetsI1)). 361.08/46.39 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binintersectSubset3)). 361.08/46.39 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binintersectLsub)). 361.08/46.39 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binintersectI)). 361.08/46.39 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binunionLsub)). 361.08/46.39 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', binunionE)). 361.08/46.39 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', powersetsubset)). 361.08/46.39 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', inPowerset)). 361.08/46.39 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', powersetE1)). 361.08/46.39 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', subsetemptysetimpeq)). 361.08/46.39 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setadjoinSub2)). 361.08/46.39 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', subsetTrans)). 361.08/46.39 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', notsubsetI)). 361.08/46.39 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', subsetE2)). 361.08/46.39 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', subsetE)). 361.08/46.39 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', emptysetsubset)). 361.08/46.39 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', eqimpsubset1)). 361.08/46.39 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', subsetI1)). 361.08/46.39 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setunion__Cong)). 361.08/46.39 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setadjoin__Cong)). 361.08/46.39 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', notdallE)). 361.08/46.39 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', notdexE)). 361.08/46.39 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', quantDeMorgan4)). 361.08/46.39 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', quantDeMorgan3)). 361.08/46.39 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', vacuousDall)). 361.08/46.39 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', upairsetIL)). 361.08/46.39 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', upairsetE)). 361.08/46.39 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', notinsingleton)). 361.08/46.39 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', subPowSU)). 361.08/46.39 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', powersetE)). 361.08/46.39 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', emptyInPowerset)). 361.08/46.39 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', emptyinPowerset)). 361.08/46.39 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setadjoinIR)). 361.08/46.39 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', emptyinunitempty)). 361.08/46.39 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', emptyI)). 361.08/46.39 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', emptysetimpfalse)). 361.08/46.39 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.2BgcLvWq1B/E---3.1_5214.p', omegaIndAx)). 361.08/46.39 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', omegaSAx)). 361.08/46.39 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setunionAx)). 361.08/46.39 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.2BgcLvWq1B/E---3.1_5214.p', setextAx)). 361.08/46.39 thf(c_0_321, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 361.08/46.39 thf(c_0_322, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 361.08/46.39 thf(c_0_323, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 361.08/46.39 thf(c_0_324, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 361.08/46.39 thf(c_0_325, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 361.08/46.39 thf(c_0_326, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 361.08/46.39 thf(c_0_327, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 361.08/46.39 thf(c_0_328, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 361.08/46.39 thf(c_0_329, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 361.08/46.39 thf(c_0_330, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 361.08/46.39 thf(c_0_331, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 361.08/46.39 thf(c_0_332, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_321])). 361.08/46.39 thf(c_0_333, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 361.08/46.39 thf(c_0_334, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 361.08/46.39 thf(c_0_335, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])). 361.08/46.39 thf(c_0_336, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_322, c_0_321])). 361.08/46.39 thf(c_0_337, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_321])). 361.08/46.39 thf(c_0_338, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 361.08/46.39 thf(c_0_339, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 361.08/46.39 thf(c_0_340, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])). 361.08/46.39 thf(c_0_341, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 361.08/46.39 thf(c_0_342, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 361.08/46.39 thf(c_0_343, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 361.08/46.39 thf(c_0_344, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 361.08/46.39 thf(c_0_345, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 361.08/46.39 thf(c_0_346, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])). 361.08/46.39 thf(c_0_347, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 248 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])). 361.08/46.39 thf(c_0_348, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 361.08/46.39 thf(c_0_349, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])). 361.08/46.39 thf(c_0_350, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 361.08/46.39 thf(c_0_351, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])). 361.08/46.39 thf(c_0_352, plain, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[Z0/* 6 */:$i]:(![X2:$i]:(((in @ X2 @ Z0)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3))))))))))), inference(fof_simplification,[status(thm)],[image1Ex1])). 361.08/46.39 thf(c_0_353, plain, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X59 @ Z0))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), inference(fof_simplification,[status(thm)],[image1Equiv])). 361.08/46.39 thf(c_0_354, plain, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X61 @ Z0))))))), inference(fof_simplification,[status(thm)],[image1I])). 361.08/46.39 thf(c_0_355, plain, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X60 @ Z0))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), inference(fof_simplification,[status(thm)],[image1E])). 361.08/46.39 thf(c_0_356, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 361.08/46.39 thf(c_0_357, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])). 361.08/46.39 thf(c_0_358, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])). 361.08/46.39 thf(c_0_359, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 248 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])). 361.08/46.39 thf(c_0_360, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])). 361.08/46.39 thf(c_0_361, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])). 361.08/46.39 thf(c_0_362, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 361.08/46.39 thf(c_0_363, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 361.08/46.39 thf(c_0_364, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 361.08/46.39 thf(c_0_365, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 361.08/46.39 thf(c_0_366, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 361.08/46.39 thf(c_0_367, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 361.08/46.39 thf(c_0_368, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 361.08/46.39 thf(c_0_369, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 361.08/46.39 thf(c_0_370, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])). 361.08/46.39 thf(c_0_371, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 361.08/46.39 thf(c_0_372, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 361.08/46.39 thf(c_0_373, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 361.08/46.39 thf(c_0_374, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 361.08/46.39 thf(c_0_375, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 361.08/46.39 thf(c_0_376, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 361.08/46.39 thf(c_0_377, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 361.08/46.39 thf(c_0_378, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 361.08/46.39 thf(c_0_379, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_321])). 361.08/46.39 thf(c_0_380, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 361.08/46.39 thf(c_0_381, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 361.08/46.39 thf(c_0_382, plain, ((epred1_0)<=>![X2137:$i]:(?[X2138:$i]:((((![X2139:$i]:(((in @ X2139 @ X2138)=>![X2140:$i]:(((in @ X2140 @ X2139)=>(in @ X2140 @ X2137)))))&![X2141:$i, X2142:$i]:((((in @ X2141 @ X2137)&(in @ X2142 @ X2137))=>(![X2143:$i]:(((in @ X2143 @ X2138)=>((in @ X2141 @ X2143)<=>(in @ X2142 @ X2143))))=>((X2141)=(X2142))))))&![X2144:$i, X2145:$i]:((((in @ X2144 @ X2138)&(in @ X2145 @ X2138))=>(![X2146:$i]:(((in @ X2146 @ X2144)=>(in @ X2146 @ X2145)))|![X2147:$i]:(((in @ X2147 @ X2145)=>(in @ X2147 @ X2144)))))))&![X2148:$i]:(((![X2149:$i]:(((in @ X2149 @ X2148)=>(in @ X2149 @ X2137)))&?[X2150:$i]:((in @ X2150 @ X2148)))=>?[X2151:$i, X2152:$i]:(((((in @ X2151 @ X2138)&(in @ X2152 @ X2148))&~(?[X2153:$i]:(((in @ X2153 @ X2151)&(in @ X2153 @ X2148)))))&![X2154:$i]:(((in @ X2154 @ X2138)=>(![X2155:$i]:(((in @ X2155 @ X2154)=>(in @ X2155 @ X2151)))|(in @ X2152 @ X2154)))))))))))), introduced(definition)). 361.08/46.39 thf(c_0_383, negated_conjecture, ~((![X1118:$i, X1119:$i]:((![X1120:$i]:(((in @ X1120 @ X1118)<=>(in @ X1120 @ X1119)))=>((X1118)=(X1119))))=>(![X2172:$i]:(~(in @ X2172 @ emptyset))=>(![X2169:$i, X2170:$i, X2171:$i]:(((in @ X2171 @ (setadjoin @ X2169 @ X2170))<=>(((X2171)=(X2169))|(in @ X2171 @ X2170))))=>(![X2166:$i, X2167:$i]:(((in @ X2167 @ (powerset @ X2166))<=>![X2168:$i]:(((in @ X2168 @ X2167)=>(in @ X2168 @ X2166)))))=>(![X1121:$i, X1122:$i]:(((in @ X1122 @ (setunion @ X1121))<=>?[X1123:$i]:(((in @ X1122 @ X1123)&(in @ X1123 @ X1121)))))=>((in @ emptyset @ omega)=>(![X1124:$i]:(((in @ X1124 @ omega)=>(in @ (setadjoin @ X1124 @ X1124) @ omega)))=>(![X1125:$i]:((((in @ emptyset @ X1125)&![X1126:$i]:((((in @ X1126 @ omega)&(in @ X1126 @ X1125))=>(in @ (setadjoin @ X1126 @ X1126) @ X1125))))=>![X1127:$i]:(((in @ X1127 @ omega)=>(in @ X1127 @ X1125)))))=>(![X2160:$i > $i > $o, X2161:$i]:((![X2162:$i]:(((in @ X2162 @ X2161)=>(exu @ (X2160 @ X2162))))=>?[X2163:$i]:(![X2164:$i]:(((in @ X2164 @ X2163)<=>?[X2165:$i]:(((in @ X2165 @ X2161)&(X2160 @ X2165 @ X2164))))))))=>(![X2156:$i]:((?[X2157:$i]:((in @ X2157 @ X2156))=>?[X2158:$i]:(((in @ X2158 @ X2156)&~(?[X2159:$i]:(((in @ X2159 @ X2158)&(in @ X2159 @ X2156))))))))=>((epred1_0)=>(![X2136:$i > $o]:(((exu @ X2136)=>(X2136 @ (descr @ (^[Z0/* 17 */:$i]:(X2136 @ Z0))))))=>(![X2133:$i, X2134:$i > $o, X2135:$i]:(((in @ X2135 @ X2133)=>((X2134 @ X2135)=>(in @ X2135 @ (dsetconstr @ X2133 @ X2134)))))=>(![X2130:$i, X2131:$i > $o, X2132:$i]:(((in @ X2132 @ (dsetconstr @ X2130 @ X2131))=>(in @ X2132 @ X2130)))=>(![X1128:$i, X1129:$i > $o, X1130:$i]:(((in @ X1130 @ (dsetconstr @ X1128 @ X1129))=>(X1129 @ X1130)))=>(![X2127:$i > $o]:(((exu @ X2127)=>?[X2128:$i]:(((X2127 @ X2128)&![X2129:$i]:(((X2127 @ X2129)=>((X2128)=(X2129))))))))=>(![X2125:$o, X2126:$i]:(((in @ X2126 @ (prop2set @ ((X2125))))=>(X2125)))=>(![X2123:$i]:(((in @ X2123 @ emptyset)=>![X2124:$o]:((X2124))))=>(![X1131:$i]:(((in @ X1131 @ emptyset)=>~($true)))=>(![X2122:$i]:(~(in @ X2122 @ emptyset))=>(![X2120:$i > $o]:(((exu @ X2120)=>?[X2121:$i]:((X2120 @ X2121))))=>(![X2116:$i, X2117:$i]:((![X2118:$i]:(((in @ X2118 @ X2116)=>(in @ X2118 @ X2117)))=>(![X2119:$i]:(((in @ X2119 @ X2117)=>(in @ X2119 @ X2116)))=>((X2116)=(X2117)))))=>(![X1132:$i]:((![X1133:$i]:(~(in @ X1133 @ X1132))=>((X1132)=(emptyset))))=>(![X2114:$i]:((![X2115:$i]:(~(in @ X2115 @ X2114))=>((X2114)=(emptyset))))=>(![X1134:$i, X1135:$i > $o, X1136:$i]:(((in @ X1136 @ X1134)=>((in @ X1136 @ (dsetconstr 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X2097)))=>(in @ X2098 @ (powerset @ X2097))))=>(![X1143:$i]:((in @ emptyset @ (powerset @ X1143)))=>(![X1144:$i]:((in @ emptyset @ (powerset @ X1144)))=>(![X1145:$i, X1146:$i, X1147:$i]:(((in @ X1146 @ (powerset @ X1145))=>((in @ X1147 @ X1146)=>(in @ X1147 @ X1145))))=>(![X2094:$i, X2095:$i, X2096:$i]:(((in @ X2095 @ X2096)=>((in @ X2096 @ X2094)=>(in @ X2095 @ (setunion @ X2094)))))=>(![X2090:$i, X2091:$i]:(((in @ X2091 @ (setunion @ X2090))=>![X2092:$o]:((![X2093:$i]:(((in @ X2091 @ X2093)=>((in @ X2093 @ X2090)=>(X2092))))=>(X2092)))))=>(![X1148:$i, X1149:$i]:(((in @ X1149 @ X1148)=>(in @ X1149 @ (powerset @ (setunion @ X1148)))))=>(![X1150:$i > $o]:(((exu @ X1150)=>?[X1151:$i]:(![X1152:$i]:(((X1150 @ X1152)<=>((X1152)=(X1151)))))))=>(![X2088:$i]:((((X2088)!=(emptyset))=>?[X2089:$i]:(((in @ X2089 @ X2088)&$true))))=>(![X2086:$i, X2087:$i]:(((in @ X2086 @ (setadjoin @ X2087 @ emptyset))=>((X2086)=(X2087))))=>(![X1153:$i, X1154:$i]:((((X1153)!=(X1154))=>~(in @ X1154 @ (setadjoin @ X1153 @ emptyset))))=>(![X2084:$i, X2085:$i]:((((X2084)=(X2085))=>(in @ X2084 @ (setadjoin @ X2085 @ emptyset))))=>(![X2082:$i, X2083:$i]:(((in @ X2082 @ (setadjoin @ X2083 @ emptyset))=>(in @ X2083 @ (setadjoin @ X2082 @ emptyset))))=>(![X1155:$i, X1156:$i, X1157:$i]:(((in @ X1157 @ (setadjoin @ X1155 @ (setadjoin @ X1156 @ emptyset)))=>(((X1157)=(X1155))|((X1157)=(X1156)))))=>(![X1158:$i, X1159:$i]:((in @ X1158 @ (setadjoin @ X1158 @ (setadjoin @ X1159 @ emptyset))))=>(![X2080:$i, X2081:$i]:((in @ X2081 @ (setadjoin @ X2080 @ (setadjoin @ X2081 @ emptyset))))=>(![X2077:$i, X2078:$i > $o]:((?[X2079:$i]:(((in @ X2079 @ X2077)&(X2078 @ X2079)))=>(((dsetconstr @ X2077 @ X2078)=(emptyset))=>~($true))))=>(![X1160:$i > $o, X1161:$i]:(((in @ X1161 @ emptyset)=>(X1160 @ X1161)))=>(![X2073:$i, X2074:$i > $o]:((~(![X2075:$i]:(((in @ X2075 @ X2073)=>(X2074 @ X2075))))=>?[X2076:$i]:(((in @ X2076 @ X2073)&~((X2074 @ X2076))))))=>(![X2069:$i, X2070:$i > $o]:((![X2071:$i]:(((in @ X2071 @ 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setukpairinjR2]), emptysetAx]), binunionRsub]), ubforcartprodlem1]), binunionEcases]), binunionIR]), upairset2IR]), setunionsingleton2]), binunionIL]), c_0_323]), c_0_324]), powersetI1]), setextsub]), subset2powerset]), singletonsuniq]), setadjoinSub]), subsetRefl]), c_0_325]), notequalI2]), notequalI1]), subsetI2]), kfstpairEq]), eqimpsubset2]), ubforcartprodlem2]), omega__Cong]), powerset__Cong]), cartprodfstin]), emptyset__Cong]), c_0_326]), c_0_327]), eqbreln]), in__Cong]), inCongP]), c_0_328]), c_0_329]), c_0_330]), prop2setI]), quantDeMorgan2]), ubforcartprodlem3]), quantDeMorgan1]), cartprodpairmemER]), c_0_331]), upairsetIR]), cartprodsndpairEq]), singletonsswitch]), eqinunit]), uniqinunit]), cartprodpairsurjEq]), c_0_332]), setunionE]), c_0_333]), setunionI]), powersetI]), setadjoinOr]), c_0_334]), setadjoinE]), setadjoinIL]), c_0_335]), c_0_336]), c_0_337]), noeltsimpempty]), app]), setext]), c_0_338]), notinemptyset]), infuncsetfunc]), emptysetE]), prop2setE]), c_0_339]), c_0_340]), c_0_341]), c_0_342]), c_0_343]), c_0_344]), wellorderingAx]), foundationAx]), brelnall2]), c_0_345]), omega0Ax]), funcextLem]), powersetAx]), setadjoinAx]), subbreln]), woz13rule0]), woz1_1]), funcext]), funcext2]), c_0_346]), c_0_347]), c_0_348]), c_0_349]), c_0_350]), theeq]), cartprodpairin]), iftrueorfalse]), binunionT_lem]), cartprodmempair]), powersetT_lem]), complementT_lem]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), contrasubsetT1]), doubleComplementSub1]), doubleComplementEq]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), inComplementUnionImpNotIn1]), binunionTEcontra]), demorgan2a1]), demorgan1a]), demorgan1]), demorgan2a]), doubleComplementI1]), contrasubsetT3]), contrasubsetT2]), contrasubsetT]), binintersectTERcontra]), woz1_2]), woz1_5]), c_0_351]), breln1all1]), eqbreln1]), breln1invprop]), breln1invE]), breln1compI]), breln1compE]), breln1compEex]), breln1unionprop]), breln1unionIL]), breln1unionEcases]), woz2W]), woz2B]), image1Ex]), c_0_352]), c_0_353]), c_0_354]), injFuncInInjFuncSet]), surjFuncSetFuncSurj]), surjCantorThm]), c_0_321]), leftInvIsSurj]), surjFuncSetFuncIn]), injFuncSetFuncInj]), injFuncSetFuncIn]), c_0_355]), woz2A]), woz2Ex]), breln1unionCommutes]), breln1unionE]), breln1unionI]), breln1unionIR]), breln1compprop]), breln1invI]), subbreln1]), breln1SetBreln1]), breln1all2]), woz1_4]), woz1_3]), woz13rule4]), woz13rule3]), woz13rule2]), woz13rule1]), demorgan2]), demorgan2b]), demorgan2b2]), demorgan1b]), demorgan2a2]), complementUnionInPowersetComplement]), binunionTE]), inComplementUnionImpInComplement1]), intersectInPowersetIntersectUnions]), binunionTIRcontra]), binunionTILcontra]), complementTcontraSubset]), contraSubsetComplement]), complementInPowersetComplementIntersect]), complementTnotintersectT]), doubleComplementSub2]), doubleComplementE1]), binintersectTELcontra]), setextT]), setminusT_lem]), binintersectT_lem]), iffalse]), iftrue]), ifp]), c_0_356]), c_0_357]), c_0_358]), c_0_359]), c_0_360]), ap2apEq2]), ap2apEq1]), funcGraphProp4]), funcGraphProp2]), funcGraphProp3]), funcGraphProp1]), c_0_361]), brelnall1]), c_0_362]), funcinfuncset]), ap2p]), c_0_363]), c_0_364]), c_0_365]), c_0_366]), c_0_367]), c_0_368]), cartprodfstpairEq]), cartprodmempaircEq]), cartprodpairmemEL]), cartprodsndin]), kpairsurjEq]), ksndpairEq]), setukpairinjR]), upairequniteq]), setukpairinjR1]), setukpairinjR12]), setukpairinjR11]), setukpairinjL]), setukpairinjL2]), theprop]), setukpairinjL1]), c_0_369]), c_0_370]), c_0_371]), setunionsingleton]), setunionE2]), cartprodmempair1]), upairsubunion]), singletoninpowunion]), singletoninpowerset]), setukpairIR]), symdiffIneg2]), symdiffI2]), symdiffI1]), setminusSubset1]), setminusIRneg]), bs114d]), binintersectSubset4]), binintersectRsub]), binintersectER]), binintersectSubset2]), binintersectEL]), binintersectSubset5]), setunionsingleton1]), upairinpowunion]), upairset2E]), singletonsubset]), kpairp]), kpairiskpair]), setukpairIL]), secondinupair]), symdiffIneg1]), symdiffE]), setminusLsub]), setminusILneg]), setminusELneg]), setminusERneg]), setminusSubset2]), setminusER]), setminusEL]), setminusI]), binintersectSubset1]), disjointsetsI1]), binintersectSubset3]), binintersectLsub]), binintersectI]), binunionLsub]), binunionE]), c_0_372]), powersetsubset]), inPowerset]), powersetE1]), subsetemptysetimpeq]), setadjoinSub2]), subsetTrans]), notsubsetI]), subsetE2]), subsetE]), emptysetsubset]), eqimpsubset1]), subsetI1]), c_0_373]), c_0_374]), c_0_375]), setunion__Cong]), setadjoin__Cong]), c_0_376]), notdallE]), notdexE]), quantDeMorgan4]), quantDeMorgan3]), vacuousDall]), upairsetIL]), upairsetE]), notinsingleton]), c_0_377]), subPowSU]), powersetE]), emptyInPowerset]), emptyinPowerset]), c_0_378]), setadjoinIR]), emptyinunitempty]), c_0_379]), c_0_380]), emptyI]), emptysetimpfalse]), c_0_381]), omegaIndAx]), omegaSAx]), setunionAx]), setextAx])])]), c_0_382])). 361.08/46.39 thf(c_0_384, negated_conjecture, ![X2173:$i, X2174:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2186:$i, X2187:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2195:$i, X2196:$i > $i > $o, X2197:$i, X2200:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2207:$i, X2208:$i > $o, X2209:$i, X2210:$i > $o, X2211:$i, X2212:$i, X2213:$i > $o, X2214:$i, X2215:$i, X2216:$i > $o, X2217:$i, X2218:$i > $o, X2220:$i, X2221:$o, X2222:$i, X2223:$i, X2224:$o, X2225:$i, X2226:$i, X2227:$i > $o, X2229:$i, X2230:$i, X2233:$i, X2235:$i, X2237:$i, X2238:$i > $o, X2239:$i, X2240:$i, X2242:$i, X2243:$i > $o, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$o, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$o, X2275:$i, X2276:$i, X2277:$i > $o, X2279:$i, X2280:$i, X2281:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i > $o, X2300:$i, X2301:$i > $o, X2302:$i, X2303:$i, X2304:$i > $o, X2305:$i, X2307:$i, X2308:$i > $o, X2310:$i, X2311:$i, X2312:$i > $o, X2314:$i, X2315:$i, X2316:$i > $o, X2317:$i, X2319:$o, X2320:$i, X2321:$i > $o, X2323:$i, X2324:$i, X2325:$i > $o, X2326:$i, X2328:$i > $o, X2329:$i, X2331:$i > $o, X2332:$i, X2335:$i > $o, X2336:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i > $o, X2347:$i, X2348:$i, X2349:$i > $o, X2350:$i > $o, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i, X2360:$i, X2361:$i > $o, X2362:$i, X2363:$i, X2364:$i > $o, X2365:$i > $o, X2368:$i, X2369:$i, X2370:$i > $o, X2371:$i > $o, X2374:$i, X2375:$i, X2377:$i, X2378:$i, 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X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$i, X2486:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2493:$i, X2494:$i, X2495:$i, X2496:$i, X2497:$i, X2498:$i, X2499:$i, X2500:$i, X2501:$i, X2502:$i, X2503:$o, X2504:$i, X2505:$i, X2506:$i, X2507:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i, X2546:$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, X2565:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i > $o, X2578:$i, X2579:$i, X2580:$i > $o, X2582:$i, X2583:$i > $o, X2584:$i, X2586:$i, X2587:$i > $o, X2590:$i, X2591:$i, X2592:$i, X2593:$i, X2594:$i, X2595:$i, X2596:$i, X2597:$i, X2598:$i, X2599:$i, X2600:$i, X2601:$i, X2602:$i, X2603:$i, X2604:$i, X2605:$i, X2606:$i, X2607:$i, X2608:$i, X2609:$i, X2610:$i, X2611:$i, X2612:$i, X2613:$i, X2614:$i, X2615:$i, X2616:$i, X2617:$i, X2618:$i, X2619:$i, X2620:$i, X2621:$i, X2622:$i, X2623:$i, X2624:$i, X2625:$i, X2626:$i, X2627:$i, X2628:$i, X2629:$i, X2630:$i, X2631:$i, X2632:$i, X2633:$i, X2634:$i, X2635:$i, X2636:$i, X2637:$i, X2638:$i, X2639:$i, X2640:$i, X2641:$i, X2642:$i, X2643:$i, X2644:$i, X2645:$i, X2646:$i, X2647:$i, X2648:$i, X2649:$i, X2650:$i, X2651:$i, X2652:$i, X2653:$i, X2654:$i, X2655:$i, X2656:$i, X2657:$i, X2658:$i, X2659:$i, X2660:$i, X2661:$i, X2662:$i > $i > $o, X2663:$i, X2664:$i, X2665:$i, X2666:$i, X2667:$i > $i > $o, X2668:$i, X2669:$i, X2670:$i > $i > $o, X2671:$i, X2672:$i, X2673:$i > $i > $o, X2674:$i, X2675:$i, X2676:$i, X2677:$i, X2678:$i > $i > $o, X2679:$i, X2680:$i, X2681:$i, X2682:$i, X2683:$i > $i > $o, X2684:$i, X2685:$i, X2686:$i, X2687:$i, X2688:$i > $i > $o, X2689:$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:$i, X2709:$i, X2710:$i, X2711:$i, X2712:$i, X2713:$i, X2714:$i, X2715:$i > $i, X2717:$i, X2718:$i, X2719:$i > $i, X2721:$i, X2722:$i, X2723:$i > $i, X2725:$i, X2726:$i, X2727:$i, X2728:$i > $o, X2731:$i, X2732:$i, X2733:$i, X2734:$i, X2735:$i > $o, X2738:$i, X2739:$i, X2740:$i > $o, X2741:$i, X2742:$i, X2743:$i, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i, X2749:$i, X2750:$i, X2751:$i, X2752:$i, X2753:$i, X2754:$i, X2755:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2761:$i, X2762:$i, X2763:$i, X2764:$i, X2765:$i, X2766:$i, X2767:$i, X2768:$i, X2769:$i, X2770:$i, X2771:$i, X2774:$i, X2775:$i, X2776:$i, X2777:$i, X2782:$i, X2783:$i, X2784:$i, X2785:$i, X2787:$i, X2788:$i, X2789:$i, X2790:$i, X2792:$i, X2793:$i, X2794:$i, X2795:$i, X2796:$i, X2797:$i, X2798:$i, X2799:$i, X2800:$i, X2801:$i, X2802:$i > $i, X2804:$i, X2805:$i, X2806:$i, X2807:$i, X2808:$i, X2809:$i, X2810:$i > $i, X2812:$i, X2813:$i, X2814:$i > $i, X2816:$i, X2817:$i, X2818:$i, X2819:$i, X2820:$i, X2821:$o, X2822:$i, X2823:$i, X2824:$i, X2825:$o, X2826:$i, X2827:$i, X2828:$i, X2829:$o, X2830:$i, X2831:$i, X2832:$i, X2833:$o, X2834:$i, X2835:$i, X2836:$i, X2837:$o, X2838:$i, X2839:$i, X2840:$i, X2841:$o, X2842:$i, X2843:$i, X2844:$i, X2845:$i, X2846:$i, X2847:$o, X2848:$i, X2849:$i, X2850:$i, X2851:$o, X2852:$i, X2853:$i, X2854:$i, X2855:$o, X2856:$i, X2857:$i, X2858:$i, X2859:$i, X2860:$i, X2861:$i, X2862:$i, X2863:$i, X2864:$i, X2865:$i, X2866:$i, X2867:$i, X2868:$i, X2869:$i, X2870:$i, X2871:$i, X2872:$i, X2873:$i, X2876:$i, X2877:$i, X2878:$i, X2880:$i, X2881:$i, X2882:$i, X2884:$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:$i, X2950:$i, X2951:$i, X2952:$i, X2953:$i, X2954:$i, X2955:$i, X2956:$i, X2957:$i, X2958:$i, X2959:$i, X2960:$i, X2961:$i, X2962:$i, X2963:$i, X2964:$i, X2965:$i, X2966:$i, X2967:$i, X2968:$i, X2969:$i, X2970:$i, X2971:$i, X2972:$i, X2973:$i, X2974:$i, X2975:$i, X2976:$i, X2977:$i, X2978:$i, X2979:$i, X2980:$i, X2981:$i, X2982:$i, X2983:$i, X2984:$i, X2985:$i, X2986:$i, X2987:$o, X2988:$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, X3003:$i, X3004:$i, X3005:$i, X3006:$i, X3007:$i, X3008:$i, X3009:$i, X3010:$i, X3011:$i, X3012:$i, X3013:$i, X3014:$i, X3015:$i, X3016:$i, X3017:$i, X3018:$i, X3019:$i, X3020:$i, X3021:$i, X3022:$i, X3023:$i, X3024:$i, X3025:$i, X3026:$i, X3027:$i, X3028:$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, X3047:$i, X3048:$i, X3049:$i, X3050:$i, X3051:$i, X3052:$i, X3053:$i, X3054:$i, X3055:$i, X3056:$i, X3057:$i, X3058:$i, X3059:$i, X3060:$i, X3061:$i, X3062:$i, X3063:$i, X3064:$i, X3065:$i, X3066:$i, X3067:$i, X3068:$i, X3069:$i, X3070:$i, X3071:$i > $o, X3074:$i, X3075:$i, X3076:$i, X3077:$i, X3078:$i > $i > $o, X3079:$i, X3080:$i, X3081:$i > $o, X3084:$i, X3085:$i, X3086:$i, X3087:$i, X3090:$i, X3091:$i, X3092:$i, X3097:$i, X3098:$i, X3099:$i, X3100:$i, X3101:$i, X3102:$i, X3103:$i, X3104:$i, X3105:$i, X3106:$i, X3107:$i, X3108:$i, X3109:$i, X3110:$i, X3111:$i, X3112:$i, X3113:$i, X3114:$i, X3115:$i, X3116:$i, X3117:$i, X3118:$i, X3119:$i, X3120:$i, X3122:$i, X3123:$i, X3124:$i, X3125:$i, X3126:$i, X3127:$o, X3129:$i, X3130:$i, X3131:$i, X3132:$i, X3133:$i, X3134:$i, X3135:$i, X3136:$i, X3137:$i, X3138:$i, X3139:$i, X3140:$i, X3141:$i, X3142:$i, 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:$o, X3158:$i, X3159:$i, X3160:$i, X3161:$i, X3162:$i, X3163:$i, X3164:$i, X3165:$i, X3166:$i, X3167:$i, X3168:$i, X3169:$i, X3170:$i, X3171:$i, X3172:$i, X3173:$i, X3174:$i, X3175:$i > $i, X3177:$i, X3179:$i, X3180:$i, X3181:$i, X3182:$i > $i, X3183:$i, X3184:$i > $i, X3185:$i, X3187:$i, X3188:$i > $i, X3189:$i, X3190:$i, X3191:$i, X3192:$i > $i, X3193:$i, X3195:$i, X3196:$i > $i, X3197:$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 > $i, X3218:$i, X3220:$i, X3221:$i, X3223:$i]:((((~(in @ (esk1_2 @ X2173 @ X2174) @ X2173)|~(in @ (esk1_2 @ X2173 @ X2174) @ X2174)|((X2173)=(X2174)))&((in @ (esk1_2 @ X2173 @ X2174) @ X2173)|(in @ (esk1_2 @ X2173 @ X2174) @ X2174)|((X2173)=(X2174))))&(~(in @ X2176 @ emptyset)&(((~(in @ X2179 @ (setadjoin @ X2177 @ X2178))|(((X2179)=(X2177))|(in @ X2179 @ X2178)))&((((X2179)!=(X2177))|(in @ X2179 @ (setadjoin @ X2177 @ X2178)))&(~(in @ X2179 @ X2178)|(in @ X2179 @ (setadjoin @ X2177 @ X2178)))))&(((~(in @ X2181 @ (powerset @ X2180))|(~(in @ X2182 @ X2181)|(in @ X2182 @ X2180)))&(((in @ (esk2_2 @ X2183 @ X2184) @ X2184)|(in @ X2184 @ (powerset @ X2183)))&(~(in @ (esk2_2 @ X2183 @ X2184) @ X2183)|(in @ X2184 @ (powerset @ X2183)))))&(((((in @ X2187 @ (esk3_2 @ X2186 @ X2187))|~(in @ X2187 @ (setunion @ X2186)))&((in @ (esk3_2 @ X2186 @ X2187) @ X2186)|~(in @ X2187 @ (setunion @ X2186))))&(~(in @ 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X3069 @ X3070))&(~(X3071 @ (kpair @ (esk71_3 @ X3069 @ X3070 @ X3071) @ (esk72_3 @ X3069 @ X3070 @ X3071)))|(~(in @ X3074 @ X3070)|(X3071 @ X3074))|~(breln1 @ X3069 @ X3070)))))&((~(in @ X3076 @ (breln1Set @ X3075))|(breln1 @ X3075 @ X3076))&((choice2fnsingleton)&((breln1 @ X3077 @ (dpsetconstr @ X3077 @ X3077 @ X3078))&((((in @ (esk73_3 @ X3079 @ X3080 @ X3081) @ X3079)|(~(in @ X3084 @ X3080)|(X3081 @ X3084))|~(breln1 @ X3079 @ X3080))&(((in @ (esk74_3 @ X3079 @ X3080 @ X3081) @ X3079)|(~(in @ X3084 @ X3080)|(X3081 @ X3084))|~(breln1 @ X3079 @ X3080))&(((in @ (kpair @ (esk73_3 @ X3079 @ X3080 @ X3081) @ (esk74_3 @ X3079 @ X3080 @ X3081)) @ X3080)|(~(in @ X3084 @ X3080)|(X3081 @ X3084))|~(breln1 @ X3079 @ X3080))&(~(X3081 @ (kpair @ (esk73_3 @ X3079 @ X3080 @ X3081) @ (esk74_3 @ X3079 @ X3080 @ X3081)))|(~(in @ X3084 @ X3080)|(X3081 @ X3084))|~(breln1 @ X3079 @ X3080)))))&((((in @ (esk75_3 @ X3085 @ X3086 @ X3087) @ X3085)|(subset @ X3086 @ X3087)|~(breln1 @ X3085 @ X3087)|~(breln1 @ X3085 @ X3086))&(((in @ (esk76_3 @ X3085 @ X3086 @ X3087) @ X3085)|(subset @ X3086 @ X3087)|~(breln1 @ X3085 @ X3087)|~(breln1 @ X3085 @ X3086))&(((in @ (kpair @ (esk75_3 @ X3085 @ X3086 @ X3087) @ (esk76_3 @ X3085 @ X3086 @ X3087)) @ X3086)|(subset @ X3086 @ X3087)|~(breln1 @ X3085 @ X3087)|~(breln1 @ X3085 @ X3086))&(~(in @ (kpair @ (esk75_3 @ X3085 @ X3086 @ X3087) @ (esk76_3 @ X3085 @ X3086 @ X3087)) @ X3087)|(subset @ X3086 @ X3087)|~(breln1 @ X3085 @ X3087)|~(breln1 @ X3085 @ X3086)))))&(((((in @ (esk79_3 @ X3090 @ X3091 @ X3092) @ X3090)|((X3091)=(X3092))|(in @ (esk77_3 @ X3090 @ X3091 @ X3092) @ X3090)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091))&(((in @ (esk80_3 @ X3090 @ X3091 @ X3092) @ X3090)|((X3091)=(X3092))|(in @ (esk77_3 @ X3090 @ X3091 @ X3092) @ X3090)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091))&(((in @ (kpair @ (esk79_3 @ X3090 @ X3091 @ X3092) @ (esk80_3 @ X3090 @ X3091 @ X3092)) @ X3092)|((X3091)=(X3092))|(in @ (esk77_3 @ X3090 @ X3091 @ X3092) @ X3090)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091))&(~(in @ (kpair @ (esk79_3 @ X3090 @ X3091 @ X3092) @ (esk80_3 @ X3090 @ X3091 @ X3092)) @ X3091)|((X3091)=(X3092))|(in @ (esk77_3 @ X3090 @ X3091 @ X3092) @ X3090)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091)))))&((((in @ (esk79_3 @ X3090 @ X3091 @ X3092) @ X3090)|((X3091)=(X3092))|(in @ (esk78_3 @ X3090 @ X3091 @ X3092) @ X3090)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091))&(((in @ (esk80_3 @ X3090 @ X3091 @ X3092) @ X3090)|((X3091)=(X3092))|(in @ (esk78_3 @ X3090 @ X3091 @ X3092) @ X3090)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091))&(((in @ (kpair @ (esk79_3 @ X3090 @ X3091 @ X3092) @ (esk80_3 @ X3090 @ X3091 @ X3092)) @ X3092)|((X3091)=(X3092))|(in @ (esk78_3 @ X3090 @ X3091 @ X3092) @ X3090)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091))&(~(in @ (kpair @ (esk79_3 @ X3090 @ X3091 @ X3092) @ (esk80_3 @ X3090 @ X3091 @ X3092)) @ X3091)|((X3091)=(X3092))|(in @ (esk78_3 @ X3090 @ X3091 @ X3092) @ X3090)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091)))))&((((in @ (esk79_3 @ X3090 @ X3091 @ X3092) @ X3090)|((X3091)=(X3092))|(in @ (kpair @ (esk77_3 @ X3090 @ X3091 @ X3092) @ (esk78_3 @ X3090 @ X3091 @ X3092)) @ X3091)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091))&(((in @ (esk80_3 @ X3090 @ X3091 @ X3092) @ X3090)|((X3091)=(X3092))|(in @ (kpair @ (esk77_3 @ X3090 @ X3091 @ X3092) @ (esk78_3 @ X3090 @ X3091 @ X3092)) @ X3091)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091))&(((in @ (kpair @ (esk79_3 @ X3090 @ X3091 @ X3092) @ (esk80_3 @ X3090 @ X3091 @ X3092)) @ X3092)|((X3091)=(X3092))|(in @ (kpair @ (esk77_3 @ X3090 @ X3091 @ X3092) @ (esk78_3 @ X3090 @ X3091 @ X3092)) @ X3091)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091))&(~(in @ (kpair @ (esk79_3 @ X3090 @ X3091 @ X3092) @ (esk80_3 @ X3090 @ X3091 @ X3092)) @ X3091)|((X3091)=(X3092))|(in @ (kpair @ (esk77_3 @ X3090 @ X3091 @ X3092) @ (esk78_3 @ X3090 @ X3091 @ X3092)) @ X3091)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091)))))&(((in @ (esk79_3 @ X3090 @ X3091 @ X3092) @ X3090)|((X3091)=(X3092))|~(in @ (kpair @ (esk77_3 @ X3090 @ X3091 @ X3092) @ (esk78_3 @ X3090 @ X3091 @ X3092)) @ X3092)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091))&(((in @ (esk80_3 @ X3090 @ X3091 @ X3092) @ X3090)|((X3091)=(X3092))|~(in @ (kpair @ (esk77_3 @ X3090 @ X3091 @ X3092) @ (esk78_3 @ X3090 @ X3091 @ X3092)) @ X3092)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091))&(((in @ (kpair @ (esk79_3 @ X3090 @ X3091 @ X3092) @ (esk80_3 @ X3090 @ X3091 @ X3092)) @ X3092)|((X3091)=(X3092))|~(in @ (kpair @ (esk77_3 @ X3090 @ X3091 @ X3092) @ (esk78_3 @ X3090 @ X3091 @ X3092)) @ X3092)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091))&(~(in @ (kpair @ (esk79_3 @ X3090 @ X3091 @ X3092) @ (esk80_3 @ X3090 @ X3091 @ X3092)) @ X3091)|((X3091)=(X3092))|~(in @ (kpair @ (esk77_3 @ X3090 @ X3091 @ X3092) @ (esk78_3 @ X3090 @ X3091 @ X3092)) @ X3092)|~(breln1 @ X3090 @ X3092)|~(breln1 @ X3090 @ X3091))))))))&((~(breln1 @ X3097 @ X3098)|(breln1 @ X3097 @ (breln1invset @ X3097 @ X3098)))&((~(breln1 @ X3099 @ X3100)|(~(in @ X3101 @ X3099)|(~(in @ X3102 @ X3099)|(~(in @ (kpair @ X3101 @ X3102) @ X3100)|(in @ (kpair @ X3102 @ X3101) @ (breln1invset @ X3099 @ X3100))))))&((~(breln1 @ X3103 @ X3104)|(~(in @ X3105 @ X3103)|(~(in @ X3106 @ X3103)|(~(in @ (kpair @ X3106 @ X3105) @ (breln1invset @ X3103 @ X3104))|(in @ (kpair @ X3105 @ X3106) @ X3104)))))&((~(breln1 @ X3107 @ X3108)|(~(breln1 @ X3107 @ X3109)|(breln1 @ X3107 @ (breln1compset @ X3107 @ X3108 @ X3109))))&((~(breln1 @ X3110 @ X3111)|(~(breln1 @ X3110 @ X3112)|(~(in @ X3113 @ X3110)|(~(in @ X3114 @ X3110)|(~(in @ X3115 @ X3110)|(~(in @ (kpair @ X3113 @ X3115) @ X3111)|(~(in @ (kpair @ X3115 @ X3114) @ X3112)|(in @ (kpair @ X3113 @ X3114) @ (breln1compset @ X3110 @ X3111 @ X3112)))))))))&(((((in @ (esk81_5 @ X3116 @ X3117 @ X3118 @ X3119 @ X3120) @ X3116)|~(in @ (kpair @ X3119 @ X3120) @ (breln1compset @ X3116 @ X3117 @ X3118))|~(in @ X3120 @ X3116)|~(in @ X3119 @ X3116)|~(breln1 @ X3116 @ X3118)|~(breln1 @ X3116 @ X3117))&((in @ (kpair @ X3119 @ (esk81_5 @ X3116 @ X3117 @ X3118 @ X3119 @ X3120)) @ X3117)|~(in @ (kpair @ X3119 @ X3120) @ (breln1compset @ X3116 @ X3117 @ X3118))|~(in @ X3120 @ X3116)|~(in @ X3119 @ X3116)|~(breln1 @ X3116 @ X3118)|~(breln1 @ X3116 @ X3117)))&((in @ (kpair @ (esk81_5 @ X3116 @ X3117 @ X3118 @ X3119 @ X3120) @ X3120) @ X3118)|~(in @ (kpair @ X3119 @ X3120) @ (breln1compset @ X3116 @ X3117 @ X3118))|~(in @ X3120 @ X3116)|~(in @ X3119 @ X3116)|~(breln1 @ X3116 @ X3118)|~(breln1 @ X3116 @ X3117)))&((((in @ (esk82_6 @ X3122 @ X3123 @ X3124 @ X3125 @ X3126 @ X3127) @ X3122)|(X3127)|~(in @ (kpair @ X3125 @ X3126) @ (breln1compset @ X3122 @ X3123 @ X3124))|~(in @ X3126 @ X3122)|~(in @ X3125 @ X3122)|~(breln1 @ X3122 @ X3124)|~(breln1 @ X3122 @ X3123))&(((in @ (kpair @ X3125 @ (esk82_6 @ X3122 @ X3123 @ X3124 @ X3125 @ X3126 @ X3127)) @ X3123)|(X3127)|~(in @ (kpair @ X3125 @ X3126) @ (breln1compset @ X3122 @ X3123 @ X3124))|~(in @ X3126 @ X3122)|~(in @ X3125 @ X3122)|~(breln1 @ X3122 @ X3124)|~(breln1 @ X3122 @ X3123))&(((in @ (kpair @ (esk82_6 @ X3122 @ X3123 @ X3124 @ X3125 @ X3126 @ X3127) @ X3126) @ X3124)|(X3127)|~(in @ (kpair @ X3125 @ X3126) @ (breln1compset @ X3122 @ X3123 @ X3124))|~(in @ X3126 @ X3122)|~(in @ X3125 @ X3122)|~(breln1 @ X3122 @ X3124)|~(breln1 @ X3122 @ X3123))&(~(X3127)|(X3127)|~(in @ (kpair @ X3125 @ X3126) @ (breln1compset @ X3122 @ X3123 @ X3124))|~(in @ X3126 @ X3122)|~(in @ X3125 @ X3122)|~(breln1 @ X3122 @ X3124)|~(breln1 @ X3122 @ X3123)))))&((~(breln1 @ X3129 @ X3130)|(~(breln1 @ X3129 @ X3131)|(breln1 @ X3129 @ (binunion @ X3130 @ X3131))))&((~(breln1 @ X3132 @ X3133)|(~(breln1 @ X3132 @ X3134)|(~(in @ X3135 @ X3132)|(~(in @ X3136 @ X3132)|(~(in @ (kpair @ X3135 @ X3136) @ X3133)|(in @ (kpair @ X3135 @ X3136) @ (binunion @ X3133 @ X3134)))))))&((~(breln1 @ X3137 @ X3138)|(~(breln1 @ X3137 @ X3139)|(~(in @ X3140 @ X3137)|(~(in @ X3141 @ X3137)|(~(in @ (kpair @ X3140 @ X3141) @ X3139)|(in @ (kpair @ X3140 @ X3141) @ (binunion @ X3138 @ X3139)))))))&(((~(in @ (kpair @ X3145 @ X3146) @ X3143)|(in @ (kpair @ X3145 @ X3146) @ (binunion @ X3143 @ X3144))|~(in @ X3146 @ X3142)|~(in @ X3145 @ X3142)|~(breln1 @ X3142 @ X3144)|~(breln1 @ X3142 @ X3143))&(~(in @ (kpair @ X3145 @ X3146) @ X3144)|(in @ (kpair @ X3145 @ X3146) @ (binunion @ X3143 @ X3144))|~(in @ X3146 @ X3142)|~(in @ X3145 @ X3142)|~(breln1 @ X3142 @ X3144)|~(breln1 @ X3142 @ X3143)))&((~(breln1 @ X3147 @ X3148)|(~(breln1 @ X3147 @ X3149)|(~(in @ X3150 @ X3147)|(~(in @ X3151 @ X3147)|(~(in @ (kpair @ X3150 @ X3151) @ (binunion @ X3148 @ X3149))|((in @ (kpair @ X3150 @ X3151) @ X3148)|(in @ (kpair @ X3150 @ X3151) @ X3149)))))))&(((((in @ (kpair @ X3155 @ X3156) @ X3154)|(X3157)|(in @ (kpair @ X3155 @ X3156) @ X3153)|~(in @ (kpair @ X3155 @ X3156) @ (binunion @ X3153 @ X3154))|~(in @ X3156 @ X3152)|~(in @ X3155 @ X3152)|~(breln1 @ X3152 @ X3154)|~(breln1 @ X3152 @ X3153))&(~(X3157)|(X3157)|(in @ (kpair @ X3155 @ X3156) @ X3153)|~(in @ (kpair @ X3155 @ X3156) @ (binunion @ X3153 @ X3154))|~(in @ X3156 @ X3152)|~(in @ X3155 @ X3152)|~(breln1 @ X3152 @ X3154)|~(breln1 @ X3152 @ X3153)))&(((in @ (kpair @ X3155 @ X3156) @ X3154)|(X3157)|~(X3157)|~(in @ (kpair @ X3155 @ X3156) @ (binunion @ X3153 @ X3154))|~(in @ X3156 @ X3152)|~(in @ X3155 @ X3152)|~(breln1 @ X3152 @ X3154)|~(breln1 @ X3152 @ X3153))&(~(X3157)|(X3157)|~(X3157)|~(in @ (kpair @ X3155 @ X3156) @ (binunion @ X3153 @ X3154))|~(in @ X3156 @ X3152)|~(in @ X3155 @ X3152)|~(breln1 @ X3152 @ X3154)|~(breln1 @ X3152 @ X3153))))&((~(breln1 @ X3158 @ X3159)|(~(breln1 @ X3158 @ X3160)|((binunion @ X3159 @ X3160)=(binunion @ X3160 @ X3159))))&((~(breln1 @ X3161 @ X3162)|((X3162)=(breln1invset @ X3161 @ (breln1invset @ X3161 @ X3162))))&((~(breln1 @ X3163 @ X3164)|(~(breln1 @ X3163 @ X3165)|((breln1invset @ X3163 @ (breln1compset @ X3163 @ X3164 @ X3165))=(breln1compset @ X3163 @ (breln1invset @ X3163 @ X3165) @ (breln1invset @ X3163 @ X3164)))))&((~(breln1 @ X3166 @ X3167)|(~(breln1 @ X3166 @ X3168)|(~(breln1 @ X3166 @ X3169)|((breln1compset @ X3166 @ (binunion @ X3167 @ X3168) @ X3169)=(binunion @ (breln1compset @ X3166 @ X3167 @ X3169) @ (breln1compset @ X3166 @ X3168 @ X3169))))))&((~(breln1 @ X3170 @ X3171)|(~(breln1 @ X3170 @ X3172)|(~(breln1 @ X3170 @ X3173)|((breln1compset @ X3170 @ (binunion @ X3171 @ X3172) @ X3173)=(binunion @ (breln1invset @ X3170 @ (breln1compset @ X3170 @ (breln1invset @ X3170 @ X3173) @ (breln1invset @ X3170 @ X3172))) @ (breln1invset @ X3170 @ (breln1compset @ X3170 @ (breln1invset @ X3170 @ X3173) @ (breln1invset @ X3170 @ X3171))))))))&(((((in @ (esk84_3 @ X3174 @ X3175 @ X3177) @ X3174)|~(in @ X3177 @ (esk83_2 @ X3174 @ X3175)))&(((X3177)=(X3175 @ (esk84_3 @ X3174 @ X3175 @ X3177)))|~(in @ X3177 @ (esk83_2 @ X3174 @ X3175))))&(~(in @ X3180 @ X3174)|((X3179)!=(X3175 @ X3180))|(in @ X3179 @ (esk83_2 @ X3174 @ X3175))))&((exu @ (^[Z0/* 6 */:$i]:(![X1596:$i]:(((in @ X1596 @ Z0)<=>?[X1597:$i]:(((in @ X1597 @ X3181)&((X1596)=(X3182 @ X1597)))))))))&(((((in @ (esk85_3 @ X3183 @ X3184 @ X3185) @ X3183)|~(in @ X3185 @ (image1 @ X3183 @ X3184)))&(((X3185)=(X3184 @ (esk85_3 @ X3183 @ X3184 @ X3185)))|~(in @ X3185 @ (image1 @ X3183 @ X3184))))&(~(in @ X3190 @ X3187)|((X3189)!=(X3188 @ X3190))|(in @ X3189 @ (image1 @ X3187 @ X3188))))&((((in @ (esk86_3 @ X3191 @ X3192 @ X3193) @ X3191)|~(in @ X3193 @ (image1 @ X3191 @ X3192)))&(((X3193)=(X3192 @ (esk86_3 @ X3191 @ X3192 @ X3193)))|~(in @ X3193 @ (image1 @ X3191 @ X3192))))&((~(in @ X3198 @ X3195)|((X3197)!=(X3196 @ X3198))|(in @ X3197 @ (image1 @ X3195 @ X3196)))&((~(in @ X3201 @ (funcSet @ X3199 @ X3200))|(~(injective @ X3199 @ X3200 @ X3201)|(in @ X3201 @ (injFuncSet @ X3199 @ X3200))))&((~(in @ X3204 @ (injFuncSet @ X3202 @ X3203))|(in @ X3204 @ (funcSet @ X3202 @ X3203)))&((~(in @ X3207 @ (injFuncSet @ X3205 @ X3206))|(injective @ X3205 @ X3206 @ X3207))&((~(in @ X3210 @ (surjFuncSet @ X3208 @ X3209))|(in @ X3210 @ (funcSet @ X3208 @ X3209)))&((~(in @ X3213 @ (surjFuncSet @ X3211 @ X3212))|(surjective @ X3211 @ X3212 @ X3213))&(((((in @ (esk88_4 @ X3214 @ X3215 @ X3216 @ X3218) @ X3214)|(surjective @ X3215 @ X3214 @ X3218)|~(in @ X3218 @ (funcSet @ X3215 @ X3214))|(in @ (esk87_3 @ X3214 @ X3215 @ X3216) @ X3214))&(((ap @ X3215 @ X3214 @ X3218 @ (X3216 @ (esk88_4 @ X3214 @ X3215 @ X3216 @ X3218)))!=(esk88_4 @ X3214 @ X3215 @ X3216 @ X3218))|(surjective @ X3215 @ X3214 @ X3218)|~(in @ X3218 @ (funcSet @ X3215 @ X3214))|(in @ (esk87_3 @ X3214 @ X3215 @ X3216) @ X3214)))&(((in @ (esk88_4 @ X3214 @ X3215 @ X3216 @ X3218) @ X3214)|(surjective @ X3215 @ X3214 @ X3218)|~(in @ X3218 @ (funcSet @ X3215 @ X3214))|~(in @ (X3216 @ (esk87_3 @ X3214 @ X3215 @ X3216)) @ X3215))&(((ap @ X3215 @ X3214 @ X3218 @ (X3216 @ (esk88_4 @ X3214 @ X3215 @ X3216 @ X3218)))!=(esk88_4 @ X3214 @ X3215 @ X3216 @ X3218))|(surjective @ X3215 @ X3214 @ X3218)|~(in @ X3218 @ (funcSet @ X3215 @ X3214))|~(in @ (X3216 @ (esk87_3 @ X3214 @ X3215 @ X3216)) @ X3215))))&((~(in @ X3221 @ (funcSet @ X3220 @ (powerset @ X3220)))|~(surjective @ X3220 @ (powerset @ X3220) @ X3221))&(((esk89_0)!=(emptyset))&(((binintersect @ X3223 @ esk89_0)!=(emptyset))|~(in @ X3223 @ esk89_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_383])])])])])])])). 361.08/46.39 thf(c_0_385, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:((~((in @ X2 @ (esk8_1 @ X3)))|~((in @ X2 @ X3))|~((in @ X4 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_384])). 361.08/46.39 thf(c_0_386, negated_conjecture, ![X2:$i, X3:$i]:((~((in @ X2 @ (esk8_1 @ X3)))|~((in @ X2 @ X3)))), inference(condense,[status(thm)],[c_0_385])). 361.08/46.39 thf(c_0_387, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk38_2 @ X2 @ X3) @ X2)|((binintersect @ X2 @ X3)=(emptyset)))), inference(split_conjunct,[status(thm)],[c_0_384])). 361.08/46.39 thf(c_0_388, negated_conjecture, ![X3:$i, X2:$i]:((((binintersect @ (esk8_1 @ X2) @ X3)=(emptyset))|~((in @ (esk38_2 @ (esk8_1 @ X2) @ X3) @ X2)))), inference(spm,[status(thm)],[c_0_386, c_0_387])). 361.08/46.39 thf(c_0_389, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk38_2 @ X2 @ X3) @ X3)|((binintersect @ X2 @ X3)=(emptyset)))), inference(split_conjunct,[status(thm)],[c_0_384])). 361.08/46.39 thf(c_0_390, negated_conjecture, ![X2:$i]:((((binintersect @ X2 @ esk89_0)!=(emptyset))|~((in @ X2 @ esk89_0)))), inference(split_conjunct,[status(thm)],[c_0_384])). 361.08/46.39 thf(c_0_391, negated_conjecture, ![X2:$i]:(((binintersect @ (esk8_1 @ X2) @ X2)=(emptyset))), inference(spm,[status(thm)],[c_0_388, c_0_389])). 361.08/46.39 thf(c_0_392, negated_conjecture, ![X3:$i, X2:$i]:(((in @ (esk8_1 @ X2) @ X2)|~((in @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_384])). 361.08/46.39 thf(c_0_393, negated_conjecture, ![X2:$i]:(((in @ (esk19_1 @ X2) @ X2)|((X2)=(emptyset)))), inference(split_conjunct,[status(thm)],[c_0_384])). 361.08/46.39 thf(c_0_394, negated_conjecture, ~((in @ (esk8_1 @ esk89_0) @ esk89_0)), inference(spm,[status(thm)],[c_0_390, c_0_391])). 361.08/46.39 thf(c_0_395, negated_conjecture, ![X2:$i]:((((X2)=(emptyset))|(in @ (esk8_1 @ X2) @ X2))), inference(spm,[status(thm)],[c_0_392, c_0_393])). 361.08/46.39 thf(c_0_396, negated_conjecture, ((esk89_0)!=(emptyset)), inference(split_conjunct,[status(thm)],[c_0_384])). 361.08/46.39 thf(c_0_397, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_394, c_0_395]), c_0_396]), ['proof']). 361.08/46.39 # SZS output end CNFRefutation 361.08/46.39 # Parsed axioms : 698 361.08/46.39 # Removed by relevancy pruning/SinE : 377 361.08/46.39 # Initial clauses : 530 361.08/46.39 # Removed in clause preprocessing : 41 361.08/46.39 # Initial clauses in saturation : 489 361.08/46.39 # Processed clauses : 1800 361.08/46.39 # ...of these trivial : 23 361.08/46.39 # ...subsumed : 447 361.08/46.39 # ...remaining for further processing : 1330 361.08/46.39 # Other redundant clauses eliminated : 112 361.08/46.39 # Clauses deleted for lack of memory : 0 361.08/46.39 # Backward-subsumed : 28 361.08/46.39 # Backward-rewritten : 27 361.08/46.39 # Generated clauses : 32296 361.08/46.39 # ...of the previous two non-redundant : 31519 361.08/46.39 # ...aggressively subsumed : 0 361.08/46.39 # Contextual simplify-reflections : 15 361.08/46.39 # Paramodulations : 32145 361.08/46.39 # Factorizations : 2 361.08/46.39 # NegExts : 2 361.08/46.39 # Equation resolutions : 119 361.08/46.39 # Disequality decompositions : 0 361.08/46.39 # Total rewrite steps : 1299 361.08/46.39 # ...of those cached : 1036 361.08/46.39 # Propositional unsat checks : 0 361.08/46.39 # Propositional check models : 0 361.08/46.39 # Propositional check unsatisfiable : 0 361.08/46.39 # Propositional clauses : 0 361.08/46.39 # Propositional clauses after purity: 0 361.08/46.39 # Propositional unsat core size : 0 361.08/46.39 # Propositional preprocessing time : 0.000 361.08/46.39 # Propositional encoding time : 0.000 361.08/46.39 # Propositional solver time : 0.000 361.08/46.39 # Success case prop preproc time : 0.000 361.08/46.39 # Success case prop encoding time : 0.000 361.08/46.39 # Success case prop solver time : 0.000 361.08/46.39 # Current number of processed clauses : 829 361.08/46.39 # Positive orientable unit clauses : 80 361.08/46.39 # Positive unorientable unit clauses: 0 361.08/46.39 # Negative unit clauses : 17 361.08/46.39 # Non-unit-clauses : 732 361.08/46.39 # Current number of unprocessed clauses: 30349 361.08/46.39 # ...number of literals in the above : 128514 361.08/46.39 # Current number of archived formulas : 0 361.08/46.39 # Current number of archived clauses : 480 361.08/46.39 # Clause-clause subsumption calls (NU) : 170602 361.08/46.39 # Rec. Clause-clause subsumption calls : 75284 361.08/46.39 # Non-unit clause-clause subsumptions : 285 361.08/46.39 # Unit Clause-clause subsumption calls : 2157 361.08/46.39 # Rewrite failures with RHS unbound : 0 361.08/46.39 # BW rewrite match attempts : 66 361.08/46.39 # BW rewrite match successes : 19 361.08/46.39 # Condensation attempts : 1800 361.08/46.39 # Condensation successes : 16 361.08/46.39 # Termbank termtop insertions : 655451 361.08/46.39 # Search garbage collected termcells : 34968 361.08/46.39 361.08/46.39 # ------------------------------------------------- 361.08/46.39 # User time : 43.703 s 361.08/46.39 # System time : 1.197 s 361.08/46.39 # Total time : 44.900 s 361.08/46.39 # Maximum resident set size: 10616 pages 361.08/46.39 361.08/46.39 # ------------------------------------------------- 361.08/46.39 # User time : 43.725 s 361.08/46.39 # System time : 1.201 s 361.08/46.39 # Total time : 44.926 s 361.08/46.39 # Maximum resident set size: 2900 pages 361.08/46.39 % E exiting 361.08/46.40 % E exiting 361.08/46.40 EOF