0.00/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.11 % Command : run_E %s %d THM 0.10/0.31 % Computer : n005.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 1440 0.10/0.31 % WCLimit : 180 0.10/0.31 % DateTime : Thu Jul 4 11:21:08 EDT 2024 0.10/0.31 % CPUTime : 0.16/0.44 Running higher-order theorem proving 0.16/0.48 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p 309.13/39.45 # Version: 3.2.0-ho 309.13/39.45 # Preprocessing class: HSLMSLSSLLLCHFA. 309.13/39.45 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 309.13/39.45 # Starting ehoh_best5 with 180s (1) cores 309.13/39.45 # Starting almost_fo_3_lam with 180s (1) cores 309.13/39.45 # Starting new_bool_5 with 180s (1) cores 309.13/39.45 # Starting pre_casc_3 with 180s (1) cores 309.13/39.45 # Starting ho_unfolding_8 with 180s (1) cores 309.13/39.45 # Starting new_ho_10_cnf2 with 180s (1) cores 309.13/39.45 # Starting new_bool_3 with 180s (1) cores 309.13/39.45 # Starting new_ho_5 with 180s (1) cores 309.13/39.45 # almost_fo_3_lam with pid 704 completed with status 0 309.13/39.45 # Result found by almost_fo_3_lam 309.13/39.45 # Preprocessing class: HSLMSLSSLLLCHFA. 309.13/39.45 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 309.13/39.45 # Starting ehoh_best5 with 180s (1) cores 309.13/39.45 # Starting almost_fo_3_lam with 180s (1) cores 309.13/39.45 # No SInE strategy applied 309.13/39.45 # Search class: HGHSM-FSLM32-MHFMMSBN 309.13/39.45 # Scheduled 10 strats onto 1 cores with 180 seconds (180 total) 309.13/39.45 # Starting ho_unfolding_8 with 33s (1) cores 309.13/39.45 # ho_unfolding_8 with pid 716 completed with status 7 309.13/39.45 # Starting almost_fo_3_lam with 19s (1) cores 309.13/39.45 # almost_fo_3_lam with pid 726 completed with status 0 309.13/39.45 # Result found by almost_fo_3_lam 309.13/39.45 # Preprocessing class: HSLMSLSSLLLCHFA. 309.13/39.45 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 309.13/39.45 # Starting ehoh_best5 with 180s (1) cores 309.13/39.45 # Starting almost_fo_3_lam with 180s (1) cores 309.13/39.45 # No SInE strategy applied 309.13/39.45 # Search class: HGHSM-FSLM32-MHFMMSBN 309.13/39.45 # Scheduled 10 strats onto 1 cores with 180 seconds (180 total) 309.13/39.45 # Starting ho_unfolding_8 with 33s (1) cores 309.13/39.45 # ho_unfolding_8 with pid 716 completed with status 7 309.13/39.45 # Starting almost_fo_3_lam with 19s (1) cores 309.13/39.45 # Preprocessing time : 0.008 s 309.13/39.45 # Presaturation interreduction done 309.13/39.45 309.13/39.45 # Proof found! 309.13/39.45 # SZS status Theorem 309.13/39.45 # SZS output start CNFRefutation 309.13/39.45 thf(decl_22, type, in: $i > $i > $o). 309.13/39.45 thf(decl_23, type, exu: ($i > $o) > $o). 309.13/39.45 thf(decl_24, type, setextAx: $o). 309.13/39.45 thf(decl_25, type, emptyset: $i). 309.13/39.45 thf(decl_26, type, emptysetAx: $o). 309.13/39.45 thf(decl_27, type, setadjoin: $i > $i > $i). 309.13/39.45 thf(decl_28, type, setadjoinAx: $o). 309.13/39.45 thf(decl_29, type, powerset: $i > $i). 309.13/39.45 thf(decl_30, type, powersetAx: $o). 309.13/39.45 thf(decl_31, type, setunion: $i > $i). 309.13/39.45 thf(decl_32, type, setunionAx: $o). 309.13/39.45 thf(decl_33, type, omega: $i). 309.13/39.45 thf(decl_34, type, omega0Ax: $o). 309.13/39.45 thf(decl_35, type, omegaSAx: $o). 309.13/39.45 thf(decl_36, type, omegaIndAx: $o). 309.13/39.45 thf(decl_37, type, replAx: $o). 309.13/39.45 thf(decl_38, type, foundationAx: $o). 309.13/39.45 thf(decl_39, type, wellorderingAx: $o). 309.13/39.45 thf(decl_40, type, descr: ($i > $o) > $i). 309.13/39.45 thf(decl_41, type, descrp: $o). 309.13/39.45 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 309.13/39.45 thf(decl_43, type, dsetconstrI: $o). 309.13/39.45 thf(decl_44, type, dsetconstrEL: $o). 309.13/39.45 thf(decl_45, type, dsetconstrER: $o). 309.13/39.45 thf(decl_46, type, exuE1: $o). 309.13/39.45 thf(decl_47, type, prop2set: $o > $i). 309.13/39.45 thf(decl_48, type, prop2setE: $o). 309.13/39.45 thf(decl_49, type, emptysetE: $o). 309.13/39.45 thf(decl_50, type, emptysetimpfalse: $o). 309.13/39.45 thf(decl_51, type, notinemptyset: $o). 309.13/39.45 thf(decl_52, type, exuE3e: $o). 309.13/39.45 thf(decl_53, type, setext: $o). 309.13/39.45 thf(decl_54, type, emptyI: $o). 309.13/39.45 thf(decl_55, type, noeltsimpempty: $o). 309.13/39.45 thf(decl_56, type, setbeta: $o). 309.13/39.45 thf(decl_57, type, nonempty: $i > $o). 309.13/39.45 thf(decl_58, type, nonemptyE1: $o). 309.13/39.45 thf(decl_59, type, nonemptyI: $o). 309.13/39.45 thf(decl_60, type, nonemptyI1: $o). 309.13/39.45 thf(decl_61, type, setadjoinIL: $o). 309.13/39.45 thf(decl_62, type, emptyinunitempty: $o). 309.13/39.45 thf(decl_63, type, setadjoinIR: $o). 309.13/39.45 thf(decl_64, type, setadjoinE: $o). 309.13/39.45 thf(decl_65, type, setadjoinOr: $o). 309.13/39.45 thf(decl_66, type, setoftrueEq: $o). 309.13/39.45 thf(decl_67, type, powersetI: $o). 309.13/39.45 thf(decl_68, type, emptyinPowerset: $o). 309.13/39.45 thf(decl_69, type, emptyInPowerset: $o). 309.13/39.45 thf(decl_70, type, powersetE: $o). 309.13/39.45 thf(decl_71, type, setunionI: $o). 309.13/39.45 thf(decl_72, type, setunionE: $o). 309.13/39.45 thf(decl_73, type, subPowSU: $o). 309.13/39.45 thf(decl_74, type, exuE2: $o). 309.13/39.45 thf(decl_75, type, nonemptyImpWitness: $o). 309.13/39.45 thf(decl_76, type, uniqinunit: $o). 309.13/39.45 thf(decl_77, type, notinsingleton: $o). 309.13/39.45 thf(decl_78, type, eqinunit: $o). 309.13/39.45 thf(decl_79, type, singletonsswitch: $o). 309.13/39.45 thf(decl_80, type, upairsetE: $o). 309.13/39.45 thf(decl_81, type, upairsetIL: $o). 309.13/39.45 thf(decl_82, type, upairsetIR: $o). 309.13/39.45 thf(decl_83, type, emptyE1: $o). 309.13/39.45 thf(decl_84, type, vacuousDall: $o). 309.13/39.45 thf(decl_85, type, quantDeMorgan1: $o). 309.13/39.45 thf(decl_86, type, quantDeMorgan2: $o). 309.13/39.45 thf(decl_87, type, quantDeMorgan3: $o). 309.13/39.45 thf(decl_88, type, quantDeMorgan4: $o). 309.13/39.45 thf(decl_89, type, prop2setI: $o). 309.13/39.45 thf(decl_90, type, set2prop: $i > $o). 309.13/39.45 thf(decl_91, type, prop2set2propI: $o). 309.13/39.45 thf(decl_92, type, notdexE: $o). 309.13/39.45 thf(decl_93, type, notdallE: $o). 309.13/39.45 thf(decl_94, type, exuI1: $o). 309.13/39.45 thf(decl_95, type, exuI3: $o). 309.13/39.45 thf(decl_96, type, exuI2: $o). 309.13/39.45 thf(decl_97, type, inCongP: $o). 309.13/39.45 thf(decl_98, type, in__Cong: $o). 309.13/39.45 thf(decl_99, type, exuE3u: $o). 309.13/39.45 thf(decl_100, type, exu__Cong: $o). 309.13/39.45 thf(decl_101, type, emptyset__Cong: $o). 309.13/39.45 thf(decl_102, type, setadjoin__Cong: $o). 309.13/39.45 thf(decl_103, type, powerset__Cong: $o). 309.13/39.45 thf(decl_104, type, setunion__Cong: $o). 309.13/39.45 thf(decl_105, type, omega__Cong: $o). 309.13/39.45 thf(decl_106, type, exuEu: $o). 309.13/39.45 thf(decl_107, type, descr__Cong: $o). 309.13/39.45 thf(decl_108, type, dsetconstr__Cong: $o). 309.13/39.45 thf(decl_109, type, subset: $i > $i > $o). 309.13/39.45 thf(decl_112, type, subsetI1: $o). 309.13/39.45 thf(decl_113, type, eqimpsubset2: $o). 309.13/39.45 thf(decl_114, type, eqimpsubset1: $o). 309.13/39.45 thf(decl_115, type, subsetI2: $o). 309.13/39.45 thf(decl_116, type, emptysetsubset: $o). 309.13/39.45 thf(decl_117, type, subsetE: $o). 309.13/39.45 thf(decl_118, type, subsetE2: $o). 309.13/39.45 thf(decl_119, type, notsubsetI: $o). 309.13/39.45 thf(decl_120, type, notequalI1: $o). 309.13/39.45 thf(decl_121, type, notequalI2: $o). 309.13/39.45 thf(decl_122, type, subsetRefl: $o). 309.13/39.45 thf(decl_123, type, subsetTrans: $o). 309.13/39.45 thf(decl_124, type, setadjoinSub: $o). 309.13/39.45 thf(decl_125, type, setadjoinSub2: $o). 309.13/39.45 thf(decl_126, type, subset2powerset: $o). 309.13/39.45 thf(decl_127, type, setextsub: $o). 309.13/39.45 thf(decl_128, type, subsetemptysetimpeq: $o). 309.13/39.45 thf(decl_129, type, powersetI1: $o). 309.13/39.45 thf(decl_130, type, powersetE1: $o). 309.13/39.45 thf(decl_131, type, inPowerset: $o). 309.13/39.45 thf(decl_132, type, powersetsubset: $o). 309.13/39.45 thf(decl_133, type, sepInPowerset: $o). 309.13/39.45 thf(decl_134, type, sepSubset: $o). 309.13/39.45 thf(decl_135, type, binunion: $i > $i > $i). 309.13/39.45 thf(decl_136, type, binunionIL: $o). 309.13/39.45 thf(decl_137, type, upairset2IR: $o). 309.13/39.45 thf(decl_138, type, binunionIR: $o). 309.13/39.45 thf(decl_139, type, binunionEcases: $o). 309.13/39.45 thf(decl_140, type, binunionE: $o). 309.13/39.45 thf(decl_141, type, binunionLsub: $o). 309.13/39.45 thf(decl_142, type, binunionRsub: $o). 309.13/39.45 thf(decl_143, type, binintersect: $i > $i > $i). 309.13/39.45 thf(decl_144, type, binintersectI: $o). 309.13/39.45 thf(decl_145, type, binintersectSubset5: $o). 309.13/39.45 thf(decl_146, type, binintersectEL: $o). 309.13/39.45 thf(decl_147, type, binintersectLsub: $o). 309.13/39.45 thf(decl_148, type, binintersectSubset2: $o). 309.13/39.45 thf(decl_149, type, binintersectSubset3: $o). 309.13/39.45 thf(decl_150, type, binintersectER: $o). 309.13/39.45 thf(decl_151, type, disjointsetsI1: $o). 309.13/39.45 thf(decl_152, type, binintersectRsub: $o). 309.13/39.45 thf(decl_153, type, binintersectSubset4: $o). 309.13/39.45 thf(decl_154, type, binintersectSubset1: $o). 309.13/39.45 thf(decl_155, type, bs114d: $o). 309.13/39.45 thf(decl_157, type, setminus: $i > $i > $i). 309.13/39.45 thf(decl_158, type, setminusI: $o). 309.13/39.45 thf(decl_159, type, setminusEL: $o). 309.13/39.45 thf(decl_160, type, setminusER: $o). 309.13/39.45 thf(decl_161, type, setminusSubset2: $o). 309.13/39.45 thf(decl_162, type, setminusERneg: $o). 309.13/39.45 thf(decl_163, type, setminusELneg: $o). 309.13/39.45 thf(decl_164, type, setminusILneg: $o). 309.13/39.45 thf(decl_165, type, setminusIRneg: $o). 309.13/39.45 thf(decl_166, type, setminusLsub: $o). 309.13/39.45 thf(decl_167, type, setminusSubset1: $o). 309.13/39.45 thf(decl_168, type, symdiff: $i > $i > $i). 309.13/39.45 thf(decl_169, type, symdiffE: $o). 309.13/39.45 thf(decl_170, type, symdiffI1: $o). 309.13/39.45 thf(decl_171, type, symdiffI2: $o). 309.13/39.45 thf(decl_172, type, symdiffIneg1: $o). 309.13/39.45 thf(decl_173, type, symdiffIneg2: $o). 309.13/39.45 thf(decl_174, type, iskpair: $i > $o). 309.13/39.45 thf(decl_175, type, secondinupair: $o). 309.13/39.45 thf(decl_176, type, setukpairIL: $o). 309.13/39.45 thf(decl_177, type, setukpairIR: $o). 309.13/39.45 thf(decl_178, type, kpairiskpair: $o). 309.13/39.45 thf(decl_179, type, kpair: $i > $i > $i). 309.13/39.45 thf(decl_180, type, kpairp: $o). 309.13/39.45 thf(decl_181, type, cartprod: $i > $i > $i). 309.13/39.45 thf(decl_182, type, singletonsubset: $o). 309.13/39.45 thf(decl_183, type, singletoninpowerset: $o). 309.13/39.45 thf(decl_184, type, singletoninpowunion: $o). 309.13/39.45 thf(decl_185, type, upairset2E: $o). 309.13/39.45 thf(decl_186, type, upairsubunion: $o). 309.13/39.45 thf(decl_187, type, upairinpowunion: $o). 309.13/39.45 thf(decl_188, type, ubforcartprodlem1: $o). 309.13/39.45 thf(decl_189, type, ubforcartprodlem2: $o). 309.13/39.45 thf(decl_190, type, ubforcartprodlem3: $o). 309.13/39.45 thf(decl_191, type, cartprodpairin: $o). 309.13/39.45 thf(decl_192, type, cartprodmempair1: $o). 309.13/39.45 thf(decl_193, type, cartprodmempair: $o). 309.13/39.45 thf(decl_194, type, setunionE2: $o). 309.13/39.45 thf(decl_195, type, setunionsingleton1: $o). 309.13/39.45 thf(decl_196, type, setunionsingleton2: $o). 309.13/39.45 thf(decl_197, type, setunionsingleton: $o). 309.13/39.45 thf(decl_198, type, singleton: $i > $o). 309.13/39.45 thf(decl_199, type, singletonprop: $o). 309.13/39.45 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 309.13/39.45 thf(decl_201, type, ex1E1: $o). 309.13/39.45 thf(decl_202, type, ex1I: $o). 309.13/39.45 thf(decl_203, type, ex1I2: $o). 309.13/39.45 thf(decl_204, type, singletonsuniq: $o). 309.13/39.45 thf(decl_209, type, setukpairinjL1: $o). 309.13/39.45 thf(decl_210, type, kfstsingleton: $o). 309.13/39.45 thf(decl_211, type, theprop: $o). 309.13/39.45 thf(decl_212, type, kfst: $i > $i). 309.13/39.45 thf(decl_213, type, kfstpairEq: $o). 309.13/39.45 thf(decl_214, type, cartprodfstin: $o). 309.13/39.45 thf(decl_215, type, setukpairinjL2: $o). 309.13/39.45 thf(decl_216, type, setukpairinjL: $o). 309.13/39.45 thf(decl_217, type, setukpairinjR11: $o). 309.13/39.45 thf(decl_218, type, setukpairinjR12: $o). 309.13/39.45 thf(decl_219, type, setukpairinjR1: $o). 309.13/39.45 thf(decl_220, type, upairequniteq: $o). 309.13/39.45 thf(decl_221, type, setukpairinjR2: $o). 309.13/39.45 thf(decl_222, type, setukpairinjR: $o). 309.13/39.45 thf(decl_223, type, ksndsingleton: $o). 309.13/39.45 thf(decl_224, type, ksnd: $i > $i). 309.13/39.45 thf(decl_225, type, ksndpairEq: $o). 309.13/39.45 thf(decl_226, type, kpairsurjEq: $o). 309.13/39.45 thf(decl_227, type, cartprodsndin: $o). 309.13/39.45 thf(decl_228, type, cartprodpairmemEL: $o). 309.13/39.45 thf(decl_229, type, cartprodpairmemER: $o). 309.13/39.45 thf(decl_230, type, cartprodmempaircEq: $o). 309.13/39.45 thf(decl_231, type, cartprodfstpairEq: $o). 309.13/39.45 thf(decl_232, type, cartprodsndpairEq: $o). 309.13/39.45 thf(decl_233, type, cartprodpairsurjEq: $o). 309.13/39.45 thf(decl_234, type, breln: $i > $i > $i > $o). 309.13/39.45 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 309.13/39.45 thf(decl_236, type, dpsetconstrI: $o). 309.13/39.45 thf(decl_237, type, dpsetconstrSub: $o). 309.13/39.45 thf(decl_238, type, setOfPairsIsBReln: $o). 309.13/39.45 thf(decl_239, type, dpsetconstrERa: $o). 309.13/39.45 thf(decl_240, type, dpsetconstrEL1: $o). 309.13/39.45 thf(decl_241, type, dpsetconstrEL2: $o). 309.13/39.45 thf(decl_242, type, dpsetconstrER: $o). 309.13/39.45 thf(decl_243, type, func: $i > $i > $i > $o). 309.13/39.45 thf(decl_244, type, funcSet: $i > $i > $i). 309.13/39.45 thf(decl_245, type, funcImageSingleton: $o). 309.13/39.45 thf(decl_246, type, apProp: $o). 309.13/39.45 thf(decl_247, type, ap: $i > $i > $i > $i > $i). 309.13/39.45 thf(decl_248, type, app: $o). 309.13/39.45 thf(decl_249, type, infuncsetfunc: $o). 309.13/39.45 thf(decl_250, type, ap2p: $o). 309.13/39.45 thf(decl_251, type, funcinfuncset: $o). 309.13/39.45 thf(decl_252, type, lamProp: $o). 309.13/39.45 thf(decl_253, type, lam: $i > $i > ($i > $i) > $i). 309.13/39.45 thf(decl_254, type, lamp: $o). 309.13/39.45 thf(decl_255, type, lam2p: $o). 309.13/39.45 thf(decl_256, type, brelnall1: $o). 309.13/39.45 thf(decl_257, type, brelnall2: $o). 309.13/39.45 thf(decl_258, type, ex1E2: $o). 309.13/39.45 thf(decl_259, type, funcGraphProp1: $o). 309.13/39.45 thf(decl_260, type, funcGraphProp3: $o). 309.13/39.45 thf(decl_261, type, funcGraphProp2: $o). 309.13/39.45 thf(decl_262, type, funcextLem: $o). 309.13/39.45 thf(decl_263, type, funcGraphProp4: $o). 309.13/39.45 thf(decl_264, type, subbreln: $o). 309.13/39.45 thf(decl_265, type, eqbreln: $o). 309.13/39.45 thf(decl_266, type, funcext: $o). 309.13/39.45 thf(decl_267, type, funcext2: $o). 309.13/39.45 thf(decl_268, type, ap2apEq1: $o). 309.13/39.45 thf(decl_269, type, ap2apEq2: $o). 309.13/39.45 thf(decl_270, type, beta1: $o). 309.13/39.45 thf(decl_271, type, eta1: $o). 309.13/39.45 thf(decl_272, type, lam2lamEq: $o). 309.13/39.45 thf(decl_273, type, beta2: $o). 309.13/39.45 thf(decl_274, type, eta2: $o). 309.13/39.45 thf(decl_275, type, iffalseProp1: $o). 309.13/39.45 thf(decl_276, type, iffalseProp2: $o). 309.13/39.45 thf(decl_277, type, iftrueProp1: $o). 309.13/39.45 thf(decl_278, type, iftrueProp2: $o). 309.13/39.45 thf(decl_279, type, ifSingleton: $o). 309.13/39.45 thf(decl_280, type, if: $i > $o > $i > $i > $i). 309.13/39.45 thf(decl_281, type, ifp: $o). 309.13/39.45 thf(decl_282, type, theeq: $o). 309.13/39.45 thf(decl_283, type, iftrue: $o). 309.13/39.45 thf(decl_284, type, iffalse: $o). 309.13/39.45 thf(decl_285, type, iftrueorfalse: $o). 309.13/39.45 thf(decl_286, type, binintersectT_lem: $o). 309.13/39.45 thf(decl_287, type, binunionT_lem: $o). 309.13/39.45 thf(decl_288, type, powersetT_lem: $o). 309.13/39.45 thf(decl_289, type, setminusT_lem: $o). 309.13/39.45 thf(decl_290, type, complementT_lem: $o). 309.13/39.45 thf(decl_291, type, setextT: $o). 309.13/39.45 thf(decl_292, type, subsetTI: $o). 309.13/39.45 thf(decl_293, type, powersetTI1: $o). 309.13/39.45 thf(decl_294, type, powersetTE1: $o). 309.13/39.45 thf(decl_295, type, complementTI1: $o). 309.13/39.45 thf(decl_296, type, complementTE1: $o). 309.13/39.45 thf(decl_297, type, binintersectTELcontra: $o). 309.13/39.45 thf(decl_298, type, binintersectTERcontra: $o). 309.13/39.45 thf(decl_299, type, contrasubsetT: $o). 309.13/39.45 thf(decl_300, type, contrasubsetT1: $o). 309.13/39.45 thf(decl_301, type, epred1_0: $o). 309.13/39.45 thf(decl_302, type, esk1_2: $i > $i > $i). 309.13/39.45 thf(decl_303, type, esk2_2: $i > $i > $i). 309.13/39.45 thf(decl_304, type, esk3_2: $i > $i > $i). 309.13/39.45 thf(decl_305, type, esk4_1: $i > $i). 309.13/39.45 thf(decl_306, type, esk5_2: ($i > $i > $o) > $i > $i). 309.13/39.45 thf(decl_307, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 309.13/39.45 thf(decl_308, type, esk7_2: ($i > $i > $o) > $i > $i). 309.13/39.45 thf(decl_309, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 309.13/39.45 thf(decl_310, type, esk9_1: $i > $i). 309.13/39.45 thf(decl_311, type, esk10_2: ($i > $o) > $i > $i). 309.13/39.45 thf(decl_312, type, esk11_2: ($i > $o) > $i > $i). 309.13/39.45 thf(decl_313, type, esk12_1: ($i > $o) > $i). 309.13/39.45 thf(decl_314, type, esk13_2: ($i > $o) > $i > $i). 309.13/39.45 thf(decl_315, type, esk14_1: ($i > $o) > $i). 309.13/39.45 thf(decl_316, type, esk15_2: $i > $i > $i). 309.13/39.45 thf(decl_317, type, esk16_2: $i > $i > $i). 309.13/39.45 thf(decl_318, type, esk17_1: $i > $i). 309.13/39.45 thf(decl_319, type, esk18_1: $i > $i). 309.13/39.45 thf(decl_320, type, esk19_1: $i > $i). 309.13/39.45 thf(decl_321, type, esk20_2: $i > $i > $i). 309.13/39.45 thf(decl_322, type, esk21_3: $i > $i > $o > $i). 309.13/39.45 thf(decl_323, type, esk22_2: ($i > $o) > $i > $i). 309.13/39.45 thf(decl_324, type, esk23_1: ($i > $o) > $i). 309.13/39.45 thf(decl_325, type, esk24_1: $i > $i). 309.13/39.45 thf(decl_326, type, esk25_2: $i > ($i > $o) > $i). 309.13/39.45 thf(decl_327, type, esk26_2: $i > ($i > $o) > $i). 309.13/39.45 thf(decl_328, type, esk27_2: $i > ($i > $o) > $i). 309.13/39.45 thf(decl_329, type, esk28_2: $i > ($i > $o) > $i). 309.13/39.45 thf(decl_330, type, esk29_2: $i > ($i > $o) > $i). 309.13/39.45 thf(decl_331, type, esk30_2: $i > ($i > $o) > $i). 309.13/39.45 thf(decl_332, type, esk31_2: ($i > $o) > $i > $i). 309.13/39.45 thf(decl_333, type, esk32_1: ($i > $o) > $i). 309.13/39.45 thf(decl_334, type, esk33_1: ($i > $o) > $i). 309.13/39.45 thf(decl_335, type, esk34_1: ($i > $o) > $i). 309.13/39.45 thf(decl_336, type, esk35_1: ($i > $o) > $i). 309.13/39.45 thf(decl_337, type, esk36_2: ($i > $o) > $i > $i). 309.13/39.45 thf(decl_338, type, esk37_1: ($i > $o) > $i). 309.13/39.45 thf(decl_339, type, esk38_2: ($i > $o) > $i > $i). 309.13/39.45 thf(decl_340, type, esk39_2: ($i > $o) > ($i > $o) > $i). 309.13/39.45 thf(decl_341, type, esk40_2: ($i > $o) > ($i > $o) > $i). 309.13/39.45 thf(decl_342, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 309.13/39.45 thf(decl_343, type, esk42_2: ($i > $o) > ($i > $o) > $i). 309.13/39.45 thf(decl_344, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 309.13/39.45 thf(decl_345, type, esk44_2: ($i > $o) > ($i > $o) > $i). 309.13/39.45 thf(decl_346, type, esk45_2: ($i > $o) > $i > $i). 309.13/39.45 thf(decl_347, type, esk46_2: ($i > $o) > ($i > $o) > $i). 309.13/39.45 thf(decl_348, type, esk47_2: ($i > $o) > ($i > $o) > $i). 309.13/39.45 thf(decl_349, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 309.13/39.45 thf(decl_350, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 309.13/39.45 thf(decl_351, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 309.13/39.45 thf(decl_352, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 309.13/39.45 thf(decl_353, type, esk52_2: $i > $i > $i). 309.13/39.45 thf(decl_354, type, esk53_2: $i > $i > $i). 309.13/39.45 thf(decl_355, type, esk54_2: $i > $i > $i). 309.13/39.45 thf(decl_356, type, esk55_3: $i > $i > $i > $i). 309.13/39.45 thf(decl_357, type, esk56_3: $i > $i > $i > $i). 309.13/39.45 thf(decl_358, type, esk57_2: $i > $i > $i). 309.13/39.45 thf(decl_359, type, esk58_2: $i > ($i > $o) > $i). 309.13/39.45 thf(decl_360, type, esk59_2: $i > ($i > $o) > $i). 309.13/39.45 thf(decl_361, type, esk60_2: $i > ($i > $o) > $i). 309.13/39.45 thf(decl_362, type, esk61_3: $i > ($i > $o) > $i > $i). 309.13/39.45 thf(decl_363, type, esk62_2: $i > ($i > $o) > $i). 309.13/39.45 thf(decl_364, type, esk63_2: $i > ($i > $o) > $i). 309.13/39.45 thf(decl_365, type, esk64_3: $i > $i > ($i > $i) > $i). 309.13/39.45 thf(decl_366, type, esk65_3: $i > $i > ($i > $i) > $i). 309.13/39.45 thf(decl_367, type, esk66_3: $i > $i > ($i > $i) > $i). 309.13/39.45 thf(decl_368, type, esk67_4: $i > $i > $i > ($i > $o) > $i). 309.13/39.45 thf(decl_369, type, esk68_4: $i > $i > $i > ($i > $o) > $i). 309.13/39.45 thf(decl_370, type, esk69_4: $i > $i > $i > ($i > $o) > $i). 309.13/39.45 thf(decl_371, type, esk70_4: $i > $i > $i > ($i > $o) > $i). 309.13/39.45 thf(decl_372, type, esk71_4: $i > $i > $i > $i > $i). 309.13/39.45 thf(decl_373, type, esk72_4: $i > $i > $i > $i > $i). 309.13/39.45 thf(decl_374, type, esk73_4: $i > $i > $i > $i > $i). 309.13/39.45 thf(decl_375, type, esk74_4: $i > $i > $i > $i > $i). 309.13/39.45 thf(decl_376, type, esk75_4: $i > $i > $i > $i > $i). 309.13/39.45 thf(decl_377, type, esk76_4: $i > $i > $i > $i > $i). 309.13/39.45 thf(decl_378, type, esk77_4: $i > $i > $i > $i > $i). 309.13/39.45 thf(decl_379, type, esk78_4: $i > $i > $i > $i > $i). 309.13/39.45 thf(decl_380, type, esk79_4: $i > $i > $i > $i > $i). 309.13/39.45 thf(decl_381, type, esk80_3: $i > $i > ($i > $i) > $i). 309.13/39.45 thf(decl_382, type, esk81_3: $i > $i > ($i > $i) > $i). 309.13/39.45 thf(decl_383, type, esk82_3: $i > $i > ($i > $i) > $i). 309.13/39.45 thf(decl_384, type, esk83_3: $i > $i > $i > $i). 309.13/39.45 thf(decl_385, type, esk84_3: $i > $i > $i > $i). 309.13/39.45 thf(decl_386, type, esk85_3: $i > $i > $i > $i). 309.13/39.45 thf(decl_387, type, esk86_3: $i > $i > $i > $i). 309.13/39.45 thf(decl_388, type, esk87_0: $i). 309.13/39.45 thf(decl_389, type, esk88_0: $i). 309.13/39.45 thf(decl_390, type, esk89_0: $i). 309.13/39.45 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', replAx)). 309.13/39.45 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', exu)). 309.13/39.45 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', descrp)). 309.13/39.45 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', exuE1)). 309.13/39.45 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', exuE3e)). 309.13/39.45 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', nonempty)). 309.13/39.45 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', nonemptyI)). 309.13/39.45 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', exuE2)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', exuI1)). 309.13/39.45 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', exuI3)). 309.13/39.45 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', exuI2)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', exuE3u)). 309.13/39.45 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', exu__Cong)). 309.13/39.45 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', exuEu)). 309.13/39.45 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', descr__Cong)). 309.13/39.45 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', ex1E1)). 309.13/39.45 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', ex1)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', ex1I)). 309.13/39.45 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', ex1I2)). 309.13/39.45 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setOfPairsIsBReln)). 309.13/39.45 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', breln)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', ex1E2)). 309.13/39.45 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', dsetconstrI)). 309.13/39.45 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', dsetconstrEL)). 309.13/39.45 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', dsetconstrER)). 309.13/39.45 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setbeta)). 309.13/39.45 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', nonemptyE1)). 309.13/39.45 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', nonemptyI1)). 309.13/39.45 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setoftrueEq)). 309.13/39.45 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', nonemptyImpWitness)). 309.13/39.45 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.f57cP6NHQL/E---3.1_604.p', emptyE1)). 309.13/39.45 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', dsetconstr__Cong)). 309.13/39.45 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', sepInPowerset)). 309.13/39.45 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', sepSubset)). 309.13/39.45 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', singletonprop)). 309.13/39.45 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', kfstsingleton)). 309.13/39.45 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', ksndsingleton)). 309.13/39.45 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', dpsetconstrI)). 309.13/39.45 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', dpsetconstrSub)). 309.13/39.45 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', dpsetconstrERa)). 309.13/39.45 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', dpsetconstrEL1)). 309.13/39.45 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', dpsetconstrEL2)). 309.13/39.45 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', dpsetconstrER)). 309.13/39.45 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.f57cP6NHQL/E---3.1_604.p', funcImageSingleton)). 309.13/39.45 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', apProp)). 309.13/39.45 thf(lamProp, axiom, ((lamProp)<=>![X4:$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.f57cP6NHQL/E---3.1_604.p', lamProp)). 309.13/39.45 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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', lamp)). 309.13/39.45 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', lam2p)). 309.13/39.45 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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.f57cP6NHQL/E---3.1_604.p', brelnall1)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', brelnall2)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', subbreln)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', eqbreln)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', beta1)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', eta1)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', lam2lamEq)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', beta2)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', eta2)). 309.13/39.45 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', iffalseProp1)). 309.13/39.45 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.f57cP6NHQL/E---3.1_604.p', iffalseProp2)). 309.13/39.45 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', iftrueProp1)). 309.13/39.45 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.f57cP6NHQL/E---3.1_604.p', iftrueProp2)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', ifSingleton)). 309.13/39.45 thf(contrasubsetT2, conjecture, ((setextAx)=>((emptysetAx)=>((((setunionAx)=>((omega0Ax)=>((omegaSAx)=>(((replAx)=>((foundationAx)=>((((((((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((((emptyI)=>(((((nonemptyI)=>((nonemptyI1)=>((((setadjoinIR)=>(((setadjoinOr)=>((((emptyinPowerset)=>((emptyInPowerset)=>(((setunionI)=>((setunionE)=>(((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>(((eqinunit)=>((singletonsswitch)=>((upairsetE)=>(((((vacuousDall)=>((((((prop2setI)=>(((notdexE)=>(((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((((exu__Cong)=>(((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>(((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((((((subsetE)=>((subsetE2)=>(((notequalI1)=>(((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>(((subsetemptysetimpeq)=>(((((powersetsubset)=>(((sepSubset)=>(((upairset2IR)=>(((binunionEcases)=>((binunionE)=>((binunionLsub)=>((((((((binintersectSubset3)=>(((disjointsetsI1)=>(((binintersectSubset4)=>((((setminusI)=>(((setminusER)=>(((setminusERneg)=>((((setminusIRneg)=>(((setminusSubset1)=>((((((symdiffIneg2)=>((((((kpairp)=>((singletonsubset)=>((((upairset2E)=>((((((((((((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>(((((((theprop)=>((kfstpairEq)=>(((((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>(((setukpairinjR)=>(((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>(((((((dpsetconstrERa)=>((((dpsetconstrER)=>((funcImageSingleton)=>(((((ap2p)=>(((((lam2p)=>(((brelnall2)=>((((funcGraphProp3)=>(((funcextLem)=>((funcGraphProp4)=>((subbreln)=>(((funcext)=>((funcext2)=>(((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>(((eta2)=>(((iffalseProp2)=>(((((ifp)=>((theeq)=>(((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((((setminusT_lem)=>((complementT_lem)=>(((subsetTI)=>(((powersetTE1)=>((((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>(![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:((((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))<=(in @ X48 @ (powerset @ X4))))))<=(contrasubsetT1)))))<=(complementTE1))<=(complementTI1)))<=(powersetTI1)))<=(setextT))))<=(powersetT_lem))<=(binunionT_lem)))))<=(iftrue))))<=(ifSingleton))<=(iftrueProp2))<=(iftrueProp1)))<=(iffalseProp1)))<=(beta2))))))<=(ap2apEq1))))<=(eqbreln)))))<=(funcGraphProp2)))<=(funcGraphProp1))<=(ex1E2)))<=(brelnall1)))<=(lamp))<=(lamProp))<=(funcinfuncset)))<=(infuncsetfunc))<=(app))<=(apProp))))<=(dpsetconstrEL2))<=(dpsetconstrEL1)))<=(setOfPairsIsBReln))<=(dpsetconstrSub))<=(dpsetconstrI))<=(cartprodpairsurjEq))<=(cartprodsndpairEq)))))))))<=(ksndsingleton)))<=(setukpairinjR2))))))<=(setukpairinjL))<=(setukpairinjL2))<=(cartprodfstin))))<=(kfstsingleton))<=(setukpairinjL1))<=(singletonsuniq))<=(ex1I2))<=(ex1I))))))<=(setunionsingleton1))<=(setunionE2))<=(cartprodmempair))<=(cartprodmempair1))<=(cartprodpairin))<=(ubforcartprodlem3))<=(ubforcartprodlem2))<=(ubforcartprodlem1))<=(upairinpowunion))<=(upairsubunion)))<=(singletoninpowunion))<=(singletoninpowerset))))<=(kpairiskpair))<=(setukpairIR))<=(setukpairIL))<=(secondinupair)))<=(symdiffIneg1))<=(symdiffI2))<=(symdiffI1))<=(symdiffE)))<=(setminusLsub)))<=(setminusILneg))<=(setminusELneg)))<=(setminusSubset2)))<=(setminusEL)))<=(bs114d))<=(binintersectSubset1)))<=(binintersectRsub)))<=(binintersectER)))<=(binintersectSubset2))<=(binintersectLsub))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI))<=(binunionRsub)))))<=(binunionIR)))<=(binunionIL)))<=(sepInPowerset)))<=(inPowerset))<=(powersetE1))<=(powersetI1)))<=(setextsub)))))))<=(notequalI2)))<=(notsubsetI))))<=(emptysetsubset))<=(subsetI2))<=(eqimpsubset1))<=(eqimpsubset2)))))<=(exuEu))))))<=(emptyset__Cong)))<=(exuE3u))<=(in__Cong))))))<=(notdallE)))<=(prop2set2propI)))<=(quantDeMorgan4))<=(quantDeMorgan3))<=(quantDeMorgan2))<=(quantDeMorgan1)))<=(emptyE1))<=(upairsetIR))<=(upairsetIL)))))<=(notinsingleton)))))<=(subPowSU))))<=(powersetE))))<=(powersetI))<=(setoftrueEq)))<=(setadjoinE)))<=(emptyinunitempty))<=(setadjoinIL))))<=(nonemptyE1))<=(setbeta))<=(noeltsimpempty)))<=(setext))<=(exuE3e))))))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL))<=(dsetconstrI))<=(descrp))<=(wellorderingAx))))<=(omegaIndAx)))))<=(powersetAx))<=(setadjoinAx)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', contrasubsetT2)). 309.13/39.45 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setextAx)). 309.13/39.45 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', emptysetAx)). 309.13/39.45 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setadjoinAx)). 309.13/39.45 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', powersetAx)). 309.13/39.45 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setunionAx)). 309.13/39.45 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', omega0Ax)). 309.13/39.45 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', omegaSAx)). 309.13/39.45 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', omegaIndAx)). 309.13/39.45 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', foundationAx)). 309.13/39.45 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.f57cP6NHQL/E---3.1_604.p', wellorderingAx)). 309.13/39.45 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', prop2setE)). 309.13/39.45 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', emptysetE)). 309.13/39.45 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', emptysetimpfalse)). 309.13/39.45 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', notinemptyset)). 309.13/39.45 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setext)). 309.13/39.45 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', emptyI)). 309.13/39.45 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', noeltsimpempty)). 309.13/39.45 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setadjoinIL)). 309.13/39.45 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', emptyinunitempty)). 309.13/39.45 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setadjoinIR)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', setadjoinE)). 309.13/39.45 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setadjoinOr)). 309.13/39.45 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', powersetI)). 309.13/39.45 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', emptyinPowerset)). 309.13/39.45 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', emptyInPowerset)). 309.13/39.45 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', powersetE)). 309.13/39.45 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setunionI)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', setunionE)). 309.13/39.45 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', subPowSU)). 309.13/39.45 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', uniqinunit)). 309.13/39.45 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', notinsingleton)). 309.13/39.45 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', eqinunit)). 309.13/39.45 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', singletonsswitch)). 309.13/39.45 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', upairsetE)). 309.13/39.45 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', upairsetIL)). 309.13/39.45 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', upairsetIR)). 309.13/39.45 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', vacuousDall)). 309.13/39.45 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', quantDeMorgan1)). 309.13/39.45 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', quantDeMorgan2)). 309.13/39.45 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', quantDeMorgan3)). 309.13/39.45 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', quantDeMorgan4)). 309.13/39.45 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', prop2setI)). 309.13/39.45 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', prop2set2propI)). 309.13/39.45 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', notdexE)). 309.13/39.45 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', notdallE)). 309.13/39.45 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', inCongP)). 309.13/39.45 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', in__Cong)). 309.13/39.45 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', emptyset__Cong)). 309.13/39.45 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setadjoin__Cong)). 309.13/39.45 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', powerset__Cong)). 309.13/39.45 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setunion__Cong)). 309.13/39.45 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', omega__Cong)). 309.13/39.45 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', subsetI1)). 309.13/39.45 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', eqimpsubset2)). 309.13/39.45 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', eqimpsubset1)). 309.13/39.45 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', subsetI2)). 309.13/39.45 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', emptysetsubset)). 309.13/39.45 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', subsetE)). 309.13/39.45 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', subsetE2)). 309.13/39.45 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', notsubsetI)). 309.13/39.45 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', notequalI1)). 309.13/39.45 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', notequalI2)). 309.13/39.45 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', subsetRefl)). 309.13/39.45 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', subsetTrans)). 309.13/39.45 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setadjoinSub)). 309.13/39.45 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setadjoinSub2)). 309.13/39.45 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', subset2powerset)). 309.13/39.45 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setextsub)). 309.13/39.45 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', subsetemptysetimpeq)). 309.13/39.45 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', powersetI1)). 309.13/39.45 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', powersetE1)). 309.13/39.45 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', inPowerset)). 309.13/39.45 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', powersetsubset)). 309.13/39.45 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binunionIL)). 309.13/39.45 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', upairset2IR)). 309.13/39.45 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binunionIR)). 309.13/39.45 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binunionEcases)). 309.13/39.45 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binunionE)). 309.13/39.45 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binunionLsub)). 309.13/39.45 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binunionRsub)). 309.13/39.45 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binintersectI)). 309.13/39.45 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binintersectSubset5)). 309.13/39.45 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binintersectEL)). 309.13/39.45 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binintersectLsub)). 309.13/39.45 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binintersectSubset2)). 309.13/39.45 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binintersectSubset3)). 309.13/39.45 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binintersectER)). 309.13/39.45 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', disjointsetsI1)). 309.13/39.45 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binintersectRsub)). 309.13/39.45 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binintersectSubset4)). 309.13/39.45 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binintersectSubset1)). 309.13/39.45 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', bs114d)). 309.13/39.45 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setminusI)). 309.13/39.45 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setminusEL)). 309.13/39.45 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setminusER)). 309.13/39.45 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setminusSubset2)). 309.13/39.45 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setminusERneg)). 309.13/39.45 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setminusELneg)). 309.13/39.45 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setminusILneg)). 309.13/39.45 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setminusIRneg)). 309.13/39.45 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setminusLsub)). 309.13/39.45 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setminusSubset1)). 309.13/39.45 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', symdiffE)). 309.13/39.45 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', symdiffI1)). 309.13/39.45 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', symdiffI2)). 309.13/39.45 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', symdiffIneg1)). 309.13/39.45 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', symdiffIneg2)). 309.13/39.45 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', secondinupair)). 309.13/39.45 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setukpairIL)). 309.13/39.45 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setukpairIR)). 309.13/39.45 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', kpairiskpair)). 309.13/39.45 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', kpairp)). 309.13/39.45 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', singletonsubset)). 309.13/39.45 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', singletoninpowerset)). 309.13/39.45 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', singletoninpowunion)). 309.13/39.45 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', upairset2E)). 309.13/39.45 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', upairsubunion)). 309.13/39.45 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', upairinpowunion)). 309.13/39.45 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', ubforcartprodlem1)). 309.13/39.45 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', ubforcartprodlem2)). 309.13/39.45 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', ubforcartprodlem3)). 309.13/39.45 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', cartprodpairin)). 309.13/39.45 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.f57cP6NHQL/E---3.1_604.p', cartprodmempair1)). 309.13/39.45 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', cartprodmempair)). 309.13/39.45 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setunionE2)). 309.13/39.45 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setunionsingleton1)). 309.13/39.45 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setunionsingleton2)). 309.13/39.45 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setunionsingleton)). 309.13/39.45 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', singletonsuniq)). 309.13/39.45 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.f57cP6NHQL/E---3.1_604.p', setukpairinjL1)). 309.13/39.45 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', theprop)). 309.13/39.45 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', kfstpairEq)). 309.13/39.45 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', cartprodfstin)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', setukpairinjL2)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', setukpairinjL)). 309.13/39.45 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setukpairinjR11)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', setukpairinjR12)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', setukpairinjR1)). 309.13/39.45 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', upairequniteq)). 309.13/39.45 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setukpairinjR2)). 309.13/39.45 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setukpairinjR)). 309.13/39.45 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', ksndpairEq)). 309.13/39.45 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', kpairsurjEq)). 309.13/39.45 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', cartprodsndin)). 309.13/39.45 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', cartprodpairmemEL)). 309.13/39.45 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', cartprodpairmemER)). 309.13/39.45 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', cartprodmempaircEq)). 309.13/39.45 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', cartprodfstpairEq)). 309.13/39.45 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', cartprodsndpairEq)). 309.13/39.45 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', cartprodpairsurjEq)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', app)). 309.13/39.45 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', infuncsetfunc)). 309.13/39.45 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', ap2p)). 309.13/39.45 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', funcinfuncset)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', funcGraphProp1)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', funcGraphProp3)). 309.13/39.45 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', funcGraphProp2)). 309.13/39.45 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.f57cP6NHQL/E---3.1_604.p', funcextLem)). 309.13/39.45 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', funcGraphProp4)). 309.13/39.45 thf(funcext, axiom, ((funcext)<=>![X4:$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.f57cP6NHQL/E---3.1_604.p', funcext)). 309.13/39.45 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', funcext2)). 309.13/39.45 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', ap2apEq1)). 309.13/39.45 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', ap2apEq2)). 309.13/39.45 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', ifp)). 309.13/39.45 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', theeq)). 309.13/39.45 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', iftrue)). 309.13/39.45 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', iffalse)). 309.13/39.45 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', iftrueorfalse)). 309.13/39.45 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$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.f57cP6NHQL/E---3.1_604.p', binintersectT_lem)). 309.13/39.45 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binunionT_lem)). 309.13/39.45 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', powersetT_lem)). 309.13/39.45 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.f57cP6NHQL/E---3.1_604.p', setminusT_lem)). 309.13/39.45 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.f57cP6NHQL/E---3.1_604.p', complementT_lem)). 309.13/39.45 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', setextT)). 309.13/39.45 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', subsetTI)). 309.13/39.45 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', powersetTI1)). 309.13/39.45 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', powersetTE1)). 309.13/39.45 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$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.f57cP6NHQL/E---3.1_604.p', complementTI1)). 309.13/39.45 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', complementTE1)). 309.13/39.45 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binintersectTELcontra)). 309.13/39.45 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', binintersectTERcontra)). 309.13/39.45 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', contrasubsetT)). 309.13/39.45 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.f57cP6NHQL/E---3.1_604.p', contrasubsetT1)). 309.13/39.45 thf(c_0_246, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 309.13/39.45 thf(c_0_247, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 309.13/39.45 thf(c_0_248, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 309.13/39.45 thf(c_0_249, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 309.13/39.45 thf(c_0_250, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 309.13/39.45 thf(c_0_251, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 309.13/39.45 thf(c_0_252, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 309.13/39.45 thf(c_0_253, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 309.13/39.45 thf(c_0_254, 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])). 309.13/39.45 thf(c_0_255, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 309.13/39.45 thf(c_0_256, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 309.13/39.45 thf(c_0_257, 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])). 309.13/39.45 thf(c_0_258, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 309.13/39.45 thf(c_0_259, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 309.13/39.45 thf(c_0_260, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 309.13/39.45 thf(c_0_261, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 309.13/39.45 thf(c_0_262, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])). 309.13/39.45 thf(c_0_263, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])). 309.13/39.45 thf(c_0_264, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 309.13/39.45 thf(c_0_265, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 309.13/39.45 thf(c_0_266, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])). 309.13/39.45 thf(c_0_267, 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])). 309.13/39.45 thf(c_0_268, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X800:$i]:((((X6 @ X2 @ X800))&![X801:$i]:((((X6 @ X2 @ X801))=>((X800)=(X801)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_246, c_0_247])). 309.13/39.45 thf(c_0_269, plain, ((descrp)=(![X1:$i > $o]:(((?[X802:$i]:((((X1 @ X802))&![X803:$i]:((((X1 @ X803))=>((X802)=(X803)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_248, c_0_247])). 309.13/39.45 thf(c_0_270, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 309.13/39.45 thf(c_0_271, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 309.13/39.45 thf(c_0_272, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 309.13/39.45 thf(c_0_273, plain, ((exuE1)=(![X1:$i > $o]:(((?[X804:$i]:((((X1 @ X804))&![X805:$i]:((((X1 @ X805))=>((X804)=(X805)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_249, c_0_247])). 309.13/39.45 thf(c_0_274, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X806:$i]:((((X1 @ X806))&![X807:$i]:((((X1 @ X807))=>((X806)=(X807)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_250, c_0_247])). 309.13/39.45 thf(c_0_275, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 309.13/39.45 thf(c_0_276, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_251])). 309.13/39.45 thf(c_0_277, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_252, c_0_251])). 309.13/39.45 thf(c_0_278, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_251])). 309.13/39.45 thf(c_0_279, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 309.13/39.45 thf(c_0_280, plain, ((exuE2)=(![X1:$i > $o]:(((?[X808:$i]:((((X1 @ X808))&![X809:$i]:((((X1 @ X809))=>((X808)=(X809)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_253, c_0_247])). 309.13/39.45 thf(c_0_281, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_251])). 309.13/39.45 thf(c_0_282, 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])). 309.13/39.45 thf(c_0_283, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X810:$i]:((((X1 @ X810))&![X811:$i]:((((X1 @ X811))=>((X810)=(X811))))))))))), inference(apply_def,[status(thm)],[c_0_254, c_0_247])). 309.13/39.45 thf(c_0_284, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X812:$i]:((((X1 @ X812))&![X813:$i]:((((X1 @ X813))=>((X812)=(X813)))))))))))), inference(apply_def,[status(thm)],[c_0_255, c_0_247])). 309.13/39.45 thf(c_0_285, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X814:$i]:((((X1 @ X814))&![X815:$i]:((((X1 @ X815))=>((X814)=(X815))))))))))), inference(apply_def,[status(thm)],[c_0_256, c_0_247])). 309.13/39.45 thf(c_0_286, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X816:$i]:((((X1 @ X816))&![X817:$i]:((((X1 @ X817))=>((X816)=(X817)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_257, c_0_247])). 309.13/39.45 thf(c_0_287, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X818:$i]:((((X1 @ X818))&![X819:$i]:((((X1 @ X819))=>((X818)=(X819)))))))<=>(?[X820:$i]:((((X17 @ X820))&![X821:$i]:((((X17 @ X821))=>((X820)=(X821)))))))))))), inference(apply_def,[status(thm)],[c_0_258, c_0_247])). 309.13/39.45 thf(c_0_288, plain, ((exuEu)=(![X1:$i > $o]:(((?[X822:$i]:((((X1 @ X822))&![X823:$i]:((((X1 @ X823))=>((X822)=(X823)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_259, c_0_247])). 309.13/39.45 thf(c_0_289, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X824:$i]:((((X1 @ X824))&![X825:$i]:((((X1 @ X825))=>((X824)=(X825)))))))=>((?[X826:$i]:((((X17 @ X826))&![X827:$i]:((((X17 @ X827))=>((X826)=(X827)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_260, c_0_247])). 309.13/39.45 thf(c_0_290, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 309.13/39.45 thf(c_0_291, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 309.13/39.45 thf(c_0_292, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 309.13/39.45 thf(c_0_293, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 309.13/39.45 thf(c_0_294, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_261, c_0_262])). 309.13/39.45 thf(c_0_295, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))))))))), inference(apply_def,[status(thm)],[c_0_263, c_0_262])). 309.13/39.45 thf(c_0_296, plain, ((ex1I2)=(![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))))))), inference(apply_def,[status(thm)],[c_0_264, c_0_262])). 309.13/39.45 thf(c_0_297, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 309.13/39.45 thf(c_0_298, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 309.13/39.45 thf(c_0_299, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 309.13/39.45 thf(c_0_300, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 309.13/39.45 thf(c_0_301, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_265, c_0_266])). 309.13/39.45 thf(c_0_302, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 309.13/39.45 thf(c_0_303, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 309.13/39.45 thf(c_0_304, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 309.13/39.45 thf(c_0_305, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 309.13/39.45 thf(c_0_306, plain, ((funcImageSingleton)<=>![X4:$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])). 309.13/39.45 thf(c_0_307, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 309.13/39.45 thf(c_0_308, plain, ((lamProp)<=>![X4:$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])). 309.13/39.45 thf(c_0_309, 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 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 309.13/39.45 thf(c_0_310, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 309.13/39.45 thf(c_0_311, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_266])). 309.13/39.45 thf(c_0_312, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_266])). 309.13/39.45 thf(c_0_313, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_267, c_0_262])). 309.13/39.45 thf(c_0_314, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln, c_0_266])). 309.13/39.45 thf(c_0_315, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_266])). 309.13/39.45 thf(c_0_316, 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])). 309.13/39.45 thf(c_0_317, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])). 309.13/39.45 thf(c_0_318, 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])). 309.13/39.45 thf(c_0_319, 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])). 309.13/39.45 thf(c_0_320, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])). 309.13/39.45 thf(c_0_321, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 309.13/39.45 thf(c_0_322, plain, ((iffalseProp2)<=>![X4:$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])). 309.13/39.45 thf(c_0_323, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 309.13/39.45 thf(c_0_324, plain, ((iftrueProp2)<=>![X4:$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])). 309.13/39.45 thf(c_0_325, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 309.13/39.45 thf(c_0_326, plain, ((epred1_0)<=>![X1576:$i]:(?[X1577:$i]:((((![X1578:$i]:(((in @ X1578 @ X1577)=>![X1579:$i]:(((in @ X1579 @ X1578)=>(in @ X1579 @ X1576)))))&![X1580:$i, X1581:$i]:((((in @ X1580 @ X1576)&(in @ X1581 @ X1576))=>(![X1582:$i]:(((in @ X1582 @ X1577)=>((in @ X1580 @ X1582)<=>(in @ X1581 @ X1582))))=>((X1580)=(X1581))))))&![X1583:$i, X1584:$i]:((((in @ X1583 @ X1577)&(in @ X1584 @ X1577))=>(![X1585:$i]:(((in @ X1585 @ X1583)=>(in @ X1585 @ X1584)))|![X1586:$i]:(((in @ X1586 @ X1584)=>(in @ X1586 @ X1583)))))))&![X1587:$i]:(((![X1588:$i]:(((in @ X1588 @ X1587)=>(in @ X1588 @ X1576)))&?[X1589:$i]:((in @ X1589 @ X1587)))=>?[X1590:$i, X1591:$i]:(((((in @ X1590 @ X1577)&(in @ X1591 @ X1587))&~(?[X1592:$i]:(((in @ X1592 @ X1590)&(in @ X1592 @ X1587)))))&![X1593:$i]:(((in @ X1593 @ X1577)=>(![X1594:$i]:(((in @ X1594 @ X1593)=>(in @ X1594 @ X1590)))|(in @ X1591 @ X1593)))))))))))), introduced(definition)). 309.13/39.45 thf(c_0_327, negated_conjecture, ~((![X828:$i, X829:$i]:((![X830:$i]:(((in @ X830 @ X828)<=>(in @ X830 @ X829)))=>((X828)=(X829))))=>(![X831:$i]:(~(in @ X831 @ emptyset))=>(![X1601:$i, X1602:$i, X1603:$i]:(((in @ X1603 @ (setadjoin @ X1601 @ X1602))<=>(((X1603)=(X1601))|(in @ X1603 @ X1602))))=>(![X1598:$i, X1599:$i]:(((in @ X1599 @ (powerset @ X1598))<=>![X1600:$i]:(((in @ X1600 @ X1599)=>(in @ X1600 @ X1598)))))=>(![X832:$i, X833:$i]:(((in @ X833 @ (setunion @ X832))<=>?[X834:$i]:(((in @ X833 @ X834)&(in @ X834 @ X832)))))=>((in @ emptyset @ omega)=>(![X835:$i]:(((in @ X835 @ omega)=>(in @ (setadjoin @ X835 @ X835) @ omega)))=>(![X1595:$i]:((((in @ emptyset @ X1595)&![X1596:$i]:((((in @ X1596 @ omega)&(in @ X1596 @ X1595))=>(in @ (setadjoin @ X1596 @ X1596) @ X1595))))=>![X1597:$i]:(((in @ X1597 @ omega)=>(in @ X1597 @ X1595)))))=>(![X836:$i > $i > $o, X837:$i]:((![X838:$i]:(((in @ X838 @ X837)=>?[X839:$i]:(((X836 @ X838 @ X839)&![X840:$i]:(((X836 @ X838 @ X840)=>((X839)=(X840))))))))=>?[X841:$i]:(![X842:$i]:(((in @ X842 @ X841)<=>?[X843:$i]:(((in @ X843 @ X837)&(X836 @ X843 @ X842))))))))=>(![X844:$i]:((?[X845:$i]:((in @ X845 @ X844))=>?[X846:$i]:(((in @ X846 @ X844)&~(?[X847:$i]:(((in @ X847 @ X846)&(in @ X847 @ X844))))))))=>((epred1_0)=>(![X1573:$i > $o]:((?[X1574:$i]:(((X1573 @ X1574)&![X1575:$i]:(((X1573 @ X1575)=>((X1574)=(X1575))))))=>(X1573 @ (descr @ (^[Z0/* 17 */:$i]:(X1573 @ Z0))))))=>(![X1570:$i, X1571:$i > $o, X1572:$i]:(((in @ X1572 @ X1570)=>((X1571 @ X1572)=>(in @ X1572 @ (dsetconstr @ X1570 @ X1571)))))=>(![X1567:$i, X1568:$i > $o, X1569:$i]:(((in @ X1569 @ (dsetconstr @ X1567 @ X1568))=>(in @ X1569 @ X1567)))=>(![X1564:$i, X1565:$i > $o, X1566:$i]:(((in @ X1566 @ (dsetconstr @ X1564 @ X1565))=>(X1565 @ X1566)))=>(![X1559:$i > $o]:((?[X1560:$i]:(((X1559 @ X1560)&![X1561:$i]:(((X1559 @ X1561)=>((X1560)=(X1561))))))=>?[X1562:$i]:(((X1559 @ X1562)&![X1563:$i]:(((X1559 @ X1563)=>((X1562)=(X1563))))))))=>(![X848:$o, X849:$i]:(((in @ X849 @ (prop2set @ ((X848))))=>(X848)))=>(![X850:$i]:(((in @ X850 @ emptyset)=>![X851:$o]:((X851))))=>(![X852:$i]:(((in @ X852 @ emptyset)=>~($true)))=>(![X853:$i]:(~(in @ X853 @ emptyset))=>(![X1555:$i > $o]:((?[X1556:$i]:(((X1555 @ X1556)&![X1557:$i]:(((X1555 @ X1557)=>((X1556)=(X1557))))))=>?[X1558:$i]:((X1555 @ X1558))))=>(![X1551:$i, X1552:$i]:((![X1553:$i]:(((in @ X1553 @ X1551)=>(in @ X1553 @ X1552)))=>(![X1554:$i]:(((in @ X1554 @ X1552)=>(in @ X1554 @ X1551)))=>((X1551)=(X1552)))))=>(![X854:$i]:((![X855:$i]:(~(in @ X855 @ X854))=>((X854)=(emptyset))))=>(![X1549:$i]:((![X1550:$i]:(~(in @ X1550 @ X1549))=>((X1549)=(emptyset))))=>(![X1546:$i, X1547:$i > $o, X1548:$i]:(((in @ X1548 @ X1546)=>((in @ X1548 @ (dsetconstr @ X1546 @ X1547))<=>(X1547 @ X1548))))=>(![X1544:$i]:((((X1544)!=(emptyset))=>?[X1545:$i]:((in @ X1545 @ X1544))))=>(![X856:$i, X857:$i > $o, X858:$i]:(((in @ X858 @ X856)=>((X857 @ X858)=>((dsetconstr @ X856 @ X857)!=(emptyset)))))=>(![X859:$i]:((?[X860:$i]:((in @ X860 @ X859))=>((X859)!=(emptyset))))=>(![X1542:$i, X1543:$i]:((in @ X1542 @ (setadjoin @ X1542 @ X1543)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X861:$i, X862:$i, X863:$i]:(((in @ X863 @ X862)=>(in @ X863 @ (setadjoin @ X861 @ X862))))=>(![X1538:$i, X1539:$i, X1540:$i]:(((in @ X1540 @ (setadjoin @ X1538 @ X1539))=>![X1541:$o]:(((((X1540)=(X1538))=>(X1541))=>(((in @ X1540 @ X1539)=>(X1541))=>(X1541))))))=>(![X864:$i, X865:$i, X866:$i]:(((in @ X866 @ (setadjoin @ X864 @ X865))=>(((X866)=(X864))|(in @ X866 @ X865))))=>(![X1537:$i]:(((dsetconstr @ X1537 @ (^[Z0/* 1 */:$i]:($true)))=(X1537)))=>(![X1534:$i, X1535:$i]:((![X1536:$i]:(((in @ X1536 @ X1535)=>(in @ X1536 @ X1534)))=>(in @ X1535 @ (powerset @ X1534))))=>(![X867:$i]:((in @ emptyset @ (powerset @ X867)))=>(![X868:$i]:((in @ emptyset @ (powerset @ X868)))=>(![X1531:$i, X1532:$i, X1533:$i]:(((in @ X1532 @ (powerset @ X1531))=>((in @ X1533 @ X1532)=>(in @ X1533 @ X1531))))=>(![X869:$i, X870:$i, X871:$i]:(((in @ X870 @ X871)=>((in @ X871 @ X869)=>(in @ X870 @ (setunion @ X869)))))=>(![X872:$i, X873:$i]:(((in @ X873 @ (setunion @ X872))=>![X874:$o]:((![X875:$i]:(((in @ X873 @ X875)=>((in @ X875 @ X872)=>(X874))))=>(X874)))))=>(![X1529:$i, X1530:$i]:(((in @ X1530 @ X1529)=>(in @ X1530 @ (powerset @ (setunion @ X1529)))))=>(![X876:$i > $o]:((?[X877:$i]:(((X876 @ X877)&![X878:$i]:(((X876 @ X878)=>((X877)=(X878))))))=>?[X879:$i]:(![X880:$i]:(((X876 @ X880)<=>((X880)=(X879)))))))=>(![X881:$i]:((((X881)!=(emptyset))=>?[X882:$i]:(((in @ X882 @ X881)&$true))))=>(![X883:$i, X884:$i]:(((in @ X883 @ (setadjoin @ X884 @ emptyset))=>((X883)=(X884))))=>(![X1527:$i, X1528:$i]:((((X1527)!=(X1528))=>~(in @ X1528 @ (setadjoin @ X1527 @ emptyset))))=>(![X885:$i, X886:$i]:((((X885)=(X886))=>(in @ X885 @ (setadjoin @ X886 @ emptyset))))=>(![X887:$i, X888:$i]:(((in @ X887 @ (setadjoin @ X888 @ emptyset))=>(in @ X888 @ (setadjoin @ X887 @ emptyset))))=>(![X889:$i, X890:$i, X891:$i]:(((in @ X891 @ (setadjoin @ X889 @ (setadjoin @ X890 @ emptyset)))=>(((X891)=(X889))|((X891)=(X890)))))=>(![X1525:$i, X1526:$i]:((in @ X1525 @ (setadjoin @ X1525 @ (setadjoin @ X1526 @ emptyset))))=>(![X1523:$i, X1524:$i]:((in @ X1524 @ (setadjoin @ X1523 @ (setadjoin @ X1524 @ emptyset))))=>(![X1520:$i, X1521:$i > $o]:((?[X1522:$i]:(((in @ X1522 @ X1520)&(X1521 @ X1522)))=>(((dsetconstr @ X1520 @ X1521)=(emptyset))=>~($true))))=>(![X892:$i > $o, X893:$i]:(((in @ X893 @ emptyset)=>(X892 @ X893)))=>(![X1516:$i, X1517:$i > $o]:((~(![X1518:$i]:(((in @ X1518 @ X1516)=>(X1517 @ X1518))))=>?[X1519:$i]:(((in @ X1519 @ X1516)&~((X1517 @ X1519))))))=>(![X1512:$i, X1513:$i > $o]:((![X1514:$i]:(((in @ X1514 @ X1512)=>~((X1513 @ X1514))))=>~(?[X1515:$i]:(((in @ X1515 @ X1512)&(X1513 @ X1515))))))=>(![X1508:$i, X1509:$i > $o]:((~(?[X1510:$i]:(((in @ X1510 @ X1508)&(X1509 @ X1510))))=>![X1511:$i]:(((in @ X1511 @ X1508)=>~((X1509 @ X1511))))))=>(![X1504:$i, X1505:$i > $o]:((?[X1506:$i]:(((in @ X1506 @ X1504)&~((X1505 @ X1506))))=>~(![X1507:$i]:(((in @ X1507 @ X1504)=>(X1505 @ X1507))))))=>(![X894:$o]:(((X894)=>(in @ emptyset @ (prop2set @ ((X894))))))=>(![X1503:$o]:(((X1503)=>(set2prop @ (prop2set @ ((X1503))))))=>(![X895:$i, X896:$i > $o]:((~(?[X897:$i]:(((in @ X897 @ X895)&(X896 @ X897))))=>![X898:$i]:(((in @ X898 @ X895)=>~((X896 @ X898))))))=>(![X1499:$i, X1500:$i > $o]:((~(![X1501:$i]:(((in @ X1501 @ X1499)=>(X1500 @ X1501))))=>?[X1502:$i]:(((in @ X1502 @ X1499)&~((X1500 @ X1502))))))=>(![X899:$i > $o]:((?[X900:$i]:(((X899 @ X900)&![X901:$i]:(((X899 @ X901)=>((X900)=(X901))))))=>?[X902:$i]:(((X899 @ X902)&![X903:$i]:(((X899 @ X903)=>((X902)=(X903))))))))=>(![X904:$i > $o]:((?[X905:$i]:((X904 @ X905))=>(![X906:$i, X907:$i]:(((X904 @ X906)=>((X904 @ X907)=>((X906)=(X907)))))=>?[X908:$i]:(((X904 @ X908)&![X909:$i]:(((X904 @ X909)=>((X908)=(X909)))))))))=>(![X910:$i > $o]:((?[X911:$i]:(![X912:$i]:(((X910 @ X912)<=>((X912)=(X911)))))=>?[X913:$i]:(((X910 @ X913)&![X914:$i]:(((X910 @ X914)=>((X913)=(X914))))))))=>(![X915:$i, X916:$i]:((((X915)=(X916))=>![X917:$i, X918:$i]:((((X917)=(X918))=>((in @ X917 @ X915)=>(in @ X918 @ X916))))))=>(![X1495:$i, X1496:$i]:((((X1495)=(X1496))=>![X1497:$i, X1498:$i]:((((X1497)=(X1498))=>((in @ X1497 @ X1495)<=>(in @ X1498 @ X1496))))))=>(![X1490:$i > $o]:((?[X1491:$i]:(((X1490 @ X1491)&![X1492:$i]:(((X1490 @ X1492)=>((X1491)=(X1492))))))=>![X1493:$i, X1494:$i]:(((X1490 @ X1493)=>((X1490 @ X1494)=>((X1493)=(X1494)))))))=>(![X919:$i > $o, X920:$i > $o]:((![X921:$i, X922:$i]:((((X921)=(X922))=>((X919 @ X921)<=>(X920 @ X922))))=>(?[X923:$i]:(((X919 @ X923)&![X924:$i]:(((X919 @ X924)=>((X923)=(X924))))))<=>?[X925:$i]:(((X920 @ X925)&![X926:$i]:(((X920 @ X926)=>((X925)=(X926)))))))))=>(((emptyset)=(emptyset))=>(![X927:$i, X928:$i]:((((X927)=(X928))=>![X929:$i, X930:$i]:((((X929)=(X930))=>((setadjoin @ X927 @ X929)=(setadjoin @ X928 @ X930))))))=>(![X931:$i, X932:$i]:((((X931)=(X932))=>((powerset @ X931)=(powerset @ X932))))=>(![X933:$i, X934:$i]:((((X933)=(X934))=>((setunion @ X933)=(setunion @ X934))))=>(((omega)=(omega))=>(![X1485:$i > $o]:((?[X1486:$i]:(((X1485 @ X1486)&![X1487:$i]:(((X1485 @ X1487)=>((X1486)=(X1487))))))=>![X1488:$i, X1489:$i]:(((X1485 @ X1488)=>((X1485 @ X1489)=>((X1488)=(X1489)))))))=>(![X935:$i > $o, X936:$i > $o]:((![X937:$i, X938:$i]:((((X937)=(X938))=>((X935 @ X937)<=>(X936 @ X938))))=>(?[X939:$i]:(((X935 @ X939)&![X940:$i]:(((X935 @ X940)=>((X939)=(X940))))))=>(?[X941:$i]:(((X936 @ X941)&![X942:$i]:(((X936 @ X942)=>((X941)=(X942))))))=>((descr @ X935)=(descr @ X936))))))=>(![X943:$i, X944:$i]:((((X943)=(X944))=>![X945:$i > $o, X946:$i > $o]:((![X947:$i]:(((in @ X947 @ X943)=>![X948:$i]:(((in @ X948 @ X944)=>(((X947)=(X948))=>((X945 @ X947)<=>(X946 @ X948)))))))=>((dsetconstr @ X943 @ X945)=(dsetconstr @ X944 @ X946))))))=>(![X949:$i, X950:$i]:((![X951:$i]:(((in @ X951 @ X949)=>(in @ X951 @ X950)))=>(subset @ X949 @ X950)))=>(![X1483:$i, X1484:$i]:((((X1483)=(X1484))=>(subset @ X1484 @ X1483)))=>(![X1481:$i, X1482:$i]:((((X1481)=(X1482))=>(subset @ X1481 @ X1482)))=>(![X1478:$i, X1479:$i]:((![X1480:$i]:(((in @ X1480 @ X1478)=>(in @ X1480 @ X1479)))=>(subset @ X1478 @ X1479)))=>(![X1477:$i]:((subset @ emptyset @ X1477))=>(![X952:$i, X953:$i, X954:$i]:(((subset @ X952 @ X953)=>((in @ X954 @ X952)=>(in @ X954 @ X953))))=>(![X955:$i, X956:$i, X957:$i]:(((subset @ X955 @ X956)=>(~(in @ X957 @ X956)=>~(in @ X957 @ X955))))=>(![X1474:$i, X1475:$i, X1476:$i]:(((in @ X1476 @ X1474)=>(~(in @ X1476 @ X1475)=>~(subset @ X1474 @ X1475))))=>(![X958:$i, X959:$i]:((~(subset @ X958 @ X959)=>((X958)!=(X959))))=>(![X1471:$i, X1472:$i, X1473:$i]:(((in @ X1473 @ X1471)=>(~(in @ X1473 @ X1472)=>((X1471)!=(X1472)))))=>(![X960:$i]:((subset @ X960 @ X960))=>(![X961:$i, X962:$i, X963:$i]:(((subset @ X961 @ X962)=>((subset @ X962 @ X963)=>(subset @ X961 @ X963))))=>(![X964:$i, X965:$i]:((subset @ X965 @ (setadjoin @ X964 @ X965)))=>(![X966:$i, X967:$i, X968:$i]:(((subset @ X966 @ X968)=>(subset @ X966 @ (setadjoin @ X967 @ X968))))=>(![X969:$i, X970:$i]:(((subset @ X969 @ X970)=>(in @ X969 @ (powerset @ X970))))=>(![X1469:$i, X1470:$i]:(((subset @ X1469 @ X1470)=>((subset @ X1470 @ X1469)=>((X1469)=(X1470)))))=>(![X971:$i]:(((subset @ X971 @ emptyset)=>((X971)=(emptyset))))=>(![X1467:$i, X1468:$i]:(((subset @ X1468 @ X1467)=>(in @ X1468 @ (powerset @ X1467))))=>(![X1465:$i, X1466:$i]:(((in @ X1466 @ (powerset @ X1465))=>(subset @ X1466 @ X1465)))=>(![X1464:$i]:((in @ X1464 @ (powerset @ X1464)))=>(![X972:$i, X973:$i]:(((subset @ X972 @ X973)=>(subset @ (powerset @ X972) @ (powerset @ X973))))=>(![X1462:$i, X1463:$i > $o]:((in @ (dsetconstr @ X1462 @ X1463) @ (powerset @ X1462)))=>(![X974:$i, X975:$i > $o]:((subset @ (dsetconstr @ X974 @ X975) @ X974))=>(![X1459:$i, X1460:$i, X1461:$i]:(((in @ X1461 @ X1459)=>(in @ X1461 @ (binunion @ X1459 @ X1460))))=>(![X976:$i, X977:$i]:((in @ X977 @ (setadjoin @ X976 @ (setadjoin @ X977 @ emptyset))))=>(![X1456:$i, X1457:$i, X1458:$i]:(((in @ X1458 @ X1457)=>(in @ X1458 @ (binunion @ X1456 @ X1457))))=>(![X978:$i, X979:$i, X980:$i, X981:$o]:(((in @ X980 @ (binunion @ X978 @ X979))=>(((in @ X980 @ X978)=>(X981))=>(((in @ X980 @ X979)=>(X981))=>(X981)))))=>(![X982:$i, X983:$i, X984:$i]:(((in @ X984 @ (binunion @ X982 @ X983))=>((in @ X984 @ X982)|(in @ X984 @ X983))))=>(![X985:$i, X986:$i]:((subset @ X985 @ (binunion @ X985 @ X986)))=>(![X1454:$i, X1455:$i]:((subset @ X1455 @ (binunion @ X1454 @ X1455)))=>(![X1451:$i, X1452:$i, X1453:$i]:(((in @ X1453 @ X1451)=>((in @ X1453 @ X1452)=>(in @ X1453 @ (binintersect @ X1451 @ X1452)))))=>(![X1448:$i, X1449:$i, X1450:$i]:(((subset @ X1450 @ X1448)=>((subset @ X1450 @ X1449)=>(subset @ X1450 @ (binintersect @ X1448 @ X1449)))))=>(![X1445:$i, X1446:$i, X1447:$i]:(((in @ X1447 @ (binintersect @ X1445 @ X1446))=>(in @ X1447 @ X1445)))=>(![X1443:$i, X1444:$i]:((subset @ (binintersect @ X1443 @ X1444) @ X1443))=>(![X1441:$i, X1442:$i]:(((subset @ X1441 @ X1442)=>((binintersect @ X1441 @ X1442)=(X1441))))=>(![X987:$i, X988:$i]:((((binintersect @ X987 @ X988)=(X988))=>(subset @ X988 @ X987)))=>(![X1438:$i, X1439:$i, X1440:$i]:(((in @ X1440 @ (binintersect @ X1438 @ X1439))=>(in @ X1440 @ X1439)))=>(![X989:$i, X990:$i]:((~(?[X991:$i]:(((in @ X991 @ X989)&(in @ X991 @ X990))))=>((binintersect @ X989 @ X990)=(emptyset))))=>(![X1436:$i, X1437:$i]:((subset @ (binintersect @ X1436 @ X1437) @ X1437))=>(![X992:$i, X993:$i]:(((subset @ X993 @ X992)=>((binintersect @ X992 @ X993)=(X993))))=>(![X1434:$i, X1435:$i]:((((binintersect @ X1434 @ X1435)=(X1434))=>(subset @ X1434 @ X1435)))=>(![X1431:$i, X1432:$i, X1433:$i]:(((binintersect @ X1431 @ (binunion @ X1432 @ X1433))=(binunion @ (binintersect @ X1431 @ X1432) @ (binintersect @ X1431 @ X1433))))=>(![X994:$i, X995:$i, X996:$i]:(((in @ X996 @ X994)=>(~(in @ X996 @ X995)=>(in @ X996 @ (setminus @ X994 @ X995)))))=>(![X1428:$i, X1429:$i, X1430:$i]:(((in @ X1430 @ (setminus @ X1428 @ X1429))=>(in @ X1430 @ X1428)))=>(![X997:$i, X998:$i, X999:$i]:(((in @ X999 @ (setminus @ X997 @ X998))=>~(in @ X999 @ X998)))=>(![X1426:$i, X1427:$i]:(((subset @ X1426 @ X1427)=>((setminus @ X1426 @ X1427)=(emptyset))))=>(![X1000:$i, X1001:$i, X1002:$i]:((~(in @ X1002 @ (setminus @ X1000 @ X1001))=>((in @ X1002 @ X1000)=>(in @ X1002 @ X1001))))=>(![X1423:$i, X1424:$i, X1425:$i]:((~(in @ X1425 @ (setminus @ X1423 @ X1424))=>(~(in @ X1425 @ X1424)=>~(in @ X1425 @ X1423))))=>(![X1420:$i, X1421:$i, X1422:$i]:((~(in @ X1422 @ X1420)=>~(in @ X1422 @ (setminus @ X1420 @ X1421))))=>(![X1003:$i, X1004:$i, X1005:$i]:(((in @ X1005 @ X1004)=>~(in @ X1005 @ (setminus @ X1003 @ X1004))))=>(![X1418:$i, X1419:$i]:((subset @ (setminus @ X1418 @ X1419) @ X1418))=>(![X1006:$i, X1007:$i]:((((setminus @ X1006 @ X1007)=(emptyset))=>(subset @ X1006 @ X1007)))=>(![X1414:$i, X1415:$i, X1416:$i]:(((in @ X1416 @ (symdiff @ X1414 @ X1415))=>![X1417:$o]:((((in @ X1416 @ X1414)=>(~(in @ X1416 @ X1415)=>(X1417)))=>((~(in @ X1416 @ X1414)=>((in @ X1416 @ X1415)=>(X1417)))=>(X1417))))))=>(![X1411:$i, X1412:$i, X1413:$i]:(((in @ X1413 @ X1411)=>(~(in @ X1413 @ X1412)=>(in @ X1413 @ (symdiff @ X1411 @ X1412)))))=>(![X1408:$i, X1409:$i, X1410:$i]:((~(in @ X1410 @ X1408)=>((in @ X1410 @ X1409)=>(in @ X1410 @ (symdiff @ X1408 @ X1409)))))=>(![X1405:$i, X1406:$i, X1407:$i]:(((in @ X1407 @ X1405)=>((in @ X1407 @ X1406)=>~(in @ X1407 @ (symdiff @ X1405 @ X1406)))))=>(![X1008:$i, X1009:$i, X1010:$i]:((~(in @ X1010 @ X1008)=>(~(in @ X1010 @ X1009)=>~(in @ X1010 @ (symdiff @ X1008 @ X1009)))))=>(![X1403:$i, X1404:$i]:((in @ X1404 @ (setadjoin @ X1403 @ (setadjoin @ X1404 @ emptyset))))=>(![X1401:$i, X1402:$i]:((in @ X1401 @ (setunion @ (setadjoin @ (setadjoin @ X1401 @ emptyset) @ (setadjoin @ (setadjoin @ X1401 @ (setadjoin @ X1402 @ emptyset)) @ emptyset)))))=>(![X1399:$i, X1400:$i]:((in @ X1400 @ (setunion @ (setadjoin @ (setadjoin @ X1399 @ emptyset) @ (setadjoin @ (setadjoin @ X1399 @ (setadjoin @ X1400 @ emptyset)) @ emptyset)))))=>(![X1397:$i, X1398:$i]:((iskpair @ (setadjoin @ (setadjoin @ X1397 @ emptyset) @ (setadjoin @ (setadjoin @ X1397 @ (setadjoin @ X1398 @ emptyset)) @ emptyset))))=>(![X1011:$i, X1012:$i]:((iskpair @ (kpair @ X1011 @ X1012)))=>(![X1013:$i, X1014:$i]:(((in @ X1014 @ X1013)=>(subset @ (setadjoin @ X1014 @ emptyset) @ X1013)))=>(![X1395:$i, X1396:$i]:(((in @ X1396 @ X1395)=>(in @ (setadjoin @ X1396 @ emptyset) @ (powerset @ X1395))))=>(![X1392:$i, X1393:$i, X1394:$i]:(((in @ X1394 @ X1392)=>(in @ (setadjoin @ X1394 @ emptyset) @ (powerset @ (binunion @ X1392 @ X1393)))))=>(![X1015:$i, X1016:$i, X1017:$i]:(((in @ X1017 @ (setadjoin @ X1015 @ (setadjoin @ X1016 @ emptyset)))=>(((X1017)=(X1015))|((X1017)=(X1016)))))=>(![X1388:$i, X1389:$i, X1390:$i]:(((in @ X1390 @ X1388)=>![X1391:$i]:(((in @ X1391 @ X1389)=>(subset @ (setadjoin @ X1390 @ (setadjoin @ X1391 @ emptyset)) @ (binunion @ X1388 @ X1389))))))=>(![X1384:$i, X1385:$i, X1386:$i]:(((in @ X1386 @ X1384)=>![X1387:$i]:(((in @ X1387 @ X1385)=>(in @ (setadjoin @ X1386 @ (setadjoin @ X1387 @ emptyset)) @ (powerset @ (binunion @ X1384 @ X1385)))))))=>(![X1380:$i, X1381:$i, X1382:$i]:(((in @ X1382 @ X1380)=>![X1383:$i]:(((in @ X1383 @ X1381)=>(subset @ (setadjoin @ (setadjoin @ X1382 @ emptyset) @ (setadjoin @ (setadjoin @ X1382 @ (setadjoin @ X1383 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1380 @ X1381)))))))=>(![X1376:$i, X1377:$i, X1378:$i]:(((in @ X1378 @ X1376)=>![X1379:$i]:(((in @ X1379 @ X1377)=>(in @ (setadjoin @ (setadjoin @ X1378 @ emptyset) @ (setadjoin @ (setadjoin @ X1378 @ (setadjoin @ X1379 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1376 @ X1377))))))))=>(![X1372:$i, X1373:$i, X1374:$i]:(((in @ X1374 @ X1372)=>![X1375:$i]:(((in @ X1375 @ X1373)=>(in @ (kpair @ X1374 @ X1375) @ (powerset @ (powerset @ (binunion @ X1372 @ X1373))))))))=>(![X1368:$i, X1369:$i, X1370:$i]:(((in @ X1370 @ X1368)=>![X1371:$i]:(((in @ X1371 @ X1369)=>(in @ (kpair @ X1370 @ X1371) @ (cartprod @ X1368 @ X1369))))))=>(![X1363:$i, X1364:$i, X1365:$i]:(((in @ X1365 @ (cartprod @ X1363 @ X1364))=>?[X1366:$i]:(((in @ X1366 @ X1363)&?[X1367:$i]:(((in @ X1367 @ X1364)&((X1365)=(kpair @ X1366 @ X1367))))))))=>(![X1360:$i, X1361:$i, X1362:$i]:(((in @ X1362 @ (cartprod @ X1360 @ X1361))=>(iskpair @ X1362)))=>(![X1357:$i, X1358:$i]:(((in @ X1358 @ (setunion @ X1357))=>?[X1359:$i]:(((in @ X1359 @ X1357)&(in @ X1358 @ X1359)))))=>(![X1356:$i]:((subset @ (setunion @ (setadjoin @ X1356 @ emptyset)) @ X1356))=>(![X1018:$i]:((subset @ X1018 @ (setunion @ (setadjoin @ X1018 @ emptyset))))=>(![X1019:$i]:(((setunion @ (setadjoin @ X1019 @ emptyset))=(X1019)))=>(![X1020:$i, X1021:$i > $o]:((![X1022:$i]:(((in @ X1022 @ X1020)=>![X1023:$i]:(((in @ X1023 @ X1020)=>((X1021 @ X1022)=>((X1021 @ X1023)=>((X1022)=(X1023))))))))=>(?[X1024:$i]:(((in @ X1024 @ X1020)&(X1021 @ X1024)))=>(singleton @ (dsetconstr @ X1020 @ X1021)))))=>(![X1025:$i, X1026:$i > $o]:(((singleton @ (dsetconstr @ X1025 @ X1026))=>?[X1027:$i]:(((in @ X1027 @ X1025)&(X1026 @ X1027)))))=>(![X1352:$i, X1353:$i > $o, X1354:$i]:(((in @ X1354 @ X1352)=>((X1353 @ X1354)=>(![X1355:$i]:(((in @ X1355 @ X1352)=>((X1353 @ X1355)=>((X1355)=(X1354)))))=>(singleton @ (dsetconstr @ X1352 @ X1353))))))=>(![X1347:$i, X1348:$i > $o]:((![X1349:$i]:(((in @ X1349 @ X1347)=>![X1350:$i]:(((in @ X1350 @ X1347)=>((X1348 @ X1349)=>((X1348 @ X1350)=>((X1349)=(X1350))))))))=>(?[X1351:$i]:(((in @ X1351 @ X1347)&(X1348 @ X1351)))=>(singleton @ (dsetconstr @ X1347 @ X1348)))))=>(![X1345:$i, X1346:$i]:((((setadjoin @ X1345 @ emptyset)=(setadjoin @ X1346 @ emptyset))=>((X1345)=(X1346))))=>(![X1342:$i, X1343:$i, X1344:$i]:(((in @ (setadjoin @ X1344 @ emptyset) @ (setadjoin @ (setadjoin @ X1342 @ emptyset) @ (setadjoin @ (setadjoin @ X1342 @ (setadjoin @ X1343 @ emptyset)) @ emptyset)))=>((X1342)=(X1344))))=>(![X1341:$i]:(((iskpair @ X1341)=>(singleton @ (dsetconstr @ (setunion @ X1341) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1341)))))))=>(![X1028:$i]:(((singleton @ X1028)=>(in @ (setunion @ X1028) @ X1028)))=>(![X1029:$i, X1030:$i]:(((kfst @ (kpair @ X1029 @ X1030))=(X1029)))=>(![X1338:$i, X1339:$i, X1340:$i]:(((in @ X1340 @ (cartprod @ X1338 @ X1339))=>(in @ (kfst @ X1340) @ X1338)))=>(![X1334:$i, X1335:$i, X1336:$i, X1337:$i]:((((setadjoin @ (setadjoin @ X1334 @ emptyset) @ (setadjoin @ (setadjoin @ X1334 @ (setadjoin @ X1335 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1336 @ emptyset) @ (setadjoin @ (setadjoin @ X1336 @ (setadjoin @ X1337 @ emptyset)) @ emptyset)))=>((X1334)=(X1336))))=>(![X1330:$i, X1331:$i, X1332:$i, X1333:$i]:((((kpair @ X1330 @ X1331)=(kpair @ X1332 @ X1333))=>((X1330)=(X1332))))=>(![X1031:$i, X1032:$i]:((((X1031)=(X1032))=>((setadjoin @ X1031 @ (setadjoin @ X1032 @ emptyset))=(setadjoin @ X1031 @ emptyset))))=>(![X1033:$i, X1034:$i]:((((X1033)=(X1034))=>((setadjoin @ (setadjoin @ X1033 @ emptyset) @ (setadjoin @ (setadjoin @ X1033 @ (setadjoin @ X1034 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1033 @ emptyset) @ emptyset))))=>(![X1035:$i, X1036:$i, X1037:$i, X1038:$i]:((((setadjoin @ (setadjoin @ X1035 @ emptyset) @ (setadjoin @ (setadjoin @ X1035 @ (setadjoin @ X1036 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1037 @ emptyset) @ (setadjoin @ (setadjoin @ X1037 @ (setadjoin @ X1038 @ emptyset)) @ emptyset)))=>(((X1037)=(X1038))=>((X1036)=(X1038)))))=>(![X1039:$i, X1040:$i, X1041:$i]:((((setadjoin @ X1039 @ (setadjoin @ X1040 @ emptyset))=(setadjoin @ X1041 @ emptyset))=>((X1039)=(X1040))))=>(![X1326:$i, X1327:$i, X1328:$i, X1329:$i]:((((setadjoin @ (setadjoin @ X1326 @ emptyset) @ (setadjoin @ (setadjoin @ X1326 @ (setadjoin @ X1327 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1328 @ emptyset) @ (setadjoin @ (setadjoin @ X1328 @ (setadjoin @ X1329 @ emptyset)) @ emptyset)))=>((X1327)=(X1329))))=>(![X1042:$i, X1043:$i, X1044:$i, X1045:$i]:((((kpair @ X1042 @ X1043)=(kpair @ X1044 @ X1045))=>((X1043)=(X1045))))=>(![X1325:$i]:(((iskpair @ X1325)=>(singleton @ (dsetconstr @ (setunion @ X1325) @ (^[Z0/* 3 */:$i]:(((X1325)=(kpair @ (kfst @ X1325) @ Z0))))))))=>(![X1046:$i, X1047:$i]:(((ksnd @ (kpair @ X1046 @ X1047))=(X1047)))=>(![X1048:$i]:(((iskpair @ X1048)=>((kpair @ (kfst @ X1048) @ (ksnd @ X1048))=(X1048))))=>(![X1049:$i, X1050:$i, X1051:$i]:(((in @ X1051 @ (cartprod @ X1049 @ X1050))=>(in @ (ksnd @ X1051) @ X1050)))=>(![X1052:$i, X1053:$i, X1054:$i, X1055:$i]:(((in @ (kpair @ X1054 @ X1055) @ (cartprod @ X1052 @ X1053))=>(in @ X1054 @ X1052)))=>(![X1056:$i, X1057:$i, X1058:$i, X1059:$i]:(((in @ (kpair @ X1058 @ X1059) @ (cartprod @ X1056 @ X1057))=>(in @ X1059 @ X1057)))=>(![X1060:$i, X1061:$i, X1062:$i]:(((in @ X1062 @ X1060)=>![X1063:$i]:(((in @ X1063 @ X1061)=>((kpair @ X1062 @ X1063)=(kpair @ X1062 @ X1063))))))=>(![X1064:$i, X1065:$i, X1066:$i]:(((in @ X1066 @ X1064)=>![X1067:$i]:(((in @ X1067 @ X1065)=>((kfst @ (kpair @ X1066 @ X1067))=(X1066))))))=>(![X1321:$i, X1322:$i, X1323:$i]:(((in @ X1323 @ X1321)=>![X1324:$i]:(((in @ X1324 @ X1322)=>((ksnd @ (kpair @ X1323 @ X1324))=(X1324))))))=>(![X1318:$i, X1319:$i, X1320:$i]:(((in @ X1320 @ (cartprod @ X1318 @ X1319))=>((kpair @ (kfst @ X1320) @ (ksnd @ X1320))=(X1320))))=>(![X1313:$i, X1314:$i, X1315:$i > $i > $o, X1316:$i]:(((in @ X1316 @ X1313)=>![X1317:$i]:(((in @ X1317 @ X1314)=>((X1315 @ X1316 @ X1317)=>(in @ (kpair @ X1316 @ X1317) @ (dpsetconstr @ X1313 @ X1314 @ X1315)))))))=>(![X1310:$i, X1311:$i, X1312:$i > $i > $o]:((subset @ (dpsetconstr @ X1310 @ X1311 @ X1312) @ (cartprod @ X1310 @ X1311)))=>(![X1307:$i, X1308:$i, X1309:$i > $i > $o]:((subset @ (dpsetconstr @ X1307 @ X1308 @ X1309) @ (cartprod @ X1307 @ X1308)))=>(![X1068:$i, X1069:$i, X1070:$i > $i > $o, X1071:$i]:(((in @ X1071 @ X1068)=>![X1072:$i]:(((in @ X1072 @ X1069)=>((in @ (kpair @ X1071 @ X1072) @ (dpsetconstr @ X1068 @ X1069 @ X1070))=>(X1070 @ X1071 @ X1072))))))=>(![X1302:$i, X1303:$i, X1304:$i > $i > $o, X1305:$i, X1306:$i]:(((in @ (kpair @ X1305 @ X1306) @ (dpsetconstr @ X1302 @ X1303 @ X1304))=>(in @ X1305 @ X1302)))=>(![X1297:$i, X1298:$i, X1299:$i > $i > $o, X1300:$i, X1301:$i]:(((in @ (kpair @ X1300 @ X1301) @ (dpsetconstr @ X1297 @ X1298 @ X1299))=>(in @ X1301 @ X1298)))=>(![X1073:$i, X1074:$i, X1075:$i > $i > $o, X1076:$i, X1077:$i]:(((in @ (kpair @ X1076 @ X1077) @ (dpsetconstr @ X1073 @ X1074 @ X1075))=>(X1075 @ X1076 @ X1077)))=>(![X1078:$i, X1079:$i, X1080:$i]:(((func @ X1078 @ X1079 @ X1080)=>![X1081:$i]:(((in @ X1081 @ X1078)=>(singleton @ (dsetconstr @ X1079 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1081 @ Z0) @ X1080)))))))))=>(![X1293:$i, X1294:$i, X1295:$i]:(((func @ X1293 @ X1294 @ X1295)=>![X1296:$i]:(((in @ X1296 @ X1293)=>(in @ (setunion @ (dsetconstr @ X1294 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1296 @ Z0) @ X1295))))) @ X1294)))))=>(![X1289:$i, X1290:$i, X1291:$i]:(((func @ X1289 @ X1290 @ X1291)=>![X1292:$i]:(((in @ X1292 @ X1289)=>(in @ (ap @ X1289 @ X1290 @ X1291 @ X1292) @ X1290)))))=>(![X1286:$i, X1287:$i, X1288:$i]:(((in @ X1288 @ (funcSet @ X1286 @ X1287))=>(func @ X1286 @ X1287 @ X1288)))=>(![X1082:$i, X1083:$i, X1084:$i]:(((in @ X1084 @ (funcSet @ X1082 @ X1083))=>![X1085:$i]:(((in @ X1085 @ X1082)=>(in @ (ap @ X1082 @ X1083 @ X1084 @ X1085) @ X1083)))))=>(![X1283:$i, X1284:$i, X1285:$i]:(((func @ X1283 @ X1284 @ X1285)=>(in @ X1285 @ (funcSet @ X1283 @ X1284))))=>(![X1279:$i, X1280:$i, X1281:$i > $i]:((![X1282:$i]:(((in @ X1282 @ X1279)=>(in @ (X1281 @ X1282) @ X1280)))=>(func @ X1279 @ X1280 @ (dpsetconstr @ X1279 @ X1280 @ (^[Z0/* 3 */:$i]:($eq @ (X1281 @ Z0)))))))=>(![X1275:$i, X1276:$i, X1277:$i > $i]:((![X1278:$i]:(((in @ X1278 @ X1275)=>(in @ (X1277 @ X1278) @ X1276)))=>(func @ X1275 @ X1276 @ (lam @ X1275 @ X1276 @ X1277))))=>(![X1086:$i, X1087:$i, X1088:$i > $i]:((![X1089:$i]:(((in @ X1089 @ X1086)=>(in @ (X1088 @ X1089) @ X1087)))=>(in @ (lam @ X1086 @ X1087 @ X1088) @ (funcSet @ X1086 @ X1087))))=>(![X1268:$i, X1269:$i, X1270:$i]:(((subset @ X1270 @ (cartprod @ X1268 @ X1269))=>![X1271:$i > $o]:((![X1272:$i]:(((in @ X1272 @ X1268)=>![X1273:$i]:(((in @ X1273 @ X1269)=>((in @ (kpair @ X1272 @ X1273) @ X1270)=>(X1271 @ (kpair @ X1272 @ X1273)))))))=>![X1274:$i]:(((in @ X1274 @ X1270)=>(X1271 @ X1274)))))))=>(![X1090:$i, X1091:$i, X1092:$i]:(((subset @ X1092 @ (cartprod @ X1090 @ X1091))=>![X1093:$i > $o]:((![X1094:$i]:(((in @ X1094 @ X1090)=>![X1095:$i]:(((in @ X1095 @ X1091)=>((in @ (kpair @ X1094 @ X1095) @ X1092)=>(X1093 @ (kpair @ X1094 @ X1095)))))))=>![X1096:$i]:(((in @ X1096 @ X1092)=>(X1093 @ X1096)))))))=>(![X1264:$i, X1265:$i > $o]:(((singleton @ (dsetconstr @ X1264 @ X1265))=>![X1266:$i]:(((in @ X1266 @ X1264)=>![X1267:$i]:(((in @ X1267 @ X1264)=>((X1265 @ X1266)=>((X1265 @ X1267)=>((X1266)=(X1267))))))))))=>(![X1260:$i, X1261:$i, X1262:$i]:(((func @ X1260 @ X1261 @ X1262)=>![X1263:$i]:(((in @ X1263 @ X1260)=>(in @ (kpair @ X1263 @ (ap @ X1260 @ X1261 @ X1262 @ X1263)) @ X1262)))))=>(![X1097:$i, X1098:$i, X1099:$i]:(((in @ X1099 @ (funcSet @ X1097 @ X1098))=>![X1100:$i]:(((in @ X1100 @ X1097)=>(in @ (kpair @ X1100 @ (ap @ X1097 @ X1098 @ X1099 @ X1100)) @ X1099)))))=>(![X1255:$i, X1256:$i, X1257:$i]:(((func @ X1255 @ X1256 @ X1257)=>![X1258:$i]:(((in @ X1258 @ X1255)=>![X1259:$i]:(((in @ X1259 @ X1256)=>((in @ (kpair @ X1258 @ X1259) @ X1257)=>((ap @ X1255 @ X1256 @ X1257 @ X1258)=(X1259)))))))))=>(![X1101:$i, X1102:$i, X1103:$i]:(((func @ X1101 @ X1102 @ X1103)=>![X1104:$i]:(((func @ X1101 @ X1102 @ X1104)=>(![X1105:$i]:(((in @ X1105 @ X1101)=>((ap @ X1101 @ X1102 @ X1103 @ X1105)=(ap @ X1101 @ X1102 @ X1104 @ X1105))))=>![X1106:$i]:(((in @ X1106 @ X1101)=>![X1107:$i]:(((in @ X1107 @ X1102)=>((in @ (kpair @ X1106 @ X1107) @ X1104)=>(in @ (kpair @ X1106 @ X1107) @ X1103)))))))))))=>(![X1108:$i, X1109:$i, X1110:$i]:(((in @ X1110 @ (funcSet @ X1108 @ X1109))=>![X1111:$i]:(((in @ X1111 @ X1108)=>![X1112:$i]:(((in @ X1112 @ X1109)=>((in @ (kpair @ X1111 @ X1112) @ X1110)=>((ap @ X1108 @ X1109 @ X1110 @ X1111)=(X1112)))))))))=>(![X1113:$i, X1114:$i, X1115:$i]:(((subset @ X1115 @ (cartprod @ X1113 @ X1114))=>![X1116:$i]:(((subset @ X1116 @ (cartprod @ X1113 @ X1114))=>(![X1117:$i]:(((in @ X1117 @ X1113)=>![X1118:$i]:(((in @ X1118 @ X1114)=>((in @ (kpair @ X1117 @ X1118) @ X1115)=>(in @ (kpair @ X1117 @ X1118) @ X1116))))))=>(subset @ X1115 @ X1116))))))=>(![X1247:$i, X1248:$i, X1249:$i]:(((subset @ X1249 @ (cartprod @ X1247 @ X1248))=>![X1250:$i]:(((subset @ X1250 @ (cartprod @ X1247 @ X1248))=>(![X1251:$i]:(((in @ X1251 @ X1247)=>![X1252:$i]:(((in @ X1252 @ X1248)=>((in @ (kpair @ X1251 @ X1252) @ X1249)=>(in @ (kpair @ X1251 @ X1252) @ X1250))))))=>(![X1253:$i]:(((in @ X1253 @ X1247)=>![X1254:$i]:(((in @ X1254 @ X1248)=>((in @ (kpair @ X1253 @ X1254) @ X1250)=>(in @ (kpair @ X1253 @ X1254) @ X1249))))))=>((X1249)=(X1250))))))))=>(![X1119:$i, X1120:$i, X1121:$i]:(((func @ X1119 @ X1120 @ X1121)=>![X1122:$i]:(((func @ X1119 @ X1120 @ X1122)=>(![X1123:$i]:(((in @ X1123 @ X1119)=>((ap @ X1119 @ X1120 @ X1121 @ X1123)=(ap @ X1119 @ X1120 @ X1122 @ X1123))))=>((X1121)=(X1122)))))))=>(![X1124:$i, X1125:$i, X1126:$i]:(((in @ X1126 @ (funcSet @ X1124 @ X1125))=>![X1127:$i]:(((in @ X1127 @ (funcSet @ X1124 @ X1125))=>(![X1128:$i]:(((in @ X1128 @ X1124)=>((ap @ X1124 @ X1125 @ X1126 @ X1128)=(ap @ X1124 @ X1125 @ X1127 @ X1128))))=>((X1126)=(X1127)))))))=>(![X1243:$i, X1244:$i, X1245:$i]:(((in @ X1245 @ (funcSet @ X1243 @ X1244))=>![X1246:$i]:(((in @ X1246 @ X1243)=>((ap @ X1243 @ X1244 @ X1245 @ X1246)=(ap @ X1243 @ X1244 @ X1245 @ X1246))))))=>(![X1129:$i, X1130:$i, X1131:$i]:(((func @ X1129 @ X1130 @ X1131)=>![X1132:$i]:(((in @ X1132 @ X1129)=>((ap @ X1129 @ X1130 @ X1131 @ X1132)=(ap @ X1129 @ X1130 @ X1131 @ X1132))))))=>(![X1133:$i, X1134:$i, X1135:$i > $i]:((![X1136:$i]:(((in @ X1136 @ X1133)=>(in @ (X1135 @ X1136) @ X1134)))=>![X1137:$i]:(((in @ X1137 @ X1133)=>((ap @ X1133 @ X1134 @ (lam @ X1133 @ X1134 @ X1135) @ X1137)=(X1135 @ X1137))))))=>(![X1138:$i, X1139:$i, X1140:$i]:(((func @ X1138 @ X1139 @ X1140)=>((lam @ X1138 @ X1139 @ (ap @ X1138 @ X1139 @ X1140))=(X1140))))=>(![X1141:$i, X1142:$i, X1143:$i > $i]:((![X1144:$i]:(((in @ X1144 @ X1141)=>(in @ (X1143 @ X1144) @ X1142)))=>((lam @ X1141 @ X1142 @ X1143)=(lam @ X1141 @ X1142 @ X1143))))=>(![X1238:$i, X1239:$i, X1240:$i > $i]:((![X1241:$i]:(((in @ X1241 @ X1238)=>(in @ (X1240 @ X1241) @ X1239)))=>![X1242:$i]:(((in @ X1242 @ X1238)=>((ap @ X1238 @ X1239 @ (lam @ X1238 @ X1239 @ X1240) @ X1242)=(X1240 @ X1242))))))=>(![X1145:$i, X1146:$i, X1147:$i]:(((in @ X1147 @ (funcSet @ X1145 @ X1146))=>((lam @ X1145 @ X1146 @ (ap @ X1145 @ X1146 @ X1147))=(X1147))))=>(![X1234:$i, X1235:$o, X1236:$i]:(((in @ X1236 @ X1234)=>![X1237:$i]:(((in @ X1237 @ X1234)=>(~(X1235)=>(in @ X1237 @ (dsetconstr @ X1234 @ (^[Z0/* 9 */:$i]:((((X1235)&((Z0)=(X1236)))|(~((X1235))&((Z0)=(X1237)))))))))))))=>(![X1148:$i, X1149:$o, X1150:$i]:(((in @ X1150 @ X1148)=>![X1151:$i]:(((in @ X1151 @ X1148)=>(~(X1149)=>((dsetconstr @ X1148 @ (^[Z0/* 9 */:$i]:((((X1149)&((Z0)=(X1150)))|(~((X1149))&((Z0)=(X1151)))))))=(setadjoin @ X1151 @ emptyset)))))))=>(![X1230:$i, X1231:$o, X1232:$i]:(((in @ X1232 @ X1230)=>![X1233:$i]:(((in @ X1233 @ X1230)=>((X1231)=>(in @ X1232 @ (dsetconstr @ X1230 @ (^[Z0/* 9 */:$i]:((((X1231)&((Z0)=(X1232)))|(~((X1231))&((Z0)=(X1233)))))))))))))=>(![X1226:$i, X1227:$o, X1228:$i]:(((in @ X1228 @ X1226)=>![X1229:$i]:(((in @ X1229 @ X1226)=>((X1227)=>((dsetconstr @ X1226 @ (^[Z0/* 9 */:$i]:((((X1227)&((Z0)=(X1228)))|(~((X1227))&((Z0)=(X1229)))))))=(setadjoin @ X1228 @ emptyset)))))))=>(![X1222:$i, X1223:$o, X1224:$i]:(((in @ X1224 @ X1222)=>![X1225:$i]:(((in @ X1225 @ X1222)=>(singleton @ (dsetconstr @ X1222 @ (^[Z0/* 9 */:$i]:((((X1223)&((Z0)=(X1224)))|(~((X1223))&((Z0)=(X1225))))))))))))=>(![X1152:$i, X1153:$o, X1154:$i]:(((in @ X1154 @ X1152)=>![X1155:$i]:(((in @ X1155 @ X1152)=>(in @ (if @ X1152 @ ((X1153)) @ X1154 @ X1155) @ X1152)))))=>(![X1156:$i]:(((singleton @ X1156)=>![X1157:$i]:(((in @ X1157 @ X1156)=>((setunion @ X1156)=(X1157))))))=>(![X1218:$i, X1219:$o, X1220:$i]:(((in @ X1220 @ X1218)=>![X1221:$i]:(((in @ X1221 @ X1218)=>((X1219)=>((if @ X1218 @ ((X1219)) @ X1220 @ X1221)=(X1220)))))))=>(![X1158:$i, X1159:$o, X1160:$i]:(((in @ X1160 @ X1158)=>![X1161:$i]:(((in @ X1161 @ X1158)=>(~(X1159)=>((if @ X1158 @ ((X1159)) @ X1160 @ X1161)=(X1161)))))))=>(![X1162:$i, X1163:$o, X1164:$i]:(((in @ X1164 @ X1162)=>![X1165:$i]:(((in @ X1165 @ X1162)=>(in @ (if @ X1162 @ ((X1163)) @ X1164 @ X1165) @ (setadjoin @ X1164 @ (setadjoin @ X1165 @ emptyset)))))))=>(![X1166:$i, X1167:$i]:(((in @ X1167 @ (powerset @ X1166))=>![X1168:$i]:(((in @ X1168 @ (powerset @ X1166))=>(in @ (binintersect @ X1167 @ X1168) @ (powerset @ X1166))))))=>(![X1215:$i, X1216:$i]:(((in @ X1216 @ (powerset @ X1215))=>![X1217:$i]:(((in @ X1217 @ (powerset @ X1215))=>(in @ (binunion @ X1216 @ X1217) @ (powerset @ X1215))))))=>(![X1213:$i, X1214:$i]:(((in @ X1214 @ (powerset @ X1213))=>(in @ (powerset @ X1214) @ (powerset @ (powerset @ X1213)))))=>(![X1169:$i, X1170:$i]:(((in @ X1170 @ (powerset @ X1169))=>![X1171:$i]:(((in @ X1171 @ (powerset @ X1169))=>(in @ (setminus @ X1170 @ X1171) @ (powerset @ X1169))))))=>(![X1172:$i, X1173:$i]:(((in @ X1173 @ (powerset @ X1172))=>(in @ (setminus @ X1172 @ X1173) @ (powerset @ X1172))))=>(![X1208:$i, X1209:$i]:(((in @ X1209 @ (powerset @ X1208))=>![X1210:$i]:(((in @ X1210 @ (powerset @ X1208))=>(![X1211:$i]:(((in @ X1211 @ X1208)=>((in @ X1211 @ X1209)=>(in @ X1211 @ X1210))))=>(![X1212:$i]:(((in @ X1212 @ X1208)=>((in @ X1212 @ X1210)=>(in @ X1212 @ X1209))))=>((X1209)=(X1210))))))))=>(![X1174:$i, X1175:$i]:(((in @ X1175 @ (powerset @ X1174))=>![X1176:$i]:(((in @ X1176 @ (powerset @ X1174))=>(![X1177:$i]:(((in @ X1177 @ X1174)=>((in @ X1177 @ X1175)=>(in @ X1177 @ X1176))))=>(subset @ X1175 @ X1176))))))=>(![X1204:$i, X1205:$i]:(((in @ X1205 @ (powerset @ X1204))=>![X1206:$i]:(((in @ X1206 @ (powerset @ X1204))=>(![X1207:$i]:(((in @ X1207 @ X1204)=>((in @ X1207 @ X1205)=>(in @ X1207 @ X1206))))=>(in @ X1205 @ (powerset @ X1206)))))))=>(![X1178:$i, X1179:$i]:(((in @ X1179 @ (powerset @ X1178))=>![X1180:$i]:(((in @ X1180 @ (powerset @ X1178))=>![X1181:$i]:(((in @ X1181 @ X1178)=>((in @ X1179 @ (powerset @ X1180))=>((in @ X1181 @ X1179)=>(in @ X1181 @ X1180)))))))))=>(![X1201:$i, X1202:$i]:(((in @ X1202 @ (powerset @ X1201))=>![X1203:$i]:(((in @ X1203 @ X1201)=>((in @ X1203 @ X1202)=>~(in @ X1203 @ (setminus @ X1201 @ X1202)))))))=>(![X1198:$i, X1199:$i]:(((in @ X1199 @ (powerset @ X1198))=>![X1200:$i]:(((in @ X1200 @ X1198)=>(~(in @ X1200 @ (setminus @ X1198 @ X1199))=>(in @ X1200 @ X1199))))))=>(![X1182:$i, X1183:$i]:(((in @ X1183 @ (powerset @ X1182))=>![X1184:$i]:(((in @ X1184 @ (powerset @ X1182))=>![X1185:$i]:(((in @ X1185 @ X1182)=>(~(in @ X1185 @ X1183)=>~(in @ X1185 @ (binintersect @ X1183 @ X1184)))))))))=>(![X1186:$i, X1187:$i]:(((in @ X1187 @ (powerset @ X1186))=>![X1188:$i]:(((in @ X1188 @ (powerset @ X1186))=>![X1189:$i]:(((in @ X1189 @ X1186)=>(~(in @ X1189 @ X1188)=>~(in @ X1189 @ (binintersect @ X1187 @ X1188)))))))))=>(![X1190:$i, X1191:$i]:(((in @ X1191 @ (powerset @ X1190))=>![X1192:$i]:(((in @ X1192 @ (powerset @ X1190))=>![X1193:$i]:(((in @ X1193 @ X1190)=>((subset @ X1191 @ (setminus @ X1190 @ X1192))=>((in @ X1193 @ X1192)=>~(in @ X1193 @ X1191)))))))))=>(![X1194:$i, X1195:$i]:(((in @ X1195 @ (powerset @ X1194))=>![X1196:$i]:(((in @ X1196 @ (powerset @ X1194))=>![X1197:$i]:(((in @ X1197 @ X1194)=>((subset @ X1195 @ X1196)=>(~(in @ X1197 @ X1196)=>~(in @ X1197 @ X1195)))))))))=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[contrasubsetT2]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_268]), foundationAx]), wellorderingAx]), c_0_269]), c_0_270]), c_0_271]), c_0_272]), c_0_273]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_274]), setext]), emptyI]), noeltsimpempty]), c_0_275]), c_0_276]), c_0_277]), c_0_278]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_279]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_280]), c_0_281]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_282]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_283]), c_0_284]), c_0_285]), inCongP]), in__Cong]), c_0_286]), c_0_287]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_288]), c_0_289]), c_0_290]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_291]), c_0_292]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_293]), c_0_294]), c_0_295]), c_0_296]), singletonsuniq]), setukpairinjL1]), c_0_297]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_298]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_299]), c_0_300]), c_0_301]), c_0_302]), c_0_303]), c_0_304]), c_0_305]), c_0_306]), c_0_307]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_308]), c_0_309]), c_0_310]), c_0_311]), c_0_312]), c_0_313]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_314]), c_0_315]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_316]), c_0_317]), c_0_318]), c_0_319]), c_0_320]), c_0_321]), c_0_322]), c_0_323]), c_0_324]), c_0_325]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1])])]), c_0_326])). 309.13/39.45 thf(c_0_328, negated_conjecture, ![X1604:$i, X1605:$i, X1607:$i, X1608:$i, X1609:$i, X1610:$i, X1611:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1617:$i, X1618:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1626:$i, X1627:$i > $i > $o, X1628:$i, X1630:$i, X1633:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1640:$i, X1641:$i > $o, X1642:$i, X1644:$i, X1645:$i > $o, X1646:$i, X1647:$i, X1648:$i > $o, X1649:$i, X1650:$i, X1651:$i > $o, X1652:$i, X1653:$i > $o, X1654:$i, X1657:$i, X1658:$o, X1659:$i, X1660:$i, X1661:$o, X1662:$i, X1663:$i, X1664:$i > $o, X1665:$i, X1668:$i, X1669:$i, X1672:$i, X1674:$i, X1676:$i, X1677:$i > $o, X1678:$i, X1679:$i, X1681:$i, X1682:$i > $o, X1683:$i, X1684:$i, X1685:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$o, X1695:$i, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$o, X1714:$i, X1715:$i, X1716:$i > $o, X1717:$i, X1720:$i, X1721:$i, X1722:$i, X1724:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i > $o, X1741:$i, X1742:$i > $o, X1743:$i, X1744:$i, X1745:$i > $o, X1746:$i, X1748:$i, X1749:$i > $o, X1751:$i, X1752:$i, X1753:$i > $o, X1755:$i, X1756:$i, X1757:$i > $o, X1758:$i, X1760:$o, X1761:$o, X1762:$i, X1763:$i > $o, X1765:$i, X1766:$i, X1767:$i > $o, X1768:$i, X1770:$i > $o, X1771:$i, X1774:$i, X1775:$i > $o, X1776:$i, X1780:$i, X1781:$i > $o, X1782:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i > $o, X1795:$i, X1797:$i, X1798:$i, X1799:$i > $o, X1800:$i > $o, X1803:$i, X1806:$i, X1807:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i > $o, X1820:$i, X1822:$i, X1823:$i, X1824:$i > $o, X1825:$i > $o, X1828:$i, X1830:$i, X1832:$i, X1833:$i, X1834:$i > $o, X1835:$i > $o, X1838:$i, X1839:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i > $o, X1886:$i, X1887:$i > $o, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$o, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$o, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i > $o, X2042:$i, X2043:$i, X2044:$i > $o, X2046:$i, X2047:$i > $o, X2048:$i, X2050:$i, X2051:$i > $o, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i > $i > $o, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i > $i > $o, X2132:$i, X2133:$i, X2134:$i > $i > $o, X2135:$i, X2136:$i, X2137:$i > $i > $o, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i > $i > $o, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i > $i > $o, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i > $i > $o, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i > $i, X2181:$i, X2182:$i, X2183:$i > $i, X2185:$i, X2186:$i, X2187:$i > $i, X2189:$i, X2190:$i, X2191:$i, X2192:$i > $o, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i > $o, X2202:$i, X2203:$i, X2204:$i > $o, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i > $i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i > $i, X2276:$i, X2277:$i, X2278:$i > $i, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$o, X2286:$i, X2287:$i, X2288:$i, X2289:$o, X2290:$i, X2291:$i, X2292:$i, X2293:$o, X2294:$i, X2295:$i, X2296:$i, X2297:$o, X2298:$i, X2299:$i, X2300:$i, X2301:$o, X2302:$i, X2303:$i, X2304:$i, X2305:$o, X2306:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$o, X2312:$i, X2313:$i, X2314:$i, X2315:$o, X2316:$i, X2317:$i, X2318:$i, X2319:$o, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2327:$i, X2328:$i, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i, X2340:$i, X2341:$i, X2342:$i, X2344:$i, X2345:$i, X2346:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$i, X2364:$i, X2365:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$i, X2372:$i, X2373:$i]:((((~(in @ (esk1_2 @ X1604 @ X1605) @ X1604)|~(in @ (esk1_2 @ X1604 @ X1605) @ X1605)|((X1604)=(X1605)))&((in @ (esk1_2 @ X1604 @ X1605) @ X1604)|(in @ (esk1_2 @ X1604 @ X1605) @ X1605)|((X1604)=(X1605))))&(~(in @ X1607 @ emptyset)&(((~(in @ X1610 @ (setadjoin @ X1608 @ X1609))|(((X1610)=(X1608))|(in @ X1610 @ X1609)))&((((X1610)!=(X1608))|(in @ X1610 @ (setadjoin @ X1608 @ X1609)))&(~(in @ X1610 @ X1609)|(in @ X1610 @ (setadjoin @ X1608 @ X1609)))))&(((~(in @ X1612 @ (powerset @ X1611))|(~(in @ X1613 @ X1612)|(in @ X1613 @ X1611)))&(((in @ (esk2_2 @ X1614 @ X1615) @ X1615)|(in @ X1615 @ (powerset @ X1614)))&(~(in @ (esk2_2 @ X1614 @ X1615) @ X1614)|(in @ X1615 @ (powerset @ X1614)))))&(((((in @ X1618 @ (esk3_2 @ X1617 @ X1618))|~(in @ X1618 @ (setunion @ X1617)))&((in @ (esk3_2 @ X1617 @ X1618) @ X1617)|~(in @ X1618 @ (setunion @ X1617))))&(~(in @ X1621 @ X1622)|~(in @ X1622 @ X1620)|(in @ X1621 @ (setunion @ X1620))))&((in @ emptyset @ omega)&((~(in @ X1623 @ omega)|(in @ (setadjoin @ X1623 @ X1623) @ omega))&(((((in @ (esk4_1 @ X1624) @ omega)|~(in @ emptyset @ X1624)|(~(in @ X1626 @ omega)|(in @ X1626 @ X1624)))&((in @ (esk4_1 @ X1624) @ X1624)|~(in @ emptyset @ X1624)|(~(in @ X1626 @ omega)|(in @ X1626 @ X1624))))&(~(in @ (setadjoin @ (esk4_1 @ X1624) @ (esk4_1 @ X1624)) @ X1624)|~(in @ emptyset @ X1624)|(~(in @ X1626 @ omega)|(in @ X1626 @ X1624))))&((((((in @ (esk8_3 @ X1627 @ X1628 @ X1633) @ X1628)|~(in @ X1633 @ (esk7_2 @ X1627 @ X1628))|(in @ (esk5_2 @ X1627 @ X1628) @ X1628))&((X1627 @ (esk8_3 @ X1627 @ X1628 @ X1633) @ X1633)|~(in @ X1633 @ (esk7_2 @ X1627 @ X1628))|(in @ (esk5_2 @ X1627 @ X1628) @ X1628)))&(~(in @ X1636 @ X1628)|~(X1627 @ X1636 @ X1635)|(in @ X1635 @ (esk7_2 @ X1627 @ X1628))|(in @ (esk5_2 @ X1627 @ X1628) @ X1628)))&(((((in @ (esk8_3 @ X1627 @ X1628 @ X1633) @ X1628)|~(in @ X1633 @ (esk7_2 @ X1627 @ X1628))|((X1627 @ (esk5_2 @ X1627 @ X1628) @ (esk6_3 @ X1627 @ X1628 @ X1630))|~(X1627 @ (esk5_2 @ X1627 @ X1628) @ X1630)))&((X1627 @ (esk8_3 @ X1627 @ X1628 @ X1633) @ X1633)|~(in @ X1633 @ (esk7_2 @ X1627 @ X1628))|((X1627 @ (esk5_2 @ X1627 @ X1628) @ (esk6_3 @ X1627 @ X1628 @ X1630))|~(X1627 @ (esk5_2 @ X1627 @ X1628) @ X1630))))&(~(in @ X1636 @ X1628)|~(X1627 @ X1636 @ X1635)|(in @ X1635 @ (esk7_2 @ X1627 @ X1628))|((X1627 @ (esk5_2 @ X1627 @ X1628) @ (esk6_3 @ X1627 @ X1628 @ X1630))|~(X1627 @ (esk5_2 @ X1627 @ X1628) @ X1630))))&((((in @ (esk8_3 @ X1627 @ X1628 @ X1633) @ X1628)|~(in @ X1633 @ (esk7_2 @ X1627 @ X1628))|(((X1630)!=(esk6_3 @ X1627 @ X1628 @ X1630))|~(X1627 @ (esk5_2 @ X1627 @ X1628) @ X1630)))&((X1627 @ (esk8_3 @ X1627 @ X1628 @ X1633) @ X1633)|~(in @ X1633 @ (esk7_2 @ X1627 @ X1628))|(((X1630)!=(esk6_3 @ X1627 @ X1628 @ X1630))|~(X1627 @ (esk5_2 @ X1627 @ X1628) @ X1630))))&(~(in @ X1636 @ X1628)|~(X1627 @ X1636 @ X1635)|(in @ X1635 @ (esk7_2 @ X1627 @ X1628))|(((X1630)!=(esk6_3 @ X1627 @ X1628 @ X1630))|~(X1627 @ (esk5_2 @ X1627 @ X1628) @ X1630))))))&((((in @ (esk9_1 @ X1637) @ X1637)|~(in @ X1638 @ X1637))&(~(in @ X1640 @ (esk9_1 @ X1637))|~(in @ X1640 @ X1637)|~(in @ X1638 @ X1637)))&((epred1_0)&((((X1641 @ (esk10_2 @ X1641 @ X1642))|~(X1641 @ X1642)|(X1641 @ (descr @ X1641)))&(((X1642)!=(esk10_2 @ X1641 @ X1642))|~(X1641 @ X1642)|(X1641 @ (descr @ X1641))))&((~(in @ X1646 @ X1644)|(~(X1645 @ X1646)|(in @ X1646 @ (dsetconstr @ X1644 @ X1645))))&((~(in @ X1649 @ (dsetconstr @ X1647 @ X1648))|(in @ X1649 @ X1647))&((~(in @ X1652 @ (dsetconstr @ X1650 @ X1651))|(X1651 @ X1652))&(((((X1653 @ (esk12_1 @ X1653))|((X1653 @ (esk11_2 @ X1653 @ X1654))|~(X1653 @ X1654)))&(~(X1653 @ X1657)|((esk12_1 @ X1653)=(X1657))|((X1653 @ (esk11_2 @ X1653 @ X1654))|~(X1653 @ X1654))))&(((X1653 @ (esk12_1 @ X1653))|(((X1654)!=(esk11_2 @ X1653 @ X1654))|~(X1653 @ X1654)))&(~(X1653 @ X1657)|((esk12_1 @ X1653)=(X1657))|(((X1654)!=(esk11_2 @ X1653 @ X1654))|~(X1653 @ X1654)))))&((~(in @ X1659 @ (prop2set @ ((X1658))))|(X1658))&((~(in @ X1660 @ emptyset)|(X1661))&((~(in @ X1662 @ emptyset)|~($true))&(~(in @ X1663 @ emptyset)&((((X1664 @ (esk13_2 @ X1664 @ X1665))|~(X1664 @ X1665)|(X1664 @ (esk14_1 @ X1664)))&(((X1665)!=(esk13_2 @ X1664 @ X1665))|~(X1664 @ X1665)|(X1664 @ (esk14_1 @ X1664))))&(((((in @ (esk16_2 @ X1668 @ X1669) @ X1669)|((X1668)=(X1669))|(in @ (esk15_2 @ X1668 @ X1669) @ X1668))&(~(in @ (esk16_2 @ X1668 @ X1669) @ X1668)|((X1668)=(X1669))|(in @ (esk15_2 @ X1668 @ X1669) @ X1668)))&(((in @ (esk16_2 @ X1668 @ X1669) @ X1669)|((X1668)=(X1669))|~(in @ (esk15_2 @ X1668 @ X1669) @ X1669))&(~(in @ (esk16_2 @ X1668 @ X1669) @ X1668)|((X1668)=(X1669))|~(in @ (esk15_2 @ X1668 @ X1669) @ X1669))))&(((in @ (esk17_1 @ X1672) @ X1672)|((X1672)=(emptyset)))&(((in @ (esk18_1 @ X1674) @ X1674)|((X1674)=(emptyset)))&(((~(in @ X1678 @ (dsetconstr @ X1676 @ X1677))|(X1677 @ X1678)|~(in @ X1678 @ X1676))&(~(X1677 @ X1678)|(in @ X1678 @ (dsetconstr @ X1676 @ X1677))|~(in @ X1678 @ X1676)))&((((X1679)=(emptyset))|(in @ (esk19_1 @ X1679) @ X1679))&((~(in @ X1683 @ X1681)|(~(X1682 @ X1683)|((dsetconstr @ X1681 @ X1682)!=(emptyset))))&((~(in @ X1685 @ X1684)|((X1684)!=(emptyset)))&((in @ X1686 @ (setadjoin @ X1686 @ X1687))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1690 @ X1689)|(in @ X1690 @ (setadjoin @ X1688 @ X1689)))&(((((in @ X1693 @ X1692)|(X1694)|((X1693)=(X1691))|~(in @ X1693 @ (setadjoin @ X1691 @ X1692)))&(~(X1694)|(X1694)|((X1693)=(X1691))|~(in @ X1693 @ (setadjoin @ X1691 @ X1692))))&(((in @ X1693 @ X1692)|(X1694)|~(X1694)|~(in @ X1693 @ (setadjoin @ X1691 @ X1692)))&(~(X1694)|(X1694)|~(X1694)|~(in @ X1693 @ (setadjoin @ X1691 @ X1692)))))&((~(in @ X1697 @ (setadjoin @ X1695 @ X1696))|(((X1697)=(X1695))|(in @ X1697 @ X1696)))&(((dsetconstr @ X1698 @ (^[Z0/* 1 */:$i]:($true)))=(X1698))&((((in @ (esk20_2 @ X1699 @ X1700) @ X1700)|(in @ X1700 @ (powerset @ X1699)))&(~(in @ (esk20_2 @ X1699 @ X1700) @ X1699)|(in @ X1700 @ (powerset @ X1699))))&((in @ emptyset @ (powerset @ X1702))&((in @ emptyset @ (powerset @ X1703))&((~(in @ X1705 @ (powerset @ X1704))|(~(in @ X1706 @ X1705)|(in @ X1706 @ X1704)))&((~(in @ X1708 @ X1709)|(~(in @ X1709 @ X1707)|(in @ X1708 @ (setunion @ X1707))))&((((in @ X1711 @ (esk21_3 @ X1710 @ X1711 @ X1712))|(X1712)|~(in @ X1711 @ (setunion @ X1710)))&(((in @ (esk21_3 @ X1710 @ X1711 @ X1712) @ X1710)|(X1712)|~(in @ X1711 @ (setunion @ X1710)))&(~(X1712)|(X1712)|~(in @ X1711 @ (setunion @ X1710)))))&((~(in @ X1715 @ X1714)|(in @ X1715 @ (powerset @ (setunion @ X1714))))&((((~(X1716 @ X1720)|((X1720)=(esk23_1 @ X1716))|((X1716 @ (esk22_2 @ X1716 @ X1717))|~(X1716 @ X1717)))&(((X1721)!=(esk23_1 @ X1716))|(X1716 @ X1721)|((X1716 @ (esk22_2 @ X1716 @ X1717))|~(X1716 @ X1717))))&((~(X1716 @ X1720)|((X1720)=(esk23_1 @ X1716))|(((X1717)!=(esk22_2 @ X1716 @ X1717))|~(X1716 @ X1717)))&(((X1721)!=(esk23_1 @ X1716))|(X1716 @ X1721)|(((X1717)!=(esk22_2 @ X1716 @ X1717))|~(X1716 @ X1717)))))&((((in @ (esk24_1 @ X1722) @ X1722)|((X1722)=(emptyset)))&(($true)|((X1722)=(emptyset))))&((~(in @ X1724 @ (setadjoin @ X1725 @ emptyset))|((X1724)=(X1725)))&((((X1726)=(X1727))|~(in @ X1727 @ (setadjoin @ X1726 @ emptyset)))&((((X1728)!=(X1729))|(in @ X1728 @ (setadjoin @ X1729 @ emptyset)))&((~(in @ X1730 @ (setadjoin @ X1731 @ emptyset))|(in @ X1731 @ (setadjoin @ X1730 @ emptyset)))&((~(in @ X1734 @ (setadjoin @ X1732 @ (setadjoin @ X1733 @ emptyset)))|(((X1734)=(X1732))|((X1734)=(X1733))))&((in @ X1735 @ (setadjoin @ X1735 @ (setadjoin @ X1736 @ emptyset)))&((in @ X1738 @ (setadjoin @ X1737 @ (setadjoin @ X1738 @ emptyset)))&((~(in @ X1741 @ X1739)|~(X1740 @ X1741)|(((dsetconstr @ X1739 @ X1740)!=(emptyset))|~($true)))&((~(in @ X1743 @ emptyset)|(X1742 @ X1743))&((((in @ (esk25_2 @ X1744 @ X1745) @ X1744)|(~(in @ X1746 @ X1744)|(X1745 @ X1746)))&(~(X1745 @ (esk25_2 @ X1744 @ X1745))|(~(in @ X1746 @ X1744)|(X1745 @ X1746))))&((((in @ (esk26_2 @ X1748 @ X1749) @ X1748)|(~(in @ X1751 @ X1748)|~(X1749 @ X1751)))&((X1749 @ (esk26_2 @ X1748 @ X1749))|(~(in @ X1751 @ X1748)|~(X1749 @ X1751))))&((((in @ (esk27_2 @ X1752 @ X1753) @ X1752)|(~(in @ X1755 @ X1752)|~(X1753 @ X1755)))&((X1753 @ (esk27_2 @ X1752 @ X1753))|(~(in @ X1755 @ X1752)|~(X1753 @ X1755))))&((((in @ (esk28_2 @ X1756 @ X1757) @ X1756)|(~(in @ X1758 @ X1756)|(X1757 @ X1758)))&(~(X1757 @ (esk28_2 @ X1756 @ X1757))|(~(in @ X1758 @ X1756)|(X1757 @ X1758))))&((~(X1760)|(in @ emptyset @ (prop2set @ ((X1760)))))&((~(X1761)|(set2prop @ (prop2set @ ((X1761)))))&((((in @ (esk29_2 @ X1762 @ X1763) @ X1762)|(~(in @ X1765 @ X1762)|~(X1763 @ X1765)))&((X1763 @ (esk29_2 @ X1762 @ X1763))|(~(in @ X1765 @ X1762)|~(X1763 @ X1765))))&((((in @ (esk30_2 @ X1766 @ X1767) @ X1766)|(~(in @ X1768 @ X1766)|(X1767 @ X1768)))&(~(X1767 @ (esk30_2 @ X1766 @ X1767))|(~(in @ X1768 @ X1766)|(X1767 @ X1768))))&(((((X1770 @ (esk32_1 @ X1770))|((X1770 @ (esk31_2 @ X1770 @ X1771))|~(X1770 @ X1771)))&(~(X1770 @ X1774)|((esk32_1 @ X1770)=(X1774))|((X1770 @ (esk31_2 @ X1770 @ X1771))|~(X1770 @ X1771))))&(((X1770 @ (esk32_1 @ X1770))|(((X1771)!=(esk31_2 @ X1770 @ X1771))|~(X1770 @ X1771)))&(~(X1770 @ X1774)|((esk32_1 @ X1770)=(X1774))|(((X1771)!=(esk31_2 @ X1770 @ X1771))|~(X1770 @ X1771)))))&(((((X1775 @ (esk35_1 @ X1775))|(X1775 @ (esk33_1 @ X1775))|~(X1775 @ X1776))&(~(X1775 @ X1780)|((esk35_1 @ X1775)=(X1780))|(X1775 @ (esk33_1 @ X1775))|~(X1775 @ X1776)))&((((X1775 @ (esk35_1 @ X1775))|(X1775 @ (esk34_1 @ X1775))|~(X1775 @ X1776))&(~(X1775 @ X1780)|((esk35_1 @ X1775)=(X1780))|(X1775 @ (esk34_1 @ X1775))|~(X1775 @ X1776)))&(((X1775 @ (esk35_1 @ X1775))|((esk33_1 @ X1775)!=(esk34_1 @ X1775))|~(X1775 @ X1776))&(~(X1775 @ X1780)|((esk35_1 @ X1775)=(X1780))|((esk33_1 @ X1775)!=(esk34_1 @ X1775))|~(X1775 @ X1776)))))&(((((X1781 @ (esk37_1 @ X1781))|(~(X1781 @ (esk36_2 @ X1781 @ X1782))|((esk36_2 @ X1781 @ X1782)!=(X1782))))&(~(X1781 @ X1785)|((esk37_1 @ X1781)=(X1785))|(~(X1781 @ (esk36_2 @ X1781 @ X1782))|((esk36_2 @ X1781 @ X1782)!=(X1782)))))&(((X1781 @ (esk37_1 @ X1781))|((X1781 @ (esk36_2 @ X1781 @ X1782))|((esk36_2 @ X1781 @ X1782)=(X1782))))&(~(X1781 @ X1785)|((esk37_1 @ X1781)=(X1785))|((X1781 @ (esk36_2 @ X1781 @ X1782))|((esk36_2 @ X1781 @ X1782)=(X1782))))))&((((X1786)!=(X1787))|(((X1788)!=(X1789))|(~(in @ X1788 @ X1786)|(in @ X1789 @ X1787))))&(((~(in @ X1792 @ X1790)|(in @ X1793 @ X1791)|((X1792)!=(X1793))|((X1790)!=(X1791)))&(~(in @ X1793 @ X1791)|(in @ X1792 @ X1790)|((X1792)!=(X1793))|((X1790)!=(X1791))))&((((X1794 @ (esk38_2 @ X1794 @ X1795))|~(X1794 @ X1795)|(~(X1794 @ X1797)|(~(X1794 @ X1798)|((X1797)=(X1798)))))&(((X1795)!=(esk38_2 @ X1794 @ X1795))|~(X1794 @ X1795)|(~(X1794 @ X1797)|(~(X1794 @ X1798)|((X1797)=(X1798))))))&(((((((X1800 @ (esk42_2 @ X1799 @ X1800))|((X1799 @ (esk41_3 @ X1799 @ X1800 @ X1803))|~(X1799 @ X1803))|((esk39_2 @ X1799 @ X1800)=(esk40_2 @ X1799 @ X1800)))&(~(X1800 @ X1806)|((esk42_2 @ X1799 @ X1800)=(X1806))|((X1799 @ (esk41_3 @ X1799 @ X1800 @ X1803))|~(X1799 @ X1803))|((esk39_2 @ X1799 @ X1800)=(esk40_2 @ X1799 @ X1800))))&(((X1800 @ (esk42_2 @ X1799 @ X1800))|(((X1803)!=(esk41_3 @ X1799 @ X1800 @ X1803))|~(X1799 @ X1803))|((esk39_2 @ X1799 @ X1800)=(esk40_2 @ X1799 @ X1800)))&(~(X1800 @ X1806)|((esk42_2 @ X1799 @ X1800)=(X1806))|(((X1803)!=(esk41_3 @ X1799 @ X1800 @ X1803))|~(X1799 @ X1803))|((esk39_2 @ X1799 @ X1800)=(esk40_2 @ X1799 @ X1800)))))&((((X1799 @ (esk44_2 @ X1799 @ X1800))|((X1800 @ (esk43_3 @ X1799 @ X1800 @ X1807))|~(X1800 @ X1807))|((esk39_2 @ X1799 @ X1800)=(esk40_2 @ X1799 @ X1800)))&(~(X1799 @ X1810)|((esk44_2 @ X1799 @ X1800)=(X1810))|((X1800 @ (esk43_3 @ X1799 @ X1800 @ X1807))|~(X1800 @ X1807))|((esk39_2 @ X1799 @ X1800)=(esk40_2 @ X1799 @ X1800))))&(((X1799 @ (esk44_2 @ X1799 @ X1800))|(((X1807)!=(esk43_3 @ X1799 @ X1800 @ X1807))|~(X1800 @ X1807))|((esk39_2 @ X1799 @ X1800)=(esk40_2 @ X1799 @ X1800)))&(~(X1799 @ X1810)|((esk44_2 @ X1799 @ X1800)=(X1810))|(((X1807)!=(esk43_3 @ X1799 @ X1800 @ X1807))|~(X1800 @ X1807))|((esk39_2 @ X1799 @ X1800)=(esk40_2 @ X1799 @ X1800))))))&((((((X1800 @ (esk42_2 @ X1799 @ X1800))|((X1799 @ (esk41_3 @ X1799 @ X1800 @ X1803))|~(X1799 @ X1803))|(~(X1799 @ (esk39_2 @ X1799 @ X1800))|~(X1800 @ (esk40_2 @ X1799 @ X1800))))&(~(X1800 @ X1806)|((esk42_2 @ X1799 @ X1800)=(X1806))|((X1799 @ (esk41_3 @ X1799 @ X1800 @ X1803))|~(X1799 @ X1803))|(~(X1799 @ (esk39_2 @ X1799 @ X1800))|~(X1800 @ (esk40_2 @ X1799 @ X1800)))))&(((X1800 @ (esk42_2 @ X1799 @ X1800))|(((X1803)!=(esk41_3 @ X1799 @ X1800 @ X1803))|~(X1799 @ X1803))|(~(X1799 @ (esk39_2 @ X1799 @ X1800))|~(X1800 @ (esk40_2 @ X1799 @ X1800))))&(~(X1800 @ X1806)|((esk42_2 @ X1799 @ X1800)=(X1806))|(((X1803)!=(esk41_3 @ X1799 @ X1800 @ X1803))|~(X1799 @ X1803))|(~(X1799 @ (esk39_2 @ X1799 @ X1800))|~(X1800 @ (esk40_2 @ X1799 @ X1800))))))&((((X1799 @ (esk44_2 @ X1799 @ X1800))|((X1800 @ (esk43_3 @ X1799 @ X1800 @ X1807))|~(X1800 @ X1807))|(~(X1799 @ (esk39_2 @ X1799 @ X1800))|~(X1800 @ (esk40_2 @ X1799 @ X1800))))&(~(X1799 @ X1810)|((esk44_2 @ X1799 @ X1800)=(X1810))|((X1800 @ (esk43_3 @ X1799 @ X1800 @ X1807))|~(X1800 @ X1807))|(~(X1799 @ (esk39_2 @ X1799 @ X1800))|~(X1800 @ (esk40_2 @ X1799 @ X1800)))))&(((X1799 @ (esk44_2 @ X1799 @ X1800))|(((X1807)!=(esk43_3 @ X1799 @ X1800 @ X1807))|~(X1800 @ X1807))|(~(X1799 @ (esk39_2 @ X1799 @ X1800))|~(X1800 @ (esk40_2 @ X1799 @ X1800))))&(~(X1799 @ X1810)|((esk44_2 @ X1799 @ X1800)=(X1810))|(((X1807)!=(esk43_3 @ X1799 @ X1800 @ X1807))|~(X1800 @ X1807))|(~(X1799 @ (esk39_2 @ X1799 @ X1800))|~(X1800 @ (esk40_2 @ X1799 @ X1800)))))))&(((((X1800 @ (esk42_2 @ X1799 @ X1800))|((X1799 @ (esk41_3 @ X1799 @ X1800 @ X1803))|~(X1799 @ X1803))|((X1799 @ (esk39_2 @ X1799 @ X1800))|(X1800 @ (esk40_2 @ X1799 @ X1800))))&(~(X1800 @ X1806)|((esk42_2 @ X1799 @ X1800)=(X1806))|((X1799 @ (esk41_3 @ X1799 @ X1800 @ X1803))|~(X1799 @ X1803))|((X1799 @ (esk39_2 @ X1799 @ X1800))|(X1800 @ (esk40_2 @ X1799 @ X1800)))))&(((X1800 @ (esk42_2 @ X1799 @ X1800))|(((X1803)!=(esk41_3 @ X1799 @ X1800 @ X1803))|~(X1799 @ X1803))|((X1799 @ (esk39_2 @ X1799 @ X1800))|(X1800 @ (esk40_2 @ X1799 @ X1800))))&(~(X1800 @ X1806)|((esk42_2 @ X1799 @ X1800)=(X1806))|(((X1803)!=(esk41_3 @ X1799 @ X1800 @ X1803))|~(X1799 @ X1803))|((X1799 @ (esk39_2 @ X1799 @ X1800))|(X1800 @ (esk40_2 @ X1799 @ X1800))))))&((((X1799 @ (esk44_2 @ X1799 @ X1800))|((X1800 @ (esk43_3 @ X1799 @ X1800 @ X1807))|~(X1800 @ X1807))|((X1799 @ (esk39_2 @ X1799 @ X1800))|(X1800 @ (esk40_2 @ X1799 @ X1800))))&(~(X1799 @ X1810)|((esk44_2 @ X1799 @ X1800)=(X1810))|((X1800 @ (esk43_3 @ X1799 @ X1800 @ X1807))|~(X1800 @ X1807))|((X1799 @ (esk39_2 @ X1799 @ X1800))|(X1800 @ (esk40_2 @ X1799 @ X1800)))))&(((X1799 @ (esk44_2 @ X1799 @ X1800))|(((X1807)!=(esk43_3 @ X1799 @ X1800 @ X1807))|~(X1800 @ X1807))|((X1799 @ (esk39_2 @ X1799 @ X1800))|(X1800 @ (esk40_2 @ X1799 @ X1800))))&(~(X1799 @ X1810)|((esk44_2 @ X1799 @ X1800)=(X1810))|(((X1807)!=(esk43_3 @ X1799 @ X1800 @ X1807))|~(X1800 @ X1807))|((X1799 @ (esk39_2 @ X1799 @ X1800))|(X1800 @ (esk40_2 @ X1799 @ X1800)))))))))&(((emptyset)=(emptyset))&((((X1811)!=(X1812))|(((X1813)!=(X1814))|((setadjoin @ X1811 @ X1813)=(setadjoin @ X1812 @ X1814))))&((((X1815)!=(X1816))|((powerset @ X1815)=(powerset @ X1816)))&((((X1817)!=(X1818))|((setunion @ X1817)=(setunion @ X1818)))&(((omega)=(omega))&((((X1819 @ (esk45_2 @ X1819 @ X1820))|~(X1819 @ X1820)|(~(X1819 @ X1822)|(~(X1819 @ X1823)|((X1822)=(X1823)))))&(((X1820)!=(esk45_2 @ X1819 @ X1820))|~(X1819 @ X1820)|(~(X1819 @ X1822)|(~(X1819 @ X1823)|((X1822)=(X1823))))))&((((((X1825 @ (esk49_3 @ X1824 @ X1825 @ X1830))|~(X1825 @ X1830)|((descr @ X1824)=(descr @ X1825))|((X1824 @ (esk48_3 @ X1824 @ X1825 @ X1828))|~(X1824 @ X1828))|((esk46_2 @ X1824 @ X1825)=(esk47_2 @ X1824 @ X1825)))&(((X1830)!=(esk49_3 @ X1824 @ X1825 @ X1830))|~(X1825 @ X1830)|((descr @ X1824)=(descr @ X1825))|((X1824 @ (esk48_3 @ X1824 @ X1825 @ X1828))|~(X1824 @ X1828))|((esk46_2 @ X1824 @ X1825)=(esk47_2 @ X1824 @ X1825))))&(((X1825 @ (esk49_3 @ X1824 @ X1825 @ X1830))|~(X1825 @ X1830)|((descr @ X1824)=(descr @ X1825))|(((X1828)!=(esk48_3 @ X1824 @ X1825 @ X1828))|~(X1824 @ X1828))|((esk46_2 @ X1824 @ X1825)=(esk47_2 @ X1824 @ X1825)))&(((X1830)!=(esk49_3 @ X1824 @ X1825 @ X1830))|~(X1825 @ X1830)|((descr @ X1824)=(descr @ X1825))|(((X1828)!=(esk48_3 @ X1824 @ X1825 @ X1828))|~(X1824 @ X1828))|((esk46_2 @ X1824 @ X1825)=(esk47_2 @ X1824 @ X1825)))))&(((((X1825 @ (esk49_3 @ X1824 @ X1825 @ X1830))|~(X1825 @ X1830)|((descr @ X1824)=(descr @ X1825))|((X1824 @ (esk48_3 @ X1824 @ X1825 @ X1828))|~(X1824 @ X1828))|(~(X1824 @ (esk46_2 @ X1824 @ X1825))|~(X1825 @ (esk47_2 @ X1824 @ X1825))))&(((X1830)!=(esk49_3 @ X1824 @ X1825 @ X1830))|~(X1825 @ X1830)|((descr @ X1824)=(descr @ X1825))|((X1824 @ (esk48_3 @ X1824 @ X1825 @ X1828))|~(X1824 @ X1828))|(~(X1824 @ (esk46_2 @ X1824 @ X1825))|~(X1825 @ (esk47_2 @ X1824 @ X1825)))))&(((X1825 @ (esk49_3 @ X1824 @ X1825 @ X1830))|~(X1825 @ X1830)|((descr @ X1824)=(descr @ X1825))|(((X1828)!=(esk48_3 @ X1824 @ X1825 @ X1828))|~(X1824 @ X1828))|(~(X1824 @ (esk46_2 @ X1824 @ X1825))|~(X1825 @ (esk47_2 @ X1824 @ X1825))))&(((X1830)!=(esk49_3 @ X1824 @ X1825 @ X1830))|~(X1825 @ X1830)|((descr @ X1824)=(descr @ X1825))|(((X1828)!=(esk48_3 @ X1824 @ X1825 @ X1828))|~(X1824 @ X1828))|(~(X1824 @ (esk46_2 @ X1824 @ X1825))|~(X1825 @ (esk47_2 @ X1824 @ X1825))))))&((((X1825 @ (esk49_3 @ X1824 @ X1825 @ X1830))|~(X1825 @ X1830)|((descr @ X1824)=(descr @ X1825))|((X1824 @ (esk48_3 @ X1824 @ X1825 @ X1828))|~(X1824 @ X1828))|((X1824 @ (esk46_2 @ X1824 @ X1825))|(X1825 @ (esk47_2 @ X1824 @ X1825))))&(((X1830)!=(esk49_3 @ X1824 @ X1825 @ X1830))|~(X1825 @ X1830)|((descr @ X1824)=(descr @ X1825))|((X1824 @ (esk48_3 @ X1824 @ X1825 @ X1828))|~(X1824 @ X1828))|((X1824 @ (esk46_2 @ X1824 @ X1825))|(X1825 @ (esk47_2 @ X1824 @ X1825)))))&(((X1825 @ (esk49_3 @ X1824 @ X1825 @ X1830))|~(X1825 @ X1830)|((descr @ X1824)=(descr @ X1825))|(((X1828)!=(esk48_3 @ X1824 @ X1825 @ X1828))|~(X1824 @ X1828))|((X1824 @ (esk46_2 @ X1824 @ X1825))|(X1825 @ (esk47_2 @ X1824 @ X1825))))&(((X1830)!=(esk49_3 @ X1824 @ X1825 @ X1830))|~(X1825 @ X1830)|((descr @ X1824)=(descr @ X1825))|(((X1828)!=(esk48_3 @ X1824 @ X1825 @ X1828))|~(X1824 @ X1828))|((X1824 @ (esk46_2 @ X1824 @ X1825))|(X1825 @ (esk47_2 @ X1824 @ X1825))))))))&((((in @ (esk50_4 @ X1832 @ X1833 @ X1834 @ X1835) @ X1832)|((dsetconstr @ X1832 @ X1834)=(dsetconstr @ X1833 @ X1835))|((X1832)!=(X1833)))&(((in @ (esk51_4 @ X1832 @ X1833 @ X1834 @ X1835) @ X1833)|((dsetconstr @ X1832 @ X1834)=(dsetconstr @ X1833 @ X1835))|((X1832)!=(X1833)))&((((esk50_4 @ X1832 @ X1833 @ X1834 @ X1835)=(esk51_4 @ X1832 @ X1833 @ X1834 @ X1835))|((dsetconstr @ X1832 @ X1834)=(dsetconstr @ X1833 @ X1835))|((X1832)!=(X1833)))&((~(X1834 @ (esk50_4 @ X1832 @ X1833 @ X1834 @ X1835))|~(X1835 @ (esk51_4 @ X1832 @ X1833 @ X1834 @ X1835))|((dsetconstr @ X1832 @ X1834)=(dsetconstr @ X1833 @ X1835))|((X1832)!=(X1833)))&((X1834 @ (esk50_4 @ X1832 @ X1833 @ X1834 @ X1835))|(X1835 @ (esk51_4 @ X1832 @ X1833 @ X1834 @ X1835))|((dsetconstr @ X1832 @ X1834)=(dsetconstr @ X1833 @ X1835))|((X1832)!=(X1833)))))))&((((in @ (esk52_2 @ X1838 @ X1839) @ X1838)|(subset @ X1838 @ X1839))&(~(in @ (esk52_2 @ X1838 @ X1839) @ X1839)|(subset @ X1838 @ X1839)))&((((X1841)!=(X1842))|(subset @ X1842 @ X1841))&((((X1843)!=(X1844))|(subset @ X1843 @ X1844))&((((in @ (esk53_2 @ X1845 @ X1846) @ X1845)|(subset @ X1845 @ X1846))&(~(in @ (esk53_2 @ X1845 @ X1846) @ X1846)|(subset @ X1845 @ X1846)))&((subset @ emptyset @ X1848)&((~(subset @ X1849 @ X1850)|(~(in @ X1851 @ X1849)|(in @ X1851 @ X1850)))&((~(subset @ X1852 @ X1853)|((in @ X1854 @ X1853)|~(in @ X1854 @ X1852)))&((~(in @ X1857 @ X1855)|((in @ X1857 @ X1856)|~(subset @ X1855 @ X1856)))&(((subset @ X1858 @ X1859)|((X1858)!=(X1859)))&((~(in @ X1862 @ X1860)|((in @ X1862 @ X1861)|((X1860)!=(X1861))))&((subset @ X1863 @ X1863)&((~(subset @ X1864 @ X1865)|(~(subset @ X1865 @ X1866)|(subset @ X1864 @ X1866)))&((subset @ X1868 @ (setadjoin @ X1867 @ X1868))&((~(subset @ X1869 @ X1871)|(subset @ X1869 @ (setadjoin @ X1870 @ X1871)))&((~(subset @ X1872 @ X1873)|(in @ X1872 @ (powerset @ X1873)))&((~(subset @ X1874 @ X1875)|(~(subset @ X1875 @ X1874)|((X1874)=(X1875))))&((~(subset @ X1876 @ emptyset)|((X1876)=(emptyset)))&((~(subset @ X1878 @ X1877)|(in @ X1878 @ (powerset @ X1877)))&((~(in @ X1880 @ (powerset @ X1879))|(subset @ X1880 @ X1879))&((in @ X1881 @ (powerset @ X1881))&((~(subset @ X1882 @ X1883)|(subset @ (powerset @ X1882) @ (powerset @ X1883)))&((in @ (dsetconstr @ X1884 @ X1885) @ (powerset @ X1884))&((subset @ (dsetconstr @ X1886 @ X1887) @ X1886)&((~(in @ X1890 @ X1888)|(in @ X1890 @ (binunion @ X1888 @ X1889)))&((in @ X1892 @ (setadjoin @ X1891 @ (setadjoin @ X1892 @ emptyset)))&((~(in @ X1895 @ X1894)|(in @ X1895 @ (binunion @ X1893 @ X1894)))&(((((in @ X1898 @ X1897)|(X1899)|(in @ X1898 @ X1896)|~(in @ X1898 @ (binunion @ X1896 @ X1897)))&(~(X1899)|(X1899)|(in @ X1898 @ X1896)|~(in @ X1898 @ (binunion @ X1896 @ X1897))))&(((in @ X1898 @ X1897)|(X1899)|~(X1899)|~(in @ X1898 @ (binunion @ X1896 @ X1897)))&(~(X1899)|(X1899)|~(X1899)|~(in @ X1898 @ (binunion @ X1896 @ X1897)))))&((~(in @ X1902 @ (binunion @ X1900 @ X1901))|((in @ X1902 @ X1900)|(in @ X1902 @ X1901)))&((subset @ X1903 @ (binunion @ X1903 @ X1904))&((subset @ X1906 @ (binunion @ X1905 @ X1906))&((~(in @ X1909 @ X1907)|(~(in @ X1909 @ X1908)|(in @ X1909 @ (binintersect @ X1907 @ X1908))))&((~(subset @ X1912 @ X1910)|(~(subset @ X1912 @ X1911)|(subset @ X1912 @ (binintersect @ X1910 @ X1911))))&((~(in @ X1915 @ (binintersect @ X1913 @ X1914))|(in @ X1915 @ X1913))&((subset @ (binintersect @ X1916 @ X1917) @ X1916)&((~(subset @ X1918 @ X1919)|((binintersect @ X1918 @ X1919)=(X1918)))&((((binintersect @ X1920 @ X1921)!=(X1921))|(subset @ X1921 @ X1920))&((~(in @ X1924 @ (binintersect @ X1922 @ X1923))|(in @ X1924 @ X1923))&((((in @ (esk54_2 @ X1925 @ X1926) @ X1925)|((binintersect @ X1925 @ X1926)=(emptyset)))&((in @ (esk54_2 @ X1925 @ X1926) @ X1926)|((binintersect @ X1925 @ X1926)=(emptyset))))&((subset @ (binintersect @ X1928 @ X1929) @ X1929)&((~(subset @ X1931 @ X1930)|((binintersect @ X1930 @ X1931)=(X1931)))&((((binintersect @ X1932 @ X1933)!=(X1932))|(subset @ X1932 @ X1933))&(((binintersect @ X1934 @ (binunion @ X1935 @ X1936))=(binunion @ (binintersect @ X1934 @ X1935) @ (binintersect @ X1934 @ X1936)))&((~(in @ X1939 @ X1937)|((in @ X1939 @ X1938)|(in @ X1939 @ (setminus @ X1937 @ X1938))))&((~(in @ X1942 @ (setminus @ X1940 @ X1941))|(in @ X1942 @ X1940))&((~(in @ X1945 @ (setminus @ X1943 @ X1944))|~(in @ X1945 @ X1944))&((~(subset @ X1946 @ X1947)|((setminus @ X1946 @ X1947)=(emptyset)))&(((in @ X1950 @ (setminus @ X1948 @ X1949))|(~(in @ X1950 @ X1948)|(in @ X1950 @ X1949)))&(((in @ X1953 @ (setminus @ X1951 @ X1952))|((in @ X1953 @ X1952)|~(in @ X1953 @ X1951)))&(((in @ X1956 @ X1954)|~(in @ X1956 @ (setminus @ X1954 @ X1955)))&((~(in @ X1959 @ X1958)|~(in @ X1959 @ (setminus @ X1957 @ X1958)))&((subset @ (setminus @ X1960 @ X1961) @ X1960)&((((setminus @ X1962 @ X1963)!=(emptyset))|(subset @ X1962 @ X1963))&((((~(in @ X1966 @ X1964)|(X1967)|(in @ X1966 @ X1964)|~(in @ X1966 @ (symdiff @ X1964 @ X1965)))&(((in @ X1966 @ X1965)|(X1967)|(in @ X1966 @ X1964)|~(in @ X1966 @ (symdiff @ X1964 @ X1965)))&(~(X1967)|(X1967)|(in @ X1966 @ X1964)|~(in @ X1966 @ (symdiff @ X1964 @ X1965)))))&(((~(in @ X1966 @ X1964)|(X1967)|~(in @ X1966 @ X1965)|~(in @ X1966 @ (symdiff @ X1964 @ X1965)))&(((in @ X1966 @ X1965)|(X1967)|~(in @ X1966 @ X1965)|~(in @ X1966 @ (symdiff @ X1964 @ X1965)))&(~(X1967)|(X1967)|~(in @ X1966 @ X1965)|~(in @ X1966 @ (symdiff @ X1964 @ X1965)))))&((~(in @ X1966 @ X1964)|(X1967)|~(X1967)|~(in @ X1966 @ (symdiff @ X1964 @ X1965)))&(((in @ X1966 @ X1965)|(X1967)|~(X1967)|~(in @ X1966 @ (symdiff @ X1964 @ X1965)))&(~(X1967)|(X1967)|~(X1967)|~(in @ X1966 @ (symdiff @ X1964 @ X1965)))))))&((~(in @ X1970 @ X1968)|((in @ X1970 @ X1969)|(in @ X1970 @ (symdiff @ X1968 @ X1969))))&(((in @ X1973 @ X1971)|(~(in @ X1973 @ X1972)|(in @ X1973 @ (symdiff @ X1971 @ X1972))))&((~(in @ X1976 @ X1974)|(~(in @ X1976 @ X1975)|~(in @ X1976 @ (symdiff @ X1974 @ X1975))))&(((in @ X1979 @ X1977)|((in @ X1979 @ X1978)|~(in @ X1979 @ (symdiff @ X1977 @ X1978))))&((in @ X1981 @ (setadjoin @ X1980 @ (setadjoin @ X1981 @ emptyset)))&((in @ X1982 @ (setunion @ (setadjoin @ (setadjoin @ X1982 @ emptyset) @ (setadjoin @ (setadjoin @ X1982 @ (setadjoin @ X1983 @ emptyset)) @ emptyset))))&((in @ X1985 @ (setunion @ (setadjoin @ (setadjoin @ X1984 @ emptyset) @ (setadjoin @ (setadjoin @ X1984 @ (setadjoin @ X1985 @ emptyset)) @ emptyset))))&((iskpair @ (setadjoin @ (setadjoin @ X1986 @ emptyset) @ (setadjoin @ (setadjoin @ X1986 @ (setadjoin @ X1987 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X1988 @ X1989))&((~(in @ X1991 @ X1990)|(subset @ (setadjoin @ X1991 @ emptyset) @ X1990))&((~(in @ X1993 @ X1992)|(in @ (setadjoin @ X1993 @ emptyset) @ (powerset @ X1992)))&((~(in @ X1996 @ X1994)|(in @ (setadjoin @ X1996 @ emptyset) @ (powerset @ (binunion @ X1994 @ X1995))))&((~(in @ X1999 @ (setadjoin @ X1997 @ (setadjoin @ X1998 @ emptyset)))|(((X1999)=(X1997))|((X1999)=(X1998))))&((~(in @ X2002 @ X2000)|(~(in @ X2003 @ X2001)|(subset @ (setadjoin @ X2002 @ (setadjoin @ X2003 @ emptyset)) @ (binunion @ X2000 @ X2001))))&((~(in @ X2006 @ X2004)|(~(in @ X2007 @ X2005)|(in @ (setadjoin @ X2006 @ (setadjoin @ X2007 @ emptyset)) @ (powerset @ (binunion @ X2004 @ X2005)))))&((~(in @ X2010 @ X2008)|(~(in @ X2011 @ X2009)|(subset @ (setadjoin @ (setadjoin @ X2010 @ emptyset) @ (setadjoin @ (setadjoin @ X2010 @ (setadjoin @ X2011 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X2008 @ X2009)))))&((~(in @ X2014 @ X2012)|(~(in @ X2015 @ X2013)|(in @ (setadjoin @ (setadjoin @ X2014 @ emptyset) @ (setadjoin @ (setadjoin @ X2014 @ (setadjoin @ X2015 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X2012 @ X2013))))))&((~(in @ X2018 @ X2016)|(~(in @ X2019 @ X2017)|(in @ (kpair @ X2018 @ X2019) @ (powerset @ (powerset @ (binunion @ X2016 @ X2017))))))&((~(in @ X2022 @ X2020)|(~(in @ X2023 @ X2021)|(in @ (kpair @ X2022 @ X2023) @ (cartprod @ X2020 @ X2021))))&((((in @ (esk55_3 @ X2024 @ X2025 @ X2026) @ X2024)|~(in @ X2026 @ (cartprod @ X2024 @ X2025)))&(((in @ (esk56_3 @ X2024 @ X2025 @ X2026) @ X2025)|~(in @ X2026 @ (cartprod @ X2024 @ X2025)))&(((X2026)=(kpair @ (esk55_3 @ X2024 @ X2025 @ X2026) @ (esk56_3 @ X2024 @ X2025 @ X2026)))|~(in @ X2026 @ (cartprod @ X2024 @ X2025)))))&((~(in @ X2031 @ (cartprod @ X2029 @ X2030))|(iskpair @ X2031))&((((in @ (esk57_2 @ X2032 @ X2033) @ X2032)|~(in @ X2033 @ (setunion @ X2032)))&((in @ X2033 @ (esk57_2 @ X2032 @ X2033))|~(in @ X2033 @ (setunion @ X2032))))&((subset @ (setunion @ (setadjoin @ X2035 @ emptyset)) @ X2035)&((subset @ X2036 @ (setunion @ (setadjoin @ X2036 @ emptyset)))&(((setunion @ (setadjoin @ X2037 @ emptyset))=(X2037))&((((in @ (esk58_2 @ X2038 @ X2039) @ X2038)|(~(in @ X2042 @ X2038)|~(X2039 @ X2042)|(singleton @ (dsetconstr @ X2038 @ X2039))))&(((in @ (esk59_2 @ X2038 @ X2039) @ X2038)|(~(in @ X2042 @ X2038)|~(X2039 @ X2042)|(singleton @ (dsetconstr @ X2038 @ X2039))))&(((X2039 @ (esk58_2 @ X2038 @ X2039))|(~(in @ X2042 @ X2038)|~(X2039 @ X2042)|(singleton @ (dsetconstr @ X2038 @ X2039))))&(((X2039 @ (esk59_2 @ X2038 @ X2039))|(~(in @ X2042 @ X2038)|~(X2039 @ X2042)|(singleton @ (dsetconstr @ X2038 @ X2039))))&(((esk58_2 @ X2038 @ X2039)!=(esk59_2 @ X2038 @ X2039))|(~(in @ X2042 @ X2038)|~(X2039 @ X2042)|(singleton @ (dsetconstr @ X2038 @ X2039))))))))&((((in @ (esk60_2 @ X2043 @ X2044) @ X2043)|~(singleton @ (dsetconstr @ X2043 @ X2044)))&((X2044 @ (esk60_2 @ X2043 @ X2044))|~(singleton @ (dsetconstr @ X2043 @ X2044))))&((((in @ (esk61_3 @ X2046 @ X2047 @ X2048) @ X2046)|(singleton @ (dsetconstr @ X2046 @ X2047))|~(X2047 @ X2048)|~(in @ X2048 @ X2046))&(((X2047 @ (esk61_3 @ X2046 @ X2047 @ X2048))|(singleton @ (dsetconstr @ X2046 @ X2047))|~(X2047 @ X2048)|~(in @ X2048 @ X2046))&(((esk61_3 @ X2046 @ X2047 @ X2048)!=(X2048))|(singleton @ (dsetconstr @ X2046 @ X2047))|~(X2047 @ X2048)|~(in @ X2048 @ X2046))))&((((in @ (esk62_2 @ X2050 @ X2051) @ X2050)|(~(in @ X2054 @ X2050)|~(X2051 @ X2054)|(singleton @ (dsetconstr @ X2050 @ X2051))))&(((in @ (esk63_2 @ X2050 @ X2051) @ X2050)|(~(in @ X2054 @ X2050)|~(X2051 @ X2054)|(singleton @ (dsetconstr @ X2050 @ X2051))))&(((X2051 @ (esk62_2 @ X2050 @ X2051))|(~(in @ X2054 @ X2050)|~(X2051 @ X2054)|(singleton @ (dsetconstr @ X2050 @ X2051))))&(((X2051 @ (esk63_2 @ X2050 @ X2051))|(~(in @ X2054 @ X2050)|~(X2051 @ X2054)|(singleton @ (dsetconstr @ X2050 @ X2051))))&(((esk62_2 @ X2050 @ X2051)!=(esk63_2 @ X2050 @ X2051))|(~(in @ X2054 @ X2050)|~(X2051 @ X2054)|(singleton @ (dsetconstr @ X2050 @ X2051))))))))&((((setadjoin @ X2055 @ emptyset)!=(setadjoin @ X2056 @ emptyset))|((X2055)=(X2056)))&((~(in @ (setadjoin @ X2059 @ emptyset) @ (setadjoin @ (setadjoin @ X2057 @ emptyset) @ (setadjoin @ (setadjoin @ X2057 @ (setadjoin @ X2058 @ emptyset)) @ emptyset)))|((X2057)=(X2059)))&((~(iskpair @ X2060)|(singleton @ (dsetconstr @ (setunion @ X2060) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X2060))))))&((~(singleton @ X2061)|(in @ (setunion @ X2061) @ X2061))&(((kfst @ (kpair @ X2062 @ X2063))=(X2062))&((~(in @ X2066 @ (cartprod @ X2064 @ X2065))|(in @ (kfst @ X2066) @ X2064))&((((setadjoin @ (setadjoin @ X2067 @ emptyset) @ (setadjoin @ (setadjoin @ X2067 @ (setadjoin @ X2068 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X2069 @ emptyset) @ (setadjoin @ (setadjoin @ X2069 @ (setadjoin @ X2070 @ emptyset)) @ emptyset)))|((X2067)=(X2069)))&((((kpair @ X2071 @ X2072)!=(kpair @ X2073 @ X2074))|((X2071)=(X2073)))&((((X2075)!=(X2076))|((setadjoin @ X2075 @ (setadjoin @ X2076 @ emptyset))=(setadjoin @ X2075 @ emptyset)))&((((X2077)!=(X2078))|((setadjoin @ (setadjoin @ X2077 @ emptyset) @ (setadjoin @ (setadjoin @ X2077 @ (setadjoin @ X2078 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2077 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X2079 @ emptyset) @ (setadjoin @ (setadjoin @ X2079 @ (setadjoin @ X2080 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X2081 @ emptyset) @ (setadjoin @ (setadjoin @ X2081 @ (setadjoin @ X2082 @ emptyset)) @ emptyset)))|(((X2081)!=(X2082))|((X2080)=(X2082))))&((((setadjoin @ X2083 @ (setadjoin @ X2084 @ emptyset))!=(setadjoin @ X2085 @ emptyset))|((X2083)=(X2084)))&((((setadjoin @ (setadjoin @ X2086 @ emptyset) @ (setadjoin @ (setadjoin @ X2086 @ (setadjoin @ X2087 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X2088 @ emptyset) @ (setadjoin @ (setadjoin @ X2088 @ (setadjoin @ X2089 @ emptyset)) @ emptyset)))|((X2087)=(X2089)))&((((kpair @ X2090 @ X2091)!=(kpair @ X2092 @ X2093))|((X2091)=(X2093)))&((~(iskpair @ X2094)|(singleton @ (dsetconstr @ (setunion @ X2094) @ (^[Z0/* 3 */:$i]:(((X2094)=(kpair @ (kfst @ X2094) @ Z0)))))))&(((ksnd @ (kpair @ X2095 @ X2096))=(X2096))&((~(iskpair @ X2097)|((kpair @ (kfst @ X2097) @ (ksnd @ X2097))=(X2097)))&((~(in @ X2100 @ (cartprod @ X2098 @ X2099))|(in @ (ksnd @ X2100) @ X2099))&((~(in @ (kpair @ X2103 @ X2104) @ (cartprod @ X2101 @ X2102))|(in @ X2103 @ X2101))&((~(in @ (kpair @ X2107 @ X2108) @ (cartprod @ X2105 @ X2106))|(in @ X2108 @ X2106))&((~(in @ X2111 @ X2109)|(~(in @ X2112 @ X2110)|((kpair @ X2111 @ X2112)=(kpair @ X2111 @ X2112))))&((~(in @ X2115 @ X2113)|(~(in @ X2116 @ X2114)|((kfst @ (kpair @ X2115 @ X2116))=(X2115))))&((~(in @ X2119 @ X2117)|(~(in @ X2120 @ X2118)|((ksnd @ (kpair @ X2119 @ X2120))=(X2120))))&((~(in @ X2123 @ (cartprod @ X2121 @ X2122))|((kpair @ (kfst @ X2123) @ (ksnd @ X2123))=(X2123)))&((~(in @ X2127 @ X2124)|(~(in @ X2128 @ X2125)|(~(X2126 @ X2127 @ X2128)|(in @ (kpair @ X2127 @ X2128) @ (dpsetconstr @ X2124 @ X2125 @ X2126)))))&((subset @ (dpsetconstr @ X2129 @ X2130 @ X2131) @ (cartprod @ X2129 @ X2130))&((subset @ (dpsetconstr @ X2132 @ X2133 @ X2134) @ (cartprod @ X2132 @ X2133))&((~(in @ X2138 @ X2135)|(~(in @ X2139 @ X2136)|(~(in @ (kpair @ X2138 @ X2139) @ (dpsetconstr @ X2135 @ X2136 @ X2137))|(X2137 @ X2138 @ X2139))))&((~(in @ (kpair @ X2143 @ X2144) @ (dpsetconstr @ X2140 @ X2141 @ X2142))|(in @ X2143 @ X2140))&((~(in @ (kpair @ X2148 @ X2149) @ (dpsetconstr @ X2145 @ X2146 @ X2147))|(in @ X2149 @ X2146))&((~(in @ (kpair @ X2153 @ X2154) @ (dpsetconstr @ X2150 @ X2151 @ X2152))|(X2152 @ X2153 @ X2154))&((~(func @ X2155 @ X2156 @ X2157)|(~(in @ X2158 @ X2155)|(singleton @ (dsetconstr @ X2156 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2158 @ Z0) @ X2157)))))))&((~(func @ X2159 @ X2160 @ X2161)|(~(in @ X2162 @ X2159)|(in @ (setunion @ (dsetconstr @ X2160 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2162 @ Z0) @ X2161))))) @ X2160)))&((~(func @ X2163 @ X2164 @ X2165)|(~(in @ X2166 @ X2163)|(in @ (ap @ X2163 @ X2164 @ X2165 @ X2166) @ X2164)))&((~(in @ X2169 @ (funcSet @ X2167 @ X2168))|(func @ X2167 @ X2168 @ X2169))&((~(in @ X2172 @ (funcSet @ X2170 @ X2171))|(~(in @ X2173 @ X2170)|(in @ (ap @ X2170 @ X2171 @ X2172 @ X2173) @ X2171)))&((~(func @ X2174 @ X2175 @ X2176)|(in @ X2176 @ (funcSet @ X2174 @ X2175)))&((((in @ (esk64_3 @ X2177 @ X2178 @ X2179) @ X2177)|(func @ X2177 @ X2178 @ (dpsetconstr @ X2177 @ X2178 @ (^[Z0/* 3 */:$i]:($eq @ (X2179 @ Z0))))))&(~(in @ (X2179 @ (esk64_3 @ X2177 @ X2178 @ X2179)) @ X2178)|(func @ X2177 @ X2178 @ (dpsetconstr @ X2177 @ X2178 @ (^[Z0/* 3 */:$i]:($eq @ (X2179 @ Z0)))))))&((((in @ (esk65_3 @ X2181 @ X2182 @ X2183) @ X2181)|(func @ X2181 @ X2182 @ (lam @ X2181 @ X2182 @ X2183)))&(~(in @ (X2183 @ (esk65_3 @ X2181 @ X2182 @ X2183)) @ X2182)|(func @ X2181 @ X2182 @ (lam @ X2181 @ X2182 @ X2183))))&((((in @ (esk66_3 @ X2185 @ X2186 @ X2187) @ X2185)|(in @ (lam @ X2185 @ X2186 @ X2187) @ (funcSet @ X2185 @ X2186)))&(~(in @ (X2187 @ (esk66_3 @ X2185 @ X2186 @ X2187)) @ X2186)|(in @ (lam @ X2185 @ X2186 @ X2187) @ (funcSet @ X2185 @ X2186))))&((((in @ (esk67_4 @ X2189 @ X2190 @ X2191 @ X2192) @ X2189)|(~(in @ X2195 @ X2191)|(X2192 @ X2195))|~(subset @ X2191 @ (cartprod @ X2189 @ X2190)))&(((in @ (esk68_4 @ X2189 @ X2190 @ X2191 @ X2192) @ X2190)|(~(in @ X2195 @ X2191)|(X2192 @ X2195))|~(subset @ X2191 @ (cartprod @ X2189 @ X2190)))&(((in @ (kpair @ (esk67_4 @ X2189 @ X2190 @ X2191 @ X2192) @ (esk68_4 @ X2189 @ X2190 @ X2191 @ X2192)) @ X2191)|(~(in @ X2195 @ X2191)|(X2192 @ X2195))|~(subset @ X2191 @ (cartprod @ X2189 @ X2190)))&(~(X2192 @ (kpair @ (esk67_4 @ X2189 @ X2190 @ X2191 @ X2192) @ (esk68_4 @ X2189 @ X2190 @ X2191 @ X2192)))|(~(in @ X2195 @ X2191)|(X2192 @ X2195))|~(subset @ X2191 @ (cartprod @ X2189 @ X2190))))))&((((in @ (esk69_4 @ X2196 @ X2197 @ X2198 @ X2199) @ X2196)|(~(in @ X2202 @ X2198)|(X2199 @ X2202))|~(subset @ X2198 @ (cartprod @ X2196 @ X2197)))&(((in @ (esk70_4 @ X2196 @ X2197 @ X2198 @ X2199) @ X2197)|(~(in @ X2202 @ X2198)|(X2199 @ X2202))|~(subset @ X2198 @ (cartprod @ X2196 @ X2197)))&(((in @ (kpair @ (esk69_4 @ X2196 @ X2197 @ X2198 @ X2199) @ (esk70_4 @ X2196 @ X2197 @ X2198 @ X2199)) @ X2198)|(~(in @ X2202 @ X2198)|(X2199 @ X2202))|~(subset @ X2198 @ (cartprod @ X2196 @ X2197)))&(~(X2199 @ (kpair @ (esk69_4 @ X2196 @ X2197 @ X2198 @ X2199) @ (esk70_4 @ X2196 @ X2197 @ X2198 @ X2199)))|(~(in @ X2202 @ X2198)|(X2199 @ X2202))|~(subset @ X2198 @ (cartprod @ X2196 @ X2197))))))&((~(singleton @ (dsetconstr @ X2203 @ X2204))|(~(in @ X2205 @ X2203)|(~(in @ X2206 @ X2203)|(~(X2204 @ X2205)|(~(X2204 @ X2206)|((X2205)=(X2206)))))))&((~(func @ X2207 @ X2208 @ X2209)|(~(in @ X2210 @ X2207)|(in @ (kpair @ X2210 @ (ap @ X2207 @ X2208 @ X2209 @ X2210)) @ X2209)))&((~(in @ X2213 @ (funcSet @ X2211 @ X2212))|(~(in @ X2214 @ X2211)|(in @ (kpair @ X2214 @ (ap @ X2211 @ X2212 @ X2213 @ X2214)) @ X2213)))&((~(func @ X2215 @ X2216 @ X2217)|(~(in @ X2218 @ X2215)|(~(in @ X2219 @ X2216)|(~(in @ (kpair @ X2218 @ X2219) @ X2217)|((ap @ X2215 @ X2216 @ X2217 @ X2218)=(X2219))))))&((((in @ (esk71_4 @ X2220 @ X2221 @ X2222 @ X2223) @ X2220)|(~(in @ X2225 @ X2220)|(~(in @ X2226 @ X2221)|(~(in @ (kpair @ X2225 @ X2226) @ X2223)|(in @ (kpair @ X2225 @ X2226) @ X2222))))|~(func @ X2220 @ X2221 @ X2223)|~(func @ X2220 @ X2221 @ X2222))&(((ap @ X2220 @ X2221 @ X2222 @ (esk71_4 @ X2220 @ X2221 @ X2222 @ X2223))!=(ap @ X2220 @ X2221 @ X2223 @ (esk71_4 @ X2220 @ X2221 @ X2222 @ X2223)))|(~(in @ X2225 @ X2220)|(~(in @ X2226 @ X2221)|(~(in @ (kpair @ X2225 @ X2226) @ X2223)|(in @ (kpair @ X2225 @ X2226) @ X2222))))|~(func @ X2220 @ X2221 @ X2223)|~(func @ X2220 @ X2221 @ X2222)))&((~(in @ X2229 @ (funcSet @ X2227 @ X2228))|(~(in @ X2230 @ X2227)|(~(in @ X2231 @ X2228)|(~(in @ (kpair @ X2230 @ X2231) @ X2229)|((ap @ X2227 @ X2228 @ X2229 @ X2230)=(X2231))))))&((((in @ (esk72_4 @ X2232 @ X2233 @ X2234 @ X2235) @ X2232)|(subset @ X2234 @ X2235)|~(subset @ X2235 @ (cartprod @ X2232 @ X2233))|~(subset @ X2234 @ (cartprod @ X2232 @ X2233)))&(((in @ (esk73_4 @ X2232 @ X2233 @ X2234 @ X2235) @ X2233)|(subset @ X2234 @ X2235)|~(subset @ X2235 @ (cartprod @ X2232 @ X2233))|~(subset @ X2234 @ (cartprod @ X2232 @ X2233)))&(((in @ (kpair @ (esk72_4 @ X2232 @ X2233 @ X2234 @ X2235) @ (esk73_4 @ X2232 @ X2233 @ X2234 @ X2235)) @ X2234)|(subset @ X2234 @ X2235)|~(subset @ X2235 @ (cartprod @ X2232 @ X2233))|~(subset @ X2234 @ (cartprod @ X2232 @ X2233)))&(~(in @ (kpair @ (esk72_4 @ X2232 @ X2233 @ X2234 @ X2235) @ (esk73_4 @ X2232 @ X2233 @ X2234 @ X2235)) @ X2235)|(subset @ X2234 @ X2235)|~(subset @ X2235 @ (cartprod @ X2232 @ X2233))|~(subset @ X2234 @ (cartprod @ X2232 @ X2233))))))&(((((in @ (esk76_4 @ X2238 @ X2239 @ X2240 @ X2241) @ X2238)|((X2240)=(X2241))|(in @ (esk74_4 @ X2238 @ X2239 @ X2240 @ X2241) @ X2238)|~(subset @ X2241 @ (cartprod @ X2238 @ X2239))|~(subset @ X2240 @ (cartprod @ X2238 @ X2239)))&(((in @ (esk77_4 @ X2238 @ X2239 @ X2240 @ X2241) @ X2239)|((X2240)=(X2241))|(in @ (esk74_4 @ X2238 @ X2239 @ X2240 @ X2241) @ X2238)|~(subset @ X2241 @ (cartprod @ X2238 @ X2239))|~(subset @ X2240 @ (cartprod @ X2238 @ X2239)))&(((in @ (kpair @ (esk76_4 @ X2238 @ X2239 @ X2240 @ X2241) @ (esk77_4 @ X2238 @ X2239 @ X2240 @ X2241)) @ X2241)|((X2240)=(X2241))|(in @ (esk74_4 @ X2238 @ X2239 @ X2240 @ X2241) @ X2238)|~(subset @ X2241 @ (cartprod @ X2238 @ X2239))|~(subset @ X2240 @ (cartprod @ X2238 @ X2239)))&(~(in @ (kpair @ (esk76_4 @ X2238 @ X2239 @ X2240 @ X2241) @ (esk77_4 @ X2238 @ X2239 @ X2240 @ X2241)) @ X2240)|((X2240)=(X2241))|(in @ (esk74_4 @ X2238 @ X2239 @ X2240 @ X2241) @ X2238)|~(subset @ X2241 @ (cartprod @ X2238 @ X2239))|~(subset @ X2240 @ (cartprod @ X2238 @ X2239))))))&((((in @ (esk76_4 @ X2238 @ X2239 @ X2240 @ X2241) @ X2238)|((X2240)=(X2241))|(in @ (esk75_4 @ X2238 @ X2239 @ X2240 @ X2241) @ X2239)|~(subset @ X2241 @ (cartprod @ X2238 @ X2239))|~(subset @ X2240 @ (cartprod @ X2238 @ X2239)))&(((in @ (esk77_4 @ X2238 @ X2239 @ X2240 @ X2241) @ X2239)|((X2240)=(X2241))|(in @ (esk75_4 @ X2238 @ X2239 @ X2240 @ X2241) @ X2239)|~(subset @ X2241 @ (cartprod @ X2238 @ X2239))|~(subset @ X2240 @ (cartprod @ X2238 @ X2239)))&(((in @ (kpair @ (esk76_4 @ X2238 @ X2239 @ X2240 @ X2241) @ (esk77_4 @ X2238 @ X2239 @ X2240 @ X2241)) @ X2241)|((X2240)=(X2241))|(in @ (esk75_4 @ X2238 @ X2239 @ X2240 @ X2241) @ X2239)|~(subset @ X2241 @ (cartprod @ X2238 @ X2239))|~(subset @ X2240 @ (cartprod @ X2238 @ X2239)))&(~(in @ (kpair @ (esk76_4 @ X2238 @ X2239 @ X2240 @ X2241) @ (esk77_4 @ X2238 @ X2239 @ X2240 @ X2241)) @ X2240)|((X2240)=(X2241))|(in @ (esk75_4 @ X2238 @ X2239 @ X2240 @ X2241) @ X2239)|~(subset @ X2241 @ (cartprod @ X2238 @ X2239))|~(subset @ X2240 @ (cartprod @ X2238 @ X2239))))))&((((in @ (esk76_4 @ X2238 @ X2239 @ X2240 @ X2241) @ X2238)|((X2240)=(X2241))|(in @ (kpair @ (esk74_4 @ X2238 @ X2239 @ X2240 @ X2241) @ (esk75_4 @ X2238 @ X2239 @ X2240 @ X2241)) @ X2240)|~(subset @ X2241 @ (cartprod @ X2238 @ X2239))|~(subset @ X2240 @ (cartprod @ X2238 @ X2239)))&(((in @ (esk77_4 @ X2238 @ X2239 @ X2240 @ X2241) @ X2239)|((X2240)=(X2241))|(in @ (kpair @ (esk74_4 @ X2238 @ X2239 @ X2240 @ X2241) @ (esk75_4 @ X2238 @ X2239 @ X2240 @ X2241)) @ X2240)|~(subset @ X2241 @ (cartprod @ X2238 @ X2239))|~(subset @ X2240 @ (cartprod @ X2238 @ X2239)))&(((in @ (kpair @ (esk76_4 @ X2238 @ X2239 @ X2240 @ X2241) @ (esk77_4 @ X2238 @ X2239 @ X2240 @ X2241)) @ X2241)|((X2240)=(X2241))|(in @ (kpair @ (esk74_4 @ X2238 @ X2239 @ X2240 @ X2241) @ (esk75_4 @ X2238 @ X2239 @ X2240 @ X2241)) @ X2240)|~(subset @ X2241 @ (cartprod @ X2238 @ X2239))|~(subset @ X2240 @ (cartprod @ X2238 @ X2239)))&(~(in @ (kpair @ (esk76_4 @ X2238 @ X2239 @ X2240 @ X2241) @ (esk77_4 @ X2238 @ X2239 @ X2240 @ X2241)) @ X2240)|((X2240)=(X2241))|(in @ (kpair @ (esk74_4 @ X2238 @ X2239 @ X2240 @ X2241) @ (esk75_4 @ X2238 @ X2239 @ X2240 @ X2241)) @ X2240)|~(subset @ X2241 @ (cartprod @ X2238 @ X2239))|~(subset @ X2240 @ (cartprod @ X2238 @ X2239))))))&(((in @ (esk76_4 @ X2238 @ X2239 @ X2240 @ X2241) @ X2238)|((X2240)=(X2241))|~(in @ (kpair @ (esk74_4 @ X2238 @ X2239 @ X2240 @ X2241) @ (esk75_4 @ X2238 @ X2239 @ X2240 @ X2241)) @ X2241)|~(subset @ X2241 @ (cartprod @ X2238 @ X2239))|~(subset @ X2240 @ (cartprod @ X2238 @ X2239)))&(((in @ (esk77_4 @ X2238 @ X2239 @ X2240 @ X2241) @ X2239)|((X2240)=(X2241))|~(in @ (kpair @ (esk74_4 @ X2238 @ X2239 @ X2240 @ X2241) @ (esk75_4 @ X2238 @ X2239 @ X2240 @ X2241)) @ X2241)|~(subset @ X2241 @ (cartprod @ X2238 @ X2239))|~(subset @ X2240 @ (cartprod @ X2238 @ X2239)))&(((in @ (kpair @ (esk76_4 @ X2238 @ X2239 @ X2240 @ X2241) @ (esk77_4 @ X2238 @ X2239 @ X2240 @ X2241)) @ X2241)|((X2240)=(X2241))|~(in @ (kpair @ (esk74_4 @ X2238 @ X2239 @ X2240 @ X2241) @ (esk75_4 @ X2238 @ X2239 @ X2240 @ X2241)) @ X2241)|~(subset @ X2241 @ (cartprod @ X2238 @ X2239))|~(subset @ X2240 @ (cartprod @ X2238 @ X2239)))&(~(in @ (kpair @ (esk76_4 @ X2238 @ X2239 @ X2240 @ X2241) @ (esk77_4 @ X2238 @ X2239 @ X2240 @ X2241)) @ X2240)|((X2240)=(X2241))|~(in @ (kpair @ (esk74_4 @ X2238 @ X2239 @ X2240 @ X2241) @ (esk75_4 @ X2238 @ X2239 @ X2240 @ X2241)) @ X2241)|~(subset @ X2241 @ (cartprod @ X2238 @ X2239))|~(subset @ X2240 @ (cartprod @ X2238 @ X2239)))))))))&((((in @ (esk78_4 @ X2246 @ X2247 @ X2248 @ X2249) @ X2246)|((X2248)=(X2249))|~(func @ X2246 @ X2247 @ X2249)|~(func @ X2246 @ X2247 @ X2248))&(((ap @ X2246 @ X2247 @ X2248 @ (esk78_4 @ X2246 @ X2247 @ X2248 @ X2249))!=(ap @ X2246 @ X2247 @ X2249 @ (esk78_4 @ X2246 @ X2247 @ X2248 @ X2249)))|((X2248)=(X2249))|~(func @ X2246 @ X2247 @ X2249)|~(func @ X2246 @ X2247 @ X2248)))&((((in @ (esk79_4 @ X2251 @ X2252 @ X2253 @ X2254) @ X2251)|((X2253)=(X2254))|~(in @ X2254 @ (funcSet @ X2251 @ X2252))|~(in @ X2253 @ (funcSet @ X2251 @ X2252)))&(((ap @ X2251 @ X2252 @ X2253 @ (esk79_4 @ X2251 @ X2252 @ X2253 @ X2254))!=(ap @ X2251 @ X2252 @ X2254 @ (esk79_4 @ X2251 @ X2252 @ X2253 @ X2254)))|((X2253)=(X2254))|~(in @ X2254 @ (funcSet @ X2251 @ X2252))|~(in @ X2253 @ (funcSet @ X2251 @ X2252))))&((~(in @ X2258 @ (funcSet @ X2256 @ X2257))|(~(in @ X2259 @ X2256)|((ap @ X2256 @ X2257 @ X2258 @ X2259)=(ap @ X2256 @ X2257 @ X2258 @ X2259))))&((~(func @ X2260 @ X2261 @ X2262)|(~(in @ X2263 @ X2260)|((ap @ X2260 @ X2261 @ X2262 @ X2263)=(ap @ X2260 @ X2261 @ X2262 @ X2263))))&((((in @ (esk80_3 @ X2264 @ X2265 @ X2266) @ X2264)|(~(in @ X2268 @ X2264)|((ap @ X2264 @ X2265 @ (lam @ X2264 @ X2265 @ X2266) @ X2268)=(X2266 @ X2268))))&(~(in @ (X2266 @ (esk80_3 @ X2264 @ X2265 @ X2266)) @ X2265)|(~(in @ X2268 @ X2264)|((ap @ X2264 @ X2265 @ (lam @ X2264 @ X2265 @ X2266) @ X2268)=(X2266 @ X2268)))))&((~(func @ X2269 @ X2270 @ X2271)|((lam @ X2269 @ X2270 @ (ap @ X2269 @ X2270 @ X2271))=(X2271)))&((((in @ (esk81_3 @ X2272 @ X2273 @ X2274) @ X2272)|((lam @ X2272 @ X2273 @ X2274)=(lam @ X2272 @ X2273 @ X2274)))&(~(in @ (X2274 @ (esk81_3 @ X2272 @ X2273 @ X2274)) @ X2273)|((lam @ X2272 @ X2273 @ X2274)=(lam @ X2272 @ X2273 @ X2274))))&((((in @ (esk82_3 @ X2276 @ X2277 @ X2278) @ X2276)|(~(in @ X2280 @ X2276)|((ap @ X2276 @ X2277 @ (lam @ X2276 @ X2277 @ X2278) @ X2280)=(X2278 @ X2280))))&(~(in @ (X2278 @ (esk82_3 @ X2276 @ X2277 @ X2278)) @ X2277)|(~(in @ X2280 @ X2276)|((ap @ X2276 @ X2277 @ (lam @ X2276 @ X2277 @ X2278) @ X2280)=(X2278 @ X2280)))))&((~(in @ X2283 @ (funcSet @ X2281 @ X2282))|((lam @ X2281 @ X2282 @ (ap @ X2281 @ X2282 @ X2283))=(X2283)))&((~(in @ X2286 @ X2284)|(~(in @ X2287 @ X2284)|((X2285)|(in @ X2287 @ (dsetconstr @ X2284 @ (^[Z0/* 9 */:$i]:((((X2285)&((Z0)=(X2286)))|(~((X2285))&((Z0)=(X2287)))))))))))&((~(in @ X2290 @ X2288)|(~(in @ X2291 @ X2288)|((X2289)|((dsetconstr @ X2288 @ (^[Z0/* 9 */:$i]:((((X2289)&((Z0)=(X2290)))|(~((X2289))&((Z0)=(X2291)))))))=(setadjoin @ X2291 @ emptyset)))))&((~(in @ X2294 @ X2292)|(~(in @ X2295 @ X2292)|(~(X2293)|(in @ X2294 @ (dsetconstr @ X2292 @ (^[Z0/* 9 */:$i]:((((X2293)&((Z0)=(X2294)))|(~((X2293))&((Z0)=(X2295)))))))))))&((~(in @ X2298 @ X2296)|(~(in @ X2299 @ X2296)|(~(X2297)|((dsetconstr @ X2296 @ (^[Z0/* 9 */:$i]:((((X2297)&((Z0)=(X2298)))|(~((X2297))&((Z0)=(X2299)))))))=(setadjoin @ X2298 @ emptyset)))))&((~(in @ X2302 @ X2300)|(~(in @ X2303 @ X2300)|(singleton @ (dsetconstr @ X2300 @ (^[Z0/* 9 */:$i]:((((X2301)&((Z0)=(X2302)))|(~((X2301))&((Z0)=(X2303))))))))))&((~(in @ X2306 @ X2304)|(~(in @ X2307 @ X2304)|(in @ (if @ X2304 @ ((X2305)) @ X2306 @ X2307) @ X2304)))&((~(singleton @ X2308)|(~(in @ X2309 @ X2308)|((setunion @ X2308)=(X2309))))&((~(in @ X2312 @ X2310)|(~(in @ X2313 @ X2310)|(~(X2311)|((if @ X2310 @ ((X2311)) @ X2312 @ X2313)=(X2312)))))&((~(in @ X2316 @ X2314)|(~(in @ X2317 @ X2314)|((X2315)|((if @ X2314 @ ((X2315)) @ X2316 @ X2317)=(X2317)))))&((~(in @ X2320 @ X2318)|(~(in @ X2321 @ X2318)|(in @ (if @ X2318 @ ((X2319)) @ X2320 @ X2321) @ (setadjoin @ X2320 @ (setadjoin @ X2321 @ emptyset)))))&((~(in @ X2323 @ (powerset @ X2322))|(~(in @ X2324 @ (powerset @ X2322))|(in @ (binintersect @ X2323 @ X2324) @ (powerset @ X2322))))&((~(in @ X2326 @ (powerset @ X2325))|(~(in @ X2327 @ (powerset @ X2325))|(in @ (binunion @ X2326 @ X2327) @ (powerset @ X2325))))&((~(in @ X2329 @ (powerset @ X2328))|(in @ (powerset @ X2329) @ (powerset @ (powerset @ X2328))))&((~(in @ X2331 @ (powerset @ X2330))|(~(in @ X2332 @ (powerset @ X2330))|(in @ (setminus @ X2331 @ X2332) @ (powerset @ X2330))))&((~(in @ X2334 @ (powerset @ X2333))|(in @ (setminus @ X2333 @ X2334) @ (powerset @ X2333)))&(((((in @ (esk84_3 @ X2335 @ X2336 @ X2337) @ X2335)|((X2336)=(X2337))|(in @ (esk83_3 @ X2335 @ X2336 @ X2337) @ X2335)|~(in @ X2337 @ (powerset @ X2335))|~(in @ X2336 @ (powerset @ X2335)))&(((in @ (esk84_3 @ X2335 @ X2336 @ X2337) @ X2337)|((X2336)=(X2337))|(in @ (esk83_3 @ X2335 @ X2336 @ X2337) @ X2335)|~(in @ X2337 @ (powerset @ X2335))|~(in @ X2336 @ (powerset @ X2335)))&(~(in @ (esk84_3 @ X2335 @ X2336 @ X2337) @ X2336)|((X2336)=(X2337))|(in @ (esk83_3 @ X2335 @ X2336 @ X2337) @ X2335)|~(in @ X2337 @ (powerset @ X2335))|~(in @ X2336 @ (powerset @ X2335)))))&((((in @ (esk84_3 @ X2335 @ X2336 @ X2337) @ X2335)|((X2336)=(X2337))|(in @ (esk83_3 @ X2335 @ X2336 @ X2337) @ X2336)|~(in @ X2337 @ (powerset @ X2335))|~(in @ X2336 @ (powerset @ X2335)))&(((in @ (esk84_3 @ X2335 @ X2336 @ X2337) @ X2337)|((X2336)=(X2337))|(in @ (esk83_3 @ X2335 @ X2336 @ X2337) @ X2336)|~(in @ X2337 @ (powerset @ X2335))|~(in @ X2336 @ (powerset @ X2335)))&(~(in @ (esk84_3 @ X2335 @ X2336 @ X2337) @ X2336)|((X2336)=(X2337))|(in @ (esk83_3 @ X2335 @ X2336 @ X2337) @ X2336)|~(in @ X2337 @ (powerset @ X2335))|~(in @ X2336 @ (powerset @ X2335)))))&(((in @ (esk84_3 @ X2335 @ X2336 @ X2337) @ X2335)|((X2336)=(X2337))|~(in @ (esk83_3 @ X2335 @ X2336 @ X2337) @ X2337)|~(in @ X2337 @ (powerset @ X2335))|~(in @ X2336 @ (powerset @ X2335)))&(((in @ (esk84_3 @ X2335 @ X2336 @ X2337) @ X2337)|((X2336)=(X2337))|~(in @ (esk83_3 @ X2335 @ X2336 @ X2337) @ X2337)|~(in @ X2337 @ (powerset @ X2335))|~(in @ X2336 @ (powerset @ X2335)))&(~(in @ (esk84_3 @ X2335 @ X2336 @ X2337) @ X2336)|((X2336)=(X2337))|~(in @ (esk83_3 @ X2335 @ X2336 @ X2337) @ X2337)|~(in @ X2337 @ (powerset @ X2335))|~(in @ X2336 @ (powerset @ X2335)))))))&((((in @ (esk85_3 @ X2340 @ X2341 @ X2342) @ X2340)|(subset @ X2341 @ X2342)|~(in @ X2342 @ (powerset @ X2340))|~(in @ X2341 @ (powerset @ X2340)))&(((in @ (esk85_3 @ X2340 @ X2341 @ X2342) @ X2341)|(subset @ X2341 @ X2342)|~(in @ X2342 @ (powerset @ X2340))|~(in @ X2341 @ (powerset @ X2340)))&(~(in @ (esk85_3 @ X2340 @ X2341 @ X2342) @ X2342)|(subset @ X2341 @ X2342)|~(in @ X2342 @ (powerset @ X2340))|~(in @ X2341 @ (powerset @ X2340)))))&((((in @ (esk86_3 @ X2344 @ X2345 @ X2346) @ X2344)|(in @ X2345 @ (powerset @ X2346))|~(in @ X2346 @ (powerset @ X2344))|~(in @ X2345 @ (powerset @ X2344)))&(((in @ (esk86_3 @ X2344 @ X2345 @ X2346) @ X2345)|(in @ X2345 @ (powerset @ X2346))|~(in @ X2346 @ (powerset @ X2344))|~(in @ X2345 @ (powerset @ X2344)))&(~(in @ (esk86_3 @ X2344 @ X2345 @ X2346) @ X2346)|(in @ X2345 @ (powerset @ X2346))|~(in @ X2346 @ (powerset @ X2344))|~(in @ X2345 @ (powerset @ X2344)))))&((~(in @ X2349 @ (powerset @ X2348))|(~(in @ X2350 @ (powerset @ X2348))|(~(in @ X2351 @ X2348)|(~(in @ X2349 @ (powerset @ X2350))|(~(in @ X2351 @ X2349)|(in @ X2351 @ X2350))))))&((~(in @ X2353 @ (powerset @ X2352))|(~(in @ X2354 @ X2352)|(~(in @ X2354 @ X2353)|~(in @ X2354 @ (setminus @ X2352 @ X2353)))))&((~(in @ X2356 @ (powerset @ X2355))|(~(in @ X2357 @ X2355)|((in @ X2357 @ (setminus @ X2355 @ X2356))|(in @ X2357 @ X2356))))&((~(in @ X2359 @ (powerset @ X2358))|(~(in @ X2360 @ (powerset @ X2358))|(~(in @ X2361 @ X2358)|((in @ X2361 @ X2359)|~(in @ X2361 @ (binintersect @ X2359 @ X2360))))))&((~(in @ X2363 @ (powerset @ X2362))|(~(in @ X2364 @ (powerset @ X2362))|(~(in @ X2365 @ X2362)|((in @ X2365 @ X2364)|~(in @ X2365 @ (binintersect @ X2363 @ X2364))))))&((~(in @ X2367 @ (powerset @ X2366))|(~(in @ X2368 @ (powerset @ X2366))|(~(in @ X2369 @ X2366)|(~(subset @ X2367 @ (setminus @ X2366 @ X2368))|(~(in @ X2369 @ X2368)|~(in @ X2369 @ X2367))))))&((~(in @ X2371 @ (powerset @ X2370))|(~(in @ X2372 @ (powerset @ X2370))|(~(in @ X2373 @ X2370)|(~(subset @ X2371 @ X2372)|((in @ X2373 @ X2372)|~(in @ X2373 @ X2371))))))&((in @ esk88_0 @ (powerset @ esk87_0))&((in @ esk89_0 @ (powerset @ esk87_0))&((subset @ esk88_0 @ esk89_0)&~(subset @ (setminus @ esk87_0 @ esk89_0) @ (setminus @ esk87_0 @ esk88_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_327])])])])])])])). 309.13/39.45 thf(c_0_329, negated_conjecture, ~((subset @ (setminus @ esk87_0 @ esk89_0) @ (setminus @ esk87_0 @ esk88_0))), inference(split_conjunct,[status(thm)],[c_0_328])). 309.13/39.45 thf(c_0_330, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk53_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_328])). 309.13/39.45 thf(c_0_331, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X3)|~((in @ X2 @ (setminus @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_328])). 309.13/39.45 thf(c_0_332, negated_conjecture, (in @ (esk53_2 @ (setminus @ esk87_0 @ esk89_0) @ (setminus @ esk87_0 @ esk88_0)) @ (setminus @ esk87_0 @ esk89_0)), inference(spm,[status(thm)],[c_0_329, c_0_330])). 309.13/39.45 thf(c_0_333, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((~((in @ X2 @ (setminus @ X3 @ X4)))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_328])). 309.13/39.45 thf(c_0_334, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((subset @ X2 @ X3))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_328])). 309.13/39.45 thf(c_0_335, negated_conjecture, (subset @ esk88_0 @ esk89_0), inference(split_conjunct,[status(thm)],[c_0_328])). 309.13/39.45 thf(c_0_336, negated_conjecture, ![X2:$i, X3:$i]:((((binintersect @ X3 @ X2)=(X2))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_328])). 309.13/39.45 thf(c_0_337, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk53_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_328])). 309.13/39.45 thf(c_0_338, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setminus @ X3 @ X4))|(in @ X2 @ X4)|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_328])). 309.13/39.45 thf(c_0_339, negated_conjecture, (in @ (esk53_2 @ (setminus @ esk87_0 @ esk89_0) @ (setminus @ esk87_0 @ esk88_0)) @ esk87_0), inference(spm,[status(thm)],[c_0_331, c_0_332])). 309.13/39.45 thf(c_0_340, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X3 @ X2)|((binintersect @ X2 @ X3)!=(X3)))), inference(split_conjunct,[status(thm)],[c_0_328])). 309.13/39.45 thf(c_0_341, negated_conjecture, ~((in @ (esk53_2 @ (setminus @ esk87_0 @ esk89_0) @ (setminus @ esk87_0 @ esk88_0)) @ esk89_0)), inference(spm,[status(thm)],[c_0_333, c_0_332])). 309.13/39.45 thf(c_0_342, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk89_0)|~((in @ X2 @ esk88_0)))), inference(spm,[status(thm)],[c_0_334, c_0_335])). 309.13/39.45 thf(c_0_343, negated_conjecture, ![X3:$i, X2:$i]:((((binintersect @ X2 @ X3)=(X3))|~((in @ (esk53_2 @ X3 @ X2) @ X2)))), inference(spm,[status(thm)],[c_0_336, c_0_337])). 309.13/39.45 thf(c_0_344, negated_conjecture, ![X2:$i]:(((in @ (esk53_2 @ (setminus @ esk87_0 @ esk89_0) @ (setminus @ esk87_0 @ esk88_0)) @ (setminus @ esk87_0 @ X2))|(in @ (esk53_2 @ (setminus @ esk87_0 @ esk89_0) @ (setminus @ esk87_0 @ esk88_0)) @ X2))), inference(spm,[status(thm)],[c_0_338, c_0_339])). 309.13/39.45 thf(c_0_345, negated_conjecture, ((binintersect @ (setminus @ esk87_0 @ esk88_0) @ (setminus @ esk87_0 @ esk89_0))!=(setminus @ esk87_0 @ esk89_0)), inference(spm,[status(thm)],[c_0_329, c_0_340])). 309.13/39.45 thf(c_0_346, negated_conjecture, ~((in @ (esk53_2 @ (setminus @ esk87_0 @ esk89_0) @ (setminus @ esk87_0 @ esk88_0)) @ esk88_0)), inference(spm,[status(thm)],[c_0_341, c_0_342])). 309.13/39.45 thf(c_0_347, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_343, c_0_344]), c_0_345]), c_0_346]), ['proof']). 309.13/39.45 # SZS output end CNFRefutation 309.13/39.45 # Parsed axioms : 525 309.13/39.45 # Removed by relevancy pruning/SinE : 0 309.13/39.45 # Initial clauses : 705 309.13/39.45 # Removed in clause preprocessing : 308 309.13/39.45 # Initial clauses in saturation : 397 309.13/39.45 # Processed clauses : 16385 309.13/39.45 # ...of these trivial : 378 309.13/39.45 # ...subsumed : 11543 309.13/39.45 # ...remaining for further processing : 4464 309.13/39.45 # Other redundant clauses eliminated : 179 309.13/39.45 # Clauses deleted for lack of memory : 0 309.13/39.45 # Backward-subsumed : 197 309.13/39.45 # Backward-rewritten : 100 309.13/39.45 # Generated clauses : 255813 309.13/39.45 # ...of the previous two non-redundant : 240368 309.13/39.45 # ...aggressively subsumed : 0 309.13/39.45 # Contextual simplify-reflections : 6 309.13/39.45 # Paramodulations : 255558 309.13/39.45 # Factorizations : 30 309.13/39.45 # NegExts : 2 309.13/39.45 # Equation resolutions : 184 309.13/39.45 # Disequality decompositions : 0 309.13/39.45 # Total rewrite steps : 25549 309.13/39.45 # ...of those cached : 23122 309.13/39.45 # Propositional unsat checks : 0 309.13/39.45 # Propositional check models : 0 309.13/39.45 # Propositional check unsatisfiable : 0 309.13/39.45 # Propositional clauses : 0 309.13/39.45 # Propositional clauses after purity: 0 309.13/39.45 # Propositional unsat core size : 0 309.13/39.45 # Propositional preprocessing time : 0.000 309.13/39.45 # Propositional encoding time : 0.000 309.13/39.45 # Propositional solver time : 0.000 309.13/39.45 # Success case prop preproc time : 0.000 309.13/39.45 # Success case prop encoding time : 0.000 309.13/39.45 # Success case prop solver time : 0.000 309.13/39.45 # Current number of processed clauses : 3783 309.13/39.45 # Positive orientable unit clauses : 551 309.13/39.45 # Positive unorientable unit clauses: 0 309.13/39.45 # Negative unit clauses : 465 309.13/39.45 # Non-unit-clauses : 2767 309.13/39.45 # Current number of unprocessed clauses: 224341 309.13/39.45 # ...number of literals in the above : 629433 309.13/39.45 # Current number of archived formulas : 0 309.13/39.45 # Current number of archived clauses : 666 309.13/39.45 # Clause-clause subsumption calls (NU) : 703979 309.13/39.45 # Rec. Clause-clause subsumption calls : 466987 309.13/39.45 # Non-unit clause-clause subsumptions : 6456 309.13/39.45 # Unit Clause-clause subsumption calls : 94953 309.13/39.45 # Rewrite failures with RHS unbound : 0 309.13/39.45 # BW rewrite match attempts : 624 309.13/39.45 # BW rewrite match successes : 114 309.13/39.45 # Condensation attempts : 0 309.13/39.45 # Condensation successes : 0 309.13/39.45 # Termbank termtop insertions : 6431404 309.13/39.45 # Search garbage collected termcells : 25153 309.13/39.45 309.13/39.45 # ------------------------------------------------- 309.13/39.45 # User time : 37.588 s 309.13/39.45 # System time : 1.159 s 309.13/39.45 # Total time : 38.747 s 309.13/39.45 # Maximum resident set size: 7956 pages 309.13/39.45 309.13/39.45 # ------------------------------------------------- 309.13/39.45 # User time : 37.602 s 309.13/39.45 # System time : 1.163 s 309.13/39.45 # Total time : 38.765 s 309.13/39.45 # Maximum resident set size: 2604 pages 309.13/39.45 % E---3.1 exiting 309.13/39.46 % E exiting 309.41/39.46 EOF