0.12/0.20 % Problem : Vampire---4.8_25226 : TPTP v0.0.0. Released v0.0.0. 0.12/0.21 % Command : run_E %s %d THM 0.20/0.42 % Computer : n017.cluster.edu 0.20/0.42 % Model : x86_64 x86_64 0.20/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.20/0.42 % Memory : 8042.1875MB 0.20/0.42 % OS : Linux 3.10.0-693.el7.x86_64 0.20/0.42 % CPULimit : 1440 0.20/0.42 % WCLimit : 180 0.20/0.42 % DateTime : Mon Jul 3 12:23:53 EDT 2023 0.20/0.42 % CPUTime : 0.47/0.63 Running higher-order theorem provingRunning: /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.rKmjcAUqsY/Vampire---4.8_25226 0.47/0.64 # Version: 3.1pre001-ho 12.35/2.21 # Preprocessing class: HSLMSLSSLLLCHFA. 12.35/2.21 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 12.35/2.21 # Starting ehoh_best5 with 180s (1) cores 12.35/2.21 # Starting almost_fo_3_lam with 180s (1) cores 12.35/2.21 # Starting new_bool_5 with 180s (1) cores 12.35/2.21 # Starting pre_casc_3 with 180s (1) cores 12.35/2.21 # Starting ho_unfolding_8 with 180s (1) cores 12.35/2.21 # Starting new_ho_10_cnf2 with 180s (1) cores 12.35/2.21 # Starting new_bool_3 with 180s (1) cores 12.35/2.21 # Starting new_ho_5 with 180s (1) cores 12.35/2.21 # new_ho_5 with pid 25584 completed with status 0 12.35/2.21 # Result found by new_ho_5 12.35/2.21 # Preprocessing class: HSLMSLSSLLLCHFA. 12.35/2.21 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 12.35/2.21 # Starting ehoh_best5 with 180s (1) cores 12.35/2.21 # Starting almost_fo_3_lam with 180s (1) cores 12.35/2.21 # Starting new_bool_5 with 180s (1) cores 12.35/2.21 # Starting pre_casc_3 with 180s (1) cores 12.35/2.21 # Starting ho_unfolding_8 with 180s (1) cores 12.35/2.21 # Starting new_ho_10_cnf2 with 180s (1) cores 12.35/2.21 # Starting new_bool_3 with 180s (1) cores 12.35/2.21 # Starting new_ho_5 with 180s (1) cores 12.35/2.21 # SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true) 12.35/2.21 # Search class: HGHSM-FSLM32-MHFMMSBN 12.35/2.21 # Scheduled 9 strats onto 1 cores with 180 seconds (180 total) 12.35/2.21 # Starting ho_unfolding_8 with 37s (1) cores 12.35/2.21 # ho_unfolding_8 with pid 25593 completed with status 0 12.35/2.21 # Result found by ho_unfolding_8 12.35/2.21 # Preprocessing class: HSLMSLSSLLLCHFA. 12.35/2.21 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 12.35/2.21 # Starting ehoh_best5 with 180s (1) cores 12.35/2.21 # Starting almost_fo_3_lam with 180s (1) cores 12.35/2.21 # Starting new_bool_5 with 180s (1) cores 12.35/2.21 # Starting pre_casc_3 with 180s (1) cores 12.35/2.21 # Starting ho_unfolding_8 with 180s (1) cores 12.35/2.21 # Starting new_ho_10_cnf2 with 180s (1) cores 12.35/2.21 # Starting new_bool_3 with 180s (1) cores 12.35/2.21 # Starting new_ho_5 with 180s (1) cores 12.35/2.21 # SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true) 12.35/2.21 # Search class: HGHSM-FSLM32-MHFMMSBN 12.35/2.21 # Scheduled 9 strats onto 1 cores with 180 seconds (180 total) 12.35/2.21 # Starting ho_unfolding_8 with 37s (1) cores 12.35/2.21 # Preprocessing time : 0.119 s 12.35/2.21 # Presaturation interreduction done 12.35/2.21 12.35/2.21 # Proof found! 12.35/2.21 # SZS status Theorem 12.35/2.21 # SZS output start CNFRefutation 12.35/2.21 thf(decl_22, type, in: $i > $i > $o). 12.35/2.21 thf(decl_23, type, exu: ($i > $o) > $o). 12.35/2.21 thf(decl_24, type, setextAx: $o). 12.35/2.21 thf(decl_25, type, emptyset: $i). 12.35/2.21 thf(decl_26, type, emptysetAx: $o). 12.35/2.21 thf(decl_27, type, setadjoin: $i > $i > $i). 12.35/2.21 thf(decl_28, type, setadjoinAx: $o). 12.35/2.21 thf(decl_29, type, powerset: $i > $i). 12.35/2.21 thf(decl_30, type, powersetAx: $o). 12.35/2.21 thf(decl_31, type, setunion: $i > $i). 12.35/2.21 thf(decl_32, type, setunionAx: $o). 12.35/2.21 thf(decl_33, type, omega: $i). 12.35/2.21 thf(decl_34, type, omega0Ax: $o). 12.35/2.21 thf(decl_35, type, omegaSAx: $o). 12.35/2.21 thf(decl_36, type, omegaIndAx: $o). 12.35/2.21 thf(decl_37, type, replAx: $o). 12.35/2.21 thf(decl_38, type, foundationAx: $o). 12.35/2.21 thf(decl_39, type, wellorderingAx: $o). 12.35/2.21 thf(decl_40, type, descr: ($i > $o) > $i). 12.35/2.21 thf(decl_41, type, descrp: $o). 12.35/2.21 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 12.35/2.21 thf(decl_43, type, dsetconstrI: $o). 12.35/2.21 thf(decl_44, type, dsetconstrEL: $o). 12.35/2.21 thf(decl_45, type, dsetconstrER: $o). 12.35/2.21 thf(decl_46, type, exuE1: $o). 12.35/2.21 thf(decl_47, type, prop2set: $o > $i). 12.35/2.21 thf(decl_48, type, prop2setE: $o). 12.35/2.21 thf(decl_49, type, emptysetE: $o). 12.35/2.21 thf(decl_50, type, emptysetimpfalse: $o). 12.35/2.21 thf(decl_51, type, notinemptyset: $o). 12.35/2.21 thf(decl_52, type, exuE3e: $o). 12.35/2.21 thf(decl_53, type, setext: $o). 12.35/2.21 thf(decl_54, type, emptyI: $o). 12.35/2.21 thf(decl_55, type, noeltsimpempty: $o). 12.35/2.21 thf(decl_56, type, setbeta: $o). 12.35/2.21 thf(decl_57, type, nonempty: $i > $o). 12.35/2.21 thf(decl_58, type, nonemptyE1: $o). 12.35/2.21 thf(decl_59, type, nonemptyI: $o). 12.35/2.21 thf(decl_60, type, nonemptyI1: $o). 12.35/2.21 thf(decl_61, type, setadjoinIL: $o). 12.35/2.21 thf(decl_62, type, emptyinunitempty: $o). 12.35/2.21 thf(decl_63, type, setadjoinIR: $o). 12.35/2.21 thf(decl_64, type, setadjoinE: $o). 12.35/2.21 thf(decl_65, type, setadjoinOr: $o). 12.35/2.21 thf(decl_66, type, setoftrueEq: $o). 12.35/2.21 thf(decl_67, type, powersetI: $o). 12.35/2.21 thf(decl_68, type, emptyinPowerset: $o). 12.35/2.21 thf(decl_69, type, emptyInPowerset: $o). 12.35/2.21 thf(decl_70, type, powersetE: $o). 12.35/2.21 thf(decl_71, type, setunionI: $o). 12.35/2.21 thf(decl_72, type, setunionE: $o). 12.35/2.21 thf(decl_73, type, subPowSU: $o). 12.35/2.21 thf(decl_74, type, exuE2: $o). 12.35/2.21 thf(decl_75, type, nonemptyImpWitness: $o). 12.35/2.21 thf(decl_76, type, uniqinunit: $o). 12.35/2.21 thf(decl_77, type, notinsingleton: $o). 12.35/2.21 thf(decl_78, type, eqinunit: $o). 12.35/2.21 thf(decl_79, type, singletonsswitch: $o). 12.35/2.21 thf(decl_80, type, upairsetE: $o). 12.35/2.21 thf(decl_81, type, upairsetIL: $o). 12.35/2.21 thf(decl_82, type, upairsetIR: $o). 12.35/2.21 thf(decl_83, type, emptyE1: $o). 12.35/2.21 thf(decl_84, type, vacuousDall: $o). 12.35/2.21 thf(decl_85, type, quantDeMorgan1: $o). 12.35/2.21 thf(decl_86, type, quantDeMorgan2: $o). 12.35/2.21 thf(decl_87, type, quantDeMorgan3: $o). 12.35/2.21 thf(decl_88, type, quantDeMorgan4: $o). 12.35/2.21 thf(decl_89, type, prop2setI: $o). 12.35/2.21 thf(decl_90, type, set2prop: $i > $o). 12.35/2.21 thf(decl_91, type, prop2set2propI: $o). 12.35/2.21 thf(decl_92, type, notdexE: $o). 12.35/2.21 thf(decl_93, type, notdallE: $o). 12.35/2.21 thf(decl_94, type, exuI1: $o). 12.35/2.21 thf(decl_95, type, exuI3: $o). 12.35/2.21 thf(decl_96, type, exuI2: $o). 12.35/2.21 thf(decl_97, type, inCongP: $o). 12.35/2.21 thf(decl_98, type, in__Cong: $o). 12.35/2.21 thf(decl_99, type, exuE3u: $o). 12.35/2.21 thf(decl_100, type, exu__Cong: $o). 12.35/2.21 thf(decl_101, type, emptyset__Cong: $o). 12.35/2.21 thf(decl_102, type, setadjoin__Cong: $o). 12.35/2.21 thf(decl_103, type, powerset__Cong: $o). 12.35/2.21 thf(decl_104, type, setunion__Cong: $o). 12.35/2.21 thf(decl_105, type, omega__Cong: $o). 12.35/2.21 thf(decl_106, type, exuEu: $o). 12.35/2.21 thf(decl_107, type, descr__Cong: $o). 12.35/2.21 thf(decl_108, type, dsetconstr__Cong: $o). 12.35/2.21 thf(decl_109, type, subset: $i > $i > $o). 12.35/2.21 thf(decl_112, type, subsetI1: $o). 12.35/2.21 thf(decl_113, type, eqimpsubset2: $o). 12.35/2.21 thf(decl_114, type, eqimpsubset1: $o). 12.35/2.21 thf(decl_115, type, subsetI2: $o). 12.35/2.21 thf(decl_116, type, emptysetsubset: $o). 12.35/2.21 thf(decl_117, type, subsetE: $o). 12.35/2.21 thf(decl_118, type, subsetE2: $o). 12.35/2.21 thf(decl_119, type, notsubsetI: $o). 12.35/2.21 thf(decl_120, type, notequalI1: $o). 12.35/2.21 thf(decl_121, type, notequalI2: $o). 12.35/2.21 thf(decl_122, type, subsetRefl: $o). 12.35/2.21 thf(decl_123, type, subsetTrans: $o). 12.35/2.21 thf(decl_124, type, setadjoinSub: $o). 12.35/2.21 thf(decl_125, type, setadjoinSub2: $o). 12.35/2.21 thf(decl_126, type, subset2powerset: $o). 12.35/2.21 thf(decl_127, type, setextsub: $o). 12.35/2.21 thf(decl_128, type, subsetemptysetimpeq: $o). 12.35/2.21 thf(decl_129, type, powersetI1: $o). 12.35/2.21 thf(decl_130, type, powersetE1: $o). 12.35/2.21 thf(decl_131, type, inPowerset: $o). 12.35/2.21 thf(decl_132, type, powersetsubset: $o). 12.35/2.21 thf(decl_133, type, sepInPowerset: $o). 12.35/2.21 thf(decl_134, type, sepSubset: $o). 12.35/2.21 thf(decl_135, type, binunion: $i > $i > $i). 12.35/2.21 thf(decl_136, type, binunionIL: $o). 12.35/2.21 thf(decl_137, type, upairset2IR: $o). 12.35/2.21 thf(decl_138, type, binunionIR: $o). 12.35/2.21 thf(decl_139, type, binunionEcases: $o). 12.35/2.21 thf(decl_140, type, binunionE: $o). 12.35/2.21 thf(decl_141, type, binunionLsub: $o). 12.35/2.21 thf(decl_142, type, binunionRsub: $o). 12.35/2.21 thf(decl_143, type, binintersect: $i > $i > $i). 12.35/2.21 thf(decl_144, type, binintersectI: $o). 12.35/2.21 thf(decl_145, type, binintersectSubset5: $o). 12.35/2.21 thf(decl_146, type, binintersectEL: $o). 12.35/2.21 thf(decl_147, type, binintersectLsub: $o). 12.35/2.21 thf(decl_148, type, binintersectSubset2: $o). 12.35/2.21 thf(decl_149, type, binintersectSubset3: $o). 12.35/2.21 thf(decl_150, type, binintersectER: $o). 12.35/2.21 thf(decl_151, type, disjointsetsI1: $o). 12.35/2.21 thf(decl_152, type, binintersectRsub: $o). 12.35/2.21 thf(decl_153, type, binintersectSubset4: $o). 12.35/2.21 thf(decl_154, type, binintersectSubset1: $o). 12.35/2.21 thf(decl_155, type, bs114d: $o). 12.35/2.21 thf(decl_157, type, setminus: $i > $i > $i). 12.35/2.21 thf(decl_158, type, setminusI: $o). 12.35/2.21 thf(decl_159, type, setminusEL: $o). 12.35/2.21 thf(decl_160, type, setminusER: $o). 12.35/2.21 thf(decl_161, type, setminusSubset2: $o). 12.35/2.21 thf(decl_162, type, setminusERneg: $o). 12.35/2.21 thf(decl_163, type, setminusELneg: $o). 12.35/2.21 thf(decl_164, type, setminusILneg: $o). 12.35/2.21 thf(decl_165, type, setminusIRneg: $o). 12.35/2.21 thf(decl_166, type, setminusLsub: $o). 12.35/2.21 thf(decl_167, type, setminusSubset1: $o). 12.35/2.21 thf(decl_168, type, symdiff: $i > $i > $i). 12.35/2.21 thf(decl_169, type, symdiffE: $o). 12.35/2.21 thf(decl_170, type, symdiffI1: $o). 12.35/2.21 thf(decl_171, type, symdiffI2: $o). 12.35/2.21 thf(decl_172, type, symdiffIneg1: $o). 12.35/2.21 thf(decl_173, type, symdiffIneg2: $o). 12.35/2.21 thf(decl_174, type, iskpair: $i > $o). 12.35/2.21 thf(decl_175, type, secondinupair: $o). 12.35/2.21 thf(decl_176, type, setukpairIL: $o). 12.35/2.21 thf(decl_177, type, setukpairIR: $o). 12.35/2.21 thf(decl_178, type, kpairiskpair: $o). 12.35/2.21 thf(decl_179, type, kpair: $i > $i > $i). 12.35/2.21 thf(decl_180, type, kpairp: $o). 12.35/2.21 thf(decl_181, type, cartprod: $i > $i > $i). 12.35/2.21 thf(decl_182, type, singletonsubset: $o). 12.35/2.21 thf(decl_183, type, singletoninpowerset: $o). 12.35/2.21 thf(decl_184, type, singletoninpowunion: $o). 12.35/2.21 thf(decl_185, type, upairset2E: $o). 12.35/2.21 thf(decl_186, type, upairsubunion: $o). 12.35/2.21 thf(decl_187, type, upairinpowunion: $o). 12.35/2.21 thf(decl_188, type, ubforcartprodlem1: $o). 12.35/2.21 thf(decl_189, type, ubforcartprodlem2: $o). 12.35/2.21 thf(decl_190, type, ubforcartprodlem3: $o). 12.35/2.21 thf(decl_191, type, cartprodpairin: $o). 12.35/2.21 thf(decl_192, type, cartprodmempair1: $o). 12.35/2.21 thf(decl_193, type, cartprodmempair: $o). 12.35/2.21 thf(decl_194, type, setunionE2: $o). 12.35/2.21 thf(decl_195, type, setunionsingleton1: $o). 12.35/2.21 thf(decl_196, type, setunionsingleton2: $o). 12.35/2.21 thf(decl_197, type, setunionsingleton: $o). 12.35/2.21 thf(decl_198, type, singleton: $i > $o). 12.35/2.21 thf(decl_199, type, singletonprop: $o). 12.35/2.21 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 12.35/2.21 thf(decl_201, type, ex1E1: $o). 12.35/2.21 thf(decl_202, type, ex1I: $o). 12.35/2.21 thf(decl_203, type, ex1I2: $o). 12.35/2.21 thf(decl_204, type, singletonsuniq: $o). 12.35/2.21 thf(decl_209, type, setukpairinjL1: $o). 12.35/2.21 thf(decl_210, type, kfstsingleton: $o). 12.35/2.21 thf(decl_211, type, theprop: $o). 12.35/2.21 thf(decl_212, type, kfst: $i > $i). 12.35/2.21 thf(decl_213, type, kfstpairEq: $o). 12.35/2.21 thf(decl_214, type, cartprodfstin: $o). 12.35/2.21 thf(decl_215, type, setukpairinjL2: $o). 12.35/2.21 thf(decl_216, type, setukpairinjL: $o). 12.35/2.21 thf(decl_217, type, setukpairinjR11: $o). 12.35/2.21 thf(decl_218, type, setukpairinjR12: $o). 12.35/2.21 thf(decl_219, type, setukpairinjR1: $o). 12.35/2.21 thf(decl_220, type, upairequniteq: $o). 12.35/2.21 thf(decl_221, type, setukpairinjR2: $o). 12.35/2.21 thf(decl_222, type, setukpairinjR: $o). 12.35/2.21 thf(decl_223, type, ksndsingleton: $o). 12.35/2.21 thf(decl_224, type, ksnd: $i > $i). 12.35/2.21 thf(decl_225, type, ksndpairEq: $o). 12.35/2.21 thf(decl_226, type, kpairsurjEq: $o). 12.35/2.21 thf(decl_227, type, cartprodsndin: $o). 12.35/2.21 thf(decl_228, type, cartprodpairmemEL: $o). 12.35/2.21 thf(decl_229, type, cartprodpairmemER: $o). 12.35/2.21 thf(decl_230, type, cartprodmempaircEq: $o). 12.35/2.21 thf(decl_231, type, cartprodfstpairEq: $o). 12.35/2.21 thf(decl_232, type, cartprodsndpairEq: $o). 12.35/2.21 thf(decl_233, type, cartprodpairsurjEq: $o). 12.35/2.21 thf(decl_234, type, breln: $i > $i > $i > $o). 12.35/2.21 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 12.35/2.21 thf(decl_236, type, dpsetconstrI: $o). 12.35/2.21 thf(decl_237, type, dpsetconstrSub: $o). 12.35/2.21 thf(decl_238, type, setOfPairsIsBReln: $o). 12.35/2.21 thf(decl_239, type, dpsetconstrERa: $o). 12.35/2.21 thf(decl_240, type, dpsetconstrEL1: $o). 12.35/2.21 thf(decl_241, type, dpsetconstrEL2: $o). 12.35/2.21 thf(decl_242, type, dpsetconstrER: $o). 12.35/2.21 thf(decl_243, type, func: $i > $i > $i > $o). 12.35/2.21 thf(decl_244, type, funcSet: $i > $i > $i). 12.35/2.21 thf(decl_245, type, funcImageSingleton: $o). 12.35/2.21 thf(decl_246, type, apProp: $o). 12.35/2.21 thf(decl_247, type, ap: $i > $i > $i > $i > $i). 12.35/2.21 thf(decl_248, type, app: $o). 12.35/2.21 thf(decl_249, type, infuncsetfunc: $o). 12.35/2.21 thf(decl_250, type, ap2p: $o). 12.35/2.21 thf(decl_251, type, funcinfuncset: $o). 12.35/2.21 thf(decl_252, type, lamProp: $o). 12.35/2.21 thf(decl_253, type, lam: $i > $i > ($i > $i) > $i). 12.35/2.21 thf(decl_254, type, lamp: $o). 12.35/2.21 thf(decl_255, type, lam2p: $o). 12.35/2.21 thf(decl_256, type, brelnall1: $o). 12.35/2.21 thf(decl_257, type, brelnall2: $o). 12.35/2.21 thf(decl_258, type, ex1E2: $o). 12.35/2.21 thf(decl_259, type, funcGraphProp1: $o). 12.35/2.21 thf(decl_260, type, funcGraphProp3: $o). 12.35/2.21 thf(decl_261, type, funcGraphProp2: $o). 12.35/2.21 thf(decl_262, type, funcextLem: $o). 12.35/2.21 thf(decl_263, type, funcGraphProp4: $o). 12.35/2.21 thf(decl_264, type, subbreln: $o). 12.35/2.21 thf(decl_265, type, eqbreln: $o). 12.35/2.21 thf(decl_266, type, funcext: $o). 12.35/2.21 thf(decl_267, type, funcext2: $o). 12.35/2.21 thf(decl_268, type, ap2apEq1: $o). 12.35/2.21 thf(decl_269, type, ap2apEq2: $o). 12.35/2.21 thf(decl_270, type, beta1: $o). 12.35/2.21 thf(decl_271, type, eta1: $o). 12.35/2.21 thf(decl_272, type, lam2lamEq: $o). 12.35/2.21 thf(decl_273, type, beta2: $o). 12.35/2.21 thf(decl_274, type, eta2: $o). 12.35/2.21 thf(decl_275, type, iffalseProp1: $o). 12.35/2.21 thf(decl_276, type, iffalseProp2: $o). 12.35/2.21 thf(decl_277, type, iftrueProp1: $o). 12.35/2.21 thf(decl_278, type, iftrueProp2: $o). 12.35/2.21 thf(decl_279, type, ifSingleton: $o). 12.35/2.21 thf(decl_280, type, if: $i > $o > $i > $i > $i). 12.35/2.21 thf(decl_281, type, ifp: $o). 12.35/2.21 thf(decl_282, type, theeq: $o). 12.35/2.21 thf(decl_283, type, iftrue: $o). 12.35/2.21 thf(decl_284, type, iffalse: $o). 12.35/2.21 thf(decl_285, type, iftrueorfalse: $o). 12.35/2.21 thf(decl_286, type, binintersectT_lem: $o). 12.35/2.21 thf(decl_287, type, binunionT_lem: $o). 12.35/2.21 thf(decl_288, type, powersetT_lem: $o). 12.35/2.21 thf(decl_289, type, setminusT_lem: $o). 12.35/2.21 thf(decl_290, type, complementT_lem: $o). 12.35/2.21 thf(decl_291, type, setextT: $o). 12.35/2.21 thf(decl_292, type, subsetTI: $o). 12.35/2.21 thf(decl_293, type, powersetTI1: $o). 12.35/2.21 thf(decl_294, type, powersetTE1: $o). 12.35/2.21 thf(decl_295, type, complementTI1: $o). 12.35/2.21 thf(decl_296, type, complementTE1: $o). 12.35/2.21 thf(decl_297, type, binintersectTELcontra: $o). 12.35/2.21 thf(decl_298, type, binintersectTERcontra: $o). 12.35/2.21 thf(decl_299, type, contrasubsetT: $o). 12.35/2.21 thf(decl_300, type, contrasubsetT1: $o). 12.35/2.21 thf(decl_301, type, contrasubsetT2: $o). 12.35/2.21 thf(decl_302, type, contrasubsetT3: $o). 12.35/2.21 thf(decl_303, type, doubleComplementI1: $o). 12.35/2.21 thf(decl_304, type, doubleComplementE1: $o). 12.35/2.21 thf(decl_305, type, doubleComplementSub1: $o). 12.35/2.21 thf(decl_306, type, doubleComplementSub2: $o). 12.35/2.21 thf(decl_307, type, doubleComplementEq: $o). 12.35/2.21 thf(decl_308, type, complementTnotintersectT: $o). 12.35/2.21 thf(decl_309, type, complementImpComplementIntersect: $o). 12.35/2.21 thf(decl_310, type, complementSubsetComplementIntersect: $o). 12.35/2.21 thf(decl_311, type, complementInPowersetComplementIntersect: $o). 12.35/2.21 thf(decl_312, type, contraSubsetComplement: $o). 12.35/2.21 thf(decl_313, type, complementTcontraSubset: $o). 12.35/2.21 thf(decl_314, type, binunionTILcontra: $o). 12.35/2.21 thf(decl_315, type, binunionTIRcontra: $o). 12.35/2.21 thf(decl_316, type, inIntersectImpInUnion: $o). 12.35/2.21 thf(decl_317, type, inIntersectImpInUnion2: $o). 12.35/2.21 thf(decl_318, type, inIntersectImpInIntersectUnions: $o). 12.35/2.21 thf(decl_319, type, intersectInPowersetIntersectUnions: $o). 12.35/2.21 thf(decl_320, type, inComplementUnionImpNotIn1: $o). 12.35/2.21 thf(decl_321, type, inComplementUnionImpInComplement1: $o). 12.35/2.21 thf(decl_322, type, binunionTE: $o). 12.35/2.21 thf(decl_323, type, binunionTEcontra: $o). 12.35/2.21 thf(decl_324, type, demorgan2a1: $o). 12.35/2.21 thf(decl_325, type, complementUnionInPowersetComplement: $o). 12.35/2.21 thf(decl_326, type, demorgan2a2: $o). 12.35/2.21 thf(decl_327, type, demorgan1a: $o). 12.35/2.21 thf(decl_328, type, demorgan1b: $o). 12.35/2.21 thf(decl_329, type, demorgan1: $o). 12.35/2.21 thf(decl_330, type, demorgan2a: $o). 12.35/2.21 thf(decl_331, type, demorgan2b2: $o). 12.35/2.21 thf(decl_332, type, demorgan2b: $o). 12.35/2.21 thf(decl_333, type, demorgan2: $o). 12.35/2.21 thf(decl_334, type, woz13rule0: $o). 12.35/2.21 thf(decl_335, type, woz13rule1: $o). 12.35/2.21 thf(decl_336, type, woz13rule2: $o). 12.35/2.21 thf(decl_337, type, woz13rule3: $o). 12.35/2.21 thf(decl_338, type, woz13rule4: $o). 12.35/2.21 thf(decl_339, type, woz1_1: $o). 12.35/2.21 thf(decl_340, type, woz1_2: $o). 12.35/2.21 thf(decl_341, type, woz1_3: $o). 12.35/2.21 thf(decl_342, type, woz1_4: $o). 12.35/2.21 thf(decl_343, type, woz1_5: $o). 12.35/2.21 thf(decl_344, type, breln1: $i > $i > $o). 12.35/2.21 thf(decl_345, type, breln1all2: $o). 12.35/2.21 thf(decl_346, type, breln1Set: $i > $i). 12.35/2.21 thf(decl_347, type, breln1SetBreln1: $o). 12.35/2.21 thf(decl_353, type, reflwellordering: $i > $i > $o). 12.35/2.21 thf(decl_354, type, choice2fnsingleton: $o). 12.35/2.21 thf(decl_355, type, setOfPairsIsBReln1: $o). 12.35/2.21 thf(decl_356, type, breln1all1: $o). 12.35/2.21 thf(decl_357, type, subbreln1: $o). 12.35/2.21 thf(decl_358, type, eqbreln1: $o). 12.35/2.21 thf(decl_359, type, breln1invset: $i > $i > $i). 12.35/2.21 thf(decl_360, type, breln1invprop: $o). 12.35/2.21 thf(decl_361, type, breln1invI: $o). 12.35/2.21 thf(decl_362, type, breln1invE: $o). 12.35/2.21 thf(decl_363, type, breln1compset: $i > $i > $i > $i). 12.35/2.21 thf(decl_364, type, breln1compprop: $o). 12.35/2.21 thf(decl_365, type, breln1compI: $o). 12.35/2.21 thf(decl_366, type, breln1compE: $o). 12.35/2.21 thf(decl_367, type, breln1compEex: $o). 12.35/2.21 thf(decl_368, type, breln1unionprop: $o). 12.35/2.21 thf(decl_369, type, breln1unionIL: $o). 12.35/2.21 thf(decl_370, type, breln1unionIR: $o). 12.35/2.21 thf(decl_371, type, breln1unionI: $o). 12.35/2.21 thf(decl_372, type, breln1unionE: $o). 12.35/2.21 thf(decl_373, type, breln1unionEcases: $o). 12.35/2.21 thf(decl_374, type, breln1unionCommutes: $o). 12.35/2.21 thf(decl_375, type, woz2Ex: $o). 12.35/2.21 thf(decl_376, type, woz2W: $o). 12.35/2.21 thf(decl_377, type, woz2A: $o). 12.35/2.21 thf(decl_378, type, woz2B: $o). 12.35/2.21 thf(decl_379, type, image1Ex: $o). 12.35/2.21 thf(decl_380, type, image1Ex1: $o). 12.35/2.21 thf(decl_381, type, image1: $i > ($i > $i) > $i). 12.35/2.21 thf(decl_382, type, image1Equiv: $o). 12.35/2.21 thf(decl_383, type, image1E: $o). 12.35/2.21 thf(decl_384, type, image1I: $o). 12.35/2.21 thf(decl_385, type, injective: $i > $i > $i > $o). 12.35/2.21 thf(decl_386, type, injFuncSet: $i > $i > $i). 12.35/2.21 thf(decl_387, type, injFuncInInjFuncSet: $o). 12.35/2.21 thf(decl_388, type, injFuncSetFuncIn: $o). 12.35/2.21 thf(decl_389, type, injFuncSetFuncInj: $o). 12.35/2.21 thf(decl_390, type, surjective: $i > $i > $i > $o). 12.35/2.21 thf(decl_391, type, surjFuncSet: $i > $i > $i). 12.35/2.21 thf(decl_392, type, surjFuncSetFuncIn: $o). 12.35/2.21 thf(decl_393, type, epred1_0: $o). 12.35/2.21 thf(decl_394, type, esk1_2: $i > $i > $i). 12.35/2.21 thf(decl_395, type, esk2_2: $i > $i > $i). 12.35/2.21 thf(decl_396, type, esk3_2: $i > $i > $i). 12.35/2.21 thf(decl_397, type, esk4_1: $i > $i). 12.35/2.21 thf(decl_398, type, esk5_2: ($i > $i > $o) > $i > $i). 12.35/2.21 thf(decl_399, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 12.35/2.21 thf(decl_400, type, esk7_2: ($i > $i > $o) > $i > $i). 12.35/2.21 thf(decl_401, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 12.35/2.21 thf(decl_402, type, esk9_1: $i > $i). 12.35/2.21 thf(decl_403, type, esk10_2: ($i > $o) > $i > $i). 12.35/2.21 thf(decl_404, type, esk11_2: ($i > $o) > $i > $i). 12.35/2.21 thf(decl_405, type, esk12_1: ($i > $o) > $i). 12.35/2.21 thf(decl_406, type, esk13_2: ($i > $o) > $i > $i). 12.35/2.21 thf(decl_407, type, esk14_1: ($i > $o) > $i). 12.35/2.21 thf(decl_408, type, esk15_2: $i > $i > $i). 12.35/2.21 thf(decl_409, type, esk16_2: $i > $i > $i). 12.35/2.21 thf(decl_410, type, esk17_1: $i > $i). 12.35/2.21 thf(decl_411, type, esk18_1: $i > $i). 12.35/2.21 thf(decl_412, type, esk19_1: $i > $i). 12.35/2.21 thf(decl_413, type, esk20_2: $i > $i > $i). 12.35/2.21 thf(decl_414, type, esk21_3: $i > $i > $o > $i). 12.35/2.21 thf(decl_415, type, esk22_2: ($i > $o) > $i > $i). 12.35/2.21 thf(decl_416, type, esk23_1: ($i > $o) > $i). 12.35/2.21 thf(decl_417, type, esk24_1: $i > $i). 12.35/2.21 thf(decl_418, type, esk25_2: $i > ($i > $o) > $i). 12.35/2.21 thf(decl_419, type, esk26_2: $i > ($i > $o) > $i). 12.35/2.21 thf(decl_420, type, esk27_2: $i > ($i > $o) > $i). 12.35/2.21 thf(decl_421, type, esk28_2: $i > ($i > $o) > $i). 12.35/2.21 thf(decl_422, type, esk29_2: $i > ($i > $o) > $i). 12.35/2.21 thf(decl_423, type, esk30_2: $i > ($i > $o) > $i). 12.35/2.21 thf(decl_424, type, esk31_2: ($i > $o) > $i > $i). 12.35/2.21 thf(decl_425, type, esk32_1: ($i > $o) > $i). 12.35/2.21 thf(decl_426, type, esk33_1: ($i > $o) > $i). 12.35/2.21 thf(decl_427, type, esk34_1: ($i > $o) > $i). 12.35/2.21 thf(decl_428, type, esk35_1: ($i > $o) > $i). 12.35/2.21 thf(decl_429, type, esk36_2: ($i > $o) > $i > $i). 12.35/2.21 thf(decl_430, type, esk37_1: ($i > $o) > $i). 12.35/2.21 thf(decl_431, type, esk38_2: ($i > $o) > $i > $i). 12.35/2.21 thf(decl_432, type, esk39_2: ($i > $o) > ($i > $o) > $i). 12.35/2.21 thf(decl_433, type, esk40_2: ($i > $o) > ($i > $o) > $i). 12.35/2.21 thf(decl_434, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 12.35/2.21 thf(decl_435, type, esk42_2: ($i > $o) > ($i > $o) > $i). 12.35/2.21 thf(decl_436, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 12.35/2.21 thf(decl_437, type, esk44_2: ($i > $o) > ($i > $o) > $i). 12.35/2.21 thf(decl_438, type, esk45_2: ($i > $o) > $i > $i). 12.35/2.21 thf(decl_439, type, esk46_2: ($i > $o) > ($i > $o) > $i). 12.35/2.21 thf(decl_440, type, esk47_2: ($i > $o) > ($i > $o) > $i). 12.35/2.21 thf(decl_441, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 12.35/2.21 thf(decl_442, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 12.35/2.21 thf(decl_443, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 12.35/2.21 thf(decl_444, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 12.35/2.21 thf(decl_445, type, esk52_2: $i > $i > $i). 12.35/2.21 thf(decl_446, type, esk53_2: $i > $i > $i). 12.35/2.21 thf(decl_447, type, esk54_2: $i > $i > $i). 12.35/2.21 thf(decl_448, type, esk55_3: $i > $i > $i > $i). 12.35/2.21 thf(decl_449, type, esk56_3: $i > $i > $i > $i). 12.35/2.21 thf(decl_450, type, esk57_2: $i > $i > $i). 12.35/2.21 thf(decl_451, type, esk58_2: $i > ($i > $o) > $i). 12.35/2.21 thf(decl_452, type, esk59_2: $i > ($i > $o) > $i). 12.35/2.21 thf(decl_453, type, esk60_2: $i > ($i > $o) > $i). 12.35/2.21 thf(decl_454, type, esk61_3: $i > ($i > $o) > $i > $i). 12.35/2.21 thf(decl_455, type, esk62_2: $i > ($i > $o) > $i). 12.35/2.21 thf(decl_456, type, esk63_2: $i > ($i > $o) > $i). 12.35/2.21 thf(decl_457, type, esk64_3: $i > $i > ($i > $i) > $i). 12.35/2.21 thf(decl_458, type, esk65_3: $i > $i > ($i > $i) > $i). 12.35/2.21 thf(decl_459, type, esk66_3: $i > $i > ($i > $i) > $i). 12.35/2.21 thf(decl_460, type, esk67_4: $i > $i > $i > ($i > $o) > $i). 12.35/2.21 thf(decl_461, type, esk68_4: $i > $i > $i > ($i > $o) > $i). 12.35/2.21 thf(decl_462, type, esk69_4: $i > $i > $i > ($i > $o) > $i). 12.35/2.21 thf(decl_463, type, esk70_4: $i > $i > $i > ($i > $o) > $i). 12.35/2.21 thf(decl_464, type, esk71_4: $i > $i > $i > $i > $i). 12.35/2.21 thf(decl_465, type, esk72_4: $i > $i > $i > $i > $i). 12.35/2.21 thf(decl_466, type, esk73_4: $i > $i > $i > $i > $i). 12.35/2.21 thf(decl_467, type, esk74_4: $i > $i > $i > $i > $i). 12.35/2.21 thf(decl_468, type, esk75_4: $i > $i > $i > $i > $i). 12.35/2.21 thf(decl_469, type, esk76_4: $i > $i > $i > $i > $i). 12.35/2.21 thf(decl_470, type, esk77_4: $i > $i > $i > $i > $i). 12.35/2.21 thf(decl_471, type, esk78_4: $i > $i > $i > $i > $i). 12.35/2.21 thf(decl_472, type, esk79_4: $i > $i > $i > $i > $i). 12.35/2.21 thf(decl_473, type, esk80_3: $i > $i > ($i > $i) > $i). 12.35/2.21 thf(decl_474, type, esk81_3: $i > $i > ($i > $i) > $i). 12.35/2.21 thf(decl_475, type, esk82_3: $i > $i > ($i > $i) > $i). 12.35/2.21 thf(decl_476, type, esk83_3: $i > $i > $i > $i). 12.35/2.21 thf(decl_477, type, esk84_3: $i > $i > $i > $i). 12.35/2.21 thf(decl_478, type, esk85_3: $i > $i > $i > $i). 12.35/2.21 thf(decl_479, type, esk86_3: $i > $i > $i > $i). 12.35/2.21 thf(decl_480, type, esk87_3: $i > $i > ($i > $o) > $i). 12.35/2.21 thf(decl_481, type, esk88_3: $i > $i > ($i > $o) > $i). 12.35/2.21 thf(decl_482, type, esk89_3: $i > $i > ($i > $i > $o) > $i). 12.35/2.21 thf(decl_483, type, esk90_3: $i > $i > ($i > $o) > $i). 12.35/2.21 thf(decl_484, type, esk91_3: $i > $i > ($i > $o) > $i). 12.35/2.21 thf(decl_485, type, esk92_3: $i > $i > $i > $i). 12.35/2.21 thf(decl_486, type, esk93_3: $i > $i > $i > $i). 12.35/2.21 thf(decl_487, type, esk94_3: $i > $i > $i > $i). 12.35/2.21 thf(decl_488, type, esk95_3: $i > $i > $i > $i). 12.35/2.21 thf(decl_489, type, esk96_3: $i > $i > $i > $i). 12.35/2.21 thf(decl_490, type, esk97_3: $i > $i > $i > $i). 12.35/2.21 thf(decl_491, type, esk98_5: $i > $i > $i > $i > $i > $i). 12.35/2.21 thf(decl_492, type, esk99_6: $i > $i > $i > $i > $i > $o > $i). 12.35/2.21 thf(decl_493, type, esk100_2: $i > ($i > $i) > $i). 12.35/2.21 thf(decl_494, type, esk101_3: $i > ($i > $i) > $i > $i). 12.35/2.21 thf(decl_495, type, esk102_2: $i > ($i > $i) > $i). 12.35/2.21 thf(decl_496, type, esk103_3: $i > ($i > $i) > $i > $i). 12.35/2.21 thf(decl_497, type, esk104_3: $i > ($i > $i) > $i > $i). 12.35/2.21 thf(decl_498, type, esk105_3: $i > ($i > $i) > $i > $i). 12.35/2.21 thf(decl_499, type, esk106_3: $i > ($i > $i) > $i > $i). 12.35/2.21 thf(decl_500, type, esk107_3: $i > ($i > $i) > $i > $i). 12.35/2.21 thf(decl_501, type, esk108_0: $i). 12.35/2.21 thf(decl_502, type, esk109_0: $i). 12.35/2.21 thf(decl_503, type, esk110_0: $i). 12.35/2.21 thf(decl_504, type, esk111_0: $i). 12.35/2.21 thf(decl_518, type, epred10_2: $i > $i > $i > $o). 12.35/2.21 thf(decl_520, type, esk118_4: $i > $i > $i > $i > $i). 12.35/2.21 thf(decl_521, type, esk119_3: $i > $i > $i > $i). 12.35/2.21 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', descr__Cong)). 12.35/2.21 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', exu)). 12.35/2.21 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', exuEu)). 12.35/2.21 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', exu__Cong)). 12.35/2.21 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', exuI1)). 12.35/2.21 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', nonempty)). 12.35/2.21 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', exuE2)). 12.35/2.21 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', exuE3e)). 12.35/2.21 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', replAx)). 12.35/2.21 thf(image1Ex1, axiom, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', image1Ex1)). 12.35/2.21 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.rKmjcAUqsY/Vampire---4.8_25226', exuE3u)). 12.35/2.21 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.rKmjcAUqsY/Vampire---4.8_25226', exuI2)). 12.35/2.21 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', exuI3)). 12.35/2.21 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', nonemptyI)). 12.35/2.21 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', exuE1)). 12.35/2.21 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', descrp)). 12.35/2.21 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', singletonprop)). 12.35/2.21 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', ex1E1)). 12.35/2.21 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.rKmjcAUqsY/Vampire---4.8_25226', ex1I)). 12.35/2.21 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', dsetconstr__Cong)). 12.35/2.21 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', kfstsingleton)). 12.35/2.21 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.rKmjcAUqsY/Vampire---4.8_25226', emptyE1)). 12.35/2.21 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', nonemptyImpWitness)). 12.35/2.21 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', nonemptyI1)). 12.35/2.21 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', dsetconstrER)). 12.35/2.21 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', dpsetconstrSub)). 12.35/2.21 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', dsetconstrEL)). 12.35/2.21 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', dsetconstrI)). 12.35/2.21 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', dpsetconstrER)). 12.35/2.21 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', lam2p)). 12.35/2.21 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.rKmjcAUqsY/Vampire---4.8_25226', ex1E2)). 12.35/2.21 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.rKmjcAUqsY/Vampire---4.8_25226', beta1)). 12.35/2.21 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.rKmjcAUqsY/Vampire---4.8_25226', lam2lamEq)). 12.35/2.21 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', iffalseProp1)). 12.35/2.21 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.rKmjcAUqsY/Vampire---4.8_25226', iffalseProp2)). 12.35/2.21 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', iftrueProp2)). 12.35/2.21 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$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.rKmjcAUqsY/Vampire---4.8_25226', ifSingleton)). 12.35/2.21 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', iftrueProp1)). 12.35/2.21 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', eta2)). 12.35/2.21 thf(beta2, axiom, ((beta2)<=>![X4:$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.rKmjcAUqsY/Vampire---4.8_25226', beta2)). 12.35/2.21 thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setOfPairsIsBReln1)). 12.35/2.21 thf(image1E, axiom, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X60 @ X3))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', image1E)). 12.35/2.21 thf(image1I, axiom, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X61 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', image1I)). 12.35/2.21 thf(surjective, axiom, ((surjective)=(^[X4:$i, X5:$i, X29:$i]:(![X2:$i]:(((in @ X2 @ X5)=>?[X3:$i]:(((in @ X3 @ X4)&((ap @ X4 @ X5 @ X29 @ X3)=(X2))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', surjective)). 12.35/2.21 thf(image1Equiv, axiom, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X59 @ X3))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', image1Equiv)). 12.35/2.21 thf(choice2fnsingleton, axiom, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:(((X52 @ X2 @ X3)&![X14:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ X3 @ X14) @ X33))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', choice2fnsingleton)). 12.35/2.21 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', eta1)). 12.35/2.21 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', lamp)). 12.35/2.21 thf(lamProp, axiom, ((lamProp)<=>![X4:$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.rKmjcAUqsY/Vampire---4.8_25226', lamProp)). 12.35/2.21 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', apProp)). 12.35/2.21 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.rKmjcAUqsY/Vampire---4.8_25226', funcImageSingleton)). 12.35/2.21 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:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', dpsetconstrEL2)). 12.35/2.21 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', dpsetconstrEL1)). 12.35/2.21 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', dpsetconstrERa)). 12.35/2.21 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setOfPairsIsBReln)). 12.35/2.21 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', dpsetconstrI)). 12.35/2.21 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', ksndsingleton)). 12.35/2.21 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', ex1I2)). 12.35/2.21 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', sepSubset)). 12.35/2.21 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', sepInPowerset)). 12.35/2.21 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setoftrueEq)). 12.35/2.21 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', nonemptyE1)). 12.35/2.21 thf(setbeta, axiom, ((setbeta)<=>![X4:$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.rKmjcAUqsY/Vampire---4.8_25226', setbeta)). 12.35/2.21 thf(surjFuncSetFuncSurj, conjecture, ((((setadjoinAx)=>((powersetAx)=>(((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>(((foundationAx)=>(((descrp)=>(((((exuE1)=>(((emptysetE)=>((emptysetimpfalse)=>(((((((setbeta)=>((nonemptyE1)=>((nonemptyI)=>(((((setadjoinIR)=>(((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((((powersetE)=>((((((((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>(((((vacuousDall)=>((quantDeMorgan1)=>(((((((notdexE)=>((notdallE)=>(((exuI3)=>((exuI2)=>((((exuE3u)=>(((emptyset__Cong)=>(((powerset__Cong)=>(((omega__Cong)=>((((((((((subsetE)=>((subsetE2)=>((notsubsetI)=>(((notequalI2)=>((subsetRefl)=>((((setadjoinSub2)=>((subset2powerset)=>(((subsetemptysetimpeq)=>(((powersetE1)=>((((((binunionIL)=>(((binunionIR)=>((binunionEcases)=>(((binunionLsub)=>(((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>(((binintersectSubset3)=>((((binintersectRsub)=>((binintersectSubset4)=>(((bs114d)=>((((setminusER)=>((setminusSubset2)=>(((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>(((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((((((((singletoninpowerset)=>((((upairsubunion)=>(((ubforcartprodlem1)=>((((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>(((setunionsingleton2)=>(((singletonprop)=>((ex1E1)=>((ex1I)=>(((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>(((((setukpairinjL2)=>(((setukpairinjR11)=>(((setukpairinjR1)=>((upairequniteq)=>((((((kpairsurjEq)=>((cartprodsndin)=>(((cartprodpairmemER)=>((cartprodmempaircEq)=>(((cartprodsndpairEq)=>((((dpsetconstrSub)=>((((((dpsetconstrER)=>((((((((((lam2p)=>((((ex1E2)=>((funcGraphProp1)=>((((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>(((ap2apEq1)=>((ap2apEq2)=>((beta1)=>(((lam2lamEq)=>((((iffalseProp1)=>((iffalseProp2)=>(((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((((binintersectT_lem)=>((((setminusT_lem)=>(((setextT)=>((((powersetTE1)=>((complementTI1)=>(((binintersectTELcontra)=>((((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>(((doubleComplementSub2)=>(((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((((complementTcontraSubset)=>((binunionTILcontra)=>(((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((((binunionTE)=>(((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((((demorgan2a)=>((demorgan2b2)=>((((woz13rule0)=>((((((woz1_1)=>(((woz1_3)=>(((woz1_5)=>((breln1all2)=>((breln1SetBreln1)=>(((setOfPairsIsBReln1)=>((((eqbreln1)=>((breln1invprop)=>(((breln1invE)=>((breln1compprop)=>((breln1compI)=>((breln1compE)=>(((((breln1unionIR)=>((((breln1unionEcases)=>((((woz2W)=>(((woz2B)=>(((((image1E)=>((image1I)=>(((injFuncSetFuncIn)=>(((surjFuncSetFuncIn)=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X2 @ X3))=>(surjective @ X2 @ X3 @ X29))))<=(injFuncSetFuncInj)))<=(injFuncInInjFuncSet))))<=(image1Equiv))<=(image1Ex1))<=(image1Ex)))<=(woz2A)))<=(woz2Ex))<=(breln1unionCommutes)))<=(breln1unionE))<=(breln1unionI)))<=(breln1unionIL))<=(breln1unionprop))<=(breln1compEex))))))<=(breln1invI))))<=(subbreln1))<=(breln1all1)))<=(choice2fnsingleton)))))<=(woz1_4)))<=(woz1_2)))<=(woz13rule4))<=(woz13rule3))<=(woz13rule2))<=(woz13rule1)))<=(demorgan2))<=(demorgan2b))))<=(demorgan1))<=(demorgan1b))))))<=(binunionTEcontra)))<=(inComplementUnionImpInComplement1))<=(inComplementUnionImpNotIn1))))))<=(binunionTIRcontra))))<=(contraSubsetComplement))<=(complementInPowersetComplementIntersect)))))<=(doubleComplementEq)))<=(doubleComplementSub1)))))))<=(contrasubsetT))<=(binintersectTERcontra)))<=(complementTE1))))<=(powersetTI1))<=(subsetTI)))<=(complementT_lem)))<=(powersetT_lem))<=(binunionT_lem)))<=(iftrueorfalse))<=(iffalse)))))))<=(iftrueProp1))))<=(eta2))<=(beta2)))<=(eta1)))))<=(funcext2)))))))<=(funcGraphProp2))<=(funcGraphProp3))))<=(brelnall2))<=(brelnall1)))<=(lamp))<=(lamProp))<=(funcinfuncset))<=(ap2p))<=(infuncsetfunc))<=(app))<=(apProp))<=(funcImageSingleton)))<=(dpsetconstrEL2))<=(dpsetconstrEL1))<=(dpsetconstrERa))<=(setOfPairsIsBReln)))<=(dpsetconstrI))<=(cartprodpairsurjEq)))<=(cartprodfstpairEq))))<=(cartprodpairmemEL))))<=(ksndpairEq))<=(ksndsingleton))<=(setukpairinjR))<=(setukpairinjR2))))<=(setukpairinjR12)))<=(setukpairinjL)))<=(cartprodfstin))<=(kfstpairEq))<=(theprop)))))<=(ex1I2)))))<=(setunionsingleton)))<=(setunionsingleton1))))))<=(ubforcartprodlem3))<=(ubforcartprodlem2)))<=(upairinpowunion)))<=(upairset2E))<=(singletoninpowunion)))<=(singletonsubset))<=(kpairp))<=(kpairiskpair))<=(setukpairIR))<=(setukpairIL))<=(secondinupair)))))<=(symdiffI1))))))))<=(setminusERneg))))<=(setminusEL))<=(setminusI)))<=(binintersectSubset1))))<=(disjointsetsI1))<=(binintersectER)))<=(binintersectSubset2))))))<=(binunionRsub)))<=(binunionE))))<=(upairset2IR)))<=(sepSubset))<=(sepInPowerset))<=(powersetsubset))<=(inPowerset)))<=(powersetI1)))<=(setextsub))))<=(setadjoinSub))<=(subsetTrans))))<=(notequalI1)))))<=(emptysetsubset))<=(subsetI2))<=(eqimpsubset1))<=(eqimpsubset2))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong))<=(exuEu)))<=(setunion__Cong)))<=(setadjoin__Cong)))<=(exu__Cong)))<=(in__Cong))<=(inCongP))))<=(exuI1))))<=(prop2set2propI))<=(prop2setI))<=(quantDeMorgan4))<=(quantDeMorgan3))<=(quantDeMorgan2))))<=(emptyE1))<=(upairsetIR))<=(upairsetIL))))))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU))<=(setunionE))<=(setunionI)))<=(emptyInPowerset))<=(emptyinPowerset)))))<=(setadjoinE)))<=(emptyinunitempty))<=(setadjoinIL))<=(nonemptyI1)))))<=(noeltsimpempty))<=(emptyI))<=(setext))<=(exuE3e))<=(notinemptyset))))<=(prop2setE)))<=(dsetconstrER))<=(dsetconstrEL))<=(dsetconstrI)))<=(wellorderingAx)))<=(replAx)))))<=(setunionAx))))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', surjFuncSetFuncSurj)). 12.35/2.21 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', cartprodmempair1)). 12.35/2.21 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', quantDeMorgan2)). 12.35/2.21 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setextAx)). 12.35/2.21 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', subsetTrans)). 12.35/2.21 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', cartprodpairin)). 12.35/2.21 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', notequalI1)). 12.35/2.21 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', emptysetsubset)). 12.35/2.21 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', subsetI2)). 12.35/2.21 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', eqimpsubset1)). 12.35/2.21 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', eqimpsubset2)). 12.35/2.21 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', subsetI1)). 12.35/2.21 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', singletonsuniq)). 12.35/2.21 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setunion__Cong)). 12.35/2.21 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.rKmjcAUqsY/Vampire---4.8_25226', setadjoin__Cong)). 12.35/2.21 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setukpairinjL1)). 12.35/2.21 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', in__Cong)). 12.35/2.21 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', inCongP)). 12.35/2.21 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', prop2set2propI)). 12.35/2.21 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', prop2setI)). 12.35/2.21 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setukpairinjL2)). 12.35/2.21 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', quantDeMorgan4)). 12.35/2.21 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', quantDeMorgan3)). 12.35/2.21 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', subbreln)). 12.35/2.21 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setukpairinjR11)). 12.35/2.21 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', upairsetIR)). 12.35/2.21 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', upairsetIL)). 12.35/2.21 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', uniqinunit)). 12.35/2.21 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setukpairinjR1)). 12.35/2.21 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', upairequniteq)). 12.35/2.21 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', subPowSU)). 12.35/2.21 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.rKmjcAUqsY/Vampire---4.8_25226', setunionE)). 12.35/2.21 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setunionI)). 12.35/2.21 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', kpairsurjEq)). 12.35/2.21 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', emptyInPowerset)). 12.35/2.21 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', emptyinPowerset)). 12.35/2.21 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', cartprodsndin)). 12.35/2.21 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setadjoinE)). 12.35/2.21 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', emptyinunitempty)). 12.35/2.21 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setadjoinIL)). 12.35/2.21 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', cartprodpairmemER)). 12.35/2.21 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', noeltsimpempty)). 12.35/2.21 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', cartprodmempaircEq)). 12.35/2.21 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', emptyI)). 12.35/2.21 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setext)). 12.35/2.21 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', cartprodsndpairEq)). 12.35/2.21 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', notinemptyset)). 12.35/2.21 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', prop2setE)). 12.35/2.21 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', cartprodmempair)). 12.35/2.21 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.rKmjcAUqsY/Vampire---4.8_25226', wellorderingAx)). 12.35/2.21 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setunionAx)). 12.35/2.21 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', emptysetAx)). 12.35/2.21 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.rKmjcAUqsY/Vampire---4.8_25226', funcGraphProp1)). 12.35/2.21 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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', funcextLem)). 12.35/2.21 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.rKmjcAUqsY/Vampire---4.8_25226', funcGraphProp4)). 12.35/2.21 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', inIntersectImpInUnion)). 12.35/2.21 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', eqbreln)). 12.35/2.21 thf(funcext, axiom, ((funcext)<=>![X4:$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.rKmjcAUqsY/Vampire---4.8_25226', funcext)). 12.35/2.21 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.rKmjcAUqsY/Vampire---4.8_25226', ap2apEq1)). 12.35/2.21 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.rKmjcAUqsY/Vampire---4.8_25226', ap2apEq2)). 12.35/2.21 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setunionE2)). 12.35/2.21 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', ifp)). 12.35/2.21 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', theeq)). 12.35/2.21 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', iftrue)). 12.35/2.21 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$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.rKmjcAUqsY/Vampire---4.8_25226', binintersectT_lem)). 12.35/2.21 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setminusT_lem)). 12.35/2.21 thf(setextT, axiom, ((setextT)<=>![X4:$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.rKmjcAUqsY/Vampire---4.8_25226', setextT)). 12.35/2.21 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.rKmjcAUqsY/Vampire---4.8_25226', powersetTE1)). 12.35/2.21 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setunionsingleton2)). 12.35/2.21 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$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.rKmjcAUqsY/Vampire---4.8_25226', complementTI1)). 12.35/2.21 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.rKmjcAUqsY/Vampire---4.8_25226', binintersectTELcontra)). 12.35/2.21 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.rKmjcAUqsY/Vampire---4.8_25226', contrasubsetT1)). 12.35/2.21 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', contrasubsetT2)). 12.35/2.21 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', contrasubsetT3)). 12.35/2.21 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', doubleComplementI1)). 12.35/2.21 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', doubleComplementE1)). 12.35/2.21 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', doubleComplementSub2)). 12.35/2.21 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', complementTnotintersectT)). 12.35/2.21 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', complementImpComplementIntersect)). 12.35/2.21 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', complementSubsetComplementIntersect)). 12.35/2.21 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', complementTcontraSubset)). 12.35/2.21 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binunionTILcontra)). 12.35/2.21 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binunionT_lem)). 12.35/2.21 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', iftrueorfalse)). 12.35/2.21 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', iffalse)). 12.35/2.21 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', inIntersectImpInUnion2)). 12.35/2.21 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', inIntersectImpInIntersectUnions)). 12.35/2.21 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', intersectInPowersetIntersectUnions)). 12.35/2.21 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binunionTE)). 12.35/2.21 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', demorgan2a1)). 12.35/2.21 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', complementUnionInPowersetComplement)). 12.35/2.21 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', demorgan2a2)). 12.35/2.21 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', demorgan1a)). 12.35/2.21 thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', demorgan2a)). 12.35/2.21 thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', demorgan2b2)). 12.35/2.21 thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', woz13rule0)). 12.35/2.21 thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', woz1_1)). 12.35/2.21 thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', woz1_3)). 12.35/2.21 thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', woz1_5)). 12.35/2.21 thf(breln1all2, axiom, ((breln1all2)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', breln1all2)). 12.35/2.21 thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', breln1SetBreln1)). 12.35/2.21 thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', eqbreln1)). 12.35/2.21 thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', breln1invprop)). 12.35/2.21 thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', breln1invE)). 12.35/2.21 thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', breln1compprop)). 12.35/2.21 thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', breln1compI)). 12.35/2.21 thf(breln1compE, axiom, ((breln1compE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35))))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', breln1compE)). 12.35/2.21 thf(breln1unionIR, axiom, ((breln1unionIR)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', breln1unionIR)). 12.35/2.21 thf(breln1unionEcases, axiom, ((breln1unionEcases)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>![X55:$o]:((((in @ (kpair @ X2 @ X3) @ X33)=>(X55))=>(((in @ (kpair @ X2 @ X3) @ X35)=>(X55))=>(X55)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', breln1unionEcases)). 12.35/2.21 thf(woz2W, axiom, ((woz2W)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((breln1invset @ X4 @ (breln1compset @ X4 @ X33 @ X35))=(breln1compset @ X4 @ (breln1invset @ X4 @ X35) @ (breln1invset @ X4 @ X33)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', woz2W)). 12.35/2.21 thf(woz2B, axiom, ((woz2B)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X35))) @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X33)))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', woz2B)). 12.35/2.21 thf(injFuncSetFuncIn, axiom, ((injFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', injFuncSetFuncIn)). 12.35/2.21 thf(surjFuncSetFuncIn, axiom, ((surjFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', surjFuncSetFuncIn)). 12.35/2.21 thf(injFuncSetFuncInj, axiom, ((injFuncSetFuncInj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X2 @ X3))=>(injective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', injFuncSetFuncInj)). 12.35/2.21 thf(injFuncInInjFuncSet, axiom, ((injFuncInInjFuncSet)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((injective @ X4 @ X5 @ X29)=>(in @ X29 @ (injFuncSet @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', injFuncInInjFuncSet)). 12.35/2.21 thf(image1Ex, axiom, ((image1Ex)<=>![X4:$i, X57:$i > $i]:(?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X57 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', image1Ex)). 12.35/2.21 thf(woz2A, axiom, ((woz2A)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1compset @ X4 @ X33 @ X56) @ (breln1compset @ X4 @ X35 @ X56)))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', woz2A)). 12.35/2.21 thf(woz2Ex, axiom, ((woz2Ex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>((X33)=(breln1invset @ X4 @ (breln1invset @ X4 @ X33)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', woz2Ex)). 12.35/2.21 thf(breln1unionCommutes, axiom, ((breln1unionCommutes)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((binunion @ X33 @ X35)=(binunion @ X35 @ X33))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', breln1unionCommutes)). 12.35/2.21 thf(breln1unionE, axiom, ((breln1unionE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', breln1unionE)). 12.35/2.21 thf(breln1unionI, axiom, ((breln1unionI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35))=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', breln1unionI)). 12.35/2.21 thf(breln1unionIL, axiom, ((breln1unionIL)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', breln1unionIL)). 12.35/2.21 thf(breln1unionprop, axiom, ((breln1unionprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', breln1unionprop)). 12.35/2.21 thf(breln1compEex, axiom, ((breln1compEex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>![X54:$o]:((![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(X54)))))=>(X54))))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', breln1compEex)). 12.35/2.21 thf(breln1invI, axiom, ((breln1invI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', breln1invI)). 12.35/2.21 thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', subbreln1)). 12.35/2.21 thf(breln1all1, axiom, ((breln1all1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', breln1all1)). 12.35/2.21 thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', woz1_4)). 12.35/2.21 thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', woz1_2)). 12.35/2.21 thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', woz13rule4)). 12.35/2.21 thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', woz13rule3)). 12.35/2.21 thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', woz13rule2)). 12.35/2.21 thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', woz13rule1)). 12.35/2.21 thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', demorgan2)). 12.35/2.21 thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', demorgan2b)). 12.35/2.21 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', demorgan1)). 12.35/2.21 thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', demorgan1b)). 12.35/2.21 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binunionTEcontra)). 12.35/2.21 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', inComplementUnionImpInComplement1)). 12.35/2.21 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', inComplementUnionImpNotIn1)). 12.35/2.21 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binunionTIRcontra)). 12.35/2.21 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', contraSubsetComplement)). 12.35/2.21 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', complementInPowersetComplementIntersect)). 12.35/2.21 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', doubleComplementEq)). 12.35/2.21 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', doubleComplementSub1)). 12.35/2.21 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.rKmjcAUqsY/Vampire---4.8_25226', contrasubsetT)). 12.35/2.21 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.rKmjcAUqsY/Vampire---4.8_25226', binintersectTERcontra)). 12.35/2.21 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', complementTE1)). 12.35/2.21 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', powersetTI1)). 12.35/2.21 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', subsetTI)). 12.35/2.21 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', complementT_lem)). 12.35/2.21 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', powersetT_lem)). 12.35/2.21 thf(funcext2, axiom, ((funcext2)<=>![X4:$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.rKmjcAUqsY/Vampire---4.8_25226', funcext2)). 12.35/2.21 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', funcGraphProp2)). 12.35/2.21 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', funcGraphProp3)). 12.35/2.21 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$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.rKmjcAUqsY/Vampire---4.8_25226', brelnall2)). 12.35/2.21 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.rKmjcAUqsY/Vampire---4.8_25226', brelnall1)). 12.35/2.21 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', funcinfuncset)). 12.35/2.21 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', ap2p)). 12.35/2.21 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', infuncsetfunc)). 12.35/2.21 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.rKmjcAUqsY/Vampire---4.8_25226', app)). 12.35/2.21 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', cartprodpairsurjEq)). 12.35/2.21 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', cartprodfstpairEq)). 12.35/2.21 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', cartprodpairmemEL)). 12.35/2.21 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', ksndpairEq)). 12.35/2.21 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setukpairinjR)). 12.35/2.21 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setukpairinjR2)). 12.35/2.21 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setukpairinjR12)). 12.35/2.21 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setukpairinjL)). 12.35/2.21 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', cartprodfstin)). 12.35/2.21 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', kfstpairEq)). 12.35/2.21 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', theprop)). 12.35/2.21 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setunionsingleton)). 12.35/2.21 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setunionsingleton1)). 12.35/2.21 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', ubforcartprodlem3)). 12.35/2.21 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', ubforcartprodlem2)). 12.35/2.21 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', upairinpowunion)). 12.35/2.21 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', upairset2E)). 12.35/2.21 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', singletoninpowunion)). 12.35/2.21 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', singletonsubset)). 12.35/2.21 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', kpairp)). 12.35/2.21 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', kpairiskpair)). 12.35/2.21 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setukpairIR)). 12.35/2.21 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setukpairIL)). 12.35/2.21 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', secondinupair)). 12.35/2.21 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', symdiffI1)). 12.35/2.21 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setminusERneg)). 12.35/2.21 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setminusEL)). 12.35/2.21 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setminusI)). 12.35/2.21 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binintersectSubset1)). 12.35/2.21 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', disjointsetsI1)). 12.35/2.21 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binintersectER)). 12.35/2.21 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binintersectSubset2)). 12.35/2.21 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binunionRsub)). 12.35/2.21 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binunionE)). 12.35/2.21 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', upairset2IR)). 12.35/2.21 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', powersetsubset)). 12.35/2.21 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', inPowerset)). 12.35/2.21 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', powersetI1)). 12.35/2.21 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setextsub)). 12.35/2.21 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setadjoinSub)). 12.35/2.21 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', ubforcartprodlem1)). 12.35/2.21 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', upairsubunion)). 12.35/2.21 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', singletoninpowerset)). 12.35/2.21 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', symdiffIneg2)). 12.35/2.21 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', symdiffIneg1)). 12.35/2.21 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', symdiffI2)). 12.35/2.21 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.rKmjcAUqsY/Vampire---4.8_25226', symdiffE)). 12.35/2.21 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setminusSubset1)). 12.35/2.21 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setminusLsub)). 12.35/2.21 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setminusIRneg)). 12.35/2.21 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setminusILneg)). 12.35/2.21 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setminusELneg)). 12.35/2.21 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setminusSubset2)). 12.35/2.21 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setminusER)). 12.35/2.21 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', bs114d)). 12.35/2.21 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binintersectSubset4)). 12.35/2.21 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binintersectRsub)). 12.35/2.21 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binintersectSubset3)). 12.35/2.21 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binintersectLsub)). 12.35/2.21 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binintersectEL)). 12.35/2.21 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binintersectSubset5)). 12.35/2.21 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binintersectI)). 12.35/2.21 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binunionLsub)). 12.35/2.21 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.rKmjcAUqsY/Vampire---4.8_25226', binunionEcases)). 12.35/2.21 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binunionIR)). 12.35/2.21 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', binunionIL)). 12.35/2.21 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', powersetE1)). 12.35/2.21 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', subsetemptysetimpeq)). 12.35/2.21 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', subset2powerset)). 12.35/2.21 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setadjoinSub2)). 12.35/2.21 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', subsetRefl)). 12.35/2.21 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', notequalI2)). 12.35/2.21 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', notsubsetI)). 12.35/2.21 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', subsetE2)). 12.35/2.21 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', subsetE)). 12.35/2.21 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', omega__Cong)). 12.35/2.21 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', powerset__Cong)). 12.35/2.21 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', emptyset__Cong)). 12.35/2.21 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', notdallE)). 12.35/2.21 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', notdexE)). 12.35/2.21 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', quantDeMorgan1)). 12.35/2.21 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', vacuousDall)). 12.35/2.21 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', upairsetE)). 12.35/2.21 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', singletonsswitch)). 12.35/2.21 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', eqinunit)). 12.35/2.21 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', notinsingleton)). 12.35/2.21 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', powersetE)). 12.35/2.21 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', powersetI)). 12.35/2.21 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setadjoinOr)). 12.35/2.21 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setadjoinIR)). 12.35/2.21 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', emptysetimpfalse)). 12.35/2.21 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', emptysetE)). 12.35/2.21 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', foundationAx)). 12.35/2.21 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.rKmjcAUqsY/Vampire---4.8_25226', omegaIndAx)). 12.35/2.21 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', omegaSAx)). 12.35/2.21 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', omega0Ax)). 12.35/2.21 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', powersetAx)). 12.35/2.21 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', setadjoinAx)). 12.35/2.21 thf(surjFuncSet, axiom, ((surjFuncSet)=(^[X4:$i, X5:$i]:(dsetconstr @ (funcSet @ X4 @ X5) @ (^[X29:$i]:((surjective @ X4 @ X5 @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.rKmjcAUqsY/Vampire---4.8_25226', surjFuncSet)). 12.35/2.21 thf(c_0_323, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 12.35/2.21 thf(c_0_324, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 12.35/2.21 thf(c_0_325, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 12.35/2.21 thf(c_0_326, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 12.35/2.21 thf(c_0_327, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 12.35/2.21 thf(c_0_328, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 12.35/2.21 thf(c_0_329, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 12.35/2.21 thf(c_0_330, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 12.35/2.21 thf(c_0_331, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 12.35/2.21 thf(c_0_332, plain, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[Z0/* 6 */:$i]:(![X2:$i]:(((in @ X2 @ Z0)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3))))))))))), inference(fof_simplification,[status(thm)],[image1Ex1])). 12.35/2.21 thf(c_0_333, 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])). 12.35/2.21 thf(c_0_334, 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])). 12.35/2.21 thf(c_0_335, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 12.35/2.21 thf(c_0_336, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 12.35/2.21 thf(c_0_337, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 12.35/2.21 thf(c_0_338, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 12.35/2.21 thf(c_0_339, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 12.35/2.21 thf(c_0_340, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 12.35/2.21 thf(c_0_341, plain, ((ex1I)<=>![X4:$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])). 12.35/2.21 thf(c_0_342, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 12.35/2.21 thf(c_0_343, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1139:$i]:((((X1 @ X1139))&![X1140:$i]:((((X1 @ X1140))=>((X1139)=(X1140)))))))=>((?[X1141:$i]:((((X17 @ X1141))&![X1142:$i]:((((X17 @ X1142))=>((X1141)=(X1142)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_323, c_0_324])). 12.35/2.21 thf(c_0_344, plain, ((exuEu)=(![X1:$i > $o]:(((?[X1137:$i]:((((X1 @ X1137))&![X1138:$i]:((((X1 @ X1138))=>((X1137)=(X1138)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_325, c_0_324])). 12.35/2.21 thf(c_0_345, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1133:$i]:((((X1 @ X1133))&![X1134:$i]:((((X1 @ X1134))=>((X1133)=(X1134)))))))<=>(?[X1135:$i]:((((X17 @ X1135))&![X1136:$i]:((((X17 @ X1136))=>((X1135)=(X1136)))))))))))), inference(apply_def,[status(thm)],[c_0_326, c_0_324])). 12.35/2.21 thf(c_0_346, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 12.35/2.21 thf(c_0_347, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X1125:$i]:((((X1 @ X1125))&![X1126:$i]:((((X1 @ X1126))=>((X1125)=(X1126))))))))))), inference(apply_def,[status(thm)],[c_0_327, c_0_324])). 12.35/2.21 thf(c_0_348, plain, ((emptyE1)<=>![X4:$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])). 12.35/2.21 thf(c_0_349, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_328])). 12.35/2.21 thf(c_0_350, plain, ((exuE2)=(![X1:$i > $o]:(((?[X1123:$i]:((((X1 @ X1123))&![X1124:$i]:((((X1 @ X1124))=>((X1123)=(X1124)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_329, c_0_324])). 12.35/2.21 thf(c_0_351, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_328])). 12.35/2.21 thf(c_0_352, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X1121:$i]:((((X1 @ X1121))&![X1122:$i]:((((X1 @ X1122))=>((X1121)=(X1122)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_330, c_0_324])). 12.35/2.21 thf(c_0_353, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 12.35/2.21 thf(c_0_354, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 12.35/2.21 thf(c_0_355, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 12.35/2.21 thf(c_0_356, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 12.35/2.21 thf(c_0_357, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 12.35/2.21 thf(c_0_358, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X1115:$i]:((((X6 @ X2 @ X1115))&![X1116:$i]:((((X6 @ X2 @ X1116))=>((X1115)=(X1116)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_331, c_0_324])). 12.35/2.21 thf(c_0_359, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 12.35/2.21 thf(c_0_360, plain, ((ex1E2)<=>![X4:$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])). 12.35/2.21 thf(c_0_361, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])). 12.35/2.21 thf(c_0_362, 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])). 12.35/2.21 thf(c_0_363, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 12.35/2.21 thf(c_0_364, plain, ((iffalseProp2)<=>![X4:$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])). 12.35/2.21 thf(c_0_365, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])). 12.35/2.21 thf(c_0_366, plain, ((ifSingleton)<=>![X4:$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])). 12.35/2.21 thf(c_0_367, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 12.35/2.21 thf(c_0_368, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])). 12.35/2.21 thf(c_0_369, plain, ((beta2)<=>![X4:$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])). 12.35/2.21 thf(c_0_370, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])). 12.35/2.21 thf(c_0_371, plain, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X60 @ Z0))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), inference(fof_simplification,[status(thm)],[image1E])). 12.35/2.21 thf(c_0_372, plain, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X61 @ Z0))))))), inference(fof_simplification,[status(thm)],[image1I])). 12.35/2.21 thf(c_0_373, plain, ((surjective)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:(![X2:$i]:(((in @ X2 @ Z1)=>?[X3:$i]:(((in @ X3 @ Z0)&((ap @ Z0 @ Z1 @ Z2 @ X3)=(X2))))))))), inference(fof_simplification,[status(thm)],[surjective])). 12.35/2.21 thf(c_0_374, plain, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X59 @ Z0))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), inference(fof_simplification,[status(thm)],[image1Equiv])). 12.35/2.21 thf(c_0_375, plain, ((image1Ex1)=(![X4:$i, X58:$i > $i]:((?[X1143:$i]:(((![X2:$i]:(((in @ X2 @ X1143)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3)))))))&![X1144:$i]:(((![X2:$i]:(((in @ X2 @ X1144)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3)))))))=>((X1143)=(X1144)))))))))), inference(apply_def,[status(thm)],[c_0_332, c_0_324])). 12.35/2.21 thf(c_0_376, plain, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 8 */:$i]:(((X52 @ X2 @ Z0)&![X14:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ Z0 @ X14) @ X33))))))))))))))))), inference(fof_simplification,[status(thm)],[choice2fnsingleton])). 12.35/2.21 thf(c_0_377, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])). 12.35/2.21 thf(c_0_378, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 12.35/2.21 thf(c_0_379, plain, ((lamProp)<=>![X4:$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])). 12.35/2.21 thf(c_0_380, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 12.35/2.21 thf(c_0_381, plain, ((funcImageSingleton)<=>![X4:$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])). 12.35/2.21 thf(c_0_382, 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:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 12.35/2.21 thf(c_0_383, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 12.35/2.21 thf(c_0_384, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 12.35/2.21 thf(c_0_385, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 12.35/2.21 thf(c_0_386, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 12.35/2.21 thf(c_0_387, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 12.35/2.21 thf(c_0_388, plain, ((ex1I2)<=>![X4:$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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 12.35/2.21 thf(c_0_389, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 12.35/2.21 thf(c_0_390, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 12.35/2.21 thf(c_0_391, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X1131:$i]:((((X1 @ X1131))&![X1132:$i]:((((X1 @ X1132))=>((X1131)=(X1132)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_333, c_0_324])). 12.35/2.21 thf(c_0_392, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X1129:$i]:((((X1 @ X1129))&![X1130:$i]:((((X1 @ X1130))=>((X1129)=(X1130))))))))))), inference(apply_def,[status(thm)],[c_0_334, c_0_324])). 12.35/2.21 thf(c_0_393, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X1127:$i]:((((X1 @ X1127))&![X1128:$i]:((((X1 @ X1128))=>((X1127)=(X1128)))))))))))), inference(apply_def,[status(thm)],[c_0_335, c_0_324])). 12.35/2.21 thf(c_0_394, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 12.35/2.21 thf(c_0_395, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_336, c_0_328])). 12.35/2.21 thf(c_0_396, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_328])). 12.35/2.21 thf(c_0_397, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 12.35/2.21 thf(c_0_398, plain, ((exuE1)=(![X1:$i > $o]:(((?[X1119:$i]:((((X1 @ X1119))&![X1120:$i]:((((X1 @ X1120))=>((X1119)=(X1120)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_337, c_0_324])). 12.35/2.21 thf(c_0_399, plain, ((descrp)=(![X1:$i > $o]:(((?[X1117:$i]:((((X1 @ X1117))&![X1118:$i]:((((X1 @ X1118))=>((X1117)=(X1118)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_338, c_0_324])). 12.35/2.21 thf(c_0_400, plain, ((epred1_0)<=>![X2198:$i]:(?[X2199:$i]:((((![X2200:$i]:(((in @ X2200 @ X2199)=>![X2201:$i]:(((in @ X2201 @ X2200)=>(in @ X2201 @ X2198)))))&![X2202:$i, X2203:$i]:((((in @ X2202 @ X2198)&(in @ X2203 @ X2198))=>(![X2204:$i]:(((in @ X2204 @ X2199)=>((in @ X2202 @ X2204)<=>(in @ X2203 @ X2204))))=>((X2202)=(X2203))))))&![X2205:$i, X2206:$i]:((((in @ X2205 @ X2199)&(in @ X2206 @ X2199))=>(![X2207:$i]:(((in @ X2207 @ X2205)=>(in @ X2207 @ X2206)))|![X2208:$i]:(((in @ X2208 @ X2206)=>(in @ X2208 @ X2205)))))))&![X2209:$i]:(((![X2210:$i]:(((in @ X2210 @ X2209)=>(in @ X2210 @ X2198)))&?[X2211:$i]:((in @ X2211 @ X2209)))=>?[X2212:$i, X2213:$i]:(((((in @ X2212 @ X2199)&(in @ X2213 @ X2209))&~(?[X2214:$i]:(((in @ X2214 @ X2212)&(in @ X2214 @ X2209)))))&![X2215:$i]:(((in @ X2215 @ X2199)=>(![X2216:$i]:(((in @ X2216 @ X2215)=>(in @ X2216 @ X2212)))|(in @ X2213 @ X2215)))))))))))), introduced(definition)). 12.35/2.21 thf(c_0_401, negated_conjecture, ~((![X2229:$i, X2230:$i]:((![X2231:$i]:(((in @ X2231 @ X2229)<=>(in @ X2231 @ X2230)))=>((X2229)=(X2230))))=>(![X2228:$i]:(~(in @ X2228 @ emptyset))=>(![X1145:$i, X1146:$i, X1147:$i]:(((in @ X1147 @ (setadjoin @ X1145 @ X1146))<=>(((X1147)=(X1145))|(in @ X1147 @ X1146))))=>(![X1148:$i, X1149:$i]:(((in @ X1149 @ (powerset @ X1148))<=>![X1150:$i]:(((in @ X1150 @ X1149)=>(in @ X1150 @ X1148)))))=>(![X2225:$i, X2226:$i]:(((in @ X2226 @ (setunion @ X2225))<=>?[X2227:$i]:(((in @ X2226 @ X2227)&(in @ X2227 @ X2225)))))=>((in @ emptyset @ omega)=>(![X1151:$i]:(((in @ X1151 @ omega)=>(in @ (setadjoin @ X1151 @ X1151) @ omega)))=>(![X1152:$i]:((((in @ emptyset @ X1152)&![X1153:$i]:((((in @ X1153 @ omega)&(in @ X1153 @ X1152))=>(in @ (setadjoin @ X1153 @ X1153) @ X1152))))=>![X1154:$i]:(((in @ X1154 @ omega)=>(in @ X1154 @ X1152)))))=>(![X2217:$i > $i > $o, X2218:$i]:((![X2219:$i]:(((in @ X2219 @ X2218)=>?[X2220:$i]:(((X2217 @ X2219 @ X2220)&![X2221:$i]:(((X2217 @ X2219 @ X2221)=>((X2220)=(X2221))))))))=>?[X2222:$i]:(![X2223:$i]:(((in @ X2223 @ X2222)<=>?[X2224:$i]:(((in @ X2224 @ X2218)&(X2217 @ X2224 @ X2223))))))))=>(![X1155:$i]:((?[X1156:$i]:((in @ X1156 @ X1155))=>?[X1157:$i]:(((in @ X1157 @ X1155)&~(?[X1158:$i]:(((in @ X1158 @ X1157)&(in @ X1158 @ X1155))))))))=>((epred1_0)=>(![X1159:$i > $o]:((?[X1160:$i]:(((X1159 @ X1160)&![X1161:$i]:(((X1159 @ X1161)=>((X1160)=(X1161))))))=>(X1159 @ (descr @ (^[Z0/* 3 */:$i]:((X1159 @ Z0)))))))=>(![X2195:$i, X2196:$i > $o, X2197:$i]:(((in @ X2197 @ X2195)=>((X2196 @ X2197)=>(in @ X2197 @ (dsetconstr @ X2195 @ (^[Z0/* 3 */:$i]:((X2196 @ Z0))))))))=>(![X2192:$i, X2193:$i > $o, X2194:$i]:(((in @ X2194 @ (dsetconstr @ X2192 @ (^[Z0/* 3 */:$i]:((X2193 @ Z0)))))=>(in @ X2194 @ X2192)))=>(![X2189:$i, X2190:$i > $o, X2191:$i]:(((in @ X2191 @ (dsetconstr @ X2189 @ (^[Z0/* 3 */:$i]:((X2190 @ Z0)))))=>(X2190 @ X2191)))=>(![X1162:$i > $o]:((?[X1163:$i]:(((X1162 @ X1163)&![X1164:$i]:(((X1162 @ X1164)=>((X1163)=(X1164))))))=>?[X1165:$i]:(((X1162 @ X1165)&![X1166:$i]:(((X1162 @ X1166)=>((X1165)=(X1166))))))))=>(![X2187:$o, X2188:$i]:(((in @ X2188 @ (prop2set @ ((X2187))))=>(X2187)))=>(![X1167:$i]:(((in @ X1167 @ emptyset)=>![X1168:$o]:((X1168))))=>(![X1169:$i]:(~(in @ X1169 @ emptyset))=>(![X2186:$i]:(~(in @ X2186 @ emptyset))=>(![X2182:$i > $o]:((?[X2183:$i]:(((X2182 @ X2183)&![X2184:$i]:(((X2182 @ X2184)=>((X2183)=(X2184))))))=>?[X2185:$i]:((X2182 @ X2185))))=>(![X2178:$i, X2179:$i]:((![X2180:$i]:(((in @ X2180 @ X2178)=>(in @ X2180 @ X2179)))=>(![X2181:$i]:(((in @ X2181 @ X2179)=>(in @ X2181 @ X2178)))=>((X2178)=(X2179)))))=>(![X2176:$i]:((![X2177:$i]:(~(in @ X2177 @ X2176))=>((X2176)=(emptyset))))=>(![X2174:$i]:((![X2175:$i]:(~(in @ X2175 @ X2174))=>((X2174)=(emptyset))))=>(![X1170:$i, X1171:$i > $o, X1172:$i]:(((in @ X1172 @ X1170)=>((in @ X1172 @ (dsetconstr @ X1170 @ (^[Z0/* 3 */:$i]:((X1171 @ Z0)))))<=>(X1171 @ X1172))))=>(![X1173:$i]:((((X1173)!=(emptyset))=>?[X1174:$i]:((in @ X1174 @ X1173))))=>(![X1175:$i, X1176:$i > $o, X1177:$i]:(((in @ X1177 @ X1175)=>((X1176 @ X1177)=>((dsetconstr @ X1175 @ (^[Z0/* 3 */:$i]:((X1176 @ Z0))))!=(emptyset)))))=>(![X2172:$i]:((?[X2173:$i]:((in @ X2173 @ X2172))=>((X2172)!=(emptyset))))=>(![X2170:$i, X2171:$i]:((in @ X2170 @ (setadjoin @ X2170 @ X2171)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1178:$i, X1179:$i, X1180:$i]:(((in @ X1180 @ X1179)=>(in @ X1180 @ (setadjoin @ X1178 @ X1179))))=>(![X2166:$i, X2167:$i, X2168:$i]:(((in @ X2168 @ (setadjoin @ X2166 @ X2167))=>![X2169:$o]:(((((X2168)=(X2166))=>(X2169))=>(((in @ X2168 @ X2167)=>(X2169))=>(X2169))))))=>(![X1181:$i, X1182:$i, X1183:$i]:(((in @ X1183 @ (setadjoin @ X1181 @ X1182))=>(((X1183)=(X1181))|(in @ X1183 @ X1182))))=>(![X1184:$i]:(((dsetconstr @ X1184 @ (^[Z0/* 3 */:$i]:(($true))))=(X1184)))=>(![X1185:$i, X1186:$i]:((![X1187:$i]:(((in @ X1187 @ X1186)=>(in @ X1187 @ X1185)))=>(in @ X1186 @ (powerset @ X1185))))=>(![X2165:$i]:((in @ emptyset @ (powerset @ X2165)))=>(![X2164:$i]:((in @ emptyset @ (powerset @ X2164)))=>(![X1188:$i, X1189:$i, X1190:$i]:(((in @ X1189 @ (powerset @ X1188))=>((in @ X1190 @ X1189)=>(in @ X1190 @ X1188))))=>(![X2161:$i, X2162:$i, X2163:$i]:(((in @ X2162 @ X2163)=>((in @ X2163 @ X2161)=>(in @ X2162 @ (setunion @ X2161)))))=>(![X2157:$i, X2158:$i]:(((in @ X2158 @ (setunion @ X2157))=>![X2159:$o]:((![X2160:$i]:(((in @ X2158 @ X2160)=>((in @ X2160 @ X2157)=>(X2159))))=>(X2159)))))=>(![X2155:$i, X2156:$i]:(((in @ X2156 @ X2155)=>(in @ X2156 @ (powerset @ (setunion @ X2155)))))=>(![X2150:$i > $o]:((?[X2151:$i]:(((X2150 @ X2151)&![X2152:$i]:(((X2150 @ X2152)=>((X2151)=(X2152))))))=>?[X2153:$i]:(![X2154:$i]:(((X2150 @ X2154)<=>((X2154)=(X2153)))))))=>(![X2148:$i]:((((X2148)!=(emptyset))=>?[X2149:$i]:((in @ X2149 @ X2148))))=>(![X2146:$i, X2147:$i]:(((in @ X2146 @ (setadjoin @ X2147 @ emptyset))=>((X2146)=(X2147))))=>(![X1191:$i, X1192:$i]:((((X1191)!=(X1192))=>~(in @ X1192 @ (setadjoin @ X1191 @ emptyset))))=>(![X1193:$i, X1194:$i]:((((X1193)=(X1194))=>(in @ X1193 @ (setadjoin @ X1194 @ emptyset))))=>(![X1195:$i, X1196:$i]:(((in @ X1195 @ (setadjoin @ X1196 @ emptyset))=>(in @ X1196 @ (setadjoin @ X1195 @ emptyset))))=>(![X1197:$i, X1198:$i, X1199:$i]:(((in @ X1199 @ (setadjoin @ X1197 @ (setadjoin @ X1198 @ emptyset)))=>(((X1199)=(X1197))|((X1199)=(X1198)))))=>(![X2144:$i, X2145:$i]:((in @ X2144 @ (setadjoin @ X2144 @ (setadjoin @ X2145 @ emptyset))))=>(![X2142:$i, X2143:$i]:((in @ X2143 @ (setadjoin @ X2142 @ (setadjoin @ X2143 @ emptyset))))=>(![X2139:$i, X2140:$i > $o]:((?[X2141:$i]:(((in @ X2141 @ X2139)&(X2140 @ X2141)))=>((dsetconstr @ X2139 @ (^[Z0/* 3 */:$i]:((X2140 @ Z0))))!=(emptyset))))=>(![X1200:$i > $o, X1201:$i]:(((in @ X1201 @ emptyset)=>(X1200 @ X1201)))=>(![X1202:$i, X1203:$i > $o]:((~(![X1204:$i]:(((in @ X1204 @ X1202)=>(X1203 @ X1204))))=>?[X1205:$i]:(((in @ X1205 @ X1202)&~(X1203 @ X1205)))))=>(![X2135:$i, X2136:$i > $o]:((![X2137:$i]:(((in @ X2137 @ X2135)=>~(X2136 @ X2137)))=>~(?[X2138:$i]:(((in @ X2138 @ X2135)&(X2136 @ X2138))))))=>(![X2131:$i, X2132:$i > $o]:((~(?[X2133:$i]:(((in @ X2133 @ X2131)&(X2132 @ X2133))))=>![X2134:$i]:(((in @ X2134 @ X2131)=>~(X2132 @ X2134)))))=>(![X2127:$i, X2128:$i > $o]:((?[X2129:$i]:(((in @ X2129 @ X2127)&~(X2128 @ X2129)))=>~(![X2130:$i]:(((in @ X2130 @ X2127)=>(X2128 @ X2130))))))=>(![X2126:$o]:(((X2126)=>(in @ emptyset @ (prop2set @ ((X2126))))))=>(![X2125:$o]:(((X2125)=>(set2prop @ (prop2set @ ((X2125))))))=>(![X1206:$i, X1207:$i > $o]:((~(?[X1208:$i]:(((in @ X1208 @ X1206)&(X1207 @ X1208))))=>![X1209:$i]:(((in @ X1209 @ X1206)=>~(X1207 @ X1209)))))=>(![X1210:$i, X1211:$i > $o]:((~(![X1212:$i]:(((in @ X1212 @ X1210)=>(X1211 @ X1212))))=>?[X1213:$i]:(((in @ X1213 @ X1210)&~(X1211 @ X1213)))))=>(![X2120:$i > $o]:((?[X2121:$i]:(((X2120 @ X2121)&![X2122:$i]:(((X2120 @ X2122)=>((X2121)=(X2122))))))=>?[X2123:$i]:(((X2120 @ X2123)&![X2124:$i]:(((X2120 @ X2124)=>((X2123)=(X2124))))))))=>(![X1214:$i > $o]:((?[X1215:$i]:((X1214 @ X1215))=>(![X1216:$i, X1217:$i]:(((X1214 @ X1216)=>((X1214 @ X1217)=>((X1216)=(X1217)))))=>?[X1218:$i]:(((X1214 @ X1218)&![X1219:$i]:(((X1214 @ X1219)=>((X1218)=(X1219)))))))))=>(![X1220:$i > $o]:((?[X1221:$i]:(![X1222:$i]:(((X1220 @ X1222)<=>((X1222)=(X1221)))))=>?[X1223:$i]:(((X1220 @ X1223)&![X1224:$i]:(((X1220 @ X1224)=>((X1223)=(X1224))))))))=>(![X2116:$i, X2117:$i]:((((X2116)=(X2117))=>![X2118:$i, X2119:$i]:((((X2118)=(X2119))=>((in @ X2118 @ X2116)=>(in @ X2119 @ X2117))))))=>(![X2112:$i, X2113:$i]:((((X2112)=(X2113))=>![X2114:$i, X2115:$i]:((((X2114)=(X2115))=>((in @ X2114 @ X2112)<=>(in @ X2115 @ X2113))))))=>(![X1225:$i > $o]:((?[X1226:$i]:(((X1225 @ X1226)&![X1227:$i]:(((X1225 @ X1227)=>((X1226)=(X1227))))))=>![X1228:$i, X1229:$i]:(((X1225 @ X1228)=>((X1225 @ X1229)=>((X1228)=(X1229)))))))=>(![X2104:$i > $o, X2105:$i > $o]:((![X2106:$i, X2107:$i]:((((X2106)=(X2107))=>((X2104 @ X2106)<=>(X2105 @ X2107))))=>(?[X2108:$i]:(((X2104 @ X2108)&![X2109:$i]:(((X2104 @ X2109)=>((X2108)=(X2109))))))<=>?[X2110:$i]:(((X2105 @ X2110)&![X2111:$i]:(((X2105 @ X2111)=>((X2110)=(X2111)))))))))=>(((emptyset)=(emptyset))=>(![X2100:$i, X2101:$i]:((((X2100)=(X2101))=>![X2102:$i, X2103:$i]:((((X2102)=(X2103))=>((setadjoin @ X2100 @ X2102)=(setadjoin @ X2101 @ X2103))))))=>(![X1230:$i, X1231:$i]:((((X1230)=(X1231))=>((powerset @ X1230)=(powerset @ X1231))))=>(![X2098:$i, X2099:$i]:((((X2098)=(X2099))=>((setunion @ X2098)=(setunion @ X2099))))=>(((omega)=(omega))=>(![X2093:$i > $o]:((?[X2094:$i]:(((X2093 @ X2094)&![X2095:$i]:(((X2093 @ X2095)=>((X2094)=(X2095))))))=>![X2096:$i, X2097:$i]:(((X2093 @ X2096)=>((X2093 @ X2097)=>((X2096)=(X2097)))))))=>(![X2085:$i > $o, X2086:$i > $o]:((![X2087:$i, X2088:$i]:((((X2087)=(X2088))=>((X2085 @ X2087)<=>(X2086 @ X2088))))=>(?[X2089:$i]:(((X2085 @ X2089)&![X2090:$i]:(((X2085 @ X2090)=>((X2089)=(X2090))))))=>(?[X2091:$i]:(((X2086 @ X2091)&![X2092:$i]:(((X2086 @ X2092)=>((X2091)=(X2092))))))=>((descr @ (^[Z0/* 3 */:$i]:((X2085 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X2086 @ Z0)))))))))=>(![X2079:$i, X2080:$i]:((((X2079)=(X2080))=>![X2081:$i > $o, X2082:$i > $o]:((![X2083:$i]:(((in @ X2083 @ X2079)=>![X2084:$i]:(((in @ X2084 @ X2080)=>(((X2083)=(X2084))=>((X2081 @ X2083)<=>(X2082 @ X2084)))))))=>((dsetconstr @ X2079 @ (^[Z0/* 3 */:$i]:((X2081 @ Z0))))=(dsetconstr @ X2080 @ (^[Z0/* 3 */:$i]:((X2082 @ Z0)))))))))=>(![X2076:$i, X2077:$i]:((![X2078:$i]:(((in @ X2078 @ X2076)=>(in @ X2078 @ X2077)))=>(subset @ X2076 @ X2077)))=>(![X2074:$i, X2075:$i]:((((X2074)=(X2075))=>(subset @ X2075 @ X2074)))=>(![X2072:$i, X2073:$i]:((((X2072)=(X2073))=>(subset @ 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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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y_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[surjFuncSetFuncSurj]), cartprodmempair1]), quantDeMorgan2]), setextAx]), subsetTrans]), cartprodpairin]), notequalI1]), c_0_339]), emptysetsubset]), subsetI2]), c_0_340]), eqimpsubset1]), eqimpsubset2]), subsetI1]), c_0_341]), c_0_342]), c_0_343]), singletonsuniq]), c_0_344]), setunion__Cong]), setadjoin__Cong]), setukpairinjL1]), c_0_345]), in__Cong]), inCongP]), c_0_346]), c_0_347]), prop2set2propI]), prop2setI]), setukpairinjL2]), quantDeMorgan4]), quantDeMorgan3]), subbreln]), c_0_348]), setukpairinjR11]), upairsetIR]), upairsetIL]), uniqinunit]), setukpairinjR1]), c_0_349]), c_0_350]), upairequniteq]), subPowSU]), setunionE]), setunionI]), kpairsurjEq]), emptyInPowerset]), emptyinPowerset]), cartprodsndin]), setadjoinE]), emptyinunitempty]), setadjoinIL]), cartprodpairmemER]), c_0_351]), noeltsimpempty]), cartprodmempaircEq]), emptyI]), setext]), c_0_352]), cartprodsndpairEq]), notinemptyset]), prop2setE]), cartprodmempair]), c_0_353]), c_0_354]), c_0_355]), c_0_356]), wellorderingAx]), c_0_357]), c_0_358]), setunionAx]), c_0_359]), emptysetAx]), c_0_360]), funcGraphProp1]), funcextLem]), funcGraphProp4]), inIntersectImpInUnion]), eqbreln]), funcext]), ap2apEq1]), ap2apEq2]), c_0_361]), c_0_362]), c_0_363]), setunionE2]), c_0_364]), c_0_365]), c_0_366]), ifp]), theeq]), iftrue]), binintersectT_lem]), setminusT_lem]), setextT]), powersetTE1]), setunionsingleton2]), complementTI1]), binintersectTELcontra]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub2]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementTcontraSubset]), binunionTILcontra]), binunionT_lem]), iftrueorfalse]), iffalse]), c_0_367]), c_0_368]), c_0_369]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), binunionTE]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan2a]), demorgan2b2]), woz13rule0]), woz1_1]), woz1_3]), woz1_5]), breln1all2]), breln1SetBreln1]), c_0_370]), eqbreln1]), breln1invprop]), breln1invE]), breln1compprop]), breln1compI]), breln1compE]), breln1unionIR]), breln1unionEcases]), woz2W]), woz2B]), c_0_371]), c_0_372]), injFuncSetFuncIn]), surjFuncSetFuncIn]), c_0_373]), injFuncSetFuncInj]), injFuncInInjFuncSet]), c_0_374]), c_0_375]), image1Ex]), woz2A]), woz2Ex]), breln1unionCommutes]), breln1unionE]), breln1unionI]), breln1unionIL]), breln1unionprop]), breln1compEex]), breln1invI]), subbreln1]), breln1all1]), c_0_376]), woz1_4]), woz1_2]), woz13rule4]), woz13rule3]), woz13rule2]), woz13rule1]), demorgan2]), demorgan2b]), demorgan1]), demorgan1b]), binunionTEcontra]), inComplementUnionImpInComplement1]), inComplementUnionImpNotIn1]), binunionTIRcontra]), contraSubsetComplement]), complementInPowersetComplementIntersect]), doubleComplementEq]), doubleComplementSub1]), contrasubsetT]), binintersectTERcontra]), complementTE1]), powersetTI1]), subsetTI]), complementT_lem]), powersetT_lem]), c_0_377]), funcext2]), funcGraphProp2]), funcGraphProp3]), brelnall2]), brelnall1]), c_0_378]), c_0_379]), funcinfuncset]), ap2p]), infuncsetfunc]), app]), c_0_380]), c_0_381]), c_0_382]), c_0_383]), c_0_384]), c_0_385]), c_0_386]), cartprodpairsurjEq]), cartprodfstpairEq]), cartprodpairmemEL]), ksndpairEq]), c_0_387]), setukpairinjR]), setukpairinjR2]), setukpairinjR12]), setukpairinjL]), cartprodfstin]), kfstpairEq]), theprop]), c_0_388]), setunionsingleton]), setunionsingleton1]), ubforcartprodlem3]), ubforcartprodlem2]), upairinpowunion]), upairset2E]), singletoninpowunion]), singletonsubset]), kpairp]), kpairiskpair]), setukpairIR]), setukpairIL]), secondinupair]), symdiffI1]), setminusERneg]), setminusEL]), setminusI]), binintersectSubset1]), disjointsetsI1]), binintersectER]), binintersectSubset2]), binunionRsub]), binunionE]), upairset2IR]), c_0_389]), c_0_390]), powersetsubset]), inPowerset]), powersetI1]), setextsub]), setadjoinSub]), ubforcartprodlem1]), upairsubunion]), singletoninpowerset]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), symdiffE]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusSubset2]), setminusER]), bs114d]), binintersectSubset4]), binintersectRsub]), binintersectSubset3]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectI]), binunionLsub]), binunionEcases]), binunionIR]), binunionIL]), powersetE1]), subsetemptysetimpeq]), subset2powerset]), setadjoinSub2]), subsetRefl]), notequalI2]), notsubsetI]), subsetE2]), subsetE]), omega__Cong]), powerset__Cong]), emptyset__Cong]), c_0_391]), c_0_392]), c_0_393]), notdallE]), notdexE]), quantDeMorgan1]), vacuousDall]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), powersetE]), powersetI]), c_0_394]), setadjoinOr]), setadjoinIR]), c_0_395]), c_0_396]), c_0_397]), emptysetimpfalse]), emptysetE]), c_0_398]), c_0_399]), foundationAx]), omegaIndAx]), omegaSAx]), omega0Ax]), powersetAx]), setadjoinAx])])]), c_0_400])). 12.35/2.21 thf(c_0_402, plain, ![X2234:$i, X2235:$i]:(((surjFuncSet @ X2234 @ X2235)=(dsetconstr @ (funcSet @ X2234 @ X2235) @ (^[Z0/* 6 */:$i]:(![X2232:$i]:(((in @ X2232 @ X2235)=>?[X2233:$i]:(((in @ X2233 @ X2234)&((ap @ X2234 @ X2235 @ Z0 @ X2233)=(X2232))))))))))), inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[surjFuncSet]), c_0_373])])). 12.35/2.21 thf(c_0_403, negated_conjecture, ![X2236:$i, X2237:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2249:$i, X2250:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2258:$i, X2259:$i > $i > $o, X2260:$i, X2262:$i, X2265:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2272:$i, X2273:$i > $o, X2274:$i, X2276:$i, X2277:$i > $o, X2278:$i, X2279:$i, X2280:$i > $o, X2281:$i, X2282:$i, X2283:$i > $o, X2284:$i, X2285:$i > $o, X2286:$i, X2289:$i, X2290:$o, X2291:$i, X2292:$i, X2293:$o, X2294:$i, X2295:$i, X2296:$i > $o, X2297:$i, X2300:$i, X2301:$i, X2304:$i, X2306:$i, X2308:$i, X2309:$i > $o, X2310:$i, X2311:$i, X2313:$i, X2314:$i > $o, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$o, X2327:$i, X2328:$i, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i, X2342:$i, X2343:$i, X2344:$o, X2346:$i, X2347:$i, X2348:$i > $o, X2349:$i, X2352:$i, X2353:$i, X2354:$i, X2356:$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 > $o, X2373:$i, X2374:$i > $o, X2375:$i, X2376:$i, X2377:$i > $o, X2378:$i, X2380:$i, X2381:$i > $o, X2383:$i, X2384:$i, X2385:$i > $o, X2387:$i, X2388:$i, X2389:$i > $o, X2390:$i, X2392:$o, X2393:$o, X2394:$i, X2395:$i > $o, X2397:$i, X2398:$i, X2399:$i > $o, X2400:$i, X2402:$i > $o, X2403:$i, X2406:$i, X2407:$i > $o, X2408:$i, X2412:$i, X2413:$i > $o, X2414:$i, X2417:$i, X2418:$i, X2419:$i, X2420:$i, X2421:$i, X2422:$i, X2423:$i, X2424:$i, X2425:$i, X2426:$i > $o, X2427:$i, X2429:$i, X2430:$i, X2431:$i > $o, X2432:$i > $o, X2435:$i, X2438:$i, X2439:$i, X2442:$i, X2443:$i, X2444:$i, X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i > $o, X2452:$i, X2454:$i, X2455:$i, X2456:$i > $o, X2457:$i > $o, X2460:$i, X2462:$i, X2464:$i, X2465:$i, X2466:$i > $o, X2467:$i > $o, X2470:$i, X2471:$i, X2473:$i, X2474:$i, X2475:$i, X2476:$i, X2477:$i, X2478:$i, X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$i, X2486:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2493:$i, X2494:$i, X2495:$i, X2496:$i, X2497:$i, X2498:$i, X2499:$i, X2500:$i, X2501:$i, X2502:$i, X2503:$i, X2504:$i, X2505:$i, X2506:$i, X2507:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$i > $o, X2518:$i, X2519:$i > $o, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$o, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i, X2546:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i, X2551:$i, X2552:$i, X2553:$i, X2554:$i, X2555:$i, X2556:$i, X2557:$i, X2558:$i, X2560:$i, X2561:$i, X2562:$i, X2563:$i, X2564:$i, X2565:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2570:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i, X2576:$i, X2577:$i, X2578:$i, X2579:$i, X2580:$i, X2581:$i, X2582:$i, X2583:$i, X2584:$i, X2585:$i, X2586:$i, X2587:$i, X2588:$i, X2589:$i, X2590:$i, X2591:$i, X2592:$i, X2593:$i, X2594:$i, X2595:$i, X2596:$i, X2597:$i, X2598:$i, X2599:$o, X2600:$i, X2601:$i, X2602:$i, X2603:$i, X2604:$i, X2605:$i, X2606:$i, X2607:$i, X2608:$i, X2609:$i, X2610:$i, X2611:$i, X2612:$i, X2613:$i, X2614:$i, X2615:$i, X2616:$i, X2617:$i, X2618:$i, X2619:$i, X2620:$i, X2621:$i, X2622:$i, X2623:$i, X2624:$i, X2625:$i, X2626:$i, X2627:$i, X2628:$i, X2629:$i, X2630:$i, X2631:$i, X2632:$i, X2633:$i, X2634:$i, X2635:$i, X2636:$i, X2637:$i, X2638:$i, X2639:$i, X2640:$i, X2641:$i, X2642:$i, X2643:$i, X2644:$i, X2645:$i, X2646:$i, X2647:$i, X2648:$i, X2649:$i, X2650:$i, X2651:$i, X2652:$i, X2653:$i, X2654:$i, X2655:$i, X2656:$i, X2657:$i, X2658:$i, X2661:$i, X2662:$i, X2663:$i, X2664:$i, X2665:$i, X2667:$i, X2668:$i, X2669:$i, X2670:$i, X2671:$i > $o, X2674:$i, X2675:$i, X2676:$i > $o, X2678:$i, X2679:$i > $o, X2680:$i, X2682:$i, X2683:$i > $o, X2686:$i, X2687:$i, X2688:$i, X2689:$i, X2690:$i, X2691:$i, X2692:$i, X2693:$i, X2694:$i, X2695:$i, X2696:$i, X2697:$i, X2698:$i, X2699:$i, X2700:$i, X2701:$i, X2702:$i, X2703:$i, X2704:$i, X2705:$i, X2706:$i, X2707:$i, X2708:$i, X2709:$i, X2710:$i, X2711:$i, X2712:$i, X2713:$i, X2714:$i, X2715:$i, X2716:$i, X2717:$i, X2718:$i, X2719:$i, X2720:$i, X2721:$i, X2722:$i, X2723:$i, X2724:$i, X2725:$i, X2726:$i, X2727:$i, X2728:$i, X2729:$i, X2730:$i, X2731:$i, X2732:$i, X2733:$i, X2734:$i, X2735:$i, X2736:$i, X2737:$i, X2738:$i, X2739:$i, X2740:$i, X2741:$i, X2742:$i, X2743:$i, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i, X2749:$i, X2750:$i, X2751:$i, X2752:$i, X2753:$i, X2754:$i, X2755:$i, X2756:$i, X2757:$i, X2758:$i > $i > $o, X2759:$i, X2760:$i, X2761:$i, X2762:$i, X2763:$i > $i > $o, X2764:$i, X2765:$i, X2766:$i > $i > $o, X2767:$i, X2768:$i, X2769:$i > $i > $o, X2770:$i, X2771:$i, X2772:$i, X2773:$i, X2774:$i > $i > $o, X2775:$i, X2776:$i, X2777:$i, X2778:$i, X2779:$i > $i > $o, X2780:$i, X2781:$i, X2782:$i, X2783:$i, X2784:$i > $i > $o, X2785:$i, X2786:$i, X2787:$i, X2788:$i, X2789:$i, X2790:$i, X2791:$i, X2792:$i, X2793:$i, X2794:$i, X2795:$i, X2796:$i, X2797:$i, X2798:$i, X2799:$i, X2800:$i, X2801:$i, X2802:$i, X2803:$i, X2804:$i, X2805:$i, X2806:$i, X2807:$i, X2808:$i, X2809:$i, X2810:$i, X2811:$i > $i, X2813:$i, X2814:$i, X2815:$i > $i, X2817:$i, X2818:$i, X2819:$i > $i, X2821:$i, X2822:$i, X2823:$i, X2824:$i > $o, X2827:$i, X2828:$i, X2829:$i, X2830:$i, X2831:$i > $o, X2834:$i, X2835:$i, X2836:$i > $o, X2837:$i, X2838:$i, X2839:$i, X2840:$i, X2841:$i, X2842:$i, X2843:$i, X2844:$i, X2845:$i, X2846:$i, X2847:$i, X2848:$i, X2849:$i, X2850:$i, X2851:$i, X2852:$i, X2853:$i, X2854:$i, X2855:$i, X2857:$i, X2858:$i, X2859:$i, X2860:$i, X2861:$i, X2862:$i, X2863:$i, X2864:$i, X2865:$i, X2866:$i, X2867:$i, X2870:$i, X2871:$i, X2872:$i, X2873:$i, X2878:$i, X2879:$i, X2880:$i, X2881:$i, X2883:$i, X2884:$i, X2885:$i, X2886:$i, X2888:$i, X2889:$i, X2890:$i, X2891:$i, X2892:$i, X2893:$i, X2894:$i, X2895:$i, X2896:$i, X2897:$i, X2898:$i > $i, X2900:$i, X2901:$i, X2902:$i, X2903:$i, X2904:$i, X2905:$i, X2906:$i > $i, X2908:$i, X2909:$i, X2910:$i > $i, X2912:$i, X2913:$i, X2914:$i, X2915:$i, X2916:$i, X2917:$o, X2918:$i, X2919:$i, X2920:$i, X2921:$o, X2922:$i, X2923:$i, X2924:$i, X2925:$o, X2926:$i, X2927:$i, X2928:$i, X2929:$o, X2930:$i, X2931:$i, X2932:$i, X2933:$o, X2934:$i, X2935:$i, X2936:$i, X2937:$o, X2938:$i, X2939:$i, X2940:$i, X2941:$i, X2942:$i, X2943:$o, X2944:$i, X2945:$i, X2946:$i, X2947:$o, X2948:$i, X2949:$i, X2950:$i, X2951:$o, X2952:$i, X2953:$i, X2954:$i, X2955:$i, X2956:$i, X2957:$i, X2958:$i, X2959:$i, X2960:$i, X2961:$i, X2962:$i, X2963:$i, X2964:$i, X2965:$i, X2966:$i, X2967:$i, X2968:$i, X2969:$i, X2972:$i, X2973:$i, X2974:$i, X2976:$i, X2977:$i, X2978:$i, X2980:$i, X2981:$i, X2982:$i, X2983:$i, X2984:$i, X2985:$i, X2986:$i, X2987:$i, X2988:$i, X2989:$i, X2990:$i, X2991:$i, X2992:$i, X2993:$i, X2994:$i, X2995:$i, X2996:$i, X2997:$i, X2998:$i, X2999:$i, X3000:$i, X3001:$i, X3002:$i, X3003:$i, X3004:$i, X3005:$i, X3006:$i, X3007:$i, X3008:$i, X3009:$i, X3010:$i, X3011:$i, X3012:$i, X3013:$i, X3014:$i, X3015:$i, X3016:$i, X3017:$i, X3018:$i, X3019:$i, X3020:$i, X3021:$i, X3022:$i, X3023:$i, X3024:$i, X3025:$i, X3026:$i, X3027:$i, X3028:$i, X3029:$i, X3030:$i, X3031:$i, X3032:$i, X3033:$i, X3034:$i, X3035:$i, X3036:$i, X3037:$i, X3038:$i, X3039:$i, X3040:$i, X3041:$i, X3042:$i, X3043:$i, X3044:$i, X3045:$i, X3046:$i, X3047:$i, X3048:$i, X3049:$i, X3050:$i, X3051:$i, X3052:$i, X3053:$i, X3054:$i, X3055:$i, X3056:$i, X3057:$i, X3058:$i, X3059:$i, X3060:$i, X3061:$i, X3062:$i, X3063:$i, X3064:$i, X3065:$i, X3066:$i, X3067:$i, X3068:$i, X3069:$i, X3070:$i, X3071:$i, X3072:$i, X3073:$i, X3074:$i, X3075:$i, X3076:$i, X3077:$i, X3078:$i, X3079:$i, X3080:$i, X3081:$i, X3082:$i, X3083:$o, X3084:$i, X3085:$i, X3086:$i, X3087:$i, X3088:$i, X3089:$i, X3090:$i, X3091:$i, X3092:$i, X3093:$i, X3094:$i, X3095:$i, X3096:$i, X3097:$i, X3098:$i, X3099:$i, X3100:$i, X3101:$i, X3102:$i, X3103:$i, X3104:$i, X3105:$i, X3106:$i, X3107:$i, X3108:$i, X3109:$i, X3110:$i, X3111:$i, X3112:$i, X3113:$i, X3114:$i, X3115:$i, X3116:$i, X3117:$i, X3118:$i, X3119:$i, X3120:$i, X3121:$i, X3122:$i, X3123:$i, X3124:$i, X3125:$i, X3126:$i, X3127:$i, X3128:$i, X3129:$i, X3130:$i, X3131:$i, X3132:$i, X3133:$i, X3134:$i, X3135:$i, X3136:$i, X3137:$i, X3138:$i, X3139:$i, X3140:$i, X3141:$i, X3142:$i, X3143:$i, X3144:$i, X3145:$i, X3146:$i, X3147:$i, X3148:$i, X3149:$i, X3150:$i, X3151:$i, X3152:$i, X3153:$i, X3154:$i, X3155:$i, X3156:$i, X3157:$i, X3158:$i, X3159:$i, X3160:$i, X3161:$i, X3162:$i, X3163:$i, X3164:$i, X3165:$i, X3166:$i, X3167:$i > $o, X3170:$i, X3171:$i, X3172:$i, X3173:$i, X3174:$i, X3175:$i > $i > $o, X3177:$i, X3178:$i, X3179:$i, X3180:$i, X3181:$i > $i > $o, X3182:$i, X3183:$i, X3184:$i > $o, X3187:$i, X3188:$i, X3189:$i, X3190:$i, X3193:$i, X3194:$i, X3195:$i, X3200:$i, X3201:$i, X3202:$i, X3203:$i, X3204:$i, X3205:$i, X3206:$i, X3207:$i, X3208:$i, X3209:$i, X3210:$i, X3211:$i, X3212:$i, X3213:$i, X3214:$i, X3215:$i, X3216:$i, X3217:$i, X3218:$i, X3219:$i, X3220:$i, X3221:$i, X3222:$i, X3223:$i, X3225:$i, X3226:$i, X3227:$i, X3228:$i, X3229:$i, X3230:$o, X3232:$i, X3233:$i, X3234:$i, X3235:$i, X3236:$i, X3237:$i, X3238:$i, X3239:$i, X3240:$i, X3241:$i, X3242:$i, X3243:$i, X3244:$i, X3245:$i, X3246:$i, 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X3194)|((X3194)=(X3195))|(in @ (esk95_3 @ X3193 @ X3194 @ X3195) @ X3193)|~(breln1 @ X3193 @ X3195)|~(breln1 @ X3193 @ X3194)))))&((((in @ (esk96_3 @ X3193 @ X3194 @ X3195) @ X3193)|((X3194)=(X3195))|(in @ (kpair @ (esk94_3 @ X3193 @ X3194 @ X3195) @ (esk95_3 @ X3193 @ X3194 @ X3195)) @ X3194)|~(breln1 @ X3193 @ X3195)|~(breln1 @ X3193 @ X3194))&(((in @ (esk97_3 @ X3193 @ X3194 @ X3195) @ X3193)|((X3194)=(X3195))|(in @ (kpair @ (esk94_3 @ X3193 @ X3194 @ X3195) @ (esk95_3 @ X3193 @ X3194 @ X3195)) @ X3194)|~(breln1 @ X3193 @ X3195)|~(breln1 @ X3193 @ X3194))&(((in @ (kpair @ (esk96_3 @ X3193 @ X3194 @ X3195) @ (esk97_3 @ X3193 @ X3194 @ X3195)) @ X3195)|((X3194)=(X3195))|(in @ (kpair @ (esk94_3 @ X3193 @ X3194 @ X3195) @ (esk95_3 @ X3193 @ X3194 @ X3195)) @ X3194)|~(breln1 @ X3193 @ X3195)|~(breln1 @ X3193 @ X3194))&(~(in @ (kpair @ (esk96_3 @ X3193 @ X3194 @ X3195) @ (esk97_3 @ X3193 @ X3194 @ X3195)) @ X3194)|((X3194)=(X3195))|(in @ (kpair @ (esk94_3 @ X3193 @ X3194 @ X3195) @ 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X3195)) @ X3195)|~(breln1 @ X3193 @ X3195)|~(breln1 @ X3193 @ X3194))))))))&((~(breln1 @ X3200 @ X3201)|(breln1 @ X3200 @ (breln1invset @ X3200 @ X3201)))&((~(breln1 @ X3202 @ X3203)|(~(in @ X3204 @ X3202)|(~(in @ X3205 @ X3202)|(~(in @ (kpair @ X3204 @ X3205) @ X3203)|(in @ (kpair @ X3205 @ X3204) @ (breln1invset @ X3202 @ X3203))))))&((~(breln1 @ X3206 @ X3207)|(~(in @ X3208 @ X3206)|(~(in @ X3209 @ X3206)|(~(in @ (kpair @ X3209 @ X3208) @ (breln1invset @ X3206 @ X3207))|(in @ (kpair @ X3208 @ X3209) @ X3207)))))&((~(breln1 @ X3210 @ X3211)|(~(breln1 @ X3210 @ X3212)|(breln1 @ X3210 @ (breln1compset @ X3210 @ X3211 @ X3212))))&((~(breln1 @ X3213 @ X3214)|(~(breln1 @ X3213 @ X3215)|(~(in @ X3216 @ X3213)|(~(in @ X3217 @ X3213)|(~(in @ X3218 @ X3213)|(~(in @ (kpair @ X3216 @ X3218) @ X3214)|(~(in @ (kpair @ X3218 @ X3217) @ X3215)|(in @ (kpair @ X3216 @ X3217) @ (breln1compset @ X3213 @ X3214 @ X3215)))))))))&(((((in @ (esk98_5 @ X3219 @ X3220 @ X3221 @ X3222 @ X3223) @ X3219)|~(in @ (kpair @ X3222 @ X3223) @ (breln1compset @ X3219 @ X3220 @ X3221))|~(in @ X3223 @ X3219)|~(in @ X3222 @ X3219)|~(breln1 @ X3219 @ X3221)|~(breln1 @ X3219 @ X3220))&((in @ (kpair @ X3222 @ (esk98_5 @ X3219 @ X3220 @ X3221 @ X3222 @ X3223)) @ X3220)|~(in @ (kpair @ X3222 @ X3223) @ (breln1compset @ X3219 @ X3220 @ X3221))|~(in @ X3223 @ X3219)|~(in @ X3222 @ X3219)|~(breln1 @ X3219 @ X3221)|~(breln1 @ X3219 @ X3220)))&((in @ (kpair @ (esk98_5 @ X3219 @ X3220 @ X3221 @ X3222 @ X3223) @ X3223) @ X3221)|~(in @ (kpair @ X3222 @ X3223) @ (breln1compset @ X3219 @ X3220 @ X3221))|~(in @ X3223 @ X3219)|~(in @ X3222 @ X3219)|~(breln1 @ X3219 @ X3221)|~(breln1 @ X3219 @ X3220)))&((((in @ (esk99_6 @ X3225 @ X3226 @ X3227 @ X3228 @ X3229 @ X3230) @ X3225)|(X3230)|~(in @ (kpair @ X3228 @ X3229) @ (breln1compset @ X3225 @ X3226 @ X3227))|~(in @ X3229 @ X3225)|~(in @ X3228 @ X3225)|~(breln1 @ X3225 @ X3227)|~(breln1 @ X3225 @ X3226))&(((in @ (kpair @ X3228 @ (esk99_6 @ X3225 @ X3226 @ X3227 @ X3228 @ X3229 @ X3230)) @ X3226)|(X3230)|~(in @ (kpair @ X3228 @ X3229) @ (breln1compset @ X3225 @ X3226 @ X3227))|~(in @ X3229 @ X3225)|~(in @ X3228 @ X3225)|~(breln1 @ X3225 @ X3227)|~(breln1 @ X3225 @ X3226))&(((in @ (kpair @ (esk99_6 @ X3225 @ X3226 @ X3227 @ X3228 @ X3229 @ X3230) @ X3229) @ X3227)|(X3230)|~(in @ (kpair @ X3228 @ X3229) @ (breln1compset @ X3225 @ X3226 @ X3227))|~(in @ X3229 @ X3225)|~(in @ X3228 @ X3225)|~(breln1 @ X3225 @ X3227)|~(breln1 @ X3225 @ X3226))&(~(X3230)|(X3230)|~(in @ (kpair @ X3228 @ X3229) @ (breln1compset @ X3225 @ X3226 @ X3227))|~(in @ X3229 @ X3225)|~(in @ X3228 @ X3225)|~(breln1 @ X3225 @ X3227)|~(breln1 @ X3225 @ X3226)))))&((~(breln1 @ X3232 @ X3233)|(~(breln1 @ X3232 @ X3234)|(breln1 @ X3232 @ (binunion @ X3233 @ X3234))))&((~(breln1 @ X3235 @ X3236)|(~(breln1 @ X3235 @ X3237)|(~(in @ X3238 @ X3235)|(~(in @ X3239 @ X3235)|(~(in @ (kpair @ X3238 @ X3239) @ X3236)|(in @ (kpair @ X3238 @ X3239) @ (binunion @ X3236 @ X3237)))))))&((~(breln1 @ X3240 @ X3241)|(~(breln1 @ X3240 @ X3242)|(~(in @ X3243 @ X3240)|(~(in @ X3244 @ X3240)|(~(in @ (kpair @ X3243 @ X3244) @ X3242)|(in @ (kpair @ X3243 @ X3244) @ (binunion @ X3241 @ X3242)))))))&(((~(in @ (kpair @ X3248 @ X3249) @ X3246)|(in @ (kpair @ X3248 @ X3249) @ (binunion @ X3246 @ X3247))|~(in @ X3249 @ X3245)|~(in @ X3248 @ X3245)|~(breln1 @ X3245 @ X3247)|~(breln1 @ X3245 @ X3246))&(~(in @ (kpair @ X3248 @ X3249) @ X3247)|(in @ (kpair @ X3248 @ X3249) @ (binunion @ X3246 @ X3247))|~(in @ X3249 @ X3245)|~(in @ X3248 @ X3245)|~(breln1 @ X3245 @ X3247)|~(breln1 @ X3245 @ X3246)))&((~(breln1 @ X3250 @ X3251)|(~(breln1 @ X3250 @ X3252)|(~(in @ X3253 @ X3250)|(~(in @ X3254 @ X3250)|(~(in @ (kpair @ X3253 @ X3254) @ (binunion @ X3251 @ X3252))|((in @ (kpair @ X3253 @ X3254) @ X3251)|(in @ (kpair @ X3253 @ X3254) @ X3252)))))))&(((((in @ (kpair @ X3258 @ X3259) @ X3257)|(X3260)|(in @ (kpair @ X3258 @ X3259) @ X3256)|~(in @ (kpair @ X3258 @ X3259) @ (binunion @ X3256 @ X3257))|~(in @ X3259 @ X3255)|~(in @ X3258 @ X3255)|~(breln1 @ X3255 @ X3257)|~(breln1 @ X3255 @ X3256))&(~(X3260)|(X3260)|(in @ (kpair @ X3258 @ X3259) @ X3256)|~(in @ (kpair @ X3258 @ X3259) @ (binunion @ X3256 @ X3257))|~(in @ X3259 @ X3255)|~(in @ X3258 @ X3255)|~(breln1 @ X3255 @ X3257)|~(breln1 @ X3255 @ X3256)))&(((in @ (kpair @ X3258 @ X3259) @ X3257)|(X3260)|~(X3260)|~(in @ (kpair @ X3258 @ X3259) @ (binunion @ X3256 @ X3257))|~(in @ X3259 @ X3255)|~(in @ X3258 @ X3255)|~(breln1 @ X3255 @ X3257)|~(breln1 @ X3255 @ X3256))&(~(X3260)|(X3260)|~(X3260)|~(in @ (kpair @ X3258 @ X3259) @ (binunion @ X3256 @ X3257))|~(in @ X3259 @ X3255)|~(in @ X3258 @ X3255)|~(breln1 @ X3255 @ X3257)|~(breln1 @ X3255 @ X3256))))&((~(breln1 @ X3261 @ X3262)|(~(breln1 @ X3261 @ X3263)|((binunion @ X3262 @ X3263)=(binunion @ X3263 @ X3262))))&((~(breln1 @ X3264 @ X3265)|((X3265)=(breln1invset @ X3264 @ (breln1invset @ X3264 @ X3265))))&((~(breln1 @ X3266 @ X3267)|(~(breln1 @ X3266 @ X3268)|((breln1invset @ X3266 @ (breln1compset @ X3266 @ X3267 @ X3268))=(breln1compset @ X3266 @ (breln1invset @ X3266 @ X3268) @ (breln1invset @ X3266 @ X3267)))))&((~(breln1 @ X3269 @ X3270)|(~(breln1 @ X3269 @ X3271)|(~(breln1 @ X3269 @ X3272)|((breln1compset @ X3269 @ (binunion @ X3270 @ X3271) @ X3272)=(binunion @ (breln1compset @ X3269 @ X3270 @ X3272) @ (breln1compset @ X3269 @ X3271 @ X3272))))))&((~(breln1 @ X3273 @ X3274)|(~(breln1 @ X3273 @ X3275)|(~(breln1 @ X3273 @ X3276)|((breln1compset @ X3273 @ (binunion @ X3274 @ X3275) @ X3276)=(binunion @ (breln1invset @ X3273 @ (breln1compset @ X3273 @ (breln1invset @ X3273 @ X3276) @ (breln1invset @ X3273 @ X3275))) @ (breln1invset @ X3273 @ (breln1compset @ X3273 @ (breln1invset @ X3273 @ X3276) @ (breln1invset @ X3273 @ X3274))))))))&(((((in @ (esk101_3 @ X3277 @ X3278 @ X3280) @ X3277)|~(in @ X3280 @ (esk100_2 @ X3277 @ X3278)))&(((X3280)=(X3278 @ (esk101_3 @ X3277 @ X3278 @ X3280)))|~(in @ X3280 @ (esk100_2 @ X3277 @ X3278))))&(~(in @ X3283 @ X3277)|((X3282)!=(X3278 @ X3283))|(in @ X3282 @ (esk100_2 @ X3277 @ X3278))))&((((((in @ (esk103_3 @ X3284 @ X3285 @ X3287) @ X3284)|~(in @ X3287 @ (esk102_2 @ X3284 @ X3285)))&(((X3287)=(X3285 @ (esk103_3 @ X3284 @ X3285 @ X3287)))|~(in @ X3287 @ (esk102_2 @ X3284 @ X3285))))&(~(in @ X3290 @ X3284)|((X3289)!=(X3285 @ X3290))|(in @ X3289 @ (esk102_2 @ X3284 @ X3285))))&((~(in @ (esk104_3 @ X3284 @ X3285 @ X3291) @ X3291)|(~(in @ X3293 @ X3284)|((esk104_3 @ X3284 @ X3285 @ X3291)!=(X3285 @ X3293)))|((esk102_2 @ X3284 @ X3285)=(X3291)))&(((in @ (esk105_3 @ X3284 @ X3285 @ X3291) @ X3284)|(in @ (esk104_3 @ X3284 @ X3285 @ X3291) @ X3291)|((esk102_2 @ X3284 @ X3285)=(X3291)))&(((esk104_3 @ X3284 @ X3285 @ X3291)=(X3285 @ (esk105_3 @ X3284 @ X3285 @ X3291)))|(in @ (esk104_3 @ X3284 @ X3285 @ X3291) @ X3291)|((esk102_2 @ X3284 @ X3285)=(X3291))))))&(((((in @ (esk106_3 @ X3295 @ X3296 @ X3297) @ X3295)|~(in @ X3297 @ (image1 @ X3295 @ X3296)))&(((X3297)=(X3296 @ (esk106_3 @ X3295 @ X3296 @ X3297)))|~(in @ X3297 @ (image1 @ X3295 @ X3296))))&(~(in @ X3302 @ X3299)|((X3301)!=(X3300 @ X3302))|(in @ X3301 @ (image1 @ X3299 @ X3300))))&((((in @ (esk107_3 @ X3303 @ X3304 @ X3305) @ X3303)|~(in @ X3305 @ (image1 @ X3303 @ X3304)))&(((X3305)=(X3304 @ (esk107_3 @ X3303 @ X3304 @ X3305)))|~(in @ X3305 @ (image1 @ X3303 @ X3304))))&((~(in @ X3310 @ X3307)|((X3309)!=(X3308 @ X3310))|(in @ X3309 @ (image1 @ X3307 @ X3308)))&((~(in @ X3313 @ (funcSet @ X3311 @ X3312))|(~(injective @ X3311 @ X3312 @ X3313)|(in @ X3313 @ (injFuncSet @ X3311 @ X3312))))&((~(in @ X3316 @ (injFuncSet @ X3314 @ X3315))|(in @ X3316 @ (funcSet @ X3314 @ X3315)))&((~(in @ X3319 @ (injFuncSet @ X3317 @ X3318))|(injective @ X3317 @ X3318 @ X3319))&((~(in @ X3322 @ (surjFuncSet @ X3320 @ X3321))|(in @ X3322 @ (funcSet @ X3320 @ X3321)))&((in @ esk110_0 @ (surjFuncSet @ esk108_0 @ esk109_0))&((in @ esk111_0 @ esk109_0)&(~(in @ X3327 @ esk108_0)|((ap @ esk108_0 @ esk109_0 @ esk110_0 @ X3327)!=(esk111_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[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_401])])])])])])). 12.35/2.21 thf(c_0_404, plain, ![X3392:$i, X3393:$i, X3394:$i, X3395:$i, X3397:$i, X3398:$i, X3399:$i, X3401:$i]:(((((in @ (esk118_4 @ X3392 @ X3393 @ X3394 @ X3395) @ X3393)|~(in @ X3395 @ X3394)|~(epred10_2 @ X3394 @ X3393 @ X3392))&(((ap @ X3393 @ X3394 @ X3392 @ (esk118_4 @ X3392 @ X3393 @ X3394 @ X3395))=(X3395))|~(in @ X3395 @ X3394)|~(epred10_2 @ X3394 @ X3393 @ X3392)))&(((in @ (esk119_3 @ X3397 @ X3398 @ X3399) @ X3399)|(epred10_2 @ X3399 @ X3398 @ X3397))&(~(in @ X3401 @ X3398)|((ap @ X3398 @ X3399 @ X3397 @ X3401)!=(esk119_3 @ X3397 @ X3398 @ X3399))|(epred10_2 @ X3399 @ X3398 @ X3397))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])])])). 12.35/2.21 thf(c_0_405, plain, ![X3328:$i, X3329:$i]:(((surjFuncSet @ X3328 @ X3329)=(dsetconstr @ (funcSet @ X3328 @ X3329) @ (^[Z0/* 6 */:$i]:(![X2232:$i]:(((in @ X2232 @ X3329)=>?[X2233:$i]:(((in @ X2233 @ X3328)&((ap @ X3328 @ X3329 @ Z0 @ X2233)=(X2232))))))))))), inference(variable_rename,[status(thm)],[c_0_402])). 12.35/2.21 thf(c_0_406, plain, ![X3367:$i, X2:$i, X3:$i]:(((epred10_2 @ X3 @ X2 @ X3367)<=>![X3365:$i]:(((in @ X3365 @ X3)=>?[X3366:$i]:(((in @ X3366 @ X2)&((ap @ X2 @ X3 @ X3367 @ X3366)=(X3365)))))))), introduced(definition)). 12.35/2.21 thf(c_0_407, negated_conjecture, ![X2:$i]:((~((in @ X2 @ esk108_0))|((ap @ esk108_0 @ esk109_0 @ esk110_0 @ X2)!=(esk111_0)))), inference(split_conjunct,[status(thm)],[c_0_403])). 12.35/2.21 thf(c_0_408, plain, ![X2:$i, X3:$i, X5:$i, X4:$i]:((((ap @ X2 @ X3 @ X4 @ (esk118_4 @ X4 @ X2 @ X3 @ X5))=(X5))|~((in @ X5 @ X3))|~((epred10_2 @ X3 @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_404])). 12.35/2.21 thf(c_0_409, negated_conjecture, (in @ esk111_0 @ esk109_0), inference(split_conjunct,[status(thm)],[c_0_403])). 12.35/2.21 thf(c_0_410, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((X1 @ X2)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_403])). 12.35/2.21 thf(c_0_411, plain, ![X3:$i, X2:$i]:(((surjFuncSet @ X2 @ X3)=(dsetconstr @ (funcSet @ X2 @ X3) @ (epred10_2 @ X3 @ X2)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_405]), c_0_406])). 12.35/2.21 thf(c_0_412, negated_conjecture, (~((in @ (esk118_4 @ esk110_0 @ esk108_0 @ esk109_0 @ esk111_0) @ esk108_0))|~((epred10_2 @ esk109_0 @ esk108_0 @ esk110_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_407, c_0_408])]), c_0_409])])). 12.35/2.21 thf(c_0_413, plain, ![X5:$i, X4:$i, X3:$i, X2:$i]:(((in @ (esk118_4 @ X2 @ X3 @ X4 @ X5) @ X3)|~((in @ X5 @ X4))|~((epred10_2 @ X4 @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_404])). 12.35/2.21 thf(c_0_414, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((epred10_2 @ X2 @ X3 @ X4)|~((in @ X4 @ (surjFuncSet @ X3 @ X2))))), inference(spm,[status(thm)],[c_0_410, c_0_411])). 12.35/2.21 thf(c_0_415, negated_conjecture, (in @ esk110_0 @ (surjFuncSet @ esk108_0 @ esk109_0)), inference(split_conjunct,[status(thm)],[c_0_403])). 12.35/2.21 thf(c_0_416, plain, ~((epred10_2 @ esk109_0 @ esk108_0 @ esk110_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_412, c_0_413]), c_0_409])])). 12.35/2.21 thf(c_0_417, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_414, c_0_415]), c_0_416]), ['proof']). 12.35/2.21 # SZS output end CNFRefutation 12.35/2.21 # Parsed axioms : 694 12.35/2.21 # Removed by relevancy pruning/SinE : 371 12.35/2.21 # Initial clauses : 574 12.35/2.21 # Removed in clause preprocessing : 36 12.35/2.21 # Initial clauses in saturation : 538 12.35/2.21 # Processed clauses : 1721 12.35/2.21 # ...of these trivial : 13 12.35/2.21 # ...subsumed : 362 12.35/2.21 # ...remaining for further processing : 1346 12.35/2.21 # Other redundant clauses eliminated : 119 12.35/2.21 # Clauses deleted for lack of memory : 0 12.35/2.21 # Backward-subsumed : 11 12.35/2.21 # Backward-rewritten : 7 12.35/2.21 # Generated clauses : 34346 12.35/2.21 # ...of the previous two non-redundant : 33651 12.35/2.21 # ...aggressively subsumed : 0 12.35/2.21 # Contextual simplify-reflections : 24 12.35/2.21 # Paramodulations : 34168 12.35/2.21 # Factorizations : 2 12.35/2.21 # NegExts : 6 12.35/2.21 # Equation resolutions : 126 12.35/2.21 # Total rewrite steps : 747 12.35/2.21 # Propositional unsat checks : 0 12.35/2.21 # Propositional check models : 0 12.35/2.21 # Propositional check unsatisfiable : 0 12.35/2.21 # Propositional clauses : 0 12.35/2.21 # Propositional clauses after purity: 0 12.35/2.21 # Propositional unsat core size : 0 12.35/2.21 # Propositional preprocessing time : 0.000 12.35/2.21 # Propositional encoding time : 0.000 12.35/2.21 # Propositional solver time : 0.000 12.35/2.21 # Success case prop preproc time : 0.000 12.35/2.21 # Success case prop encoding time : 0.000 12.35/2.21 # Success case prop solver time : 0.000 12.35/2.21 # Current number of processed clauses : 832 12.35/2.21 # Positive orientable unit clauses : 64 12.35/2.21 # Positive unorientable unit clauses: 0 12.35/2.21 # Negative unit clauses : 63 12.35/2.21 # Non-unit-clauses : 705 12.35/2.21 # Current number of unprocessed clauses: 32859 12.35/2.21 # ...number of literals in the above : 145086 12.35/2.21 # Current number of archived formulas : 0 12.35/2.21 # Current number of archived clauses : 492 12.35/2.21 # Clause-clause subsumption calls (NU) : 162303 12.35/2.21 # Rec. Clause-clause subsumption calls : 56754 12.35/2.21 # Non-unit clause-clause subsumptions : 315 12.35/2.21 # Unit Clause-clause subsumption calls : 4590 12.35/2.21 # Rewrite failures with RHS unbound : 0 12.35/2.21 # BW rewrite match attempts : 36 12.35/2.21 # BW rewrite match successes : 7 12.35/2.21 # Condensation attempts : 0 12.35/2.21 # Condensation successes : 0 12.35/2.21 # Termbank termtop insertions : 767302 12.35/2.21 12.35/2.21 # ------------------------------------------------- 12.35/2.21 # User time : 1.471 s 12.35/2.21 # System time : 0.060 s 12.35/2.21 # Total time : 1.531 s 12.35/2.21 # Maximum resident set size: 10460 pages 97.78/87.84 eprover: Parsing a user given option argument: "(3.PNRefinedweight(PreferGoals,1,1,1,2,2,2,0.5),5.PNRefinedweight(PreferNonGoals,2,1,1,1,2,2,2),3.OrientLMaxWeight(PreferEasyHO,2,1,2,1,1),4.Diversityweight(DeferLambdas,1,1,1.5,1,1,-1.000000,0.000000,1.000000,1.000000)),1.FIFOWeight(ConstPrio),1.PNRefinedweight(PreferLambdas,2,1,1,1,2,2,2))":1:(Column 221):(just read ','): No token (probably EOF) expected, but Comma (',') read 189.97/180.03 189.97/180.03 # ------------------------------------------------- 189.97/180.03 # User time : 1.508 s 189.97/180.03 # System time : 0.065 s 189.97/180.03 # Total time : 1.573 s 189.97/180.03 # Maximum resident set size: 2884 pages 189.97/180.03 % E---3.1 exiting 189.97/180.03 EOF