0.17/0.18 % Problem : Vampire---4.8_9768 : TPTP v0.0.0. Released v0.0.0. 0.17/0.19 % Command : run_E %s %d THM 0.19/0.40 % Computer : n018.cluster.edu 0.19/0.40 % Model : x86_64 x86_64 0.19/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.19/0.40 % Memory : 8042.1875MB 0.19/0.40 % OS : Linux 3.10.0-693.el7.x86_64 0.19/0.40 % CPULimit : 1440 0.19/0.40 % WCLimit : 180 0.19/0.40 % DateTime : Mon Jul 3 13:13:31 EDT 2023 0.19/0.40 % CPUTime : 0.40/0.58 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.XTVzWcq4tA/Vampire---4.8_9768 0.40/0.58 # Version: 3.1pre001-ho 142.40/18.46 # Preprocessing class: HSLMSLSSLLLCHFA. 142.40/18.46 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 142.40/18.46 # Starting ehoh_best5 with 180s (1) cores 142.40/18.46 # Starting almost_fo_3_lam with 180s (1) cores 142.40/18.46 # Starting new_bool_5 with 180s (1) cores 142.40/18.46 # Starting pre_casc_3 with 180s (1) cores 142.40/18.46 # Starting ho_unfolding_8 with 180s (1) cores 142.40/18.46 # Starting new_ho_10_cnf2 with 180s (1) cores 142.40/18.46 # Starting new_bool_3 with 180s (1) cores 142.40/18.46 # Starting new_ho_5 with 180s (1) cores 142.40/18.46 # new_bool_5 with pid 9948 completed with status 0 142.40/18.46 # Result found by new_bool_5 142.40/18.46 # Preprocessing class: HSLMSLSSLLLCHFA. 142.40/18.46 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 142.40/18.46 # Starting ehoh_best5 with 180s (1) cores 142.40/18.46 # Starting almost_fo_3_lam with 180s (1) cores 142.40/18.46 # Starting new_bool_5 with 180s (1) cores 142.40/18.46 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 142.40/18.46 # Search class: HGHSM-FSLM32-MHFMMSBN 142.40/18.46 # Scheduled 10 strats onto 1 cores with 180 seconds (180 total) 142.40/18.46 # Starting ho_unfolding_8 with 33s (1) cores 142.40/18.46 # ho_unfolding_8 with pid 9956 completed with status 0 142.40/18.46 # Result found by ho_unfolding_8 142.40/18.46 # Preprocessing class: HSLMSLSSLLLCHFA. 142.40/18.46 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 142.40/18.46 # Starting ehoh_best5 with 180s (1) cores 142.40/18.46 # Starting almost_fo_3_lam with 180s (1) cores 142.40/18.46 # Starting new_bool_5 with 180s (1) cores 142.40/18.46 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 142.40/18.46 # Search class: HGHSM-FSLM32-MHFMMSBN 142.40/18.46 # Scheduled 10 strats onto 1 cores with 180 seconds (180 total) 142.40/18.46 # Starting ho_unfolding_8 with 33s (1) cores 142.40/18.46 # Preprocessing time : 0.078 s 142.40/18.46 # Presaturation interreduction done 142.40/18.46 142.40/18.46 # Proof found! 142.40/18.46 # SZS status Theorem 142.40/18.46 # SZS output start CNFRefutation 142.40/18.46 thf(decl_22, type, in: $i > $i > $o). 142.40/18.46 thf(decl_23, type, exu: ($i > $o) > $o). 142.40/18.46 thf(decl_24, type, setextAx: $o). 142.40/18.46 thf(decl_25, type, emptyset: $i). 142.40/18.46 thf(decl_26, type, emptysetAx: $o). 142.40/18.46 thf(decl_27, type, setadjoin: $i > $i > $i). 142.40/18.46 thf(decl_28, type, setadjoinAx: $o). 142.40/18.46 thf(decl_29, type, powerset: $i > $i). 142.40/18.46 thf(decl_30, type, powersetAx: $o). 142.40/18.46 thf(decl_31, type, setunion: $i > $i). 142.40/18.46 thf(decl_32, type, setunionAx: $o). 142.40/18.46 thf(decl_33, type, omega: $i). 142.40/18.46 thf(decl_34, type, omega0Ax: $o). 142.40/18.46 thf(decl_35, type, omegaSAx: $o). 142.40/18.46 thf(decl_36, type, omegaIndAx: $o). 142.40/18.46 thf(decl_37, type, replAx: $o). 142.40/18.46 thf(decl_38, type, foundationAx: $o). 142.40/18.46 thf(decl_39, type, wellorderingAx: $o). 142.40/18.46 thf(decl_40, type, descr: ($i > $o) > $i). 142.40/18.46 thf(decl_41, type, descrp: $o). 142.40/18.46 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 142.40/18.46 thf(decl_43, type, dsetconstrI: $o). 142.40/18.46 thf(decl_44, type, dsetconstrEL: $o). 142.40/18.46 thf(decl_45, type, dsetconstrER: $o). 142.40/18.46 thf(decl_46, type, exuE1: $o). 142.40/18.46 thf(decl_47, type, prop2set: $o > $i). 142.40/18.46 thf(decl_48, type, prop2setE: $o). 142.40/18.46 thf(decl_49, type, emptysetE: $o). 142.40/18.46 thf(decl_50, type, emptysetimpfalse: $o). 142.40/18.46 thf(decl_51, type, notinemptyset: $o). 142.40/18.46 thf(decl_52, type, exuE3e: $o). 142.40/18.46 thf(decl_53, type, setext: $o). 142.40/18.46 thf(decl_54, type, emptyI: $o). 142.40/18.46 thf(decl_55, type, noeltsimpempty: $o). 142.40/18.46 thf(decl_56, type, setbeta: $o). 142.40/18.46 thf(decl_57, type, nonempty: $i > $o). 142.40/18.46 thf(decl_58, type, nonemptyE1: $o). 142.40/18.46 thf(decl_59, type, nonemptyI: $o). 142.40/18.46 thf(decl_60, type, nonemptyI1: $o). 142.40/18.46 thf(decl_61, type, setadjoinIL: $o). 142.40/18.46 thf(decl_62, type, emptyinunitempty: $o). 142.40/18.46 thf(decl_63, type, setadjoinIR: $o). 142.40/18.46 thf(decl_64, type, setadjoinE: $o). 142.40/18.46 thf(decl_65, type, setadjoinOr: $o). 142.40/18.46 thf(decl_66, type, setoftrueEq: $o). 142.40/18.46 thf(decl_67, type, powersetI: $o). 142.40/18.46 thf(decl_68, type, emptyinPowerset: $o). 142.40/18.46 thf(decl_69, type, emptyInPowerset: $o). 142.40/18.46 thf(decl_70, type, powersetE: $o). 142.40/18.46 thf(decl_71, type, setunionI: $o). 142.40/18.46 thf(decl_72, type, setunionE: $o). 142.40/18.46 thf(decl_73, type, subPowSU: $o). 142.40/18.46 thf(decl_74, type, exuE2: $o). 142.40/18.46 thf(decl_75, type, nonemptyImpWitness: $o). 142.40/18.46 thf(decl_76, type, uniqinunit: $o). 142.40/18.46 thf(decl_77, type, notinsingleton: $o). 142.40/18.46 thf(decl_78, type, eqinunit: $o). 142.40/18.46 thf(decl_79, type, singletonsswitch: $o). 142.40/18.46 thf(decl_80, type, upairsetE: $o). 142.40/18.46 thf(decl_81, type, upairsetIL: $o). 142.40/18.46 thf(decl_82, type, upairsetIR: $o). 142.40/18.46 thf(decl_83, type, emptyE1: $o). 142.40/18.46 thf(decl_84, type, vacuousDall: $o). 142.40/18.46 thf(decl_85, type, quantDeMorgan1: $o). 142.40/18.46 thf(decl_86, type, quantDeMorgan2: $o). 142.40/18.46 thf(decl_87, type, quantDeMorgan3: $o). 142.40/18.46 thf(decl_88, type, quantDeMorgan4: $o). 142.40/18.46 thf(decl_89, type, prop2setI: $o). 142.40/18.46 thf(decl_91, type, prop2set2propI: $o). 142.40/18.46 thf(decl_92, type, notdexE: $o). 142.40/18.46 thf(decl_93, type, notdallE: $o). 142.40/18.46 thf(decl_94, type, exuI1: $o). 142.40/18.46 thf(decl_95, type, exuI3: $o). 142.40/18.46 thf(decl_96, type, exuI2: $o). 142.40/18.46 thf(decl_97, type, inCongP: $o). 142.40/18.46 thf(decl_98, type, in__Cong: $o). 142.40/18.46 thf(decl_99, type, exuE3u: $o). 142.40/18.46 thf(decl_100, type, exu__Cong: $o). 142.40/18.46 thf(decl_101, type, emptyset__Cong: $o). 142.40/18.46 thf(decl_102, type, setadjoin__Cong: $o). 142.40/18.46 thf(decl_103, type, powerset__Cong: $o). 142.40/18.46 thf(decl_104, type, setunion__Cong: $o). 142.40/18.46 thf(decl_105, type, omega__Cong: $o). 142.40/18.46 thf(decl_106, type, exuEu: $o). 142.40/18.46 thf(decl_107, type, descr__Cong: $o). 142.40/18.46 thf(decl_108, type, dsetconstr__Cong: $o). 142.40/18.46 thf(decl_109, type, subset: $i > $i > $o). 142.40/18.46 thf(decl_112, type, subsetI1: $o). 142.40/18.46 thf(decl_113, type, eqimpsubset2: $o). 142.40/18.46 thf(decl_114, type, eqimpsubset1: $o). 142.40/18.46 thf(decl_115, type, subsetI2: $o). 142.40/18.46 thf(decl_116, type, emptysetsubset: $o). 142.40/18.46 thf(decl_117, type, subsetE: $o). 142.40/18.46 thf(decl_118, type, subsetE2: $o). 142.40/18.46 thf(decl_119, type, notsubsetI: $o). 142.40/18.46 thf(decl_120, type, notequalI1: $o). 142.40/18.46 thf(decl_121, type, notequalI2: $o). 142.40/18.46 thf(decl_122, type, subsetRefl: $o). 142.40/18.46 thf(decl_123, type, subsetTrans: $o). 142.40/18.46 thf(decl_124, type, setadjoinSub: $o). 142.40/18.46 thf(decl_125, type, setadjoinSub2: $o). 142.40/18.46 thf(decl_126, type, subset2powerset: $o). 142.40/18.46 thf(decl_127, type, setextsub: $o). 142.40/18.46 thf(decl_128, type, subsetemptysetimpeq: $o). 142.40/18.46 thf(decl_129, type, powersetI1: $o). 142.40/18.46 thf(decl_130, type, powersetE1: $o). 142.40/18.46 thf(decl_131, type, inPowerset: $o). 142.40/18.46 thf(decl_132, type, powersetsubset: $o). 142.40/18.46 thf(decl_133, type, sepInPowerset: $o). 142.40/18.46 thf(decl_134, type, sepSubset: $o). 142.40/18.46 thf(decl_135, type, binunion: $i > $i > $i). 142.40/18.46 thf(decl_136, type, binunionIL: $o). 142.40/18.46 thf(decl_137, type, upairset2IR: $o). 142.40/18.46 thf(decl_138, type, binunionIR: $o). 142.40/18.46 thf(decl_139, type, binunionEcases: $o). 142.40/18.46 thf(decl_140, type, binunionE: $o). 142.40/18.46 thf(decl_141, type, binunionLsub: $o). 142.40/18.46 thf(decl_142, type, binunionRsub: $o). 142.40/18.46 thf(decl_143, type, binintersect: $i > $i > $i). 142.40/18.46 thf(decl_144, type, binintersectI: $o). 142.40/18.46 thf(decl_145, type, binintersectSubset5: $o). 142.40/18.46 thf(decl_146, type, binintersectEL: $o). 142.40/18.46 thf(decl_147, type, binintersectLsub: $o). 142.40/18.46 thf(decl_148, type, binintersectSubset2: $o). 142.40/18.46 thf(decl_149, type, binintersectSubset3: $o). 142.40/18.46 thf(decl_150, type, binintersectER: $o). 142.40/18.46 thf(decl_151, type, disjointsetsI1: $o). 142.40/18.46 thf(decl_152, type, binintersectRsub: $o). 142.40/18.46 thf(decl_153, type, binintersectSubset4: $o). 142.40/18.46 thf(decl_154, type, binintersectSubset1: $o). 142.40/18.46 thf(decl_155, type, bs114d: $o). 142.40/18.46 thf(decl_157, type, setminus: $i > $i > $i). 142.40/18.46 thf(decl_158, type, setminusI: $o). 142.40/18.46 thf(decl_159, type, setminusEL: $o). 142.40/18.46 thf(decl_160, type, setminusER: $o). 142.40/18.46 thf(decl_161, type, setminusSubset2: $o). 142.40/18.46 thf(decl_162, type, setminusERneg: $o). 142.40/18.46 thf(decl_163, type, setminusELneg: $o). 142.40/18.46 thf(decl_164, type, setminusILneg: $o). 142.40/18.46 thf(decl_165, type, setminusIRneg: $o). 142.40/18.46 thf(decl_166, type, setminusLsub: $o). 142.40/18.46 thf(decl_167, type, setminusSubset1: $o). 142.40/18.46 thf(decl_168, type, symdiff: $i > $i > $i). 142.40/18.46 thf(decl_169, type, symdiffE: $o). 142.40/18.46 thf(decl_170, type, symdiffI1: $o). 142.40/18.46 thf(decl_171, type, symdiffI2: $o). 142.40/18.46 thf(decl_172, type, symdiffIneg1: $o). 142.40/18.46 thf(decl_173, type, symdiffIneg2: $o). 142.40/18.46 thf(decl_174, type, iskpair: $i > $o). 142.40/18.46 thf(decl_175, type, secondinupair: $o). 142.40/18.46 thf(decl_176, type, setukpairIL: $o). 142.40/18.46 thf(decl_177, type, setukpairIR: $o). 142.40/18.46 thf(decl_178, type, kpairiskpair: $o). 142.40/18.46 thf(decl_179, type, kpair: $i > $i > $i). 142.40/18.46 thf(decl_180, type, kpairp: $o). 142.40/18.46 thf(decl_181, type, cartprod: $i > $i > $i). 142.40/18.46 thf(decl_182, type, singletonsubset: $o). 142.40/18.46 thf(decl_183, type, singletoninpowerset: $o). 142.40/18.46 thf(decl_184, type, singletoninpowunion: $o). 142.40/18.46 thf(decl_185, type, upairset2E: $o). 142.40/18.46 thf(decl_186, type, upairsubunion: $o). 142.40/18.46 thf(decl_187, type, upairinpowunion: $o). 142.40/18.46 thf(decl_188, type, ubforcartprodlem1: $o). 142.40/18.46 thf(decl_189, type, ubforcartprodlem2: $o). 142.40/18.46 thf(decl_190, type, ubforcartprodlem3: $o). 142.40/18.46 thf(decl_191, type, cartprodpairin: $o). 142.40/18.46 thf(decl_192, type, cartprodmempair1: $o). 142.40/18.46 thf(decl_193, type, cartprodmempair: $o). 142.40/18.46 thf(decl_194, type, setunionE2: $o). 142.40/18.46 thf(decl_195, type, setunionsingleton1: $o). 142.40/18.46 thf(decl_196, type, setunionsingleton2: $o). 142.40/18.46 thf(decl_197, type, setunionsingleton: $o). 142.40/18.46 thf(decl_198, type, singleton: $i > $o). 142.40/18.46 thf(decl_199, type, singletonprop: $o). 142.40/18.46 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 142.40/18.46 thf(decl_201, type, ex1E1: $o). 142.40/18.46 thf(decl_202, type, ex1I: $o). 142.40/18.46 thf(decl_203, type, ex1I2: $o). 142.40/18.46 thf(decl_204, type, singletonsuniq: $o). 142.40/18.46 thf(decl_209, type, setukpairinjL1: $o). 142.40/18.46 thf(decl_210, type, kfstsingleton: $o). 142.40/18.46 thf(decl_211, type, theprop: $o). 142.40/18.46 thf(decl_212, type, kfst: $i > $i). 142.40/18.46 thf(decl_213, type, kfstpairEq: $o). 142.40/18.46 thf(decl_214, type, cartprodfstin: $o). 142.40/18.46 thf(decl_215, type, setukpairinjL2: $o). 142.40/18.46 thf(decl_216, type, setukpairinjL: $o). 142.40/18.46 thf(decl_217, type, setukpairinjR11: $o). 142.40/18.46 thf(decl_218, type, setukpairinjR12: $o). 142.40/18.46 thf(decl_219, type, setukpairinjR1: $o). 142.40/18.46 thf(decl_220, type, upairequniteq: $o). 142.40/18.46 thf(decl_221, type, setukpairinjR2: $o). 142.40/18.46 thf(decl_222, type, setukpairinjR: $o). 142.40/18.46 thf(decl_223, type, ksndsingleton: $o). 142.40/18.46 thf(decl_224, type, ksnd: $i > $i). 142.40/18.46 thf(decl_225, type, ksndpairEq: $o). 142.40/18.46 thf(decl_226, type, kpairsurjEq: $o). 142.40/18.46 thf(decl_227, type, cartprodsndin: $o). 142.40/18.46 thf(decl_228, type, cartprodpairmemEL: $o). 142.40/18.46 thf(decl_229, type, cartprodpairmemER: $o). 142.40/18.46 thf(decl_230, type, cartprodmempaircEq: $o). 142.40/18.46 thf(decl_231, type, cartprodfstpairEq: $o). 142.40/18.46 thf(decl_232, type, cartprodsndpairEq: $o). 142.40/18.46 thf(decl_233, type, cartprodpairsurjEq: $o). 142.40/18.46 thf(decl_234, type, breln: $i > $i > $i > $o). 142.40/18.46 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 142.40/18.46 thf(decl_236, type, dpsetconstrI: $o). 142.40/18.46 thf(decl_237, type, dpsetconstrSub: $o). 142.40/18.46 thf(decl_238, type, setOfPairsIsBReln: $o). 142.40/18.46 thf(decl_239, type, dpsetconstrERa: $o). 142.40/18.46 thf(decl_240, type, dpsetconstrEL1: $o). 142.40/18.46 thf(decl_241, type, dpsetconstrEL2: $o). 142.40/18.46 thf(decl_242, type, dpsetconstrER: $o). 142.40/18.46 thf(decl_243, type, func: $i > $i > $i > $o). 142.40/18.46 thf(decl_244, type, funcSet: $i > $i > $i). 142.40/18.46 thf(decl_245, type, funcImageSingleton: $o). 142.40/18.46 thf(decl_246, type, apProp: $o). 142.40/18.46 thf(decl_247, type, ap: $i > $i > $i > $i > $i). 142.40/18.46 thf(decl_248, type, app: $o). 142.40/18.46 thf(decl_249, type, infuncsetfunc: $o). 142.40/18.46 thf(decl_250, type, ap2p: $o). 142.40/18.46 thf(decl_251, type, funcinfuncset: $o). 142.40/18.46 thf(decl_252, type, lamProp: $o). 142.40/18.46 thf(decl_253, type, lam: $i > $i > ($i > $i) > $i). 142.40/18.46 thf(decl_254, type, lamp: $o). 142.40/18.46 thf(decl_255, type, lam2p: $o). 142.40/18.46 thf(decl_256, type, brelnall1: $o). 142.40/18.46 thf(decl_257, type, brelnall2: $o). 142.40/18.46 thf(decl_258, type, ex1E2: $o). 142.40/18.46 thf(decl_259, type, funcGraphProp1: $o). 142.40/18.46 thf(decl_260, type, funcGraphProp3: $o). 142.40/18.46 thf(decl_261, type, funcGraphProp2: $o). 142.40/18.46 thf(decl_262, type, funcextLem: $o). 142.40/18.46 thf(decl_263, type, funcGraphProp4: $o). 142.40/18.46 thf(decl_264, type, subbreln: $o). 142.40/18.46 thf(decl_265, type, eqbreln: $o). 142.40/18.46 thf(decl_266, type, funcext: $o). 142.40/18.46 thf(decl_267, type, funcext2: $o). 142.40/18.46 thf(decl_268, type, ap2apEq1: $o). 142.40/18.46 thf(decl_269, type, ap2apEq2: $o). 142.40/18.46 thf(decl_270, type, beta1: $o). 142.40/18.46 thf(decl_271, type, eta1: $o). 142.40/18.46 thf(decl_272, type, lam2lamEq: $o). 142.40/18.46 thf(decl_273, type, beta2: $o). 142.40/18.46 thf(decl_274, type, eta2: $o). 142.40/18.46 thf(decl_275, type, iffalseProp1: $o). 142.40/18.46 thf(decl_276, type, iffalseProp2: $o). 142.40/18.46 thf(decl_277, type, iftrueProp1: $o). 142.40/18.46 thf(decl_278, type, iftrueProp2: $o). 142.40/18.46 thf(decl_279, type, ifSingleton: $o). 142.40/18.46 thf(decl_280, type, if: $i > $o > $i > $i > $i). 142.40/18.46 thf(decl_281, type, ifp: $o). 142.40/18.46 thf(decl_282, type, theeq: $o). 142.40/18.46 thf(decl_283, type, iftrue: $o). 142.40/18.46 thf(decl_284, type, iffalse: $o). 142.40/18.46 thf(decl_285, type, iftrueorfalse: $o). 142.40/18.46 thf(decl_286, type, binintersectT_lem: $o). 142.40/18.46 thf(decl_287, type, binunionT_lem: $o). 142.40/18.46 thf(decl_288, type, powersetT_lem: $o). 142.40/18.46 thf(decl_289, type, setminusT_lem: $o). 142.40/18.46 thf(decl_290, type, complementT_lem: $o). 142.40/18.46 thf(decl_291, type, setextT: $o). 142.40/18.46 thf(decl_292, type, subsetTI: $o). 142.40/18.46 thf(decl_293, type, powersetTI1: $o). 142.40/18.46 thf(decl_294, type, powersetTE1: $o). 142.40/18.46 thf(decl_295, type, complementTI1: $o). 142.40/18.46 thf(decl_296, type, complementTE1: $o). 142.40/18.46 thf(decl_297, type, binintersectTELcontra: $o). 142.40/18.46 thf(decl_298, type, binintersectTERcontra: $o). 142.40/18.46 thf(decl_299, type, contrasubsetT: $o). 142.40/18.46 thf(decl_300, type, contrasubsetT1: $o). 142.40/18.46 thf(decl_301, type, contrasubsetT2: $o). 142.40/18.46 thf(decl_302, type, contrasubsetT3: $o). 142.40/18.46 thf(decl_303, type, doubleComplementI1: $o). 142.40/18.46 thf(decl_304, type, doubleComplementE1: $o). 142.40/18.46 thf(decl_305, type, doubleComplementSub1: $o). 142.40/18.46 thf(decl_306, type, epred1_0: $o). 142.40/18.46 thf(decl_307, type, esk1_2: $i > $i > $i). 142.40/18.46 thf(decl_308, type, esk2_2: $i > $i > $i). 142.40/18.46 thf(decl_309, type, esk3_2: $i > $i > $i). 142.40/18.46 thf(decl_310, type, esk4_1: $i > $i). 142.40/18.46 thf(decl_311, type, esk5_2: ($i > $i > $o) > $i > $i). 142.40/18.46 thf(decl_312, type, esk6_2: ($i > $i > $o) > $i > $i). 142.40/18.46 thf(decl_313, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 142.40/18.46 thf(decl_314, type, esk8_1: $i > $i). 142.40/18.46 thf(decl_315, type, esk9_1: ($i > $o) > $i). 142.40/18.46 thf(decl_316, type, esk10_1: ($i > $o) > $i). 142.40/18.46 thf(decl_317, type, esk11_2: $i > $i > $i). 142.40/18.46 thf(decl_318, type, esk12_2: $i > $i > $i). 142.40/18.46 thf(decl_319, type, esk13_1: $i > $i). 142.40/18.46 thf(decl_320, type, esk14_1: $i > $i). 142.40/18.46 thf(decl_321, type, esk15_1: $i > $i). 142.40/18.46 thf(decl_322, type, esk16_2: $i > $i > $i). 142.40/18.46 thf(decl_323, type, esk17_3: $i > $i > $o > $i). 142.40/18.46 thf(decl_324, type, esk18_1: ($i > $o) > $i). 142.40/18.46 thf(decl_325, type, esk19_1: $i > $i). 142.40/18.46 thf(decl_326, type, esk20_2: $i > ($i > $o) > $i). 142.40/18.46 thf(decl_327, type, esk21_2: $i > ($i > $o) > $i). 142.40/18.46 thf(decl_328, type, esk22_2: $i > ($i > $o) > $i). 142.40/18.46 thf(decl_329, type, esk23_2: $i > ($i > $o) > $i). 142.40/18.46 thf(decl_330, type, esk24_2: $i > ($i > $o) > $i). 142.40/18.46 thf(decl_331, type, esk25_2: $i > ($i > $o) > $i). 142.40/18.46 thf(decl_332, type, esk26_2: ($i > $o) > $i > $i). 142.40/18.46 thf(decl_333, type, esk27_1: ($i > $o) > $i). 142.40/18.46 thf(decl_334, type, esk28_1: ($i > $o) > $i). 142.40/18.46 thf(decl_335, type, esk29_2: ($i > $o) > $i > $i). 142.40/18.46 thf(decl_336, type, esk30_2: ($i > $o) > ($i > $o) > $i). 142.40/18.46 thf(decl_337, type, esk31_2: ($i > $o) > ($i > $o) > $i). 142.40/18.46 thf(decl_338, type, esk32_2: ($i > $o) > ($i > $o) > $i). 142.40/18.46 thf(decl_339, type, esk33_2: ($i > $o) > ($i > $o) > $i). 142.40/18.46 thf(decl_340, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i). 142.40/18.46 thf(decl_341, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i). 142.40/18.46 thf(decl_342, type, esk36_2: $i > $i > $i). 142.40/18.46 thf(decl_343, type, esk37_2: $i > $i > $i). 142.40/18.46 thf(decl_344, type, esk38_2: $i > $i > $i). 142.40/18.46 thf(decl_345, type, esk39_3: $i > $i > $i > $i). 142.40/18.46 thf(decl_346, type, esk40_3: $i > $i > $i > $i). 142.40/18.46 thf(decl_347, type, esk41_2: $i > $i > $i). 142.40/18.46 thf(decl_348, type, esk42_2: $i > ($i > $o) > $i). 142.40/18.46 thf(decl_349, type, esk43_2: $i > ($i > $o) > $i). 142.40/18.46 thf(decl_350, type, esk44_2: $i > ($i > $o) > $i). 142.40/18.46 thf(decl_351, type, esk45_3: $i > ($i > $o) > $i > $i). 142.40/18.46 thf(decl_352, type, esk46_2: $i > ($i > $o) > $i). 142.40/18.46 thf(decl_353, type, esk47_2: $i > ($i > $o) > $i). 142.40/18.46 thf(decl_354, type, esk48_3: $i > $i > ($i > $i) > $i). 142.40/18.46 thf(decl_355, type, esk49_3: $i > $i > ($i > $i) > $i). 142.40/18.46 thf(decl_356, type, esk50_3: $i > $i > ($i > $i) > $i). 142.40/18.46 thf(decl_357, type, esk51_4: $i > $i > $i > ($i > $o) > $i). 142.40/18.46 thf(decl_358, type, esk52_4: $i > $i > $i > ($i > $o) > $i). 142.40/18.46 thf(decl_359, type, esk53_4: $i > $i > $i > ($i > $o) > $i). 142.40/18.46 thf(decl_360, type, esk54_4: $i > $i > $i > ($i > $o) > $i). 142.40/18.46 thf(decl_361, type, esk55_4: $i > $i > $i > $i > $i). 142.40/18.46 thf(decl_362, type, esk56_4: $i > $i > $i > $i > $i). 142.40/18.46 thf(decl_363, type, esk57_4: $i > $i > $i > $i > $i). 142.40/18.46 thf(decl_364, type, esk58_4: $i > $i > $i > $i > $i). 142.40/18.46 thf(decl_365, type, esk59_4: $i > $i > $i > $i > $i). 142.40/18.46 thf(decl_366, type, esk60_4: $i > $i > $i > $i > $i). 142.40/18.46 thf(decl_367, type, esk61_4: $i > $i > $i > $i > $i). 142.40/18.46 thf(decl_368, type, esk62_4: $i > $i > $i > $i > $i). 142.40/18.46 thf(decl_369, type, esk63_4: $i > $i > $i > $i > $i). 142.40/18.46 thf(decl_370, type, esk64_3: $i > $i > ($i > $i) > $i). 142.40/18.46 thf(decl_371, type, esk65_3: $i > $i > ($i > $i) > $i). 142.40/18.46 thf(decl_372, type, esk66_3: $i > $i > ($i > $i) > $i). 142.40/18.46 thf(decl_373, type, esk67_3: $i > $i > $i > $i). 142.40/18.46 thf(decl_374, type, esk68_3: $i > $i > $i > $i). 142.40/18.46 thf(decl_375, type, esk69_3: $i > $i > $i > $i). 142.40/18.46 thf(decl_376, type, esk70_3: $i > $i > $i > $i). 142.40/18.46 thf(decl_377, type, esk71_0: $i). 142.40/18.46 thf(decl_378, type, esk72_0: $i). 142.40/18.46 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', dsetconstr__Cong)). 142.40/18.46 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', descr__Cong)). 142.40/18.46 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', exu__Cong)). 142.40/18.46 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', exuI3)). 142.40/18.46 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', exuI1)). 142.40/18.46 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setoftrueEq)). 142.40/18.46 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', nonemptyI)). 142.40/18.46 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setbeta)). 142.40/18.46 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', exuE1)). 142.40/18.46 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', dsetconstrER)). 142.40/18.46 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', dsetconstrEL)). 142.40/18.46 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', replAx)). 142.40/18.46 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', singletonprop)). 142.40/18.46 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', ex1E1)). 142.40/18.46 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', kfstsingleton)). 142.40/18.46 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', dpsetconstrI)). 142.40/18.46 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', dpsetconstrEL1)). 142.40/18.46 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', dpsetconstrEL2)). 142.40/18.46 thf(apProp, axiom, ((apProp)<=>![X4:$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.XTVzWcq4tA/Vampire---4.8_9768', apProp)). 142.40/18.46 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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', lamp)). 142.40/18.46 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', lam2p)). 142.40/18.46 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.XTVzWcq4tA/Vampire---4.8_9768', ex1E2)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', beta1)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', eta2)). 142.40/18.46 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', iffalseProp2)). 142.40/18.46 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$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.XTVzWcq4tA/Vampire---4.8_9768', iftrueProp1)). 142.40/18.46 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', iftrueProp2)). 142.40/18.46 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$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.XTVzWcq4tA/Vampire---4.8_9768', ifSingleton)). 142.40/18.46 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', iffalseProp1)). 142.40/18.46 thf(beta2, axiom, ((beta2)<=>![X4:$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.XTVzWcq4tA/Vampire---4.8_9768', beta2)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', lam2lamEq)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', eta1)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', lamProp)). 142.40/18.46 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', funcImageSingleton)). 142.40/18.46 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', dpsetconstrER)). 142.40/18.46 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', dpsetconstrERa)). 142.40/18.46 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setOfPairsIsBReln)). 142.40/18.46 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', dpsetconstrSub)). 142.40/18.46 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', ksndsingleton)). 142.40/18.46 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', ex1I2)). 142.40/18.46 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.XTVzWcq4tA/Vampire---4.8_9768', ex1I)). 142.40/18.46 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', sepSubset)). 142.40/18.46 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', sepInPowerset)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', exuEu)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', exuE3u)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', exuI2)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', emptyE1)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', exuE2)). 142.40/18.46 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', exuE3e)). 142.40/18.46 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', dsetconstrI)). 142.40/18.46 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', descrp)). 142.40/18.46 thf(doubleComplementSub2, conjecture, (((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>(((((omegaIndAx)=>(((foundationAx)=>(((descrp)=>((dsetconstrI)=>((((((emptysetE)=>(((notinemptyset)=>((exuE3e)=>(((emptyI)=>(((((((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((((((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>(((notinsingleton)=>(((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>(((quantDeMorgan1)=>(((quantDeMorgan3)=>((quantDeMorgan4)=>(((prop2set2propI)=>((((((exuI2)=>((inCongP)=>(((exuE3u)=>((((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>(((exuEu)=>(((((((subsetI2)=>(((subsetE)=>(((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>(((setadjoinSub)=>(((subset2powerset)=>((((powersetI1)=>((((powersetsubset)=>((sepInPowerset)=>(((binunionIL)=>(((binunionIR)=>(((binunionE)=>(((binunionRsub)=>((((binintersectEL)=>(((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>(((binintersectRsub)=>(((binintersectSubset1)=>(((((setminusER)=>((setminusSubset2)=>(((setminusELneg)=>((setminusILneg)=>(((setminusLsub)=>(((symdiffE)=>((((((secondinupair)=>((setukpairIL)=>(((kpairiskpair)=>((kpairp)=>((((singletoninpowunion)=>(((upairsubunion)=>(((((ubforcartprodlem3)=>((((((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((((singletonsuniq)=>(((kfstsingleton)=>(((((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>(((setukpairinjR1)=>((upairequniteq)=>(((((ksndpairEq)=>(((cartprodsndin)=>((cartprodpairmemEL)=>(((((((dpsetconstrI)=>(((((dpsetconstrEL1)=>((dpsetconstrEL2)=>((((apProp)=>((app)=>((((((lamp)=>((lam2p)=>((((ex1E2)=>(((((funcextLem)=>((funcGraphProp4)=>((((funcext)=>((funcext2)=>((((beta1)=>(((((eta2)=>(((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((((theeq)=>(((iffalse)=>((((binunionT_lem)=>((powersetT_lem)=>((((((powersetTI1)=>((powersetTE1)=>((complementTI1)=>(((binintersectTELcontra)=>((binintersectTERcontra)=>(((contrasubsetT1)=>((contrasubsetT2)=>((((![X4:$i, X21:$i]:(((subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)<=(in @ X21 @ (powerset @ X4))))<=(doubleComplementSub1))<=(doubleComplementE1))<=(doubleComplementI1))<=(contrasubsetT3))))<=(contrasubsetT))))<=(complementTE1)))))<=(subsetTI))<=(setextT))<=(complementT_lem))<=(setminusT_lem))))<=(binintersectT_lem))<=(iftrueorfalse)))<=(iftrue)))<=(ifp))<=(ifSingleton)))))<=(iffalseProp1)))<=(beta2))<=(lam2lamEq))<=(eta1)))<=(ap2apEq2))<=(ap2apEq1))))<=(eqbreln))<=(subbreln))))<=(funcGraphProp2))<=(funcGraphProp3))<=(funcGraphProp1)))<=(brelnall2))<=(brelnall1))))<=(lamProp))<=(funcinfuncset))<=(ap2p))<=(infuncsetfunc))))<=(funcImageSingleton))<=(dpsetconstrER))))<=(dpsetconstrERa))<=(setOfPairsIsBReln))<=(dpsetconstrSub)))<=(cartprodpairsurjEq))<=(cartprodsndpairEq))<=(cartprodfstpairEq))<=(cartprodmempaircEq))<=(cartprodpairmemER))))<=(kpairsurjEq)))<=(ksndsingleton))<=(setukpairinjR))<=(setukpairinjR2))))<=(setukpairinjR12)))))<=(cartprodfstin))<=(kfstpairEq))<=(theprop)))<=(setukpairinjL1)))<=(ex1I2))<=(ex1I)))))))<=(setunionE2))<=(cartprodmempair))<=(cartprodmempair1))<=(cartprodpairin)))<=(ubforcartprodlem2))<=(ubforcartprodlem1))<=(upairinpowunion)))<=(upairset2E)))<=(singletoninpowerset))<=(singletonsubset))))<=(setukpairIR))))<=(symdiffIneg2))<=(symdiffIneg1))<=(symdiffI2))<=(symdiffI1)))<=(setminusSubset1)))<=(setminusIRneg))))<=(setminusERneg))))<=(setminusEL))<=(setminusI))<=(bs114d)))<=(binintersectSubset4)))<=(disjointsetsI1)))))<=(binintersectLsub)))<=(binintersectSubset5))<=(binintersectI)))<=(binunionLsub)))<=(binunionEcases)))<=(upairset2IR)))<=(sepSubset))))<=(inPowerset))<=(powersetE1)))<=(subsetemptysetimpeq))<=(setextsub)))<=(setadjoinSub2)))<=(subsetTrans))))))<=(subsetE2)))<=(emptysetsubset)))<=(eqimpsubset1))<=(eqimpsubset2))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong)))<=(omega__Cong)))))<=(emptyset__Cong))<=(exu__Cong)))<=(in__Cong))))<=(exuI3))<=(exuI1))<=(notdallE))<=(notdexE)))<=(prop2setI))))<=(quantDeMorgan2)))<=(vacuousDall)))))))<=(eqinunit)))<=(uniqinunit)))))<=(setunionE))<=(setunionI)))))<=(powersetI))<=(setoftrueEq))<=(setadjoinOr))<=(setadjoinE)))))<=(nonemptyI1))<=(nonemptyI))<=(nonemptyE1))<=(setbeta))<=(noeltsimpempty)))<=(setext))))<=(emptysetimpfalse)))<=(prop2setE))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL))))<=(wellorderingAx)))<=(replAx)))<=(omegaSAx))<=(omega0Ax))<=(setunionAx)))))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', doubleComplementSub2)). 142.40/18.46 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', binintersectER)). 142.40/18.46 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', uniqinunit)). 142.40/18.46 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setextAx)). 142.40/18.46 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setadjoinSub2)). 142.40/18.46 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', subsetTrans)). 142.40/18.46 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setminusSubset2)). 142.40/18.46 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', subsetE2)). 142.40/18.46 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', emptysetsubset)). 142.40/18.46 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', eqimpsubset1)). 142.40/18.46 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setminusELneg)). 142.40/18.46 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', eqimpsubset2)). 142.40/18.46 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', subsetI1)). 142.40/18.46 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setminusILneg)). 142.40/18.46 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', omega__Cong)). 142.40/18.46 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setminusLsub)). 142.40/18.46 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', emptyset__Cong)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', symdiffE)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', in__Cong)). 142.40/18.46 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', binintersectSubset3)). 142.40/18.46 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', notdallE)). 142.40/18.46 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', secondinupair)). 142.40/18.46 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', notdexE)). 142.40/18.46 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', prop2setI)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', setukpairIL)). 142.40/18.46 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', quantDeMorgan2)). 142.40/18.46 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', vacuousDall)). 142.40/18.46 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', eqinunit)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', setunionE)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', kpairiskpair)). 142.40/18.46 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setunionI)). 142.40/18.46 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', powersetI)). 142.40/18.46 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', kpairp)). 142.40/18.46 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setadjoinOr)). 142.40/18.46 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setadjoinE)). 142.40/18.46 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', singletoninpowunion)). 142.40/18.46 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', nonemptyI1)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', upairsubunion)). 142.40/18.46 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', nonemptyE1)). 142.40/18.46 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', noeltsimpempty)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', ubforcartprodlem3)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', setext)). 142.40/18.46 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', emptysetimpfalse)). 142.40/18.46 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setunionsingleton1)). 142.40/18.46 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', prop2setE)). 142.40/18.46 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setunionsingleton2)). 142.40/18.46 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', wellorderingAx)). 142.40/18.46 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setunionsingleton)). 142.40/18.46 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', omegaSAx)). 142.40/18.46 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', omega0Ax)). 142.40/18.46 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setunionAx)). 142.40/18.46 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', binintersectRsub)). 142.40/18.46 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', singletonsuniq)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', setukpairinjL2)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', setukpairinjL)). 142.40/18.46 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setukpairinjR11)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', setukpairinjR1)). 142.40/18.46 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', contrasubsetT2)). 142.40/18.46 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', upairequniteq)). 142.40/18.46 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', ksndpairEq)). 142.40/18.46 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', cartprodsndin)). 142.40/18.46 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', cartprodpairmemEL)). 142.40/18.46 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', app)). 142.40/18.46 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', binintersectSubset1)). 142.40/18.46 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.XTVzWcq4tA/Vampire---4.8_9768', funcextLem)). 142.40/18.46 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', funcGraphProp4)). 142.40/18.46 thf(funcext, axiom, ((funcext)<=>![X4:$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.XTVzWcq4tA/Vampire---4.8_9768', funcext)). 142.40/18.46 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', funcext2)). 142.40/18.46 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setminusER)). 142.40/18.46 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', theeq)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', iffalse)). 142.40/18.46 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', binunionT_lem)). 142.40/18.46 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', powersetT_lem)). 142.40/18.46 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', powersetTI1)). 142.40/18.46 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', powersetTE1)). 142.40/18.46 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$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.XTVzWcq4tA/Vampire---4.8_9768', complementTI1)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', binintersectTELcontra)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', binintersectTERcontra)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', contrasubsetT1)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', doubleComplementSub1)). 142.40/18.46 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', doubleComplementE1)). 142.40/18.46 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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.XTVzWcq4tA/Vampire---4.8_9768', doubleComplementI1)). 142.40/18.46 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', contrasubsetT3)). 142.40/18.46 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', contrasubsetT)). 142.40/18.46 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$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.XTVzWcq4tA/Vampire---4.8_9768', complementTE1)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', subsetTI)). 142.40/18.46 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setextT)). 142.40/18.46 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', complementT_lem)). 142.40/18.46 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.XTVzWcq4tA/Vampire---4.8_9768', setminusT_lem)). 142.40/18.46 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', binintersectT_lem)). 142.40/18.46 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', iftrueorfalse)). 142.40/18.46 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', iftrue)). 142.40/18.46 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', ifp)). 142.40/18.46 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', ap2apEq2)). 142.40/18.46 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', ap2apEq1)). 142.40/18.46 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', eqbreln)). 142.40/18.46 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', subbreln)). 142.40/18.46 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$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.XTVzWcq4tA/Vampire---4.8_9768', funcGraphProp2)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', funcGraphProp3)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', funcGraphProp1)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', brelnall2)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', brelnall1)). 142.40/18.46 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', funcinfuncset)). 142.40/18.46 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', ap2p)). 142.40/18.46 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', infuncsetfunc)). 142.40/18.46 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', cartprodpairsurjEq)). 142.40/18.46 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', cartprodsndpairEq)). 142.40/18.46 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', cartprodfstpairEq)). 142.40/18.46 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', cartprodmempaircEq)). 142.40/18.46 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', cartprodpairmemER)). 142.40/18.46 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', kpairsurjEq)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', setukpairinjR)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', setukpairinjR2)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', setukpairinjR12)). 142.40/18.46 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', cartprodfstin)). 142.40/18.46 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', kfstpairEq)). 142.40/18.46 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', theprop)). 142.40/18.46 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setukpairinjL1)). 142.40/18.46 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setunionE2)). 142.40/18.46 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', cartprodmempair)). 142.40/18.46 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.XTVzWcq4tA/Vampire---4.8_9768', cartprodmempair1)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', cartprodpairin)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', ubforcartprodlem2)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', ubforcartprodlem1)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', upairinpowunion)). 142.40/18.46 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', upairset2E)). 142.40/18.46 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', singletoninpowerset)). 142.40/18.46 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', singletonsubset)). 142.40/18.46 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setukpairIR)). 142.40/18.46 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', symdiffIneg2)). 142.40/18.46 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', symdiffIneg1)). 142.40/18.46 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', symdiffI2)). 142.40/18.46 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', symdiffI1)). 142.40/18.46 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setminusSubset1)). 142.40/18.46 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setminusIRneg)). 142.40/18.46 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setminusERneg)). 142.40/18.46 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setminusEL)). 142.40/18.46 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setminusI)). 142.40/18.46 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', bs114d)). 142.40/18.46 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', binintersectSubset4)). 142.40/18.46 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', disjointsetsI1)). 142.40/18.46 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', binintersectLsub)). 142.40/18.46 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', binintersectSubset5)). 142.40/18.46 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', binintersectI)). 142.40/18.46 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', binunionLsub)). 142.40/18.46 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', binunionEcases)). 142.40/18.46 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', upairset2IR)). 142.40/18.46 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', inPowerset)). 142.40/18.46 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', powersetE1)). 142.40/18.46 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', subsetemptysetimpeq)). 142.40/18.46 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setextsub)). 142.40/18.46 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', binintersectSubset2)). 142.40/18.46 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', binintersectEL)). 142.40/18.46 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', binunionRsub)). 142.40/18.46 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', binunionE)). 142.40/18.46 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', binunionIR)). 142.40/18.46 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', binunionIL)). 142.40/18.46 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', powersetsubset)). 142.40/18.46 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', powersetI1)). 142.40/18.46 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', subset2powerset)). 142.40/18.46 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setadjoinSub)). 142.40/18.46 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', subsetRefl)). 142.40/18.46 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', notequalI2)). 142.40/18.46 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', notequalI1)). 142.40/18.46 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', notsubsetI)). 142.40/18.46 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', subsetE)). 142.40/18.46 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', subsetI2)). 142.40/18.46 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setunion__Cong)). 142.40/18.46 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', powerset__Cong)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', setadjoin__Cong)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', inCongP)). 142.40/18.46 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', quantDeMorgan4)). 142.40/18.46 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', quantDeMorgan3)). 142.40/18.46 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', quantDeMorgan1)). 142.40/18.46 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', upairsetIR)). 142.40/18.46 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', upairsetIL)). 142.40/18.46 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', upairsetE)). 142.40/18.46 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', singletonsswitch)). 142.40/18.46 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', notinsingleton)). 142.40/18.46 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', nonemptyImpWitness)). 142.40/18.46 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', subPowSU)). 142.40/18.46 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', powersetE)). 142.40/18.46 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', emptyInPowerset)). 142.40/18.46 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', emptyinPowerset)). 142.40/18.46 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setadjoinIR)). 142.40/18.46 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', emptyinunitempty)). 142.40/18.46 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setadjoinIL)). 142.40/18.46 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', emptyI)). 142.40/18.46 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', notinemptyset)). 142.40/18.46 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', emptysetE)). 142.40/18.46 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.XTVzWcq4tA/Vampire---4.8_9768', foundationAx)). 142.40/18.46 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', omegaIndAx)). 142.40/18.46 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', powersetAx)). 142.40/18.46 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', setadjoinAx)). 142.40/18.46 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.XTVzWcq4tA/Vampire---4.8_9768', emptysetAx)). 142.40/18.46 thf(c_0_246, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 142.40/18.46 thf(c_0_247, plain, ((descr__Cong)<=>![X1:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 142.40/18.46 thf(c_0_248, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 142.40/18.46 thf(c_0_249, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 142.40/18.46 thf(c_0_250, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 142.40/18.46 thf(c_0_251, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 142.40/18.46 thf(c_0_252, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 142.40/18.46 thf(c_0_253, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 142.40/18.46 thf(c_0_254, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 142.40/18.46 thf(c_0_255, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 142.40/18.46 thf(c_0_256, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 142.40/18.46 thf(c_0_257, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 142.40/18.46 thf(c_0_258, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 142.40/18.46 thf(c_0_259, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 142.40/18.46 thf(c_0_260, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 142.40/18.46 thf(c_0_261, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 142.40/18.46 thf(c_0_262, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 142.40/18.46 thf(c_0_263, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 142.40/18.46 thf(c_0_264, plain, ((apProp)<=>![X4:$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])). 142.40/18.46 thf(c_0_265, 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 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 142.40/18.46 thf(c_0_266, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 142.40/18.46 thf(c_0_267, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])). 142.40/18.46 thf(c_0_268, 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])). 142.40/18.46 thf(c_0_269, 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])). 142.40/18.46 thf(c_0_270, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])). 142.40/18.46 thf(c_0_271, plain, ((iftrueProp1)<=>![X4:$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])). 142.40/18.46 thf(c_0_272, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])). 142.40/18.46 thf(c_0_273, plain, ((ifSingleton)<=>![X4:$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])). 142.40/18.46 thf(c_0_274, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 142.40/18.46 thf(c_0_275, plain, ((beta2)<=>![X4:$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])). 142.40/18.46 thf(c_0_276, 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])). 142.40/18.46 thf(c_0_277, 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])). 142.40/18.46 thf(c_0_278, 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])). 142.40/18.46 thf(c_0_279, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])). 142.40/18.46 thf(c_0_280, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 142.40/18.46 thf(c_0_281, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 142.40/18.46 thf(c_0_282, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 142.40/18.46 thf(c_0_283, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 142.40/18.46 thf(c_0_284, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 142.40/18.46 thf(c_0_285, plain, ((ex1I2)<=>![X4:$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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 142.40/18.46 thf(c_0_286, plain, ((ex1I)<=>![X4:$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])). 142.40/18.46 thf(c_0_287, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 142.40/18.46 thf(c_0_288, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 142.40/18.46 thf(c_0_289, 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])). 142.40/18.46 thf(c_0_290, 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])). 142.40/18.46 thf(c_0_291, 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])). 142.40/18.46 thf(c_0_292, 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])). 142.40/18.46 thf(c_0_293, 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])). 142.40/18.46 thf(c_0_294, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 142.40/18.46 thf(c_0_295, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 142.40/18.46 thf(c_0_296, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 142.40/18.46 thf(c_0_297, plain, ((epred1_0)<=>![X1541:$i]:(?[X1542:$i]:((((![X1543:$i]:(((in @ X1543 @ X1542)=>![X1544:$i]:(((in @ X1544 @ X1543)=>(in @ X1544 @ X1541)))))&![X1545:$i, X1546:$i]:((((in @ X1545 @ X1541)&(in @ X1546 @ X1541))=>(![X1547:$i]:(((in @ X1547 @ X1542)=>((in @ X1545 @ X1547)<=>(in @ X1546 @ X1547))))=>((X1545)=(X1546))))))&![X1548:$i, X1549:$i]:((((in @ X1548 @ X1542)&(in @ X1549 @ X1542))=>(![X1550:$i]:(((in @ X1550 @ X1548)=>(in @ X1550 @ X1549)))|![X1551:$i]:(((in @ X1551 @ X1549)=>(in @ X1551 @ X1548)))))))&![X1552:$i]:(((![X1553:$i]:(((in @ X1553 @ X1552)=>(in @ X1553 @ X1541)))&?[X1554:$i]:((in @ X1554 @ X1552)))=>?[X1555:$i, X1556:$i]:(((((in @ X1555 @ X1542)&(in @ X1556 @ X1552))&~(?[X1557:$i]:(((in @ X1557 @ X1555)&(in @ X1557 @ X1552)))))&![X1558:$i]:(((in @ X1558 @ X1542)=>(![X1559:$i]:(((in @ X1559 @ X1558)=>(in @ X1559 @ X1555)))|(in @ X1556 @ X1558)))))))))))), introduced(definition)). 142.40/18.46 thf(c_0_298, negated_conjecture, ~((![X1570:$i, X1571:$i]:((![X1572:$i]:(((in @ X1572 @ X1570)<=>(in @ X1572 @ X1571)))=>((X1570)=(X1571))))=>(![X812:$i]:(~(in @ X812 @ emptyset))=>(![X813:$i, X814:$i, X815:$i]:(((in @ X815 @ (setadjoin @ X813 @ X814))<=>(((X815)=(X813))|(in @ X815 @ X814))))=>(![X816:$i, X817:$i]:(((in @ X817 @ (powerset @ X816))<=>![X818:$i]:(((in @ X818 @ X817)=>(in @ X818 @ X816)))))=>(![X1567:$i, X1568:$i]:(((in @ X1568 @ (setunion @ X1567))<=>?[X1569:$i]:(((in @ X1568 @ X1569)&(in @ X1569 @ X1567)))))=>((in @ emptyset @ omega)=>(![X1566:$i]:(((in @ X1566 @ omega)=>(in @ (setadjoin @ X1566 @ X1566) @ omega)))=>(![X819:$i]:((((in @ emptyset @ X819)&![X820:$i]:((((in @ X820 @ omega)&(in @ X820 @ X819))=>(in @ (setadjoin @ X820 @ X820) @ X819))))=>![X821:$i]:(((in @ X821 @ omega)=>(in @ X821 @ X819)))))=>(![X1560:$i > $i > $o, X1561:$i]:((![X1562:$i]:(((in @ X1562 @ X1561)=>(exu @ (^[Z0/* 3 */:$i]:((X1560 @ X1562 @ Z0))))))=>?[X1563:$i]:(![X1564:$i]:(((in @ X1564 @ X1563)<=>?[X1565:$i]:(((in @ X1565 @ X1561)&(X1560 @ X1565 @ X1564))))))))=>(![X822:$i]:((?[X823:$i]:((in @ X823 @ X822))=>?[X824:$i]:(((in @ X824 @ X822)&~(?[X825:$i]:(((in @ X825 @ X824)&(in @ X825 @ X822))))))))=>((epred1_0)=>(![X826:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X826 @ Z0))))=>(X826 @ (descr @ (^[Z0/* 3 */:$i]:((X826 @ Z0)))))))=>(![X827:$i, X828:$i > $o, X829:$i]:(((in @ X829 @ X827)=>((X828 @ X829)=>(in @ X829 @ (dsetconstr @ X827 @ (^[Z0/* 3 */:$i]:((X828 @ Z0))))))))=>(![X1538:$i, X1539:$i > $o, X1540:$i]:(((in @ X1540 @ (dsetconstr @ X1538 @ (^[Z0/* 3 */:$i]:((X1539 @ Z0)))))=>(in @ X1540 @ X1538)))=>(![X1535:$i, X1536:$i > $o, X1537:$i]:(((in @ X1537 @ (dsetconstr @ X1535 @ (^[Z0/* 3 */:$i]:((X1536 @ Z0)))))=>(X1536 @ X1537)))=>(![X1532:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1532 @ Z0))))=>?[X1533:$i]:(((X1532 @ X1533)&![X1534:$i]:(((X1532 @ X1534)=>((X1533)=(X1534))))))))=>(![X1530:$o, X1531:$i]:(((in @ X1531 @ (prop2set @ ((X1530))))=>(X1530)))=>(![X830:$i]:(((in @ X830 @ emptyset)=>![X831:$o]:((X831))))=>(![X1529:$i]:(~(in @ X1529 @ emptyset))=>(![X832:$i]:(~(in @ X832 @ emptyset))=>(![X833:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X833 @ Z0))))=>?[X834:$i]:((X833 @ X834))))=>(![X1525:$i, X1526:$i]:((![X1527:$i]:(((in @ X1527 @ X1525)=>(in @ X1527 @ X1526)))=>(![X1528:$i]:(((in @ X1528 @ X1526)=>(in @ X1528 @ X1525)))=>((X1525)=(X1526)))))=>(![X835:$i]:((![X836:$i]:(~(in @ X836 @ X835))=>((X835)=(emptyset))))=>(![X1523:$i]:((![X1524:$i]:(~(in @ X1524 @ X1523))=>((X1523)=(emptyset))))=>(![X1520:$i, X1521:$i > $o, X1522:$i]:(((in @ X1522 @ X1520)=>((in @ X1522 @ (dsetconstr @ X1520 @ (^[Z0/* 3 */:$i]:((X1521 @ Z0)))))<=>(X1521 @ X1522))))=>(![X1518:$i]:(((nonempty @ X1518)=>?[X1519:$i]:((in @ X1519 @ X1518))))=>(![X1515:$i, X1516:$i > $o, X1517:$i]:(((in @ X1517 @ X1515)=>((X1516 @ X1517)=>(nonempty @ (dsetconstr @ X1515 @ (^[Z0/* 3 */:$i]:((X1516 @ Z0))))))))=>(![X1513:$i]:((?[X1514:$i]:((in @ X1514 @ X1513))=>(nonempty @ X1513)))=>(![X837:$i, X838:$i]:((in @ X837 @ (setadjoin @ X837 @ X838)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X839:$i, X840:$i, X841:$i]:(((in @ X841 @ X840)=>(in @ X841 @ (setadjoin @ X839 @ X840))))=>(![X1509:$i, X1510:$i, X1511:$i]:(((in @ X1511 @ (setadjoin @ X1509 @ X1510))=>![X1512:$o]:(((((X1511)=(X1509))=>(X1512))=>(((in @ X1511 @ X1510)=>(X1512))=>(X1512))))))=>(![X1506:$i, X1507:$i, X1508:$i]:(((in @ X1508 @ (setadjoin @ X1506 @ X1507))=>(((X1508)=(X1506))|(in @ X1508 @ X1507))))=>(![X1505:$i]:(((dsetconstr @ X1505 @ (^[Z0/* 3 */:$i]:(($true))))=(X1505)))=>(![X1502:$i, X1503:$i]:((![X1504:$i]:(((in @ X1504 @ X1503)=>(in @ X1504 @ X1502)))=>(in @ X1503 @ (powerset @ X1502))))=>(![X842:$i]:((in @ emptyset @ (powerset @ X842)))=>(![X843:$i]:((in @ emptyset @ (powerset @ X843)))=>(![X844:$i, X845:$i, X846:$i]:(((in @ X845 @ (powerset @ X844))=>((in @ X846 @ X845)=>(in @ X846 @ X844))))=>(![X1499:$i, X1500:$i, X1501:$i]:(((in @ X1500 @ X1501)=>((in @ X1501 @ X1499)=>(in @ X1500 @ (setunion @ X1499)))))=>(![X1495:$i, X1496:$i]:(((in @ X1496 @ (setunion @ X1495))=>![X1497:$o]:((![X1498:$i]:(((in @ X1496 @ X1498)=>((in @ X1498 @ X1495)=>(X1497))))=>(X1497)))))=>(![X847:$i, X848:$i]:(((in @ X848 @ X847)=>(in @ X848 @ (powerset @ (setunion @ X847)))))=>(![X849:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X849 @ Z0))))=>?[X850:$i]:(![X851:$i]:(((X849 @ X851)<=>((X851)=(X850)))))))=>(![X852:$i]:(((nonempty @ X852)=>?[X853:$i]:((in @ X853 @ X852))))=>(![X1493:$i, X1494:$i]:(((in @ X1493 @ (setadjoin @ X1494 @ emptyset))=>((X1493)=(X1494))))=>(![X854:$i, X855:$i]:((((X854)!=(X855))=>~(in @ X855 @ (setadjoin @ X854 @ emptyset))))=>(![X1491:$i, X1492:$i]:((((X1491)=(X1492))=>(in @ X1491 @ (setadjoin @ X1492 @ emptyset))))=>(![X856:$i, X857:$i]:(((in @ X856 @ (setadjoin @ X857 @ emptyset))=>(in @ X857 @ (setadjoin @ X856 @ emptyset))))=>(![X858:$i, X859:$i, X860:$i]:(((in @ X860 @ (setadjoin @ X858 @ (setadjoin @ X859 @ emptyset)))=>(((X860)=(X858))|((X860)=(X859)))))=>(![X861:$i, X862:$i]:((in @ X861 @ (setadjoin @ X861 @ (setadjoin @ X862 @ emptyset))))=>(![X863:$i, X864:$i]:((in @ X864 @ (setadjoin @ X863 @ (setadjoin @ X864 @ emptyset))))=>(![X865:$i, X866:$i > $o]:((?[X867:$i]:(((in @ X867 @ X865)&(X866 @ X867)))=>((dsetconstr @ X865 @ (^[Z0/* 3 */:$i]:((X866 @ Z0))))!=(emptyset))))=>(![X1489:$i > $o, X1490:$i]:(((in @ X1490 @ emptyset)=>(X1489 @ X1490)))=>(![X868:$i, X869:$i > $o]:((~(![X870:$i]:(((in @ X870 @ X868)=>(X869 @ X870))))=>?[X871:$i]:(((in @ X871 @ X868)&~(X869 @ X871)))))=>(![X1485:$i, X1486:$i > $o]:((![X1487:$i]:(((in @ X1487 @ X1485)=>~(X1486 @ X1487)))=>~(?[X1488:$i]:(((in @ X1488 @ X1485)&(X1486 @ X1488))))))=>(![X872:$i, X873:$i > $o]:((~(?[X874:$i]:(((in @ X874 @ X872)&(X873 @ X874))))=>![X875:$i]:(((in @ X875 @ X872)=>~(X873 @ X875)))))=>(![X876:$i, X877:$i > $o]:((?[X878:$i]:(((in @ X878 @ X876)&~(X877 @ X878)))=>~(![X879:$i]:(((in @ X879 @ X876)=>(X877 @ X879))))))=>(![X1484:$o]:(((X1484)=>(in @ emptyset @ (prop2set @ ((X1484))))))=>((prop2set2propI)=>(![X1480:$i, X1481:$i > $o]:((~(?[X1482:$i]:(((in @ X1482 @ X1480)&(X1481 @ X1482))))=>![X1483:$i]:(((in @ X1483 @ X1480)=>~(X1481 @ X1483)))))=>(![X1476:$i, X1477:$i > $o]:((~(![X1478:$i]:(((in @ X1478 @ X1476)=>(X1477 @ X1478))))=>?[X1479:$i]:(((in @ X1479 @ X1476)&~(X1477 @ X1479)))))=>(![X1473:$i > $o]:((?[X1474:$i]:(((X1473 @ X1474)&![X1475:$i]:(((X1473 @ X1475)=>((X1474)=(X1475))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1473 @ Z0))))))=>(![X1469:$i > $o]:((?[X1470:$i]:((X1469 @ X1470))=>(![X1471:$i, X1472:$i]:(((X1469 @ X1471)=>((X1469 @ X1472)=>((X1471)=(X1472)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1469 @ Z0)))))))=>(![X880:$i > $o]:((?[X881:$i]:(![X882:$i]:(((X880 @ X882)<=>((X882)=(X881)))))=>(exu @ (^[Z0/* 3 */:$i]:((X880 @ Z0))))))=>(![X883:$i, X884:$i]:((((X883)=(X884))=>![X885:$i, X886:$i]:((((X885)=(X886))=>((in @ X885 @ X883)=>(in @ X886 @ X884))))))=>(![X1465:$i, X1466:$i]:((((X1465)=(X1466))=>![X1467:$i, X1468:$i]:((((X1467)=(X1468))=>((in @ X1467 @ X1465)<=>(in @ X1468 @ X1466))))))=>(![X887:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X887 @ Z0))))=>![X888:$i, X889:$i]:(((X887 @ X888)=>((X887 @ X889)=>((X888)=(X889)))))))=>(![X1461:$i > $o, X1462:$i > $o]:((![X1463:$i, X1464:$i]:((((X1463)=(X1464))=>((X1461 @ X1463)<=>(X1462 @ X1464))))=>((exu @ (^[Z0/* 3 */:$i]:((X1461 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X1462 @ Z0)))))))=>(((emptyset)=(emptyset))=>(![X890:$i, X891:$i]:((((X890)=(X891))=>![X892:$i, X893:$i]:((((X892)=(X893))=>((setadjoin @ X890 @ X892)=(setadjoin @ X891 @ X893))))))=>(![X894:$i, X895:$i]:((((X894)=(X895))=>((powerset @ X894)=(powerset @ X895))))=>(![X896:$i, X897:$i]:((((X896)=(X897))=>((setunion @ X896)=(setunion @ X897))))=>(((omega)=(omega))=>(![X898:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X898 @ Z0))))=>![X899:$i, X900:$i]:(((X898 @ X899)=>((X898 @ X900)=>((X899)=(X900)))))))=>(![X1457:$i > $o, X1458:$i > $o]:((![X1459:$i, 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binintersectER]), uniqinunit]), setextAx]), setadjoinSub2]), subsetTrans]), setminusSubset2]), subsetE2]), emptysetsubset]), eqimpsubset1]), setminusELneg]), eqimpsubset2]), subsetI1]), setminusILneg]), c_0_246]), c_0_247]), omega__Cong]), setminusLsub]), emptyset__Cong]), c_0_248]), symdiffE]), in__Cong]), c_0_249]), c_0_250]), binintersectSubset3]), notdallE]), secondinupair]), notdexE]), prop2setI]), setukpairIL]), quantDeMorgan2]), vacuousDall]), eqinunit]), setunionE]), kpairiskpair]), setunionI]), powersetI]), kpairp]), c_0_251]), setadjoinOr]), setadjoinE]), singletoninpowunion]), nonemptyI1]), c_0_252]), upairsubunion]), nonemptyE1]), c_0_253]), noeltsimpempty]), ubforcartprodlem3]), setext]), emptysetimpfalse]), setunionsingleton1]), prop2setE]), c_0_254]), c_0_255]), setunionsingleton2]), c_0_256]), wellorderingAx]), setunionsingleton]), c_0_257]), omegaSAx]), omega0Ax]), c_0_258]), setunionAx]), binintersectRsub]), c_0_259]), singletonsuniq]), c_0_260]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR1]), contrasubsetT2]), upairequniteq]), ksndpairEq]), cartprodsndin]), cartprodpairmemEL]), c_0_261]), c_0_262]), c_0_263]), c_0_264]), app]), c_0_265]), binintersectSubset1]), c_0_266]), c_0_267]), funcextLem]), funcGraphProp4]), funcext]), funcext2]), c_0_268]), c_0_269]), setminusER]), c_0_270]), c_0_271]), c_0_272]), theeq]), iffalse]), binunionT_lem]), powersetT_lem]), powersetTI1]), powersetTE1]), complementTI1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT1]), doubleComplementSub1]), doubleComplementE1]), doubleComplementI1]), contrasubsetT3]), contrasubsetT]), complementTE1]), subsetTI]), setextT]), complementT_lem]), setminusT_lem]), binintersectT_lem]), iftrueorfalse]), iftrue]), ifp]), c_0_273]), c_0_274]), c_0_275]), c_0_276]), c_0_277]), ap2apEq2]), ap2apEq1]), eqbreln]), subbreln]), funcGraphProp2]), funcGraphProp3]), funcGraphProp1]), brelnall2]), brelnall1]), c_0_278]), funcinfuncset]), ap2p]), infuncsetfunc]), c_0_279]), c_0_280]), c_0_281]), c_0_282]), c_0_283]), cartprodpairsurjEq]), cartprodsndpairEq]), cartprodfstpairEq]), cartprodmempaircEq]), cartprodpairmemER]), kpairsurjEq]), c_0_284]), setukpairinjR]), setukpairinjR2]), setukpairinjR12]), cartprodfstin]), kfstpairEq]), theprop]), setukpairinjL1]), c_0_285]), c_0_286]), setunionE2]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), upairset2E]), singletoninpowerset]), singletonsubset]), setukpairIR]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), symdiffI1]), setminusSubset1]), setminusIRneg]), setminusERneg]), setminusEL]), setminusI]), bs114d]), binintersectSubset4]), disjointsetsI1]), binintersectLsub]), binintersectSubset5]), binintersectI]), binunionLsub]), binunionEcases]), upairset2IR]), c_0_287]), inPowerset]), powersetE1]), subsetemptysetimpeq]), setextsub]), binintersectSubset2]), binintersectEL]), binunionRsub]), binunionE]), binunionIR]), binunionIL]), c_0_288]), powersetsubset]), powersetI1]), subset2powerset]), setadjoinSub]), subsetRefl]), notequalI2]), notequalI1]), notsubsetI]), subsetE]), subsetI2]), c_0_289]), setunion__Cong]), powerset__Cong]), setadjoin__Cong]), c_0_290]), inCongP]), c_0_291]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan1]), c_0_292]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), notinsingleton]), nonemptyImpWitness]), c_0_293]), subPowSU]), powersetE]), emptyInPowerset]), emptyinPowerset]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), emptyI]), c_0_294]), notinemptyset]), emptysetE]), c_0_295]), c_0_296]), foundationAx]), omegaIndAx]), powersetAx]), setadjoinAx]), emptysetAx])])]), c_0_297])). 142.40/18.46 thf(c_0_299, negated_conjecture, ![X1573:$i, X1574:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1586:$i, X1587:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1595:$i, X1596:$i > $i > $o, X1597:$i, X1600:$i, X1602:$i, X1603:$i, X1604:$i, X1605:$i, X1607:$i, X1608:$i > $o, X1609:$i, X1610:$i > $o, X1611:$i, X1612:$i, X1613:$i > $o, X1614:$i, X1615:$i, X1616:$i > $o, X1617:$i, X1618:$i > $o, X1620:$i, X1621:$o, X1622:$i, X1623:$i, X1624:$o, X1625:$i, X1626:$i, X1627:$i > $o, X1629:$i, X1630:$i, X1633:$i, X1635:$i, X1637:$i, X1638:$i > $o, X1639:$i, X1640:$i, X1642:$i, X1643:$i > $o, X1644:$i, X1645:$i, X1646:$i, X1647:$i, X1648:$i, X1649:$i, X1650:$i, X1651:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$o, X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$o, X1675:$i, X1676:$i, X1677:$i > $o, X1679:$i, X1680:$i, X1681:$i, X1683:$i, X1684:$i, X1685:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i, X1697:$i, X1698:$i, X1699:$i > $o, X1700:$i, X1701:$i > $o, X1702:$i, X1703:$i, X1704:$i > $o, X1705:$i, X1707:$i, X1708:$i > $o, X1710:$i, X1711:$i, X1712:$i > $o, X1714:$i, X1715:$i, X1716:$i > $o, X1717:$i, X1719:$o, X1720:$i, X1721:$i > $o, X1723:$i, X1724:$i, X1725:$i > $o, X1726:$i, X1728:$i > $o, X1729:$i, X1731:$i > $o, X1732:$i, X1735:$i > $o, X1736:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i > $o, X1747:$i, X1748:$i, X1749:$i > $o, X1750:$i > $o, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i > $o, X1762:$i, X1763:$i, X1764:$i > $o, X1765:$i > $o, X1768:$i, X1769:$i, X1770:$i > $o, X1771:$i > $o, X1774:$i, X1775:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i > $o, X1822:$i, X1823:$i > $o, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$o, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$o, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i > $o, X1978:$i, X1979:$i, X1980:$i > $o, X1982:$i, X1983:$i > $o, X1984:$i, X1986:$i, X1987:$i > $o, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i > $i > $o, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i > $i > $o, X2068:$i, X2069:$i, X2070:$i > $i > $o, X2071:$i, X2072:$i, X2073:$i > $i > $o, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i > $i > $o, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i > $i > $o, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i > $i > $o, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i > $i, X2117:$i, 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@ X2252 @ X2253)=(X2253)))))&((~(in @ X2256 @ X2254)|(~(in @ X2257 @ X2254)|(in @ (if @ X2254 @ ((X2255)) @ X2256 @ X2257) @ (setadjoin @ X2256 @ (setadjoin @ X2257 @ emptyset)))))&((~(in @ X2259 @ (powerset @ X2258))|(~(in @ X2260 @ (powerset @ X2258))|(in @ (binintersect @ X2259 @ X2260) @ (powerset @ X2258))))&((~(in @ X2262 @ (powerset @ X2261))|(~(in @ X2263 @ (powerset @ X2261))|(in @ (binunion @ X2262 @ X2263) @ (powerset @ X2261))))&((~(in @ X2265 @ (powerset @ X2264))|(in @ (powerset @ X2265) @ (powerset @ (powerset @ X2264))))&((~(in @ X2267 @ (powerset @ X2266))|(~(in @ X2268 @ (powerset @ X2266))|(in @ (setminus @ X2267 @ X2268) @ (powerset @ X2266))))&((~(in @ X2270 @ (powerset @ X2269))|(in @ (setminus @ X2269 @ X2270) @ (powerset @ X2269)))&(((((in @ (esk68_3 @ X2271 @ X2272 @ X2273) @ X2271)|((X2272)=(X2273))|(in @ (esk67_3 @ X2271 @ X2272 @ X2273) @ X2271)|~(in @ X2273 @ (powerset @ X2271))|~(in @ X2272 @ (powerset @ X2271)))&(((in @ (esk68_3 @ X2271 @ X2272 @ X2273) @ X2273)|((X2272)=(X2273))|(in @ (esk67_3 @ X2271 @ X2272 @ X2273) @ X2271)|~(in @ X2273 @ (powerset @ X2271))|~(in @ X2272 @ (powerset @ X2271)))&(~(in @ (esk68_3 @ X2271 @ X2272 @ X2273) @ X2272)|((X2272)=(X2273))|(in @ (esk67_3 @ X2271 @ X2272 @ X2273) @ X2271)|~(in @ X2273 @ (powerset @ X2271))|~(in @ X2272 @ (powerset @ X2271)))))&((((in @ (esk68_3 @ X2271 @ X2272 @ X2273) @ X2271)|((X2272)=(X2273))|(in @ (esk67_3 @ X2271 @ X2272 @ X2273) @ X2272)|~(in @ X2273 @ (powerset @ X2271))|~(in @ X2272 @ (powerset @ X2271)))&(((in @ (esk68_3 @ X2271 @ X2272 @ X2273) @ X2273)|((X2272)=(X2273))|(in @ (esk67_3 @ X2271 @ X2272 @ X2273) @ X2272)|~(in @ X2273 @ (powerset @ X2271))|~(in @ X2272 @ (powerset @ X2271)))&(~(in @ (esk68_3 @ X2271 @ X2272 @ X2273) @ X2272)|((X2272)=(X2273))|(in @ (esk67_3 @ X2271 @ X2272 @ X2273) @ X2272)|~(in @ X2273 @ (powerset @ X2271))|~(in @ X2272 @ (powerset @ X2271)))))&(((in @ (esk68_3 @ X2271 @ X2272 @ X2273) @ X2271)|((X2272)=(X2273))|~(in @ (esk67_3 @ X2271 @ X2272 @ X2273) @ X2273)|~(in @ X2273 @ (powerset @ X2271))|~(in @ X2272 @ (powerset @ X2271)))&(((in @ (esk68_3 @ X2271 @ X2272 @ X2273) @ X2273)|((X2272)=(X2273))|~(in @ (esk67_3 @ X2271 @ X2272 @ X2273) @ X2273)|~(in @ X2273 @ (powerset @ X2271))|~(in @ X2272 @ (powerset @ X2271)))&(~(in @ (esk68_3 @ X2271 @ X2272 @ X2273) @ X2272)|((X2272)=(X2273))|~(in @ (esk67_3 @ X2271 @ X2272 @ X2273) @ X2273)|~(in @ X2273 @ (powerset @ X2271))|~(in @ X2272 @ (powerset @ X2271)))))))&((((in @ (esk69_3 @ X2276 @ X2277 @ X2278) @ X2276)|(subset @ X2277 @ X2278)|~(in @ X2278 @ (powerset @ X2276))|~(in @ X2277 @ (powerset @ X2276)))&(((in @ (esk69_3 @ X2276 @ X2277 @ X2278) @ X2277)|(subset @ X2277 @ X2278)|~(in @ X2278 @ (powerset @ X2276))|~(in @ X2277 @ (powerset @ X2276)))&(~(in @ (esk69_3 @ X2276 @ X2277 @ X2278) @ X2278)|(subset @ X2277 @ X2278)|~(in @ X2278 @ (powerset @ X2276))|~(in @ X2277 @ (powerset @ X2276)))))&((((in @ (esk70_3 @ X2280 @ X2281 @ X2282) @ X2280)|(in @ X2281 @ (powerset @ X2282))|~(in @ X2282 @ (powerset @ X2280))|~(in @ X2281 @ (powerset @ X2280)))&(((in @ (esk70_3 @ X2280 @ X2281 @ X2282) @ X2281)|(in @ X2281 @ (powerset @ X2282))|~(in @ X2282 @ (powerset @ X2280))|~(in @ X2281 @ (powerset @ X2280)))&(~(in @ (esk70_3 @ X2280 @ X2281 @ X2282) @ X2282)|(in @ X2281 @ (powerset @ X2282))|~(in @ X2282 @ (powerset @ X2280))|~(in @ X2281 @ (powerset @ X2280)))))&((~(in @ X2285 @ (powerset @ X2284))|(~(in @ X2286 @ (powerset @ X2284))|(~(in @ X2287 @ X2284)|(~(in @ X2285 @ (powerset @ X2286))|(~(in @ X2287 @ X2285)|(in @ X2287 @ X2286))))))&((~(in @ X2289 @ (powerset @ X2288))|(~(in @ X2290 @ X2288)|(~(in @ X2290 @ X2289)|~(in @ X2290 @ (setminus @ X2288 @ X2289)))))&((~(in @ X2292 @ (powerset @ X2291))|(~(in @ X2293 @ X2291)|((in @ X2293 @ (setminus @ X2291 @ X2292))|(in @ X2293 @ X2292))))&((~(in @ X2295 @ (powerset @ X2294))|(~(in @ X2296 @ (powerset @ X2294))|(~(in @ X2297 @ X2294)|((in @ X2297 @ X2295)|~(in @ X2297 @ (binintersect @ X2295 @ X2296))))))&((~(in @ X2299 @ (powerset @ X2298))|(~(in @ X2300 @ (powerset @ X2298))|(~(in @ X2301 @ X2298)|((in @ X2301 @ X2300)|~(in @ X2301 @ (binintersect @ X2299 @ X2300))))))&((~(in @ X2303 @ (powerset @ X2302))|(~(in @ X2304 @ (powerset @ X2302))|(~(in @ X2305 @ X2302)|(~(subset @ X2303 @ (setminus @ X2302 @ X2304))|(~(in @ X2305 @ X2304)|~(in @ X2305 @ X2303))))))&((~(in @ X2307 @ (powerset @ X2306))|(~(in @ X2308 @ (powerset @ X2306))|(~(in @ X2309 @ X2306)|(~(subset @ X2307 @ X2308)|((in @ X2309 @ X2308)|~(in @ X2309 @ X2307))))))&((~(in @ X2311 @ (powerset @ X2310))|(~(in @ X2312 @ (powerset @ X2310))|(~(subset @ X2311 @ X2312)|(subset @ (setminus @ X2310 @ X2312) @ (setminus @ X2310 @ X2311)))))&((~(in @ X2314 @ (powerset @ X2313))|(~(in @ X2315 @ (powerset @ X2313))|(~(subset @ (setminus @ X2313 @ X2315) @ (setminus @ X2313 @ X2314))|(subset @ X2314 @ X2315))))&((~(in @ X2317 @ (powerset @ X2316))|(~(in @ X2318 @ X2316)|(~(in @ X2318 @ X2317)|(in @ X2318 @ (setminus @ X2316 @ (setminus @ X2316 @ X2317))))))&((~(in @ X2320 @ (powerset @ X2319))|(~(in @ X2321 @ X2319)|(~(in @ X2321 @ (setminus @ X2319 @ (setminus @ X2319 @ X2320)))|(in @ X2321 @ X2320))))&((~(in @ X2323 @ (powerset @ X2322))|(subset @ X2323 @ (setminus @ X2322 @ (setminus @ X2322 @ X2323))))&((in @ esk72_0 @ (powerset @ esk71_0))&~(subset @ (setminus @ esk71_0 @ (setminus @ esk71_0 @ esk72_0)) @ esk72_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_298])])])])])])). 142.40/18.46 thf(c_0_300, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ X3))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_299])). 142.40/18.46 thf(c_0_301, negated_conjecture, ![X3:$i, X2:$i]:((subset @ (setminus @ X2 @ X3) @ X2)), inference(split_conjunct,[status(thm)],[c_0_299])). 142.40/18.46 thf(c_0_302, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((subset @ X2 @ X4)|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3)))|~((subset @ (setminus @ X3 @ X4) @ (setminus @ X3 @ X2))))), inference(split_conjunct,[status(thm)],[c_0_299])). 142.40/18.46 thf(c_0_303, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ (setminus @ X3 @ (setminus @ X3 @ X2)))|~((in @ X2 @ (powerset @ X3))))), inference(split_conjunct,[status(thm)],[c_0_299])). 142.40/18.46 thf(c_0_304, negated_conjecture, ![X3:$i, X2:$i]:((in @ (setminus @ X2 @ X3) @ (powerset @ X2))), inference(spm,[status(thm)],[c_0_300, c_0_301])). 142.40/18.46 thf(c_0_305, negated_conjecture, ~((subset @ (setminus @ esk71_0 @ (setminus @ esk71_0 @ esk72_0)) @ esk72_0)), inference(split_conjunct,[status(thm)],[c_0_299])). 142.40/18.46 thf(c_0_306, negated_conjecture, ![X3:$i, X2:$i]:(((subset @ (setminus @ X2 @ (setminus @ X2 @ X3)) @ X3)|~((in @ X3 @ (powerset @ X2))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_302, c_0_303]), c_0_304]), c_0_304])])). 142.40/18.46 thf(c_0_307, negated_conjecture, (in @ esk72_0 @ (powerset @ esk71_0)), inference(split_conjunct,[status(thm)],[c_0_299])). 142.40/18.46 thf(c_0_308, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_305, c_0_306]), c_0_307])]), ['proof']). 142.40/18.46 # SZS output end CNFRefutation 142.40/18.46 # Parsed axioms : 535 142.40/18.46 # Removed by relevancy pruning/SinE : 289 142.40/18.46 # Initial clauses : 399 142.40/18.46 # Removed in clause preprocessing : 29 142.40/18.46 # Initial clauses in saturation : 370 142.40/18.46 # Processed clauses : 11165 142.40/18.46 # ...of these trivial : 41 142.40/18.46 # ...subsumed : 6306 142.40/18.46 # ...remaining for further processing : 4818 142.40/18.46 # Other redundant clauses eliminated : 175 142.40/18.46 # Clauses deleted for lack of memory : 0 142.40/18.46 # Backward-subsumed : 296 142.40/18.46 # Backward-rewritten : 47 142.40/18.46 # Generated clauses : 743433 142.40/18.46 # ...of the previous two non-redundant : 739966 142.40/18.46 # ...aggressively subsumed : 0 142.40/18.46 # Contextual simplify-reflections : 104 142.40/18.46 # Paramodulations : 743063 142.40/18.46 # Factorizations : 118 142.40/18.46 # NegExts : 32 142.40/18.46 # Equation resolutions : 194 142.40/18.46 # Total rewrite steps : 13945 142.40/18.46 # Propositional unsat checks : 0 142.40/18.46 # Propositional check models : 0 142.40/18.46 # Propositional check unsatisfiable : 0 142.40/18.46 # Propositional clauses : 0 142.40/18.46 # Propositional clauses after purity: 0 142.40/18.46 # Propositional unsat core size : 0 142.40/18.46 # Propositional preprocessing time : 0.000 142.40/18.46 # Propositional encoding time : 0.000 142.40/18.46 # Propositional solver time : 0.000 142.40/18.46 # Success case prop preproc time : 0.000 142.40/18.46 # Success case prop encoding time : 0.000 142.40/18.46 # Success case prop solver time : 0.000 142.40/18.46 # Current number of processed clauses : 4135 142.40/18.46 # Positive orientable unit clauses : 91 142.40/18.46 # Positive unorientable unit clauses: 0 142.40/18.46 # Negative unit clauses : 235 142.40/18.46 # Non-unit-clauses : 3809 142.40/18.46 # Current number of unprocessed clauses: 728423 142.40/18.46 # ...number of literals in the above : 3284722 142.40/18.46 # Current number of archived formulas : 0 142.40/18.46 # Current number of archived clauses : 667 142.40/18.46 # Clause-clause subsumption calls (NU) : 2982678 142.40/18.46 # Rec. Clause-clause subsumption calls : 1511754 142.40/18.46 # Non-unit clause-clause subsumptions : 5010 142.40/18.46 # Unit Clause-clause subsumption calls : 55539 142.40/18.46 # Rewrite failures with RHS unbound : 0 142.40/18.46 # BW rewrite match attempts : 73 142.40/18.46 # BW rewrite match successes : 24 142.40/18.46 # Condensation attempts : 0 142.40/18.46 # Condensation successes : 0 142.40/18.46 # Termbank termtop insertions : 16286401 142.40/18.46 142.40/18.46 # ------------------------------------------------- 142.40/18.46 # User time : 17.385 s 142.40/18.46 # System time : 0.472 s 142.40/18.46 # Total time : 17.856 s 142.40/18.46 # Maximum resident set size: 7724 pages 143.85/18.78 143.85/18.78 # ------------------------------------------------- 143.85/18.78 # User time : 17.401 s 143.85/18.78 # System time : 0.474 s 143.85/18.78 # Total time : 17.874 s 143.85/18.78 # Maximum resident set size: 2616 pages 143.85/18.78 % E---3.1 exiting 143.85/18.78 EOF