0.07/0.16 % Problem : Vampire---4.8_8102 : TPTP v0.0.0. Released v0.0.0. 0.17/0.17 % Command : run_E %s %d THM 0.17/0.38 % Computer : n002.cluster.edu 0.17/0.38 % Model : x86_64 x86_64 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.17/0.38 % Memory : 8042.1875MB 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64 0.17/0.38 % CPULimit : 1440 0.17/0.38 % WCLimit : 180 0.17/0.38 % DateTime : Mon Jul 3 13:17:22 EDT 2023 0.17/0.39 % CPUTime : 0.36/0.56 Running higher-order theorem provingRunning: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102 0.36/0.56 # Version: 3.1pre001-ho 0.41/0.78 # Preprocessing class: HSLMSLSSLLLCHFA. 0.41/0.78 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.41/0.78 # Starting ehoh_best5 with 180s (1) cores 0.41/0.78 # Starting almost_fo_3_lam with 180s (1) cores 0.41/0.78 # Starting new_bool_5 with 180s (1) cores 0.41/0.78 # Starting pre_casc_3 with 180s (1) cores 0.41/0.78 # Starting ho_unfolding_8 with 180s (1) cores 0.41/0.78 # Starting new_ho_10_cnf2 with 180s (1) cores 0.41/0.78 # Starting new_bool_3 with 180s (1) cores 0.41/0.78 # Starting new_ho_5 with 180s (1) cores 0.41/0.78 # new_bool_5 with pid 8286 completed with status 0 0.41/0.78 # Result found by new_bool_5 0.41/0.78 # Preprocessing class: HSLMSLSSLLLCHFA. 0.41/0.78 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.41/0.78 # Starting ehoh_best5 with 180s (1) cores 0.41/0.78 # Starting almost_fo_3_lam with 180s (1) cores 0.41/0.78 # Starting new_bool_5 with 180s (1) cores 0.41/0.78 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 0.41/0.78 # Search class: HGHSM-FSLM32-MHFMMSBN 0.41/0.78 # Scheduled 10 strats onto 1 cores with 180 seconds (180 total) 0.41/0.78 # Starting ho_unfolding_8 with 33s (1) cores 0.41/0.78 # ho_unfolding_8 with pid 8292 completed with status 0 0.41/0.78 # Result found by ho_unfolding_8 0.41/0.78 # Preprocessing class: HSLMSLSSLLLCHFA. 0.41/0.78 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.41/0.78 # Starting ehoh_best5 with 180s (1) cores 0.41/0.78 # Starting almost_fo_3_lam with 180s (1) cores 0.41/0.78 # Starting new_bool_5 with 180s (1) cores 0.41/0.78 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 0.41/0.78 # Search class: HGHSM-FSLM32-MHFMMSBN 0.41/0.78 # Scheduled 10 strats onto 1 cores with 180 seconds (180 total) 0.41/0.78 # Starting ho_unfolding_8 with 33s (1) cores 0.41/0.78 # Preprocessing time : 0.059 s 0.41/0.78 # Presaturation interreduction done 0.41/0.78 0.41/0.78 # Proof found! 0.41/0.78 # SZS status Theorem 0.41/0.78 # SZS output start CNFRefutation 0.41/0.78 thf(decl_22, type, in: $i > $i > $o). 0.41/0.78 thf(decl_23, type, exu: ($i > $o) > $o). 0.41/0.78 thf(decl_24, type, setextAx: $o). 0.41/0.78 thf(decl_25, type, emptyset: $i). 0.41/0.78 thf(decl_26, type, emptysetAx: $o). 0.41/0.78 thf(decl_27, type, setadjoin: $i > $i > $i). 0.41/0.78 thf(decl_28, type, setadjoinAx: $o). 0.41/0.78 thf(decl_29, type, powerset: $i > $i). 0.41/0.78 thf(decl_30, type, powersetAx: $o). 0.41/0.78 thf(decl_31, type, setunion: $i > $i). 0.41/0.78 thf(decl_32, type, setunionAx: $o). 0.41/0.78 thf(decl_33, type, omega: $i). 0.41/0.78 thf(decl_34, type, omega0Ax: $o). 0.41/0.78 thf(decl_35, type, omegaSAx: $o). 0.41/0.78 thf(decl_36, type, omegaIndAx: $o). 0.41/0.78 thf(decl_37, type, replAx: $o). 0.41/0.78 thf(decl_38, type, foundationAx: $o). 0.41/0.78 thf(decl_39, type, wellorderingAx: $o). 0.41/0.78 thf(decl_40, type, descr: ($i > $o) > $i). 0.41/0.78 thf(decl_41, type, descrp: $o). 0.41/0.78 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 0.41/0.78 thf(decl_43, type, dsetconstrI: $o). 0.41/0.78 thf(decl_44, type, dsetconstrEL: $o). 0.41/0.78 thf(decl_45, type, dsetconstrER: $o). 0.41/0.78 thf(decl_46, type, exuE1: $o). 0.41/0.78 thf(decl_47, type, prop2set: $o > $i). 0.41/0.78 thf(decl_48, type, prop2setE: $o). 0.41/0.78 thf(decl_49, type, emptysetE: $o). 0.41/0.78 thf(decl_50, type, emptysetimpfalse: $o). 0.41/0.78 thf(decl_51, type, notinemptyset: $o). 0.41/0.78 thf(decl_52, type, exuE3e: $o). 0.41/0.78 thf(decl_53, type, setext: $o). 0.41/0.78 thf(decl_54, type, emptyI: $o). 0.41/0.78 thf(decl_55, type, noeltsimpempty: $o). 0.41/0.78 thf(decl_56, type, setbeta: $o). 0.41/0.78 thf(decl_57, type, nonempty: $i > $o). 0.41/0.78 thf(decl_58, type, nonemptyE1: $o). 0.41/0.78 thf(decl_59, type, nonemptyI: $o). 0.41/0.78 thf(decl_60, type, nonemptyI1: $o). 0.41/0.78 thf(decl_61, type, setadjoinIL: $o). 0.41/0.78 thf(decl_62, type, emptyinunitempty: $o). 0.41/0.78 thf(decl_63, type, setadjoinIR: $o). 0.41/0.78 thf(decl_64, type, setadjoinE: $o). 0.41/0.78 thf(decl_65, type, setadjoinOr: $o). 0.41/0.78 thf(decl_66, type, setoftrueEq: $o). 0.41/0.78 thf(decl_67, type, powersetI: $o). 0.41/0.78 thf(decl_68, type, emptyinPowerset: $o). 0.41/0.78 thf(decl_69, type, emptyInPowerset: $o). 0.41/0.78 thf(decl_70, type, powersetE: $o). 0.41/0.78 thf(decl_71, type, setunionI: $o). 0.41/0.78 thf(decl_72, type, setunionE: $o). 0.41/0.78 thf(decl_73, type, subPowSU: $o). 0.41/0.78 thf(decl_74, type, exuE2: $o). 0.41/0.78 thf(decl_75, type, nonemptyImpWitness: $o). 0.41/0.78 thf(decl_76, type, uniqinunit: $o). 0.41/0.78 thf(decl_77, type, notinsingleton: $o). 0.41/0.78 thf(decl_78, type, eqinunit: $o). 0.41/0.78 thf(decl_79, type, singletonsswitch: $o). 0.41/0.78 thf(decl_80, type, upairsetE: $o). 0.41/0.78 thf(decl_81, type, upairsetIL: $o). 0.41/0.78 thf(decl_82, type, upairsetIR: $o). 0.41/0.78 thf(decl_83, type, emptyE1: $o). 0.41/0.78 thf(decl_84, type, vacuousDall: $o). 0.41/0.78 thf(decl_85, type, quantDeMorgan1: $o). 0.41/0.78 thf(decl_86, type, quantDeMorgan2: $o). 0.41/0.78 thf(decl_87, type, quantDeMorgan3: $o). 0.41/0.78 thf(decl_88, type, quantDeMorgan4: $o). 0.41/0.78 thf(decl_89, type, prop2setI: $o). 0.41/0.78 thf(decl_91, type, prop2set2propI: $o). 0.41/0.78 thf(decl_92, type, notdexE: $o). 0.41/0.78 thf(decl_93, type, notdallE: $o). 0.41/0.78 thf(decl_94, type, exuI1: $o). 0.41/0.78 thf(decl_95, type, exuI3: $o). 0.41/0.78 thf(decl_96, type, exuI2: $o). 0.41/0.78 thf(decl_97, type, inCongP: $o). 0.41/0.78 thf(decl_98, type, in__Cong: $o). 0.41/0.78 thf(decl_99, type, exuE3u: $o). 0.41/0.78 thf(decl_100, type, exu__Cong: $o). 0.41/0.78 thf(decl_101, type, emptyset__Cong: $o). 0.41/0.78 thf(decl_102, type, setadjoin__Cong: $o). 0.41/0.78 thf(decl_103, type, powerset__Cong: $o). 0.41/0.78 thf(decl_104, type, setunion__Cong: $o). 0.41/0.78 thf(decl_105, type, omega__Cong: $o). 0.41/0.78 thf(decl_106, type, exuEu: $o). 0.41/0.78 thf(decl_107, type, descr__Cong: $o). 0.41/0.78 thf(decl_108, type, dsetconstr__Cong: $o). 0.41/0.78 thf(decl_109, type, subset: $i > $i > $o). 0.41/0.78 thf(decl_112, type, subsetI1: $o). 0.41/0.78 thf(decl_113, type, eqimpsubset2: $o). 0.41/0.78 thf(decl_114, type, eqimpsubset1: $o). 0.41/0.78 thf(decl_115, type, subsetI2: $o). 0.41/0.78 thf(decl_116, type, emptysetsubset: $o). 0.41/0.78 thf(decl_117, type, subsetE: $o). 0.41/0.78 thf(decl_118, type, subsetE2: $o). 0.41/0.78 thf(decl_119, type, notsubsetI: $o). 0.41/0.78 thf(decl_120, type, notequalI1: $o). 0.41/0.78 thf(decl_121, type, notequalI2: $o). 0.41/0.78 thf(decl_122, type, subsetRefl: $o). 0.41/0.78 thf(decl_123, type, subsetTrans: $o). 0.41/0.78 thf(decl_124, type, setadjoinSub: $o). 0.41/0.78 thf(decl_125, type, setadjoinSub2: $o). 0.41/0.78 thf(decl_126, type, subset2powerset: $o). 0.41/0.78 thf(decl_127, type, setextsub: $o). 0.41/0.78 thf(decl_128, type, subsetemptysetimpeq: $o). 0.41/0.78 thf(decl_129, type, powersetI1: $o). 0.41/0.78 thf(decl_130, type, powersetE1: $o). 0.41/0.78 thf(decl_131, type, inPowerset: $o). 0.41/0.78 thf(decl_132, type, powersetsubset: $o). 0.41/0.78 thf(decl_133, type, sepInPowerset: $o). 0.41/0.78 thf(decl_134, type, sepSubset: $o). 0.41/0.78 thf(decl_135, type, binunion: $i > $i > $i). 0.41/0.78 thf(decl_136, type, binunionIL: $o). 0.41/0.78 thf(decl_137, type, upairset2IR: $o). 0.41/0.78 thf(decl_138, type, binunionIR: $o). 0.41/0.78 thf(decl_139, type, binunionEcases: $o). 0.41/0.78 thf(decl_140, type, binunionE: $o). 0.41/0.78 thf(decl_141, type, binunionLsub: $o). 0.41/0.78 thf(decl_142, type, binunionRsub: $o). 0.41/0.78 thf(decl_143, type, binintersect: $i > $i > $i). 0.41/0.78 thf(decl_144, type, binintersectI: $o). 0.41/0.78 thf(decl_145, type, binintersectSubset5: $o). 0.41/0.78 thf(decl_146, type, binintersectEL: $o). 0.41/0.78 thf(decl_147, type, binintersectLsub: $o). 0.41/0.78 thf(decl_148, type, binintersectSubset2: $o). 0.41/0.78 thf(decl_149, type, binintersectSubset3: $o). 0.41/0.78 thf(decl_150, type, binintersectER: $o). 0.41/0.78 thf(decl_151, type, disjointsetsI1: $o). 0.41/0.78 thf(decl_152, type, binintersectRsub: $o). 0.41/0.78 thf(decl_153, type, binintersectSubset4: $o). 0.41/0.78 thf(decl_154, type, binintersectSubset1: $o). 0.41/0.78 thf(decl_155, type, bs114d: $o). 0.41/0.78 thf(decl_157, type, setminus: $i > $i > $i). 0.41/0.78 thf(decl_158, type, setminusI: $o). 0.41/0.78 thf(decl_159, type, setminusEL: $o). 0.41/0.78 thf(decl_160, type, setminusER: $o). 0.41/0.78 thf(decl_161, type, setminusSubset2: $o). 0.41/0.78 thf(decl_162, type, setminusERneg: $o). 0.41/0.78 thf(decl_163, type, setminusELneg: $o). 0.41/0.78 thf(decl_164, type, setminusILneg: $o). 0.41/0.78 thf(decl_165, type, setminusIRneg: $o). 0.41/0.78 thf(decl_166, type, setminusLsub: $o). 0.41/0.78 thf(decl_167, type, setminusSubset1: $o). 0.41/0.78 thf(decl_168, type, symdiff: $i > $i > $i). 0.41/0.78 thf(decl_169, type, symdiffE: $o). 0.41/0.78 thf(decl_170, type, symdiffI1: $o). 0.41/0.78 thf(decl_171, type, symdiffI2: $o). 0.41/0.78 thf(decl_172, type, symdiffIneg1: $o). 0.41/0.78 thf(decl_173, type, symdiffIneg2: $o). 0.41/0.78 thf(decl_174, type, iskpair: $i > $o). 0.41/0.78 thf(decl_175, type, secondinupair: $o). 0.41/0.78 thf(decl_176, type, setukpairIL: $o). 0.41/0.78 thf(decl_177, type, setukpairIR: $o). 0.41/0.78 thf(decl_178, type, kpairiskpair: $o). 0.41/0.78 thf(decl_179, type, kpair: $i > $i > $i). 0.41/0.78 thf(decl_180, type, kpairp: $o). 0.41/0.78 thf(decl_181, type, cartprod: $i > $i > $i). 0.41/0.78 thf(decl_182, type, singletonsubset: $o). 0.41/0.78 thf(decl_183, type, singletoninpowerset: $o). 0.41/0.78 thf(decl_184, type, singletoninpowunion: $o). 0.41/0.78 thf(decl_185, type, upairset2E: $o). 0.41/0.78 thf(decl_186, type, upairsubunion: $o). 0.41/0.78 thf(decl_187, type, upairinpowunion: $o). 0.41/0.78 thf(decl_188, type, ubforcartprodlem1: $o). 0.41/0.78 thf(decl_189, type, ubforcartprodlem2: $o). 0.41/0.78 thf(decl_190, type, ubforcartprodlem3: $o). 0.41/0.78 thf(decl_191, type, cartprodpairin: $o). 0.41/0.78 thf(decl_192, type, cartprodmempair1: $o). 0.41/0.78 thf(decl_193, type, cartprodmempair: $o). 0.41/0.78 thf(decl_194, type, setunionE2: $o). 0.41/0.78 thf(decl_195, type, setunionsingleton1: $o). 0.41/0.78 thf(decl_196, type, setunionsingleton2: $o). 0.41/0.78 thf(decl_197, type, setunionsingleton: $o). 0.41/0.78 thf(decl_198, type, singleton: $i > $o). 0.41/0.78 thf(decl_199, type, singletonprop: $o). 0.41/0.78 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 0.41/0.78 thf(decl_201, type, ex1E1: $o). 0.41/0.78 thf(decl_202, type, ex1I: $o). 0.41/0.78 thf(decl_203, type, ex1I2: $o). 0.41/0.78 thf(decl_204, type, singletonsuniq: $o). 0.41/0.78 thf(decl_209, type, setukpairinjL1: $o). 0.41/0.78 thf(decl_210, type, kfstsingleton: $o). 0.41/0.78 thf(decl_211, type, theprop: $o). 0.41/0.78 thf(decl_212, type, kfst: $i > $i). 0.41/0.78 thf(decl_213, type, kfstpairEq: $o). 0.41/0.78 thf(decl_214, type, cartprodfstin: $o). 0.41/0.78 thf(decl_215, type, setukpairinjL2: $o). 0.41/0.78 thf(decl_216, type, setukpairinjL: $o). 0.41/0.78 thf(decl_217, type, setukpairinjR11: $o). 0.41/0.78 thf(decl_218, type, setukpairinjR12: $o). 0.41/0.78 thf(decl_219, type, setukpairinjR1: $o). 0.41/0.78 thf(decl_220, type, upairequniteq: $o). 0.41/0.78 thf(decl_221, type, setukpairinjR2: $o). 0.41/0.78 thf(decl_222, type, setukpairinjR: $o). 0.41/0.78 thf(decl_223, type, ksndsingleton: $o). 0.41/0.78 thf(decl_224, type, ksnd: $i > $i). 0.41/0.78 thf(decl_225, type, ksndpairEq: $o). 0.41/0.78 thf(decl_226, type, kpairsurjEq: $o). 0.41/0.78 thf(decl_227, type, cartprodsndin: $o). 0.41/0.78 thf(decl_228, type, cartprodpairmemEL: $o). 0.41/0.78 thf(decl_229, type, cartprodpairmemER: $o). 0.41/0.78 thf(decl_230, type, cartprodmempaircEq: $o). 0.41/0.78 thf(decl_231, type, cartprodfstpairEq: $o). 0.41/0.78 thf(decl_232, type, cartprodsndpairEq: $o). 0.41/0.78 thf(decl_233, type, cartprodpairsurjEq: $o). 0.41/0.78 thf(decl_234, type, breln: $i > $i > $i > $o). 0.41/0.78 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 0.41/0.78 thf(decl_236, type, dpsetconstrI: $o). 0.41/0.78 thf(decl_237, type, dpsetconstrSub: $o). 0.41/0.78 thf(decl_238, type, setOfPairsIsBReln: $o). 0.41/0.78 thf(decl_239, type, dpsetconstrERa: $o). 0.41/0.78 thf(decl_240, type, dpsetconstrEL1: $o). 0.41/0.78 thf(decl_241, type, dpsetconstrEL2: $o). 0.41/0.78 thf(decl_242, type, dpsetconstrER: $o). 0.41/0.78 thf(decl_243, type, func: $i > $i > $i > $o). 0.41/0.78 thf(decl_244, type, funcSet: $i > $i > $i). 0.41/0.78 thf(decl_245, type, funcImageSingleton: $o). 0.41/0.78 thf(decl_246, type, apProp: $o). 0.41/0.78 thf(decl_247, type, ap: $i > $i > $i > $i > $i). 0.41/0.78 thf(decl_248, type, app: $o). 0.41/0.78 thf(decl_249, type, infuncsetfunc: $o). 0.41/0.78 thf(decl_250, type, ap2p: $o). 0.41/0.78 thf(decl_251, type, funcinfuncset: $o). 0.41/0.78 thf(decl_252, type, lamProp: $o). 0.41/0.78 thf(decl_253, type, lam: $i > $i > ($i > $i) > $i). 0.41/0.78 thf(decl_254, type, lamp: $o). 0.41/0.78 thf(decl_255, type, lam2p: $o). 0.41/0.78 thf(decl_256, type, brelnall1: $o). 0.41/0.78 thf(decl_257, type, brelnall2: $o). 0.41/0.78 thf(decl_258, type, ex1E2: $o). 0.41/0.78 thf(decl_259, type, funcGraphProp1: $o). 0.41/0.78 thf(decl_260, type, epred1_0: $o). 0.41/0.78 thf(decl_261, type, esk1_2: $i > $i > $i). 0.41/0.78 thf(decl_262, type, esk2_2: $i > $i > $i). 0.41/0.78 thf(decl_263, type, esk3_2: $i > $i > $i). 0.41/0.78 thf(decl_264, type, esk4_1: $i > $i). 0.41/0.78 thf(decl_265, type, esk5_2: ($i > $i > $o) > $i > $i). 0.41/0.78 thf(decl_266, type, esk6_2: ($i > $i > $o) > $i > $i). 0.41/0.78 thf(decl_267, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 0.41/0.78 thf(decl_268, type, esk8_1: $i > $i). 0.41/0.78 thf(decl_269, type, esk9_1: ($i > $o) > $i). 0.41/0.78 thf(decl_270, type, esk10_1: ($i > $o) > $i). 0.41/0.78 thf(decl_271, type, esk11_2: $i > $i > $i). 0.41/0.78 thf(decl_272, type, esk12_2: $i > $i > $i). 0.41/0.78 thf(decl_273, type, esk13_1: $i > $i). 0.41/0.78 thf(decl_274, type, esk14_1: $i > $i). 0.41/0.78 thf(decl_275, type, esk15_1: $i > $i). 0.41/0.78 thf(decl_276, type, esk16_2: $i > $i > $i). 0.41/0.78 thf(decl_277, type, esk17_3: $i > $i > $o > $i). 0.41/0.78 thf(decl_278, type, esk18_1: ($i > $o) > $i). 0.41/0.78 thf(decl_279, type, esk19_1: $i > $i). 0.41/0.78 thf(decl_280, type, esk20_2: $i > ($i > $o) > $i). 0.41/0.78 thf(decl_281, type, esk21_2: $i > ($i > $o) > $i). 0.41/0.78 thf(decl_282, type, esk22_2: $i > ($i > $o) > $i). 0.41/0.78 thf(decl_283, type, esk23_2: $i > ($i > $o) > $i). 0.41/0.78 thf(decl_284, type, esk24_2: $i > ($i > $o) > $i). 0.41/0.78 thf(decl_285, type, esk25_2: $i > ($i > $o) > $i). 0.41/0.78 thf(decl_286, type, esk26_2: ($i > $o) > $i > $i). 0.41/0.78 thf(decl_287, type, esk27_1: ($i > $o) > $i). 0.41/0.78 thf(decl_288, type, esk28_1: ($i > $o) > $i). 0.41/0.78 thf(decl_289, type, esk29_2: ($i > $o) > $i > $i). 0.41/0.78 thf(decl_290, type, esk30_2: ($i > $o) > ($i > $o) > $i). 0.41/0.78 thf(decl_291, type, esk31_2: ($i > $o) > ($i > $o) > $i). 0.41/0.78 thf(decl_292, type, esk32_2: ($i > $o) > ($i > $o) > $i). 0.41/0.78 thf(decl_293, type, esk33_2: ($i > $o) > ($i > $o) > $i). 0.41/0.78 thf(decl_294, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.41/0.78 thf(decl_295, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.41/0.78 thf(decl_296, type, esk36_2: $i > $i > $i). 0.41/0.78 thf(decl_297, type, esk37_2: $i > $i > $i). 0.41/0.78 thf(decl_298, type, esk38_2: $i > $i > $i). 0.41/0.78 thf(decl_299, type, esk39_3: $i > $i > $i > $i). 0.41/0.78 thf(decl_300, type, esk40_3: $i > $i > $i > $i). 0.41/0.78 thf(decl_301, type, esk41_2: $i > $i > $i). 0.41/0.78 thf(decl_302, type, esk42_2: $i > ($i > $o) > $i). 0.41/0.78 thf(decl_303, type, esk43_2: $i > ($i > $o) > $i). 0.41/0.78 thf(decl_304, type, esk44_2: $i > ($i > $o) > $i). 0.41/0.78 thf(decl_305, type, esk45_3: $i > ($i > $o) > $i > $i). 0.41/0.78 thf(decl_306, type, esk46_2: $i > ($i > $o) > $i). 0.41/0.78 thf(decl_307, type, esk47_2: $i > ($i > $o) > $i). 0.41/0.78 thf(decl_308, type, esk48_3: $i > $i > ($i > $i) > $i). 0.41/0.78 thf(decl_309, type, esk49_3: $i > $i > ($i > $i) > $i). 0.41/0.78 thf(decl_310, type, esk50_3: $i > $i > ($i > $i) > $i). 0.41/0.78 thf(decl_311, type, esk51_4: $i > $i > $i > ($i > $o) > $i). 0.41/0.78 thf(decl_312, type, esk52_4: $i > $i > $i > ($i > $o) > $i). 0.41/0.78 thf(decl_313, type, esk53_4: $i > $i > $i > ($i > $o) > $i). 0.41/0.78 thf(decl_314, type, esk54_4: $i > $i > $i > ($i > $o) > $i). 0.41/0.78 thf(decl_315, type, esk55_0: $i). 0.41/0.78 thf(decl_316, type, esk56_0: $i). 0.41/0.78 thf(decl_317, type, esk57_0: $i). 0.41/0.78 thf(decl_318, type, esk58_0: $i). 0.41/0.78 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', dsetconstr__Cong)). 0.41/0.78 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', emptyE1)). 0.41/0.78 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setoftrueEq)). 0.41/0.78 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setbeta)). 0.41/0.78 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', exuE1)). 0.41/0.78 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', dsetconstrER)). 0.41/0.78 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', dsetconstrEL)). 0.41/0.78 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', dsetconstrI)). 0.41/0.78 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', replAx)). 0.41/0.78 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', ex1E2)). 0.41/0.78 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', singletonprop)). 0.41/0.78 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', ex1I2)). 0.41/0.78 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', dpsetconstrSub)). 0.41/0.78 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setOfPairsIsBReln)). 0.41/0.78 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', dpsetconstrERa)). 0.41/0.78 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', dpsetconstrEL2)). 0.41/0.78 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', apProp)). 0.41/0.78 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X31 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', lamProp)). 0.41/0.78 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X33 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', lamp)). 0.41/0.78 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X34:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X34 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X34 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', lam2p)). 0.41/0.78 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', funcImageSingleton)). 0.41/0.78 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:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', dpsetconstrER)). 0.41/0.78 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', dpsetconstrEL1)). 0.41/0.78 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', dpsetconstrI)). 0.41/0.78 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', ksndsingleton)). 0.41/0.78 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', kfstsingleton)). 0.41/0.78 thf(ex1I, axiom, ((ex1I)<=>![X4:$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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', ex1I)). 0.41/0.78 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', ex1E1)). 0.41/0.78 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', sepSubset)). 0.41/0.78 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', sepInPowerset)). 0.41/0.78 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', descr__Cong)). 0.41/0.78 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', exuEu)). 0.41/0.78 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', exu__Cong)). 0.41/0.78 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', exuE3u)). 0.41/0.78 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', exuI2)). 0.41/0.78 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', exuI3)). 0.41/0.78 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', exuI1)). 0.41/0.78 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', exuE2)). 0.41/0.78 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', nonemptyI)). 0.41/0.78 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', exuE3e)). 0.41/0.78 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', descrp)). 0.41/0.78 thf(funcGraphProp3, conjecture, ((setextAx)=>((((((omega0Ax)=>(((omegaIndAx)=>(((foundationAx)=>(((descrp)=>(((((((emptysetE)=>(((notinemptyset)=>((exuE3e)=>((setext)=>((((((nonemptyI)=>(((setadjoinIL)=>((emptyinunitempty)=>((((setadjoinOr)=>(((((emptyInPowerset)=>((((((exuE2)=>((((notinsingleton)=>(((singletonsswitch)=>(((upairsetIL)=>((upairsetIR)=>(((vacuousDall)=>(((((((prop2set2propI)=>((notdexE)=>(((exuI1)=>((exuI3)=>((exuI2)=>((((exuE3u)=>((exu__Cong)=>((((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>(((((notequalI1)=>((notequalI2)=>((subsetRefl)=>(((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((((((((((((binunionIR)=>((binunionEcases)=>(((((((binintersectEL)=>(((binintersectSubset2)=>((binintersectSubset3)=>(((((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>(((((((setminusELneg)=>(((setminusIRneg)=>(((setminusSubset1)=>(((((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>(((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((((upairinpowunion)=>((ubforcartprodlem1)=>(((((cartprodmempair1)=>((cartprodmempair)=>((((((singletonprop)=>((((ex1I2)=>((singletonsuniq)=>(((((kfstpairEq)=>((cartprodfstin)=>(((setukpairinjL)=>((setukpairinjR11)=>(((setukpairinjR1)=>(((setukpairinjR2)=>((((ksndpairEq)=>((((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((((cartprodpairsurjEq)=>(((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>(((dpsetconstrEL2)=>((((apProp)=>((((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>(((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X30 @ X2)) @ X30)))))))))<=(lam2p))))))<=(infuncsetfunc))<=(app)))<=(funcImageSingleton))<=(dpsetconstrER)))<=(dpsetconstrEL1)))))<=(dpsetconstrI)))<=(cartprodsndpairEq))<=(cartprodfstpairEq)))))<=(cartprodsndin))<=(kpairsurjEq)))<=(ksndsingleton))<=(setukpairinjR)))<=(upairequniteq)))<=(setukpairinjR12))))<=(setukpairinjL2))))<=(theprop))<=(kfstsingleton))<=(setukpairinjL1))))<=(ex1I))<=(ex1E1)))<=(setunionsingleton))<=(setunionsingleton2))<=(setunionsingleton1))<=(setunionE2))))<=(cartprodpairin))<=(ubforcartprodlem3))<=(ubforcartprodlem2))))<=(upairsubunion))<=(upairset2E))))))<=(kpairiskpair)))))))<=(symdiffI2))<=(symdiffI1))<=(symdiffE)))<=(setminusLsub)))<=(setminusILneg)))<=(setminusERneg))<=(setminusSubset2))<=(setminusER))<=(setminusEL))<=(setminusI)))))<=(binintersectRsub))<=(disjointsetsI1))<=(binintersectER))))<=(binintersectLsub)))<=(binintersectSubset5))<=(binintersectI))<=(binunionRsub))<=(binunionLsub))<=(binunionE))))<=(upairset2IR))<=(binunionIL))<=(sepSubset))<=(sepInPowerset))<=(powersetsubset))<=(inPowerset))<=(powersetE1))<=(powersetI1))<=(subsetemptysetimpeq))<=(setextsub)))))<=(subsetTrans)))))<=(notsubsetI))<=(subsetE2))<=(subsetE))))))<=(subsetI1))<=(dsetconstr__Cong)))))))<=(setadjoin__Cong))<=(emptyset__Cong))))<=(in__Cong))<=(inCongP)))))<=(notdallE))))<=(prop2setI))<=(quantDeMorgan4))<=(quantDeMorgan3))<=(quantDeMorgan2))<=(quantDeMorgan1)))<=(emptyE1))))<=(upairsetE)))<=(eqinunit)))<=(uniqinunit))<=(nonemptyImpWitness)))<=(subPowSU))<=(setunionE))<=(setunionI))<=(powersetE)))<=(emptyinPowerset))<=(powersetI))<=(setoftrueEq)))<=(setadjoinE))<=(setadjoinIR))))<=(nonemptyI1)))<=(nonemptyE1))<=(setbeta))<=(noeltsimpempty))<=(emptyI)))))<=(emptysetimpfalse)))<=(prop2setE))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL))<=(dsetconstrI)))<=(wellorderingAx)))<=(replAx)))<=(omegaSAx)))<=(setunionAx))<=(powersetAx))<=(setadjoinAx))<=(emptysetAx))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', funcGraphProp3)). 0.41/0.78 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setunionE)). 0.41/0.78 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', emptysetAx)). 0.41/0.78 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', notsubsetI)). 0.41/0.78 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', subsetE2)). 0.41/0.78 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', notequalI2)). 0.41/0.78 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', subsetE)). 0.41/0.78 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', subsetI1)). 0.41/0.78 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', subsetRefl)). 0.41/0.78 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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setadjoin__Cong)). 0.41/0.78 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', emptyset__Cong)). 0.41/0.78 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setadjoinSub)). 0.41/0.78 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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', in__Cong)). 0.41/0.78 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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', inCongP)). 0.41/0.78 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setadjoinSub2)). 0.41/0.78 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', notdallE)). 0.41/0.78 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', prop2setI)). 0.41/0.78 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', quantDeMorgan4)). 0.41/0.78 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', subset2powerset)). 0.41/0.78 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', quantDeMorgan3)). 0.41/0.78 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', quantDeMorgan2)). 0.41/0.78 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', binunionIR)). 0.41/0.78 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', quantDeMorgan1)). 0.41/0.78 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', eqimpsubset1)). 0.41/0.78 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', upairsetE)). 0.41/0.78 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', eqinunit)). 0.41/0.78 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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', binunionEcases)). 0.41/0.78 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', uniqinunit)). 0.41/0.78 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', nonemptyImpWitness)). 0.41/0.78 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', binintersectEL)). 0.41/0.78 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', subPowSU)). 0.41/0.78 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', singletoninpowerset)). 0.41/0.78 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', subsetI2)). 0.41/0.78 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setunionI)). 0.41/0.78 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', powersetE)). 0.41/0.78 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', emptyinPowerset)). 0.41/0.78 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', binintersectSubset2)). 0.41/0.78 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', powersetI)). 0.41/0.78 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', binintersectSubset3)). 0.41/0.78 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setadjoinE)). 0.41/0.78 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setadjoinIR)). 0.41/0.78 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', nonemptyI1)). 0.41/0.78 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', binintersectSubset4)). 0.41/0.78 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', nonemptyE1)). 0.41/0.78 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', binintersectSubset1)). 0.41/0.78 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', noeltsimpempty)). 0.41/0.78 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', emptyI)). 0.41/0.78 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', emptysetimpfalse)). 0.41/0.78 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', bs114d)). 0.41/0.78 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', prop2setE)). 0.41/0.78 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setminusELneg)). 0.41/0.78 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setminusIRneg)). 0.41/0.78 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', wellorderingAx)). 0.41/0.78 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setminusSubset1)). 0.41/0.78 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', omegaSAx)). 0.41/0.78 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setunionAx)). 0.41/0.78 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', emptysetsubset)). 0.41/0.78 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', powersetAx)). 0.41/0.78 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setadjoinAx)). 0.41/0.78 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', symdiffIneg1)). 0.41/0.78 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', symdiffIneg2)). 0.41/0.78 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', secondinupair)). 0.41/0.78 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setukpairIL)). 0.41/0.78 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setukpairIR)). 0.41/0.78 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', kpairp)). 0.41/0.78 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', singletonsubset)). 0.41/0.78 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X30 @ X2)) @ X30)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', funcGraphProp1)). 0.41/0.78 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', singletoninpowunion)). 0.41/0.78 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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', upairinpowunion)). 0.41/0.78 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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', ubforcartprodlem1)). 0.41/0.78 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', cartprodmempair1)). 0.41/0.78 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', cartprodmempair)). 0.41/0.78 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', singletonsuniq)). 0.41/0.78 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', kfstpairEq)). 0.41/0.78 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', notequalI1)). 0.41/0.78 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', cartprodfstin)). 0.41/0.78 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setukpairinjL)). 0.41/0.78 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setukpairinjR11)). 0.41/0.78 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setukpairinjR1)). 0.41/0.78 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setukpairinjR2)). 0.41/0.78 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', ksndpairEq)). 0.41/0.78 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', cartprodpairmemEL)). 0.41/0.78 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', cartprodpairmemER)). 0.41/0.78 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', cartprodmempaircEq)). 0.41/0.78 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', cartprodpairsurjEq)). 0.41/0.78 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', ap2p)). 0.41/0.78 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>(in @ X30 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', funcinfuncset)). 0.41/0.78 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X29:$i]:(((breln @ X4 @ X5 @ X29)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X29)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', brelnall1)). 0.41/0.78 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X29:$i]:(((breln @ X4 @ X5 @ X29)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X29)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', brelnall2)). 0.41/0.78 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X30:$i]:(((in @ X30 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X30)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', infuncsetfunc)). 0.41/0.78 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X30 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', app)). 0.41/0.78 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', cartprodsndpairEq)). 0.41/0.78 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', cartprodfstpairEq)). 0.41/0.78 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', cartprodsndin)). 0.41/0.78 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', kpairsurjEq)). 0.41/0.78 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setukpairinjR)). 0.41/0.78 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', upairequniteq)). 0.41/0.78 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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setukpairinjR12)). 0.41/0.78 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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setukpairinjL2)). 0.41/0.78 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', theprop)). 0.41/0.78 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setukpairinjL1)). 0.41/0.78 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setunionsingleton)). 0.41/0.78 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setunionsingleton2)). 0.41/0.78 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setunionsingleton1)). 0.41/0.78 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setunionE2)). 0.41/0.78 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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', cartprodpairin)). 0.41/0.78 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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', ubforcartprodlem3)). 0.41/0.78 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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', ubforcartprodlem2)). 0.41/0.78 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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', upairsubunion)). 0.41/0.78 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', upairset2E)). 0.41/0.78 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', kpairiskpair)). 0.41/0.78 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', symdiffI2)). 0.41/0.78 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', symdiffI1)). 0.41/0.78 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', symdiffE)). 0.41/0.78 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setminusLsub)). 0.41/0.78 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setminusILneg)). 0.41/0.78 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setminusERneg)). 0.41/0.78 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setminusSubset2)). 0.41/0.78 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setminusER)). 0.41/0.78 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setminusEL)). 0.41/0.78 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setminusI)). 0.41/0.78 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', binintersectRsub)). 0.41/0.78 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', disjointsetsI1)). 0.41/0.78 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', binintersectER)). 0.41/0.78 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', binintersectLsub)). 0.41/0.78 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', binintersectSubset5)). 0.41/0.78 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', binintersectI)). 0.41/0.78 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', binunionRsub)). 0.41/0.78 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', binunionLsub)). 0.41/0.78 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', binunionE)). 0.41/0.78 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', upairset2IR)). 0.41/0.78 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', binunionIL)). 0.41/0.78 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', powersetsubset)). 0.41/0.78 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', inPowerset)). 0.41/0.78 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', powersetE1)). 0.41/0.78 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', powersetI1)). 0.41/0.78 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', subsetemptysetimpeq)). 0.41/0.78 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setextsub)). 0.41/0.78 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', subsetTrans)). 0.41/0.78 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', eqimpsubset2)). 0.41/0.78 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', omega__Cong)). 0.41/0.78 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setunion__Cong)). 0.41/0.78 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', powerset__Cong)). 0.41/0.78 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', notdexE)). 0.41/0.78 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', vacuousDall)). 0.41/0.78 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', upairsetIR)). 0.41/0.78 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', upairsetIL)). 0.41/0.78 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', singletonsswitch)). 0.41/0.78 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', notinsingleton)). 0.41/0.78 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', emptyInPowerset)). 0.41/0.78 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setadjoinOr)). 0.41/0.78 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', emptyinunitempty)). 0.41/0.78 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setadjoinIL)). 0.41/0.78 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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setext)). 0.41/0.78 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', notinemptyset)). 0.41/0.78 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', emptysetE)). 0.41/0.78 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', foundationAx)). 0.41/0.78 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', omegaIndAx)). 0.41/0.78 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', omega0Ax)). 0.41/0.78 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.Ii1gfe0El9/Vampire---4.8_8102', setextAx)). 0.41/0.78 thf(c_0_201, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 0.41/0.78 thf(c_0_202, plain, ((emptyE1)<=>![X4:$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])). 0.41/0.78 thf(c_0_203, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.41/0.78 thf(c_0_204, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.41/0.78 thf(c_0_205, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 0.41/0.78 thf(c_0_206, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.41/0.78 thf(c_0_207, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.41/0.78 thf(c_0_208, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.41/0.78 thf(c_0_209, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.41/0.78 thf(c_0_210, plain, ((ex1E2)<=>![X4:$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])). 0.41/0.78 thf(c_0_211, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 0.41/0.78 thf(c_0_212, plain, ((ex1I2)<=>![X4:$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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 0.41/0.78 thf(c_0_213, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 0.41/0.78 thf(c_0_214, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 0.41/0.78 thf(c_0_215, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 0.41/0.78 thf(c_0_216, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 0.41/0.78 thf(c_0_217, plain, ((apProp)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 0.41/0.78 thf(c_0_218, plain, ((lamProp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X31 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])). 0.41/0.78 thf(c_0_219, plain, ((lamp)<=>![X4:$i, X5:$i, X33:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X33 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X33 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 0.41/0.78 thf(c_0_220, plain, ((lam2p)<=>![X4:$i, X5:$i, X34:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X34 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X34 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 0.41/0.78 thf(c_0_221, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])). 0.41/0.78 thf(c_0_222, 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:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 0.41/0.78 thf(c_0_223, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 0.41/0.78 thf(c_0_224, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 0.41/0.78 thf(c_0_225, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 0.41/0.78 thf(c_0_226, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 0.41/0.78 thf(c_0_227, plain, ((ex1I)<=>![X4:$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])). 0.41/0.78 thf(c_0_228, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 0.41/0.78 thf(c_0_229, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 0.41/0.78 thf(c_0_230, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 0.41/0.78 thf(c_0_231, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 0.41/0.78 thf(c_0_232, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 0.41/0.78 thf(c_0_233, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 0.41/0.78 thf(c_0_234, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 0.41/0.78 thf(c_0_235, 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])). 0.41/0.78 thf(c_0_236, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 0.41/0.78 thf(c_0_237, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 0.41/0.78 thf(c_0_238, 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])). 0.41/0.78 thf(c_0_239, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.41/0.78 thf(c_0_240, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.41/0.78 thf(c_0_241, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 0.41/0.78 thf(c_0_242, plain, ((epred1_0)<=>![X1171:$i]:(?[X1172:$i]:((((![X1173:$i]:(((in @ X1173 @ X1172)=>![X1174:$i]:(((in @ X1174 @ X1173)=>(in @ X1174 @ X1171)))))&![X1175:$i, X1176:$i]:((((in @ X1175 @ X1171)&(in @ X1176 @ X1171))=>(![X1177:$i]:(((in @ X1177 @ X1172)=>((in @ X1175 @ X1177)<=>(in @ X1176 @ X1177))))=>((X1175)=(X1176))))))&![X1178:$i, X1179:$i]:((((in @ X1178 @ X1172)&(in @ X1179 @ X1172))=>(![X1180:$i]:(((in @ X1180 @ X1178)=>(in @ X1180 @ X1179)))|![X1181:$i]:(((in @ X1181 @ X1179)=>(in @ X1181 @ X1178)))))))&![X1182:$i]:(((![X1183:$i]:(((in @ X1183 @ X1182)=>(in @ X1183 @ X1171)))&?[X1184:$i]:((in @ X1184 @ X1182)))=>?[X1185:$i, X1186:$i]:(((((in @ X1185 @ X1172)&(in @ X1186 @ X1182))&~(?[X1187:$i]:(((in @ X1187 @ X1185)&(in @ X1187 @ X1182)))))&![X1188:$i]:(((in @ X1188 @ X1172)=>(![X1189:$i]:(((in @ X1189 @ X1188)=>(in @ X1189 @ X1185)))|(in @ X1186 @ X1188)))))))))))), introduced(definition)). 0.41/0.78 thf(c_0_243, negated_conjecture, ~((![X623:$i, X624:$i]:((![X625:$i]:(((in @ X625 @ X623)<=>(in @ X625 @ X624)))=>((X623)=(X624))))=>(![X1206:$i]:(~(in @ X1206 @ emptyset))=>(![X1203:$i, X1204:$i, X1205:$i]:(((in @ X1205 @ (setadjoin @ X1203 @ X1204))<=>(((X1205)=(X1203))|(in @ X1205 @ X1204))))=>(![X1200:$i, X1201:$i]:(((in @ X1201 @ (powerset @ X1200))<=>![X1202:$i]:(((in @ X1202 @ X1201)=>(in @ X1202 @ X1200)))))=>(![X1197:$i, X1198:$i]:(((in @ X1198 @ (setunion @ X1197))<=>?[X1199:$i]:(((in @ X1198 @ X1199)&(in @ X1199 @ X1197)))))=>((in @ emptyset @ omega)=>(![X1196:$i]:(((in @ X1196 @ omega)=>(in @ (setadjoin @ X1196 @ X1196) @ omega)))=>(![X626:$i]:((((in @ emptyset @ X626)&![X627:$i]:((((in @ X627 @ omega)&(in @ X627 @ X626))=>(in @ (setadjoin @ X627 @ X627) @ X626))))=>![X628:$i]:(((in @ X628 @ omega)=>(in @ X628 @ X626)))))=>(![X1190:$i > $i > $o, X1191:$i]:((![X1192:$i]:(((in @ X1192 @ X1191)=>(exu @ (^[Z0/* 3 */:$i]:((X1190 @ X1192 @ Z0))))))=>?[X1193:$i]:(![X1194:$i]:(((in @ X1194 @ X1193)<=>?[X1195:$i]:(((in @ X1195 @ X1191)&(X1190 @ X1195 @ X1194))))))))=>(![X629:$i]:((?[X630:$i]:((in @ X630 @ X629))=>?[X631:$i]:(((in @ X631 @ X629)&~(?[X632:$i]:(((in @ X632 @ X631)&(in @ X632 @ X629))))))))=>((epred1_0)=>(![X633:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X633 @ Z0))))=>(X633 @ (descr @ (^[Z0/* 3 */:$i]:((X633 @ Z0)))))))=>(![X1168:$i, X1169:$i > $o, X1170:$i]:(((in @ X1170 @ X1168)=>((X1169 @ X1170)=>(in @ X1170 @ (dsetconstr @ X1168 @ (^[Z0/* 3 */:$i]:((X1169 @ Z0))))))))=>(![X1165:$i, X1166:$i > $o, X1167:$i]:(((in @ X1167 @ (dsetconstr @ X1165 @ (^[Z0/* 3 */:$i]:((X1166 @ Z0)))))=>(in @ X1167 @ X1165)))=>(![X1162:$i, X1163:$i > $o, X1164:$i]:(((in @ X1164 @ (dsetconstr @ X1162 @ (^[Z0/* 3 */:$i]:((X1163 @ Z0)))))=>(X1163 @ X1164)))=>(![X1159:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1159 @ Z0))))=>?[X1160:$i]:(((X1159 @ X1160)&![X1161:$i]:(((X1159 @ X1161)=>((X1160)=(X1161))))))))=>(![X1157:$o, X1158:$i]:(((in @ X1158 @ (prop2set @ ((X1157))))=>(X1157)))=>(![X634:$i]:(((in @ X634 @ emptyset)=>![X635:$o]:((X635))))=>(![X1156:$i]:(~(in @ X1156 @ emptyset))=>(![X636:$i]:(~(in @ X636 @ emptyset))=>(![X637:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X637 @ Z0))))=>?[X638:$i]:((X637 @ X638))))=>(![X639:$i, X640:$i]:((![X641:$i]:(((in @ X641 @ X639)=>(in @ X641 @ X640)))=>(![X642:$i]:(((in @ X642 @ X640)=>(in @ X642 @ X639)))=>((X639)=(X640)))))=>(![X1154:$i]:((![X1155:$i]:(~(in @ X1155 @ X1154))=>((X1154)=(emptyset))))=>(![X1152:$i]:((![X1153:$i]:(~(in @ X1153 @ 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X649))))=>(![X1137:$i]:(((dsetconstr @ X1137 @ (^[Z0/* 3 */:$i]:(($true))))=(X1137)))=>(![X1134:$i, X1135:$i]:((![X1136:$i]:(((in @ X1136 @ X1135)=>(in @ X1136 @ X1134)))=>(in @ X1135 @ (powerset @ X1134))))=>(![X1133:$i]:((in @ emptyset @ (powerset @ X1133)))=>(![X651:$i]:((in @ emptyset @ (powerset @ X651)))=>(![X1130:$i, X1131:$i, X1132:$i]:(((in @ X1131 @ (powerset @ X1130))=>((in @ X1132 @ X1131)=>(in @ X1132 @ X1130))))=>(![X1127:$i, X1128:$i, X1129:$i]:(((in @ X1128 @ X1129)=>((in @ X1129 @ X1127)=>(in @ X1128 @ (setunion @ X1127)))))=>(![X1123:$i, X1124:$i]:(((in @ X1124 @ (setunion @ X1123))=>![X1125:$o]:((![X1126:$i]:(((in @ X1124 @ X1126)=>((in @ X1126 @ X1123)=>(X1125))))=>(X1125)))))=>(![X1121:$i, X1122:$i]:(((in @ X1122 @ X1121)=>(in @ X1122 @ (powerset @ (setunion @ X1121)))))=>(![X652:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X652 @ Z0))))=>?[X653:$i]:(![X654:$i]:(((X652 @ X654)<=>((X654)=(X653)))))))=>(![X1119:$i]:(((nonempty @ X1119)=>?[X1120:$i]:((in @ X1120 @ 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X30))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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setunionE]), emptysetAx]), notsubsetI]), subsetE2]), notequalI2]), subsetE]), subsetI1]), subsetRefl]), c_0_201]), setadjoin__Cong]), emptyset__Cong]), setadjoinSub]), in__Cong]), inCongP]), setadjoinSub2]), notdallE]), prop2setI]), quantDeMorgan4]), subset2powerset]), quantDeMorgan3]), quantDeMorgan2]), binunionIR]), quantDeMorgan1]), eqimpsubset1]), c_0_202]), upairsetE]), eqinunit]), binunionEcases]), uniqinunit]), nonemptyImpWitness]), binintersectEL]), subPowSU]), singletoninpowerset]), subsetI2]), setunionI]), powersetE]), emptyinPowerset]), binintersectSubset2]), powersetI]), c_0_203]), binintersectSubset3]), setadjoinE]), setadjoinIR]), nonemptyI1]), binintersectSubset4]), nonemptyE1]), c_0_204]), binintersectSubset1]), noeltsimpempty]), emptyI]), emptysetimpfalse]), bs114d]), prop2setE]), c_0_205]), setminusELneg]), c_0_206]), c_0_207]), c_0_208]), setminusIRneg]), wellorderingAx]), c_0_209]), setminusSubset1]), omegaSAx]), setunionAx]), emptysetsubset]), powersetAx]), setadjoinAx]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairp]), singletonsubset]), c_0_210]), funcGraphProp1]), singletoninpowunion]), upairinpowunion]), ubforcartprodlem1]), cartprodmempair1]), cartprodmempair]), c_0_211]), c_0_212]), singletonsuniq]), kfstpairEq]), notequalI1]), cartprodfstin]), setukpairinjL]), setukpairinjR11]), setukpairinjR1]), setukpairinjR2]), ksndpairEq]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodpairsurjEq]), c_0_213]), c_0_214]), c_0_215]), c_0_216]), c_0_217]), ap2p]), funcinfuncset]), c_0_218]), c_0_219]), brelnall1]), brelnall2]), c_0_220]), infuncsetfunc]), app]), c_0_221]), c_0_222]), c_0_223]), c_0_224]), cartprodsndpairEq]), cartprodfstpairEq]), cartprodsndin]), kpairsurjEq]), c_0_225]), setukpairinjR]), upairequniteq]), setukpairinjR12]), setukpairinjL2]), theprop]), c_0_226]), setukpairinjL1]), c_0_227]), c_0_228]), setunionsingleton]), setunionsingleton2]), setunionsingleton1]), setunionE2]), cartprodpairin]), ubforcartprodlem3]), ubforcartprodlem2]), upairsubunion]), upairset2E]), kpairiskpair]), symdiffI2]), symdiffI1]), symdiffE]), setminusLsub]), setminusILneg]), setminusERneg]), setminusSubset2]), setminusER]), setminusEL]), setminusI]), binintersectRsub]), disjointsetsI1]), binintersectER]), binintersectLsub]), binintersectSubset5]), binintersectI]), binunionRsub]), binunionLsub]), binunionE]), upairset2IR]), binunionIL]), c_0_229]), c_0_230]), powersetsubset]), inPowerset]), powersetE1]), powersetI1]), subsetemptysetimpeq]), setextsub]), subsetTrans]), eqimpsubset2]), c_0_231]), c_0_232]), omega__Cong]), setunion__Cong]), powerset__Cong]), c_0_233]), c_0_234]), c_0_235]), c_0_236]), c_0_237]), notdexE]), vacuousDall]), upairsetIR]), upairsetIL]), singletonsswitch]), notinsingleton]), c_0_238]), emptyInPowerset]), setadjoinOr]), emptyinunitempty]), setadjoinIL]), c_0_239]), setext]), c_0_240]), notinemptyset]), emptysetE]), c_0_241]), foundationAx]), omegaIndAx]), omega0Ax]), setextAx])])]), c_0_242])). 0.41/0.78 thf(c_0_244, negated_conjecture, ![X1207:$i, X1208:$i, X1210:$i, X1211:$i, X1212:$i, X1213:$i, X1214:$i, X1215:$i, X1216:$i, X1217:$i, X1218:$i, X1220:$i, X1221:$i, X1223:$i, X1224:$i, X1225:$i, X1226:$i, X1227:$i, X1229:$i, X1230:$i > $i > $o, X1231:$i, X1234:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, X1241:$i, X1242:$i > $o, X1243:$i, X1244:$i > $o, X1245:$i, X1246:$i, X1247:$i > $o, X1248:$i, X1249:$i, X1250:$i > $o, X1251:$i, X1252:$i > $o, X1254:$i, X1255:$o, X1256:$i, X1257:$i, X1258:$o, X1259:$i, X1260:$i, X1261:$i > $o, X1263:$i, X1264:$i, X1267:$i, X1269:$i, X1271:$i, X1272:$i > $o, X1273:$i, X1274:$i, X1276:$i, X1277:$i > $o, X1278:$i, X1279:$i, X1280:$i, X1281:$i, X1282:$i, X1283:$i, X1284:$i, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$o, X1290:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1305:$i, X1306:$i, X1307:$o, X1309:$i, X1310:$i, X1311:$i > $o, X1313:$i, X1314:$i, X1315:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1326:$i, X1327:$i, X1328:$i, X1329:$i, X1330:$i, X1331:$i, X1332:$i, X1333:$i > $o, X1334:$i, X1335:$i > $o, X1336:$i, X1337:$i, X1338:$i > $o, X1339:$i, X1341:$i, X1342:$i > $o, X1344:$i, X1345:$i, X1346:$i > $o, X1348:$i, X1349:$i, X1350:$i > $o, X1351:$i, X1353:$o, X1354:$i, X1355:$i > $o, X1357:$i, X1358:$i, X1359:$i > $o, X1360:$i, X1362:$i > $o, X1363:$i, X1365:$i > $o, X1366:$i, X1369:$i > $o, X1370:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i > $o, X1381:$i, X1382:$i, X1383:$i > $o, X1384:$i > $o, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$i, X1393:$i, X1394:$i, X1395:$i > $o, X1396:$i, X1397:$i, X1398:$i > $o, X1399:$i > $o, X1402:$i, X1403:$i, X1404:$i > $o, X1405:$i > $o, X1408:$i, X1409:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1418:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1423:$i, X1424:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$i, X1432:$i, X1433:$i, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i > $o, X1456:$i, X1457:$i > $o, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$o, X1470:$i, X1471:$i, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$i, X1483:$i, X1484:$i, X1485:$i, X1486:$i, X1487:$i, X1488:$i, X1489:$i, X1490:$i, X1491:$i, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1512:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$o, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1599:$i, X1600:$i, X1601:$i, X1602:$i, X1603:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i > $o, X1612:$i, X1613:$i, X1614:$i > $o, X1616:$i, X1617:$i > $o, X1618:$i, X1620:$i, X1621:$i > $o, X1624:$i, X1625:$i, X1626:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i, X1633:$i, X1634:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i, X1643:$i, X1644:$i, X1645:$i, X1646:$i, X1647:$i, X1648:$i, X1649:$i, X1650:$i, X1651:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$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 > $i > $o, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i > $i > $o, X1702:$i, X1703:$i, X1704:$i > $i > $o, X1705:$i, X1706:$i, X1707:$i > $i > $o, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i > $i > $o, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i > $i > $o, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i > $i > $o, X1723:$i, X1724:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i > $i, X1751:$i, X1752:$i, X1753:$i > $i, X1755:$i, X1756:$i, X1757:$i > $i, X1759:$i, X1760:$i, X1761:$i, X1762:$i > $o, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i > $o, X1772:$i, X1773:$i, X1774:$i > $o, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i]:((((~(in @ (esk1_2 @ X1207 @ X1208) @ X1207)|~(in @ (esk1_2 @ X1207 @ X1208) @ X1208)|((X1207)=(X1208)))&((in @ (esk1_2 @ X1207 @ X1208) @ X1207)|(in @ (esk1_2 @ X1207 @ X1208) @ X1208)|((X1207)=(X1208))))&(~(in @ X1210 @ emptyset)&(((~(in @ X1213 @ (setadjoin @ X1211 @ X1212))|(((X1213)=(X1211))|(in @ X1213 @ X1212)))&((((X1213)!=(X1211))|(in @ X1213 @ (setadjoin @ X1211 @ X1212)))&(~(in @ X1213 @ X1212)|(in @ X1213 @ (setadjoin @ X1211 @ X1212)))))&(((~(in @ X1215 @ (powerset @ X1214))|(~(in @ X1216 @ X1215)|(in @ X1216 @ X1214)))&(((in @ (esk2_2 @ X1217 @ X1218) @ X1218)|(in @ X1218 @ (powerset @ X1217)))&(~(in @ (esk2_2 @ X1217 @ X1218) @ X1217)|(in @ X1218 @ (powerset @ X1217)))))&(((((in @ X1221 @ (esk3_2 @ X1220 @ X1221))|~(in @ X1221 @ (setunion @ X1220)))&((in @ (esk3_2 @ X1220 @ X1221) @ X1220)|~(in @ X1221 @ (setunion @ X1220))))&(~(in @ X1224 @ X1225)|~(in @ X1225 @ X1223)|(in @ X1224 @ (setunion @ X1223))))&((in @ emptyset @ omega)&((~(in @ X1226 @ omega)|(in @ (setadjoin @ X1226 @ X1226) @ omega))&(((((in @ (esk4_1 @ X1227) @ omega)|~(in @ emptyset @ X1227)|(~(in @ X1229 @ omega)|(in @ X1229 @ X1227)))&((in @ (esk4_1 @ X1227) @ X1227)|~(in @ emptyset @ X1227)|(~(in @ X1229 @ omega)|(in @ X1229 @ X1227))))&(~(in @ (setadjoin @ (esk4_1 @ X1227) @ (esk4_1 @ X1227)) @ X1227)|~(in @ emptyset @ X1227)|(~(in @ X1229 @ omega)|(in @ X1229 @ X1227))))&((((((in @ (esk7_3 @ X1230 @ X1231 @ X1234) @ X1231)|~(in @ X1234 @ (esk6_2 @ X1230 @ X1231))|(in @ (esk5_2 @ X1230 @ X1231) @ X1231))&((X1230 @ (esk7_3 @ X1230 @ X1231 @ X1234) @ X1234)|~(in @ X1234 @ (esk6_2 @ X1230 @ X1231))|(in @ (esk5_2 @ X1230 @ X1231) @ X1231)))&(~(in @ X1237 @ X1231)|~(X1230 @ X1237 @ X1236)|(in @ X1236 @ (esk6_2 @ X1230 @ X1231))|(in @ (esk5_2 @ X1230 @ X1231) @ X1231)))&((((in @ (esk7_3 @ X1230 @ X1231 @ X1234) @ X1231)|~(in @ X1234 @ (esk6_2 @ X1230 @ X1231))|~(exu @ (^[Z0/* 3 */:$i]:((X1230 @ (esk5_2 @ X1230 @ X1231) @ Z0)))))&((X1230 @ (esk7_3 @ X1230 @ X1231 @ X1234) @ X1234)|~(in @ X1234 @ (esk6_2 @ X1230 @ X1231))|~(exu @ (^[Z0/* 3 */:$i]:((X1230 @ (esk5_2 @ X1230 @ X1231) @ Z0))))))&(~(in @ X1237 @ X1231)|~(X1230 @ X1237 @ X1236)|(in @ X1236 @ (esk6_2 @ X1230 @ X1231))|~(exu @ (^[Z0/* 3 */:$i]:((X1230 @ (esk5_2 @ X1230 @ X1231) @ Z0)))))))&((((in @ (esk8_1 @ X1238) @ X1238)|~(in @ X1239 @ X1238))&(~(in @ X1241 @ (esk8_1 @ X1238))|~(in @ X1241 @ X1238)|~(in @ X1239 @ X1238)))&((epred1_0)&((~(exu @ (^[Z0/* 3 */:$i]:((X1242 @ Z0))))|(X1242 @ (descr @ (^[Z0/* 3 */:$i]:((X1242 @ Z0))))))&((~(in @ X1245 @ X1243)|(~(X1244 @ X1245)|(in @ X1245 @ (dsetconstr @ X1243 @ (^[Z0/* 3 */:$i]:((X1244 @ Z0)))))))&((~(in @ X1248 @ (dsetconstr @ X1246 @ (^[Z0/* 3 */:$i]:((X1247 @ Z0)))))|(in @ X1248 @ X1246))&((~(in @ X1251 @ (dsetconstr @ X1249 @ (^[Z0/* 3 */:$i]:((X1250 @ Z0)))))|(X1250 @ X1251))&((((X1252 @ (esk9_1 @ X1252))|~(exu @ (^[Z0/* 3 */:$i]:((X1252 @ Z0)))))&(~(X1252 @ X1254)|((esk9_1 @ X1252)=(X1254))|~(exu @ (^[Z0/* 3 */:$i]:((X1252 @ Z0))))))&((~(in @ X1256 @ (prop2set @ ((X1255))))|(X1255))&((~(in @ X1257 @ emptyset)|(X1258))&(~(in @ X1259 @ emptyset)&(~(in @ X1260 @ emptyset)&((~(exu @ (^[Z0/* 3 */:$i]:((X1261 @ Z0))))|(X1261 @ (esk10_1 @ X1261)))&(((((in @ (esk12_2 @ X1263 @ X1264) @ X1264)|((X1263)=(X1264))|(in @ (esk11_2 @ X1263 @ X1264) @ X1263))&(~(in @ (esk12_2 @ X1263 @ X1264) @ X1263)|((X1263)=(X1264))|(in @ (esk11_2 @ X1263 @ X1264) @ X1263)))&(((in @ (esk12_2 @ X1263 @ X1264) @ X1264)|((X1263)=(X1264))|~(in @ (esk11_2 @ X1263 @ X1264) @ X1264))&(~(in @ (esk12_2 @ X1263 @ X1264) @ X1263)|((X1263)=(X1264))|~(in @ (esk11_2 @ X1263 @ X1264) @ X1264))))&(((in @ (esk13_1 @ X1267) @ X1267)|((X1267)=(emptyset)))&(((in @ (esk14_1 @ X1269) @ X1269)|((X1269)=(emptyset)))&(((~(in @ X1273 @ (dsetconstr @ X1271 @ (^[Z0/* 3 */:$i]:((X1272 @ Z0)))))|(X1272 @ X1273)|~(in @ X1273 @ X1271))&(~(X1272 @ X1273)|(in @ X1273 @ (dsetconstr @ X1271 @ (^[Z0/* 3 */:$i]:((X1272 @ Z0)))))|~(in @ X1273 @ X1271)))&((~(nonempty @ X1274)|(in @ (esk15_1 @ X1274) @ X1274))&((~(in @ X1278 @ X1276)|(~(X1277 @ X1278)|(nonempty @ (dsetconstr @ X1276 @ (^[Z0/* 3 */:$i]:((X1277 @ Z0)))))))&((~(in @ X1280 @ X1279)|(nonempty @ X1279))&((in @ X1281 @ (setadjoin @ X1281 @ X1282))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1285 @ X1284)|(in @ X1285 @ (setadjoin @ X1283 @ X1284)))&(((((in @ X1288 @ X1287)|(X1289)|((X1288)=(X1286))|~(in @ X1288 @ (setadjoin @ X1286 @ X1287)))&(~(X1289)|(X1289)|((X1288)=(X1286))|~(in @ X1288 @ (setadjoin @ X1286 @ X1287))))&(((in @ X1288 @ X1287)|(X1289)|~(X1289)|~(in @ X1288 @ (setadjoin @ X1286 @ X1287)))&(~(X1289)|(X1289)|~(X1289)|~(in @ X1288 @ (setadjoin @ X1286 @ X1287)))))&((~(in @ X1292 @ (setadjoin @ X1290 @ X1291))|(((X1292)=(X1290))|(in @ X1292 @ X1291)))&(((dsetconstr @ X1293 @ (^[Z0/* 3 */:$i]:(($true))))=(X1293))&((((in @ (esk16_2 @ X1294 @ X1295) @ X1295)|(in @ X1295 @ (powerset @ X1294)))&(~(in @ (esk16_2 @ X1294 @ X1295) @ X1294)|(in @ X1295 @ (powerset @ X1294))))&((in @ emptyset @ (powerset @ X1297))&((in @ emptyset @ (powerset @ X1298))&((~(in @ X1300 @ (powerset @ X1299))|(~(in @ X1301 @ X1300)|(in @ X1301 @ X1299)))&((~(in @ X1303 @ X1304)|(~(in @ X1304 @ X1302)|(in @ X1303 @ (setunion @ X1302))))&((((in @ X1306 @ (esk17_3 @ X1305 @ X1306 @ X1307))|(X1307)|~(in @ X1306 @ (setunion @ X1305)))&(((in @ (esk17_3 @ X1305 @ X1306 @ X1307) @ X1305)|(X1307)|~(in @ X1306 @ (setunion @ X1305)))&(~(X1307)|(X1307)|~(in @ X1306 @ (setunion @ X1305)))))&((~(in @ X1310 @ X1309)|(in @ X1310 @ (powerset @ (setunion @ X1309))))&(((~(X1311 @ X1313)|((X1313)=(esk18_1 @ X1311))|~(exu @ (^[Z0/* 3 */:$i]:((X1311 @ Z0)))))&(((X1314)!=(esk18_1 @ X1311))|(X1311 @ X1314)|~(exu @ (^[Z0/* 3 */:$i]:((X1311 @ Z0))))))&((~(nonempty @ X1315)|(in @ (esk19_1 @ X1315) @ X1315))&((~(in @ X1317 @ (setadjoin @ X1318 @ emptyset))|((X1317)=(X1318)))&((((X1319)=(X1320))|~(in @ X1320 @ (setadjoin @ X1319 @ emptyset)))&((((X1321)!=(X1322))|(in @ X1321 @ (setadjoin @ X1322 @ emptyset)))&((~(in @ X1323 @ (setadjoin @ X1324 @ emptyset))|(in @ X1324 @ (setadjoin @ X1323 @ emptyset)))&((~(in @ X1327 @ (setadjoin @ X1325 @ (setadjoin @ X1326 @ emptyset)))|(((X1327)=(X1325))|((X1327)=(X1326))))&((in @ X1328 @ (setadjoin @ X1328 @ (setadjoin @ X1329 @ emptyset)))&((in @ X1331 @ (setadjoin @ X1330 @ (setadjoin @ X1331 @ emptyset)))&((~(in @ X1334 @ X1332)|~(X1333 @ X1334)|((dsetconstr @ X1332 @ (^[Z0/* 3 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@ (setadjoin @ X1656 @ emptyset) @ (setadjoin @ (setadjoin @ X1656 @ (setadjoin @ X1657 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1658 @ emptyset) @ (setadjoin @ (setadjoin @ X1658 @ (setadjoin @ X1659 @ emptyset)) @ emptyset)))|((X1657)=(X1659)))&((((kpair @ X1660 @ X1661)!=(kpair @ X1662 @ X1663))|((X1661)=(X1663)))&((~(iskpair @ X1664)|(singleton @ (dsetconstr @ (setunion @ X1664) @ (^[Z0/* 3 */:$i]:(((X1664)=(kpair @ (kfst @ X1664) @ Z0)))))))&(((ksnd @ (kpair @ X1665 @ X1666))=(X1666))&((~(iskpair @ X1667)|((kpair @ (kfst @ X1667) @ (ksnd @ X1667))=(X1667)))&((~(in @ X1670 @ (cartprod @ X1668 @ X1669))|(in @ (ksnd @ X1670) @ X1669))&((~(in @ (kpair @ X1673 @ X1674) @ (cartprod @ X1671 @ X1672))|(in @ X1673 @ X1671))&((~(in @ (kpair @ X1677 @ X1678) @ (cartprod @ X1675 @ X1676))|(in @ X1678 @ X1676))&((~(in @ X1681 @ X1679)|(~(in @ X1682 @ X1680)|((kpair @ X1681 @ X1682)=(kpair @ X1681 @ X1682))))&((~(in @ X1685 @ X1683)|(~(in @ X1686 @ X1684)|((kfst @ (kpair @ X1685 @ X1686))=(X1685))))&((~(in @ X1689 @ X1687)|(~(in @ X1690 @ X1688)|((ksnd @ (kpair @ X1689 @ X1690))=(X1690))))&((~(in @ X1693 @ (cartprod @ X1691 @ X1692))|((kpair @ (kfst @ X1693) @ (ksnd @ X1693))=(X1693)))&((~(in @ X1697 @ X1694)|(~(in @ X1698 @ X1695)|(~(X1696 @ X1697 @ X1698)|(in @ (kpair @ X1697 @ X1698) @ (dpsetconstr @ X1694 @ X1695 @ (^[Z0/* 19 */:$i, Z1:$i]:((X1696 @ Z0 @ Z1))))))))&((subset @ (dpsetconstr @ X1699 @ X1700 @ (^[Z0/* 19 */:$i, Z1:$i]:((X1701 @ Z0 @ Z1)))) @ (cartprod @ X1699 @ X1700))&((breln @ X1702 @ X1703 @ (dpsetconstr @ X1702 @ X1703 @ (^[Z0/* 19 */:$i, Z1:$i]:((X1704 @ Z0 @ Z1)))))&((~(in @ X1708 @ X1705)|(~(in @ X1709 @ X1706)|(~(in @ (kpair @ X1708 @ X1709) @ (dpsetconstr @ X1705 @ X1706 @ (^[Z0/* 19 */:$i, Z1:$i]:((X1707 @ Z0 @ Z1)))))|(X1707 @ X1708 @ X1709))))&((~(in @ (kpair @ X1713 @ X1714) @ (dpsetconstr @ X1710 @ X1711 @ (^[Z0/* 19 */:$i, Z1:$i]:((X1712 @ Z0 @ Z1)))))|(in @ X1713 @ X1710))&((~(in @ (kpair @ X1718 @ X1719) @ (dpsetconstr @ X1715 @ X1716 @ (^[Z0/* 19 */:$i, Z1:$i]:((X1717 @ Z0 @ Z1)))))|(in @ X1719 @ X1716))&((~(in @ (kpair @ X1723 @ X1724) @ (dpsetconstr @ X1720 @ X1721 @ (^[Z0/* 19 */:$i, Z1:$i]:((X1722 @ Z0 @ Z1)))))|(X1722 @ X1723 @ X1724))&((~(func @ X1725 @ X1726 @ X1727)|(~(in @ X1728 @ X1725)|(singleton @ (dsetconstr @ X1726 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1728 @ Z0) @ X1727)))))))&((~(func @ X1729 @ X1730 @ X1731)|(~(in @ X1732 @ X1729)|(in @ (setunion @ (dsetconstr @ X1730 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1732 @ Z0) @ X1731))))) @ X1730)))&((~(func @ X1733 @ X1734 @ X1735)|(~(in @ X1736 @ X1733)|(in @ (ap @ X1733 @ X1734 @ X1735 @ X1736) @ X1734)))&((~(in @ X1739 @ (funcSet @ X1737 @ X1738))|(func @ X1737 @ X1738 @ X1739))&((~(in @ X1742 @ (funcSet @ X1740 @ X1741))|(~(in @ X1743 @ X1740)|(in @ (ap @ X1740 @ X1741 @ X1742 @ X1743) @ X1741)))&((~(func @ X1744 @ X1745 @ X1746)|(in @ X1746 @ (funcSet @ X1744 @ X1745)))&((((in @ (esk48_3 @ X1747 @ X1748 @ X1749) @ X1747)|(func @ X1747 @ X1748 @ (dpsetconstr @ X1747 @ X1748 @ (^[Z0/* 3 */:$i]:($eq @ (X1749 @ Z0))))))&(~(in @ (X1749 @ (esk48_3 @ X1747 @ X1748 @ X1749)) @ X1748)|(func @ X1747 @ X1748 @ (dpsetconstr @ X1747 @ X1748 @ (^[Z0/* 3 */:$i]:($eq @ (X1749 @ Z0)))))))&((((in @ (esk49_3 @ X1751 @ X1752 @ X1753) @ X1751)|(func @ X1751 @ X1752 @ (lam @ X1751 @ X1752 @ X1753)))&(~(in @ (X1753 @ (esk49_3 @ X1751 @ X1752 @ X1753)) @ X1752)|(func @ X1751 @ X1752 @ (lam @ X1751 @ X1752 @ X1753))))&((((in @ (esk50_3 @ X1755 @ X1756 @ X1757) @ X1755)|(in @ (lam @ X1755 @ X1756 @ X1757) @ (funcSet @ X1755 @ X1756)))&(~(in @ (X1757 @ (esk50_3 @ X1755 @ X1756 @ X1757)) @ X1756)|(in @ (lam @ X1755 @ X1756 @ X1757) @ (funcSet @ X1755 @ X1756))))&((((in @ (esk51_4 @ X1759 @ X1760 @ X1761 @ X1762) @ X1759)|(~(in @ X1765 @ X1761)|(X1762 @ X1765))|~(breln @ X1759 @ X1760 @ X1761))&(((in @ (esk52_4 @ X1759 @ X1760 @ X1761 @ X1762) @ X1760)|(~(in @ X1765 @ X1761)|(X1762 @ X1765))|~(breln @ X1759 @ X1760 @ X1761))&(((in @ (kpair @ (esk51_4 @ X1759 @ X1760 @ X1761 @ X1762) @ (esk52_4 @ X1759 @ X1760 @ X1761 @ X1762)) @ X1761)|(~(in @ X1765 @ X1761)|(X1762 @ X1765))|~(breln @ X1759 @ X1760 @ X1761))&(~(X1762 @ (kpair @ (esk51_4 @ X1759 @ X1760 @ X1761 @ X1762) @ (esk52_4 @ X1759 @ X1760 @ X1761 @ X1762)))|(~(in @ X1765 @ X1761)|(X1762 @ X1765))|~(breln @ X1759 @ X1760 @ X1761)))))&((((in @ (esk53_4 @ X1766 @ X1767 @ X1768 @ X1769) @ X1766)|(~(in @ X1772 @ X1768)|(X1769 @ X1772))|~(breln @ X1766 @ X1767 @ X1768))&(((in @ (esk54_4 @ X1766 @ X1767 @ X1768 @ X1769) @ X1767)|(~(in @ X1772 @ X1768)|(X1769 @ X1772))|~(breln @ X1766 @ X1767 @ X1768))&(((in @ (kpair @ (esk53_4 @ X1766 @ X1767 @ X1768 @ X1769) @ (esk54_4 @ X1766 @ X1767 @ X1768 @ X1769)) @ X1768)|(~(in @ X1772 @ X1768)|(X1769 @ X1772))|~(breln @ X1766 @ X1767 @ X1768))&(~(X1769 @ (kpair @ (esk53_4 @ X1766 @ X1767 @ X1768 @ X1769) @ (esk54_4 @ X1766 @ X1767 @ X1768 @ X1769)))|(~(in @ X1772 @ X1768)|(X1769 @ X1772))|~(breln @ X1766 @ X1767 @ X1768)))))&((~(ex1 @ X1773 @ (^[Z0/* 3 */:$i]:((X1774 @ Z0))))|(~(in @ X1775 @ X1773)|(~(in @ X1776 @ X1773)|(~(X1774 @ X1775)|(~(X1774 @ X1776)|((X1775)=(X1776)))))))&((~(func @ X1777 @ X1778 @ X1779)|(~(in @ X1780 @ X1777)|(in @ (kpair @ X1780 @ (ap @ X1777 @ X1778 @ X1779 @ X1780)) @ X1779)))&((in @ esk57_0 @ (funcSet @ esk55_0 @ esk56_0))&((in @ esk58_0 @ esk55_0)&~(in @ (kpair @ esk58_0 @ (ap @ esk55_0 @ esk56_0 @ esk57_0 @ esk58_0)) @ esk57_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_243])])])])])])). 0.41/0.78 thf(c_0_245, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((func @ X3 @ X4 @ X2)|~((in @ X2 @ (funcSet @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_244])). 0.41/0.78 thf(c_0_246, negated_conjecture, (in @ esk57_0 @ (funcSet @ esk55_0 @ esk56_0)), inference(split_conjunct,[status(thm)],[c_0_244])). 0.41/0.78 thf(c_0_247, negated_conjecture, ~((in @ (kpair @ esk58_0 @ (ap @ esk55_0 @ esk56_0 @ esk57_0 @ esk58_0)) @ esk57_0)), inference(split_conjunct,[status(thm)],[c_0_244])). 0.41/0.78 thf(c_0_248, negated_conjecture, ![X3:$i, X5:$i, X4:$i, X2:$i]:(((in @ (kpair @ X5 @ (ap @ X2 @ X3 @ X4 @ X5)) @ X4)|~((func @ X2 @ X3 @ X4))|~((in @ X5 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_244])). 0.41/0.78 thf(c_0_249, negated_conjecture, (in @ esk58_0 @ esk55_0), inference(split_conjunct,[status(thm)],[c_0_244])). 0.41/0.78 thf(c_0_250, negated_conjecture, (func @ esk55_0 @ esk56_0 @ esk57_0), inference(spm,[status(thm)],[c_0_245, c_0_246])). 0.41/0.78 thf(c_0_251, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247, c_0_248]), c_0_249])]), c_0_250])]), ['proof']). 0.41/0.78 # SZS output end CNFRefutation 0.41/0.78 # Parsed axioms : 447 0.41/0.78 # Removed by relevancy pruning/SinE : 246 0.41/0.78 # Initial clauses : 311 0.41/0.78 # Removed in clause preprocessing : 24 0.41/0.78 # Initial clauses in saturation : 287 0.41/0.78 # Processed clauses : 548 0.41/0.78 # ...of these trivial : 9 0.41/0.78 # ...subsumed : 27 0.41/0.78 # ...remaining for further processing : 511 0.41/0.78 # Other redundant clauses eliminated : 33 0.41/0.78 # Clauses deleted for lack of memory : 0 0.41/0.78 # Backward-subsumed : 0 0.41/0.78 # Backward-rewritten : 2 0.41/0.78 # Generated clauses : 4427 0.41/0.78 # ...of the previous two non-redundant : 4277 0.41/0.78 # ...aggressively subsumed : 0 0.41/0.78 # Contextual simplify-reflections : 0 0.41/0.78 # Paramodulations : 4379 0.41/0.78 # Factorizations : 2 0.41/0.78 # NegExts : 0 0.41/0.78 # Equation resolutions : 38 0.41/0.78 # Total rewrite steps : 124 0.41/0.78 # Propositional unsat checks : 0 0.41/0.78 # Propositional check models : 0 0.41/0.78 # Propositional check unsatisfiable : 0 0.41/0.78 # Propositional clauses : 0 0.41/0.78 # Propositional clauses after purity: 0 0.41/0.78 # Propositional unsat core size : 0 0.41/0.78 # Propositional preprocessing time : 0.000 0.41/0.78 # Propositional encoding time : 0.000 0.41/0.78 # Propositional solver time : 0.000 0.41/0.78 # Success case prop preproc time : 0.000 0.41/0.78 # Success case prop encoding time : 0.000 0.41/0.78 # Success case prop solver time : 0.000 0.41/0.78 # Current number of processed clauses : 249 0.41/0.78 # Positive orientable unit clauses : 37 0.41/0.78 # Positive unorientable unit clauses: 0 0.41/0.78 # Negative unit clauses : 3 0.41/0.78 # Non-unit-clauses : 209 0.41/0.78 # Current number of unprocessed clauses: 4260 0.41/0.78 # ...number of literals in the above : 14959 0.41/0.78 # Current number of archived formulas : 0 0.41/0.78 # Current number of archived clauses : 249 0.41/0.78 # Clause-clause subsumption calls (NU) : 15718 0.41/0.78 # Rec. Clause-clause subsumption calls : 9486 0.41/0.78 # Non-unit clause-clause subsumptions : 22 0.41/0.78 # Unit Clause-clause subsumption calls : 73 0.41/0.78 # Rewrite failures with RHS unbound : 0 0.41/0.78 # BW rewrite match attempts : 24 0.41/0.78 # BW rewrite match successes : 2 0.41/0.78 # Condensation attempts : 0 0.41/0.78 # Condensation successes : 0 0.41/0.78 # Termbank termtop insertions : 106180 0.41/0.78 0.41/0.78 # ------------------------------------------------- 0.41/0.78 # User time : 0.180 s 0.41/0.78 # System time : 0.027 s 0.41/0.78 # Total time : 0.207 s 0.41/0.78 # Maximum resident set size: 6284 pages 0.41/0.81 0.41/0.81 # ------------------------------------------------- 0.41/0.81 # User time : 0.192 s 0.41/0.81 # System time : 0.030 s 0.41/0.81 # Total time : 0.222 s 0.41/0.81 # Maximum resident set size: 2296 pages 0.41/0.81 % E---3.1 exiting 0.41/0.81 EOF