0.06/0.16 % Problem : Vampire---4.8_24538 : TPTP v0.0.0. Released v0.0.0. 0.17/0.17 % Command : run_E %s %d THM 0.17/0.38 % Computer : n013.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 13:03:47 EDT 2023 0.17/0.38 % CPUTime : 0.40/0.55 Running higher-order theorem provingRunning: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538 0.40/0.56 # Version: 3.1pre001-ho 60.84/8.23 # Preprocessing class: HSLMSLSSLLLCHFA. 60.84/8.23 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 60.84/8.23 # Starting ehoh_best5 with 180s (1) cores 60.84/8.23 # Starting almost_fo_3_lam with 180s (1) cores 60.84/8.23 # Starting new_bool_5 with 180s (1) cores 60.84/8.23 # Starting pre_casc_3 with 180s (1) cores 60.84/8.23 # Starting ho_unfolding_8 with 180s (1) cores 60.84/8.23 # Starting new_ho_10_cnf2 with 180s (1) cores 60.84/8.23 # Starting new_bool_3 with 180s (1) cores 60.84/8.23 # Starting new_ho_5 with 180s (1) cores 60.84/8.23 # ho_unfolding_8 with pid 24720 completed with status 0 60.84/8.23 # Result found by ho_unfolding_8 60.84/8.23 # Preprocessing class: HSLMSLSSLLLCHFA. 60.84/8.23 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 60.84/8.23 # Starting ehoh_best5 with 180s (1) cores 60.84/8.23 # Starting almost_fo_3_lam with 180s (1) cores 60.84/8.23 # Starting new_bool_5 with 180s (1) cores 60.84/8.23 # Starting pre_casc_3 with 180s (1) cores 60.84/8.23 # Starting ho_unfolding_8 with 180s (1) cores 60.84/8.23 # No SInE strategy applied 60.84/8.23 # Search class: HGHSM-FSLM32-DHFMMSBN 60.84/8.23 # partial match(1): HGHSM-FSLM32-MHFMMSBN 60.84/8.23 # Scheduled 9 strats onto 1 cores with 180 seconds (180 total) 60.84/8.23 # Starting ho_unfolding_8 with 37s (1) cores 60.84/8.23 # ho_unfolding_8 with pid 24730 completed with status 0 60.84/8.23 # Result found by ho_unfolding_8 60.84/8.23 # Preprocessing class: HSLMSLSSLLLCHFA. 60.84/8.23 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 60.84/8.23 # Starting ehoh_best5 with 180s (1) cores 60.84/8.23 # Starting almost_fo_3_lam with 180s (1) cores 60.84/8.23 # Starting new_bool_5 with 180s (1) cores 60.84/8.23 # Starting pre_casc_3 with 180s (1) cores 60.84/8.23 # Starting ho_unfolding_8 with 180s (1) cores 60.84/8.23 # No SInE strategy applied 60.84/8.23 # Search class: HGHSM-FSLM32-DHFMMSBN 60.84/8.23 # partial match(1): HGHSM-FSLM32-MHFMMSBN 60.84/8.23 # Scheduled 9 strats onto 1 cores with 180 seconds (180 total) 60.84/8.23 # Starting ho_unfolding_8 with 37s (1) cores 60.84/8.23 # Preprocessing time : 0.135 s 60.84/8.23 # Presaturation interreduction done 60.84/8.23 60.84/8.23 # Proof found! 60.84/8.23 # SZS status Theorem 60.84/8.23 # SZS output start CNFRefutation 60.84/8.23 thf(decl_22, type, in: $i > $i > $o). 60.84/8.23 thf(decl_23, type, exu: ($i > $o) > $o). 60.84/8.23 thf(decl_24, type, setextAx: $o). 60.84/8.23 thf(decl_25, type, emptyset: $i). 60.84/8.23 thf(decl_26, type, emptysetAx: $o). 60.84/8.23 thf(decl_27, type, setadjoin: $i > $i > $i). 60.84/8.23 thf(decl_28, type, setadjoinAx: $o). 60.84/8.23 thf(decl_29, type, powerset: $i > $i). 60.84/8.23 thf(decl_30, type, powersetAx: $o). 60.84/8.23 thf(decl_31, type, setunion: $i > $i). 60.84/8.23 thf(decl_32, type, setunionAx: $o). 60.84/8.23 thf(decl_33, type, omega: $i). 60.84/8.23 thf(decl_34, type, omega0Ax: $o). 60.84/8.23 thf(decl_35, type, omegaSAx: $o). 60.84/8.23 thf(decl_36, type, omegaIndAx: $o). 60.84/8.23 thf(decl_37, type, replAx: $o). 60.84/8.23 thf(decl_38, type, foundationAx: $o). 60.84/8.23 thf(decl_39, type, wellorderingAx: $o). 60.84/8.23 thf(decl_40, type, descr: ($i > $o) > $i). 60.84/8.23 thf(decl_41, type, descrp: $o). 60.84/8.23 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 60.84/8.23 thf(decl_43, type, dsetconstrI: $o). 60.84/8.23 thf(decl_44, type, dsetconstrEL: $o). 60.84/8.23 thf(decl_45, type, dsetconstrER: $o). 60.84/8.23 thf(decl_46, type, exuE1: $o). 60.84/8.23 thf(decl_47, type, prop2set: $o > $i). 60.84/8.23 thf(decl_48, type, prop2setE: $o). 60.84/8.23 thf(decl_49, type, emptysetE: $o). 60.84/8.23 thf(decl_50, type, emptysetimpfalse: $o). 60.84/8.23 thf(decl_51, type, notinemptyset: $o). 60.84/8.23 thf(decl_52, type, exuE3e: $o). 60.84/8.23 thf(decl_53, type, setext: $o). 60.84/8.23 thf(decl_54, type, emptyI: $o). 60.84/8.23 thf(decl_55, type, noeltsimpempty: $o). 60.84/8.23 thf(decl_56, type, setbeta: $o). 60.84/8.23 thf(decl_57, type, nonempty: $i > $o). 60.84/8.23 thf(decl_58, type, nonemptyE1: $o). 60.84/8.23 thf(decl_59, type, nonemptyI: $o). 60.84/8.23 thf(decl_60, type, nonemptyI1: $o). 60.84/8.23 thf(decl_61, type, setadjoinIL: $o). 60.84/8.23 thf(decl_62, type, emptyinunitempty: $o). 60.84/8.23 thf(decl_63, type, setadjoinIR: $o). 60.84/8.23 thf(decl_64, type, setadjoinE: $o). 60.84/8.23 thf(decl_65, type, setadjoinOr: $o). 60.84/8.23 thf(decl_66, type, setoftrueEq: $o). 60.84/8.23 thf(decl_67, type, powersetI: $o). 60.84/8.23 thf(decl_68, type, emptyinPowerset: $o). 60.84/8.23 thf(decl_69, type, emptyInPowerset: $o). 60.84/8.23 thf(decl_70, type, powersetE: $o). 60.84/8.23 thf(decl_71, type, setunionI: $o). 60.84/8.23 thf(decl_72, type, setunionE: $o). 60.84/8.23 thf(decl_73, type, subPowSU: $o). 60.84/8.23 thf(decl_74, type, exuE2: $o). 60.84/8.23 thf(decl_75, type, nonemptyImpWitness: $o). 60.84/8.23 thf(decl_76, type, uniqinunit: $o). 60.84/8.23 thf(decl_77, type, notinsingleton: $o). 60.84/8.23 thf(decl_78, type, eqinunit: $o). 60.84/8.23 thf(decl_79, type, singletonsswitch: $o). 60.84/8.23 thf(decl_80, type, upairsetE: $o). 60.84/8.23 thf(decl_81, type, upairsetIL: $o). 60.84/8.23 thf(decl_82, type, upairsetIR: $o). 60.84/8.23 thf(decl_83, type, emptyE1: $o). 60.84/8.23 thf(decl_84, type, vacuousDall: $o). 60.84/8.23 thf(decl_85, type, quantDeMorgan1: $o). 60.84/8.23 thf(decl_86, type, quantDeMorgan2: $o). 60.84/8.23 thf(decl_87, type, quantDeMorgan3: $o). 60.84/8.23 thf(decl_88, type, quantDeMorgan4: $o). 60.84/8.23 thf(decl_89, type, prop2setI: $o). 60.84/8.23 thf(decl_90, type, set2prop: $i > $o). 60.84/8.23 thf(decl_91, type, prop2set2propI: $o). 60.84/8.23 thf(decl_92, type, notdexE: $o). 60.84/8.23 thf(decl_93, type, notdallE: $o). 60.84/8.23 thf(decl_94, type, exuI1: $o). 60.84/8.23 thf(decl_95, type, exuI3: $o). 60.84/8.23 thf(decl_96, type, exuI2: $o). 60.84/8.23 thf(decl_97, type, inCongP: $o). 60.84/8.23 thf(decl_98, type, in__Cong: $o). 60.84/8.23 thf(decl_99, type, exuE3u: $o). 60.84/8.23 thf(decl_100, type, exu__Cong: $o). 60.84/8.23 thf(decl_101, type, emptyset__Cong: $o). 60.84/8.23 thf(decl_102, type, setadjoin__Cong: $o). 60.84/8.23 thf(decl_103, type, powerset__Cong: $o). 60.84/8.23 thf(decl_104, type, setunion__Cong: $o). 60.84/8.23 thf(decl_105, type, omega__Cong: $o). 60.84/8.23 thf(decl_106, type, exuEu: $o). 60.84/8.23 thf(decl_107, type, descr__Cong: $o). 60.84/8.23 thf(decl_108, type, dsetconstr__Cong: $o). 60.84/8.23 thf(decl_109, type, subset: $i > $i > $o). 60.84/8.23 thf(decl_112, type, subsetI1: $o). 60.84/8.23 thf(decl_113, type, eqimpsubset2: $o). 60.84/8.23 thf(decl_114, type, eqimpsubset1: $o). 60.84/8.23 thf(decl_115, type, subsetI2: $o). 60.84/8.23 thf(decl_116, type, emptysetsubset: $o). 60.84/8.23 thf(decl_117, type, subsetE: $o). 60.84/8.23 thf(decl_118, type, subsetE2: $o). 60.84/8.23 thf(decl_119, type, notsubsetI: $o). 60.84/8.23 thf(decl_120, type, notequalI1: $o). 60.84/8.23 thf(decl_121, type, notequalI2: $o). 60.84/8.23 thf(decl_122, type, subsetRefl: $o). 60.84/8.23 thf(decl_123, type, subsetTrans: $o). 60.84/8.23 thf(decl_124, type, setadjoinSub: $o). 60.84/8.23 thf(decl_125, type, setadjoinSub2: $o). 60.84/8.23 thf(decl_126, type, subset2powerset: $o). 60.84/8.23 thf(decl_127, type, setextsub: $o). 60.84/8.23 thf(decl_128, type, subsetemptysetimpeq: $o). 60.84/8.23 thf(decl_129, type, powersetI1: $o). 60.84/8.23 thf(decl_130, type, powersetE1: $o). 60.84/8.23 thf(decl_131, type, inPowerset: $o). 60.84/8.23 thf(decl_132, type, powersetsubset: $o). 60.84/8.23 thf(decl_133, type, sepInPowerset: $o). 60.84/8.23 thf(decl_134, type, sepSubset: $o). 60.84/8.23 thf(decl_135, type, binunion: $i > $i > $i). 60.84/8.23 thf(decl_136, type, binunionIL: $o). 60.84/8.23 thf(decl_137, type, upairset2IR: $o). 60.84/8.23 thf(decl_138, type, binunionIR: $o). 60.84/8.23 thf(decl_139, type, binunionEcases: $o). 60.84/8.23 thf(decl_140, type, binunionE: $o). 60.84/8.23 thf(decl_141, type, binunionLsub: $o). 60.84/8.23 thf(decl_142, type, binunionRsub: $o). 60.84/8.23 thf(decl_143, type, binintersect: $i > $i > $i). 60.84/8.23 thf(decl_144, type, binintersectI: $o). 60.84/8.23 thf(decl_145, type, binintersectSubset5: $o). 60.84/8.23 thf(decl_146, type, binintersectEL: $o). 60.84/8.23 thf(decl_147, type, binintersectLsub: $o). 60.84/8.23 thf(decl_148, type, binintersectSubset2: $o). 60.84/8.23 thf(decl_149, type, binintersectSubset3: $o). 60.84/8.23 thf(decl_150, type, binintersectER: $o). 60.84/8.23 thf(decl_151, type, disjointsetsI1: $o). 60.84/8.23 thf(decl_152, type, binintersectRsub: $o). 60.84/8.23 thf(decl_153, type, binintersectSubset4: $o). 60.84/8.23 thf(decl_154, type, binintersectSubset1: $o). 60.84/8.23 thf(decl_155, type, bs114d: $o). 60.84/8.23 thf(decl_157, type, setminus: $i > $i > $i). 60.84/8.23 thf(decl_158, type, setminusI: $o). 60.84/8.23 thf(decl_159, type, setminusEL: $o). 60.84/8.23 thf(decl_160, type, setminusER: $o). 60.84/8.23 thf(decl_161, type, setminusSubset2: $o). 60.84/8.23 thf(decl_162, type, setminusERneg: $o). 60.84/8.23 thf(decl_163, type, setminusELneg: $o). 60.84/8.23 thf(decl_164, type, setminusILneg: $o). 60.84/8.23 thf(decl_165, type, setminusIRneg: $o). 60.84/8.23 thf(decl_166, type, setminusLsub: $o). 60.84/8.23 thf(decl_167, type, setminusSubset1: $o). 60.84/8.23 thf(decl_168, type, symdiff: $i > $i > $i). 60.84/8.23 thf(decl_169, type, symdiffE: $o). 60.84/8.23 thf(decl_170, type, symdiffI1: $o). 60.84/8.23 thf(decl_171, type, symdiffI2: $o). 60.84/8.23 thf(decl_172, type, symdiffIneg1: $o). 60.84/8.23 thf(decl_173, type, symdiffIneg2: $o). 60.84/8.23 thf(decl_174, type, iskpair: $i > $o). 60.84/8.23 thf(decl_175, type, secondinupair: $o). 60.84/8.23 thf(decl_176, type, setukpairIL: $o). 60.84/8.23 thf(decl_177, type, setukpairIR: $o). 60.84/8.23 thf(decl_178, type, kpairiskpair: $o). 60.84/8.23 thf(decl_179, type, kpair: $i > $i > $i). 60.84/8.23 thf(decl_180, type, kpairp: $o). 60.84/8.23 thf(decl_181, type, cartprod: $i > $i > $i). 60.84/8.23 thf(decl_182, type, singletonsubset: $o). 60.84/8.23 thf(decl_183, type, singletoninpowerset: $o). 60.84/8.23 thf(decl_184, type, singletoninpowunion: $o). 60.84/8.23 thf(decl_185, type, upairset2E: $o). 60.84/8.23 thf(decl_186, type, upairsubunion: $o). 60.84/8.23 thf(decl_187, type, upairinpowunion: $o). 60.84/8.23 thf(decl_188, type, ubforcartprodlem1: $o). 60.84/8.23 thf(decl_189, type, ubforcartprodlem2: $o). 60.84/8.23 thf(decl_190, type, ubforcartprodlem3: $o). 60.84/8.23 thf(decl_191, type, cartprodpairin: $o). 60.84/8.23 thf(decl_192, type, cartprodmempair1: $o). 60.84/8.23 thf(decl_193, type, cartprodmempair: $o). 60.84/8.23 thf(decl_194, type, setunionE2: $o). 60.84/8.23 thf(decl_195, type, setunionsingleton1: $o). 60.84/8.23 thf(decl_196, type, setunionsingleton2: $o). 60.84/8.23 thf(decl_197, type, setunionsingleton: $o). 60.84/8.23 thf(decl_198, type, singleton: $i > $o). 60.84/8.23 thf(decl_199, type, singletonprop: $o). 60.84/8.23 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 60.84/8.23 thf(decl_201, type, ex1E1: $o). 60.84/8.23 thf(decl_202, type, ex1I: $o). 60.84/8.23 thf(decl_203, type, ex1I2: $o). 60.84/8.23 thf(decl_204, type, singletonsuniq: $o). 60.84/8.23 thf(decl_209, type, setukpairinjL1: $o). 60.84/8.23 thf(decl_210, type, kfstsingleton: $o). 60.84/8.23 thf(decl_211, type, theprop: $o). 60.84/8.23 thf(decl_212, type, kfst: $i > $i). 60.84/8.23 thf(decl_213, type, kfstpairEq: $o). 60.84/8.23 thf(decl_214, type, cartprodfstin: $o). 60.84/8.23 thf(decl_215, type, setukpairinjL2: $o). 60.84/8.23 thf(decl_216, type, setukpairinjL: $o). 60.84/8.23 thf(decl_217, type, setukpairinjR11: $o). 60.84/8.23 thf(decl_218, type, setukpairinjR12: $o). 60.84/8.23 thf(decl_219, type, setukpairinjR1: $o). 60.84/8.23 thf(decl_220, type, upairequniteq: $o). 60.84/8.23 thf(decl_221, type, setukpairinjR2: $o). 60.84/8.23 thf(decl_222, type, setukpairinjR: $o). 60.84/8.23 thf(decl_223, type, ksndsingleton: $o). 60.84/8.23 thf(decl_224, type, ksnd: $i > $i). 60.84/8.23 thf(decl_225, type, ksndpairEq: $o). 60.84/8.23 thf(decl_226, type, kpairsurjEq: $o). 60.84/8.23 thf(decl_227, type, cartprodsndin: $o). 60.84/8.23 thf(decl_228, type, cartprodpairmemEL: $o). 60.84/8.23 thf(decl_229, type, cartprodpairmemER: $o). 60.84/8.23 thf(decl_230, type, cartprodmempaircEq: $o). 60.84/8.23 thf(decl_231, type, cartprodfstpairEq: $o). 60.84/8.23 thf(decl_232, type, cartprodsndpairEq: $o). 60.84/8.23 thf(decl_233, type, cartprodpairsurjEq: $o). 60.84/8.23 thf(decl_234, type, breln: $i > $i > $i > $o). 60.84/8.23 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 60.84/8.23 thf(decl_236, type, dpsetconstrI: $o). 60.84/8.23 thf(decl_237, type, dpsetconstrSub: $o). 60.84/8.23 thf(decl_238, type, setOfPairsIsBReln: $o). 60.84/8.23 thf(decl_239, type, dpsetconstrERa: $o). 60.84/8.23 thf(decl_240, type, dpsetconstrEL1: $o). 60.84/8.23 thf(decl_241, type, dpsetconstrEL2: $o). 60.84/8.23 thf(decl_242, type, dpsetconstrER: $o). 60.84/8.23 thf(decl_243, type, func: $i > $i > $i > $o). 60.84/8.23 thf(decl_244, type, funcSet: $i > $i > $i). 60.84/8.23 thf(decl_245, type, funcImageSingleton: $o). 60.84/8.23 thf(decl_246, type, apProp: $o). 60.84/8.23 thf(decl_247, type, ap: $i > $i > $i > $i > $i). 60.84/8.23 thf(decl_248, type, app: $o). 60.84/8.23 thf(decl_249, type, infuncsetfunc: $o). 60.84/8.23 thf(decl_250, type, ap2p: $o). 60.84/8.23 thf(decl_251, type, funcinfuncset: $o). 60.84/8.23 thf(decl_252, type, lamProp: $o). 60.84/8.23 thf(decl_253, type, lam: $i > $i > ($i > $i) > $i). 60.84/8.23 thf(decl_254, type, lamp: $o). 60.84/8.23 thf(decl_255, type, lam2p: $o). 60.84/8.23 thf(decl_256, type, brelnall1: $o). 60.84/8.23 thf(decl_257, type, brelnall2: $o). 60.84/8.23 thf(decl_258, type, ex1E2: $o). 60.84/8.23 thf(decl_259, type, funcGraphProp1: $o). 60.84/8.23 thf(decl_260, type, funcGraphProp3: $o). 60.84/8.23 thf(decl_261, type, funcGraphProp2: $o). 60.84/8.23 thf(decl_262, type, funcextLem: $o). 60.84/8.23 thf(decl_263, type, funcGraphProp4: $o). 60.84/8.23 thf(decl_264, type, subbreln: $o). 60.84/8.23 thf(decl_265, type, eqbreln: $o). 60.84/8.23 thf(decl_266, type, funcext: $o). 60.84/8.23 thf(decl_267, type, funcext2: $o). 60.84/8.23 thf(decl_268, type, ap2apEq1: $o). 60.84/8.23 thf(decl_269, type, ap2apEq2: $o). 60.84/8.23 thf(decl_270, type, beta1: $o). 60.84/8.23 thf(decl_271, type, eta1: $o). 60.84/8.23 thf(decl_272, type, lam2lamEq: $o). 60.84/8.23 thf(decl_273, type, beta2: $o). 60.84/8.23 thf(decl_274, type, eta2: $o). 60.84/8.23 thf(decl_275, type, iffalseProp1: $o). 60.84/8.23 thf(decl_276, type, iffalseProp2: $o). 60.84/8.23 thf(decl_277, type, iftrueProp1: $o). 60.84/8.23 thf(decl_278, type, iftrueProp2: $o). 60.84/8.23 thf(decl_279, type, ifSingleton: $o). 60.84/8.23 thf(decl_280, type, if: $i > $o > $i > $i > $i). 60.84/8.23 thf(decl_281, type, epred1_0: $o). 60.84/8.23 thf(decl_282, type, esk1_2: $i > $i > $i). 60.84/8.23 thf(decl_283, type, esk2_2: $i > $i > $i). 60.84/8.23 thf(decl_284, type, esk3_2: $i > $i > $i). 60.84/8.23 thf(decl_285, type, esk4_1: $i > $i). 60.84/8.23 thf(decl_286, type, esk5_2: ($i > $i > $o) > $i > $i). 60.84/8.23 thf(decl_287, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 60.84/8.23 thf(decl_288, type, esk7_2: ($i > $i > $o) > $i > $i). 60.84/8.23 thf(decl_289, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 60.84/8.23 thf(decl_290, type, esk9_1: $i > $i). 60.84/8.23 thf(decl_291, type, esk10_2: ($i > $o) > $i > $i). 60.84/8.23 thf(decl_292, type, esk11_2: ($i > $o) > $i > $i). 60.84/8.23 thf(decl_293, type, esk12_1: ($i > $o) > $i). 60.84/8.23 thf(decl_294, type, esk13_2: ($i > $o) > $i > $i). 60.84/8.23 thf(decl_295, type, esk14_1: ($i > $o) > $i). 60.84/8.23 thf(decl_296, type, esk15_2: $i > $i > $i). 60.84/8.23 thf(decl_297, type, esk16_2: $i > $i > $i). 60.84/8.23 thf(decl_298, type, esk17_1: $i > $i). 60.84/8.23 thf(decl_299, type, esk18_1: $i > $i). 60.84/8.23 thf(decl_300, type, esk19_1: $i > $i). 60.84/8.23 thf(decl_301, type, esk20_2: $i > $i > $i). 60.84/8.23 thf(decl_302, type, esk21_3: $i > $i > $o > $i). 60.84/8.23 thf(decl_303, type, esk22_2: ($i > $o) > $i > $i). 60.84/8.23 thf(decl_304, type, esk23_1: ($i > $o) > $i). 60.84/8.23 thf(decl_305, type, esk24_1: $i > $i). 60.84/8.23 thf(decl_306, type, esk25_2: $i > ($i > $o) > $i). 60.84/8.23 thf(decl_307, type, esk26_2: $i > ($i > $o) > $i). 60.84/8.23 thf(decl_308, type, esk27_2: $i > ($i > $o) > $i). 60.84/8.23 thf(decl_309, type, esk28_2: $i > ($i > $o) > $i). 60.84/8.23 thf(decl_310, type, esk29_2: $i > ($i > $o) > $i). 60.84/8.23 thf(decl_311, type, esk30_2: $i > ($i > $o) > $i). 60.84/8.23 thf(decl_312, type, esk31_2: ($i > $o) > $i > $i). 60.84/8.23 thf(decl_313, type, esk32_1: ($i > $o) > $i). 60.84/8.23 thf(decl_314, type, esk33_1: ($i > $o) > $i). 60.84/8.23 thf(decl_315, type, esk34_1: ($i > $o) > $i). 60.84/8.23 thf(decl_316, type, esk35_1: ($i > $o) > $i). 60.84/8.23 thf(decl_317, type, esk36_2: ($i > $o) > $i > $i). 60.84/8.23 thf(decl_318, type, esk37_1: ($i > $o) > $i). 60.84/8.23 thf(decl_319, type, esk38_2: ($i > $o) > $i > $i). 60.84/8.23 thf(decl_320, type, esk39_2: ($i > $o) > ($i > $o) > $i). 60.84/8.23 thf(decl_321, type, esk40_2: ($i > $o) > ($i > $o) > $i). 60.84/8.23 thf(decl_322, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 60.84/8.23 thf(decl_323, type, esk42_2: ($i > $o) > ($i > $o) > $i). 60.84/8.23 thf(decl_324, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 60.84/8.23 thf(decl_325, type, esk44_2: ($i > $o) > ($i > $o) > $i). 60.84/8.23 thf(decl_326, type, esk45_2: ($i > $o) > $i > $i). 60.84/8.23 thf(decl_327, type, esk46_2: ($i > $o) > ($i > $o) > $i). 60.84/8.23 thf(decl_328, type, esk47_2: ($i > $o) > ($i > $o) > $i). 60.84/8.23 thf(decl_329, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 60.84/8.23 thf(decl_330, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 60.84/8.23 thf(decl_331, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 60.84/8.23 thf(decl_332, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 60.84/8.23 thf(decl_333, type, esk52_2: $i > $i > $i). 60.84/8.23 thf(decl_334, type, esk53_2: $i > $i > $i). 60.84/8.23 thf(decl_335, type, esk54_2: $i > $i > $i). 60.84/8.23 thf(decl_336, type, esk55_3: $i > $i > $i > $i). 60.84/8.23 thf(decl_337, type, esk56_3: $i > $i > $i > $i). 60.84/8.23 thf(decl_338, type, esk57_2: $i > $i > $i). 60.84/8.23 thf(decl_339, type, esk58_2: $i > ($i > $o) > $i). 60.84/8.23 thf(decl_340, type, esk59_2: $i > ($i > $o) > $i). 60.84/8.23 thf(decl_341, type, esk60_2: $i > ($i > $o) > $i). 60.84/8.23 thf(decl_342, type, esk61_2: $i > ($i > $o) > $i). 60.84/8.23 thf(decl_343, type, esk62_3: $i > ($i > $o) > $i > $i). 60.84/8.23 thf(decl_344, type, esk63_3: $i > ($i > $o) > $i > $i). 60.84/8.23 thf(decl_345, type, esk64_2: $i > ($i > $o) > $i). 60.84/8.23 thf(decl_346, type, esk65_2: $i > ($i > $o) > $i). 60.84/8.23 thf(decl_347, type, esk66_2: $i > ($i > $o) > $i). 60.84/8.23 thf(decl_348, type, esk67_1: $i > $i). 60.84/8.23 thf(decl_349, type, esk68_1: $i > $i). 60.84/8.23 thf(decl_350, type, esk69_4: $i > $i > $i > $i > $i). 60.84/8.23 thf(decl_351, type, esk70_3: $i > $i > ($i > $i) > $i). 60.84/8.23 thf(decl_352, type, esk71_3: $i > $i > ($i > $i) > $i). 60.84/8.23 thf(decl_353, type, esk72_3: $i > $i > ($i > $i) > $i). 60.84/8.23 thf(decl_354, type, esk73_4: $i > $i > $i > ($i > $o) > $i). 60.84/8.23 thf(decl_355, type, esk74_4: $i > $i > $i > ($i > $o) > $i). 60.84/8.23 thf(decl_356, type, esk75_4: $i > $i > $i > ($i > $o) > $i). 60.84/8.23 thf(decl_357, type, esk76_4: $i > $i > $i > ($i > $o) > $i). 60.84/8.23 thf(decl_358, type, esk77_4: $i > $i > $i > $i > $i). 60.84/8.23 thf(decl_359, type, esk78_4: $i > $i > $i > $i > $i). 60.84/8.23 thf(decl_360, type, esk79_4: $i > $i > $i > $i > $i). 60.84/8.23 thf(decl_361, type, esk80_4: $i > $i > $i > $i > $i). 60.84/8.23 thf(decl_362, type, esk81_4: $i > $i > $i > $i > $i). 60.84/8.23 thf(decl_363, type, esk82_4: $i > $i > $i > $i > $i). 60.84/8.23 thf(decl_364, type, esk83_4: $i > $i > $i > $i > $i). 60.84/8.23 thf(decl_365, type, esk84_4: $i > $i > $i > $i > $i). 60.84/8.23 thf(decl_366, type, esk85_4: $i > $i > $i > $i > $i). 60.84/8.23 thf(decl_367, type, esk86_3: $i > $i > ($i > $i) > $i). 60.84/8.23 thf(decl_368, type, esk87_3: $i > $i > ($i > $i) > $i). 60.84/8.23 thf(decl_369, type, esk88_3: $i > $i > ($i > $i) > $i). 60.84/8.23 thf(decl_370, type, esk89_4: $i > $o > $i > $i > $i). 60.84/8.23 thf(decl_371, type, esk90_0: $i). 60.84/8.23 thf(decl_372, type, epred2_0: $o). 60.84/8.23 thf(decl_373, type, esk91_0: $i). 60.84/8.23 thf(decl_374, type, esk92_0: $i). 60.84/8.23 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', ex1)). 60.84/8.23 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', singleton)). 60.84/8.23 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', replAx)). 60.84/8.23 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', exu)). 60.84/8.23 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', descrp)). 60.84/8.23 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', exuE1)). 60.84/8.23 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', exuE3e)). 60.84/8.23 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', nonempty)). 60.84/8.23 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', nonemptyI)). 60.84/8.23 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', exuE2)). 60.84/8.23 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', exuI1)). 60.84/8.23 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', exuI3)). 60.84/8.23 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', exuI2)). 60.84/8.23 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', exuE3u)). 60.84/8.23 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', exu__Cong)). 60.84/8.23 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', exuEu)). 60.84/8.23 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', descr__Cong)). 60.84/8.23 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', singletonprop)). 60.84/8.23 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', ex1E1)). 60.84/8.23 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', ex1I)). 60.84/8.23 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', ex1I2)). 60.84/8.23 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', kfstsingleton)). 60.84/8.23 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', ksndsingleton)). 60.84/8.23 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setOfPairsIsBReln)). 60.84/8.23 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', breln)). 60.84/8.23 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', funcImageSingleton)). 60.84/8.23 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', ex1E2)). 60.84/8.23 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', ifSingleton)). 60.84/8.23 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', dsetconstrI)). 60.84/8.23 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', dsetconstrEL)). 60.84/8.23 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', dsetconstrER)). 60.84/8.23 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setbeta)). 60.84/8.23 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', nonemptyE1)). 60.84/8.23 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', nonemptyI1)). 60.84/8.23 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setoftrueEq)). 60.84/8.23 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', nonemptyImpWitness)). 60.84/8.23 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', emptyE1)). 60.84/8.23 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', dsetconstr__Cong)). 60.84/8.23 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', sepInPowerset)). 60.84/8.23 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', sepSubset)). 60.84/8.23 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', theprop)). 60.84/8.23 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', dpsetconstrI)). 60.84/8.23 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', dpsetconstrSub)). 60.84/8.23 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', dpsetconstrERa)). 60.84/8.23 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', dpsetconstrEL1)). 60.84/8.23 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', dpsetconstrEL2)). 60.84/8.23 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', dpsetconstrER)). 60.84/8.23 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', apProp)). 60.84/8.23 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', lamProp)). 60.84/8.23 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', lamp)). 60.84/8.23 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', lam2p)). 60.84/8.23 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', brelnall1)). 60.84/8.23 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', brelnall2)). 60.84/8.23 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', subbreln)). 60.84/8.23 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', eqbreln)). 60.84/8.23 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', beta1)). 60.84/8.23 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', eta1)). 60.84/8.23 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', lam2lamEq)). 60.84/8.23 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', beta2)). 60.84/8.23 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', eta2)). 60.84/8.23 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', iffalseProp1)). 60.84/8.23 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', iffalseProp2)). 60.84/8.23 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', iftrueProp1)). 60.84/8.23 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', iftrueProp2)). 60.84/8.23 thf(ifp, conjecture, (((emptysetAx)=>((((setunionAx)=>(((omegaSAx)=>((((foundationAx)=>(((((dsetconstrEL)=>(((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((((((((((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((((((emptyInPowerset)=>((powersetE)=>((setunionI)=>(((subPowSU)=>(((nonemptyImpWitness)=>(((notinsingleton)=>((((((((((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((((notdallE)=>((exuI1)=>((exuI3)=>(((inCongP)=>((((((((((exuEu)=>(((dsetconstr__Cong)=>((((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>(((notequalI2)=>(((subsetTrans)=>(((setadjoinSub2)=>((((subsetemptysetimpeq)=>(((powersetE1)=>(((powersetsubset)=>(((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>(((((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>(((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>(((((((setminusEL)=>((setminusER)=>(((setminusERneg)=>((setminusELneg)=>(((((setminusSubset1)=>((((symdiffI2)=>((((((((kpairp)=>((singletonsubset)=>((((upairset2E)=>(((((ubforcartprodlem2)=>(((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>(((((ex1I)=>((ex1I2)=>((((kfstsingleton)=>(((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>(((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((((kpairsurjEq)=>((cartprodsndin)=>((((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>(((dpsetconstrSub)=>((((dpsetconstrEL1)=>((dpsetconstrEL2)=>(((funcImageSingleton)=>(((app)=>((infuncsetfunc)=>((((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((((funcGraphProp3)=>((funcGraphProp2)=>(((funcGraphProp4)=>((subbreln)=>((((funcext2)=>(((((eta1)=>((lam2lamEq)=>(((((((iftrueProp2)=>(![X4:$i, X45:$o, X2:$i]:((![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X45)) @ X2 @ X3) @ X4)))<=(in @ X2 @ X4)))<=(ifSingleton)))<=(iftrueProp1))<=(iffalseProp2))<=(iffalseProp1))<=(eta2))<=(beta2))))<=(beta1))<=(ap2apEq2))<=(ap2apEq1)))<=(funcext))<=(eqbreln))))<=(funcextLem))))<=(funcGraphProp1))<=(ex1E2)))))))<=(funcinfuncset))<=(ap2p))))<=(apProp)))<=(dpsetconstrER))))<=(dpsetconstrERa))<=(setOfPairsIsBReln)))<=(dpsetconstrI))))))<=(cartprodpairmemER))<=(cartprodpairmemEL))))<=(ksndpairEq))<=(ksndsingleton))))))))<=(setukpairinjL)))))<=(theprop)))<=(setukpairinjL1))<=(singletonsuniq))))<=(ex1E1))<=(singletonprop))<=(setunionsingleton))))))))<=(ubforcartprodlem3)))<=(ubforcartprodlem1))<=(upairinpowunion))<=(upairsubunion)))<=(singletoninpowunion))<=(singletoninpowerset))))<=(kpairiskpair))<=(setukpairIR))<=(setukpairIL))<=(secondinupair))<=(symdiffIneg2))<=(symdiffIneg1)))<=(symdiffI1))<=(symdiffE)))<=(setminusLsub))<=(setminusIRneg))<=(setminusILneg))))<=(setminusSubset2))))<=(setminusI))<=(bs114d))<=(binintersectSubset1))<=(binintersectSubset4))<=(binintersectRsub)))))))<=(binintersectEL)))))<=(binunionLsub))<=(binunionE))<=(binunionEcases))))))<=(sepInPowerset)))<=(inPowerset)))<=(powersetI1)))<=(setextsub))<=(subset2powerset)))<=(setadjoinSub)))<=(subsetRefl)))<=(notequalI1))))))))<=(eqimpsubset2))<=(subsetI1)))<=(descr__Cong)))<=(omega__Cong))<=(setunion__Cong))<=(powerset__Cong))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong))<=(exuE3u))<=(in__Cong)))<=(exuI2)))))<=(notdexE))<=(prop2set2propI))))))<=(quantDeMorgan1))<=(vacuousDall))<=(emptyE1))<=(upairsetIR))<=(upairsetIL))<=(upairsetE))<=(singletonsswitch))<=(eqinunit)))<=(uniqinunit)))<=(exuE2)))<=(setunionE)))))<=(emptyinPowerset))<=(powersetI))<=(setoftrueEq))<=(setadjoinOr)))))<=(setadjoinIL))<=(nonemptyI1))<=(nonemptyI))<=(nonemptyE1))<=(setbeta))<=(noeltsimpempty))<=(emptyI))<=(setext))))))))<=(dsetconstrER)))<=(dsetconstrI))<=(descrp))<=(wellorderingAx)))<=(replAx))<=(omegaIndAx)))<=(omega0Ax)))<=(powersetAx))<=(setadjoinAx)))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', ifp)). 60.84/8.23 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setextAx)). 60.84/8.23 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', emptysetAx)). 60.84/8.23 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setadjoinAx)). 60.84/8.23 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', powersetAx)). 60.84/8.23 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setunionAx)). 60.84/8.23 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', omega0Ax)). 60.84/8.23 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', omegaSAx)). 60.84/8.23 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', omegaIndAx)). 60.84/8.23 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', foundationAx)). 60.84/8.23 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', wellorderingAx)). 60.84/8.23 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', prop2setE)). 60.84/8.23 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', emptysetE)). 60.84/8.23 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', emptysetimpfalse)). 60.84/8.23 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', notinemptyset)). 60.84/8.23 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setext)). 60.84/8.23 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', emptyI)). 60.84/8.23 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', noeltsimpempty)). 60.84/8.23 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setadjoinIL)). 60.84/8.23 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', emptyinunitempty)). 60.84/8.23 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setadjoinIR)). 60.84/8.23 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setadjoinE)). 60.84/8.23 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setadjoinOr)). 60.84/8.23 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', powersetI)). 60.84/8.23 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', emptyinPowerset)). 60.84/8.23 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', emptyInPowerset)). 60.84/8.23 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', powersetE)). 60.84/8.23 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setunionI)). 60.84/8.23 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setunionE)). 60.84/8.23 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', subPowSU)). 60.84/8.23 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', uniqinunit)). 60.84/8.23 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', notinsingleton)). 60.84/8.23 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', eqinunit)). 60.84/8.23 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', singletonsswitch)). 60.84/8.23 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', upairsetE)). 60.84/8.23 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', upairsetIL)). 60.84/8.23 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', upairsetIR)). 60.84/8.23 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', vacuousDall)). 60.84/8.23 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', quantDeMorgan1)). 60.84/8.23 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', quantDeMorgan2)). 60.84/8.23 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', quantDeMorgan3)). 60.84/8.23 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', quantDeMorgan4)). 60.84/8.23 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', prop2setI)). 60.84/8.23 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', prop2set2propI)). 60.84/8.23 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', notdexE)). 60.84/8.23 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', notdallE)). 60.84/8.23 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', inCongP)). 60.84/8.23 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', in__Cong)). 60.84/8.23 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', emptyset__Cong)). 60.84/8.23 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setadjoin__Cong)). 60.84/8.23 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', powerset__Cong)). 60.84/8.23 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setunion__Cong)). 60.84/8.23 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', omega__Cong)). 60.84/8.23 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', subsetI1)). 60.84/8.23 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', eqimpsubset2)). 60.84/8.23 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', eqimpsubset1)). 60.84/8.23 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', subsetI2)). 60.84/8.23 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', emptysetsubset)). 60.84/8.23 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', subsetE)). 60.84/8.23 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', subsetE2)). 60.84/8.23 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', notsubsetI)). 60.84/8.23 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', notequalI1)). 60.84/8.23 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', notequalI2)). 60.84/8.23 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', subsetRefl)). 60.84/8.23 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', subsetTrans)). 60.84/8.23 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setadjoinSub)). 60.84/8.23 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setadjoinSub2)). 60.84/8.23 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', subset2powerset)). 60.84/8.23 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setextsub)). 60.84/8.23 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', subsetemptysetimpeq)). 60.84/8.23 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', powersetI1)). 60.84/8.23 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', powersetE1)). 60.84/8.23 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', inPowerset)). 60.84/8.23 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', powersetsubset)). 60.84/8.23 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', binunionIL)). 60.84/8.23 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', upairset2IR)). 60.84/8.23 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', binunionIR)). 60.84/8.23 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', binunionEcases)). 60.84/8.23 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', binunionE)). 60.84/8.23 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', binunionLsub)). 60.84/8.23 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', binunionRsub)). 60.84/8.23 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', binintersectI)). 60.84/8.23 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', binintersectSubset5)). 60.84/8.23 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', binintersectEL)). 60.84/8.23 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', binintersectLsub)). 60.84/8.23 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', binintersectSubset2)). 60.84/8.23 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', binintersectSubset3)). 60.84/8.23 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', binintersectER)). 60.84/8.23 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', disjointsetsI1)). 60.84/8.23 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', binintersectRsub)). 60.84/8.23 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', binintersectSubset4)). 60.84/8.23 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', binintersectSubset1)). 60.84/8.23 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', bs114d)). 60.84/8.23 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setminusI)). 60.84/8.23 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setminusEL)). 60.84/8.23 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setminusER)). 60.84/8.23 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setminusSubset2)). 60.84/8.23 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setminusERneg)). 60.84/8.23 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setminusELneg)). 60.84/8.23 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setminusILneg)). 60.84/8.23 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setminusIRneg)). 60.84/8.23 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setminusLsub)). 60.84/8.23 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setminusSubset1)). 60.84/8.23 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', symdiffE)). 60.84/8.23 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', symdiffI1)). 60.84/8.23 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', symdiffI2)). 60.84/8.23 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', symdiffIneg1)). 60.84/8.23 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', symdiffIneg2)). 60.84/8.23 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', secondinupair)). 60.84/8.23 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setukpairIL)). 60.84/8.23 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setukpairIR)). 60.84/8.23 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', kpairiskpair)). 60.84/8.23 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', kpairp)). 60.84/8.23 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', singletonsubset)). 60.84/8.23 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', singletoninpowerset)). 60.84/8.23 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', singletoninpowunion)). 60.84/8.23 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', upairset2E)). 60.84/8.23 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', upairsubunion)). 60.84/8.23 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', upairinpowunion)). 60.84/8.23 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', ubforcartprodlem1)). 60.84/8.23 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', ubforcartprodlem2)). 60.84/8.23 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', ubforcartprodlem3)). 60.84/8.23 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', cartprodpairin)). 60.84/8.23 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', cartprodmempair1)). 60.84/8.23 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', cartprodmempair)). 60.84/8.23 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setunionE2)). 60.84/8.23 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setunionsingleton1)). 60.84/8.23 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setunionsingleton2)). 60.84/8.23 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setunionsingleton)). 60.84/8.23 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', singletonsuniq)). 60.84/8.23 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setukpairinjL1)). 60.84/8.23 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', kfstpairEq)). 60.84/8.23 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', cartprodfstin)). 60.84/8.23 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setukpairinjL2)). 60.84/8.23 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setukpairinjL)). 60.84/8.23 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setukpairinjR11)). 60.84/8.23 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setukpairinjR12)). 60.84/8.23 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setukpairinjR1)). 60.84/8.23 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', upairequniteq)). 60.84/8.23 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setukpairinjR2)). 60.84/8.23 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', setukpairinjR)). 60.84/8.23 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', ksndpairEq)). 60.84/8.23 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', kpairsurjEq)). 60.84/8.23 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', cartprodsndin)). 60.84/8.23 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', cartprodpairmemEL)). 60.84/8.23 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', cartprodpairmemER)). 60.84/8.23 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', cartprodmempaircEq)). 60.84/8.23 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', cartprodfstpairEq)). 60.84/8.23 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', cartprodsndpairEq)). 60.84/8.23 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', cartprodpairsurjEq)). 60.84/8.23 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', app)). 60.84/8.23 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', infuncsetfunc)). 60.84/8.23 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', ap2p)). 60.84/8.23 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', funcinfuncset)). 60.84/8.23 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', funcGraphProp1)). 60.84/8.23 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', funcGraphProp3)). 60.84/8.23 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', funcGraphProp2)). 60.84/8.23 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', funcextLem)). 60.84/8.23 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', funcGraphProp4)). 60.84/8.23 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', funcext)). 60.84/8.23 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', funcext2)). 60.84/8.23 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', ap2apEq1)). 60.84/8.23 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', ap2apEq2)). 60.84/8.23 thf(if, axiom, ((if)=(^[X4:$i, X44:$o, X2:$i, X3:$i]:(setunion @ (dsetconstr @ X4 @ (^[X14:$i]:((((X44)&((X14)=(X2)))|(~((X44))&((X14)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.eTZH7g4K6Y/Vampire---4.8_24538', if)). 60.84/8.23 thf(c_0_228, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X757:$i]:(((in @ X757 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X757 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])). 60.84/8.23 thf(c_0_229, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])). 60.84/8.23 thf(c_0_230, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 60.84/8.23 thf(c_0_231, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 60.84/8.23 thf(c_0_232, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 60.84/8.23 thf(c_0_233, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 60.84/8.23 thf(c_0_234, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 60.84/8.23 thf(c_0_235, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 60.84/8.23 thf(c_0_236, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 60.84/8.23 thf(c_0_237, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 60.84/8.23 thf(c_0_238, 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])). 60.84/8.23 thf(c_0_239, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 60.84/8.23 thf(c_0_240, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 60.84/8.23 thf(c_0_241, 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])). 60.84/8.23 thf(c_0_242, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 60.84/8.23 thf(c_0_243, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 60.84/8.23 thf(c_0_244, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 60.84/8.23 thf(c_0_245, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 60.84/8.23 thf(c_0_246, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 60.84/8.23 thf(c_0_247, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X757:$i]:(((in @ X757 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X757 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_228, c_0_229])). 60.84/8.23 thf(c_0_248, 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])). 60.84/8.23 thf(c_0_249, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 60.84/8.23 thf(c_0_250, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 60.84/8.23 thf(c_0_251, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 60.84/8.23 thf(c_0_252, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 60.84/8.23 thf(c_0_253, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])). 60.84/8.23 thf(c_0_254, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])). 60.84/8.23 thf(c_0_255, plain, ((ex1E2)<=>![X4:$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])). 60.84/8.23 thf(c_0_256, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 60.84/8.23 thf(c_0_257, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X728:$i]:((((X6 @ X2 @ X728))&![X729:$i]:((((X6 @ X2 @ X729))=>((X728)=(X729)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_230, c_0_231])). 60.84/8.23 thf(c_0_258, plain, ((descrp)=(![X1:$i > $o]:(((?[X730:$i]:((((X1 @ X730))&![X731:$i]:((((X1 @ X731))=>((X730)=(X731)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_232, c_0_231])). 60.84/8.23 thf(c_0_259, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 60.84/8.23 thf(c_0_260, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 60.84/8.23 thf(c_0_261, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 60.84/8.23 thf(c_0_262, plain, ((exuE1)=(![X1:$i > $o]:(((?[X732:$i]:((((X1 @ X732))&![X733:$i]:((((X1 @ X733))=>((X732)=(X733)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_233, c_0_231])). 60.84/8.23 thf(c_0_263, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X734:$i]:((((X1 @ X734))&![X735:$i]:((((X1 @ X735))=>((X734)=(X735)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_234, c_0_231])). 60.84/8.23 thf(c_0_264, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 60.84/8.23 thf(c_0_265, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_235])). 60.84/8.23 thf(c_0_266, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_236, c_0_235])). 60.84/8.23 thf(c_0_267, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_235])). 60.84/8.23 thf(c_0_268, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 60.84/8.23 thf(c_0_269, plain, ((exuE2)=(![X1:$i > $o]:(((?[X736:$i]:((((X1 @ X736))&![X737:$i]:((((X1 @ X737))=>((X736)=(X737)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_237, c_0_231])). 60.84/8.23 thf(c_0_270, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_235])). 60.84/8.23 thf(c_0_271, 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])). 60.84/8.23 thf(c_0_272, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X738:$i]:((((X1 @ X738))&![X739:$i]:((((X1 @ X739))=>((X738)=(X739))))))))))), inference(apply_def,[status(thm)],[c_0_238, c_0_231])). 60.84/8.23 thf(c_0_273, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X740:$i]:((((X1 @ X740))&![X741:$i]:((((X1 @ X741))=>((X740)=(X741)))))))))))), inference(apply_def,[status(thm)],[c_0_239, c_0_231])). 60.84/8.23 thf(c_0_274, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X742:$i]:((((X1 @ X742))&![X743:$i]:((((X1 @ X743))=>((X742)=(X743))))))))))), inference(apply_def,[status(thm)],[c_0_240, c_0_231])). 60.84/8.23 thf(c_0_275, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X744:$i]:((((X1 @ X744))&![X745:$i]:((((X1 @ X745))=>((X744)=(X745)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_241, c_0_231])). 60.84/8.23 thf(c_0_276, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X746:$i]:((((X1 @ X746))&![X747:$i]:((((X1 @ X747))=>((X746)=(X747)))))))<=>(?[X748:$i]:((((X17 @ X748))&![X749:$i]:((((X17 @ X749))=>((X748)=(X749)))))))))))), inference(apply_def,[status(thm)],[c_0_242, c_0_231])). 60.84/8.23 thf(c_0_277, plain, ((exuEu)=(![X1:$i > $o]:(((?[X750:$i]:((((X1 @ X750))&![X751:$i]:((((X1 @ X751))=>((X750)=(X751)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_243, c_0_231])). 60.84/8.23 thf(c_0_278, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X752:$i]:((((X1 @ X752))&![X753:$i]:((((X1 @ X753))=>((X752)=(X753)))))))=>((?[X754:$i]:((((X17 @ X754))&![X755:$i]:((((X17 @ X755))=>((X754)=(X755)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_244, c_0_231])). 60.84/8.23 thf(c_0_279, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 60.84/8.23 thf(c_0_280, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 60.84/8.23 thf(c_0_281, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 60.84/8.23 thf(c_0_282, 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)))=>(?[X756:$i]:(((in @ X756 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X756 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_245, c_0_229])). 60.84/8.23 thf(c_0_283, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X758:$i]:(((in @ X758 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X758 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_246, c_0_247])). 60.84/8.23 thf(c_0_284, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X759:$i]:(((in @ X759 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X759 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_248, c_0_247])). 60.84/8.23 thf(c_0_285, plain, ((ex1I2)=(![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(?[X760:$i]:(((in @ X760 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X760 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_249, c_0_247])). 60.84/8.23 thf(c_0_286, plain, ((kfstsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X761:$i]:(((in @ X761 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X761 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_250, c_0_229])). 60.84/8.23 thf(c_0_287, axiom, ((theprop)=(![X21:$i]:(((?[X762:$i]:(((in @ X762 @ X21)&((X21)=(setadjoin @ X762 @ emptyset)))))=>(in @ (setunion @ X21) @ X21))))), inference(apply_def,[status(thm)],[theprop, c_0_229])). 60.84/8.23 thf(c_0_288, plain, ((ksndsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X763:$i]:(((in @ X763 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X763 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_251, c_0_229])). 60.84/8.23 thf(c_0_289, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 60.84/8.23 thf(c_0_290, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 60.84/8.23 thf(c_0_291, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_252, c_0_253])). 60.84/8.23 thf(c_0_292, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 60.84/8.23 thf(c_0_293, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 60.84/8.23 thf(c_0_294, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 60.84/8.23 thf(c_0_295, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 60.84/8.23 thf(c_0_296, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(?[X764:$i]:(((in @ X764 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))=(setadjoin @ X764 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_254, c_0_229])). 60.84/8.23 thf(c_0_297, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 60.84/8.23 thf(c_0_298, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])). 60.84/8.23 thf(c_0_299, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 60.84/8.23 thf(c_0_300, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 60.84/8.23 thf(c_0_301, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_253])). 60.84/8.23 thf(c_0_302, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_253])). 60.84/8.23 thf(c_0_303, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:(((?[X765:$i]:(((in @ X765 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X765 @ emptyset)))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_255, c_0_247])). 60.84/8.23 thf(c_0_304, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln, c_0_253])). 60.84/8.23 thf(c_0_305, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_253])). 60.84/8.23 thf(c_0_306, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])). 60.84/8.23 thf(c_0_307, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])). 60.84/8.23 thf(c_0_308, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])). 60.84/8.23 thf(c_0_309, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])). 60.84/8.23 thf(c_0_310, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])). 60.84/8.23 thf(c_0_311, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 60.84/8.23 thf(c_0_312, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])). 60.84/8.23 thf(c_0_313, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 60.84/8.23 thf(c_0_314, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])). 60.84/8.23 thf(c_0_315, plain, ((ifSingleton)=(![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(?[X766:$i]:(((in @ X766 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))&((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3)))))))=(setadjoin @ X766 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_256, c_0_229])). 60.84/8.23 thf(c_0_316, plain, ((epred1_0)<=>![X1444:$i]:(?[X1445:$i]:((((![X1446:$i]:(((in @ X1446 @ X1445)=>![X1447:$i]:(((in @ X1447 @ X1446)=>(in @ X1447 @ X1444)))))&![X1448:$i, X1449:$i]:((((in @ X1448 @ X1444)&(in @ X1449 @ X1444))=>(![X1450:$i]:(((in @ X1450 @ X1445)=>((in @ X1448 @ X1450)<=>(in @ X1449 @ X1450))))=>((X1448)=(X1449))))))&![X1451:$i, X1452:$i]:((((in @ X1451 @ X1445)&(in @ X1452 @ X1445))=>(![X1453:$i]:(((in @ X1453 @ X1451)=>(in @ X1453 @ X1452)))|![X1454:$i]:(((in @ X1454 @ X1452)=>(in @ X1454 @ X1451)))))))&![X1455:$i]:(((![X1456:$i]:(((in @ X1456 @ X1455)=>(in @ X1456 @ X1444)))&?[X1457:$i]:((in @ X1457 @ X1455)))=>?[X1458:$i, X1459:$i]:(((((in @ X1458 @ X1445)&(in @ X1459 @ X1455))&~(?[X1460:$i]:(((in @ X1460 @ X1458)&(in @ X1460 @ X1455)))))&![X1461:$i]:(((in @ X1461 @ X1445)=>(![X1462:$i]:(((in @ X1462 @ X1461)=>(in @ X1462 @ X1458)))|(in @ X1459 @ X1461)))))))))))), introduced(definition)). 60.84/8.23 thf(c_0_317, negated_conjecture, ~((![X1480:$i, X1481:$i]:((![X1482:$i]:(((in @ X1482 @ X1480)<=>(in @ X1482 @ X1481)))=>((X1480)=(X1481))))=>(![X767:$i]:(~(in @ X767 @ emptyset))=>(![X1477:$i, X1478:$i, X1479:$i]:(((in @ X1479 @ (setadjoin @ X1477 @ X1478))<=>(((X1479)=(X1477))|(in @ X1479 @ X1478))))=>(![X1474:$i, X1475:$i]:(((in @ X1475 @ (powerset @ X1474))<=>![X1476:$i]:(((in @ X1476 @ X1475)=>(in @ X1476 @ X1474)))))=>(![X768:$i, X769:$i]:(((in @ X769 @ (setunion @ X768))<=>?[X770:$i]:(((in @ X769 @ X770)&(in @ X770 @ X768)))))=>((in @ emptyset @ omega)=>(![X771:$i]:(((in @ X771 @ omega)=>(in @ (setadjoin @ X771 @ X771) @ omega)))=>(![X1471:$i]:((((in @ emptyset @ X1471)&![X1472:$i]:((((in @ X1472 @ omega)&(in @ X1472 @ X1471))=>(in @ (setadjoin @ X1472 @ X1472) @ X1471))))=>![X1473:$i]:(((in @ X1473 @ omega)=>(in @ X1473 @ X1471)))))=>(![X1463:$i > $i > $o, X1464:$i]:((![X1465:$i]:(((in @ X1465 @ X1464)=>?[X1466:$i]:(((X1463 @ X1465 @ X1466)&![X1467:$i]:(((X1463 @ X1465 @ X1467)=>((X1466)=(X1467))))))))=>?[X1468:$i]:(![X1469:$i]:(((in @ X1469 @ X1468)<=>?[X1470:$i]:(((in @ X1470 @ X1464)&(X1463 @ X1470 @ X1469))))))))=>(![X772:$i]:((?[X773:$i]:((in @ X773 @ X772))=>?[X774:$i]:(((in @ X774 @ X772)&~(?[X775:$i]:(((in @ X775 @ X774)&(in @ X775 @ X772))))))))=>((epred1_0)=>(![X1441:$i > $o]:((?[X1442:$i]:(((X1441 @ X1442)&![X1443:$i]:(((X1441 @ X1443)=>((X1442)=(X1443))))))=>(X1441 @ (descr @ (^[Z0/* 3 */:$i]:((X1441 @ Z0)))))))=>(![X1438:$i, X1439:$i > $o, X1440:$i]:(((in @ X1440 @ X1438)=>((X1439 @ X1440)=>(in @ X1440 @ (dsetconstr @ X1438 @ (^[Z0/* 3 */:$i]:((X1439 @ Z0))))))))=>(![X776:$i, X777:$i > $o, X778:$i]:(((in @ X778 @ (dsetconstr @ X776 @ (^[Z0/* 3 */:$i]:((X777 @ Z0)))))=>(in @ X778 @ X776)))=>(![X1435:$i, X1436:$i > $o, X1437:$i]:(((in @ X1437 @ (dsetconstr @ X1435 @ (^[Z0/* 3 */:$i]:((X1436 @ Z0)))))=>(X1436 @ X1437)))=>(![X779:$i > $o]:((?[X780:$i]:(((X779 @ X780)&![X781:$i]:(((X779 @ X781)=>((X780)=(X781))))))=>?[X782:$i]:(((X779 @ X782)&![X783:$i]:(((X779 @ X783)=>((X782)=(X783))))))))=>(![X784:$o, X785:$i]:(((in @ X785 @ (prop2set @ ((X784))))=>(X784)))=>(![X786:$i]:(((in @ X786 @ emptyset)=>![X787:$o]:((X787))))=>(![X788:$i]:(~(in @ X788 @ emptyset))=>(![X789:$i]:(~(in @ X789 @ emptyset))=>(![X790:$i > $o]:((?[X791:$i]:(((X790 @ X791)&![X792:$i]:(((X790 @ X792)=>((X791)=(X792))))))=>?[X793:$i]:((X790 @ X793))))=>(![X1431:$i, X1432:$i]:((![X1433:$i]:(((in @ X1433 @ X1431)=>(in @ X1433 @ X1432)))=>(![X1434:$i]:(((in @ X1434 @ X1432)=>(in @ X1434 @ X1431)))=>((X1431)=(X1432)))))=>(![X1429:$i]:((![X1430:$i]:(~(in @ X1430 @ X1429))=>((X1429)=(emptyset))))=>(![X1427:$i]:((![X1428:$i]:(~(in @ X1428 @ X1427))=>((X1427)=(emptyset))))=>(![X1424:$i, X1425:$i > $o, X1426:$i]:(((in @ X1426 @ X1424)=>((in @ X1426 @ (dsetconstr @ X1424 @ (^[Z0/* 3 */:$i]:((X1425 @ Z0)))))<=>(X1425 @ X1426))))=>(![X1422:$i]:((((X1422)!=(emptyset))=>?[X1423:$i]:((in @ X1423 @ X1422))))=>(![X1419:$i, X1420:$i > $o, X1421:$i]:(((in @ X1421 @ X1419)=>((X1420 @ X1421)=>((dsetconstr @ X1419 @ (^[Z0/* 3 */:$i]:((X1420 @ Z0))))!=(emptyset)))))=>(![X1417:$i]:((?[X1418:$i]:((in @ X1418 @ X1417))=>((X1417)!=(emptyset))))=>(![X1415:$i, X1416:$i]:((in @ X1415 @ (setadjoin @ X1415 @ X1416)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X794:$i, X795:$i, X796:$i]:(((in @ X796 @ X795)=>(in @ X796 @ (setadjoin @ X794 @ X795))))=>(![X797:$i, X798:$i, X799:$i]:(((in @ X799 @ (setadjoin @ X797 @ X798))=>![X800:$o]:(((((X799)=(X797))=>(X800))=>(((in @ X799 @ X798)=>(X800))=>(X800))))))=>(![X1412:$i, X1413:$i, X1414:$i]:(((in @ X1414 @ (setadjoin @ X1412 @ X1413))=>(((X1414)=(X1412))|(in @ X1414 @ X1413))))=>(![X1411:$i]:(((dsetconstr @ X1411 @ (^[Z0/* 3 */:$i]:(($true))))=(X1411)))=>(![X1408:$i, X1409:$i]:((![X1410:$i]:(((in @ X1410 @ X1409)=>(in @ X1410 @ X1408)))=>(in @ X1409 @ (powerset @ X1408))))=>(![X1407:$i]:((in @ emptyset @ (powerset @ 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inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_257]), foundationAx]), wellorderingAx]), c_0_258]), c_0_259]), c_0_260]), c_0_261]), c_0_262]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_263]), setext]), emptyI]), noeltsimpempty]), c_0_264]), c_0_265]), c_0_266]), c_0_267]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_268]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_269]), c_0_270]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_271]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_272]), c_0_273]), c_0_274]), inCongP]), in__Cong]), c_0_275]), c_0_276]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_277]), c_0_278]), c_0_279]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_280]), c_0_281]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_282]), c_0_283]), c_0_284]), c_0_285]), singletonsuniq]), setukpairinjL1]), c_0_286]), c_0_287]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_288]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_289]), c_0_290]), c_0_291]), c_0_292]), c_0_293]), c_0_294]), c_0_295]), c_0_296]), c_0_297]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_298]), c_0_299]), c_0_300]), c_0_301]), c_0_302]), c_0_303]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_304]), c_0_305]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_306]), c_0_307]), c_0_308]), c_0_309]), c_0_310]), c_0_311]), c_0_312]), c_0_313]), c_0_314]), c_0_315])])]), c_0_316])). 60.84/8.23 thf(c_0_318, plain, ![X1483:$i, X1484:$o, X1485:$i, X1486:$i]:(((if @ X1483 @ ((X1484)) @ X1485 @ X1486)=(setunion @ (dsetconstr @ X1483 @ (^[Z0/* 9 */:$i]:(((((X1484))&((Z0)=(X1485)))|(~(((X1484)))&((Z0)=(X1486)))))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[if])])). 60.84/8.23 thf(c_0_319, negated_conjecture, ![X1491:$i, X1492:$i, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1504:$i, X1505:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1513:$i, X1514:$i > $i > $o, X1515:$i, X1517:$i, X1520:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1527:$i, X1528:$i > $o, X1529:$i, X1531:$i, X1532:$i > $o, X1533:$i, X1534:$i, X1535:$i > $o, X1536:$i, X1537:$i, X1538:$i > $o, X1539:$i, X1540:$i > $o, X1541:$i, X1544:$i, X1545:$o, X1546:$i, X1547:$i, X1548:$o, X1549:$i, X1550:$i, X1551:$i > $o, X1552:$i, X1555:$i, X1556:$i, X1559:$i, X1561:$i, X1563:$i, X1564:$i > $o, X1565:$i, X1566:$i, X1568:$i, X1569:$i > $o, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$o, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1599:$o, X1601:$i, X1602:$i, X1603:$i > $o, X1604:$i, X1607:$i, X1608:$i, X1609:$i, X1611:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i, X1626:$i, X1627:$i > $o, X1628:$i, X1629:$i > $o, X1630:$i, X1631:$i, X1632:$i > $o, X1633:$i, X1635:$i, X1636:$i > $o, X1638:$i, X1639:$i, X1640:$i > $o, X1642:$i, X1643:$i, X1644:$i > $o, X1645:$i, X1647:$o, X1648:$o, X1649:$i, X1650:$i > $o, X1652:$i, X1653:$i, X1654:$i > $o, X1655:$i, X1657:$i > $o, X1658:$i, X1661:$i, X1662:$i > $o, X1663:$i, X1667:$i, X1668:$i > $o, X1669:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i > $o, X1682:$i, X1684:$i, X1685:$i, X1686:$i > $o, X1687:$i > $o, X1690:$i, X1693:$i, X1694:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i > $o, X1707:$i, X1709:$i, X1710:$i, X1711:$i > $o, X1712:$i > $o, X1715:$i, X1717:$i, X1719:$i, X1720:$i, X1721:$i > $o, X1722:$i > $o, X1725:$i, X1726:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1735:$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, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i > $o, X1773:$i, X1774:$i > $o, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$o, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$o, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i > $o, X1929:$i, X1931:$i, X1932:$i > $o, X1933:$i, X1935:$i, X1936:$i > $o, X1937:$i, X1940:$i, X1941:$i > $o, X1944:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i > $i > $o, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i > $i > $o, X2026:$i, X2027:$i, X2028:$i > $i > $o, X2029:$i, X2030:$i, X2031:$i > $i > $o, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i > $i > $o, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i > $i > $o, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i > $i > $o, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, 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X2091 @ X2092 @ X2093 @ X2094)))|(~(in @ X2097 @ X2093)|(X2094 @ X2097))|~(subset @ X2093 @ (cartprod @ X2091 @ X2092))))))&((~(in @ X2100 @ (dsetconstr @ X2098 @ (^[Z0/* 3 */:$i]:((X2099 @ Z0)))))|((dsetconstr @ X2098 @ (^[Z0/* 3 */:$i]:((X2099 @ Z0))))!=(setadjoin @ X2100 @ emptyset))|(~(in @ X2101 @ X2098)|(~(in @ X2102 @ X2098)|(~(X2099 @ X2101)|(~(X2099 @ X2102)|((X2101)=(X2102)))))))&((~(func @ X2103 @ X2104 @ X2105)|(~(in @ X2106 @ X2103)|(in @ (kpair @ X2106 @ (ap @ X2103 @ X2104 @ X2105 @ X2106)) @ X2105)))&((~(in @ X2109 @ (funcSet @ X2107 @ X2108))|(~(in @ X2110 @ X2107)|(in @ (kpair @ X2110 @ (ap @ X2107 @ X2108 @ X2109 @ X2110)) @ X2109)))&((~(func @ X2111 @ X2112 @ X2113)|(~(in @ X2114 @ X2111)|(~(in @ X2115 @ X2112)|(~(in @ (kpair @ X2114 @ X2115) @ X2113)|((ap @ X2111 @ X2112 @ X2113 @ X2114)=(X2115))))))&((((in @ (esk77_4 @ X2116 @ X2117 @ X2118 @ X2119) @ X2116)|(~(in @ X2121 @ X2116)|(~(in @ X2122 @ X2117)|(~(in @ (kpair @ X2121 @ X2122) @ X2119)|(in @ (kpair @ X2121 @ X2122) @ X2118))))|~(func @ X2116 @ X2117 @ X2119)|~(func @ X2116 @ X2117 @ X2118))&(((ap @ X2116 @ X2117 @ X2118 @ (esk77_4 @ X2116 @ X2117 @ X2118 @ X2119))!=(ap @ X2116 @ X2117 @ X2119 @ (esk77_4 @ X2116 @ X2117 @ X2118 @ X2119)))|(~(in @ X2121 @ X2116)|(~(in @ X2122 @ X2117)|(~(in @ (kpair @ X2121 @ X2122) @ X2119)|(in @ (kpair @ X2121 @ X2122) @ X2118))))|~(func @ X2116 @ X2117 @ X2119)|~(func @ X2116 @ X2117 @ X2118)))&((~(in @ X2125 @ (funcSet @ X2123 @ X2124))|(~(in @ X2126 @ X2123)|(~(in @ X2127 @ X2124)|(~(in @ (kpair @ X2126 @ X2127) @ X2125)|((ap @ X2123 @ X2124 @ X2125 @ X2126)=(X2127))))))&((((in @ (esk78_4 @ X2128 @ X2129 @ X2130 @ X2131) @ X2128)|(subset @ X2130 @ X2131)|~(subset @ X2131 @ (cartprod @ X2128 @ X2129))|~(subset @ X2130 @ (cartprod @ X2128 @ X2129)))&(((in @ (esk79_4 @ X2128 @ X2129 @ X2130 @ X2131) @ X2129)|(subset @ X2130 @ X2131)|~(subset @ X2131 @ (cartprod @ X2128 @ X2129))|~(subset @ X2130 @ (cartprod @ X2128 @ X2129)))&(((in @ (kpair @ (esk78_4 @ X2128 @ X2129 @ X2130 @ X2131) @ (esk79_4 @ X2128 @ X2129 @ X2130 @ X2131)) @ X2130)|(subset @ X2130 @ X2131)|~(subset @ X2131 @ (cartprod @ X2128 @ X2129))|~(subset @ X2130 @ (cartprod @ X2128 @ X2129)))&(~(in @ (kpair @ (esk78_4 @ X2128 @ X2129 @ X2130 @ X2131) @ (esk79_4 @ X2128 @ X2129 @ X2130 @ X2131)) @ X2131)|(subset @ X2130 @ X2131)|~(subset @ X2131 @ (cartprod @ X2128 @ X2129))|~(subset @ X2130 @ (cartprod @ X2128 @ X2129))))))&(((((in @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2134)|((X2136)=(X2137))|(in @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2134)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(((in @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2135)|((X2136)=(X2137))|(in @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2134)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(((in @ (kpair @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2137)|((X2136)=(X2137))|(in @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2134)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(~(in @ (kpair @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2136)|((X2136)=(X2137))|(in @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2134)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135))))))&((((in @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2134)|((X2136)=(X2137))|(in @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2135)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(((in @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2135)|((X2136)=(X2137))|(in @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2135)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(((in @ (kpair @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2137)|((X2136)=(X2137))|(in @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2135)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(~(in @ (kpair @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2136)|((X2136)=(X2137))|(in @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2135)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135))))))&((((in @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2134)|((X2136)=(X2137))|(in @ (kpair @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2136)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(((in @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2135)|((X2136)=(X2137))|(in @ (kpair @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2136)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(((in @ (kpair @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2137)|((X2136)=(X2137))|(in @ (kpair @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2136)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(~(in @ (kpair @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2136)|((X2136)=(X2137))|(in @ (kpair @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2136)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135))))))&(((in @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2134)|((X2136)=(X2137))|~(in @ (kpair @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2137)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(((in @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2135)|((X2136)=(X2137))|~(in @ (kpair @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2137)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(((in @ (kpair @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2137)|((X2136)=(X2137))|~(in @ (kpair @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2137)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))&(~(in @ (kpair @ (esk82_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk83_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2136)|((X2136)=(X2137))|~(in @ (kpair @ (esk80_4 @ X2134 @ X2135 @ X2136 @ X2137) @ (esk81_4 @ X2134 @ X2135 @ X2136 @ X2137)) @ X2137)|~(subset @ X2137 @ (cartprod @ X2134 @ X2135))|~(subset @ X2136 @ (cartprod @ X2134 @ X2135)))))))))&((((in @ (esk84_4 @ X2142 @ X2143 @ X2144 @ X2145) @ X2142)|((X2144)=(X2145))|~(func @ X2142 @ X2143 @ X2145)|~(func @ X2142 @ X2143 @ X2144))&(((ap @ X2142 @ X2143 @ X2144 @ (esk84_4 @ X2142 @ X2143 @ X2144 @ X2145))!=(ap @ X2142 @ X2143 @ X2145 @ (esk84_4 @ X2142 @ X2143 @ X2144 @ X2145)))|((X2144)=(X2145))|~(func @ X2142 @ X2143 @ X2145)|~(func @ X2142 @ X2143 @ X2144)))&((((in @ (esk85_4 @ X2147 @ X2148 @ X2149 @ X2150) @ X2147)|((X2149)=(X2150))|~(in @ X2150 @ (funcSet @ X2147 @ X2148))|~(in @ X2149 @ (funcSet @ X2147 @ X2148)))&(((ap @ X2147 @ X2148 @ X2149 @ (esk85_4 @ X2147 @ X2148 @ X2149 @ X2150))!=(ap @ X2147 @ X2148 @ X2150 @ (esk85_4 @ X2147 @ X2148 @ X2149 @ X2150)))|((X2149)=(X2150))|~(in @ X2150 @ (funcSet @ X2147 @ X2148))|~(in @ X2149 @ (funcSet @ X2147 @ X2148))))&((~(in @ X2154 @ (funcSet @ X2152 @ X2153))|(~(in @ X2155 @ X2152)|((ap @ X2152 @ X2153 @ X2154 @ X2155)=(ap @ X2152 @ X2153 @ X2154 @ X2155))))&((~(func @ X2156 @ X2157 @ X2158)|(~(in @ X2159 @ X2156)|((ap @ X2156 @ X2157 @ X2158 @ X2159)=(ap @ X2156 @ X2157 @ X2158 @ X2159))))&((((in @ (esk86_3 @ X2160 @ X2161 @ X2162) @ X2160)|(~(in @ X2164 @ X2160)|((ap @ X2160 @ X2161 @ (lam @ X2160 @ X2161 @ X2162) @ X2164)=(X2162 @ X2164))))&(~(in @ (X2162 @ (esk86_3 @ X2160 @ X2161 @ X2162)) @ X2161)|(~(in @ X2164 @ X2160)|((ap @ X2160 @ X2161 @ (lam @ X2160 @ X2161 @ X2162) @ X2164)=(X2162 @ X2164)))))&((~(func @ X2165 @ X2166 @ X2167)|((lam @ X2165 @ X2166 @ (ap @ X2165 @ X2166 @ X2167))=(X2167)))&((((in @ (esk87_3 @ X2168 @ X2169 @ X2170) @ X2168)|((lam @ X2168 @ X2169 @ X2170)=(lam @ X2168 @ X2169 @ X2170)))&(~(in @ (X2170 @ (esk87_3 @ X2168 @ X2169 @ X2170)) @ X2169)|((lam @ X2168 @ X2169 @ X2170)=(lam @ X2168 @ X2169 @ X2170))))&((((in @ (esk88_3 @ X2172 @ X2173 @ X2174) @ X2172)|(~(in @ X2176 @ X2172)|((ap @ X2172 @ X2173 @ (lam @ X2172 @ X2173 @ X2174) @ X2176)=(X2174 @ X2176))))&(~(in @ (X2174 @ (esk88_3 @ X2172 @ X2173 @ X2174)) @ X2173)|(~(in @ X2176 @ X2172)|((ap @ X2172 @ X2173 @ (lam @ X2172 @ X2173 @ X2174) @ X2176)=(X2174 @ X2176)))))&((~(in @ X2179 @ (funcSet @ X2177 @ X2178))|((lam @ X2177 @ X2178 @ (ap @ X2177 @ X2178 @ X2179))=(X2179)))&((~(in @ X2182 @ X2180)|(~(in @ X2183 @ X2180)|((X2181)|(in @ X2183 @ (dsetconstr @ X2180 @ (^[Z0/* 9 */:$i]:((((X2181)&((Z0)=(X2182)))|(~((X2181))&((Z0)=(X2183)))))))))))&((~(in @ X2186 @ X2184)|(~(in @ X2187 @ X2184)|((X2185)|((dsetconstr @ X2184 @ (^[Z0/* 9 */:$i]:((((X2185)&((Z0)=(X2186)))|(~((X2185))&((Z0)=(X2187)))))))=(setadjoin @ X2187 @ emptyset)))))&((~(in @ X2190 @ X2188)|(~(in @ X2191 @ X2188)|(~(X2189)|(in @ X2190 @ (dsetconstr @ X2188 @ (^[Z0/* 9 */:$i]:((((X2189)&((Z0)=(X2190)))|(~((X2189))&((Z0)=(X2191)))))))))))&((~(in @ X2194 @ X2192)|(~(in @ X2195 @ X2192)|(~(X2193)|((dsetconstr @ X2192 @ (^[Z0/* 9 */:$i]:((((X2193)&((Z0)=(X2194)))|(~((X2193))&((Z0)=(X2195)))))))=(setadjoin @ X2194 @ emptyset)))))&((((in @ (esk89_4 @ X2196 @ X2197 @ X2198 @ X2199) @ (dsetconstr @ X2196 @ (^[Z0/* 9 */:$i]:((((X2197)&((Z0)=(X2198)))|(~((X2197))&((Z0)=(X2199))))))))|~(in @ X2199 @ X2196)|~(in @ X2198 @ X2196))&(((dsetconstr @ X2196 @ (^[Z0/* 9 */:$i]:((((X2197)&((Z0)=(X2198)))|(~((X2197))&((Z0)=(X2199)))))))=(setadjoin @ (esk89_4 @ X2196 @ X2197 @ X2198 @ X2199) @ emptyset))|~(in @ X2199 @ X2196)|~(in @ X2198 @ X2196)))&((in @ esk91_0 @ esk90_0)&((in @ esk92_0 @ esk90_0)&((~(epred2_0)|~(in @ (if @ esk90_0 @ $true @ esk91_0 @ esk92_0) @ esk90_0))&((epred2_0)|~(in @ (if @ esk90_0 @ $false @ esk91_0 @ esk92_0) @ esk90_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_317])])])])])])])). 60.84/8.23 thf(c_0_320, plain, ![X1487:$i, X1488:$o, X1489:$i, X1490:$i]:(((if @ X1487 @ ((X1488)) @ X1489 @ X1490)=(setunion @ (dsetconstr @ X1487 @ (^[Z0/* 9 */:$i]:(((((X1488))&((Z0)=(X1489)))|(~(((X1488)))&((Z0)=(X1490)))))))))), inference(variable_rename,[status(thm)],[c_0_318])). 60.84/8.23 thf(c_0_321, negated_conjecture, (~((epred2_0))|~((in @ (if @ esk90_0 @ (($true)) @ esk91_0 @ esk92_0) @ esk90_0))), inference(split_conjunct,[status(thm)],[c_0_319])). 60.84/8.23 thf(c_0_322, plain, ![X2:$i, X3:$i, X10:$o, X4:$i]:(((if @ X2 @ ((X10)) @ X3 @ X4)=(setunion @ (dsetconstr @ X2 @ (^[Z0/* 9 */:$i]:((((X10)&((Z0)=(X3)))|(~((X10))&((Z0)=(X4)))))))))), inference(split_conjunct,[status(thm)],[c_0_320])). 60.84/8.23 thf(c_0_323, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:((((dsetconstr @ X3 @ (^[Z0/* 9 */:$i]:(((~($true)&((Z0)=(X2)))|(~(~($true))&((Z0)=(X4)))))))=(setadjoin @ X4 @ emptyset))|~((in @ X2 @ X3))|~((in @ X4 @ X3)))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_319])])])). 60.84/8.23 thf(c_0_324, negated_conjecture, ((epred2_0)|~((in @ (if @ esk90_0 @ (~($true)) @ esk91_0 @ esk92_0) @ esk90_0))), inference(split_conjunct,[status(thm)],[c_0_319])). 60.84/8.23 thf(c_0_325, negated_conjecture, (~((epred2_0))|~((in @ (setunion @ (dsetconstr @ esk90_0 @ (^[Z0/* 9 */:$i]:(((($true)&((Z0)=(esk91_0)))|(~(($true))&((Z0)=(esk92_0)))))))) @ esk90_0))), inference(rw,[status(thm)],[c_0_321, c_0_322])). 60.84/8.23 thf(c_0_326, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:((((dsetconstr @ X2 @ (^[Z0/* 3 */:$i]:(((Z0)=(X3)))))=(setadjoin @ X3 @ emptyset))|~((in @ X3 @ X2))|~((in @ X4 @ X2)))), inference(cn,[status(thm)],[c_0_323])). 60.84/8.23 thf(c_0_327, negated_conjecture, (in @ esk92_0 @ esk90_0), inference(split_conjunct,[status(thm)],[c_0_319])). 60.84/8.23 thf(c_0_328, negated_conjecture, ((epred2_0)|~((in @ (setunion @ (dsetconstr @ esk90_0 @ (^[Z0/* 9 */:$i]:(((~($true)&((Z0)=(esk91_0)))|(~(~($true))&((Z0)=(esk92_0)))))))) @ esk90_0))), inference(rw,[status(thm)],[c_0_324, c_0_322])). 60.84/8.23 thf(c_0_329, negated_conjecture, (~((in @ (setunion @ (dsetconstr @ esk90_0 @ (^[Z0/* 3 */:$i]:(((Z0)=(esk91_0)))))) @ esk90_0))|~((epred2_0))), inference(cn,[status(thm)],[c_0_325])). 60.84/8.23 thf(c_0_330, negated_conjecture, ![X2:$i]:((((dsetconstr @ esk90_0 @ (^[Z0/* 3 */:$i]:(((Z0)=(X2)))))=(setadjoin @ X2 @ emptyset))|~((in @ X2 @ esk90_0)))), inference(spm,[status(thm)],[c_0_326, c_0_327])). 60.84/8.23 thf(c_0_331, negated_conjecture, ![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2))), inference(split_conjunct,[status(thm)],[c_0_319])). 60.84/8.23 thf(c_0_332, negated_conjecture, (in @ esk91_0 @ esk90_0), inference(split_conjunct,[status(thm)],[c_0_319])). 60.84/8.23 thf(c_0_333, negated_conjecture, ((epred2_0)|~((in @ (setunion @ (dsetconstr @ esk90_0 @ (^[Z0/* 3 */:$i]:(((Z0)=(esk92_0)))))) @ esk90_0))), inference(cn,[status(thm)],[c_0_328])). 60.84/8.23 thf(c_0_334, negated_conjecture, ~((epred2_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_329, c_0_330]), c_0_331]), c_0_332]), c_0_332])])). 60.84/8.23 thf(c_0_335, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_333, c_0_330]), c_0_331]), c_0_327]), c_0_327])]), c_0_334]), ['proof']). 60.84/8.23 # SZS output end CNFRefutation 60.84/8.23 # Parsed axioms : 487 60.84/8.23 # Removed by relevancy pruning/SinE : 0 60.84/8.23 # Initial clauses : 670 60.84/8.23 # Removed in clause preprocessing : 288 60.84/8.23 # Initial clauses in saturation : 382 60.84/8.23 # Processed clauses : 7034 60.84/8.23 # ...of these trivial : 43 60.84/8.23 # ...subsumed : 3911 60.84/8.23 # ...remaining for further processing : 3079 60.84/8.23 # Other redundant clauses eliminated : 179 60.84/8.23 # Clauses deleted for lack of memory : 0 60.84/8.23 # Backward-subsumed : 296 60.84/8.23 # Backward-rewritten : 6 60.84/8.23 # Generated clauses : 339247 60.84/8.23 # ...of the previous two non-redundant : 335045 60.84/8.23 # ...aggressively subsumed : 0 60.84/8.23 # Contextual simplify-reflections : 83 60.84/8.23 # Paramodulations : 338773 60.84/8.23 # Factorizations : 62 60.84/8.23 # NegExts : 92 60.84/8.23 # Equation resolutions : 193 60.84/8.23 # Total rewrite steps : 27540 60.84/8.23 # Propositional unsat checks : 0 60.84/8.23 # Propositional check models : 0 60.84/8.23 # Propositional check unsatisfiable : 0 60.84/8.23 # Propositional clauses : 0 60.84/8.23 # Propositional clauses after purity: 0 60.84/8.23 # Propositional unsat core size : 0 60.84/8.23 # Propositional preprocessing time : 0.000 60.84/8.23 # Propositional encoding time : 0.000 60.84/8.23 # Propositional solver time : 0.000 60.84/8.23 # Success case prop preproc time : 0.000 60.84/8.23 # Success case prop encoding time : 0.000 60.84/8.23 # Success case prop solver time : 0.000 60.84/8.23 # Current number of processed clauses : 2397 60.84/8.23 # Positive orientable unit clauses : 54 60.84/8.23 # Positive unorientable unit clauses: 0 60.84/8.23 # Negative unit clauses : 38 60.84/8.23 # Non-unit-clauses : 2305 60.84/8.23 # Current number of unprocessed clauses: 328421 60.84/8.23 # ...number of literals in the above : 1444288 60.84/8.23 # Current number of archived formulas : 0 60.84/8.23 # Current number of archived clauses : 667 60.84/8.23 # Clause-clause subsumption calls (NU) : 839093 60.84/8.23 # Rec. Clause-clause subsumption calls : 357022 60.84/8.23 # Non-unit clause-clause subsumptions : 2370 60.84/8.23 # Unit Clause-clause subsumption calls : 4856 60.84/8.23 # Rewrite failures with RHS unbound : 0 60.84/8.23 # BW rewrite match attempts : 32 60.84/8.23 # BW rewrite match successes : 6 60.84/8.23 # Condensation attempts : 0 60.84/8.23 # Condensation successes : 0 60.84/8.23 # Termbank termtop insertions : 7957254 60.84/8.23 60.84/8.23 # ------------------------------------------------- 60.84/8.23 # User time : 7.402 s 60.84/8.23 # System time : 0.253 s 60.84/8.23 # Total time : 7.655 s 60.84/8.23 # Maximum resident set size: 7176 pages 62.00/8.40 62.00/8.40 # ------------------------------------------------- 62.00/8.40 # User time : 7.412 s 62.00/8.40 # System time : 0.259 s 62.00/8.40 # Total time : 7.671 s 62.00/8.40 # Maximum resident set size: 2348 pages 62.00/8.40 % E---3.1 exiting 62.00/8.40 EOF