0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : run_E %s %d THM 0.12/0.32 % Computer : n019.cluster.edu 0.12/0.32 % Model : x86_64 x86_64 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.32 % Memory : 8042.1875MB 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.32 % CPULimit : 1440 0.12/0.32 % WCLimit : 180 0.12/0.32 % DateTime : Thu Jul 4 06:51:24 EDT 2024 0.12/0.32 % CPUTime : 0.20/0.47 Running higher-order theorem proving 0.20/0.52 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p 8.68/1.64 # Version: 3.2.0-ho 8.68/1.64 # Preprocessing class: HSLMSLSSLLLCHFA. 8.68/1.64 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 8.68/1.64 # Starting ehoh_best5 with 180s (1) cores 8.68/1.64 # Starting almost_fo_3_lam with 180s (1) cores 8.68/1.64 # Starting new_bool_5 with 180s (1) cores 8.68/1.64 # Starting pre_casc_3 with 180s (1) cores 8.68/1.64 # Starting ho_unfolding_8 with 180s (1) cores 8.68/1.64 # Starting new_ho_10_cnf2 with 180s (1) cores 8.68/1.64 # Starting new_bool_3 with 180s (1) cores 8.68/1.64 # Starting new_ho_5 with 180s (1) cores 8.68/1.64 # new_bool_5 with pid 6948 completed with status 0 8.68/1.64 # Result found by new_bool_5 8.68/1.64 # Preprocessing class: HSLMSLSSLLLCHFA. 8.68/1.64 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 8.68/1.64 # Starting ehoh_best5 with 180s (1) cores 8.68/1.64 # Starting almost_fo_3_lam with 180s (1) cores 8.68/1.64 # Starting new_bool_5 with 180s (1) cores 8.68/1.64 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 8.68/1.64 # Search class: HGHSM-FSLM32-MHFMMSBN 8.68/1.64 # Scheduled 10 strats onto 1 cores with 180 seconds (180 total) 8.68/1.64 # Starting ho_unfolding_8 with 33s (1) cores 8.68/1.64 # ho_unfolding_8 with pid 6995 completed with status 0 8.68/1.64 # Result found by ho_unfolding_8 8.68/1.64 # Preprocessing class: HSLMSLSSLLLCHFA. 8.68/1.64 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 8.68/1.64 # Starting ehoh_best5 with 180s (1) cores 8.68/1.64 # Starting almost_fo_3_lam with 180s (1) cores 8.68/1.64 # Starting new_bool_5 with 180s (1) cores 8.68/1.64 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 8.68/1.64 # Search class: HGHSM-FSLM32-MHFMMSBN 8.68/1.64 # Scheduled 10 strats onto 1 cores with 180 seconds (180 total) 8.68/1.64 # Starting ho_unfolding_8 with 33s (1) cores 8.68/1.64 # Preprocessing time : 0.050 s 8.68/1.64 # Presaturation interreduction done 8.68/1.64 8.68/1.64 # Proof found! 8.68/1.64 # SZS status Theorem 8.68/1.64 # SZS output start CNFRefutation 8.68/1.64 thf(decl_22, type, in: $i > $i > $o). 8.68/1.64 thf(decl_23, type, exu: ($i > $o) > $o). 8.68/1.64 thf(decl_24, type, setextAx: $o). 8.68/1.64 thf(decl_25, type, emptyset: $i). 8.68/1.64 thf(decl_26, type, emptysetAx: $o). 8.68/1.64 thf(decl_27, type, setadjoin: $i > $i > $i). 8.68/1.64 thf(decl_28, type, setadjoinAx: $o). 8.68/1.64 thf(decl_29, type, powerset: $i > $i). 8.68/1.64 thf(decl_30, type, powersetAx: $o). 8.68/1.64 thf(decl_31, type, setunion: $i > $i). 8.68/1.64 thf(decl_32, type, setunionAx: $o). 8.68/1.64 thf(decl_33, type, omega: $i). 8.68/1.64 thf(decl_34, type, omega0Ax: $o). 8.68/1.64 thf(decl_35, type, omegaSAx: $o). 8.68/1.64 thf(decl_36, type, omegaIndAx: $o). 8.68/1.64 thf(decl_37, type, replAx: $o). 8.68/1.64 thf(decl_38, type, foundationAx: $o). 8.68/1.64 thf(decl_39, type, wellorderingAx: $o). 8.68/1.64 thf(decl_40, type, descr: ($i > $o) > $i). 8.68/1.64 thf(decl_41, type, descrp: $o). 8.68/1.64 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 8.68/1.64 thf(decl_43, type, dsetconstrI: $o). 8.68/1.64 thf(decl_44, type, dsetconstrEL: $o). 8.68/1.64 thf(decl_45, type, dsetconstrER: $o). 8.68/1.64 thf(decl_46, type, exuE1: $o). 8.68/1.64 thf(decl_47, type, prop2set: $o > $i). 8.68/1.64 thf(decl_48, type, prop2setE: $o). 8.68/1.64 thf(decl_49, type, emptysetE: $o). 8.68/1.64 thf(decl_50, type, emptysetimpfalse: $o). 8.68/1.64 thf(decl_51, type, notinemptyset: $o). 8.68/1.64 thf(decl_52, type, exuE3e: $o). 8.68/1.64 thf(decl_53, type, setext: $o). 8.68/1.64 thf(decl_54, type, emptyI: $o). 8.68/1.64 thf(decl_55, type, noeltsimpempty: $o). 8.68/1.64 thf(decl_56, type, setbeta: $o). 8.68/1.64 thf(decl_57, type, nonempty: $i > $o). 8.68/1.64 thf(decl_58, type, nonemptyE1: $o). 8.68/1.64 thf(decl_59, type, nonemptyI: $o). 8.68/1.64 thf(decl_60, type, nonemptyI1: $o). 8.68/1.64 thf(decl_61, type, setadjoinIL: $o). 8.68/1.64 thf(decl_62, type, emptyinunitempty: $o). 8.68/1.64 thf(decl_63, type, setadjoinIR: $o). 8.68/1.64 thf(decl_64, type, setadjoinE: $o). 8.68/1.64 thf(decl_65, type, setadjoinOr: $o). 8.68/1.64 thf(decl_66, type, setoftrueEq: $o). 8.68/1.64 thf(decl_67, type, powersetI: $o). 8.68/1.64 thf(decl_68, type, emptyinPowerset: $o). 8.68/1.64 thf(decl_69, type, emptyInPowerset: $o). 8.68/1.64 thf(decl_70, type, powersetE: $o). 8.68/1.64 thf(decl_71, type, setunionI: $o). 8.68/1.64 thf(decl_72, type, setunionE: $o). 8.68/1.64 thf(decl_73, type, subPowSU: $o). 8.68/1.64 thf(decl_74, type, exuE2: $o). 8.68/1.64 thf(decl_75, type, nonemptyImpWitness: $o). 8.68/1.64 thf(decl_76, type, uniqinunit: $o). 8.68/1.64 thf(decl_77, type, notinsingleton: $o). 8.68/1.64 thf(decl_78, type, eqinunit: $o). 8.68/1.64 thf(decl_79, type, singletonsswitch: $o). 8.68/1.64 thf(decl_80, type, upairsetE: $o). 8.68/1.64 thf(decl_81, type, upairsetIL: $o). 8.68/1.64 thf(decl_82, type, upairsetIR: $o). 8.68/1.64 thf(decl_83, type, emptyE1: $o). 8.68/1.64 thf(decl_84, type, vacuousDall: $o). 8.68/1.64 thf(decl_85, type, quantDeMorgan1: $o). 8.68/1.64 thf(decl_86, type, quantDeMorgan2: $o). 8.68/1.64 thf(decl_87, type, quantDeMorgan3: $o). 8.68/1.64 thf(decl_88, type, quantDeMorgan4: $o). 8.68/1.64 thf(decl_89, type, prop2setI: $o). 8.68/1.64 thf(decl_91, type, prop2set2propI: $o). 8.68/1.64 thf(decl_92, type, notdexE: $o). 8.68/1.64 thf(decl_93, type, notdallE: $o). 8.68/1.64 thf(decl_94, type, exuI1: $o). 8.68/1.64 thf(decl_95, type, exuI3: $o). 8.68/1.64 thf(decl_96, type, exuI2: $o). 8.68/1.64 thf(decl_97, type, inCongP: $o). 8.68/1.64 thf(decl_98, type, in__Cong: $o). 8.68/1.64 thf(decl_99, type, exuE3u: $o). 8.68/1.64 thf(decl_100, type, exu__Cong: $o). 8.68/1.64 thf(decl_101, type, emptyset__Cong: $o). 8.68/1.64 thf(decl_102, type, setadjoin__Cong: $o). 8.68/1.64 thf(decl_103, type, powerset__Cong: $o). 8.68/1.64 thf(decl_104, type, setunion__Cong: $o). 8.68/1.64 thf(decl_105, type, omega__Cong: $o). 8.68/1.64 thf(decl_106, type, exuEu: $o). 8.68/1.64 thf(decl_107, type, descr__Cong: $o). 8.68/1.64 thf(decl_108, type, dsetconstr__Cong: $o). 8.68/1.64 thf(decl_109, type, subset: $i > $i > $o). 8.68/1.64 thf(decl_112, type, subsetI1: $o). 8.68/1.64 thf(decl_113, type, eqimpsubset2: $o). 8.68/1.64 thf(decl_114, type, eqimpsubset1: $o). 8.68/1.64 thf(decl_115, type, subsetI2: $o). 8.68/1.64 thf(decl_116, type, emptysetsubset: $o). 8.68/1.64 thf(decl_117, type, subsetE: $o). 8.68/1.64 thf(decl_118, type, subsetE2: $o). 8.68/1.64 thf(decl_119, type, notsubsetI: $o). 8.68/1.64 thf(decl_120, type, notequalI1: $o). 8.68/1.64 thf(decl_121, type, notequalI2: $o). 8.68/1.64 thf(decl_122, type, subsetRefl: $o). 8.68/1.64 thf(decl_123, type, subsetTrans: $o). 8.68/1.64 thf(decl_124, type, setadjoinSub: $o). 8.68/1.64 thf(decl_125, type, setadjoinSub2: $o). 8.68/1.64 thf(decl_126, type, subset2powerset: $o). 8.68/1.64 thf(decl_127, type, setextsub: $o). 8.68/1.64 thf(decl_128, type, subsetemptysetimpeq: $o). 8.68/1.64 thf(decl_129, type, powersetI1: $o). 8.68/1.64 thf(decl_130, type, powersetE1: $o). 8.68/1.64 thf(decl_131, type, inPowerset: $o). 8.68/1.64 thf(decl_132, type, powersetsubset: $o). 8.68/1.64 thf(decl_133, type, sepInPowerset: $o). 8.68/1.64 thf(decl_134, type, sepSubset: $o). 8.68/1.64 thf(decl_135, type, binunion: $i > $i > $i). 8.68/1.64 thf(decl_136, type, binunionIL: $o). 8.68/1.64 thf(decl_137, type, upairset2IR: $o). 8.68/1.64 thf(decl_138, type, binunionIR: $o). 8.68/1.64 thf(decl_139, type, binunionEcases: $o). 8.68/1.64 thf(decl_140, type, binunionE: $o). 8.68/1.64 thf(decl_141, type, binunionLsub: $o). 8.68/1.64 thf(decl_142, type, binunionRsub: $o). 8.68/1.64 thf(decl_143, type, binintersect: $i > $i > $i). 8.68/1.64 thf(decl_144, type, binintersectI: $o). 8.68/1.64 thf(decl_145, type, binintersectSubset5: $o). 8.68/1.64 thf(decl_146, type, binintersectEL: $o). 8.68/1.64 thf(decl_147, type, binintersectLsub: $o). 8.68/1.64 thf(decl_148, type, binintersectSubset2: $o). 8.68/1.64 thf(decl_149, type, binintersectSubset3: $o). 8.68/1.64 thf(decl_150, type, binintersectER: $o). 8.68/1.64 thf(decl_151, type, disjointsetsI1: $o). 8.68/1.64 thf(decl_152, type, binintersectRsub: $o). 8.68/1.64 thf(decl_153, type, binintersectSubset4: $o). 8.68/1.64 thf(decl_154, type, binintersectSubset1: $o). 8.68/1.64 thf(decl_155, type, bs114d: $o). 8.68/1.64 thf(decl_157, type, setminus: $i > $i > $i). 8.68/1.64 thf(decl_158, type, setminusI: $o). 8.68/1.64 thf(decl_159, type, setminusEL: $o). 8.68/1.64 thf(decl_160, type, setminusER: $o). 8.68/1.64 thf(decl_161, type, setminusSubset2: $o). 8.68/1.64 thf(decl_162, type, setminusERneg: $o). 8.68/1.64 thf(decl_163, type, setminusELneg: $o). 8.68/1.64 thf(decl_164, type, setminusILneg: $o). 8.68/1.64 thf(decl_165, type, setminusIRneg: $o). 8.68/1.64 thf(decl_166, type, setminusLsub: $o). 8.68/1.64 thf(decl_167, type, setminusSubset1: $o). 8.68/1.64 thf(decl_168, type, symdiff: $i > $i > $i). 8.68/1.64 thf(decl_169, type, symdiffE: $o). 8.68/1.64 thf(decl_170, type, symdiffI1: $o). 8.68/1.64 thf(decl_171, type, symdiffI2: $o). 8.68/1.64 thf(decl_172, type, symdiffIneg1: $o). 8.68/1.64 thf(decl_173, type, symdiffIneg2: $o). 8.68/1.64 thf(decl_174, type, iskpair: $i > $o). 8.68/1.64 thf(decl_175, type, secondinupair: $o). 8.68/1.64 thf(decl_176, type, setukpairIL: $o). 8.68/1.64 thf(decl_177, type, setukpairIR: $o). 8.68/1.64 thf(decl_178, type, kpairiskpair: $o). 8.68/1.64 thf(decl_179, type, kpair: $i > $i > $i). 8.68/1.64 thf(decl_180, type, kpairp: $o). 8.68/1.64 thf(decl_181, type, cartprod: $i > $i > $i). 8.68/1.64 thf(decl_182, type, singletonsubset: $o). 8.68/1.64 thf(decl_183, type, singletoninpowerset: $o). 8.68/1.64 thf(decl_184, type, singletoninpowunion: $o). 8.68/1.64 thf(decl_185, type, upairset2E: $o). 8.68/1.64 thf(decl_186, type, upairsubunion: $o). 8.68/1.64 thf(decl_187, type, upairinpowunion: $o). 8.68/1.64 thf(decl_188, type, ubforcartprodlem1: $o). 8.68/1.64 thf(decl_189, type, ubforcartprodlem2: $o). 8.68/1.64 thf(decl_190, type, ubforcartprodlem3: $o). 8.68/1.64 thf(decl_191, type, cartprodpairin: $o). 8.68/1.64 thf(decl_192, type, cartprodmempair1: $o). 8.68/1.64 thf(decl_193, type, cartprodmempair: $o). 8.68/1.64 thf(decl_194, type, setunionE2: $o). 8.68/1.64 thf(decl_195, type, setunionsingleton1: $o). 8.68/1.64 thf(decl_196, type, setunionsingleton2: $o). 8.68/1.64 thf(decl_197, type, setunionsingleton: $o). 8.68/1.64 thf(decl_198, type, singleton: $i > $o). 8.68/1.64 thf(decl_199, type, singletonprop: $o). 8.68/1.64 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 8.68/1.64 thf(decl_201, type, ex1E1: $o). 8.68/1.64 thf(decl_202, type, ex1I: $o). 8.68/1.64 thf(decl_203, type, ex1I2: $o). 8.68/1.64 thf(decl_204, type, singletonsuniq: $o). 8.68/1.64 thf(decl_209, type, setukpairinjL1: $o). 8.68/1.64 thf(decl_210, type, kfstsingleton: $o). 8.68/1.64 thf(decl_211, type, theprop: $o). 8.68/1.64 thf(decl_212, type, kfst: $i > $i). 8.68/1.64 thf(decl_213, type, kfstpairEq: $o). 8.68/1.64 thf(decl_214, type, cartprodfstin: $o). 8.68/1.64 thf(decl_215, type, setukpairinjL2: $o). 8.68/1.64 thf(decl_216, type, setukpairinjL: $o). 8.68/1.64 thf(decl_217, type, setukpairinjR11: $o). 8.68/1.64 thf(decl_218, type, setukpairinjR12: $o). 8.68/1.64 thf(decl_219, type, setukpairinjR1: $o). 8.68/1.64 thf(decl_220, type, upairequniteq: $o). 8.68/1.64 thf(decl_221, type, setukpairinjR2: $o). 8.68/1.64 thf(decl_222, type, setukpairinjR: $o). 8.68/1.64 thf(decl_223, type, ksndsingleton: $o). 8.68/1.64 thf(decl_224, type, ksnd: $i > $i). 8.68/1.64 thf(decl_225, type, ksndpairEq: $o). 8.68/1.64 thf(decl_226, type, kpairsurjEq: $o). 8.68/1.64 thf(decl_227, type, cartprodsndin: $o). 8.68/1.64 thf(decl_228, type, cartprodpairmemEL: $o). 8.68/1.64 thf(decl_229, type, cartprodpairmemER: $o). 8.68/1.64 thf(decl_230, type, cartprodmempaircEq: $o). 8.68/1.64 thf(decl_231, type, cartprodfstpairEq: $o). 8.68/1.64 thf(decl_232, type, cartprodsndpairEq: $o). 8.68/1.64 thf(decl_233, type, cartprodpairsurjEq: $o). 8.68/1.64 thf(decl_234, type, breln: $i > $i > $i > $o). 8.68/1.64 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 8.68/1.64 thf(decl_236, type, dpsetconstrI: $o). 8.68/1.64 thf(decl_237, type, dpsetconstrSub: $o). 8.68/1.64 thf(decl_238, type, setOfPairsIsBReln: $o). 8.68/1.64 thf(decl_239, type, dpsetconstrERa: $o). 8.68/1.64 thf(decl_240, type, dpsetconstrEL1: $o). 8.68/1.64 thf(decl_241, type, dpsetconstrEL2: $o). 8.68/1.64 thf(decl_242, type, dpsetconstrER: $o). 8.68/1.64 thf(decl_243, type, func: $i > $i > $i > $o). 8.68/1.64 thf(decl_244, type, funcSet: $i > $i > $i). 8.68/1.64 thf(decl_245, type, funcImageSingleton: $o). 8.68/1.64 thf(decl_246, type, apProp: $o). 8.68/1.64 thf(decl_247, type, ap: $i > $i > $i > $i > $i). 8.68/1.64 thf(decl_248, type, app: $o). 8.68/1.64 thf(decl_249, type, infuncsetfunc: $o). 8.68/1.64 thf(decl_250, type, ap2p: $o). 8.68/1.64 thf(decl_251, type, funcinfuncset: $o). 8.68/1.64 thf(decl_252, type, lamProp: $o). 8.68/1.64 thf(decl_253, type, lam: $i > $i > ($i > $i) > $i). 8.68/1.64 thf(decl_254, type, lamp: $o). 8.68/1.64 thf(decl_255, type, lam2p: $o). 8.68/1.64 thf(decl_256, type, brelnall1: $o). 8.68/1.64 thf(decl_257, type, brelnall2: $o). 8.68/1.64 thf(decl_258, type, ex1E2: $o). 8.68/1.64 thf(decl_259, type, funcGraphProp1: $o). 8.68/1.64 thf(decl_260, type, funcGraphProp3: $o). 8.68/1.64 thf(decl_261, type, funcGraphProp2: $o). 8.68/1.64 thf(decl_262, type, funcextLem: $o). 8.68/1.64 thf(decl_263, type, funcGraphProp4: $o). 8.68/1.64 thf(decl_264, type, subbreln: $o). 8.68/1.64 thf(decl_265, type, eqbreln: $o). 8.68/1.64 thf(decl_266, type, funcext: $o). 8.68/1.64 thf(decl_267, type, funcext2: $o). 8.68/1.64 thf(decl_268, type, ap2apEq1: $o). 8.68/1.64 thf(decl_269, type, ap2apEq2: $o). 8.68/1.64 thf(decl_270, type, beta1: $o). 8.68/1.64 thf(decl_271, type, eta1: $o). 8.68/1.64 thf(decl_272, type, lam2lamEq: $o). 8.68/1.64 thf(decl_273, type, beta2: $o). 8.68/1.64 thf(decl_274, type, eta2: $o). 8.68/1.64 thf(decl_275, type, iffalseProp1: $o). 8.68/1.64 thf(decl_276, type, iffalseProp2: $o). 8.68/1.64 thf(decl_277, type, iftrueProp1: $o). 8.68/1.64 thf(decl_278, type, iftrueProp2: $o). 8.68/1.64 thf(decl_279, type, ifSingleton: $o). 8.68/1.64 thf(decl_280, type, if: $i > $o > $i > $i > $i). 8.68/1.64 thf(decl_281, type, ifp: $o). 8.68/1.64 thf(decl_282, type, theeq: $o). 8.68/1.64 thf(decl_283, type, iftrue: $o). 8.68/1.64 thf(decl_284, type, iffalse: $o). 8.68/1.64 thf(decl_285, type, iftrueorfalse: $o). 8.68/1.64 thf(decl_286, type, binintersectT_lem: $o). 8.68/1.64 thf(decl_287, type, binunionT_lem: $o). 8.68/1.64 thf(decl_288, type, powersetT_lem: $o). 8.68/1.64 thf(decl_289, type, setminusT_lem: $o). 8.68/1.64 thf(decl_290, type, complementT_lem: $o). 8.68/1.64 thf(decl_291, type, setextT: $o). 8.68/1.64 thf(decl_292, type, subsetTI: $o). 8.68/1.64 thf(decl_293, type, epred1_0: $o). 8.68/1.64 thf(decl_294, type, esk1_2: $i > $i > $i). 8.68/1.64 thf(decl_295, type, esk2_2: $i > $i > $i). 8.68/1.64 thf(decl_296, type, esk3_2: $i > $i > $i). 8.68/1.64 thf(decl_297, type, esk4_1: $i > $i). 8.68/1.64 thf(decl_298, type, esk5_2: ($i > $i > $o) > $i > $i). 8.68/1.64 thf(decl_299, type, esk6_2: ($i > $i > $o) > $i > $i). 8.68/1.64 thf(decl_300, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 8.68/1.64 thf(decl_301, type, esk8_1: $i > $i). 8.68/1.64 thf(decl_302, type, esk9_1: ($i > $o) > $i). 8.68/1.64 thf(decl_303, type, esk10_1: ($i > $o) > $i). 8.68/1.64 thf(decl_304, type, esk11_2: $i > $i > $i). 8.68/1.64 thf(decl_305, type, esk12_2: $i > $i > $i). 8.68/1.64 thf(decl_306, type, esk13_1: $i > $i). 8.68/1.64 thf(decl_307, type, esk14_1: $i > $i). 8.68/1.64 thf(decl_308, type, esk15_1: $i > $i). 8.68/1.64 thf(decl_309, type, esk16_2: $i > $i > $i). 8.68/1.64 thf(decl_310, type, esk17_3: $i > $i > $o > $i). 8.68/1.64 thf(decl_311, type, esk18_1: ($i > $o) > $i). 8.68/1.64 thf(decl_312, type, esk19_1: $i > $i). 8.68/1.64 thf(decl_313, type, esk20_2: $i > ($i > $o) > $i). 8.68/1.64 thf(decl_314, type, esk21_2: $i > ($i > $o) > $i). 8.68/1.64 thf(decl_315, type, esk22_2: $i > ($i > $o) > $i). 8.68/1.64 thf(decl_316, type, esk23_2: $i > ($i > $o) > $i). 8.68/1.64 thf(decl_317, type, esk24_2: $i > ($i > $o) > $i). 8.68/1.64 thf(decl_318, type, esk25_2: $i > ($i > $o) > $i). 8.68/1.64 thf(decl_319, type, esk26_2: ($i > $o) > $i > $i). 8.68/1.64 thf(decl_320, type, esk27_1: ($i > $o) > $i). 8.68/1.64 thf(decl_321, type, esk28_1: ($i > $o) > $i). 8.68/1.64 thf(decl_322, type, esk29_2: ($i > $o) > $i > $i). 8.68/1.64 thf(decl_323, type, esk30_2: ($i > $o) > ($i > $o) > $i). 8.68/1.64 thf(decl_324, type, esk31_2: ($i > $o) > ($i > $o) > $i). 8.68/1.64 thf(decl_325, type, esk32_2: ($i > $o) > ($i > $o) > $i). 8.68/1.64 thf(decl_326, type, esk33_2: ($i > $o) > ($i > $o) > $i). 8.68/1.64 thf(decl_327, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i). 8.68/1.64 thf(decl_328, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i). 8.68/1.64 thf(decl_329, type, esk36_2: $i > $i > $i). 8.68/1.64 thf(decl_330, type, esk37_2: $i > $i > $i). 8.68/1.64 thf(decl_331, type, esk38_2: $i > $i > $i). 8.68/1.64 thf(decl_332, type, esk39_3: $i > $i > $i > $i). 8.68/1.64 thf(decl_333, type, esk40_3: $i > $i > $i > $i). 8.68/1.64 thf(decl_334, type, esk41_2: $i > $i > $i). 8.68/1.64 thf(decl_335, type, esk42_2: $i > ($i > $o) > $i). 8.68/1.64 thf(decl_336, type, esk43_2: $i > ($i > $o) > $i). 8.68/1.64 thf(decl_337, type, esk44_2: $i > ($i > $o) > $i). 8.68/1.64 thf(decl_338, type, esk45_3: $i > ($i > $o) > $i > $i). 8.68/1.64 thf(decl_339, type, esk46_2: $i > ($i > $o) > $i). 8.68/1.64 thf(decl_340, type, esk47_2: $i > ($i > $o) > $i). 8.68/1.64 thf(decl_341, type, esk48_3: $i > $i > ($i > $i) > $i). 8.68/1.64 thf(decl_342, type, esk49_3: $i > $i > ($i > $i) > $i). 8.68/1.64 thf(decl_343, type, esk50_3: $i > $i > ($i > $i) > $i). 8.68/1.64 thf(decl_344, type, esk51_4: $i > $i > $i > ($i > $o) > $i). 8.68/1.64 thf(decl_345, type, esk52_4: $i > $i > $i > ($i > $o) > $i). 8.68/1.64 thf(decl_346, type, esk53_4: $i > $i > $i > ($i > $o) > $i). 8.68/1.64 thf(decl_347, type, esk54_4: $i > $i > $i > ($i > $o) > $i). 8.68/1.64 thf(decl_348, type, esk55_4: $i > $i > $i > $i > $i). 8.68/1.64 thf(decl_349, type, esk56_4: $i > $i > $i > $i > $i). 8.68/1.64 thf(decl_350, type, esk57_4: $i > $i > $i > $i > $i). 8.68/1.64 thf(decl_351, type, esk58_4: $i > $i > $i > $i > $i). 8.68/1.64 thf(decl_352, type, esk59_4: $i > $i > $i > $i > $i). 8.68/1.64 thf(decl_353, type, esk60_4: $i > $i > $i > $i > $i). 8.68/1.64 thf(decl_354, type, esk61_4: $i > $i > $i > $i > $i). 8.68/1.64 thf(decl_355, type, esk62_4: $i > $i > $i > $i > $i). 8.68/1.64 thf(decl_356, type, esk63_4: $i > $i > $i > $i > $i). 8.68/1.64 thf(decl_357, type, esk64_3: $i > $i > ($i > $i) > $i). 8.68/1.64 thf(decl_358, type, esk65_3: $i > $i > ($i > $i) > $i). 8.68/1.64 thf(decl_359, type, esk66_3: $i > $i > ($i > $i) > $i). 8.68/1.64 thf(decl_360, type, esk67_3: $i > $i > $i > $i). 8.68/1.64 thf(decl_361, type, esk68_3: $i > $i > $i > $i). 8.68/1.64 thf(decl_362, type, esk69_3: $i > $i > $i > $i). 8.68/1.64 thf(decl_363, type, esk70_0: $i). 8.68/1.64 thf(decl_364, type, esk71_0: $i). 8.68/1.64 thf(decl_365, type, esk72_0: $i). 8.68/1.64 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', exuI2)). 8.68/1.64 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', sepInPowerset)). 8.68/1.64 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', sepSubset)). 8.68/1.64 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', dsetconstr__Cong)). 8.68/1.64 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', descr__Cong)). 8.68/1.64 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', exuEu)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', exuI1)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', emptyE1)). 8.68/1.64 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', nonemptyI)). 8.68/1.64 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setbeta)). 8.68/1.64 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', exuE3e)). 8.68/1.64 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', dsetconstrER)). 8.68/1.64 thf(lamProp, axiom, ((lamProp)<=>![X4:$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.P3PzYVIRv0/E---3.1_6827.p', lamProp)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', kfstsingleton)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', ksndsingleton)). 8.68/1.64 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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', dpsetconstrI)). 8.68/1.64 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', dpsetconstrSub)). 8.68/1.64 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setOfPairsIsBReln)). 8.68/1.64 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', dpsetconstrERa)). 8.68/1.64 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', dpsetconstrEL1)). 8.68/1.64 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', dpsetconstrEL2)). 8.68/1.64 thf(apProp, axiom, ((apProp)<=>![X4:$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.P3PzYVIRv0/E---3.1_6827.p', apProp)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', ex1E2)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', eta1)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', lam2lamEq)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', beta2)). 8.68/1.64 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', iftrueProp1)). 8.68/1.64 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.P3PzYVIRv0/E---3.1_6827.p', iftrueProp2)). 8.68/1.64 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', ifSingleton)). 8.68/1.64 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.P3PzYVIRv0/E---3.1_6827.p', iffalseProp2)). 8.68/1.64 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', iffalseProp1)). 8.68/1.64 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', eta2)). 8.68/1.64 thf(beta1, axiom, ((beta1)<=>![X4:$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.P3PzYVIRv0/E---3.1_6827.p', beta1)). 8.68/1.64 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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', lam2p)). 8.68/1.64 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', lamp)). 8.68/1.64 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.P3PzYVIRv0/E---3.1_6827.p', funcImageSingleton)). 8.68/1.64 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:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', dpsetconstrER)). 8.68/1.64 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', ex1I2)). 8.68/1.64 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.P3PzYVIRv0/E---3.1_6827.p', ex1I)). 8.68/1.64 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', ex1E1)). 8.68/1.64 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', singletonprop)). 8.68/1.64 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', exu__Cong)). 8.68/1.64 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', exuE3u)). 8.68/1.64 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', exuI3)). 8.68/1.64 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', exuE2)). 8.68/1.64 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setoftrueEq)). 8.68/1.64 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', exuE1)). 8.68/1.64 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', dsetconstrEL)). 8.68/1.64 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', dsetconstrI)). 8.68/1.64 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', descrp)). 8.68/1.64 thf(replAx, axiom, ((replAx)<=>![X6:$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.P3PzYVIRv0/E---3.1_6827.p', replAx)). 8.68/1.64 thf(powersetTI1, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>(((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>(((exuE1)=>(((emptysetE)=>((((((emptyI)=>((noeltsimpempty)=>(((nonemptyE1)=>(((nonemptyI1)=>((setadjoinIL)=>(((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>(((emptyinPowerset)=>((emptyInPowerset)=>(((setunionI)=>(((subPowSU)=>((exuE2)=>(((uniqinunit)=>(((eqinunit)=>(((upairsetE)=>((((((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>(((prop2setI)=>((prop2set2propI)=>((notdexE)=>((((exuI3)=>(((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>(((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>(((((((((emptysetsubset)=>(((subsetE2)=>((notsubsetI)=>(((notequalI2)=>((subsetRefl)=>(((setadjoinSub)=>(((subset2powerset)=>((setextsub)=>(((powersetI1)=>(((inPowerset)=>((((sepSubset)=>((binunionIL)=>((upairset2IR)=>(((((binunionLsub)=>((binunionRsub)=>(((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>(((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>(((setminusEL)=>((setminusER)=>((setminusSubset2)=>((((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>(((symdiffE)=>(((((((setukpairIL)=>((setukpairIR)=>(((((singletoninpowerset)=>(((upairset2E)=>((((ubforcartprodlem1)=>((ubforcartprodlem2)=>(((cartprodpairin)=>((cartprodmempair1)=>(((setunionE2)=>(((((((((((kfstsingleton)=>((theprop)=>((((((setukpairinjR11)=>(((setukpairinjR1)=>((((setukpairinjR)=>((ksndsingleton)=>((((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>(((cartprodfstpairEq)=>((((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((((apProp)=>((((ap2p)=>((funcinfuncset)=>((lamProp)=>((((brelnall1)=>((brelnall2)=>((ex1E2)=>(((funcGraphProp3)=>((funcGraphProp2)=>((((subbreln)=>((((funcext2)=>((ap2apEq1)=>((((eta1)=>((lam2lamEq)=>((beta2)=>(((((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((((iftrueorfalse)=>((((powersetT_lem)=>(((complementT_lem)=>((setextT)=>(![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)<=(in @ X2 @ X21))))=>(in @ X21 @ (powerset @ X48)))))))<=(subsetTI))))<=(setminusT_lem)))<=(binunionT_lem))<=(binintersectT_lem)))<=(iffalse))<=(iftrue)))))))<=(iffalseProp2))<=(iffalseProp1))<=(eta2)))))<=(beta1))<=(ap2apEq2))))<=(funcext))<=(eqbreln)))<=(funcGraphProp4))<=(funcextLem))))<=(funcGraphProp1)))))<=(lam2p))<=(lamp)))))<=(infuncsetfunc))<=(app)))<=(funcImageSingleton))<=(dpsetconstrER))))))))<=(cartprodpairsurjEq))<=(cartprodsndpairEq)))<=(cartprodmempaircEq)))))<=(kpairsurjEq))<=(ksndpairEq))))<=(setukpairinjR2))<=(upairequniteq)))<=(setukpairinjR12)))<=(setukpairinjL))<=(setukpairinjL2))<=(cartprodfstin))<=(kfstpairEq))))<=(setukpairinjL1))<=(singletonsuniq))<=(ex1I2))<=(ex1I))<=(ex1E1))<=(singletonprop))<=(setunionsingleton))<=(setunionsingleton2))<=(setunionsingleton1)))<=(cartprodmempair))))<=(ubforcartprodlem3))))<=(upairinpowunion))<=(upairsubunion)))<=(singletoninpowunion)))<=(singletonsubset))<=(kpairp))<=(kpairiskpair))))<=(secondinupair))<=(symdiffIneg2))<=(symdiffIneg1))<=(symdiffI2))<=(symdiffI1)))<=(setminusSubset1)))))<=(setminusELneg))<=(setminusERneg)))))<=(setminusI)))))))<=(binintersectER)))))))<=(binintersectI))))<=(binunionE))<=(binunionEcases))<=(binunionIR)))))<=(sepInPowerset))<=(powersetsubset)))<=(powersetE1)))<=(subsetemptysetimpeq))))<=(setadjoinSub2)))<=(subsetTrans))))<=(notequalI1))))<=(subsetE)))<=(subsetI2))<=(eqimpsubset1))<=(eqimpsubset2))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong))<=(exuEu)))))<=(setadjoin__Cong)))))))<=(exuI2)))<=(exuI1))<=(notdallE)))))<=(quantDeMorgan4)))))<=(vacuousDall))<=(emptyE1))<=(upairsetIR))<=(upairsetIL)))<=(singletonsswitch)))<=(notinsingleton)))<=(nonemptyImpWitness))))<=(setunionE)))<=(powersetE))))<=(powersetI))))))<=(emptyinunitempty))))<=(nonemptyI)))<=(setbeta))))<=(setext))<=(exuE3e))<=(notinemptyset))<=(emptysetimpfalse)))<=(prop2setE)))<=(dsetconstrER))))))))))))<=(powersetAx))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', powersetTI1)). 8.68/1.64 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', notequalI2)). 8.68/1.64 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', powersetAx)). 8.68/1.64 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', binintersectER)). 8.68/1.64 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', notsubsetI)). 8.68/1.64 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', binintersectI)). 8.68/1.64 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', binunionE)). 8.68/1.64 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', binunionEcases)). 8.68/1.64 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', subset2powerset)). 8.68/1.64 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', binunionIR)). 8.68/1.64 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setextsub)). 8.68/1.64 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', powersetsubset)). 8.68/1.64 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', powersetE1)). 8.68/1.64 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', subsetemptysetimpeq)). 8.68/1.64 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', powersetI1)). 8.68/1.64 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setadjoinSub2)). 8.68/1.64 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', subsetTrans)). 8.68/1.64 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', inPowerset)). 8.68/1.64 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', notequalI1)). 8.68/1.64 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', subsetE)). 8.68/1.64 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', subsetI2)). 8.68/1.64 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', eqimpsubset1)). 8.68/1.64 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', eqimpsubset2)). 8.68/1.64 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', subsetI1)). 8.68/1.64 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', binunionIL)). 8.68/1.64 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', upairset2IR)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', setadjoin__Cong)). 8.68/1.64 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setminusILneg)). 8.68/1.64 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', binunionLsub)). 8.68/1.64 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', notdallE)). 8.68/1.64 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', quantDeMorgan4)). 8.68/1.64 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', vacuousDall)). 8.68/1.64 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', binunionRsub)). 8.68/1.64 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', upairsetIR)). 8.68/1.64 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', binintersectSubset5)). 8.68/1.64 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', upairsetIL)). 8.68/1.64 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', singletonsswitch)). 8.68/1.64 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', notinsingleton)). 8.68/1.64 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', binintersectEL)). 8.68/1.64 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', nonemptyImpWitness)). 8.68/1.64 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setunionE)). 8.68/1.64 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', binintersectLsub)). 8.68/1.64 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', powersetE)). 8.68/1.64 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', powersetI)). 8.68/1.64 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', emptyinunitempty)). 8.68/1.64 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', binintersectSubset2)). 8.68/1.64 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', binintersectSubset3)). 8.68/1.64 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setext)). 8.68/1.64 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', notinemptyset)). 8.68/1.64 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', disjointsetsI1)). 8.68/1.64 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', emptysetimpfalse)). 8.68/1.64 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', prop2setE)). 8.68/1.64 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', binintersectRsub)). 8.68/1.64 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', binintersectSubset4)). 8.68/1.64 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', binintersectSubset1)). 8.68/1.64 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', bs114d)). 8.68/1.64 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setminusEL)). 8.68/1.64 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setminusER)). 8.68/1.64 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setminusSubset2)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', brelnall1)). 8.68/1.64 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setminusIRneg)). 8.68/1.64 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setminusLsub)). 8.68/1.64 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', symdiffE)). 8.68/1.64 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setukpairIL)). 8.68/1.64 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setukpairIR)). 8.68/1.64 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', singletoninpowerset)). 8.68/1.64 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', upairset2E)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', ubforcartprodlem1)). 8.68/1.64 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', subsetRefl)). 8.68/1.64 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', ubforcartprodlem2)). 8.68/1.64 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setadjoinSub)). 8.68/1.64 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', cartprodpairin)). 8.68/1.64 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.P3PzYVIRv0/E---3.1_6827.p', cartprodmempair1)). 8.68/1.64 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setunionE2)). 8.68/1.64 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', theprop)). 8.68/1.64 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setukpairinjR11)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', setukpairinjR1)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', setukpairinjR)). 8.68/1.64 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', cartprodsndin)). 8.68/1.64 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', cartprodpairmemEL)). 8.68/1.64 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', cartprodpairmemER)). 8.68/1.64 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', cartprodfstpairEq)). 8.68/1.64 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', ap2p)). 8.68/1.64 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', funcinfuncset)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', brelnall2)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', funcGraphProp3)). 8.68/1.64 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', funcGraphProp2)). 8.68/1.64 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', subbreln)). 8.68/1.64 thf(funcext2, axiom, ((funcext2)<=>![X4:$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.P3PzYVIRv0/E---3.1_6827.p', funcext2)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', ap2apEq1)). 8.68/1.64 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', ifp)). 8.68/1.64 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', theeq)). 8.68/1.64 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', iftrueorfalse)). 8.68/1.64 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', powersetT_lem)). 8.68/1.64 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', complementT_lem)). 8.68/1.64 thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setextT)). 8.68/1.64 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', subsetTI)). 8.68/1.64 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setminusT_lem)). 8.68/1.64 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', binunionT_lem)). 8.68/1.64 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', binintersectT_lem)). 8.68/1.64 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', iffalse)). 8.68/1.64 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', iftrue)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', ap2apEq2)). 8.68/1.64 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', funcext)). 8.68/1.64 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', eqbreln)). 8.68/1.64 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.P3PzYVIRv0/E---3.1_6827.p', funcGraphProp4)). 8.68/1.64 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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', funcextLem)). 8.68/1.64 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', funcGraphProp1)). 8.68/1.64 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', infuncsetfunc)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', app)). 8.68/1.64 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', cartprodpairsurjEq)). 8.68/1.64 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', cartprodsndpairEq)). 8.68/1.64 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', cartprodmempaircEq)). 8.68/1.64 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', kpairsurjEq)). 8.68/1.64 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', ksndpairEq)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', setukpairinjR2)). 8.68/1.64 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', upairequniteq)). 8.68/1.64 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setukpairinjR12)). 8.68/1.64 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setukpairinjL)). 8.68/1.64 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setukpairinjL2)). 8.68/1.64 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', cartprodfstin)). 8.68/1.64 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', kfstpairEq)). 8.68/1.64 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setukpairinjL1)). 8.68/1.64 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', singletonsuniq)). 8.68/1.64 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setunionsingleton)). 8.68/1.64 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setunionsingleton2)). 8.68/1.64 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setunionsingleton1)). 8.68/1.64 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', cartprodmempair)). 8.68/1.64 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', ubforcartprodlem3)). 8.68/1.64 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', upairinpowunion)). 8.68/1.64 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', upairsubunion)). 8.68/1.64 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', singletoninpowunion)). 8.68/1.64 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', singletonsubset)). 8.68/1.64 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', kpairp)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', kpairiskpair)). 8.68/1.64 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', secondinupair)). 8.68/1.64 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', symdiffIneg2)). 8.68/1.64 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', symdiffIneg1)). 8.68/1.64 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', symdiffI2)). 8.68/1.64 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', symdiffI1)). 8.68/1.64 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setminusSubset1)). 8.68/1.64 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setminusELneg)). 8.68/1.64 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setminusERneg)). 8.68/1.64 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setminusI)). 8.68/1.64 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', subsetE2)). 8.68/1.64 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', emptysetsubset)). 8.68/1.64 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', omega__Cong)). 8.68/1.64 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setunion__Cong)). 8.68/1.64 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', powerset__Cong)). 8.68/1.64 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', emptyset__Cong)). 8.68/1.64 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', in__Cong)). 8.68/1.64 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', inCongP)). 8.68/1.64 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', notdexE)). 8.68/1.64 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', prop2setI)). 8.68/1.64 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', quantDeMorgan3)). 8.68/1.64 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', quantDeMorgan2)). 8.68/1.64 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', quantDeMorgan1)). 8.68/1.64 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', upairsetE)). 8.68/1.64 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', eqinunit)). 8.68/1.64 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', uniqinunit)). 8.68/1.64 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', subPowSU)). 8.68/1.64 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setunionI)). 8.68/1.64 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', emptyInPowerset)). 8.68/1.64 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', emptyinPowerset)). 8.68/1.64 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setadjoinOr)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', setadjoinE)). 8.68/1.64 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setadjoinIR)). 8.68/1.64 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setadjoinIL)). 8.68/1.64 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', nonemptyI1)). 8.68/1.64 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', nonemptyE1)). 8.68/1.64 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', noeltsimpempty)). 8.68/1.64 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', emptyI)). 8.68/1.64 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', emptysetE)). 8.68/1.64 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.P3PzYVIRv0/E---3.1_6827.p', wellorderingAx)). 8.68/1.64 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.P3PzYVIRv0/E---3.1_6827.p', foundationAx)). 8.68/1.64 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', omegaIndAx)). 8.68/1.64 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', omegaSAx)). 8.68/1.64 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', omega0Ax)). 8.68/1.64 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setunionAx)). 8.68/1.64 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setadjoinAx)). 8.68/1.64 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', emptysetAx)). 8.68/1.64 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.P3PzYVIRv0/E---3.1_6827.p', setextAx)). 8.68/1.64 thf(c_0_233, 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])). 8.68/1.64 thf(c_0_234, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 8.68/1.64 thf(c_0_235, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 8.68/1.64 thf(c_0_236, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 8.68/1.64 thf(c_0_237, plain, ((descr__Cong)<=>![X1:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 8.68/1.64 thf(c_0_238, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 8.68/1.64 thf(c_0_239, 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])). 8.68/1.64 thf(c_0_240, 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])). 8.68/1.64 thf(c_0_241, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 8.68/1.64 thf(c_0_242, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 8.68/1.64 thf(c_0_243, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 8.68/1.64 thf(c_0_244, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 8.68/1.64 thf(c_0_245, plain, ((lamProp)<=>![X4:$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])). 8.68/1.64 thf(c_0_246, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 8.68/1.64 thf(c_0_247, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 8.68/1.64 thf(c_0_248, 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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 8.68/1.64 thf(c_0_249, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 8.68/1.64 thf(c_0_250, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 8.68/1.64 thf(c_0_251, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 8.68/1.64 thf(c_0_252, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 8.68/1.64 thf(c_0_253, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 8.68/1.65 thf(c_0_254, plain, ((apProp)<=>![X4:$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])). 8.68/1.65 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])). 8.68/1.65 thf(c_0_256, 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])). 8.68/1.65 thf(c_0_257, 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])). 8.68/1.65 thf(c_0_258, 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])). 8.68/1.65 thf(c_0_259, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 8.68/1.65 thf(c_0_260, plain, ((iftrueProp2)<=>![X4:$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])). 8.68/1.65 thf(c_0_261, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 8.68/1.65 thf(c_0_262, plain, ((iffalseProp2)<=>![X4:$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])). 8.68/1.65 thf(c_0_263, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 8.68/1.65 thf(c_0_264, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])). 8.68/1.65 thf(c_0_265, plain, ((beta1)<=>![X4:$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])). 8.68/1.65 thf(c_0_266, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 8.68/1.65 thf(c_0_267, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 8.68/1.65 thf(c_0_268, plain, ((funcImageSingleton)<=>![X4:$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])). 8.68/1.65 thf(c_0_269, 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:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 8.68/1.65 thf(c_0_270, plain, ((ex1I2)<=>![X4:$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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 8.68/1.65 thf(c_0_271, plain, ((ex1I)<=>![X4:$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])). 8.68/1.65 thf(c_0_272, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 8.68/1.65 thf(c_0_273, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 8.68/1.65 thf(c_0_274, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 8.68/1.65 thf(c_0_275, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 8.68/1.65 thf(c_0_276, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 8.68/1.65 thf(c_0_277, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 8.68/1.65 thf(c_0_278, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 8.68/1.65 thf(c_0_279, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 8.68/1.65 thf(c_0_280, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 8.68/1.65 thf(c_0_281, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 8.68/1.65 thf(c_0_282, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 8.68/1.65 thf(c_0_283, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 8.68/1.65 thf(c_0_284, plain, ((epred1_0)<=>![X794:$i]:(?[X795:$i]:((((![X796:$i]:(((in @ X796 @ X795)=>![X797:$i]:(((in @ X797 @ X796)=>(in @ X797 @ X794)))))&![X798:$i, X799:$i]:((((in @ X798 @ X794)&(in @ X799 @ X794))=>(![X800:$i]:(((in @ X800 @ X795)=>((in @ X798 @ X800)<=>(in @ X799 @ X800))))=>((X798)=(X799))))))&![X801:$i, X802:$i]:((((in @ X801 @ X795)&(in @ X802 @ X795))=>(![X803:$i]:(((in @ X803 @ X801)=>(in @ X803 @ X802)))|![X804:$i]:(((in @ X804 @ X802)=>(in @ X804 @ X801)))))))&![X805:$i]:(((![X806:$i]:(((in @ X806 @ X805)=>(in @ X806 @ X794)))&?[X807:$i]:((in @ X807 @ X805)))=>?[X808:$i, X809:$i]:(((((in @ X808 @ X795)&(in @ X809 @ X805))&~(?[X810:$i]:(((in @ X810 @ X808)&(in @ X810 @ X805)))))&![X811:$i]:(((in @ X811 @ X795)=>(![X812:$i]:(((in @ X812 @ X811)=>(in @ X812 @ X808)))|(in @ X809 @ X811)))))))))))), introduced(definition)). 8.68/1.65 thf(c_0_285, negated_conjecture, ~((![X770:$i, X771:$i]:((![X772:$i]:(((in @ X772 @ X770)<=>(in @ X772 @ X771)))=>((X770)=(X771))))=>(![X773:$i]:(~(in @ X773 @ emptyset))=>(![X774:$i, X775:$i, X776:$i]:(((in @ X776 @ (setadjoin @ X774 @ X775))<=>(((X776)=(X774))|(in @ X776 @ X775))))=>(![X1484:$i, X1485:$i]:(((in @ X1485 @ (powerset @ X1484))<=>![X1486:$i]:(((in @ X1486 @ X1485)=>(in @ X1486 @ X1484)))))=>(![X777:$i, X778:$i]:(((in @ X778 @ (setunion @ X777))<=>?[X779:$i]:(((in @ X778 @ X779)&(in @ X779 @ X777)))))=>((in @ emptyset @ omega)=>(![X780:$i]:(((in @ X780 @ omega)=>(in @ (setadjoin @ X780 @ X780) @ omega)))=>(![X781:$i]:((((in @ emptyset @ X781)&![X782:$i]:((((in @ X782 @ omega)&(in @ X782 @ X781))=>(in @ (setadjoin @ X782 @ X782) @ X781))))=>![X783:$i]:(((in @ X783 @ omega)=>(in @ X783 @ X781)))))=>(![X784:$i > $i > $o, X785:$i]:((![X786:$i]:(((in @ X786 @ X785)=>(exu @ (X784 @ X786))))=>?[X787:$i]:(![X788:$i]:(((in @ X788 @ X787)<=>?[X789:$i]:(((in @ X789 @ X785)&(X784 @ X789 @ X788))))))))=>(![X790:$i]:((?[X791:$i]:((in @ X791 @ X790))=>?[X792:$i]:(((in @ X792 @ X790)&~(?[X793:$i]:(((in @ X793 @ X792)&(in @ X793 @ X790))))))))=>((epred1_0)=>(![X813:$i > $o]:(((exu @ X813)=>(X813 @ (descr @ (^[Z0/* 17 */:$i]:(X813 @ Z0))))))=>(![X814:$i, X815:$i > $o, X816:$i]:(((in @ X816 @ X814)=>((X815 @ X816)=>(in @ X816 @ (dsetconstr @ X814 @ X815)))))=>(![X817:$i, X818:$i > $o, X819:$i]:(((in @ X819 @ (dsetconstr @ X817 @ X818))=>(in @ X819 @ X817)))=>(![X1481:$i, X1482:$i > $o, X1483:$i]:(((in @ X1483 @ (dsetconstr @ X1481 @ X1482))=>(X1482 @ X1483)))=>(![X820:$i > $o]:(((exu @ X820)=>?[X821:$i]:(((X820 @ X821)&![X822:$i]:(((X820 @ X822)=>((X821)=(X822))))))))=>(![X1479:$o, X1480:$i]:(((in @ X1480 @ (prop2set @ ((X1479))))=>(X1479)))=>(![X823:$i]:(((in @ X823 @ emptyset)=>![X824:$o]:((X824))))=>(![X1478:$i]:(((in @ X1478 @ emptyset)=>~($true)))=>(![X1477:$i]:(~(in @ X1477 @ emptyset))=>(![X1475:$i > $o]:(((exu @ X1475)=>?[X1476:$i]:((X1475 @ X1476))))=>(![X1471:$i, X1472:$i]:((![X1473:$i]:(((in @ X1473 @ X1471)=>(in @ X1473 @ X1472)))=>(![X1474:$i]:(((in @ X1474 @ X1472)=>(in @ X1474 @ X1471)))=>((X1471)=(X1472)))))=>(![X825:$i]:((![X826:$i]:(~(in @ X826 @ X825))=>((X825)=(emptyset))))=>(![X827:$i]:((![X828:$i]:(~(in @ X828 @ X827))=>((X827)=(emptyset))))=>(![X1468:$i, X1469:$i > $o, X1470:$i]:(((in @ X1470 @ X1468)=>((in @ X1470 @ (dsetconstr @ X1468 @ X1469))<=>(X1469 @ X1470))))=>(![X829:$i]:(((nonempty @ X829)=>?[X830:$i]:((in @ X830 @ X829))))=>(![X1465:$i, X1466:$i > $o, X1467:$i]:(((in @ X1467 @ X1465)=>((X1466 @ X1467)=>(nonempty @ (dsetconstr @ X1465 @ X1466)))))=>(![X831:$i]:((?[X832:$i]:((in @ X832 @ X831))=>(nonempty @ X831)))=>(![X833:$i, X834:$i]:((in @ X833 @ (setadjoin @ X833 @ X834)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X835:$i, X836:$i, X837:$i]:(((in @ X837 @ X836)=>(in @ X837 @ (setadjoin @ X835 @ X836))))=>(![X838:$i, X839:$i, X840:$i]:(((in @ X840 @ (setadjoin @ X838 @ X839))=>![X841:$o]:(((((X840)=(X838))=>(X841))=>(((in @ X840 @ X839)=>(X841))=>(X841))))))=>(![X842:$i, X843:$i, X844:$i]:(((in @ X844 @ (setadjoin @ X842 @ X843))=>(((X844)=(X842))|(in @ X844 @ X843))))=>(![X845:$i]:(((dsetconstr @ X845 @ (^[Z0/* 1 */:$i]:($true)))=(X845)))=>(![X1462:$i, X1463:$i]:((![X1464:$i]:(((in @ X1464 @ X1463)=>(in @ X1464 @ X1462)))=>(in @ X1463 @ (powerset @ X1462))))=>(![X846:$i]:((in @ emptyset @ (powerset @ X846)))=>(![X847:$i]:((in @ emptyset @ (powerset @ X847)))=>(![X1459:$i, X1460:$i, X1461:$i]:(((in @ X1460 @ (powerset @ X1459))=>((in @ X1461 @ X1460)=>(in @ X1461 @ X1459))))=>(![X848:$i, X849:$i, X850:$i]:(((in @ X849 @ X850)=>((in @ X850 @ X848)=>(in @ X849 @ (setunion @ X848)))))=>(![X1455:$i, X1456:$i]:(((in @ X1456 @ (setunion @ X1455))=>![X1457:$o]:((![X1458:$i]:(((in @ X1456 @ X1458)=>((in @ X1458 @ X1455)=>(X1457))))=>(X1457)))))=>(![X851:$i, X852:$i]:(((in @ X852 @ X851)=>(in @ X852 @ (powerset @ (setunion @ X851)))))=>(![X853:$i > $o]:(((exu @ X853)=>?[X854:$i]:(![X855:$i]:(((X853 @ X855)<=>((X855)=(X854)))))))=>(![X1453:$i]:(((nonempty @ X1453)=>?[X1454:$i]:(((in @ X1454 @ X1453)&$true))))=>(![X856:$i, X857:$i]:(((in @ X856 @ (setadjoin @ X857 @ emptyset))=>((X856)=(X857))))=>(![X1451:$i, X1452:$i]:((((X1451)!=(X1452))=>~(in @ X1452 @ (setadjoin @ X1451 @ emptyset))))=>(![X858:$i, X859:$i]:((((X858)=(X859))=>(in @ X858 @ (setadjoin @ X859 @ emptyset))))=>(![X1449:$i, X1450:$i]:(((in @ X1449 @ (setadjoin @ X1450 @ emptyset))=>(in @ X1450 @ (setadjoin @ X1449 @ emptyset))))=>(![X860:$i, X861:$i, X862:$i]:(((in @ X862 @ (setadjoin @ X860 @ (setadjoin @ X861 @ emptyset)))=>(((X862)=(X860))|((X862)=(X861)))))=>(![X1447:$i, X1448:$i]:((in @ X1447 @ (setadjoin @ X1447 @ (setadjoin @ X1448 @ emptyset))))=>(![X1445:$i, X1446:$i]:((in @ X1446 @ (setadjoin @ X1445 @ (setadjoin @ X1446 @ emptyset))))=>(![X1442:$i, X1443:$i > $o]:((?[X1444:$i]:(((in @ X1444 @ X1442)&(X1443 @ X1444)))=>(((dsetconstr @ X1442 @ X1443)=(emptyset))=>~($true))))=>(![X1440:$i > $o, X1441:$i]:(((in @ X1441 @ emptyset)=>(X1440 @ X1441)))=>(![X863:$i, X864:$i > $o]:((~(![X865:$i]:(((in @ X865 @ X863)=>(X864 @ X865))))=>?[X866:$i]:(((in @ X866 @ X863)&~((X864 @ X866))))))=>(![X867:$i, X868:$i > $o]:((![X869:$i]:(((in @ X869 @ X867)=>~((X868 @ X869))))=>~(?[X870:$i]:(((in @ X870 @ X867)&(X868 @ X870))))))=>(![X871:$i, X872:$i > $o]:((~(?[X873:$i]:(((in @ X873 @ X871)&(X872 @ X873))))=>![X874:$i]:(((in @ X874 @ X871)=>~((X872 @ X874))))))=>(![X1436:$i, X1437:$i > $o]:((?[X1438:$i]:(((in @ X1438 @ X1436)&~((X1437 @ X1438))))=>~(![X1439:$i]:(((in @ X1439 @ X1436)=>(X1437 @ X1439))))))=>(![X875:$o]:(((X875)=>(in @ emptyset @ (prop2set @ ((X875))))))=>((prop2set2propI)=>(![X876:$i, X877:$i > $o]:((~(?[X878:$i]:(((in @ X878 @ X876)&(X877 @ X878))))=>![X879:$i]:(((in @ X879 @ X876)=>~((X877 @ X879))))))=>(![X1432:$i, X1433:$i > $o]:((~(![X1434:$i]:(((in @ X1434 @ X1432)=>(X1433 @ X1434))))=>?[X1435:$i]:(((in @ X1435 @ X1432)&~((X1433 @ X1435))))))=>(![X1429:$i > $o]:((?[X1430:$i]:(((X1429 @ X1430)&![X1431:$i]:(((X1429 @ X1431)=>((X1430)=(X1431))))))=>(exu @ X1429)))=>(![X880:$i > $o]:((?[X881:$i]:((X880 @ X881))=>(![X882:$i, X883:$i]:(((X880 @ X882)=>((X880 @ X883)=>((X882)=(X883)))))=>(exu @ X880))))=>(![X1426:$i > $o]:((?[X1427:$i]:(![X1428:$i]:(((X1426 @ X1428)<=>((X1428)=(X1427)))))=>(exu @ X1426)))=>(![X884:$i, X885:$i]:((((X884)=(X885))=>![X886:$i, X887:$i]:((((X886)=(X887))=>((in @ X886 @ X884)=>(in @ X887 @ X885))))))=>(![X888:$i, X889:$i]:((((X888)=(X889))=>![X890:$i, X891:$i]:((((X890)=(X891))=>((in @ X890 @ X888)<=>(in @ X891 @ X889))))))=>(![X892:$i > $o]:(((exu @ X892)=>![X893:$i, X894:$i]:(((X892 @ X893)=>((X892 @ X894)=>((X893)=(X894)))))))=>(![X895:$i > $o, X896:$i > $o]:((![X897:$i, X898:$i]:((((X897)=(X898))=>((X895 @ X897)<=>(X896 @ X898))))=>((exu @ X895)<=>(exu @ X896))))=>(((emptyset)=(emptyset))=>(![X1422:$i, X1423:$i]:((((X1422)=(X1423))=>![X1424:$i, X1425:$i]:((((X1424)=(X1425))=>((setadjoin @ X1422 @ X1424)=(setadjoin @ X1423 @ X1425))))))=>(![X899:$i, X900:$i]:((((X899)=(X900))=>((powerset @ X899)=(powerset @ X900))))=>(![X901:$i, X902:$i]:((((X901)=(X902))=>((setunion @ X901)=(setunion @ X902))))=>(((omega)=(omega))=>(![X1419:$i > $o]:(((exu @ X1419)=>![X1420:$i, X1421:$i]:(((X1419 @ X1420)=>((X1419 @ X1421)=>((X1420)=(X1421)))))))=>(![X1415:$i > $o, X1416:$i > $o]:((![X1417:$i, X1418:$i]:((((X1417)=(X1418))=>((X1415 @ X1417)<=>(X1416 @ X1418))))=>((exu @ X1415)=>((exu @ X1416)=>((descr @ X1415)=(descr @ X1416))))))=>(![X1409:$i, X1410:$i]:((((X1409)=(X1410))=>![X1411:$i > $o, X1412:$i > $o]:((![X1413:$i]:(((in @ X1413 @ X1409)=>![X1414:$i]:(((in @ X1414 @ X1410)=>(((X1413)=(X1414))=>((X1411 @ X1413)<=>(X1412 @ X1414)))))))=>((dsetconstr @ X1409 @ X1411)=(dsetconstr @ X1410 @ X1412))))))=>(![X1406:$i, X1407:$i]:((![X1408:$i]:(((in @ X1408 @ X1406)=>(in @ X1408 @ X1407)))=>(subset @ X1406 @ X1407)))=>(![X1404:$i, X1405:$i]:((((X1404)=(X1405))=>(subset @ X1405 @ X1404)))=>(![X1402:$i, X1403:$i]:((((X1402)=(X1403))=>(subset @ X1402 @ X1403)))=>(![X1399:$i, X1400:$i]:((![X1401:$i]:(((in @ X1401 @ X1399)=>(in @ X1401 @ X1400)))=>(subset @ X1399 @ X1400)))=>(![X903:$i]:((subset @ emptyset @ X903))=>(![X1396:$i, X1397:$i, X1398:$i]:(((subset @ X1396 @ X1397)=>((in @ X1398 @ X1396)=>(in @ X1398 @ X1397))))=>(![X904:$i, X905:$i, X906:$i]:(((subset @ X904 @ X905)=>(~(in @ X906 @ X905)=>~(in @ X906 @ X904))))=>(![X907:$i, X908:$i, X909:$i]:(((in @ X909 @ X907)=>(~(in @ X909 @ X908)=>~(subset @ X907 @ X908))))=>(![X1394:$i, X1395:$i]:((~(subset @ X1394 @ X1395)=>((X1394)!=(X1395))))=>(![X910:$i, X911:$i, X912:$i]:(((in @ X912 @ X910)=>(~(in @ X912 @ X911)=>((X910)!=(X911)))))=>(![X913:$i]:((subset @ X913 @ X913))=>(![X1391:$i, X1392:$i, X1393:$i]:(((subset @ X1391 @ X1392)=>((subset @ X1392 @ X1393)=>(subset @ X1391 @ X1393))))=>(![X914:$i, X915:$i]:((subset @ X915 @ (setadjoin @ X914 @ X915)))=>(![X1388:$i, X1389:$i, X1390:$i]:(((subset @ X1388 @ X1390)=>(subset @ X1388 @ (setadjoin @ X1389 @ X1390))))=>(![X916:$i, X917:$i]:(((subset @ X916 @ X917)=>(in @ X916 @ (powerset @ X917))))=>(![X918:$i, X919:$i]:(((subset @ X918 @ X919)=>((subset @ X919 @ X918)=>((X918)=(X919)))))=>(![X1387:$i]:(((subset @ X1387 @ emptyset)=>((X1387)=(emptyset))))=>(![X920:$i, X921:$i]:(((subset @ X921 @ X920)=>(in @ X921 @ (powerset @ X920))))=>(![X1385:$i, X1386:$i]:(((in @ X1386 @ (powerset @ X1385))=>(subset @ X1386 @ X1385)))=>(![X922:$i]:((in @ X922 @ (powerset @ X922)))=>(![X1383:$i, X1384:$i]:(((subset @ X1383 @ X1384)=>(subset @ (powerset @ X1383) @ (powerset @ X1384))))=>(![X1381:$i, X1382:$i > $o]:((in @ (dsetconstr @ X1381 @ X1382) @ (powerset @ X1381)))=>(![X923:$i, X924:$i > $o]:((subset @ (dsetconstr @ X923 @ X924) @ X923))=>(![X925:$i, X926:$i, X927:$i]:(((in @ X927 @ X925)=>(in @ X927 @ (binunion @ X925 @ X926))))=>(![X928:$i, X929:$i]:((in @ X929 @ (setadjoin @ X928 @ (setadjoin @ X929 @ emptyset))))=>(![X1378:$i, X1379:$i, X1380:$i]:(((in @ X1380 @ X1379)=>(in @ X1380 @ (binunion @ X1378 @ X1379))))=>(![X1374:$i, X1375:$i, X1376:$i, X1377:$o]:(((in @ X1376 @ (binunion @ X1374 @ X1375))=>(((in @ X1376 @ X1374)=>(X1377))=>(((in @ X1376 @ X1375)=>(X1377))=>(X1377)))))=>(![X1371:$i, X1372:$i, X1373:$i]:(((in @ X1373 @ (binunion @ X1371 @ X1372))=>((in @ X1373 @ X1371)|(in @ X1373 @ X1372))))=>(![X930:$i, X931:$i]:((subset @ X930 @ (binunion @ X930 @ X931)))=>(![X932:$i, X933:$i]:((subset @ X933 @ (binunion @ X932 @ X933)))=>(![X1368:$i, X1369:$i, X1370:$i]:(((in @ X1370 @ X1368)=>((in @ X1370 @ X1369)=>(in @ X1370 @ (binintersect @ X1368 @ X1369)))))=>(![X934:$i, X935:$i, X936:$i]:(((subset @ X936 @ X934)=>((subset @ X936 @ X935)=>(subset @ X936 @ (binintersect @ X934 @ X935)))))=>(![X937:$i, X938:$i, X939:$i]:(((in @ X939 @ (binintersect @ X937 @ X938))=>(in @ X939 @ X937)))=>(![X940:$i, X941:$i]:((subset @ (binintersect @ X940 @ X941) @ X940))=>(![X942:$i, X943:$i]:(((subset @ X942 @ X943)=>((binintersect @ X942 @ X943)=(X942))))=>(![X944:$i, X945:$i]:((((binintersect @ X944 @ X945)=(X945))=>(subset @ X945 @ X944)))=>(![X1365:$i, X1366:$i, X1367:$i]:(((in @ X1367 @ (binintersect @ X1365 @ X1366))=>(in @ X1367 @ X1366)))=>(![X946:$i, X947:$i]:((~(?[X948:$i]:(((in @ X948 @ X946)&(in @ X948 @ X947))))=>((binintersect @ X946 @ X947)=(emptyset))))=>(![X949:$i, X950:$i]:((subset @ (binintersect @ X949 @ X950) @ X950))=>(![X951:$i, X952:$i]:(((subset @ X952 @ X951)=>((binintersect @ X951 @ X952)=(X952))))=>(![X953:$i, X954:$i]:((((binintersect @ X953 @ X954)=(X953))=>(subset @ X953 @ X954)))=>(![X955:$i, X956:$i, X957:$i]:(((binintersect @ X955 @ (binunion @ X956 @ X957))=(binunion @ (binintersect @ X955 @ X956) @ (binintersect @ X955 @ X957))))=>(![X1362:$i, X1363:$i, X1364:$i]:(((in @ X1364 @ X1362)=>(~(in @ X1364 @ X1363)=>(in @ X1364 @ (setminus @ X1362 @ X1363)))))=>(![X958:$i, X959:$i, X960:$i]:(((in @ X960 @ (setminus @ X958 @ X959))=>(in @ X960 @ X958)))=>(![X961:$i, X962:$i, X963:$i]:(((in @ X963 @ (setminus @ X961 @ X962))=>~(in @ X963 @ X962)))=>(![X964:$i, X965:$i]:(((subset @ X964 @ X965)=>((setminus @ X964 @ X965)=(emptyset))))=>(![X1359:$i, X1360:$i, X1361:$i]:((~(in @ X1361 @ (setminus @ X1359 @ X1360))=>((in @ X1361 @ X1359)=>(in @ X1361 @ X1360))))=>(![X1356:$i, X1357:$i, X1358:$i]:((~(in @ X1358 @ (setminus @ X1356 @ X1357))=>(~(in @ X1358 @ X1357)=>~(in @ X1358 @ X1356))))=>(![X966:$i, X967:$i, X968:$i]:((~(in @ X968 @ X966)=>~(in @ X968 @ (setminus @ X966 @ X967))))=>(![X969:$i, X970:$i, X971:$i]:(((in @ X971 @ X970)=>~(in @ X971 @ (setminus @ X969 @ X970))))=>(![X972:$i, X973:$i]:((subset @ (setminus @ X972 @ X973) @ X972))=>(![X1354:$i, X1355:$i]:((((setminus @ X1354 @ X1355)=(emptyset))=>(subset @ X1354 @ X1355)))=>(![X974:$i, X975:$i, X976:$i]:(((in @ X976 @ (symdiff @ X974 @ X975))=>![X977:$o]:((((in @ X976 @ X974)=>(~(in @ X976 @ X975)=>(X977)))=>((~(in @ X976 @ X974)=>((in @ 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X1176:$i]:(((in @ X1176 @ X1174)=>![X1177:$i]:(((in @ X1177 @ X1174)=>(~(X1175)=>((if @ X1174 @ ((X1175)) @ X1176 @ X1177)=(X1177)))))))=>(![X1148:$i, X1149:$o, X1150:$i]:(((in @ X1150 @ X1148)=>![X1151:$i]:(((in @ X1151 @ X1148)=>(in @ (if @ X1148 @ ((X1149)) @ X1150 @ X1151) @ (setadjoin @ X1150 @ (setadjoin @ X1151 @ emptyset)))))))=>(![X1171:$i, X1172:$i]:(((in @ X1172 @ (powerset @ X1171))=>![X1173:$i]:(((in @ X1173 @ (powerset @ X1171))=>(in @ (binintersect @ X1172 @ X1173) @ (powerset @ X1171))))))=>(![X1168:$i, X1169:$i]:(((in @ X1169 @ (powerset @ X1168))=>![X1170:$i]:(((in @ X1170 @ (powerset @ X1168))=>(in @ (binunion @ X1169 @ X1170) @ (powerset @ X1168))))))=>(![X1152:$i, X1153:$i]:(((in @ X1153 @ (powerset @ X1152))=>(in @ (powerset @ X1153) @ (powerset @ (powerset @ X1152)))))=>(![X1165:$i, X1166:$i]:(((in @ X1166 @ (powerset @ X1165))=>![X1167:$i]:(((in @ X1167 @ (powerset @ X1165))=>(in @ (setminus @ X1166 @ X1167) @ (powerset @ X1165))))))=>(![X1154:$i, X1155:$i]:(((in @ X1155 @ (powerset @ X1154))=>(in @ (setminus @ X1154 @ X1155) @ (powerset @ X1154))))=>(![X1156:$i, X1157:$i]:(((in @ X1157 @ (powerset @ X1156))=>![X1158:$i]:(((in @ X1158 @ (powerset @ X1156))=>(![X1159:$i]:(((in @ X1159 @ X1156)=>((in @ X1159 @ X1157)=>(in @ X1159 @ X1158))))=>(![X1160:$i]:(((in @ X1160 @ X1156)=>((in @ X1160 @ X1158)=>(in @ X1160 @ X1157))))=>((X1157)=(X1158))))))))=>(![X1161:$i, X1162:$i]:(((in @ X1162 @ (powerset @ X1161))=>![X1163:$i]:(((in @ X1163 @ (powerset @ X1161))=>(![X1164:$i]:(((in @ X1164 @ X1161)=>((in @ X1164 @ X1162)=>(in @ X1164 @ X1163))))=>(subset @ X1162 @ X1163))))))=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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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notequalI2]), c_0_233]), powersetAx]), binintersectER]), notsubsetI]), binintersectI]), binunionE]), binunionEcases]), subset2powerset]), binunionIR]), c_0_234]), setextsub]), powersetsubset]), powersetE1]), subsetemptysetimpeq]), powersetI1]), setadjoinSub2]), subsetTrans]), inPowerset]), notequalI1]), subsetE]), subsetI2]), c_0_235]), eqimpsubset1]), eqimpsubset2]), subsetI1]), binunionIL]), c_0_236]), c_0_237]), c_0_238]), upairset2IR]), setadjoin__Cong]), setminusILneg]), c_0_239]), binunionLsub]), notdallE]), quantDeMorgan4]), vacuousDall]), binunionRsub]), c_0_240]), upairsetIR]), binintersectSubset5]), upairsetIL]), singletonsswitch]), notinsingleton]), binintersectEL]), nonemptyImpWitness]), setunionE]), binintersectLsub]), powersetE]), powersetI]), emptyinunitempty]), binintersectSubset2]), c_0_241]), c_0_242]), binintersectSubset3]), setext]), c_0_243]), notinemptyset]), disjointsetsI1]), emptysetimpfalse]), prop2setE]), binintersectRsub]), c_0_244]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusEL]), setminusER]), setminusSubset2]), c_0_245]), brelnall1]), setminusIRneg]), setminusLsub]), symdiffE]), setukpairIL]), setukpairIR]), singletoninpowerset]), upairset2E]), ubforcartprodlem1]), subsetRefl]), ubforcartprodlem2]), setadjoinSub]), cartprodpairin]), cartprodmempair1]), setunionE2]), c_0_246]), theprop]), setukpairinjR11]), setukpairinjR1]), setukpairinjR]), c_0_247]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodfstpairEq]), c_0_248]), c_0_249]), c_0_250]), c_0_251]), c_0_252]), c_0_253]), c_0_254]), ap2p]), funcinfuncset]), brelnall2]), c_0_255]), funcGraphProp3]), funcGraphProp2]), subbreln]), funcext2]), ap2apEq1]), c_0_256]), c_0_257]), c_0_258]), c_0_259]), c_0_260]), c_0_261]), ifp]), theeq]), iftrueorfalse]), powersetT_lem]), complementT_lem]), setextT]), subsetTI]), setminusT_lem]), binunionT_lem]), binintersectT_lem]), iffalse]), iftrue]), c_0_262]), c_0_263]), c_0_264]), c_0_265]), ap2apEq2]), funcext]), eqbreln]), funcGraphProp4]), funcextLem]), funcGraphProp1]), c_0_266]), c_0_267]), infuncsetfunc]), app]), c_0_268]), c_0_269]), cartprodpairsurjEq]), cartprodsndpairEq]), cartprodmempaircEq]), kpairsurjEq]), ksndpairEq]), setukpairinjR2]), upairequniteq]), setukpairinjR12]), setukpairinjL]), setukpairinjL2]), cartprodfstin]), kfstpairEq]), setukpairinjL1]), singletonsuniq]), c_0_270]), c_0_271]), c_0_272]), c_0_273]), setunionsingleton]), setunionsingleton2]), setunionsingleton1]), cartprodmempair]), ubforcartprodlem3]), upairinpowunion]), upairsubunion]), singletoninpowunion]), singletonsubset]), kpairp]), kpairiskpair]), secondinupair]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), symdiffI1]), setminusSubset1]), setminusELneg]), setminusERneg]), setminusI]), subsetE2]), emptysetsubset]), omega__Cong]), setunion__Cong]), powerset__Cong]), emptyset__Cong]), c_0_274]), c_0_275]), in__Cong]), inCongP]), c_0_276]), notdexE]), prop2setI]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), upairsetE]), eqinunit]), uniqinunit]), c_0_277]), subPowSU]), setunionI]), emptyInPowerset]), emptyinPowerset]), c_0_278]), setadjoinOr]), setadjoinE]), setadjoinIR]), setadjoinIL]), nonemptyI1]), nonemptyE1]), noeltsimpempty]), emptyI]), emptysetE]), c_0_279]), c_0_280]), c_0_281]), c_0_282]), wellorderingAx]), foundationAx]), c_0_283]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_284])). 8.68/1.65 thf(c_0_286, negated_conjecture, ![X1487:$i, X1488:$i, X1490:$i, X1491:$i, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1500:$i, X1501:$i, X1503:$i, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1509:$i, X1510:$i > $i > $o, X1511:$i, X1514:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1521:$i, X1522:$i > $o, X1523:$i, X1524:$i > $o, X1525:$i, X1526:$i, X1527:$i > $o, X1528:$i, X1529:$i, X1530:$i > $o, X1531:$i, X1532:$i > $o, X1534:$i, X1535:$o, X1536:$i, X1537:$i, X1538:$o, X1539:$i, X1540:$i, X1541:$i > $o, X1543:$i, X1544:$i, X1547:$i, X1549:$i, X1551:$i, X1552:$i > $o, X1553:$i, X1554:$i, X1556:$i, X1557:$i > $o, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$o, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$o, X1589:$i, X1590:$i, X1591:$i > $o, X1593:$i, X1594:$i, X1595:$i, X1597:$i, X1598:$i, X1599:$i, X1600:$i, X1601:$i, X1602:$i, X1603:$i, X1604:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i, X1610:$i, X1611:$i, X1612:$i, X1613:$i > $o, X1614:$i, X1615:$i > $o, X1616:$i, X1617:$i, X1618:$i > $o, X1619:$i, X1621:$i, X1622:$i > $o, X1624:$i, X1625:$i, X1626:$i > $o, X1628:$i, X1629:$i, X1630:$i > $o, X1631:$i, X1633:$o, X1634:$i, X1635:$i > $o, X1637:$i, X1638:$i, X1639:$i > $o, X1640:$i, X1642:$i > $o, X1643:$i, X1645:$i > $o, X1646:$i, X1649:$i > $o, X1650:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i > $o, X1661:$i, X1662:$i, X1663:$i > $o, X1664:$i > $o, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i > $o, X1676:$i, X1677:$i, X1678:$i > $o, X1679:$i > $o, X1682:$i, X1683:$i, X1684:$i > $o, X1685:$i > $o, X1688:$i, X1689:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i > $o, X1736:$i, X1737:$i > $o, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$o, X1750:$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, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$o, 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:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i > $o, X1892:$i, X1893:$i, X1894:$i > $o, X1896:$i, X1897:$i > $o, X1898:$i, X1900:$i, X1901:$i > $o, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, 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 > $i > $o, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i > $i > $o, X1982:$i, X1983:$i, X1984:$i > $i > $o, X1985:$i, X1986:$i, X1987:$i > $i > $o, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i > $i > $o, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i > $i > $o, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i > $i > $o, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i > $i, X2031:$i, X2032:$i, X2033:$i > $i, X2035:$i, X2036:$i, X2037:$i > $i, X2039:$i, X2040:$i, X2041:$i, X2042:$i > $o, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i > $o, X2052:$i, X2053:$i, X2054:$i > $o, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i > $i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i > $i, X2126:$i, X2127:$i, X2128:$i > $i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$o, X2136:$i, X2137:$i, X2138:$i, X2139:$o, X2140:$i, X2141:$i, X2142:$i, X2143:$o, X2144:$i, X2145:$i, X2146:$i, X2147:$o, X2148:$i, X2149:$i, X2150:$i, X2151:$o, X2152:$i, X2153:$i, X2154:$i, X2155:$o, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$o, X2162:$i, X2163:$i, X2164:$i, X2165:$o, X2166:$i, X2167:$i, X2168:$i, X2169:$o, X2170:$i, 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@ X2166 @ X2167)=(X2167)))))&((~(in @ X2170 @ X2168)|(~(in @ X2171 @ X2168)|(in @ (if @ X2168 @ ((X2169)) @ X2170 @ X2171) @ (setadjoin @ X2170 @ (setadjoin @ X2171 @ emptyset)))))&((~(in @ X2173 @ (powerset @ X2172))|(~(in @ X2174 @ (powerset @ X2172))|(in @ (binintersect @ X2173 @ X2174) @ (powerset @ X2172))))&((~(in @ X2176 @ (powerset @ X2175))|(~(in @ X2177 @ (powerset @ X2175))|(in @ (binunion @ X2176 @ X2177) @ (powerset @ X2175))))&((~(in @ X2179 @ (powerset @ X2178))|(in @ (powerset @ X2179) @ (powerset @ (powerset @ X2178))))&((~(in @ X2181 @ (powerset @ X2180))|(~(in @ X2182 @ (powerset @ X2180))|(in @ (setminus @ X2181 @ X2182) @ (powerset @ X2180))))&((~(in @ X2184 @ (powerset @ X2183))|(in @ (setminus @ X2183 @ X2184) @ (powerset @ X2183)))&(((((in @ (esk68_3 @ X2185 @ X2186 @ X2187) @ X2185)|((X2186)=(X2187))|(in @ (esk67_3 @ X2185 @ X2186 @ X2187) @ X2185)|~(in @ X2187 @ (powerset @ X2185))|~(in @ X2186 @ (powerset @ X2185)))&(((in @ (esk68_3 @ X2185 @ X2186 @ X2187) @ X2187)|((X2186)=(X2187))|(in @ (esk67_3 @ X2185 @ X2186 @ X2187) @ X2185)|~(in @ X2187 @ (powerset @ X2185))|~(in @ X2186 @ (powerset @ X2185)))&(~(in @ (esk68_3 @ X2185 @ X2186 @ X2187) @ X2186)|((X2186)=(X2187))|(in @ (esk67_3 @ X2185 @ X2186 @ X2187) @ X2185)|~(in @ X2187 @ (powerset @ X2185))|~(in @ X2186 @ (powerset @ X2185)))))&((((in @ (esk68_3 @ X2185 @ X2186 @ X2187) @ X2185)|((X2186)=(X2187))|(in @ (esk67_3 @ X2185 @ X2186 @ X2187) @ X2186)|~(in @ X2187 @ (powerset @ X2185))|~(in @ X2186 @ (powerset @ X2185)))&(((in @ (esk68_3 @ X2185 @ X2186 @ X2187) @ X2187)|((X2186)=(X2187))|(in @ (esk67_3 @ X2185 @ X2186 @ X2187) @ X2186)|~(in @ X2187 @ (powerset @ X2185))|~(in @ X2186 @ (powerset @ X2185)))&(~(in @ (esk68_3 @ X2185 @ X2186 @ X2187) @ X2186)|((X2186)=(X2187))|(in @ (esk67_3 @ X2185 @ X2186 @ X2187) @ X2186)|~(in @ X2187 @ (powerset @ X2185))|~(in @ X2186 @ (powerset @ X2185)))))&(((in @ (esk68_3 @ X2185 @ X2186 @ X2187) @ X2185)|((X2186)=(X2187))|~(in @ (esk67_3 @ X2185 @ X2186 @ X2187) @ X2187)|~(in @ X2187 @ (powerset @ X2185))|~(in @ X2186 @ (powerset @ X2185)))&(((in @ (esk68_3 @ X2185 @ X2186 @ X2187) @ X2187)|((X2186)=(X2187))|~(in @ (esk67_3 @ X2185 @ X2186 @ X2187) @ X2187)|~(in @ X2187 @ (powerset @ X2185))|~(in @ X2186 @ (powerset @ X2185)))&(~(in @ (esk68_3 @ X2185 @ X2186 @ X2187) @ X2186)|((X2186)=(X2187))|~(in @ (esk67_3 @ X2185 @ X2186 @ X2187) @ X2187)|~(in @ X2187 @ (powerset @ X2185))|~(in @ X2186 @ (powerset @ X2185)))))))&((((in @ (esk69_3 @ X2190 @ X2191 @ X2192) @ X2190)|(subset @ X2191 @ X2192)|~(in @ X2192 @ (powerset @ X2190))|~(in @ X2191 @ (powerset @ X2190)))&(((in @ (esk69_3 @ X2190 @ X2191 @ X2192) @ X2191)|(subset @ X2191 @ X2192)|~(in @ X2192 @ (powerset @ X2190))|~(in @ X2191 @ (powerset @ X2190)))&(~(in @ (esk69_3 @ X2190 @ X2191 @ X2192) @ X2192)|(subset @ X2191 @ X2192)|~(in @ X2192 @ (powerset @ X2190))|~(in @ X2191 @ (powerset @ X2190)))))&((in @ esk71_0 @ (powerset @ esk70_0))&((in @ esk72_0 @ (powerset @ esk70_0))&((~(in @ X2197 @ esk70_0)|(~(in @ X2197 @ esk71_0)|(in @ X2197 @ esk72_0)))&~(in @ esk71_0 @ (powerset @ esk72_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_285])])])])])])])). 8.68/1.65 thf(c_0_287, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((~((in @ X2 @ (setminus @ X3 @ X4)))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_286])). 8.68/1.65 thf(c_0_288, negated_conjecture, ![X2:$i]:(((in @ (esk19_1 @ X2) @ X2)|~((nonempty @ X2)))), inference(split_conjunct,[status(thm)],[c_0_286])). 8.68/1.65 thf(c_0_289, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_286])). 8.68/1.65 thf(c_0_290, negated_conjecture, (in @ esk71_0 @ (powerset @ esk70_0)), inference(split_conjunct,[status(thm)],[c_0_286])). 8.68/1.65 thf(c_0_291, negated_conjecture, ![X2:$i, X3:$i]:((~((in @ (esk19_1 @ (setminus @ X2 @ X3)) @ X3))|~((nonempty @ (setminus @ X2 @ X3))))), inference(spm,[status(thm)],[c_0_287, c_0_288])). 8.68/1.65 thf(c_0_292, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk72_0)|~((in @ X2 @ esk70_0))|~((in @ X2 @ esk71_0)))), inference(split_conjunct,[status(thm)],[c_0_286])). 8.68/1.65 thf(c_0_293, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk70_0)|~((in @ X2 @ esk71_0)))), inference(spm,[status(thm)],[c_0_289, c_0_290])). 8.68/1.65 thf(c_0_294, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X3)|~((in @ X2 @ (setminus @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_286])). 8.68/1.65 thf(c_0_295, negated_conjecture, ![X2:$i]:((~((in @ (esk19_1 @ (setminus @ X2 @ esk72_0)) @ esk71_0))|~((nonempty @ (setminus @ X2 @ esk72_0))))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_291, c_0_292]), c_0_293])). 8.68/1.65 thf(c_0_296, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk19_1 @ (setminus @ X2 @ X3)) @ X2)|~((nonempty @ (setminus @ X2 @ X3))))), inference(spm,[status(thm)],[c_0_294, c_0_288])). 8.68/1.65 thf(c_0_297, negated_conjecture, ![X2:$i, X3:$i]:(((nonempty @ X3)|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_286])). 8.68/1.65 thf(c_0_298, negated_conjecture, ![X2:$i]:(((in @ (esk13_1 @ X2) @ X2)|((X2)=(emptyset)))), inference(split_conjunct,[status(thm)],[c_0_286])). 8.68/1.65 thf(c_0_299, negated_conjecture, ~((nonempty @ (setminus @ esk71_0 @ esk72_0))), inference(spm,[status(thm)],[c_0_295, c_0_296])). 8.68/1.65 thf(c_0_300, negated_conjecture, ![X2:$i]:((((X2)=(emptyset))|(nonempty @ X2))), inference(spm,[status(thm)],[c_0_297, c_0_298])). 8.68/1.65 thf(c_0_301, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|((setminus @ X2 @ X3)!=(emptyset)))), inference(split_conjunct,[status(thm)],[c_0_286])). 8.68/1.65 thf(c_0_302, negated_conjecture, ((setminus @ esk71_0 @ esk72_0)=(emptyset)), inference(spm,[status(thm)],[c_0_299, c_0_300])). 8.68/1.65 thf(c_0_303, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ X3))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_286])). 8.68/1.65 thf(c_0_304, negated_conjecture, (subset @ esk71_0 @ esk72_0), inference(spm,[status(thm)],[c_0_301, c_0_302])). 8.68/1.65 thf(c_0_305, negated_conjecture, ~((in @ esk71_0 @ (powerset @ esk72_0))), inference(split_conjunct,[status(thm)],[c_0_286])). 8.68/1.65 thf(c_0_306, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_303, c_0_304]), c_0_305]), ['proof']). 8.68/1.65 # SZS output end CNFRefutation 8.68/1.65 # Parsed axioms : 509 8.68/1.65 # Removed by relevancy pruning/SinE : 276 8.68/1.65 # Initial clauses : 392 8.68/1.65 # Removed in clause preprocessing : 34 8.68/1.65 # Initial clauses in saturation : 358 8.68/1.65 # Processed clauses : 3330 8.68/1.65 # ...of these trivial : 35 8.68/1.65 # ...subsumed : 1489 8.68/1.65 # ...remaining for further processing : 1806 8.68/1.65 # Other redundant clauses eliminated : 82 8.68/1.65 # Clauses deleted for lack of memory : 0 8.68/1.65 # Backward-subsumed : 90 8.68/1.65 # Backward-rewritten : 10 8.68/1.65 # Generated clauses : 47484 8.68/1.65 # ...of the previous two non-redundant : 46169 8.68/1.65 # ...aggressively subsumed : 0 8.68/1.65 # Contextual simplify-reflections : 27 8.68/1.65 # Paramodulations : 47359 8.68/1.65 # Factorizations : 2 8.68/1.65 # NegExts : 7 8.68/1.65 # Equation resolutions : 90 8.68/1.65 # Disequality decompositions : 0 8.68/1.65 # Total rewrite steps : 1574 8.68/1.65 # ...of those cached : 1288 8.68/1.65 # Propositional unsat checks : 0 8.68/1.65 # Propositional check models : 0 8.68/1.65 # Propositional check unsatisfiable : 0 8.68/1.65 # Propositional clauses : 0 8.68/1.65 # Propositional clauses after purity: 0 8.68/1.65 # Propositional unsat core size : 0 8.68/1.65 # Propositional preprocessing time : 0.000 8.68/1.65 # Propositional encoding time : 0.000 8.68/1.65 # Propositional solver time : 0.000 8.68/1.65 # Success case prop preproc time : 0.000 8.68/1.65 # Success case prop encoding time : 0.000 8.68/1.65 # Success case prop solver time : 0.000 8.68/1.65 # Current number of processed clauses : 1373 8.68/1.65 # Positive orientable unit clauses : 71 8.68/1.65 # Positive unorientable unit clauses: 0 8.68/1.65 # Negative unit clauses : 121 8.68/1.65 # Non-unit-clauses : 1181 8.68/1.65 # Current number of unprocessed clauses: 43226 8.68/1.65 # ...number of literals in the above : 147057 8.68/1.65 # Current number of archived formulas : 0 8.68/1.65 # Current number of archived clauses : 417 8.68/1.65 # Clause-clause subsumption calls (NU) : 266965 8.68/1.65 # Rec. Clause-clause subsumption calls : 142227 8.68/1.65 # Non-unit clause-clause subsumptions : 1272 8.68/1.65 # Unit Clause-clause subsumption calls : 7392 8.68/1.65 # Rewrite failures with RHS unbound : 0 8.68/1.65 # BW rewrite match attempts : 53 8.68/1.65 # BW rewrite match successes : 10 8.68/1.65 # Condensation attempts : 0 8.68/1.65 # Condensation successes : 0 8.68/1.65 # Termbank termtop insertions : 832159 8.68/1.65 # Search garbage collected termcells : 22906 8.68/1.65 8.68/1.65 # ------------------------------------------------- 8.68/1.65 # User time : 1.020 s 8.68/1.65 # System time : 0.042 s 8.68/1.65 # Total time : 1.062 s 8.68/1.65 # Maximum resident set size: 7476 pages 8.68/1.65 8.68/1.65 # ------------------------------------------------- 8.68/1.65 # User time : 1.035 s 8.68/1.65 # System time : 0.044 s 8.68/1.65 # Total time : 1.079 s 8.68/1.65 # Maximum resident set size: 2604 pages 8.68/1.65 % E---3.1 exiting 8.68/1.65 % E exiting 8.68/1.65 EOF