0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.13 % Command : run_E %s %d THM 0.13/0.34 % Computer : n005.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1440 0.13/0.34 % WCLimit : 180 0.13/0.34 % DateTime : Thu Jul 4 07:11:39 EDT 2024 0.13/0.34 % CPUTime : 0.22/0.49 Running higher-order theorem proving 0.38/0.55 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.3c3f8yYgNh/E---3.1_6970.p 0.41/0.80 # Version: 3.2.0-ho 0.41/0.80 # Preprocessing class: HSLMSLSSLLLCHFA. 0.41/0.80 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.41/0.80 # Starting ehoh_best5 with 180s (1) cores 0.41/0.80 # Starting almost_fo_3_lam with 180s (1) cores 0.41/0.80 # Starting new_bool_5 with 180s (1) cores 0.41/0.80 # Starting pre_casc_3 with 180s (1) cores 0.41/0.80 # Starting ho_unfolding_8 with 180s (1) cores 0.41/0.80 # Starting new_ho_10_cnf2 with 180s (1) cores 0.41/0.80 # Starting new_bool_3 with 180s (1) cores 0.41/0.80 # Starting new_ho_5 with 180s (1) cores 0.41/0.80 # new_ho_5 with pid 7055 completed with status 0 0.41/0.80 # Result found by new_ho_5 0.41/0.80 # Preprocessing class: HSLMSLSSLLLCHFA. 0.41/0.80 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.41/0.80 # Starting ehoh_best5 with 180s (1) cores 0.41/0.80 # Starting almost_fo_3_lam with 180s (1) cores 0.41/0.80 # Starting new_bool_5 with 180s (1) cores 0.41/0.80 # Starting pre_casc_3 with 180s (1) cores 0.41/0.80 # Starting ho_unfolding_8 with 180s (1) cores 0.41/0.80 # Starting new_ho_10_cnf2 with 180s (1) cores 0.41/0.80 # Starting new_bool_3 with 180s (1) cores 0.41/0.80 # Starting new_ho_5 with 180s (1) cores 0.41/0.80 # SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true) 0.41/0.80 # Search class: HGHSM-FSLM32-MHFMMSBN 0.41/0.80 # Scheduled 9 strats onto 1 cores with 180 seconds (180 total) 0.41/0.80 # Starting ho_unfolding_8 with 37s (1) cores 0.41/0.80 # ho_unfolding_8 with pid 7056 completed with status 0 0.41/0.80 # Result found by ho_unfolding_8 0.41/0.80 # Preprocessing class: HSLMSLSSLLLCHFA. 0.41/0.80 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.41/0.80 # Starting ehoh_best5 with 180s (1) cores 0.41/0.80 # Starting almost_fo_3_lam with 180s (1) cores 0.41/0.80 # Starting new_bool_5 with 180s (1) cores 0.41/0.80 # Starting pre_casc_3 with 180s (1) cores 0.41/0.80 # Starting ho_unfolding_8 with 180s (1) cores 0.41/0.80 # Starting new_ho_10_cnf2 with 180s (1) cores 0.41/0.80 # Starting new_bool_3 with 180s (1) cores 0.41/0.80 # Starting new_ho_5 with 180s (1) cores 0.41/0.80 # SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true) 0.41/0.80 # Search class: HGHSM-FSLM32-MHFMMSBN 0.41/0.80 # Scheduled 9 strats onto 1 cores with 180 seconds (180 total) 0.41/0.80 # Starting ho_unfolding_8 with 37s (1) cores 0.41/0.80 # Preprocessing time : 0.044 s 0.41/0.80 # Presaturation interreduction done 0.41/0.80 0.41/0.80 # Proof found! 0.41/0.80 # SZS status Theorem 0.41/0.80 # SZS output start CNFRefutation 0.41/0.80 thf(decl_22, type, in: $i > $i > $o). 0.41/0.80 thf(decl_23, type, exu: ($i > $o) > $o). 0.41/0.80 thf(decl_24, type, setextAx: $o). 0.41/0.80 thf(decl_25, type, emptyset: $i). 0.41/0.80 thf(decl_26, type, emptysetAx: $o). 0.41/0.80 thf(decl_27, type, setadjoin: $i > $i > $i). 0.41/0.80 thf(decl_28, type, setadjoinAx: $o). 0.41/0.80 thf(decl_29, type, powerset: $i > $i). 0.41/0.80 thf(decl_30, type, powersetAx: $o). 0.41/0.80 thf(decl_31, type, setunion: $i > $i). 0.41/0.80 thf(decl_32, type, setunionAx: $o). 0.41/0.80 thf(decl_33, type, omega: $i). 0.41/0.80 thf(decl_34, type, omega0Ax: $o). 0.41/0.80 thf(decl_35, type, omegaSAx: $o). 0.41/0.80 thf(decl_36, type, omegaIndAx: $o). 0.41/0.80 thf(decl_37, type, replAx: $o). 0.41/0.80 thf(decl_38, type, foundationAx: $o). 0.41/0.80 thf(decl_39, type, wellorderingAx: $o). 0.41/0.80 thf(decl_40, type, descr: ($i > $o) > $i). 0.41/0.80 thf(decl_41, type, descrp: $o). 0.41/0.80 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 0.41/0.80 thf(decl_43, type, dsetconstrI: $o). 0.41/0.80 thf(decl_44, type, dsetconstrEL: $o). 0.41/0.80 thf(decl_45, type, dsetconstrER: $o). 0.41/0.80 thf(decl_46, type, exuE1: $o). 0.41/0.80 thf(decl_47, type, prop2set: $o > $i). 0.41/0.80 thf(decl_48, type, prop2setE: $o). 0.41/0.80 thf(decl_49, type, emptysetE: $o). 0.41/0.80 thf(decl_50, type, emptysetimpfalse: $o). 0.41/0.80 thf(decl_51, type, notinemptyset: $o). 0.41/0.80 thf(decl_52, type, exuE3e: $o). 0.41/0.80 thf(decl_53, type, setext: $o). 0.41/0.80 thf(decl_54, type, emptyI: $o). 0.41/0.80 thf(decl_55, type, noeltsimpempty: $o). 0.41/0.80 thf(decl_56, type, setbeta: $o). 0.41/0.80 thf(decl_57, type, nonempty: $i > $o). 0.41/0.80 thf(decl_58, type, nonemptyE1: $o). 0.41/0.80 thf(decl_59, type, nonemptyI: $o). 0.41/0.80 thf(decl_60, type, nonemptyI1: $o). 0.41/0.80 thf(decl_61, type, setadjoinIL: $o). 0.41/0.80 thf(decl_62, type, emptyinunitempty: $o). 0.41/0.80 thf(decl_63, type, setadjoinIR: $o). 0.41/0.80 thf(decl_64, type, setadjoinE: $o). 0.41/0.80 thf(decl_65, type, setadjoinOr: $o). 0.41/0.80 thf(decl_66, type, setoftrueEq: $o). 0.41/0.80 thf(decl_67, type, powersetI: $o). 0.41/0.80 thf(decl_68, type, emptyinPowerset: $o). 0.41/0.80 thf(decl_69, type, emptyInPowerset: $o). 0.41/0.80 thf(decl_70, type, powersetE: $o). 0.41/0.80 thf(decl_71, type, setunionI: $o). 0.41/0.80 thf(decl_72, type, setunionE: $o). 0.41/0.80 thf(decl_73, type, subPowSU: $o). 0.41/0.80 thf(decl_74, type, exuE2: $o). 0.41/0.80 thf(decl_75, type, nonemptyImpWitness: $o). 0.41/0.80 thf(decl_76, type, uniqinunit: $o). 0.41/0.80 thf(decl_77, type, notinsingleton: $o). 0.41/0.80 thf(decl_78, type, eqinunit: $o). 0.41/0.80 thf(decl_79, type, singletonsswitch: $o). 0.41/0.80 thf(decl_80, type, upairsetE: $o). 0.41/0.80 thf(decl_81, type, upairsetIL: $o). 0.41/0.80 thf(decl_82, type, upairsetIR: $o). 0.41/0.80 thf(decl_83, type, emptyE1: $o). 0.41/0.80 thf(decl_84, type, vacuousDall: $o). 0.41/0.80 thf(decl_85, type, quantDeMorgan1: $o). 0.41/0.80 thf(decl_86, type, quantDeMorgan2: $o). 0.41/0.80 thf(decl_87, type, quantDeMorgan3: $o). 0.41/0.80 thf(decl_88, type, quantDeMorgan4: $o). 0.41/0.80 thf(decl_89, type, prop2setI: $o). 0.41/0.80 thf(decl_90, type, set2prop: $i > $o). 0.41/0.80 thf(decl_91, type, prop2set2propI: $o). 0.41/0.80 thf(decl_92, type, notdexE: $o). 0.41/0.80 thf(decl_93, type, notdallE: $o). 0.41/0.80 thf(decl_94, type, exuI1: $o). 0.41/0.80 thf(decl_95, type, exuI3: $o). 0.41/0.80 thf(decl_96, type, exuI2: $o). 0.41/0.80 thf(decl_97, type, inCongP: $o). 0.41/0.80 thf(decl_98, type, in__Cong: $o). 0.41/0.80 thf(decl_99, type, exuE3u: $o). 0.41/0.80 thf(decl_100, type, exu__Cong: $o). 0.41/0.80 thf(decl_101, type, emptyset__Cong: $o). 0.41/0.80 thf(decl_102, type, setadjoin__Cong: $o). 0.41/0.80 thf(decl_103, type, powerset__Cong: $o). 0.41/0.80 thf(decl_104, type, setunion__Cong: $o). 0.41/0.80 thf(decl_105, type, omega__Cong: $o). 0.41/0.80 thf(decl_106, type, exuEu: $o). 0.41/0.80 thf(decl_107, type, descr__Cong: $o). 0.41/0.80 thf(decl_108, type, dsetconstr__Cong: $o). 0.41/0.80 thf(decl_109, type, subset: $i > $i > $o). 0.41/0.80 thf(decl_112, type, subsetI1: $o). 0.41/0.80 thf(decl_113, type, eqimpsubset2: $o). 0.41/0.80 thf(decl_114, type, eqimpsubset1: $o). 0.41/0.80 thf(decl_115, type, subsetI2: $o). 0.41/0.80 thf(decl_116, type, emptysetsubset: $o). 0.41/0.80 thf(decl_117, type, subsetE: $o). 0.41/0.80 thf(decl_118, type, subsetE2: $o). 0.41/0.80 thf(decl_119, type, notsubsetI: $o). 0.41/0.80 thf(decl_120, type, notequalI1: $o). 0.41/0.80 thf(decl_121, type, notequalI2: $o). 0.41/0.80 thf(decl_122, type, subsetRefl: $o). 0.41/0.80 thf(decl_123, type, subsetTrans: $o). 0.41/0.80 thf(decl_124, type, setadjoinSub: $o). 0.41/0.80 thf(decl_125, type, setadjoinSub2: $o). 0.41/0.80 thf(decl_126, type, subset2powerset: $o). 0.41/0.80 thf(decl_127, type, setextsub: $o). 0.41/0.80 thf(decl_128, type, subsetemptysetimpeq: $o). 0.41/0.80 thf(decl_129, type, powersetI1: $o). 0.41/0.80 thf(decl_130, type, powersetE1: $o). 0.41/0.80 thf(decl_131, type, inPowerset: $o). 0.41/0.80 thf(decl_132, type, powersetsubset: $o). 0.41/0.80 thf(decl_133, type, sepInPowerset: $o). 0.41/0.80 thf(decl_134, type, sepSubset: $o). 0.41/0.80 thf(decl_135, type, binunion: $i > $i > $i). 0.41/0.80 thf(decl_136, type, binunionIL: $o). 0.41/0.80 thf(decl_137, type, upairset2IR: $o). 0.41/0.80 thf(decl_138, type, binunionIR: $o). 0.41/0.80 thf(decl_139, type, binunionEcases: $o). 0.41/0.80 thf(decl_140, type, binunionE: $o). 0.41/0.80 thf(decl_141, type, binunionLsub: $o). 0.41/0.80 thf(decl_142, type, binunionRsub: $o). 0.41/0.80 thf(decl_143, type, binintersect: $i > $i > $i). 0.41/0.80 thf(decl_144, type, binintersectI: $o). 0.41/0.80 thf(decl_145, type, binintersectSubset5: $o). 0.41/0.80 thf(decl_146, type, binintersectEL: $o). 0.41/0.80 thf(decl_147, type, binintersectLsub: $o). 0.41/0.80 thf(decl_148, type, binintersectSubset2: $o). 0.41/0.80 thf(decl_149, type, binintersectSubset3: $o). 0.41/0.80 thf(decl_150, type, binintersectER: $o). 0.41/0.80 thf(decl_151, type, disjointsetsI1: $o). 0.41/0.80 thf(decl_152, type, binintersectRsub: $o). 0.41/0.80 thf(decl_153, type, binintersectSubset4: $o). 0.41/0.80 thf(decl_154, type, binintersectSubset1: $o). 0.41/0.80 thf(decl_155, type, bs114d: $o). 0.41/0.80 thf(decl_157, type, setminus: $i > $i > $i). 0.41/0.80 thf(decl_158, type, setminusI: $o). 0.41/0.80 thf(decl_159, type, setminusEL: $o). 0.41/0.80 thf(decl_160, type, setminusER: $o). 0.41/0.80 thf(decl_161, type, setminusSubset2: $o). 0.41/0.80 thf(decl_162, type, setminusERneg: $o). 0.41/0.80 thf(decl_163, type, setminusELneg: $o). 0.41/0.80 thf(decl_164, type, setminusILneg: $o). 0.41/0.80 thf(decl_165, type, setminusIRneg: $o). 0.41/0.80 thf(decl_166, type, setminusLsub: $o). 0.41/0.80 thf(decl_167, type, setminusSubset1: $o). 0.41/0.80 thf(decl_168, type, symdiff: $i > $i > $i). 0.41/0.80 thf(decl_169, type, symdiffE: $o). 0.41/0.80 thf(decl_170, type, symdiffI1: $o). 0.41/0.80 thf(decl_171, type, symdiffI2: $o). 0.41/0.80 thf(decl_172, type, symdiffIneg1: $o). 0.41/0.80 thf(decl_173, type, symdiffIneg2: $o). 0.41/0.80 thf(decl_174, type, iskpair: $i > $o). 0.41/0.80 thf(decl_175, type, secondinupair: $o). 0.41/0.80 thf(decl_176, type, setukpairIL: $o). 0.41/0.80 thf(decl_177, type, setukpairIR: $o). 0.41/0.80 thf(decl_178, type, kpairiskpair: $o). 0.41/0.80 thf(decl_179, type, kpair: $i > $i > $i). 0.41/0.80 thf(decl_180, type, kpairp: $o). 0.41/0.80 thf(decl_181, type, cartprod: $i > $i > $i). 0.41/0.80 thf(decl_182, type, singletonsubset: $o). 0.41/0.80 thf(decl_183, type, singletoninpowerset: $o). 0.41/0.80 thf(decl_184, type, singletoninpowunion: $o). 0.41/0.80 thf(decl_185, type, upairset2E: $o). 0.41/0.80 thf(decl_186, type, upairsubunion: $o). 0.41/0.80 thf(decl_187, type, upairinpowunion: $o). 0.41/0.80 thf(decl_188, type, ubforcartprodlem1: $o). 0.41/0.80 thf(decl_189, type, ubforcartprodlem2: $o). 0.41/0.80 thf(decl_190, type, ubforcartprodlem3: $o). 0.41/0.80 thf(decl_191, type, cartprodpairin: $o). 0.41/0.80 thf(decl_192, type, cartprodmempair1: $o). 0.41/0.80 thf(decl_193, type, cartprodmempair: $o). 0.41/0.80 thf(decl_194, type, setunionE2: $o). 0.41/0.80 thf(decl_195, type, setunionsingleton1: $o). 0.41/0.80 thf(decl_196, type, setunionsingleton2: $o). 0.41/0.80 thf(decl_197, type, setunionsingleton: $o). 0.41/0.80 thf(decl_198, type, singleton: $i > $o). 0.41/0.80 thf(decl_199, type, singletonprop: $o). 0.41/0.80 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 0.41/0.80 thf(decl_201, type, ex1E1: $o). 0.41/0.80 thf(decl_202, type, ex1I: $o). 0.41/0.80 thf(decl_203, type, ex1I2: $o). 0.41/0.80 thf(decl_204, type, singletonsuniq: $o). 0.41/0.80 thf(decl_209, type, setukpairinjL1: $o). 0.41/0.80 thf(decl_210, type, kfstsingleton: $o). 0.41/0.80 thf(decl_211, type, theprop: $o). 0.41/0.80 thf(decl_212, type, kfst: $i > $i). 0.41/0.80 thf(decl_213, type, kfstpairEq: $o). 0.41/0.80 thf(decl_214, type, cartprodfstin: $o). 0.41/0.80 thf(decl_215, type, setukpairinjL2: $o). 0.41/0.80 thf(decl_216, type, setukpairinjL: $o). 0.41/0.80 thf(decl_217, type, setukpairinjR11: $o). 0.41/0.80 thf(decl_218, type, setukpairinjR12: $o). 0.41/0.80 thf(decl_219, type, setukpairinjR1: $o). 0.41/0.80 thf(decl_220, type, upairequniteq: $o). 0.41/0.80 thf(decl_221, type, setukpairinjR2: $o). 0.41/0.80 thf(decl_222, type, setukpairinjR: $o). 0.41/0.80 thf(decl_223, type, ksndsingleton: $o). 0.41/0.80 thf(decl_224, type, ksnd: $i > $i). 0.41/0.80 thf(decl_225, type, ksndpairEq: $o). 0.41/0.80 thf(decl_226, type, kpairsurjEq: $o). 0.41/0.80 thf(decl_227, type, cartprodsndin: $o). 0.41/0.80 thf(decl_228, type, cartprodpairmemEL: $o). 0.41/0.80 thf(decl_229, type, cartprodpairmemER: $o). 0.41/0.80 thf(decl_230, type, cartprodmempaircEq: $o). 0.41/0.80 thf(decl_231, type, cartprodfstpairEq: $o). 0.41/0.80 thf(decl_232, type, cartprodsndpairEq: $o). 0.41/0.80 thf(decl_233, type, cartprodpairsurjEq: $o). 0.41/0.80 thf(decl_234, type, breln: $i > $i > $i > $o). 0.41/0.80 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 0.41/0.80 thf(decl_236, type, dpsetconstrI: $o). 0.41/0.80 thf(decl_237, type, dpsetconstrSub: $o). 0.41/0.80 thf(decl_238, type, setOfPairsIsBReln: $o). 0.41/0.80 thf(decl_239, type, dpsetconstrERa: $o). 0.41/0.80 thf(decl_240, type, dpsetconstrEL1: $o). 0.41/0.80 thf(decl_241, type, dpsetconstrEL2: $o). 0.41/0.80 thf(decl_242, type, dpsetconstrER: $o). 0.41/0.80 thf(decl_243, type, func: $i > $i > $i > $o). 0.41/0.80 thf(decl_244, type, funcSet: $i > $i > $i). 0.41/0.80 thf(decl_245, type, funcImageSingleton: $o). 0.41/0.80 thf(decl_246, type, apProp: $o). 0.41/0.80 thf(decl_247, type, ap: $i > $i > $i > $i > $i). 0.41/0.80 thf(decl_248, type, app: $o). 0.41/0.80 thf(decl_249, type, infuncsetfunc: $o). 0.41/0.80 thf(decl_250, type, ap2p: $o). 0.41/0.80 thf(decl_251, type, funcinfuncset: $o). 0.41/0.80 thf(decl_252, type, lamProp: $o). 0.41/0.80 thf(decl_253, type, lam: $i > $i > ($i > $i) > $i). 0.41/0.80 thf(decl_254, type, lamp: $o). 0.41/0.80 thf(decl_255, type, lam2p: $o). 0.41/0.80 thf(decl_256, type, brelnall1: $o). 0.41/0.80 thf(decl_257, type, brelnall2: $o). 0.41/0.80 thf(decl_258, type, ex1E2: $o). 0.41/0.80 thf(decl_259, type, funcGraphProp1: $o). 0.41/0.80 thf(decl_260, type, funcGraphProp3: $o). 0.41/0.80 thf(decl_261, type, funcGraphProp2: $o). 0.41/0.80 thf(decl_262, type, funcextLem: $o). 0.41/0.80 thf(decl_263, type, funcGraphProp4: $o). 0.41/0.80 thf(decl_264, type, subbreln: $o). 0.41/0.80 thf(decl_265, type, eqbreln: $o). 0.41/0.80 thf(decl_266, type, funcext: $o). 0.41/0.80 thf(decl_267, type, funcext2: $o). 0.41/0.80 thf(decl_268, type, ap2apEq1: $o). 0.41/0.80 thf(decl_269, type, ap2apEq2: $o). 0.41/0.80 thf(decl_270, type, beta1: $o). 0.41/0.80 thf(decl_271, type, eta1: $o). 0.41/0.80 thf(decl_272, type, lam2lamEq: $o). 0.41/0.80 thf(decl_273, type, beta2: $o). 0.41/0.80 thf(decl_274, type, eta2: $o). 0.41/0.80 thf(decl_275, type, iffalseProp1: $o). 0.41/0.80 thf(decl_276, type, iffalseProp2: $o). 0.41/0.80 thf(decl_277, type, iftrueProp1: $o). 0.41/0.80 thf(decl_278, type, iftrueProp2: $o). 0.41/0.80 thf(decl_279, type, ifSingleton: $o). 0.41/0.80 thf(decl_280, type, if: $i > $o > $i > $i > $i). 0.41/0.80 thf(decl_281, type, ifp: $o). 0.41/0.80 thf(decl_282, type, theeq: $o). 0.41/0.80 thf(decl_283, type, iftrue: $o). 0.41/0.80 thf(decl_284, type, iffalse: $o). 0.41/0.80 thf(decl_285, type, iftrueorfalse: $o). 0.41/0.80 thf(decl_286, type, binintersectT_lem: $o). 0.41/0.80 thf(decl_287, type, binunionT_lem: $o). 0.41/0.80 thf(decl_288, type, powersetT_lem: $o). 0.41/0.80 thf(decl_289, type, setminusT_lem: $o). 0.41/0.80 thf(decl_290, type, complementT_lem: $o). 0.41/0.80 thf(decl_291, type, setextT: $o). 0.41/0.80 thf(decl_292, type, subsetTI: $o). 0.41/0.80 thf(decl_293, type, powersetTI1: $o). 0.41/0.80 thf(decl_294, type, powersetTE1: $o). 0.41/0.80 thf(decl_295, type, complementTI1: $o). 0.41/0.80 thf(decl_296, type, complementTE1: $o). 0.41/0.80 thf(decl_297, type, binintersectTELcontra: $o). 0.41/0.80 thf(decl_298, type, binintersectTERcontra: $o). 0.41/0.80 thf(decl_299, type, contrasubsetT: $o). 0.41/0.80 thf(decl_300, type, contrasubsetT1: $o). 0.41/0.80 thf(decl_301, type, contrasubsetT2: $o). 0.41/0.80 thf(decl_302, type, contrasubsetT3: $o). 0.41/0.80 thf(decl_303, type, doubleComplementI1: $o). 0.41/0.80 thf(decl_304, type, doubleComplementE1: $o). 0.41/0.80 thf(decl_305, type, doubleComplementSub1: $o). 0.41/0.80 thf(decl_306, type, doubleComplementSub2: $o). 0.41/0.80 thf(decl_307, type, doubleComplementEq: $o). 0.41/0.80 thf(decl_308, type, complementTnotintersectT: $o). 0.41/0.80 thf(decl_309, type, complementImpComplementIntersect: $o). 0.41/0.80 thf(decl_310, type, complementSubsetComplementIntersect: $o). 0.41/0.80 thf(decl_311, type, complementInPowersetComplementIntersect: $o). 0.41/0.80 thf(decl_312, type, contraSubsetComplement: $o). 0.41/0.80 thf(decl_313, type, complementTcontraSubset: $o). 0.41/0.80 thf(decl_314, type, epred1_0: $o). 0.41/0.80 thf(decl_315, type, esk1_2: $i > $i > $i). 0.41/0.80 thf(decl_316, type, esk2_2: $i > $i > $i). 0.41/0.80 thf(decl_317, type, esk3_2: $i > $i > $i). 0.41/0.80 thf(decl_318, type, esk4_1: $i > $i). 0.41/0.80 thf(decl_319, type, esk5_2: ($i > $i > $o) > $i > $i). 0.41/0.80 thf(decl_320, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 0.41/0.80 thf(decl_321, type, esk7_2: ($i > $i > $o) > $i > $i). 0.41/0.80 thf(decl_322, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 0.41/0.80 thf(decl_323, type, esk9_1: $i > $i). 0.41/0.80 thf(decl_324, type, esk10_2: ($i > $o) > $i > $i). 0.41/0.80 thf(decl_325, type, esk11_2: ($i > $o) > $i > $i). 0.41/0.80 thf(decl_326, type, esk12_1: ($i > $o) > $i). 0.41/0.80 thf(decl_327, type, esk13_2: ($i > $o) > $i > $i). 0.41/0.80 thf(decl_328, type, esk14_1: ($i > $o) > $i). 0.41/0.80 thf(decl_329, type, esk15_2: $i > $i > $i). 0.41/0.80 thf(decl_330, type, esk16_2: $i > $i > $i). 0.41/0.80 thf(decl_331, type, esk17_1: $i > $i). 0.41/0.80 thf(decl_332, type, esk18_1: $i > $i). 0.41/0.80 thf(decl_333, type, esk19_1: $i > $i). 0.41/0.80 thf(decl_334, type, esk20_2: $i > $i > $i). 0.41/0.80 thf(decl_335, type, esk21_3: $i > $i > $o > $i). 0.41/0.80 thf(decl_336, type, esk22_2: ($i > $o) > $i > $i). 0.41/0.80 thf(decl_337, type, esk23_1: ($i > $o) > $i). 0.41/0.80 thf(decl_338, type, esk24_1: $i > $i). 0.41/0.80 thf(decl_339, type, esk25_2: $i > ($i > $o) > $i). 0.41/0.80 thf(decl_340, type, esk26_2: $i > ($i > $o) > $i). 0.41/0.80 thf(decl_341, type, esk27_2: $i > ($i > $o) > $i). 0.41/0.80 thf(decl_342, type, esk28_2: $i > ($i > $o) > $i). 0.41/0.80 thf(decl_343, type, esk29_2: $i > ($i > $o) > $i). 0.41/0.80 thf(decl_344, type, esk30_2: $i > ($i > $o) > $i). 0.41/0.80 thf(decl_345, type, esk31_2: ($i > $o) > $i > $i). 0.41/0.80 thf(decl_346, type, esk32_1: ($i > $o) > $i). 0.41/0.80 thf(decl_347, type, esk33_1: ($i > $o) > $i). 0.41/0.80 thf(decl_348, type, esk34_1: ($i > $o) > $i). 0.41/0.80 thf(decl_349, type, esk35_1: ($i > $o) > $i). 0.41/0.80 thf(decl_350, type, esk36_2: ($i > $o) > $i > $i). 0.41/0.80 thf(decl_351, type, esk37_1: ($i > $o) > $i). 0.41/0.80 thf(decl_352, type, esk38_2: ($i > $o) > $i > $i). 0.41/0.80 thf(decl_353, type, esk39_2: ($i > $o) > ($i > $o) > $i). 0.41/0.80 thf(decl_354, type, esk40_2: ($i > $o) > ($i > $o) > $i). 0.41/0.80 thf(decl_355, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 0.41/0.80 thf(decl_356, type, esk42_2: ($i > $o) > ($i > $o) > $i). 0.41/0.80 thf(decl_357, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 0.41/0.80 thf(decl_358, type, esk44_2: ($i > $o) > ($i > $o) > $i). 0.41/0.80 thf(decl_359, type, esk45_2: ($i > $o) > $i > $i). 0.41/0.80 thf(decl_360, type, esk46_2: ($i > $o) > ($i > $o) > $i). 0.41/0.80 thf(decl_361, type, esk47_2: ($i > $o) > ($i > $o) > $i). 0.41/0.80 thf(decl_362, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 0.41/0.80 thf(decl_363, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 0.41/0.80 thf(decl_364, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.41/0.80 thf(decl_365, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.41/0.80 thf(decl_366, type, esk52_2: $i > $i > $i). 0.41/0.80 thf(decl_367, type, esk53_2: $i > $i > $i). 0.41/0.80 thf(decl_368, type, esk54_2: $i > $i > $i). 0.41/0.80 thf(decl_369, type, esk55_3: $i > $i > $i > $i). 0.41/0.80 thf(decl_370, type, esk56_3: $i > $i > $i > $i). 0.41/0.80 thf(decl_371, type, esk57_2: $i > $i > $i). 0.41/0.80 thf(decl_372, type, esk58_2: $i > ($i > $o) > $i). 0.41/0.80 thf(decl_373, type, esk59_2: $i > ($i > $o) > $i). 0.41/0.80 thf(decl_374, type, esk60_2: $i > ($i > $o) > $i). 0.41/0.80 thf(decl_375, type, esk61_3: $i > ($i > $o) > $i > $i). 0.41/0.80 thf(decl_376, type, esk62_2: $i > ($i > $o) > $i). 0.41/0.80 thf(decl_377, type, esk63_2: $i > ($i > $o) > $i). 0.41/0.80 thf(decl_378, type, esk64_3: $i > $i > ($i > $i) > $i). 0.41/0.80 thf(decl_379, type, esk65_3: $i > $i > ($i > $i) > $i). 0.41/0.80 thf(decl_380, type, esk66_3: $i > $i > ($i > $i) > $i). 0.41/0.80 thf(decl_381, type, esk67_4: $i > $i > $i > ($i > $o) > $i). 0.41/0.80 thf(decl_382, type, esk68_4: $i > $i > $i > ($i > $o) > $i). 0.41/0.80 thf(decl_383, type, esk69_4: $i > $i > $i > ($i > $o) > $i). 0.41/0.80 thf(decl_384, type, esk70_4: $i > $i > $i > ($i > $o) > $i). 0.41/0.80 thf(decl_385, type, esk71_4: $i > $i > $i > $i > $i). 0.41/0.80 thf(decl_386, type, esk72_4: $i > $i > $i > $i > $i). 0.41/0.80 thf(decl_387, type, esk73_4: $i > $i > $i > $i > $i). 0.41/0.80 thf(decl_388, type, esk74_4: $i > $i > $i > $i > $i). 0.41/0.80 thf(decl_389, type, esk75_4: $i > $i > $i > $i > $i). 0.41/0.80 thf(decl_390, type, esk76_4: $i > $i > $i > $i > $i). 0.41/0.80 thf(decl_391, type, esk77_4: $i > $i > $i > $i > $i). 0.41/0.80 thf(decl_392, type, esk78_4: $i > $i > $i > $i > $i). 0.41/0.80 thf(decl_393, type, esk79_4: $i > $i > $i > $i > $i). 0.41/0.80 thf(decl_394, type, esk80_3: $i > $i > ($i > $i) > $i). 0.41/0.80 thf(decl_395, type, esk81_3: $i > $i > ($i > $i) > $i). 0.41/0.80 thf(decl_396, type, esk82_3: $i > $i > ($i > $i) > $i). 0.41/0.80 thf(decl_397, type, esk83_3: $i > $i > $i > $i). 0.41/0.80 thf(decl_398, type, esk84_3: $i > $i > $i > $i). 0.41/0.80 thf(decl_399, type, esk85_3: $i > $i > $i > $i). 0.41/0.80 thf(decl_400, type, esk86_3: $i > $i > $i > $i). 0.41/0.80 thf(decl_401, type, esk87_0: $i). 0.41/0.80 thf(decl_402, type, esk88_0: $i). 0.41/0.80 thf(decl_403, type, esk89_0: $i). 0.41/0.80 thf(decl_404, type, esk90_0: $i). 0.41/0.80 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', exu__Cong)). 0.41/0.80 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', exu)). 0.41/0.80 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', exuI1)). 0.41/0.80 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', nonempty)). 0.41/0.80 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', exuE1)). 0.41/0.80 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', descrp)). 0.41/0.80 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', replAx)). 0.41/0.80 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', ex1E1)). 0.41/0.80 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', ex1)). 0.41/0.80 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', ex1I2)). 0.41/0.80 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setOfPairsIsBReln)). 0.41/0.80 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', breln)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', ex1E2)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', ex1I)). 0.41/0.80 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', descr__Cong)). 0.41/0.80 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', exuEu)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', exuE3u)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', exuI2)). 0.41/0.80 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', exuI3)). 0.41/0.80 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', exuE2)). 0.41/0.80 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', nonemptyI)). 0.41/0.80 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', exuE3e)). 0.41/0.80 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', nonemptyE1)). 0.41/0.80 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', dsetconstrER)). 0.41/0.80 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', dsetconstrEL)). 0.41/0.80 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', singletonprop)). 0.41/0.80 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', dpsetconstrERa)). 0.41/0.80 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', dpsetconstrEL2)). 0.41/0.80 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', lamp)). 0.41/0.80 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', lam2p)). 0.41/0.80 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$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.3c3f8yYgNh/E---3.1_6970.p', brelnall1)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', brelnall2)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', lam2lamEq)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', beta2)). 0.41/0.80 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', iffalseProp1)). 0.41/0.80 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.3c3f8yYgNh/E---3.1_6970.p', iftrueProp2)). 0.41/0.80 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', ifSingleton)). 0.41/0.80 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$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.3c3f8yYgNh/E---3.1_6970.p', iftrueProp1)). 0.41/0.80 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', iffalseProp2)). 0.41/0.80 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', eta2)). 0.41/0.80 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', eta1)). 0.41/0.80 thf(beta1, axiom, ((beta1)<=>![X4:$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.3c3f8yYgNh/E---3.1_6970.p', beta1)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', eqbreln)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', subbreln)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', lamProp)). 0.41/0.80 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', apProp)). 0.41/0.80 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.3c3f8yYgNh/E---3.1_6970.p', funcImageSingleton)). 0.41/0.80 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:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', dpsetconstrER)). 0.41/0.80 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', dpsetconstrEL1)). 0.41/0.80 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', dpsetconstrSub)). 0.41/0.80 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', dpsetconstrI)). 0.41/0.80 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', ksndsingleton)). 0.41/0.80 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', kfstsingleton)). 0.41/0.80 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', dsetconstr__Cong)). 0.41/0.80 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', sepSubset)). 0.41/0.80 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', sepInPowerset)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', emptyE1)). 0.41/0.80 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', nonemptyImpWitness)). 0.41/0.80 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setoftrueEq)). 0.41/0.80 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', nonemptyI1)). 0.41/0.80 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setbeta)). 0.41/0.80 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$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.3c3f8yYgNh/E---3.1_6970.p', dsetconstrI)). 0.41/0.80 thf(binunionTILcontra, conjecture, (((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>(((omega0Ax)=>(((((foundationAx)=>((((dsetconstrI)=>(((((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>(((exuE3e)=>((((noeltsimpempty)=>((setbeta)=>(((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>(((setadjoinIR)=>((((setoftrueEq)=>((((((setunionI)=>((setunionE)=>(((exuE2)=>((nonemptyImpWitness)=>(((((singletonsswitch)=>(((upairsetIL)=>(((emptyE1)=>((vacuousDall)=>(((quantDeMorgan2)=>(((quantDeMorgan4)=>(((((notdallE)=>(((exuI3)=>((exuI2)=>((inCongP)=>(((exuE3u)=>((((((setunion__Cong)=>((omega__Cong)=>(((((subsetI1)=>((eqimpsubset2)=>((((emptysetsubset)=>(((subsetE2)=>((notsubsetI)=>((((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>(((setextsub)=>((((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((((binunionIR)=>(((((binunionRsub)=>((((binintersectEL)=>((binintersectLsub)=>(((binintersectSubset3)=>((binintersectER)=>(((binintersectRsub)=>(((binintersectSubset1)=>((bs114d)=>(((setminusEL)=>((setminusER)=>((((((setminusIRneg)=>((setminusLsub)=>((((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>(((setukpairIR)=>((kpairiskpair)=>(((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((((ubforcartprodlem1)=>((ubforcartprodlem2)=>(((cartprodpairin)=>(((cartprodmempair)=>((((setunionsingleton2)=>(((singletonprop)=>((ex1E1)=>(((ex1I2)=>(((setukpairinjL1)=>(((((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>(((upairequniteq)=>((setukpairinjR2)=>((((((cartprodsndin)=>(((((cartprodfstpairEq)=>((cartprodsndpairEq)=>(((((setOfPairsIsBReln)=>((dpsetconstrERa)=>(((dpsetconstrEL2)=>((((((((((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>(((((funcextLem)=>((funcGraphProp4)=>(((((((ap2apEq2)=>((((lam2lamEq)=>((beta2)=>(((iffalseProp1)=>((((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((((((((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>(((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>(((doubleComplementI1)=>((doubleComplementE1)=>((((doubleComplementEq)=>((complementTnotintersectT)=>(((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>(((complementTcontraSubset)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:((![X2:$i]:(((~((in @ X2 @ X21))<=~((in @ X2 @ (binunion @ X21 @ X48))))<=(in @ X2 @ X4)))<=(in @ X48 @ (powerset @ X4)))))))<=(contraSubsetComplement))))<=(complementImpComplementIntersect))))<=(doubleComplementSub2))<=(doubleComplementSub1))))<=(contrasubsetT3)))))<=(binintersectTERcontra)))))<=(powersetTE1))<=(powersetTI1))<=(subsetTI))<=(setextT))<=(complementT_lem))<=(setminusT_lem)))))<=(iftrueorfalse))<=(iffalse)))))))<=(iftrueProp1))<=(iffalseProp2)))<=(eta2))))<=(eta1))<=(beta1)))<=(ap2apEq1))<=(funcext2))<=(funcext))<=(eqbreln))<=(subbreln))))<=(funcGraphProp2))<=(funcGraphProp3))<=(funcGraphProp1)))))))<=(lamProp))<=(funcinfuncset))<=(ap2p))<=(infuncsetfunc))<=(app))<=(apProp))<=(funcImageSingleton))<=(dpsetconstrER)))<=(dpsetconstrEL1))))<=(dpsetconstrSub))<=(dpsetconstrI))<=(cartprodpairsurjEq))))<=(cartprodmempaircEq))<=(cartprodpairmemER))<=(cartprodpairmemEL)))<=(kpairsurjEq))<=(ksndpairEq))<=(ksndsingleton))<=(setukpairinjR))))<=(setukpairinjR1)))))))<=(kfstpairEq))<=(theprop))<=(kfstsingleton)))<=(singletonsuniq)))<=(ex1I))))<=(setunionsingleton)))<=(setunionsingleton1))<=(setunionE2)))<=(cartprodmempair1)))<=(ubforcartprodlem3))))<=(upairinpowunion))<=(upairsubunion))))))<=(kpairp))))<=(setukpairIL)))))))<=(symdiffE))<=(setminusSubset1))))<=(setminusILneg))<=(setminusELneg))<=(setminusERneg))<=(setminusSubset2))))<=(setminusI))))<=(binintersectSubset4)))<=(disjointsetsI1))))<=(binintersectSubset2))))<=(binintersectSubset5))<=(binintersectI)))<=(binunionLsub))<=(binunionE))<=(binunionEcases)))<=(upairset2IR))<=(binunionIL)))))))<=(powersetI1))<=(subsetemptysetimpeq)))<=(subset2powerset))))))<=(notequalI2))<=(notequalI1))))<=(subsetE)))<=(subsetI2))<=(eqimpsubset1))))<=(dsetconstr__Cong))<=(descr__Cong))<=(exuEu))))<=(powerset__Cong))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong)))<=(in__Cong)))))<=(exuI1)))<=(notdexE))<=(prop2set2propI))<=(prop2setI)))<=(quantDeMorgan3)))<=(quantDeMorgan1))))<=(upairsetIR)))<=(upairsetE)))<=(eqinunit))<=(notinsingleton))<=(uniqinunit))))<=(subPowSU))))<=(powersetE))<=(emptyInPowerset))<=(emptyinPowerset))<=(powersetI)))<=(setadjoinOr))<=(setadjoinE)))<=(emptyinunitempty)))))<=(nonemptyE1))))<=(emptyI))<=(setext)))<=(notinemptyset)))))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL)))<=(descrp))<=(wellorderingAx)))<=(replAx))<=(omegaIndAx))<=(omegaSAx)))<=(setunionAx)))))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binunionTILcontra)). 0.41/0.80 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', emptyinunitempty)). 0.41/0.80 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setextAx)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', in__Cong)). 0.41/0.80 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', symdiffIneg1)). 0.41/0.80 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', notdexE)). 0.41/0.80 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', prop2set2propI)). 0.41/0.80 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', symdiffIneg2)). 0.41/0.80 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', prop2setI)). 0.41/0.80 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', quantDeMorgan3)). 0.41/0.80 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', secondinupair)). 0.41/0.80 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', quantDeMorgan1)). 0.41/0.80 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', upairsetIR)). 0.41/0.80 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', upairsetE)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', setukpairIR)). 0.41/0.80 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', eqinunit)). 0.41/0.80 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', notinsingleton)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', kpairiskpair)). 0.41/0.80 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', uniqinunit)). 0.41/0.80 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', subPowSU)). 0.41/0.80 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setminusLsub)). 0.41/0.80 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', powersetE)). 0.41/0.80 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', emptyInPowerset)). 0.41/0.80 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', singletonsubset)). 0.41/0.80 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', emptyinPowerset)). 0.41/0.80 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', powersetI)). 0.41/0.80 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', singletoninpowerset)). 0.41/0.80 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setadjoinOr)). 0.41/0.80 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setadjoinE)). 0.41/0.80 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setukpairinjR12)). 0.41/0.80 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', singletoninpowunion)). 0.41/0.80 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', emptyI)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', setext)). 0.41/0.80 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', upairset2E)). 0.41/0.80 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', notinemptyset)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', ubforcartprodlem1)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', ubforcartprodlem2)). 0.41/0.80 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', wellorderingAx)). 0.41/0.80 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.3c3f8yYgNh/E---3.1_6970.p', omegaIndAx)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', cartprodpairin)). 0.41/0.80 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', omegaSAx)). 0.41/0.80 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setunionAx)). 0.41/0.80 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', cartprodmempair)). 0.41/0.80 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setunionsingleton2)). 0.41/0.80 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', symdiffI1)). 0.41/0.80 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.3c3f8yYgNh/E---3.1_6970.p', setukpairinjL1)). 0.41/0.80 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', cartprodfstin)). 0.41/0.80 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setukpairinjL2)). 0.41/0.80 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setukpairinjL)). 0.41/0.80 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setukpairinjR11)). 0.41/0.80 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', contrasubsetT)). 0.41/0.80 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', contrasubsetT1)). 0.41/0.80 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', upairequniteq)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', setukpairinjR2)). 0.41/0.80 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', cartprodsndin)). 0.41/0.80 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', cartprodfstpairEq)). 0.41/0.80 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', cartprodsndpairEq)). 0.41/0.80 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', symdiffI2)). 0.41/0.80 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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', funcextLem)). 0.41/0.80 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.3c3f8yYgNh/E---3.1_6970.p', funcGraphProp4)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', ap2apEq2)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', ifp)). 0.41/0.80 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', theeq)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', iftrue)). 0.41/0.80 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binintersectT_lem)). 0.41/0.80 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$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.3c3f8yYgNh/E---3.1_6970.p', binunionT_lem)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', powersetT_lem)). 0.41/0.80 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', complementTI1)). 0.41/0.80 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', complementTE1)). 0.41/0.80 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binintersectTELcontra)). 0.41/0.80 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', contrasubsetT2)). 0.41/0.80 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', doubleComplementI1)). 0.41/0.80 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', doubleComplementE1)). 0.41/0.80 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', doubleComplementEq)). 0.41/0.80 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', complementTnotintersectT)). 0.41/0.80 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', complementSubsetComplementIntersect)). 0.41/0.80 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', complementInPowersetComplementIntersect)). 0.41/0.80 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', complementTcontraSubset)). 0.41/0.80 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', contraSubsetComplement)). 0.41/0.80 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', complementImpComplementIntersect)). 0.41/0.80 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', doubleComplementSub2)). 0.41/0.80 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', doubleComplementSub1)). 0.41/0.80 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', contrasubsetT3)). 0.41/0.80 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binintersectTERcontra)). 0.41/0.80 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', powersetTE1)). 0.41/0.80 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', powersetTI1)). 0.41/0.80 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', subsetTI)). 0.41/0.80 thf(setextT, axiom, ((setextT)<=>![X4:$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.3c3f8yYgNh/E---3.1_6970.p', setextT)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', complementT_lem)). 0.41/0.80 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setminusT_lem)). 0.41/0.80 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', iftrueorfalse)). 0.41/0.80 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', iffalse)). 0.41/0.80 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', ap2apEq1)). 0.41/0.80 thf(funcext2, axiom, ((funcext2)<=>![X4:$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.3c3f8yYgNh/E---3.1_6970.p', funcext2)). 0.41/0.80 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', funcext)). 0.41/0.80 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$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.3c3f8yYgNh/E---3.1_6970.p', funcGraphProp2)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', funcGraphProp3)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', funcGraphProp1)). 0.41/0.80 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', funcinfuncset)). 0.41/0.80 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', ap2p)). 0.41/0.80 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', infuncsetfunc)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', app)). 0.41/0.80 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', cartprodpairsurjEq)). 0.41/0.80 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', cartprodmempaircEq)). 0.41/0.80 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', cartprodpairmemER)). 0.41/0.80 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', cartprodpairmemEL)). 0.41/0.80 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', kpairsurjEq)). 0.41/0.80 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', ksndpairEq)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', setukpairinjR)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', setukpairinjR1)). 0.41/0.80 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', kfstpairEq)). 0.41/0.80 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', theprop)). 0.41/0.80 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', singletonsuniq)). 0.41/0.80 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setunionsingleton)). 0.41/0.80 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setunionsingleton1)). 0.41/0.80 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setunionE2)). 0.41/0.80 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', cartprodmempair1)). 0.41/0.80 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', ubforcartprodlem3)). 0.41/0.80 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', upairinpowunion)). 0.41/0.80 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', upairsubunion)). 0.41/0.80 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', kpairp)). 0.41/0.80 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setukpairIL)). 0.41/0.80 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', symdiffE)). 0.41/0.80 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setminusSubset1)). 0.41/0.80 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setminusILneg)). 0.41/0.80 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setminusELneg)). 0.41/0.80 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setminusERneg)). 0.41/0.80 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setminusSubset2)). 0.41/0.80 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setminusI)). 0.41/0.80 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binintersectSubset4)). 0.41/0.80 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', disjointsetsI1)). 0.41/0.80 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binintersectSubset2)). 0.41/0.80 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binintersectSubset5)). 0.41/0.80 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binintersectI)). 0.41/0.80 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binunionLsub)). 0.41/0.80 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binunionE)). 0.41/0.80 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binunionEcases)). 0.41/0.80 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', upairset2IR)). 0.41/0.80 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binunionIL)). 0.41/0.80 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', powersetI1)). 0.41/0.80 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', subsetemptysetimpeq)). 0.41/0.80 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', subset2powerset)). 0.41/0.80 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', notequalI2)). 0.41/0.80 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', notequalI1)). 0.41/0.80 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', subsetE)). 0.41/0.80 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', subsetI2)). 0.41/0.80 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', eqimpsubset1)). 0.41/0.80 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', powerset__Cong)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', setadjoin__Cong)). 0.41/0.80 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', emptyset__Cong)). 0.41/0.80 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setminusIRneg)). 0.41/0.80 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setminusER)). 0.41/0.80 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setminusEL)). 0.41/0.80 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', bs114d)). 0.41/0.80 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binintersectSubset1)). 0.41/0.80 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binintersectRsub)). 0.41/0.80 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binintersectER)). 0.41/0.80 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binintersectSubset3)). 0.41/0.80 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binintersectLsub)). 0.41/0.80 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binintersectEL)). 0.41/0.80 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binunionRsub)). 0.41/0.80 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', binunionIR)). 0.41/0.80 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', powersetsubset)). 0.41/0.80 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', inPowerset)). 0.41/0.80 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', powersetE1)). 0.41/0.80 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setextsub)). 0.41/0.80 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setadjoinSub2)). 0.41/0.80 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setadjoinSub)). 0.41/0.80 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', subsetTrans)). 0.41/0.80 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', subsetRefl)). 0.41/0.80 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', notsubsetI)). 0.41/0.80 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', subsetE2)). 0.41/0.80 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', emptysetsubset)). 0.41/0.80 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', eqimpsubset2)). 0.41/0.80 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', subsetI1)). 0.41/0.80 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', omega__Cong)). 0.41/0.80 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setunion__Cong)). 0.41/0.80 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', inCongP)). 0.41/0.80 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', notdallE)). 0.41/0.80 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', quantDeMorgan4)). 0.41/0.80 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', quantDeMorgan2)). 0.41/0.80 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', vacuousDall)). 0.41/0.80 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', upairsetIL)). 0.41/0.80 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', singletonsswitch)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', setunionE)). 0.41/0.80 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setunionI)). 0.41/0.80 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setadjoinIR)). 0.41/0.80 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setadjoinIL)). 0.41/0.80 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', noeltsimpempty)). 0.41/0.80 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', emptysetimpfalse)). 0.41/0.80 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', emptysetE)). 0.41/0.80 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', prop2setE)). 0.41/0.80 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.3c3f8yYgNh/E---3.1_6970.p', foundationAx)). 0.41/0.80 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', omega0Ax)). 0.41/0.80 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', powersetAx)). 0.41/0.80 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', setadjoinAx)). 0.41/0.80 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.3c3f8yYgNh/E---3.1_6970.p', emptysetAx)). 0.41/0.80 thf(c_0_259, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 0.41/0.80 thf(c_0_260, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 0.41/0.80 thf(c_0_261, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 0.41/0.80 thf(c_0_262, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 0.41/0.80 thf(c_0_263, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 0.41/0.80 thf(c_0_264, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 0.41/0.80 thf(c_0_265, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.41/0.80 thf(c_0_266, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 0.41/0.80 thf(c_0_267, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])). 0.41/0.80 thf(c_0_268, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 0.41/0.80 thf(c_0_269, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 0.41/0.80 thf(c_0_270, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])). 0.41/0.80 thf(c_0_271, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])). 0.41/0.80 thf(c_0_272, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])). 0.41/0.80 thf(c_0_273, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 0.41/0.80 thf(c_0_274, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 0.41/0.80 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])). 0.41/0.80 thf(c_0_276, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 0.41/0.80 thf(c_0_277, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 0.41/0.80 thf(c_0_278, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 0.41/0.80 thf(c_0_279, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.41/0.80 thf(c_0_280, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.41/0.80 thf(c_0_281, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X858:$i]:((((X1 @ X858))&![X859:$i]:((((X1 @ X859))=>((X858)=(X859)))))))<=>(?[X860:$i]:((((X17 @ X860))&![X861:$i]:((((X17 @ X861))=>((X860)=(X861)))))))))))), inference(apply_def,[status(thm)],[c_0_259, c_0_260])). 0.41/0.80 thf(c_0_282, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X850:$i]:((((X1 @ X850))&![X851:$i]:((((X1 @ X851))=>((X850)=(X851))))))))))), inference(apply_def,[status(thm)],[c_0_261, c_0_260])). 0.41/0.80 thf(c_0_283, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_262])). 0.41/0.80 thf(c_0_284, plain, ((exuE1)=(![X1:$i > $o]:(((?[X844:$i]:((((X1 @ X844))&![X845:$i]:((((X1 @ X845))=>((X844)=(X845)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_263, c_0_260])). 0.41/0.80 thf(c_0_285, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.41/0.80 thf(c_0_286, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.41/0.80 thf(c_0_287, plain, ((descrp)=(![X1:$i > $o]:(((?[X842:$i]:((((X1 @ X842))&![X843:$i]:((((X1 @ X843))=>((X842)=(X843)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_264, c_0_260])). 0.41/0.80 thf(c_0_288, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X840:$i]:((((X6 @ X2 @ X840))&![X841:$i]:((((X6 @ X2 @ X841))=>((X840)=(X841)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_265, c_0_260])). 0.41/0.80 thf(c_0_289, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 0.41/0.80 thf(c_0_290, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_266, c_0_267])). 0.41/0.80 thf(c_0_291, plain, ((ex1I2)=(![X4:$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)))=>((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))))))), inference(apply_def,[status(thm)],[c_0_268, c_0_267])). 0.41/0.80 thf(c_0_292, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_269, c_0_270])). 0.41/0.80 thf(c_0_293, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 0.41/0.80 thf(c_0_294, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 0.41/0.80 thf(c_0_295, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 0.41/0.80 thf(c_0_296, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 0.41/0.80 thf(c_0_297, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_270])). 0.41/0.80 thf(c_0_298, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_270])). 0.41/0.80 thf(c_0_299, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_271, c_0_267])). 0.41/0.80 thf(c_0_300, 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])). 0.41/0.80 thf(c_0_301, 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])). 0.41/0.80 thf(c_0_302, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 0.41/0.80 thf(c_0_303, plain, ((iftrueProp2)<=>![X4:$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])). 0.41/0.80 thf(c_0_304, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 0.41/0.80 thf(c_0_305, plain, ((iftrueProp1)<=>![X4:$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])). 0.41/0.80 thf(c_0_306, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])). 0.41/0.80 thf(c_0_307, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])). 0.41/0.80 thf(c_0_308, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])). 0.41/0.80 thf(c_0_309, plain, ((beta1)<=>![X4:$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])). 0.41/0.80 thf(c_0_310, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_270])). 0.41/0.80 thf(c_0_311, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln, c_0_270])). 0.41/0.80 thf(c_0_312, 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])). 0.41/0.80 thf(c_0_313, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 0.41/0.80 thf(c_0_314, plain, ((funcImageSingleton)<=>![X4:$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])). 0.41/0.80 thf(c_0_315, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 0.41/0.80 thf(c_0_316, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 0.41/0.80 thf(c_0_317, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 0.41/0.80 thf(c_0_318, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 0.41/0.80 thf(c_0_319, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 0.41/0.80 thf(c_0_320, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 0.41/0.80 thf(c_0_321, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))))))))), inference(apply_def,[status(thm)],[c_0_272, c_0_267])). 0.41/0.80 thf(c_0_322, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 0.41/0.80 thf(c_0_323, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X864:$i]:((((X1 @ X864))&![X865:$i]:((((X1 @ X865))=>((X864)=(X865)))))))=>((?[X866:$i]:((((X17 @ X866))&![X867:$i]:((((X17 @ X867))=>((X866)=(X867)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_273, c_0_260])). 0.41/0.80 thf(c_0_324, plain, ((exuEu)=(![X1:$i > $o]:(((?[X862:$i]:((((X1 @ X862))&![X863:$i]:((((X1 @ X863))=>((X862)=(X863)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_274, c_0_260])). 0.41/0.80 thf(c_0_325, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 0.41/0.80 thf(c_0_326, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 0.41/0.80 thf(c_0_327, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X856:$i]:((((X1 @ X856))&![X857:$i]:((((X1 @ X857))=>((X856)=(X857)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_275, c_0_260])). 0.41/0.80 thf(c_0_328, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X854:$i]:((((X1 @ X854))&![X855:$i]:((((X1 @ X855))=>((X854)=(X855))))))))))), inference(apply_def,[status(thm)],[c_0_276, c_0_260])). 0.41/0.80 thf(c_0_329, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X852:$i]:((((X1 @ X852))&![X853:$i]:((((X1 @ X853))=>((X852)=(X853)))))))))))), inference(apply_def,[status(thm)],[c_0_277, c_0_260])). 0.41/0.80 thf(c_0_330, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 0.41/0.80 thf(c_0_331, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_262])). 0.41/0.80 thf(c_0_332, plain, ((exuE2)=(![X1:$i > $o]:(((?[X848:$i]:((((X1 @ X848))&![X849:$i]:((((X1 @ X849))=>((X848)=(X849)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_278, c_0_260])). 0.41/0.80 thf(c_0_333, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.41/0.80 thf(c_0_334, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_262])). 0.41/0.80 thf(c_0_335, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_279, c_0_262])). 0.41/0.80 thf(c_0_336, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.41/0.80 thf(c_0_337, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X846:$i]:((((X1 @ X846))&![X847:$i]:((((X1 @ X847))=>((X846)=(X847)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_280, c_0_260])). 0.41/0.80 thf(c_0_338, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.41/0.80 thf(c_0_339, plain, ((epred1_0)<=>![X1646:$i]:(?[X1647:$i]:((((![X1648:$i]:(((in @ X1648 @ X1647)=>![X1649:$i]:(((in @ X1649 @ X1648)=>(in @ X1649 @ X1646)))))&![X1650:$i, X1651:$i]:((((in @ X1650 @ X1646)&(in @ X1651 @ X1646))=>(![X1652:$i]:(((in @ X1652 @ X1647)=>((in @ X1650 @ X1652)<=>(in @ X1651 @ X1652))))=>((X1650)=(X1651))))))&![X1653:$i, X1654:$i]:((((in @ X1653 @ X1647)&(in @ X1654 @ X1647))=>(![X1655:$i]:(((in @ X1655 @ X1653)=>(in @ X1655 @ X1654)))|![X1656:$i]:(((in @ X1656 @ X1654)=>(in @ X1656 @ X1653)))))))&![X1657:$i]:(((![X1658:$i]:(((in @ X1658 @ X1657)=>(in @ X1658 @ X1646)))&?[X1659:$i]:((in @ X1659 @ X1657)))=>?[X1660:$i, X1661:$i]:(((((in @ X1660 @ X1647)&(in @ X1661 @ X1657))&~(?[X1662:$i]:(((in @ X1662 @ X1660)&(in @ X1662 @ X1657)))))&![X1663:$i]:(((in @ X1663 @ X1647)=>(![X1664:$i]:(((in @ X1664 @ X1663)=>(in @ X1664 @ X1660)))|(in @ X1661 @ X1663)))))))))))), introduced(definition)). 0.41/0.80 thf(c_0_340, negated_conjecture, ~((![X1680:$i, X1681:$i]:((![X1682:$i]:(((in @ X1682 @ X1680)<=>(in @ X1682 @ X1681)))=>((X1680)=(X1681))))=>(![X868:$i]:(~(in @ X868 @ emptyset))=>(![X869:$i, X870:$i, X871:$i]:(((in @ X871 @ (setadjoin @ X869 @ X870))<=>(((X871)=(X869))|(in @ X871 @ X870))))=>(![X872:$i, X873:$i]:(((in @ X873 @ (powerset @ X872))<=>![X874:$i]:(((in @ X874 @ X873)=>(in @ X874 @ X872)))))=>(![X1677:$i, X1678:$i]:(((in @ X1678 @ (setunion @ X1677))<=>?[X1679:$i]:(((in @ X1678 @ X1679)&(in @ X1679 @ X1677)))))=>((in @ emptyset @ omega)=>(![X1676:$i]:(((in @ X1676 @ omega)=>(in @ (setadjoin @ X1676 @ X1676) @ omega)))=>(![X1673:$i]:((((in @ emptyset @ X1673)&![X1674:$i]:((((in @ X1674 @ omega)&(in @ X1674 @ X1673))=>(in @ (setadjoin @ X1674 @ X1674) @ X1673))))=>![X1675:$i]:(((in @ X1675 @ omega)=>(in @ X1675 @ X1673)))))=>(![X1665:$i > $i > $o, X1666:$i]:((![X1667:$i]:(((in @ X1667 @ X1666)=>?[X1668:$i]:(((X1665 @ X1667 @ X1668)&![X1669:$i]:(((X1665 @ X1667 @ X1669)=>((X1668)=(X1669))))))))=>?[X1670:$i]:(![X1671:$i]:(((in @ X1671 @ X1670)<=>?[X1672:$i]:(((in @ X1672 @ X1666)&(X1665 @ X1672 @ X1671))))))))=>(![X875:$i]:((?[X876:$i]:((in @ X876 @ X875))=>?[X877:$i]:(((in @ X877 @ X875)&~(?[X878:$i]:(((in @ X878 @ X877)&(in @ X878 @ X875))))))))=>((epred1_0)=>(![X1643:$i > $o]:((?[X1644:$i]:(((X1643 @ X1644)&![X1645:$i]:(((X1643 @ X1645)=>((X1644)=(X1645))))))=>(X1643 @ (descr @ (^[Z0/* 17 */:$i]:(X1643 @ Z0))))))=>(![X879:$i, X880:$i > $o, X881:$i]:(((in @ X881 @ X879)=>((X880 @ X881)=>(in @ X881 @ (dsetconstr @ X879 @ X880)))))=>(![X1640:$i, X1641:$i > $o, X1642:$i]:(((in @ X1642 @ (dsetconstr @ X1640 @ X1641))=>(in @ X1642 @ X1640)))=>(![X1637:$i, X1638:$i > $o, X1639:$i]:(((in @ X1639 @ (dsetconstr @ X1637 @ X1638))=>(X1638 @ X1639)))=>(![X1632:$i > $o]:((?[X1633:$i]:(((X1632 @ X1633)&![X1634:$i]:(((X1632 @ X1634)=>((X1633)=(X1634))))))=>?[X1635:$i]:(((X1632 @ X1635)&![X1636:$i]:(((X1632 @ X1636)=>((X1635)=(X1636))))))))=>(![X882:$o, X883:$i]:(((in @ X883 @ (prop2set @ ((X882))))=>(X882)))=>(![X884:$i]:(((in @ X884 @ emptyset)=>![X885:$o]:((X885))))=>(![X886:$i]:(((in @ X886 @ emptyset)=>~($true)))=>(![X1631:$i]:(~(in @ X1631 @ emptyset))=>(![X887:$i > $o]:((?[X888:$i]:(((X887 @ X888)&![X889:$i]:(((X887 @ X889)=>((X888)=(X889))))))=>?[X890:$i]:((X887 @ X890))))=>(![X1627:$i, X1628:$i]:((![X1629:$i]:(((in @ X1629 @ X1627)=>(in @ X1629 @ X1628)))=>(![X1630:$i]:(((in @ X1630 @ X1628)=>(in @ X1630 @ X1627)))=>((X1627)=(X1628)))))=>(![X1625:$i]:((![X1626:$i]:(~(in @ X1626 @ X1625))=>((X1625)=(emptyset))))=>(![X891:$i]:((![X892:$i]:(~(in @ X892 @ X891))=>((X891)=(emptyset))))=>(![X893:$i, X894:$i > $o, X895:$i]:(((in @ X895 @ X893)=>((in @ X895 @ (dsetconstr @ X893 @ X894))<=>(X894 @ X895))))=>(![X1623:$i]:((((X1623)!=(emptyset))=>?[X1624:$i]:((in @ X1624 @ X1623))))=>(![X896:$i, X897:$i > $o, X898:$i]:(((in @ X898 @ X896)=>((X897 @ X898)=>((dsetconstr @ X896 @ X897)!=(emptyset)))))=>(![X899:$i]:((?[X900:$i]:((in @ X900 @ X899))=>((X899)!=(emptyset))))=>(![X901:$i, X902:$i]:((in @ X901 @ (setadjoin @ X901 @ X902)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X903:$i, X904:$i, X905:$i]:(((in @ X905 @ X904)=>(in @ X905 @ (setadjoin @ X903 @ X904))))=>(![X1619:$i, X1620:$i, X1621:$i]:(((in @ X1621 @ (setadjoin @ X1619 @ X1620))=>![X1622:$o]:(((((X1621)=(X1619))=>(X1622))=>(((in @ X1621 @ X1620)=>(X1622))=>(X1622))))))=>(![X1616:$i, X1617:$i, X1618:$i]:(((in @ X1618 @ (setadjoin @ X1616 @ X1617))=>(((X1618)=(X1616))|(in @ X1618 @ X1617))))=>(![X906:$i]:(((dsetconstr @ X906 @ (^[Z0/* 1 */:$i]:($true)))=(X906)))=>(![X1613:$i, X1614:$i]:((![X1615:$i]:(((in @ X1615 @ X1614)=>(in @ X1615 @ X1613)))=>(in @ X1614 @ (powerset @ X1613))))=>(![X1612:$i]:((in @ emptyset @ (powerset @ X1612)))=>(![X1611:$i]:((in @ emptyset @ (powerset @ X1611)))=>(![X1608:$i, X1609:$i, X1610:$i]:(((in @ X1609 @ (powerset @ X1608))=>((in @ X1610 @ X1609)=>(in @ X1610 @ X1608))))=>(![X907:$i, X908:$i, X909:$i]:(((in @ X908 @ X909)=>((in @ X909 @ X907)=>(in @ X908 @ (setunion @ X907)))))=>(![X910:$i, X911:$i]:(((in @ X911 @ (setunion @ X910))=>![X912:$o]:((![X913:$i]:(((in @ X911 @ X913)=>((in @ X913 @ X910)=>(X912))))=>(X912)))))=>(![X1606:$i, X1607:$i]:(((in @ X1607 @ X1606)=>(in @ X1607 @ (powerset @ (setunion @ X1606)))))=>(![X914:$i > $o]:((?[X915:$i]:(((X914 @ X915)&![X916:$i]:(((X914 @ X916)=>((X915)=(X916))))))=>?[X917:$i]:(![X918:$i]:(((X914 @ X918)<=>((X918)=(X917)))))))=>(![X919:$i]:((((X919)!=(emptyset))=>?[X920:$i]:(((in @ X920 @ X919)&$true))))=>(![X1604:$i, X1605:$i]:(((in @ X1604 @ (setadjoin @ X1605 @ emptyset))=>((X1604)=(X1605))))=>(![X1602:$i, X1603:$i]:((((X1602)!=(X1603))=>~(in @ X1603 @ (setadjoin @ X1602 @ emptyset))))=>(![X1600:$i, X1601:$i]:((((X1600)=(X1601))=>(in @ X1600 @ (setadjoin @ X1601 @ emptyset))))=>(![X921:$i, X922:$i]:(((in @ X921 @ (setadjoin @ X922 @ emptyset))=>(in @ X922 @ (setadjoin @ X921 @ emptyset))))=>(![X1597:$i, X1598:$i, X1599:$i]:(((in @ X1599 @ (setadjoin @ X1597 @ (setadjoin @ X1598 @ emptyset)))=>(((X1599)=(X1597))|((X1599)=(X1598)))))=>(![X923:$i, X924:$i]:((in @ X923 @ (setadjoin @ X923 @ (setadjoin @ X924 @ emptyset))))=>(![X1595:$i, X1596:$i]:((in @ X1596 @ (setadjoin @ X1595 @ (setadjoin @ X1596 @ emptyset))))=>(![X925:$i, X926:$i > $o]:((?[X927:$i]:(((in @ X927 @ X925)&(X926 @ X927)))=>(((dsetconstr @ X925 @ X926)=(emptyset))=>~($true))))=>(![X928:$i > $o, X929:$i]:(((in @ X929 @ emptyset)=>(X928 @ X929)))=>(![X1591:$i, X1592:$i > $o]:((~(![X1593:$i]:(((in @ X1593 @ X1591)=>(X1592 @ X1593))))=>?[X1594:$i]:(((in @ X1594 @ X1591)&~((X1592 @ X1594))))))=>(![X930:$i, X931:$i > $o]:((![X932:$i]:(((in @ X932 @ X930)=>~((X931 @ X932))))=>~(?[X933:$i]:(((in @ X933 @ X930)&(X931 @ X933))))))=>(![X1587:$i, X1588:$i > $o]:((~(?[X1589:$i]:(((in @ X1589 @ X1587)&(X1588 @ X1589))))=>![X1590:$i]:(((in @ X1590 @ X1587)=>~((X1588 @ X1590))))))=>(![X934:$i, X935:$i > $o]:((?[X936:$i]:(((in @ X936 @ X934)&~((X935 @ X936))))=>~(![X937:$i]:(((in @ X937 @ X934)=>(X935 @ X937))))))=>(![X1586:$o]:(((X1586)=>(in @ emptyset @ (prop2set @ ((X1586))))))=>(![X1585:$o]:(((X1585)=>(set2prop @ (prop2set @ ((X1585))))))=>(![X1581:$i, X1582:$i > $o]:((~(?[X1583:$i]:(((in @ X1583 @ X1581)&(X1582 @ X1583))))=>![X1584:$i]:(((in @ X1584 @ X1581)=>~((X1582 @ X1584))))))=>(![X938:$i, X939:$i > $o]:((~(![X940:$i]:(((in @ X940 @ X938)=>(X939 @ X940))))=>?[X941:$i]:(((in @ X941 @ X938)&~((X939 @ X941))))))=>(![X1576:$i > $o]:((?[X1577:$i]:(((X1576 @ X1577)&![X1578:$i]:(((X1576 @ X1578)=>((X1577)=(X1578))))))=>?[X1579:$i]:(((X1576 @ X1579)&![X1580:$i]:(((X1576 @ X1580)=>((X1579)=(X1580))))))))=>(![X942:$i > $o]:((?[X943:$i]:((X942 @ X943))=>(![X944:$i, X945:$i]:(((X942 @ X944)=>((X942 @ X945)=>((X944)=(X945)))))=>?[X946:$i]:(((X942 @ X946)&![X947:$i]:(((X942 @ X947)=>((X946)=(X947)))))))))=>(![X948:$i > $o]:((?[X949:$i]:(![X950:$i]:(((X948 @ X950)<=>((X950)=(X949)))))=>?[X951:$i]:(((X948 @ X951)&![X952:$i]:(((X948 @ X952)=>((X951)=(X952))))))))=>(![X953:$i, X954:$i]:((((X953)=(X954))=>![X955:$i, X956:$i]:((((X955)=(X956))=>((in @ X955 @ X953)=>(in @ X956 @ X954))))))=>(![X1572:$i, X1573:$i]:((((X1572)=(X1573))=>![X1574:$i, X1575:$i]:((((X1574)=(X1575))=>((in @ X1574 @ X1572)<=>(in @ X1575 @ X1573))))))=>(![X957:$i > $o]:((?[X958:$i]:(((X957 @ X958)&![X959:$i]:(((X957 @ X959)=>((X958)=(X959))))))=>![X960:$i, X961:$i]:(((X957 @ X960)=>((X957 @ X961)=>((X960)=(X961)))))))=>(![X1564:$i > $o, X1565:$i > $o]:((![X1566:$i, X1567:$i]:((((X1566)=(X1567))=>((X1564 @ X1566)<=>(X1565 @ X1567))))=>(?[X1568:$i]:(((X1564 @ X1568)&![X1569:$i]:(((X1564 @ X1569)=>((X1568)=(X1569))))))<=>?[X1570:$i]:(((X1565 @ X1570)&![X1571:$i]:(((X1565 @ X1571)=>((X1570)=(X1571)))))))))=>(((emptyset)=(emptyset))=>(![X1560:$i, X1561:$i]:((((X1560)=(X1561))=>![X1562:$i, X1563:$i]:((((X1562)=(X1563))=>((setadjoin @ X1560 @ X1562)=(setadjoin @ X1561 @ X1563))))))=>(![X1558:$i, X1559:$i]:((((X1558)=(X1559))=>((powerset @ 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inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[binunionTILcontra]), emptyinunitempty]), setextAx]), c_0_281]), in__Cong]), symdiffIneg1]), c_0_282]), notdexE]), prop2set2propI]), symdiffIneg2]), prop2setI]), quantDeMorgan3]), secondinupair]), quantDeMorgan1]), upairsetIR]), upairsetE]), setukpairIR]), eqinunit]), notinsingleton]), kpairiskpair]), uniqinunit]), subPowSU]), setminusLsub]), powersetE]), emptyInPowerset]), singletonsubset]), emptyinPowerset]), powersetI]), singletoninpowerset]), setadjoinOr]), setadjoinE]), setukpairinjR12]), c_0_283]), singletoninpowunion]), emptyI]), setext]), upairset2E]), notinemptyset]), c_0_284]), c_0_285]), ubforcartprodlem1]), c_0_286]), c_0_287]), ubforcartprodlem2]), wellorderingAx]), c_0_288]), omegaIndAx]), cartprodpairin]), omegaSAx]), setunionAx]), cartprodmempair]), setunionsingleton2]), c_0_289]), symdiffI1]), c_0_290]), c_0_291]), setukpairinjL1]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), contrasubsetT]), contrasubsetT1]), upairequniteq]), setukpairinjR2]), cartprodsndin]), cartprodfstpairEq]), cartprodsndpairEq]), c_0_292]), c_0_293]), c_0_294]), symdiffI2]), c_0_295]), c_0_296]), c_0_297]), c_0_298]), c_0_299]), funcextLem]), funcGraphProp4]), ap2apEq2]), c_0_300]), c_0_301]), c_0_302]), c_0_303]), c_0_304]), ifp]), theeq]), iftrue]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), complementTI1]), complementTE1]), binintersectTELcontra]), contrasubsetT2]), doubleComplementI1]), doubleComplementE1]), doubleComplementEq]), complementTnotintersectT]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), complementTcontraSubset]), contraSubsetComplement]), complementImpComplementIntersect]), doubleComplementSub2]), doubleComplementSub1]), contrasubsetT3]), binintersectTERcontra]), powersetTE1]), powersetTI1]), subsetTI]), setextT]), complementT_lem]), setminusT_lem]), iftrueorfalse]), iffalse]), c_0_305]), c_0_306]), c_0_307]), c_0_308]), c_0_309]), ap2apEq1]), funcext2]), funcext]), c_0_310]), c_0_311]), funcGraphProp2]), funcGraphProp3]), funcGraphProp1]), c_0_312]), funcinfuncset]), ap2p]), infuncsetfunc]), app]), c_0_313]), c_0_314]), c_0_315]), c_0_316]), c_0_317]), c_0_318]), cartprodpairsurjEq]), cartprodmempaircEq]), cartprodpairmemER]), cartprodpairmemEL]), kpairsurjEq]), ksndpairEq]), c_0_319]), setukpairinjR]), setukpairinjR1]), kfstpairEq]), theprop]), c_0_320]), singletonsuniq]), c_0_321]), setunionsingleton]), setunionsingleton1]), setunionE2]), cartprodmempair1]), ubforcartprodlem3]), upairinpowunion]), upairsubunion]), kpairp]), setukpairIL]), symdiffE]), setminusSubset1]), setminusILneg]), setminusELneg]), setminusERneg]), setminusSubset2]), setminusI]), binintersectSubset4]), disjointsetsI1]), binintersectSubset2]), binintersectSubset5]), binintersectI]), binunionLsub]), binunionE]), binunionEcases]), upairset2IR]), binunionIL]), powersetI1]), subsetemptysetimpeq]), subset2powerset]), notequalI2]), notequalI1]), subsetE]), subsetI2]), eqimpsubset1]), c_0_322]), c_0_323]), c_0_324]), powerset__Cong]), setadjoin__Cong]), emptyset__Cong]), setminusIRneg]), setminusER]), setminusEL]), bs114d]), binintersectSubset1]), binintersectRsub]), binintersectER]), binintersectSubset3]), binintersectLsub]), binintersectEL]), binunionRsub]), binunionIR]), c_0_325]), c_0_326]), powersetsubset]), inPowerset]), powersetE1]), setextsub]), setadjoinSub2]), setadjoinSub]), subsetTrans]), subsetRefl]), notsubsetI]), subsetE2]), emptysetsubset]), eqimpsubset2]), subsetI1]), omega__Cong]), setunion__Cong]), c_0_327]), inCongP]), c_0_328]), c_0_329]), notdallE]), quantDeMorgan4]), quantDeMorgan2]), vacuousDall]), c_0_330]), upairsetIL]), singletonsswitch]), c_0_331]), c_0_332]), setunionE]), setunionI]), c_0_333]), setadjoinIR]), setadjoinIL]), c_0_334]), c_0_335]), c_0_336]), noeltsimpempty]), c_0_337]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_338]), foundationAx]), omega0Ax]), powersetAx]), setadjoinAx]), emptysetAx])])]), c_0_339])). 0.41/0.80 thf(c_0_341, negated_conjecture, ![X1683:$i, X1684:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1696:$i, X1697:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1705:$i, X1706:$i > $i > $o, X1707:$i, X1709:$i, X1712:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$i, X1719:$i, X1720:$i > $o, X1721:$i, X1723:$i, X1724:$i > $o, X1725:$i, X1726:$i, X1727:$i > $o, X1728:$i, X1729:$i, X1730:$i > $o, X1731:$i, X1732:$i > $o, X1733:$i, X1736:$i, X1737:$o, X1738:$i, X1739:$i, X1740:$o, X1741:$i, X1742:$i, X1743:$i > $o, X1744:$i, X1747:$i, X1748:$i, X1751:$i, X1753:$i, X1755:$i, X1756:$i > $o, X1757:$i, X1758:$i, X1760:$i, X1761:$i > $o, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i, X1773:$o, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$o, X1793:$i, X1794:$i, X1795:$i > $o, X1796:$i, X1799:$i, X1800:$i, X1801:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i > $o, X1820:$i, X1821:$i > $o, X1822:$i, X1823:$i, X1824:$i > $o, X1825:$i, X1827:$i, X1828:$i > $o, X1830:$i, X1831:$i, X1832:$i > $o, X1834:$i, X1835:$i, X1836:$i > $o, X1837:$i, X1839:$o, X1840:$o, X1841:$i, X1842:$i > $o, X1844:$i, X1845:$i, X1846:$i > $o, X1847:$i, X1849:$i > $o, X1850:$i, X1853:$i, X1854:$i > $o, X1855:$i, X1859:$i, X1860:$i > $o, X1861:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i > $o, X1874:$i, X1876:$i, X1877:$i, X1878:$i > $o, X1879:$i > $o, X1882:$i, X1885:$i, X1886:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i > $o, X1899:$i, X1901:$i, X1902:$i, X1903:$i > $o, X1904:$i > $o, X1907:$i, X1909:$i, X1911:$i, X1912:$i, X1913:$i > $o, X1914:$i > $o, X1917:$i, X1918:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1927:$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 > $o, X1965:$i, X1966:$i > $o, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$o, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$o, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i > $o, X2121:$i, X2122:$i, X2123:$i > $o, X2125:$i, X2126:$i > $o, X2127:$i, X2129:$i, X2130:$i > $o, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i > $i > $o, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i > $i > $o, X2211:$i, X2212:$i, X2213:$i > $i > $o, X2214:$i, X2215:$i, X2216:$i > $i > $o, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i > $i > $o, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i > $i > $o, X2227:$i, X2228:$i, X2229:$i, X2230:$i, X2231:$i > $i > $o, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i > $i, X2260:$i, X2261:$i, X2262:$i > $i, X2264:$i, X2265:$i, X2266:$i > $i, X2268:$i, X2269:$i, X2270:$i, X2271:$i > $o, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i > $o, X2281:$i, X2282:$i, X2283:$i > $o, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2325:$i, X2326:$i, 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(esk74_4 @ X2317 @ X2318 @ X2319 @ X2320) @ X2317)|~(subset @ X2320 @ (cartprod @ X2317 @ X2318))|~(subset @ X2319 @ (cartprod @ X2317 @ X2318))))))&((((in @ (esk76_4 @ X2317 @ X2318 @ X2319 @ X2320) @ X2317)|((X2319)=(X2320))|(in @ (esk75_4 @ X2317 @ X2318 @ X2319 @ X2320) @ X2318)|~(subset @ X2320 @ (cartprod @ X2317 @ X2318))|~(subset @ X2319 @ (cartprod @ X2317 @ X2318)))&(((in @ (esk77_4 @ X2317 @ X2318 @ X2319 @ X2320) @ X2318)|((X2319)=(X2320))|(in @ (esk75_4 @ X2317 @ X2318 @ X2319 @ X2320) @ X2318)|~(subset @ X2320 @ (cartprod @ X2317 @ X2318))|~(subset @ X2319 @ (cartprod @ X2317 @ X2318)))&(((in @ (kpair @ (esk76_4 @ X2317 @ X2318 @ X2319 @ X2320) @ (esk77_4 @ X2317 @ X2318 @ X2319 @ X2320)) @ X2320)|((X2319)=(X2320))|(in @ (esk75_4 @ X2317 @ X2318 @ X2319 @ X2320) @ X2318)|~(subset @ X2320 @ (cartprod @ X2317 @ X2318))|~(subset @ X2319 @ (cartprod @ X2317 @ X2318)))&(~(in @ (kpair @ (esk76_4 @ X2317 @ X2318 @ X2319 @ X2320) @ (esk77_4 @ X2317 @ X2318 @ X2319 @ X2320)) @ X2319)|((X2319)=(X2320))|(in @ (esk75_4 @ X2317 @ X2318 @ X2319 @ X2320) @ X2318)|~(subset @ X2320 @ (cartprod @ X2317 @ X2318))|~(subset @ X2319 @ (cartprod @ X2317 @ X2318))))))&((((in @ (esk76_4 @ X2317 @ X2318 @ X2319 @ X2320) @ X2317)|((X2319)=(X2320))|(in @ (kpair @ (esk74_4 @ X2317 @ X2318 @ X2319 @ X2320) @ (esk75_4 @ X2317 @ X2318 @ X2319 @ X2320)) @ X2319)|~(subset @ X2320 @ (cartprod @ X2317 @ X2318))|~(subset @ X2319 @ (cartprod @ X2317 @ X2318)))&(((in @ (esk77_4 @ X2317 @ X2318 @ X2319 @ X2320) @ X2318)|((X2319)=(X2320))|(in @ (kpair @ (esk74_4 @ X2317 @ X2318 @ X2319 @ X2320) @ (esk75_4 @ X2317 @ X2318 @ X2319 @ X2320)) @ X2319)|~(subset @ X2320 @ (cartprod @ X2317 @ X2318))|~(subset @ X2319 @ (cartprod @ X2317 @ X2318)))&(((in @ (kpair @ (esk76_4 @ X2317 @ X2318 @ X2319 @ X2320) @ (esk77_4 @ X2317 @ X2318 @ X2319 @ X2320)) @ X2320)|((X2319)=(X2320))|(in @ (kpair @ (esk74_4 @ X2317 @ X2318 @ X2319 @ X2320) @ (esk75_4 @ X2317 @ X2318 @ X2319 @ X2320)) @ X2319)|~(subset @ X2320 @ (cartprod @ X2317 @ X2318))|~(subset @ X2319 @ (cartprod @ X2317 @ X2318)))&(~(in @ (kpair @ (esk76_4 @ X2317 @ X2318 @ X2319 @ X2320) @ (esk77_4 @ X2317 @ X2318 @ X2319 @ X2320)) @ X2319)|((X2319)=(X2320))|(in @ (kpair @ (esk74_4 @ X2317 @ X2318 @ X2319 @ X2320) @ (esk75_4 @ X2317 @ X2318 @ X2319 @ X2320)) @ X2319)|~(subset @ X2320 @ (cartprod @ X2317 @ X2318))|~(subset @ X2319 @ (cartprod @ X2317 @ X2318))))))&(((in @ (esk76_4 @ X2317 @ X2318 @ X2319 @ X2320) @ X2317)|((X2319)=(X2320))|~(in @ (kpair @ (esk74_4 @ X2317 @ X2318 @ X2319 @ X2320) @ (esk75_4 @ X2317 @ X2318 @ X2319 @ X2320)) @ X2320)|~(subset @ X2320 @ (cartprod @ X2317 @ X2318))|~(subset @ X2319 @ (cartprod @ X2317 @ X2318)))&(((in @ (esk77_4 @ X2317 @ X2318 @ X2319 @ X2320) @ X2318)|((X2319)=(X2320))|~(in @ (kpair @ (esk74_4 @ X2317 @ X2318 @ X2319 @ X2320) @ (esk75_4 @ X2317 @ X2318 @ X2319 @ X2320)) @ X2320)|~(subset @ X2320 @ (cartprod @ X2317 @ X2318))|~(subset @ X2319 @ (cartprod @ X2317 @ X2318)))&(((in @ (kpair @ (esk76_4 @ X2317 @ X2318 @ X2319 @ X2320) @ (esk77_4 @ X2317 @ X2318 @ X2319 @ X2320)) @ X2320)|((X2319)=(X2320))|~(in @ (kpair @ (esk74_4 @ X2317 @ X2318 @ X2319 @ X2320) @ (esk75_4 @ X2317 @ X2318 @ X2319 @ X2320)) @ X2320)|~(subset @ X2320 @ (cartprod @ X2317 @ X2318))|~(subset @ X2319 @ (cartprod @ X2317 @ X2318)))&(~(in @ (kpair @ (esk76_4 @ X2317 @ X2318 @ X2319 @ X2320) @ (esk77_4 @ X2317 @ X2318 @ X2319 @ X2320)) @ X2319)|((X2319)=(X2320))|~(in @ (kpair @ (esk74_4 @ X2317 @ X2318 @ X2319 @ X2320) @ (esk75_4 @ X2317 @ X2318 @ X2319 @ X2320)) @ X2320)|~(subset @ X2320 @ (cartprod @ X2317 @ X2318))|~(subset @ X2319 @ (cartprod @ X2317 @ X2318)))))))))&((((in @ (esk78_4 @ X2325 @ X2326 @ X2327 @ X2328) @ X2325)|((X2327)=(X2328))|~(func @ X2325 @ X2326 @ X2328)|~(func @ X2325 @ X2326 @ X2327))&(((ap @ X2325 @ X2326 @ X2327 @ (esk78_4 @ X2325 @ X2326 @ X2327 @ X2328))!=(ap @ X2325 @ X2326 @ X2328 @ (esk78_4 @ X2325 @ X2326 @ X2327 @ X2328)))|((X2327)=(X2328))|~(func @ X2325 @ X2326 @ X2328)|~(func @ X2325 @ X2326 @ X2327)))&((((in @ (esk79_4 @ X2330 @ X2331 @ X2332 @ X2333) @ X2330)|((X2332)=(X2333))|~(in @ X2333 @ (funcSet @ X2330 @ X2331))|~(in @ X2332 @ (funcSet @ X2330 @ X2331)))&(((ap @ X2330 @ X2331 @ X2332 @ (esk79_4 @ X2330 @ X2331 @ X2332 @ X2333))!=(ap @ X2330 @ X2331 @ X2333 @ (esk79_4 @ X2330 @ X2331 @ X2332 @ X2333)))|((X2332)=(X2333))|~(in @ X2333 @ (funcSet @ X2330 @ X2331))|~(in @ X2332 @ (funcSet @ X2330 @ X2331))))&((~(in @ X2337 @ (funcSet @ X2335 @ X2336))|(~(in @ X2338 @ X2335)|((ap @ X2335 @ X2336 @ X2337 @ X2338)=(ap @ X2335 @ X2336 @ X2337 @ X2338))))&((~(func @ X2339 @ X2340 @ X2341)|(~(in @ X2342 @ X2339)|((ap @ X2339 @ X2340 @ X2341 @ X2342)=(ap @ X2339 @ X2340 @ X2341 @ X2342))))&((((in @ (esk80_3 @ X2343 @ X2344 @ X2345) @ X2343)|(~(in @ X2347 @ X2343)|((ap @ X2343 @ X2344 @ (lam @ X2343 @ X2344 @ X2345) @ X2347)=(X2345 @ X2347))))&(~(in @ (X2345 @ (esk80_3 @ X2343 @ X2344 @ X2345)) @ X2344)|(~(in @ X2347 @ X2343)|((ap @ X2343 @ X2344 @ (lam @ X2343 @ X2344 @ X2345) @ X2347)=(X2345 @ X2347)))))&((~(func @ X2348 @ X2349 @ X2350)|((lam @ X2348 @ X2349 @ (ap @ X2348 @ X2349 @ X2350))=(X2350)))&((((in @ (esk81_3 @ X2351 @ X2352 @ X2353) @ X2351)|((lam @ X2351 @ X2352 @ X2353)=(lam @ X2351 @ X2352 @ X2353)))&(~(in @ (X2353 @ (esk81_3 @ X2351 @ X2352 @ X2353)) @ X2352)|((lam @ X2351 @ X2352 @ X2353)=(lam @ X2351 @ X2352 @ X2353))))&((((in @ (esk82_3 @ X2355 @ X2356 @ X2357) @ X2355)|(~(in @ X2359 @ X2355)|((ap @ X2355 @ X2356 @ (lam @ X2355 @ X2356 @ X2357) @ X2359)=(X2357 @ X2359))))&(~(in @ (X2357 @ (esk82_3 @ X2355 @ X2356 @ X2357)) @ X2356)|(~(in @ X2359 @ X2355)|((ap @ X2355 @ X2356 @ (lam @ X2355 @ X2356 @ X2357) @ X2359)=(X2357 @ X2359)))))&((~(in @ X2362 @ (funcSet @ X2360 @ X2361))|((lam @ X2360 @ X2361 @ (ap @ X2360 @ X2361 @ X2362))=(X2362)))&((~(in @ X2365 @ X2363)|(~(in @ X2366 @ X2363)|((X2364)|(in @ X2366 @ (dsetconstr @ X2363 @ (^[Z0/* 9 */:$i]:((((X2364)&((Z0)=(X2365)))|(~((X2364))&((Z0)=(X2366)))))))))))&((~(in @ X2369 @ X2367)|(~(in @ X2370 @ X2367)|((X2368)|((dsetconstr @ X2367 @ (^[Z0/* 9 */:$i]:((((X2368)&((Z0)=(X2369)))|(~((X2368))&((Z0)=(X2370)))))))=(setadjoin @ X2370 @ emptyset)))))&((~(in @ X2373 @ X2371)|(~(in @ X2374 @ X2371)|(~(X2372)|(in @ X2373 @ (dsetconstr @ X2371 @ (^[Z0/* 9 */:$i]:((((X2372)&((Z0)=(X2373)))|(~((X2372))&((Z0)=(X2374)))))))))))&((~(in @ X2377 @ X2375)|(~(in @ X2378 @ X2375)|(~(X2376)|((dsetconstr @ X2375 @ (^[Z0/* 9 */:$i]:((((X2376)&((Z0)=(X2377)))|(~((X2376))&((Z0)=(X2378)))))))=(setadjoin @ X2377 @ emptyset)))))&((~(in @ X2381 @ X2379)|(~(in @ X2382 @ X2379)|(singleton @ (dsetconstr @ X2379 @ (^[Z0/* 9 */:$i]:((((X2380)&((Z0)=(X2381)))|(~((X2380))&((Z0)=(X2382))))))))))&((~(in @ X2385 @ X2383)|(~(in @ X2386 @ X2383)|(in @ (if @ X2383 @ ((X2384)) @ X2385 @ X2386) @ X2383)))&((~(singleton @ X2387)|(~(in @ X2388 @ X2387)|((setunion @ X2387)=(X2388))))&((~(in @ X2391 @ X2389)|(~(in @ X2392 @ X2389)|(~(X2390)|((if @ X2389 @ ((X2390)) @ X2391 @ X2392)=(X2391)))))&((~(in @ X2395 @ X2393)|(~(in @ X2396 @ X2393)|((X2394)|((if @ X2393 @ ((X2394)) @ X2395 @ X2396)=(X2396)))))&((~(in @ X2399 @ X2397)|(~(in @ X2400 @ X2397)|(in @ (if @ X2397 @ ((X2398)) @ X2399 @ X2400) @ (setadjoin @ X2399 @ (setadjoin @ X2400 @ emptyset)))))&((~(in @ X2402 @ (powerset @ X2401))|(~(in @ X2403 @ (powerset @ X2401))|(in @ (binintersect @ X2402 @ X2403) @ (powerset @ X2401))))&((~(in @ X2405 @ (powerset @ X2404))|(~(in @ X2406 @ (powerset @ X2404))|(in @ (binunion @ X2405 @ X2406) @ (powerset @ X2404))))&((~(in @ X2408 @ (powerset @ X2407))|(in @ (powerset @ X2408) @ (powerset @ (powerset @ X2407))))&((~(in @ X2410 @ (powerset @ X2409))|(~(in @ X2411 @ (powerset @ X2409))|(in @ (setminus @ X2410 @ X2411) @ (powerset @ X2409))))&((~(in @ X2413 @ (powerset @ X2412))|(in @ (setminus @ X2412 @ X2413) @ (powerset @ X2412)))&(((((in @ (esk84_3 @ X2414 @ X2415 @ X2416) @ X2414)|((X2415)=(X2416))|(in @ (esk83_3 @ X2414 @ X2415 @ X2416) @ X2414)|~(in @ X2416 @ (powerset @ X2414))|~(in @ X2415 @ (powerset @ X2414)))&(((in @ (esk84_3 @ X2414 @ X2415 @ X2416) @ X2416)|((X2415)=(X2416))|(in @ (esk83_3 @ X2414 @ X2415 @ X2416) @ X2414)|~(in @ X2416 @ (powerset @ X2414))|~(in @ X2415 @ (powerset @ X2414)))&(~(in @ (esk84_3 @ X2414 @ X2415 @ X2416) @ X2415)|((X2415)=(X2416))|(in @ (esk83_3 @ X2414 @ X2415 @ X2416) @ X2414)|~(in @ X2416 @ (powerset @ X2414))|~(in @ X2415 @ (powerset @ X2414)))))&((((in @ (esk84_3 @ X2414 @ X2415 @ X2416) @ X2414)|((X2415)=(X2416))|(in @ (esk83_3 @ X2414 @ X2415 @ X2416) @ X2415)|~(in @ X2416 @ (powerset @ X2414))|~(in @ X2415 @ (powerset @ X2414)))&(((in @ (esk84_3 @ X2414 @ X2415 @ X2416) @ X2416)|((X2415)=(X2416))|(in @ (esk83_3 @ X2414 @ X2415 @ X2416) @ X2415)|~(in @ X2416 @ (powerset @ X2414))|~(in @ X2415 @ (powerset @ X2414)))&(~(in @ (esk84_3 @ X2414 @ X2415 @ X2416) @ X2415)|((X2415)=(X2416))|(in @ (esk83_3 @ X2414 @ X2415 @ X2416) @ X2415)|~(in @ X2416 @ (powerset @ X2414))|~(in @ X2415 @ (powerset @ X2414)))))&(((in @ (esk84_3 @ X2414 @ X2415 @ X2416) @ X2414)|((X2415)=(X2416))|~(in @ (esk83_3 @ X2414 @ X2415 @ X2416) @ X2416)|~(in @ X2416 @ (powerset @ X2414))|~(in @ X2415 @ (powerset @ X2414)))&(((in @ (esk84_3 @ X2414 @ X2415 @ X2416) @ X2416)|((X2415)=(X2416))|~(in @ (esk83_3 @ X2414 @ X2415 @ X2416) @ X2416)|~(in @ X2416 @ (powerset @ X2414))|~(in @ X2415 @ (powerset @ X2414)))&(~(in @ (esk84_3 @ X2414 @ X2415 @ X2416) @ X2415)|((X2415)=(X2416))|~(in @ (esk83_3 @ X2414 @ X2415 @ X2416) @ X2416)|~(in @ X2416 @ (powerset @ X2414))|~(in @ X2415 @ (powerset @ X2414)))))))&((((in @ (esk85_3 @ X2419 @ X2420 @ X2421) @ X2419)|(subset @ X2420 @ X2421)|~(in @ X2421 @ (powerset @ X2419))|~(in @ X2420 @ (powerset @ X2419)))&(((in @ (esk85_3 @ X2419 @ X2420 @ X2421) @ X2420)|(subset @ X2420 @ X2421)|~(in @ X2421 @ (powerset @ X2419))|~(in @ X2420 @ (powerset @ X2419)))&(~(in @ (esk85_3 @ X2419 @ X2420 @ X2421) @ X2421)|(subset @ X2420 @ X2421)|~(in @ X2421 @ (powerset @ X2419))|~(in @ X2420 @ (powerset @ X2419)))))&((((in @ (esk86_3 @ X2423 @ X2424 @ X2425) @ X2423)|(in @ X2424 @ (powerset @ X2425))|~(in @ X2425 @ (powerset @ X2423))|~(in @ X2424 @ (powerset @ X2423)))&(((in @ (esk86_3 @ X2423 @ X2424 @ X2425) @ X2424)|(in @ X2424 @ (powerset @ X2425))|~(in @ X2425 @ (powerset @ X2423))|~(in @ X2424 @ (powerset @ X2423)))&(~(in @ (esk86_3 @ X2423 @ X2424 @ X2425) @ X2425)|(in @ X2424 @ (powerset @ X2425))|~(in @ X2425 @ (powerset @ X2423))|~(in @ X2424 @ (powerset @ X2423)))))&((~(in @ X2428 @ (powerset @ X2427))|(~(in @ X2429 @ (powerset @ X2427))|(~(in @ X2430 @ X2427)|(~(in @ X2428 @ (powerset @ X2429))|(~(in @ X2430 @ X2428)|(in @ X2430 @ X2429))))))&((~(in @ X2432 @ (powerset @ X2431))|(~(in @ X2433 @ X2431)|(~(in @ X2433 @ X2432)|~(in @ X2433 @ (setminus @ X2431 @ X2432)))))&((~(in @ X2435 @ (powerset @ X2434))|(~(in @ X2436 @ X2434)|((in @ X2436 @ (setminus @ X2434 @ X2435))|(in @ X2436 @ X2435))))&((~(in @ X2438 @ (powerset @ X2437))|(~(in @ X2439 @ (powerset @ X2437))|(~(in @ X2440 @ X2437)|((in @ X2440 @ X2438)|~(in @ X2440 @ (binintersect @ X2438 @ X2439))))))&((~(in @ X2442 @ (powerset @ X2441))|(~(in @ X2443 @ (powerset @ X2441))|(~(in @ X2444 @ X2441)|((in @ X2444 @ X2443)|~(in @ X2444 @ (binintersect @ X2442 @ X2443))))))&((~(in @ X2446 @ (powerset @ X2445))|(~(in @ X2447 @ (powerset @ X2445))|(~(in @ X2448 @ X2445)|(~(subset @ X2446 @ (setminus @ X2445 @ X2447))|(~(in @ X2448 @ X2447)|~(in @ X2448 @ X2446))))))&((~(in @ X2450 @ (powerset @ X2449))|(~(in @ X2451 @ (powerset @ X2449))|(~(in @ X2452 @ X2449)|(~(subset @ X2450 @ X2451)|((in @ X2452 @ X2451)|~(in @ X2452 @ X2450))))))&((~(in @ X2454 @ (powerset @ X2453))|(~(in @ X2455 @ (powerset @ X2453))|(~(subset @ X2454 @ X2455)|(subset @ (setminus @ X2453 @ X2455) @ (setminus @ X2453 @ X2454)))))&((~(in @ X2457 @ (powerset @ X2456))|(~(in @ X2458 @ (powerset @ X2456))|(~(subset @ (setminus @ X2456 @ X2458) @ (setminus @ X2456 @ X2457))|(subset @ X2457 @ X2458))))&((~(in @ X2460 @ (powerset @ X2459))|(~(in @ X2461 @ X2459)|(~(in @ X2461 @ X2460)|(in @ X2461 @ (setminus @ X2459 @ (setminus @ X2459 @ X2460))))))&((~(in @ X2463 @ (powerset @ X2462))|(~(in @ X2464 @ X2462)|(~(in @ X2464 @ (setminus @ X2462 @ (setminus @ X2462 @ X2463)))|(in @ X2464 @ X2463))))&((~(in @ X2466 @ (powerset @ X2465))|(subset @ X2466 @ (setminus @ X2465 @ (setminus @ X2465 @ X2466))))&((~(in @ X2468 @ (powerset @ X2467))|(subset @ (setminus @ X2467 @ (setminus @ X2467 @ X2468)) @ X2468))&((~(in @ X2470 @ (powerset @ X2469))|((X2470)=(setminus @ X2469 @ (setminus @ X2469 @ X2470))))&((~(in @ X2472 @ (powerset @ X2471))|(~(in @ X2473 @ (powerset @ X2471))|(~(in @ X2474 @ X2471)|(~(in @ X2474 @ (setminus @ X2471 @ X2472))|~(in @ X2474 @ (binintersect @ X2472 @ X2473))))))&((~(in @ X2476 @ (powerset @ X2475))|(~(in @ X2477 @ (powerset @ X2475))|(~(in @ X2478 @ X2475)|(~(in @ X2478 @ (setminus @ X2475 @ X2476))|(in @ X2478 @ (setminus @ X2475 @ (binintersect @ X2476 @ X2477)))))))&((~(in @ X2480 @ (powerset @ X2479))|(~(in @ X2481 @ (powerset @ X2479))|(subset @ (setminus @ X2479 @ X2480) @ (setminus @ X2479 @ (binintersect @ X2480 @ X2481)))))&((~(in @ X2483 @ (powerset @ X2482))|(~(in @ X2484 @ (powerset @ X2482))|(in @ (setminus @ X2482 @ X2483) @ (powerset @ (setminus @ X2482 @ (binintersect @ X2483 @ X2484))))))&((~(in @ X2486 @ (powerset @ X2485))|(~(in @ X2487 @ (powerset @ X2485))|(~(subset @ X2486 @ (setminus @ X2485 @ X2487))|(~(in @ X2488 @ X2485)|(~(in @ X2488 @ X2487)|(in @ X2488 @ (setminus @ X2485 @ X2486)))))))&((~(in @ X2490 @ (powerset @ X2489))|(~(in @ X2491 @ (powerset @ X2489))|(~(subset @ X2490 @ (setminus @ X2489 @ X2491))|(subset @ X2491 @ (setminus @ X2489 @ X2490)))))&((in @ esk88_0 @ (powerset @ esk87_0))&((in @ esk89_0 @ (powerset @ esk87_0))&((in @ esk90_0 @ esk87_0)&(~(in @ esk90_0 @ (binunion @ esk88_0 @ esk89_0))&(in @ esk90_0 @ esk88_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_340])])])])])])])). 0.41/0.80 thf(c_0_342, negated_conjecture, ~((in @ esk90_0 @ (binunion @ esk88_0 @ esk89_0))), inference(split_conjunct,[status(thm)],[c_0_341])). 0.41/0.80 thf(c_0_343, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X3 @ X4))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_341])). 0.41/0.80 thf(c_0_344, negated_conjecture, (in @ esk90_0 @ esk88_0), inference(split_conjunct,[status(thm)],[c_0_341])). 0.41/0.80 thf(c_0_345, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_342, c_0_343]), c_0_344])]), ['proof']). 0.41/0.80 # SZS output end CNFRefutation 0.41/0.80 # Parsed axioms : 551 0.41/0.80 # Removed by relevancy pruning/SinE : 292 0.41/0.80 # Initial clauses : 461 0.41/0.80 # Removed in clause preprocessing : 34 0.41/0.80 # Initial clauses in saturation : 427 0.41/0.80 # Processed clauses : 562 0.41/0.80 # ...of these trivial : 10 0.41/0.80 # ...subsumed : 34 0.41/0.80 # ...remaining for further processing : 518 0.41/0.80 # Other redundant clauses eliminated : 31 0.41/0.80 # Clauses deleted for lack of memory : 0 0.41/0.80 # Backward-subsumed : 0 0.41/0.80 # Backward-rewritten : 1 0.41/0.80 # Generated clauses : 662 0.41/0.80 # ...of the previous two non-redundant : 571 0.41/0.80 # ...aggressively subsumed : 0 0.41/0.80 # Contextual simplify-reflections : 6 0.41/0.80 # Paramodulations : 622 0.41/0.80 # Factorizations : 0 0.41/0.80 # NegExts : 0 0.41/0.80 # Equation resolutions : 36 0.41/0.80 # Disequality decompositions : 0 0.41/0.80 # Total rewrite steps : 101 0.41/0.80 # ...of those cached : 66 0.41/0.80 # Propositional unsat checks : 0 0.41/0.80 # Propositional check models : 0 0.41/0.80 # Propositional check unsatisfiable : 0 0.41/0.80 # Propositional clauses : 0 0.41/0.80 # Propositional clauses after purity: 0 0.41/0.80 # Propositional unsat core size : 0 0.41/0.80 # Propositional preprocessing time : 0.000 0.41/0.80 # Propositional encoding time : 0.000 0.41/0.80 # Propositional solver time : 0.000 0.41/0.80 # Success case prop preproc time : 0.000 0.41/0.80 # Success case prop encoding time : 0.000 0.41/0.80 # Success case prop solver time : 0.000 0.41/0.80 # Current number of processed clauses : 122 0.41/0.80 # Positive orientable unit clauses : 38 0.41/0.80 # Positive unorientable unit clauses: 0 0.41/0.80 # Negative unit clauses : 3 0.41/0.80 # Non-unit-clauses : 81 0.41/0.80 # Current number of unprocessed clauses: 811 0.41/0.80 # ...number of literals in the above : 2287 0.41/0.80 # Current number of archived formulas : 0 0.41/0.80 # Current number of archived clauses : 378 0.41/0.80 # Clause-clause subsumption calls (NU) : 30335 0.41/0.80 # Rec. Clause-clause subsumption calls : 10290 0.41/0.80 # Non-unit clause-clause subsumptions : 35 0.41/0.80 # Unit Clause-clause subsumption calls : 714 0.41/0.80 # Rewrite failures with RHS unbound : 0 0.41/0.80 # BW rewrite match attempts : 32 0.41/0.80 # BW rewrite match successes : 1 0.41/0.80 # Condensation attempts : 0 0.41/0.80 # Condensation successes : 0 0.41/0.80 # Termbank termtop insertions : 84790 0.41/0.80 # Search garbage collected termcells : 26760 0.41/0.80 0.41/0.80 # ------------------------------------------------- 0.41/0.80 # User time : 0.174 s 0.41/0.80 # System time : 0.023 s 0.41/0.80 # Total time : 0.197 s 0.41/0.80 # Maximum resident set size: 8464 pages 0.41/0.80 0.41/0.80 # ------------------------------------------------- 0.41/0.80 # User time : 0.189 s 0.41/0.80 # System time : 0.026 s 0.41/0.80 # Total time : 0.215 s 0.41/0.80 # Maximum resident set size: 2484 pages 0.41/0.80 % E---3.1 exiting 2.12/0.80 % E exiting 2.12/0.80 EOF