0.02/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.11 % Command : run_E %s %d THM 0.09/0.31 % Computer : n015.cluster.edu 0.09/0.31 % Model : x86_64 x86_64 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.31 % Memory : 8042.1875MB 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.31 % CPULimit : 1440 0.09/0.31 % WCLimit : 180 0.09/0.31 % DateTime : Thu Jul 4 08:15:24 EDT 2024 0.09/0.31 % CPUTime : 0.15/0.43 Running higher-order theorem proving 0.15/0.47 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.hRbm8JgpWK/E---3.1_26402.p 0.90/180.05 # Version: 3.2.0-ho 0.90/180.05 # Preprocessing class: HSLMSLSSLLLCHFA. 0.90/180.05 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.90/180.05 # Starting ehoh_best5 with 180s (1) cores 0.90/180.05 # Starting almost_fo_3_lam with 180s (1) cores 0.90/180.05 # Starting new_bool_5 with 180s (1) cores 0.90/180.05 # Starting pre_casc_3 with 180s (1) cores 0.90/180.05 # Starting ho_unfolding_8 with 180s (1) cores 0.90/180.05 # Starting new_ho_10_cnf2 with 180s (1) cores 0.90/180.05 # Starting new_bool_3 with 180s (1) cores 0.90/180.05 # Starting new_ho_5 with 180s (1) cores 0.90/180.05 # new_bool_5 with pid 26482 completed with status 0 0.90/180.05 # Result found by new_bool_5 0.90/180.05 # Preprocessing class: HSLMSLSSLLLCHFA. 0.90/180.05 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.90/180.05 # Starting ehoh_best5 with 180s (1) cores 0.90/180.05 # Starting almost_fo_3_lam with 180s (1) cores 0.90/180.05 # Starting new_bool_5 with 180s (1) cores 0.90/180.05 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 0.90/180.05 # Search class: HGHSM-FSLM31-MHFMMSBN 0.90/180.05 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 0.90/180.05 # Starting new_ho_10_cnf2 with 98s (1) cores 0.90/180.05 # new_ho_10_cnf2 with pid 26492 completed with status 0 0.90/180.05 # Result found by new_ho_10_cnf2 0.90/180.05 # Preprocessing class: HSLMSLSSLLLCHFA. 0.90/180.05 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 0.90/180.05 # Starting ehoh_best5 with 180s (1) cores 0.90/180.05 # Starting almost_fo_3_lam with 180s (1) cores 0.90/180.05 # Starting new_bool_5 with 180s (1) cores 0.90/180.05 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 0.90/180.05 # Search class: HGHSM-FSLM31-MHFMMSBN 0.90/180.05 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 0.90/180.05 # Starting new_ho_10_cnf2 with 98s (1) cores 0.90/180.05 # Preprocessing time : 0.004 s 0.90/180.05 # Presaturation interreduction done 0.90/180.05 0.90/180.05 # Proof found! 0.90/180.05 # SZS status Theorem 0.90/180.05 # SZS output start CNFRefutation 0.90/180.05 thf(decl_22, type, in: $i > $i > $o). 0.90/180.05 thf(decl_23, type, exu: ($i > $o) > $o). 0.90/180.05 thf(decl_24, type, setextAx: $o). 0.90/180.05 thf(decl_25, type, emptyset: $i). 0.90/180.05 thf(decl_26, type, emptysetAx: $o). 0.90/180.05 thf(decl_27, type, setadjoin: $i > $i > $i). 0.90/180.05 thf(decl_28, type, setadjoinAx: $o). 0.90/180.05 thf(decl_29, type, powerset: $i > $i). 0.90/180.05 thf(decl_30, type, powersetAx: $o). 0.90/180.05 thf(decl_31, type, setunion: $i > $i). 0.90/180.05 thf(decl_32, type, setunionAx: $o). 0.90/180.05 thf(decl_33, type, omega: $i). 0.90/180.05 thf(decl_34, type, omega0Ax: $o). 0.90/180.05 thf(decl_35, type, omegaSAx: $o). 0.90/180.05 thf(decl_36, type, omegaIndAx: $o). 0.90/180.05 thf(decl_37, type, replAx: $o). 0.90/180.05 thf(decl_38, type, foundationAx: $o). 0.90/180.05 thf(decl_39, type, wellorderingAx: $o). 0.90/180.05 thf(decl_40, type, descr: ($i > $o) > $i). 0.90/180.05 thf(decl_41, type, descrp: $o). 0.90/180.05 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 0.90/180.05 thf(decl_43, type, dsetconstrI: $o). 0.90/180.05 thf(decl_44, type, dsetconstrEL: $o). 0.90/180.05 thf(decl_45, type, dsetconstrER: $o). 0.90/180.05 thf(decl_46, type, exuE1: $o). 0.90/180.05 thf(decl_47, type, prop2set: $o > $i). 0.90/180.05 thf(decl_48, type, prop2setE: $o). 0.90/180.05 thf(decl_49, type, emptysetE: $o). 0.90/180.05 thf(decl_50, type, emptysetimpfalse: $o). 0.90/180.05 thf(decl_51, type, notinemptyset: $o). 0.90/180.05 thf(decl_52, type, exuE3e: $o). 0.90/180.05 thf(decl_53, type, setext: $o). 0.90/180.05 thf(decl_54, type, emptyI: $o). 0.90/180.05 thf(decl_55, type, noeltsimpempty: $o). 0.90/180.05 thf(decl_56, type, setbeta: $o). 0.90/180.05 thf(decl_57, type, nonempty: $i > $o). 0.90/180.05 thf(decl_58, type, nonemptyE1: $o). 0.90/180.05 thf(decl_59, type, nonemptyI: $o). 0.90/180.05 thf(decl_60, type, nonemptyI1: $o). 0.90/180.05 thf(decl_61, type, setadjoinIL: $o). 0.90/180.05 thf(decl_62, type, emptyinunitempty: $o). 0.90/180.05 thf(decl_63, type, setadjoinIR: $o). 0.90/180.05 thf(decl_64, type, setadjoinE: $o). 0.90/180.05 thf(decl_65, type, setadjoinOr: $o). 0.90/180.05 thf(decl_66, type, setoftrueEq: $o). 0.90/180.05 thf(decl_67, type, powersetI: $o). 0.90/180.05 thf(decl_68, type, emptyinPowerset: $o). 0.90/180.05 thf(decl_69, type, emptyInPowerset: $o). 0.90/180.05 thf(decl_70, type, powersetE: $o). 0.90/180.05 thf(decl_71, type, setunionI: $o). 0.90/180.05 thf(decl_72, type, setunionE: $o). 0.90/180.05 thf(decl_73, type, subPowSU: $o). 0.90/180.05 thf(decl_74, type, exuE2: $o). 0.90/180.05 thf(decl_75, type, nonemptyImpWitness: $o). 0.90/180.05 thf(decl_76, type, uniqinunit: $o). 0.90/180.05 thf(decl_77, type, notinsingleton: $o). 0.90/180.05 thf(decl_78, type, eqinunit: $o). 0.90/180.05 thf(decl_79, type, singletonsswitch: $o). 0.90/180.05 thf(decl_80, type, upairsetE: $o). 0.90/180.05 thf(decl_81, type, upairsetIL: $o). 0.90/180.05 thf(decl_82, type, upairsetIR: $o). 0.90/180.05 thf(decl_83, type, emptyE1: $o). 0.90/180.05 thf(decl_84, type, vacuousDall: $o). 0.90/180.05 thf(decl_85, type, quantDeMorgan1: $o). 0.90/180.05 thf(decl_86, type, quantDeMorgan2: $o). 0.90/180.05 thf(decl_87, type, quantDeMorgan3: $o). 0.90/180.05 thf(decl_88, type, quantDeMorgan4: $o). 0.90/180.05 thf(decl_89, type, prop2setI: $o). 0.90/180.05 thf(decl_91, type, prop2set2propI: $o). 0.90/180.05 thf(decl_92, type, notdexE: $o). 0.90/180.05 thf(decl_93, type, notdallE: $o). 0.90/180.05 thf(decl_94, type, exuI1: $o). 0.90/180.05 thf(decl_95, type, exuI3: $o). 0.90/180.05 thf(decl_96, type, exuI2: $o). 0.90/180.05 thf(decl_97, type, inCongP: $o). 0.90/180.05 thf(decl_98, type, in__Cong: $o). 0.90/180.05 thf(decl_99, type, exuE3u: $o). 0.90/180.05 thf(decl_100, type, exu__Cong: $o). 0.90/180.05 thf(decl_101, type, emptyset__Cong: $o). 0.90/180.05 thf(decl_102, type, setadjoin__Cong: $o). 0.90/180.05 thf(decl_103, type, powerset__Cong: $o). 0.90/180.05 thf(decl_104, type, setunion__Cong: $o). 0.90/180.05 thf(decl_105, type, omega__Cong: $o). 0.90/180.05 thf(decl_106, type, exuEu: $o). 0.90/180.05 thf(decl_107, type, descr__Cong: $o). 0.90/180.05 thf(decl_108, type, dsetconstr__Cong: $o). 0.90/180.05 thf(decl_109, type, subset: $i > $i > $o). 0.90/180.05 thf(decl_112, type, subsetI1: $o). 0.90/180.05 thf(decl_113, type, eqimpsubset2: $o). 0.90/180.05 thf(decl_114, type, eqimpsubset1: $o). 0.90/180.05 thf(decl_115, type, subsetI2: $o). 0.90/180.05 thf(decl_116, type, emptysetsubset: $o). 0.90/180.05 thf(decl_117, type, subsetE: $o). 0.90/180.05 thf(decl_118, type, subsetE2: $o). 0.90/180.05 thf(decl_119, type, notsubsetI: $o). 0.90/180.05 thf(decl_120, type, notequalI1: $o). 0.90/180.05 thf(decl_121, type, notequalI2: $o). 0.90/180.05 thf(decl_122, type, subsetRefl: $o). 0.90/180.05 thf(decl_123, type, subsetTrans: $o). 0.90/180.05 thf(decl_124, type, setadjoinSub: $o). 0.90/180.05 thf(decl_125, type, setadjoinSub2: $o). 0.90/180.05 thf(decl_126, type, subset2powerset: $o). 0.90/180.05 thf(decl_127, type, setextsub: $o). 0.90/180.05 thf(decl_128, type, subsetemptysetimpeq: $o). 0.90/180.05 thf(decl_129, type, powersetI1: $o). 0.90/180.05 thf(decl_130, type, powersetE1: $o). 0.90/180.05 thf(decl_131, type, inPowerset: $o). 0.90/180.05 thf(decl_132, type, powersetsubset: $o). 0.90/180.05 thf(decl_133, type, sepInPowerset: $o). 0.90/180.05 thf(decl_134, type, sepSubset: $o). 0.90/180.05 thf(decl_135, type, binunion: $i > $i > $i). 0.90/180.05 thf(decl_136, type, binunionIL: $o). 0.90/180.05 thf(decl_137, type, upairset2IR: $o). 0.90/180.05 thf(decl_138, type, binunionIR: $o). 0.90/180.05 thf(decl_139, type, binunionEcases: $o). 0.90/180.05 thf(decl_140, type, binunionE: $o). 0.90/180.05 thf(decl_141, type, binunionLsub: $o). 0.90/180.05 thf(decl_142, type, binunionRsub: $o). 0.90/180.05 thf(decl_143, type, binintersect: $i > $i > $i). 0.90/180.05 thf(decl_144, type, binintersectI: $o). 0.90/180.05 thf(decl_145, type, binintersectSubset5: $o). 0.90/180.05 thf(decl_146, type, binintersectEL: $o). 0.90/180.05 thf(decl_147, type, binintersectLsub: $o). 0.90/180.05 thf(decl_148, type, binintersectSubset2: $o). 0.90/180.05 thf(decl_149, type, binintersectSubset3: $o). 0.90/180.05 thf(decl_150, type, binintersectER: $o). 0.90/180.05 thf(decl_151, type, disjointsetsI1: $o). 0.90/180.05 thf(decl_152, type, binintersectRsub: $o). 0.90/180.05 thf(decl_153, type, binintersectSubset4: $o). 0.90/180.05 thf(decl_154, type, binintersectSubset1: $o). 0.90/180.05 thf(decl_155, type, bs114d: $o). 0.90/180.05 thf(decl_157, type, setminus: $i > $i > $i). 0.90/180.05 thf(decl_158, type, setminusI: $o). 0.90/180.05 thf(decl_159, type, setminusEL: $o). 0.90/180.05 thf(decl_160, type, setminusER: $o). 0.90/180.05 thf(decl_161, type, setminusSubset2: $o). 0.90/180.05 thf(decl_162, type, setminusERneg: $o). 0.90/180.05 thf(decl_163, type, setminusELneg: $o). 0.90/180.05 thf(decl_164, type, setminusILneg: $o). 0.90/180.05 thf(decl_165, type, setminusIRneg: $o). 0.90/180.05 thf(decl_166, type, setminusLsub: $o). 0.90/180.05 thf(decl_167, type, setminusSubset1: $o). 0.90/180.05 thf(decl_168, type, symdiff: $i > $i > $i). 0.90/180.05 thf(decl_169, type, symdiffE: $o). 0.90/180.05 thf(decl_170, type, symdiffI1: $o). 0.90/180.05 thf(decl_171, type, symdiffI2: $o). 0.90/180.05 thf(decl_172, type, symdiffIneg1: $o). 0.90/180.05 thf(decl_173, type, symdiffIneg2: $o). 0.90/180.05 thf(decl_174, type, iskpair: $i > $o). 0.90/180.05 thf(decl_175, type, secondinupair: $o). 0.90/180.05 thf(decl_176, type, setukpairIL: $o). 0.90/180.05 thf(decl_177, type, setukpairIR: $o). 0.90/180.05 thf(decl_178, type, kpairiskpair: $o). 0.90/180.05 thf(decl_179, type, kpair: $i > $i > $i). 0.90/180.05 thf(decl_180, type, kpairp: $o). 0.90/180.05 thf(decl_181, type, cartprod: $i > $i > $i). 0.90/180.05 thf(decl_182, type, singletonsubset: $o). 0.90/180.05 thf(decl_183, type, singletoninpowerset: $o). 0.90/180.05 thf(decl_184, type, singletoninpowunion: $o). 0.90/180.05 thf(decl_185, type, upairset2E: $o). 0.90/180.05 thf(decl_186, type, upairsubunion: $o). 0.90/180.05 thf(decl_187, type, upairinpowunion: $o). 0.90/180.05 thf(decl_188, type, ubforcartprodlem1: $o). 0.90/180.05 thf(decl_189, type, ubforcartprodlem2: $o). 0.90/180.05 thf(decl_190, type, ubforcartprodlem3: $o). 0.90/180.05 thf(decl_191, type, cartprodpairin: $o). 0.90/180.05 thf(decl_192, type, cartprodmempair1: $o). 0.90/180.05 thf(decl_193, type, cartprodmempair: $o). 0.90/180.05 thf(decl_194, type, setunionE2: $o). 0.90/180.05 thf(decl_195, type, setunionsingleton1: $o). 0.90/180.05 thf(decl_196, type, setunionsingleton2: $o). 0.90/180.05 thf(decl_197, type, setunionsingleton: $o). 0.90/180.05 thf(decl_198, type, singleton: $i > $o). 0.90/180.05 thf(decl_199, type, singletonprop: $o). 0.90/180.05 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 0.90/180.05 thf(decl_201, type, ex1E1: $o). 0.90/180.05 thf(decl_202, type, ex1I: $o). 0.90/180.05 thf(decl_203, type, ex1I2: $o). 0.90/180.05 thf(decl_204, type, singletonsuniq: $o). 0.90/180.05 thf(decl_209, type, setukpairinjL1: $o). 0.90/180.05 thf(decl_210, type, kfstsingleton: $o). 0.90/180.05 thf(decl_211, type, theprop: $o). 0.90/180.05 thf(decl_212, type, kfst: $i > $i). 0.90/180.05 thf(decl_213, type, kfstpairEq: $o). 0.90/180.05 thf(decl_214, type, cartprodfstin: $o). 0.90/180.05 thf(decl_215, type, setukpairinjL2: $o). 0.90/180.05 thf(decl_216, type, setukpairinjL: $o). 0.90/180.05 thf(decl_217, type, setukpairinjR11: $o). 0.90/180.05 thf(decl_218, type, setukpairinjR12: $o). 0.90/180.05 thf(decl_219, type, setukpairinjR1: $o). 0.90/180.05 thf(decl_220, type, epred1_0: $o). 0.90/180.05 thf(decl_221, type, esk1_2: $i > $i > $i). 0.90/180.05 thf(decl_222, type, esk2_2: $i > $i > $i). 0.90/180.05 thf(decl_223, type, esk3_2: $i > $i > $i). 0.90/180.05 thf(decl_224, type, esk4_1: $i > $i). 0.90/180.05 thf(decl_225, type, esk5_2: ($i > $i > $o) > $i > $i). 0.90/180.05 thf(decl_226, type, esk6_2: ($i > $i > $o) > $i > $i). 0.90/180.05 thf(decl_227, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 0.90/180.05 thf(decl_228, type, esk8_1: $i > $i). 0.90/180.05 thf(decl_229, type, esk9_1: ($i > $o) > $i). 0.90/180.05 thf(decl_230, type, esk10_1: ($i > $o) > $i). 0.90/180.05 thf(decl_231, type, esk11_2: $i > $i > $i). 0.90/180.05 thf(decl_232, type, esk12_2: $i > $i > $i). 0.90/180.05 thf(decl_233, type, esk13_1: $i > $i). 0.90/180.05 thf(decl_234, type, esk14_1: $i > $i). 0.90/180.05 thf(decl_235, type, esk15_1: $i > $i). 0.90/180.05 thf(decl_236, type, esk16_2: $i > $i > $i). 0.90/180.05 thf(decl_237, type, esk17_3: $i > $i > $o > $i). 0.90/180.05 thf(decl_238, type, esk18_1: ($i > $o) > $i). 0.90/180.05 thf(decl_239, type, esk19_1: $i > $i). 0.90/180.05 thf(decl_240, type, esk20_2: $i > ($i > $o) > $i). 0.90/180.05 thf(decl_241, type, esk21_2: $i > ($i > $o) > $i). 0.90/180.05 thf(decl_242, type, esk22_2: $i > ($i > $o) > $i). 0.90/180.05 thf(decl_243, type, esk23_2: $i > ($i > $o) > $i). 0.90/180.05 thf(decl_244, type, esk24_2: $i > ($i > $o) > $i). 0.90/180.05 thf(decl_245, type, esk25_2: $i > ($i > $o) > $i). 0.90/180.05 thf(decl_246, type, esk26_2: ($i > $o) > $i > $i). 0.90/180.05 thf(decl_247, type, esk27_1: ($i > $o) > $i). 0.90/180.05 thf(decl_248, type, esk28_1: ($i > $o) > $i). 0.90/180.05 thf(decl_249, type, esk29_2: ($i > $o) > $i > $i). 0.90/180.05 thf(decl_250, type, esk30_2: ($i > $o) > ($i > $o) > $i). 0.90/180.05 thf(decl_251, type, esk31_2: ($i > $o) > ($i > $o) > $i). 0.90/180.05 thf(decl_252, type, esk32_2: ($i > $o) > ($i > $o) > $i). 0.90/180.05 thf(decl_253, type, esk33_2: ($i > $o) > ($i > $o) > $i). 0.90/180.05 thf(decl_254, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.90/180.05 thf(decl_255, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.90/180.05 thf(decl_256, type, esk36_2: $i > $i > $i). 0.90/180.05 thf(decl_257, type, esk37_2: $i > $i > $i). 0.90/180.05 thf(decl_258, type, esk38_2: $i > $i > $i). 0.90/180.05 thf(decl_259, type, esk39_3: $i > $i > $i > $i). 0.90/180.05 thf(decl_260, type, esk40_3: $i > $i > $i > $i). 0.90/180.05 thf(decl_261, type, esk41_2: $i > $i > $i). 0.90/180.05 thf(decl_262, type, esk42_2: $i > ($i > $o) > $i). 0.90/180.05 thf(decl_263, type, esk43_2: $i > ($i > $o) > $i). 0.90/180.05 thf(decl_264, type, esk44_2: $i > ($i > $o) > $i). 0.90/180.05 thf(decl_265, type, esk45_3: $i > ($i > $o) > $i > $i). 0.90/180.05 thf(decl_266, type, esk46_2: $i > ($i > $o) > $i). 0.90/180.05 thf(decl_267, type, esk47_2: $i > ($i > $o) > $i). 0.90/180.05 thf(decl_268, type, esk48_0: $i). 0.90/180.05 thf(decl_269, type, esk49_0: $i). 0.90/180.05 thf(decl_270, type, esk50_0: $i). 0.90/180.05 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', dsetconstr__Cong)). 0.90/180.05 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', exu__Cong)). 0.90/180.05 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', exuE3u)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', exuI1)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', exuI2)). 0.90/180.05 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', exuI3)). 0.90/180.05 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.hRbm8JgpWK/E---3.1_26402.p', emptyE1)). 0.90/180.05 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', nonemptyI)). 0.90/180.05 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', exuE3e)). 0.90/180.05 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', exuEu)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', exuE1)). 0.90/180.05 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', descr__Cong)). 0.90/180.05 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', dsetconstrER)). 0.90/180.05 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', dsetconstrEL)). 0.90/180.05 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', dsetconstrI)). 0.90/180.05 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', descrp)). 0.90/180.05 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', replAx)). 0.90/180.05 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', sepInPowerset)). 0.90/180.05 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', ex1E1)). 0.90/180.05 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', sepSubset)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', kfstsingleton)). 0.90/180.05 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', ex1I2)). 0.90/180.05 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.hRbm8JgpWK/E---3.1_26402.p', ex1I)). 0.90/180.05 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', singletonprop)). 0.90/180.05 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', exuE2)). 0.90/180.05 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setoftrueEq)). 0.90/180.05 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setbeta)). 0.90/180.05 thf(upairequniteq, conjecture, ((((setadjoinAx)=>(((setunionAx)=>((omega0Ax)=>((((((wellorderingAx)=>(((((((((emptysetimpfalse)=>((((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>(((((((setadjoinE)=>(((setoftrueEq)=>(((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>(((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>(((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>(((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((((((((emptyset__Cong)=>((setadjoin__Cong)=>(((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>(((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>(((emptysetsubset)=>(((subsetE2)=>(((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>(((setadjoinSub2)=>((((((powersetE1)=>((inPowerset)=>(((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>(((binunionEcases)=>((binunionE)=>(((binunionRsub)=>(((((((((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>(((bs114d)=>((setminusI)=>((((setminusSubset2)=>((((setminusILneg)=>(((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>(((symdiffI2)=>((symdiffIneg1)=>(((secondinupair)=>(((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((((((ubforcartprodlem1)=>((ubforcartprodlem2)=>(((cartprodpairin)=>(((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>(((setunionsingleton)=>(((ex1E1)=>((((singletonsuniq)=>((setukpairinjL1)=>(((theprop)=>((kfstpairEq)=>(((((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>![X2:$i, X3:$i, X14:$i]:((((X2)=(X3))<=((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset)))))))<=(setukpairinjL))<=(setukpairinjL2))<=(cartprodfstin))))<=(kfstsingleton))))<=(ex1I2))<=(ex1I)))<=(singletonprop)))<=(setunionsingleton2)))))<=(cartprodmempair1)))<=(ubforcartprodlem3))))<=(upairinpowunion))<=(upairsubunion))<=(upairset2E))<=(singletoninpowunion)))))))<=(setukpairIL)))<=(symdiffIneg2))))<=(symdiffI1)))))<=(setminusIRneg)))<=(setminusELneg))<=(setminusERneg)))<=(setminusER))<=(setminusEL))))<=(binintersectSubset1)))))<=(binintersectER))<=(binintersectSubset3))<=(binintersectSubset2))<=(binintersectLsub))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI)))<=(binunionLsub))))<=(binunionIR))))))<=(powersetsubset))))<=(powersetI1))<=(subsetemptysetimpeq))<=(setextsub))<=(subset2powerset)))<=(setadjoinSub))))))<=(notsubsetI)))<=(subsetE)))<=(subsetI2)))))<=(dsetconstr__Cong))))))<=(powerset__Cong))))<=(exu__Cong))<=(exuE3u))<=(in__Cong))<=(inCongP))<=(exuI2))<=(exuI3))))))<=(prop2setI))))))<=(vacuousDall))))))))))))))<=(setunionI)))))<=(powersetI)))<=(setadjoinOr)))<=(setadjoinIR))<=(emptyinunitempty))<=(setadjoinIL))<=(nonemptyI1))<=(nonemptyI)))))))<=(exuE3e))<=(notinemptyset)))<=(emptysetE))<=(prop2setE))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL))<=(dsetconstrI))<=(descrp)))<=(foundationAx))<=(replAx))<=(omegaIndAx))<=(omegaSAx))))<=(powersetAx)))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', upairequniteq)). 0.90/180.05 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', quantDeMorgan1)). 0.90/180.05 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', nonemptyI1)). 0.90/180.05 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setextAx)). 0.90/180.05 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', subset2powerset)). 0.90/180.05 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setadjoinSub)). 0.90/180.05 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', notsubsetI)). 0.90/180.05 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', quantDeMorgan4)). 0.90/180.05 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', subsetE)). 0.90/180.05 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', subsetI2)). 0.90/180.05 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', notdexE)). 0.90/180.05 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', powerset__Cong)). 0.90/180.05 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', notdallE)). 0.90/180.05 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', in__Cong)). 0.90/180.05 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', inCongP)). 0.90/180.05 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', emptyset__Cong)). 0.90/180.05 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', prop2setI)). 0.90/180.05 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', vacuousDall)). 0.90/180.05 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setunionI)). 0.90/180.05 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', powersetI)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', setadjoin__Cong)). 0.90/180.05 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setadjoinOr)). 0.90/180.05 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setadjoinIR)). 0.90/180.05 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setunion__Cong)). 0.90/180.05 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', emptyinunitempty)). 0.90/180.05 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setadjoinIL)). 0.90/180.05 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', omega__Cong)). 0.90/180.05 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', notinemptyset)). 0.90/180.05 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', emptysetE)). 0.90/180.05 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', prop2setE)). 0.90/180.05 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', subsetI1)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', foundationAx)). 0.90/180.05 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', eqimpsubset2)). 0.90/180.05 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', omegaIndAx)). 0.90/180.05 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', eqimpsubset1)). 0.90/180.05 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', omegaSAx)). 0.90/180.05 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', powersetAx)). 0.90/180.05 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', emptysetAx)). 0.90/180.05 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', emptysetsubset)). 0.90/180.05 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', subsetE2)). 0.90/180.05 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', notequalI1)). 0.90/180.05 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', notequalI2)). 0.90/180.05 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', subsetRefl)). 0.90/180.05 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', subsetTrans)). 0.90/180.05 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setadjoinSub2)). 0.90/180.05 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', powersetE1)). 0.90/180.05 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', inPowerset)). 0.90/180.05 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', singletonsuniq)). 0.90/180.05 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', binunionIL)). 0.90/180.05 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', upairset2IR)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', binunionEcases)). 0.90/180.05 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', binunionE)). 0.90/180.05 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', binunionRsub)). 0.90/180.05 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', disjointsetsI1)). 0.90/180.05 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', binintersectRsub)). 0.90/180.05 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', quantDeMorgan2)). 0.90/180.05 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', binintersectSubset4)). 0.90/180.05 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', bs114d)). 0.90/180.05 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setminusI)). 0.90/180.05 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setminusSubset2)). 0.90/180.05 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setminusILneg)). 0.90/180.05 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setminusLsub)). 0.90/180.05 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setminusSubset1)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', symdiffE)). 0.90/180.05 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', symdiffI2)). 0.90/180.05 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', symdiffIneg1)). 0.90/180.05 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', secondinupair)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', setukpairIR)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', kpairiskpair)). 0.90/180.05 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', kpairp)). 0.90/180.05 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', singletonsubset)). 0.90/180.05 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', singletoninpowerset)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', ubforcartprodlem1)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', ubforcartprodlem2)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', cartprodpairin)). 0.90/180.05 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', cartprodmempair)). 0.90/180.05 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setunionE2)). 0.90/180.05 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setunionsingleton1)). 0.90/180.05 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setunionsingleton)). 0.90/180.05 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setukpairinjL1)). 0.90/180.05 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', theprop)). 0.90/180.05 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', kfstpairEq)). 0.90/180.05 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setukpairinjR11)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', setukpairinjR12)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', setukpairinjR1)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', setukpairinjL)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', setukpairinjL2)). 0.90/180.05 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', cartprodfstin)). 0.90/180.05 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setunionsingleton2)). 0.90/180.05 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', cartprodmempair1)). 0.90/180.05 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', ubforcartprodlem3)). 0.90/180.05 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', upairinpowunion)). 0.90/180.05 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', upairsubunion)). 0.90/180.05 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', upairset2E)). 0.90/180.05 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', singletoninpowunion)). 0.90/180.05 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setukpairIL)). 0.90/180.05 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', symdiffIneg2)). 0.90/180.05 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', symdiffI1)). 0.90/180.05 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setminusIRneg)). 0.90/180.05 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setminusELneg)). 0.90/180.05 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setminusERneg)). 0.90/180.05 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setminusER)). 0.90/180.05 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setminusEL)). 0.90/180.05 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', binintersectSubset1)). 0.90/180.05 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', binintersectER)). 0.90/180.05 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', binintersectSubset3)). 0.90/180.05 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', binintersectSubset2)). 0.90/180.05 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', binintersectLsub)). 0.90/180.05 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', binintersectEL)). 0.90/180.05 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', binintersectSubset5)). 0.90/180.05 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', binintersectI)). 0.90/180.05 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', binunionLsub)). 0.90/180.05 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', binunionIR)). 0.90/180.05 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', powersetsubset)). 0.90/180.05 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', powersetI1)). 0.90/180.05 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', subsetemptysetimpeq)). 0.90/180.05 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setextsub)). 0.90/180.05 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', quantDeMorgan3)). 0.90/180.05 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', upairsetIR)). 0.90/180.05 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', upairsetIL)). 0.90/180.05 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', upairsetE)). 0.90/180.05 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', singletonsswitch)). 0.90/180.05 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', eqinunit)). 0.90/180.05 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', notinsingleton)). 0.90/180.05 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', uniqinunit)). 0.90/180.05 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', nonemptyImpWitness)). 0.90/180.05 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', subPowSU)). 0.90/180.05 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setunionE)). 0.90/180.05 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', powersetE)). 0.90/180.05 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', emptyInPowerset)). 0.90/180.05 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', emptyinPowerset)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', setadjoinE)). 0.90/180.05 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', nonemptyE1)). 0.90/180.05 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', noeltsimpempty)). 0.90/180.05 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', emptyI)). 0.90/180.05 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.hRbm8JgpWK/E---3.1_26402.p', setext)). 0.90/180.05 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', emptysetimpfalse)). 0.90/180.05 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', wellorderingAx)). 0.90/180.05 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', omega0Ax)). 0.90/180.05 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setunionAx)). 0.90/180.05 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.hRbm8JgpWK/E---3.1_26402.p', setadjoinAx)). 0.90/180.05 thf(c_0_168, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 0.90/180.05 thf(c_0_169, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 0.90/180.05 thf(c_0_170, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 0.90/180.05 thf(c_0_171, 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])). 0.90/180.05 thf(c_0_172, 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])). 0.90/180.05 thf(c_0_173, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 0.90/180.05 thf(c_0_174, plain, ((emptyE1)<=>![X4:$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])). 0.90/180.05 thf(c_0_175, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.90/180.05 thf(c_0_176, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.90/180.05 thf(c_0_177, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 0.90/180.05 thf(c_0_178, 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])). 0.90/180.05 thf(c_0_179, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 0.90/180.05 thf(c_0_180, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.90/180.05 thf(c_0_181, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.90/180.05 thf(c_0_182, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.90/180.05 thf(c_0_183, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 0.90/180.05 thf(c_0_184, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.90/180.05 thf(c_0_185, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 0.90/180.05 thf(c_0_186, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 0.90/180.05 thf(c_0_187, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 0.90/180.05 thf(c_0_188, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 0.90/180.05 thf(c_0_189, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 0.90/180.05 thf(c_0_190, plain, ((ex1I)<=>![X4:$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])). 0.90/180.05 thf(c_0_191, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 0.90/180.05 thf(c_0_192, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 0.90/180.05 thf(c_0_193, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.90/180.05 thf(c_0_194, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.90/180.05 thf(c_0_195, plain, ((epred1_0)<=>![X487:$i]:(?[X488:$i]:((((![X489:$i]:(((in @ X489 @ X488)=>![X490:$i]:(((in @ X490 @ X489)=>(in @ X490 @ X487)))))&![X491:$i, X492:$i]:((((in @ X491 @ X487)&(in @ X492 @ X487))=>(![X493:$i]:(((in @ X493 @ X488)=>((in @ X491 @ X493)<=>(in @ X492 @ X493))))=>((X491)=(X492))))))&![X494:$i, X495:$i]:((((in @ X494 @ X488)&(in @ X495 @ X488))=>(![X496:$i]:(((in @ X496 @ X494)=>(in @ X496 @ X495)))|![X497:$i]:(((in @ X497 @ X495)=>(in @ X497 @ X494)))))))&![X498:$i]:(((![X499:$i]:(((in @ X499 @ X498)=>(in @ X499 @ X487)))&?[X500:$i]:((in @ X500 @ X498)))=>?[X501:$i, X502:$i]:(((((in @ X501 @ X488)&(in @ X502 @ X498))&~(?[X503:$i]:(((in @ X503 @ X501)&(in @ X503 @ X498)))))&![X504:$i]:(((in @ X504 @ X488)=>(![X505:$i]:(((in @ X505 @ X504)=>(in @ X505 @ X501)))|(in @ X502 @ X504)))))))))))), introduced(definition)). 0.90/180.05 thf(c_0_196, negated_conjecture, ~((![X934:$i, X935:$i]:((![X936:$i]:(((in @ X936 @ X934)<=>(in @ X936 @ X935)))=>((X934)=(X935))))=>(![X933:$i]:(~(in @ X933 @ emptyset))=>(![X481:$i, X482:$i, X483:$i]:(((in @ X483 @ (setadjoin @ X481 @ X482))<=>(((X483)=(X481))|(in @ X483 @ X482))))=>(![X930:$i, X931:$i]:(((in @ X931 @ (powerset @ X930))<=>![X932:$i]:(((in @ X932 @ X931)=>(in @ X932 @ X930)))))=>(![X484:$i, X485:$i]:(((in @ X485 @ (setunion @ X484))<=>?[X486:$i]:(((in @ X485 @ X486)&(in @ X486 @ X484)))))=>((in @ emptyset @ omega)=>(![X929:$i]:(((in @ X929 @ omega)=>(in @ (setadjoin @ X929 @ X929) @ omega)))=>(![X926:$i]:((((in @ emptyset @ X926)&![X927:$i]:((((in @ X927 @ omega)&(in @ X927 @ X926))=>(in @ (setadjoin @ X927 @ X927) @ X926))))=>![X928:$i]:(((in @ X928 @ omega)=>(in @ X928 @ X926)))))=>(![X920:$i > $i > $o, X921:$i]:((![X922:$i]:(((in @ X922 @ X921)=>(exu @ (X920 @ X922))))=>?[X923:$i]:(![X924:$i]:(((in @ X924 @ X923)<=>?[X925:$i]:(((in @ X925 @ X921)&(X920 @ X925 @ X924))))))))=>(![X916:$i]:((?[X917:$i]:((in @ X917 @ X916))=>?[X918:$i]:(((in @ X918 @ X916)&~(?[X919:$i]:(((in @ X919 @ X918)&(in @ X919 @ X916))))))))=>((epred1_0)=>(![X915:$i > $o]:(((exu @ X915)=>(X915 @ (descr @ (^[Z0/* 17 */:$i]:(X915 @ Z0))))))=>(![X912:$i, X913:$i > $o, X914:$i]:(((in @ X914 @ X912)=>((X913 @ X914)=>(in @ X914 @ (dsetconstr @ X912 @ X913)))))=>(![X909:$i, X910:$i > $o, X911:$i]:(((in @ X911 @ (dsetconstr @ X909 @ X910))=>(in @ X911 @ X909)))=>(![X906:$i, X907:$i > $o, X908:$i]:(((in @ X908 @ (dsetconstr @ X906 @ X907))=>(X907 @ X908)))=>(![X903:$i > $o]:(((exu @ X903)=>?[X904:$i]:(((X903 @ X904)&![X905:$i]:(((X903 @ X905)=>((X904)=(X905))))))))=>(![X901:$o, X902:$i]:(((in @ X902 @ (prop2set @ ((X901))))=>(X901)))=>(![X899:$i]:(((in @ X899 @ emptyset)=>![X900:$o]:((X900))))=>(![X506:$i]:(((in @ X506 @ emptyset)=>~($true)))=>(![X898:$i]:(~(in @ X898 @ emptyset))=>(![X896:$i > $o]:(((exu @ X896)=>?[X897:$i]:((X896 @ X897))))=>(![X507:$i, X508:$i]:((![X509:$i]:(((in @ X509 @ X507)=>(in @ X509 @ X508)))=>(![X510:$i]:(((in @ X510 @ X508)=>(in @ X510 @ X507)))=>((X507)=(X508)))))=>(![X511:$i]:((![X512:$i]:(~(in @ X512 @ X511))=>((X511)=(emptyset))))=>(![X513:$i]:((![X514:$i]:(~(in @ X514 @ X513))=>((X513)=(emptyset))))=>(![X515:$i, X516:$i > $o, X517:$i]:(((in @ X517 @ X515)=>((in @ X517 @ (dsetconstr @ X515 @ X516))<=>(X516 @ X517))))=>(![X518:$i]:(((nonempty @ X518)=>?[X519:$i]:((in @ X519 @ X518))))=>(![X893:$i, X894:$i > $o, X895:$i]:(((in @ X895 @ X893)=>((X894 @ X895)=>(nonempty @ (dsetconstr @ X893 @ X894)))))=>(![X891:$i]:((?[X892:$i]:((in @ X892 @ X891))=>(nonempty @ X891)))=>(![X889:$i, X890:$i]:((in @ X889 @ (setadjoin @ X889 @ X890)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X886:$i, X887:$i, X888:$i]:(((in @ X888 @ X887)=>(in @ X888 @ (setadjoin @ X886 @ X887))))=>(![X520:$i, X521:$i, X522:$i]:(((in @ X522 @ (setadjoin @ X520 @ X521))=>![X523:$o]:(((((X522)=(X520))=>(X523))=>(((in @ X522 @ X521)=>(X523))=>(X523))))))=>(![X883:$i, X884:$i, X885:$i]:(((in @ X885 @ (setadjoin @ X883 @ X884))=>(((X885)=(X883))|(in @ X885 @ X884))))=>(![X524:$i]:(((dsetconstr @ X524 @ (^[Z0/* 1 */:$i]:($true)))=(X524)))=>(![X880:$i, X881:$i]:((![X882:$i]:(((in @ X882 @ X881)=>(in @ X882 @ X880)))=>(in @ X881 @ (powerset @ X880))))=>(![X525:$i]:((in @ emptyset @ (powerset @ X525)))=>(![X526:$i]:((in @ emptyset @ (powerset @ X526)))=>(![X527:$i, X528:$i, X529:$i]:(((in @ X528 @ (powerset @ X527))=>((in @ X529 @ X528)=>(in @ X529 @ X527))))=>(![X877:$i, X878:$i, X879:$i]:(((in @ X878 @ X879)=>((in @ X879 @ X877)=>(in @ X878 @ (setunion @ X877)))))=>(![X530:$i, X531:$i]:(((in @ X531 @ (setunion @ X530))=>![X532:$o]:((![X533:$i]:(((in @ X531 @ X533)=>((in @ X533 @ X530)=>(X532))))=>(X532)))))=>(![X534:$i, X535:$i]:(((in @ X535 @ X534)=>(in @ X535 @ (powerset @ (setunion @ X534)))))=>(![X536:$i > $o]:(((exu @ X536)=>?[X537:$i]:(![X538:$i]:(((X536 @ X538)<=>((X538)=(X537)))))))=>(![X539:$i]:(((nonempty @ X539)=>?[X540:$i]:(((in @ X540 @ X539)&$true))))=>(![X541:$i, X542:$i]:(((in @ X541 @ (setadjoin @ X542 @ emptyset))=>((X541)=(X542))))=>(![X543:$i, X544:$i]:((((X543)!=(X544))=>~(in @ X544 @ (setadjoin @ X543 @ emptyset))))=>(![X545:$i, X546:$i]:((((X545)=(X546))=>(in @ X545 @ (setadjoin @ X546 @ emptyset))))=>(![X547:$i, X548:$i]:(((in @ X547 @ (setadjoin @ X548 @ emptyset))=>(in @ X548 @ (setadjoin @ X547 @ emptyset))))=>(![X549:$i, X550:$i, X551:$i]:(((in @ X551 @ (setadjoin @ X549 @ (setadjoin @ X550 @ emptyset)))=>(((X551)=(X549))|((X551)=(X550)))))=>(![X552:$i, X553:$i]:((in @ X552 @ (setadjoin @ X552 @ (setadjoin @ X553 @ emptyset))))=>(![X554:$i, X555:$i]:((in @ X555 @ (setadjoin @ X554 @ (setadjoin @ X555 @ emptyset))))=>(![X556:$i, X557:$i > $o]:((?[X558:$i]:(((in @ X558 @ X556)&(X557 @ X558)))=>(((dsetconstr @ X556 @ X557)=(emptyset))=>~($true))))=>(![X875:$i > $o, X876:$i]:(((in @ X876 @ emptyset)=>(X875 @ X876)))=>(![X559:$i, X560:$i > $o]:((~(![X561:$i]:(((in @ X561 @ X559)=>(X560 @ X561))))=>?[X562:$i]:(((in @ X562 @ X559)&~((X560 @ X562))))))=>(![X563:$i, X564:$i > $o]:((![X565:$i]:(((in @ X565 @ X563)=>~((X564 @ X565))))=>~(?[X566:$i]:(((in @ X566 @ X563)&(X564 @ X566))))))=>(![X567:$i, X568:$i > $o]:((~(?[X569:$i]:(((in @ X569 @ X567)&(X568 @ X569))))=>![X570:$i]:(((in @ X570 @ X567)=>~((X568 @ X570))))))=>(![X571:$i, X572:$i > $o]:((?[X573:$i]:(((in @ X573 @ X571)&~((X572 @ X573))))=>~(![X574:$i]:(((in @ X574 @ X571)=>(X572 @ X574))))))=>(![X874:$o]:(((X874)=>(in @ emptyset @ (prop2set @ ((X874))))))=>((prop2set2propI)=>(![X575:$i, X576:$i > $o]:((~(?[X577:$i]:(((in @ X577 @ X575)&(X576 @ X577))))=>![X578:$i]:(((in @ X578 @ X575)=>~((X576 @ X578))))))=>(![X579:$i, X580:$i > $o]:((~(![X581:$i]:(((in @ X581 @ X579)=>(X580 @ X581))))=>?[X582:$i]:(((in @ X582 @ X579)&~((X580 @ X582))))))=>(![X583:$i > $o]:((?[X584:$i]:(((X583 @ X584)&![X585:$i]:(((X583 @ X585)=>((X584)=(X585))))))=>(exu @ X583)))=>(![X870:$i > $o]:((?[X871:$i]:((X870 @ X871))=>(![X872:$i, X873:$i]:(((X870 @ X872)=>((X870 @ X873)=>((X872)=(X873)))))=>(exu @ X870))))=>(![X867:$i > $o]:((?[X868:$i]:(![X869:$i]:(((X867 @ X869)<=>((X869)=(X868)))))=>(exu @ X867)))=>(![X863:$i, X864:$i]:((((X863)=(X864))=>![X865:$i, X866:$i]:((((X865)=(X866))=>((in @ X865 @ X863)=>(in @ X866 @ X864))))))=>(![X859:$i, X860:$i]:((((X859)=(X860))=>![X861:$i, X862:$i]:((((X861)=(X862))=>((in @ X861 @ X859)<=>(in @ X862 @ X860))))))=>(![X856:$i > $o]:(((exu @ X856)=>![X857:$i, X858:$i]:(((X856 @ X857)=>((X856 @ X858)=>((X857)=(X858)))))))=>(![X852:$i > $o, X853:$i > $o]:((![X854:$i, X855:$i]:((((X854)=(X855))=>((X852 @ X854)<=>(X853 @ X855))))=>((exu @ X852)<=>(exu @ X853))))=>(((emptyset)=(emptyset))=>(![X586:$i, X587:$i]:((((X586)=(X587))=>![X588:$i, X589:$i]:((((X588)=(X589))=>((setadjoin @ X586 @ X588)=(setadjoin @ X587 @ X589))))))=>(![X850:$i, X851:$i]:((((X850)=(X851))=>((powerset @ X850)=(powerset @ X851))))=>(![X590:$i, X591:$i]:((((X590)=(X591))=>((setunion @ X590)=(setunion @ X591))))=>(((omega)=(omega))=>(![X592:$i > $o]:(((exu @ X592)=>![X593:$i, X594:$i]:(((X592 @ X593)=>((X592 @ X594)=>((X593)=(X594)))))))=>(![X595:$i > $o, X596:$i > $o]:((![X597:$i, X598:$i]:((((X597)=(X598))=>((X595 @ X597)<=>(X596 @ X598))))=>((exu @ X595)=>((exu @ X596)=>((descr @ X595)=(descr @ X596))))))=>(![X844:$i, X845:$i]:((((X844)=(X845))=>![X846:$i > $o, X847:$i > $o]:((![X848:$i]:(((in @ X848 @ X844)=>![X849:$i]:(((in @ X849 @ X845)=>(((X848)=(X849))=>((X846 @ X848)<=>(X847 @ X849)))))))=>((dsetconstr @ X844 @ X846)=(dsetconstr @ X845 @ X847))))))=>(![X599:$i, X600:$i]:((![X601:$i]:(((in @ X601 @ X599)=>(in @ X601 @ X600)))=>(subset @ X599 @ X600)))=>(![X602:$i, X603:$i]:((((X602)=(X603))=>(subset @ X603 @ X602)))=>(![X604:$i, X605:$i]:((((X604)=(X605))=>(subset @ X604 @ X605)))=>(![X841:$i, X842:$i]:((![X843:$i]:(((in @ X843 @ X841)=>(in @ X843 @ X842)))=>(subset @ X841 @ X842)))=>(![X606:$i]:((subset @ emptyset @ X606))=>(![X838:$i, X839:$i, X840:$i]:(((subset @ X838 @ X839)=>((in @ X840 @ X838)=>(in @ X840 @ X839))))=>(![X607:$i, X608:$i, X609:$i]:(((subset @ X607 @ X608)=>(~(in @ X609 @ X608)=>~(in @ X609 @ X607))))=>(![X835:$i, X836:$i, X837:$i]:(((in @ X837 @ X835)=>(~(in @ X837 @ X836)=>~(subset @ X835 @ X836))))=>(![X610:$i, X611:$i]:((~(subset @ X610 @ X611)=>((X610)!=(X611))))=>(![X612:$i, X613:$i, X614:$i]:(((in @ X614 @ X612)=>(~(in @ X614 @ X613)=>((X612)!=(X613)))))=>(![X615:$i]:((subset @ X615 @ X615))=>(![X616:$i, X617:$i, X618:$i]:(((subset @ X616 @ X617)=>((subset @ X617 @ X618)=>(subset @ X616 @ X618))))=>(![X833:$i, X834:$i]:((subset @ X834 @ (setadjoin @ X833 @ X834)))=>(![X619:$i, X620:$i, X621:$i]:(((subset @ X619 @ X621)=>(subset @ X619 @ (setadjoin @ X620 @ X621))))=>(![X831:$i, X832:$i]:(((subset @ X831 @ X832)=>(in @ X831 @ (powerset @ X832))))=>(![X829:$i, X830:$i]:(((subset @ X829 @ X830)=>((subset @ X830 @ X829)=>((X829)=(X830)))))=>(![X828:$i]:(((subset @ X828 @ emptyset)=>((X828)=(emptyset))))=>(![X826:$i, X827:$i]:(((subset @ X827 @ X826)=>(in @ X827 @ (powerset @ X826))))=>(![X622:$i, X623:$i]:(((in @ X623 @ (powerset @ X622))=>(subset @ X623 @ X622)))=>(![X624:$i]:((in @ X624 @ (powerset @ X624)))=>(![X824:$i, X825:$i]:(((subset @ X824 @ X825)=>(subset @ (powerset @ X824) @ (powerset @ X825))))=>(![X625:$i, X626:$i > $o]:((in @ (dsetconstr @ X625 @ X626) @ (powerset @ X625)))=>(![X627:$i, X628:$i > $o]:((subset @ (dsetconstr @ X627 @ X628) @ X627))=>(![X629:$i, X630:$i, X631:$i]:(((in @ X631 @ X629)=>(in @ X631 @ (binunion @ X629 @ X630))))=>(![X632:$i, X633:$i]:((in @ X633 @ (setadjoin @ X632 @ (setadjoin @ X633 @ emptyset))))=>(![X821:$i, X822:$i, X823:$i]:(((in @ X823 @ X822)=>(in @ X823 @ (binunion @ X821 @ X822))))=>(![X634:$i, X635:$i, X636:$i, X637:$o]:(((in @ X636 @ (binunion @ X634 @ X635))=>(((in @ X636 @ X634)=>(X637))=>(((in @ X636 @ X635)=>(X637))=>(X637)))))=>(![X638:$i, X639:$i, X640:$i]:(((in @ X640 @ (binunion @ X638 @ X639))=>((in @ X640 @ X638)|(in @ X640 @ X639))))=>(![X819:$i, X820:$i]:((subset @ X819 @ (binunion @ X819 @ X820)))=>(![X641:$i, X642:$i]:((subset @ X642 @ (binunion @ X641 @ X642)))=>(![X816:$i, X817:$i, X818:$i]:(((in @ X818 @ X816)=>((in @ X818 @ X817)=>(in @ X818 @ (binintersect @ X816 @ X817)))))=>(![X813:$i, X814:$i, X815:$i]:(((subset @ X815 @ X813)=>((subset @ X815 @ X814)=>(subset @ X815 @ (binintersect @ X813 @ X814)))))=>(![X810:$i, X811:$i, X812:$i]:(((in @ X812 @ (binintersect @ X810 @ X811))=>(in @ X812 @ X810)))=>(![X808:$i, X809:$i]:((subset @ (binintersect @ X808 @ X809) @ X808))=>(![X806:$i, X807:$i]:(((subset @ X806 @ X807)=>((binintersect @ X806 @ X807)=(X806))))=>(![X804:$i, X805:$i]:((((binintersect @ X804 @ X805)=(X805))=>(subset @ X805 @ X804)))=>(![X801:$i, X802:$i, X803:$i]:(((in @ X803 @ (binintersect @ X801 @ X802))=>(in @ X803 @ X802)))=>(![X643:$i, X644:$i]:((~(?[X645:$i]:(((in @ X645 @ X643)&(in @ X645 @ X644))))=>((binintersect @ X643 @ X644)=(emptyset))))=>(![X646:$i, X647:$i]:((subset @ (binintersect @ X646 @ X647) @ X647))=>(![X648:$i, X649:$i]:(((subset @ X649 @ X648)=>((binintersect @ X648 @ X649)=(X649))))=>(![X799:$i, X800:$i]:((((binintersect @ X799 @ X800)=(X799))=>(subset @ X799 @ X800)))=>(![X650:$i, X651:$i, X652:$i]:(((binintersect @ X650 @ (binunion @ X651 @ X652))=(binunion @ (binintersect @ X650 @ X651) @ (binintersect @ X650 @ X652))))=>(![X653:$i, X654:$i, X655:$i]:(((in @ X655 @ X653)=>(~(in @ X655 @ X654)=>(in @ X655 @ (setminus @ X653 @ X654)))))=>(![X796:$i, X797:$i, X798:$i]:(((in @ X798 @ (setminus @ X796 @ X797))=>(in @ X798 @ X796)))=>(![X793:$i, X794:$i, X795:$i]:(((in @ X795 @ (setminus @ X793 @ X794))=>~(in @ X795 @ X794)))=>(![X656:$i, X657:$i]:(((subset @ X656 @ X657)=>((setminus @ X656 @ X657)=(emptyset))))=>(![X790:$i, X791:$i, X792:$i]:((~(in @ X792 @ (setminus @ X790 @ X791))=>((in @ X792 @ X790)=>(in @ X792 @ X791))))=>(![X787:$i, X788:$i, X789:$i]:((~(in @ X789 @ (setminus @ X787 @ X788))=>(~(in @ X789 @ X788)=>~(in @ X789 @ X787))))=>(![X658:$i, X659:$i, X660:$i]:((~(in @ X660 @ X658)=>~(in @ X660 @ (setminus @ X658 @ X659))))=>(![X784:$i, X785:$i, X786:$i]:(((in @ X786 @ X785)=>~(in @ X786 @ (setminus @ X784 @ X785))))=>(![X661:$i, X662:$i]:((subset @ (setminus @ X661 @ X662) @ X661))=>(![X663:$i, X664:$i]:((((setminus @ X663 @ X664)=(emptyset))=>(subset @ X663 @ X664)))=>(![X665:$i, X666:$i, X667:$i]:(((in @ X667 @ (symdiff @ X665 @ X666))=>![X668:$o]:((((in @ X667 @ X665)=>(~(in @ X667 @ X666)=>(X668)))=>((~(in @ X667 @ X665)=>((in @ X667 @ X666)=>(X668)))=>(X668))))))=>(![X781:$i, X782:$i, X783:$i]:(((in @ X783 @ X781)=>(~(in @ X783 @ X782)=>(in @ X783 @ (symdiff @ X781 @ X782)))))=>(![X669:$i, X670:$i, X671:$i]:((~(in @ X671 @ X669)=>((in @ X671 @ X670)=>(in @ X671 @ (symdiff @ X669 @ X670)))))=>(![X672:$i, X673:$i, X674:$i]:(((in @ X674 @ X672)=>((in @ X674 @ X673)=>~(in @ X674 @ (symdiff @ X672 @ X673)))))=>(![X778:$i, X779:$i, X780:$i]:((~(in @ X780 @ X778)=>(~(in @ X780 @ X779)=>~(in @ X780 @ (symdiff @ X778 @ X779)))))=>(![X675:$i, X676:$i]:((in @ X676 @ (setadjoin @ X675 @ (setadjoin @ X676 @ emptyset))))=>(![X776:$i, X777:$i]:((in @ X776 @ (setunion @ (setadjoin @ (setadjoin @ X776 @ emptyset) @ (setadjoin @ (setadjoin @ X776 @ (setadjoin @ X777 @ emptyset)) @ emptyset)))))=>(![X677:$i, X678:$i]:((in @ X678 @ (setunion @ (setadjoin @ (setadjoin @ X677 @ emptyset) @ (setadjoin @ (setadjoin @ X677 @ (setadjoin @ X678 @ emptyset)) @ emptyset)))))=>(![X679:$i, X680:$i]:((iskpair @ (setadjoin @ (setadjoin @ X679 @ emptyset) @ (setadjoin @ (setadjoin @ X679 @ (setadjoin @ X680 @ emptyset)) @ emptyset))))=>(![X681:$i, X682:$i]:((iskpair @ (kpair @ X681 @ X682)))=>(![X683:$i, X684:$i]:(((in @ X684 @ X683)=>(subset @ (setadjoin @ X684 @ emptyset) @ X683)))=>(![X685:$i, X686:$i]:(((in @ X686 @ X685)=>(in @ (setadjoin @ X686 @ emptyset) @ (powerset @ X685))))=>(![X773:$i, X774:$i, X775:$i]:(((in @ X775 @ X773)=>(in @ (setadjoin @ X775 @ emptyset) @ (powerset @ (binunion @ X773 @ X774)))))=>(![X770:$i, X771:$i, X772:$i]:(((in @ X772 @ (setadjoin @ X770 @ (setadjoin @ X771 @ emptyset)))=>(((X772)=(X770))|((X772)=(X771)))))=>(![X766:$i, X767:$i, X768:$i]:(((in @ X768 @ X766)=>![X769:$i]:(((in @ X769 @ X767)=>(subset @ (setadjoin @ X768 @ (setadjoin @ X769 @ emptyset)) @ (binunion @ X766 @ X767))))))=>(![X762:$i, X763:$i, X764:$i]:(((in @ X764 @ X762)=>![X765:$i]:(((in @ X765 @ X763)=>(in @ (setadjoin @ X764 @ (setadjoin @ X765 @ emptyset)) @ (powerset @ (binunion @ X762 @ X763)))))))=>(![X687:$i, X688:$i, X689:$i]:(((in @ X689 @ X687)=>![X690:$i]:(((in @ X690 @ X688)=>(subset @ (setadjoin @ (setadjoin @ X689 @ emptyset) @ (setadjoin @ (setadjoin @ X689 @ (setadjoin @ X690 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X687 @ X688)))))))=>(![X691:$i, X692:$i, X693:$i]:(((in @ X693 @ X691)=>![X694:$i]:(((in @ X694 @ X692)=>(in @ (setadjoin @ (setadjoin @ X693 @ emptyset) @ (setadjoin @ (setadjoin @ X693 @ (setadjoin @ X694 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X691 @ X692))))))))=>(![X758:$i, X759:$i, X760:$i]:(((in @ X760 @ X758)=>![X761:$i]:(((in @ X761 @ X759)=>(in @ (kpair @ X760 @ X761) @ (powerset @ (powerset @ (binunion @ X758 @ X759))))))))=>(![X695:$i, X696:$i, X697:$i]:(((in @ X697 @ X695)=>![X698:$i]:(((in @ X698 @ X696)=>(in @ (kpair @ X697 @ X698) @ (cartprod @ X695 @ X696))))))=>(![X753:$i, X754:$i, X755:$i]:(((in @ X755 @ (cartprod @ X753 @ X754))=>?[X756:$i]:(((in @ X756 @ X753)&?[X757:$i]:(((in @ X757 @ X754)&((X755)=(kpair @ X756 @ X757))))))))=>(![X699:$i, X700:$i, X701:$i]:(((in @ X701 @ (cartprod @ X699 @ X700))=>(iskpair @ X701)))=>(![X702:$i, X703:$i]:(((in @ X703 @ (setunion @ X702))=>?[X704:$i]:(((in @ X704 @ X702)&(in @ X703 @ X704)))))=>(![X705:$i]:((subset @ (setunion @ (setadjoin @ X705 @ emptyset)) @ X705))=>(![X752:$i]:((subset @ X752 @ (setunion @ (setadjoin @ X752 @ emptyset))))=>(![X706:$i]:(((setunion @ (setadjoin @ X706 @ emptyset))=(X706)))=>(![X747:$i, X748:$i > $o]:((![X749:$i]:(((in @ X749 @ X747)=>![X750:$i]:(((in @ X750 @ X747)=>((X748 @ X749)=>((X748 @ X750)=>((X749)=(X750))))))))=>(?[X751:$i]:(((in @ X751 @ X747)&(X748 @ X751)))=>(singleton @ (dsetconstr @ X747 @ X748)))))=>(![X707:$i, X708:$i > $o]:(((ex1 @ X707 @ X708)=>?[X709:$i]:(((in @ X709 @ X707)&(X708 @ X709)))))=>(![X743:$i, X744:$i > $o, X745:$i]:(((in @ X745 @ X743)=>((X744 @ X745)=>(![X746:$i]:(((in @ X746 @ X743)=>((X744 @ X746)=>((X746)=(X745)))))=>(ex1 @ X743 @ X744)))))=>(![X738:$i, X739:$i > $o]:((![X740:$i]:(((in @ X740 @ X738)=>![X741:$i]:(((in @ X741 @ X738)=>((X739 @ X740)=>((X739 @ X741)=>((X740)=(X741))))))))=>(?[X742:$i]:(((in @ X742 @ X738)&(X739 @ X742)))=>(ex1 @ X738 @ X739))))=>(![X710:$i, X711:$i]:((((setadjoin @ X710 @ emptyset)=(setadjoin @ X711 @ emptyset))=>((X710)=(X711))))=>(![X712:$i, X713:$i, X714:$i]:(((in @ (setadjoin @ X714 @ emptyset) @ (setadjoin @ (setadjoin @ X712 @ emptyset) @ (setadjoin @ (setadjoin @ X712 @ (setadjoin @ X713 @ emptyset)) @ emptyset)))=>((X712)=(X714))))=>(![X737:$i]:(((iskpair @ X737)=>(singleton @ (dsetconstr @ (setunion @ X737) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X737)))))))=>(![X715:$i]:(((singleton @ X715)=>(in @ (setunion @ X715) @ X715)))=>(![X716:$i, X717:$i]:(((kfst @ (kpair @ X716 @ X717))=(X716)))=>(![X734:$i, X735:$i, X736:$i]:(((in @ X736 @ (cartprod @ X734 @ X735))=>(in @ (kfst @ X736) @ X734)))=>(![X730:$i, X731:$i, X732:$i, X733:$i]:((((setadjoin @ (setadjoin @ X730 @ emptyset) @ (setadjoin @ (setadjoin @ X730 @ (setadjoin @ X731 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X732 @ emptyset) @ (setadjoin @ (setadjoin @ X732 @ (setadjoin @ X733 @ emptyset)) @ emptyset)))=>((X730)=(X732))))=>(![X726:$i, X727:$i, X728:$i, X729:$i]:((((kpair @ X726 @ X727)=(kpair @ X728 @ X729))=>((X726)=(X728))))=>(![X718:$i, X719:$i]:((((X718)=(X719))=>((setadjoin @ X718 @ (setadjoin @ X719 @ emptyset))=(setadjoin @ X718 @ emptyset))))=>(![X720:$i, X721:$i]:((((X720)=(X721))=>((setadjoin @ (setadjoin @ X720 @ emptyset) @ (setadjoin @ (setadjoin @ X720 @ (setadjoin @ X721 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X720 @ emptyset) @ emptyset))))=>(![X722:$i, X723:$i, X724:$i, X725:$i]:((((setadjoin @ (setadjoin @ X722 @ emptyset) @ (setadjoin @ (setadjoin @ X722 @ (setadjoin @ X723 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X724 @ emptyset) @ (setadjoin @ (setadjoin @ X724 @ (setadjoin @ X725 @ emptyset)) @ emptyset)))=>(((X724)=(X725))=>((X723)=(X725)))))=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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(assume_negation,[status(cth)],[upairequniteq]), quantDeMorgan1]), nonemptyI1]), setextAx]), subset2powerset]), setadjoinSub]), notsubsetI]), quantDeMorgan4]), subsetE]), subsetI2]), c_0_168]), notdexE]), powerset__Cong]), c_0_169]), notdallE]), c_0_170]), in__Cong]), inCongP]), c_0_171]), c_0_172]), c_0_173]), emptyset__Cong]), prop2setI]), vacuousDall]), c_0_174]), setunionI]), powersetI]), setadjoin__Cong]), setadjoinOr]), setadjoinIR]), setunion__Cong]), emptyinunitempty]), setadjoinIL]), c_0_175]), omega__Cong]), c_0_176]), notinemptyset]), c_0_177]), emptysetE]), prop2setE]), c_0_178]), c_0_179]), c_0_180]), c_0_181]), subsetI1]), c_0_182]), c_0_183]), foundationAx]), eqimpsubset2]), c_0_184]), omegaIndAx]), eqimpsubset1]), omegaSAx]), powersetAx]), emptysetAx]), emptysetsubset]), subsetE2]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub2]), powersetE1]), inPowerset]), c_0_185]), c_0_186]), singletonsuniq]), c_0_187]), binunionIL]), upairset2IR]), binunionEcases]), binunionE]), binunionRsub]), disjointsetsI1]), binintersectRsub]), quantDeMorgan2]), binintersectSubset4]), bs114d]), setminusI]), setminusSubset2]), setminusILneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI2]), symdiffIneg1]), secondinupair]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), ubforcartprodlem1]), ubforcartprodlem2]), cartprodpairin]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton]), setukpairinjL1]), theprop]), kfstpairEq]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), setukpairinjL]), setukpairinjL2]), cartprodfstin]), c_0_188]), c_0_189]), c_0_190]), c_0_191]), setunionsingleton2]), cartprodmempair1]), ubforcartprodlem3]), upairinpowunion]), upairsubunion]), upairset2E]), singletoninpowunion]), setukpairIL]), symdiffIneg2]), symdiffI1]), setminusIRneg]), setminusELneg]), setminusERneg]), setminusER]), setminusEL]), binintersectSubset1]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binintersectSubset5]), binintersectI]), binunionLsub]), binunionIR]), powersetsubset]), powersetI1]), subsetemptysetimpeq]), setextsub]), quantDeMorgan3]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), nonemptyImpWitness]), c_0_192]), subPowSU]), setunionE]), powersetE]), emptyInPowerset]), emptyinPowerset]), c_0_193]), setadjoinE]), nonemptyE1]), c_0_194]), noeltsimpempty]), emptyI]), setext]), emptysetimpfalse]), wellorderingAx]), omega0Ax]), setunionAx]), setadjoinAx])])]), c_0_195])). 0.90/180.05 thf(c_0_197, negated_conjecture, ![X937:$i, X938:$i, X940:$i, X941:$i, X942:$i, X943:$i, X944:$i, X945:$i, X946:$i, X947:$i, X948:$i, X950:$i, X951:$i, X953:$i, X954:$i, X955:$i, X956:$i, X957:$i, X959:$i, X960:$i > $i > $o, X961:$i, X964:$i, X966:$i, X967:$i, X968:$i, X969:$i, X971:$i, X972:$i > $o, X973:$i, X974:$i > $o, X975:$i, X976:$i, X977:$i > $o, X978:$i, X979:$i, X980:$i > $o, X981:$i, X982:$i > $o, X984:$i, X985:$o, X986:$i, X987:$i, X988:$o, X989:$i, X990:$i, X991:$i > $o, X993:$i, X994:$i, X997:$i, X999:$i, X1001:$i, X1002:$i > $o, X1003:$i, X1004:$i, X1006:$i, X1007:$i > $o, X1008:$i, X1009:$i, X1010:$i, X1011:$i, X1012:$i, X1013:$i, X1014:$i, X1015:$i, X1016:$i, X1017:$i, X1018:$i, X1019:$o, X1020:$i, X1021:$i, X1022:$i, X1023:$i, X1024:$i, X1025:$i, X1027:$i, X1028:$i, X1029:$i, X1030:$i, X1031:$i, X1032:$i, X1033:$i, X1034:$i, X1035:$i, X1036:$i, X1037:$o, X1039:$i, X1040:$i, X1041:$i > $o, X1043:$i, X1044:$i, X1045:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$i, X1053:$i, X1054:$i, X1055:$i, X1056:$i, X1057:$i, X1058:$i, X1059:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i > $o, X1064:$i, X1065:$i > $o, X1066:$i, X1067:$i, X1068:$i > $o, X1069:$i, X1071:$i, X1072:$i > $o, X1074:$i, X1075:$i, X1076:$i > $o, X1078:$i, X1079:$i, X1080:$i > $o, X1081:$i, X1083:$o, X1084:$i, X1085:$i > $o, X1087:$i, X1088:$i, X1089:$i > $o, X1090:$i, X1092:$i > $o, X1093:$i, X1095:$i > $o, X1096:$i, X1099:$i > $o, X1100:$i, X1102:$i, X1103:$i, X1104:$i, X1105:$i, X1106:$i, X1107:$i, X1108:$i, X1109:$i, X1110:$i > $o, X1111:$i, X1112:$i, X1113:$i > $o, X1114:$i > $o, X1117:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i > $o, X1126:$i, X1127:$i, X1128:$i > $o, X1129:$i > $o, X1132:$i, X1133:$i, X1134:$i > $o, X1135:$i > $o, X1138:$i, X1139:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1148:$i, X1149:$i, X1150:$i, X1151:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$i, X1162:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$i, X1171:$i, X1172:$i, X1173:$i, X1174:$i, X1175:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1185:$i > $o, X1186:$i, X1187:$i > $o, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i, X1198:$i, X1199:$o, X1200:$i, X1201:$i, X1202:$i, X1203:$i, X1204:$i, X1205:$i, X1206:$i, X1207:$i, X1208:$i, X1209:$i, X1210:$i, X1211:$i, X1212:$i, X1213:$i, X1214:$i, X1215:$i, X1216:$i, X1217:$i, X1218:$i, X1219:$i, X1220:$i, X1221:$i, X1222:$i, X1223:$i, X1224:$i, X1225:$i, X1226:$i, X1228:$i, X1229:$i, X1230:$i, X1231:$i, X1232:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, X1240:$i, X1241:$i, X1242:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i, X1251:$i, X1252:$i, X1253:$i, X1254:$i, X1255:$i, X1256:$i, X1257:$i, X1258:$i, X1259:$i, X1260:$i, X1261:$i, X1262:$i, X1263:$i, X1264:$i, X1265:$i, X1266:$i, X1267:$o, X1268:$i, X1269:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$i, X1278:$i, X1279:$i, X1280:$i, X1281:$i, X1282:$i, X1283:$i, X1284:$i, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$i, X1290:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1305:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1326:$i, X1329:$i, X1330:$i, X1331:$i, X1332:$i, X1333:$i, X1335:$i, X1336:$i, X1337:$i, X1338:$i, X1339:$i > $o, X1342:$i, X1343:$i, X1344:$i > $o, X1346:$i, X1347:$i > $o, X1348:$i, X1350:$i, X1351:$i > $o, X1354:$i, X1355:$i, X1356:$i, X1357:$i, X1358:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i, X1365:$i, X1366:$i, X1367:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i, X1381:$i, X1382:$i]:((((~(in @ (esk1_2 @ X937 @ X938) @ X937)|~(in @ (esk1_2 @ X937 @ X938) @ X938)|((X937)=(X938)))&((in @ (esk1_2 @ X937 @ X938) @ X937)|(in @ (esk1_2 @ X937 @ X938) @ X938)|((X937)=(X938))))&(~(in @ X940 @ emptyset)&(((~(in @ X943 @ (setadjoin @ X941 @ X942))|(((X943)=(X941))|(in @ X943 @ X942)))&((((X943)!=(X941))|(in @ X943 @ (setadjoin @ X941 @ X942)))&(~(in @ X943 @ X942)|(in @ X943 @ (setadjoin @ X941 @ X942)))))&(((~(in @ X945 @ (powerset @ X944))|(~(in @ X946 @ X945)|(in @ X946 @ X944)))&(((in @ (esk2_2 @ X947 @ X948) @ X948)|(in @ X948 @ (powerset @ X947)))&(~(in @ (esk2_2 @ X947 @ X948) @ X947)|(in @ X948 @ (powerset @ X947)))))&(((((in @ X951 @ (esk3_2 @ X950 @ X951))|~(in @ X951 @ (setunion @ X950)))&((in @ (esk3_2 @ X950 @ X951) @ X950)|~(in @ X951 @ (setunion @ X950))))&(~(in @ X954 @ X955)|~(in @ X955 @ X953)|(in @ X954 @ (setunion @ X953))))&((in @ emptyset @ omega)&((~(in @ X956 @ omega)|(in @ (setadjoin @ X956 @ X956) @ omega))&(((((in @ (esk4_1 @ X957) @ omega)|~(in @ emptyset @ X957)|(~(in @ X959 @ omega)|(in @ X959 @ X957)))&((in @ (esk4_1 @ X957) @ X957)|~(in @ emptyset @ X957)|(~(in @ X959 @ omega)|(in @ X959 @ X957))))&(~(in @ (setadjoin @ (esk4_1 @ X957) @ (esk4_1 @ X957)) @ X957)|~(in @ emptyset @ X957)|(~(in @ X959 @ omega)|(in @ X959 @ X957))))&((((((in @ (esk7_3 @ X960 @ X961 @ X964) @ X961)|~(in @ X964 @ (esk6_2 @ X960 @ X961))|(in @ (esk5_2 @ X960 @ X961) @ X961))&((X960 @ (esk7_3 @ X960 @ X961 @ X964) @ X964)|~(in @ X964 @ (esk6_2 @ X960 @ X961))|(in @ (esk5_2 @ X960 @ X961) @ X961)))&(~(in @ X967 @ X961)|~(X960 @ X967 @ X966)|(in @ X966 @ (esk6_2 @ X960 @ X961))|(in @ (esk5_2 @ X960 @ X961) @ X961)))&((((in @ (esk7_3 @ X960 @ X961 @ X964) @ X961)|~(in @ X964 @ (esk6_2 @ X960 @ X961))|~(exu @ (X960 @ (esk5_2 @ X960 @ X961))))&((X960 @ (esk7_3 @ X960 @ X961 @ X964) @ X964)|~(in @ X964 @ (esk6_2 @ X960 @ X961))|~(exu @ (X960 @ (esk5_2 @ X960 @ X961)))))&(~(in @ X967 @ X961)|~(X960 @ X967 @ X966)|(in @ X966 @ (esk6_2 @ X960 @ X961))|~(exu @ (X960 @ (esk5_2 @ X960 @ X961))))))&((((in @ (esk8_1 @ X968) @ X968)|~(in @ X969 @ X968))&(~(in @ X971 @ (esk8_1 @ X968))|~(in @ X971 @ X968)|~(in @ X969 @ X968)))&((epred1_0)&((~(exu @ X972)|(X972 @ (descr @ X972)))&((~(in @ X975 @ X973)|(~(X974 @ X975)|(in @ X975 @ (dsetconstr @ X973 @ X974))))&((~(in @ X978 @ (dsetconstr @ X976 @ X977))|(in @ X978 @ X976))&((~(in @ X981 @ (dsetconstr @ X979 @ X980))|(X980 @ X981))&((((X982 @ (esk9_1 @ X982))|~(exu @ X982))&(~(X982 @ X984)|((esk9_1 @ X982)=(X984))|~(exu @ X982)))&((~(in @ X986 @ (prop2set @ ((X985))))|(X985))&((~(in @ X987 @ emptyset)|(X988))&((~(in @ X989 @ emptyset)|~($true))&(~(in @ X990 @ emptyset)&((~(exu @ X991)|(X991 @ (esk10_1 @ X991)))&(((((in @ (esk12_2 @ X993 @ X994) @ X994)|((X993)=(X994))|(in @ (esk11_2 @ X993 @ X994) @ X993))&(~(in @ (esk12_2 @ X993 @ X994) @ X993)|((X993)=(X994))|(in @ (esk11_2 @ X993 @ X994) @ X993)))&(((in @ (esk12_2 @ X993 @ X994) @ X994)|((X993)=(X994))|~(in @ (esk11_2 @ X993 @ X994) @ X994))&(~(in @ (esk12_2 @ X993 @ X994) @ X993)|((X993)=(X994))|~(in @ (esk11_2 @ X993 @ X994) @ X994))))&(((in @ (esk13_1 @ X997) @ X997)|((X997)=(emptyset)))&(((in @ (esk14_1 @ X999) @ X999)|((X999)=(emptyset)))&(((~(in @ X1003 @ (dsetconstr @ X1001 @ X1002))|(X1002 @ X1003)|~(in @ X1003 @ X1001))&(~(X1002 @ X1003)|(in @ X1003 @ (dsetconstr @ X1001 @ X1002))|~(in @ X1003 @ X1001)))&((~(nonempty @ X1004)|(in @ (esk15_1 @ X1004) @ X1004))&((~(in @ X1008 @ X1006)|(~(X1007 @ X1008)|(nonempty @ (dsetconstr @ X1006 @ X1007))))&((~(in @ X1010 @ X1009)|(nonempty @ X1009))&((in @ X1011 @ (setadjoin @ X1011 @ X1012))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1015 @ X1014)|(in @ X1015 @ (setadjoin @ X1013 @ X1014)))&(((((in @ X1018 @ X1017)|(X1019)|((X1018)=(X1016))|~(in @ X1018 @ (setadjoin @ X1016 @ X1017)))&(~(X1019)|(X1019)|((X1018)=(X1016))|~(in @ X1018 @ (setadjoin @ X1016 @ X1017))))&(((in @ X1018 @ X1017)|(X1019)|~(X1019)|~(in @ X1018 @ (setadjoin @ X1016 @ X1017)))&(~(X1019)|(X1019)|~(X1019)|~(in @ X1018 @ (setadjoin @ X1016 @ X1017)))))&((~(in @ X1022 @ (setadjoin @ X1020 @ X1021))|(((X1022)=(X1020))|(in @ X1022 @ X1021)))&(((dsetconstr @ X1023 @ (^[Z0/* 1 */:$i]:($true)))=(X1023))&((((in @ (esk16_2 @ X1024 @ X1025) @ X1025)|(in @ X1025 @ (powerset @ X1024)))&(~(in @ (esk16_2 @ X1024 @ X1025) @ X1024)|(in @ X1025 @ (powerset @ X1024))))&((in @ emptyset @ (powerset @ X1027))&((in @ emptyset @ (powerset @ X1028))&((~(in @ X1030 @ (powerset @ X1029))|(~(in @ X1031 @ X1030)|(in @ X1031 @ X1029)))&((~(in @ X1033 @ X1034)|(~(in @ X1034 @ X1032)|(in @ X1033 @ (setunion @ X1032))))&((((in @ X1036 @ (esk17_3 @ X1035 @ X1036 @ X1037))|(X1037)|~(in @ X1036 @ (setunion @ X1035)))&(((in @ (esk17_3 @ X1035 @ X1036 @ X1037) @ X1035)|(X1037)|~(in @ X1036 @ (setunion @ X1035)))&(~(X1037)|(X1037)|~(in @ X1036 @ (setunion @ X1035)))))&((~(in @ X1040 @ X1039)|(in @ X1040 @ (powerset @ (setunion @ X1039))))&(((~(X1041 @ X1043)|((X1043)=(esk18_1 @ X1041))|~(exu @ X1041))&(((X1044)!=(esk18_1 @ X1041))|(X1041 @ X1044)|~(exu @ X1041)))&((((in @ (esk19_1 @ X1045) @ X1045)|~(nonempty @ X1045))&(($true)|~(nonempty @ X1045)))&((~(in @ X1047 @ (setadjoin @ X1048 @ emptyset))|((X1047)=(X1048)))&((((X1049)=(X1050))|~(in @ X1050 @ (setadjoin @ X1049 @ emptyset)))&((((X1051)!=(X1052))|(in @ X1051 @ (setadjoin @ X1052 @ emptyset)))&((~(in @ X1053 @ (setadjoin @ X1054 @ emptyset))|(in @ X1054 @ (setadjoin @ X1053 @ emptyset)))&((~(in @ X1057 @ (setadjoin @ X1055 @ (setadjoin @ X1056 @ emptyset)))|(((X1057)=(X1055))|((X1057)=(X1056))))&((in @ X1058 @ (setadjoin @ X1058 @ (setadjoin @ X1059 @ emptyset)))&((in @ X1061 @ (setadjoin @ X1060 @ (setadjoin @ X1061 @ emptyset)))&((~(in @ X1064 @ X1062)|~(X1063 @ X1064)|(((dsetconstr @ X1062 @ X1063)!=(emptyset))|~($true)))&((~(in @ X1066 @ emptyset)|(X1065 @ X1066))&((((in @ (esk20_2 @ X1067 @ X1068) @ X1067)|(~(in @ X1069 @ X1067)|(X1068 @ X1069)))&(~(X1068 @ (esk20_2 @ X1067 @ X1068))|(~(in @ X1069 @ X1067)|(X1068 @ X1069))))&((((in @ (esk21_2 @ X1071 @ X1072) @ X1071)|(~(in @ X1074 @ X1071)|~(X1072 @ X1074)))&((X1072 @ (esk21_2 @ X1071 @ X1072))|(~(in @ X1074 @ X1071)|~(X1072 @ X1074))))&((((in @ (esk22_2 @ X1075 @ X1076) @ X1075)|(~(in @ X1078 @ X1075)|~(X1076 @ X1078)))&((X1076 @ (esk22_2 @ X1075 @ X1076))|(~(in @ X1078 @ X1075)|~(X1076 @ X1078))))&((((in @ (esk23_2 @ X1079 @ X1080) @ X1079)|(~(in @ X1081 @ X1079)|(X1080 @ X1081)))&(~(X1080 @ (esk23_2 @ X1079 @ X1080))|(~(in @ X1081 @ X1079)|(X1080 @ X1081))))&((~(X1083)|(in @ emptyset @ (prop2set @ ((X1083)))))&((prop2set2propI)&((((in @ (esk24_2 @ X1084 @ X1085) @ X1084)|(~(in @ X1087 @ X1084)|~(X1085 @ X1087)))&((X1085 @ (esk24_2 @ X1084 @ X1085))|(~(in @ X1087 @ X1084)|~(X1085 @ X1087))))&((((in @ (esk25_2 @ X1088 @ X1089) @ X1088)|(~(in @ X1090 @ X1088)|(X1089 @ X1090)))&(~(X1089 @ (esk25_2 @ X1088 @ X1089))|(~(in @ X1090 @ X1088)|(X1089 @ X1090))))&((((X1092 @ (esk26_2 @ X1092 @ X1093))|~(X1092 @ X1093)|(exu @ X1092))&(((X1093)!=(esk26_2 @ X1092 @ X1093))|~(X1092 @ X1093)|(exu @ X1092)))&((((X1095 @ (esk27_1 @ X1095))|(exu @ X1095)|~(X1095 @ X1096))&(((X1095 @ (esk28_1 @ X1095))|(exu @ X1095)|~(X1095 @ X1096))&(((esk27_1 @ X1095)!=(esk28_1 @ X1095))|(exu @ X1095)|~(X1095 @ X1096))))&(((~(X1099 @ (esk29_2 @ X1099 @ X1100))|((esk29_2 @ X1099 @ X1100)!=(X1100))|(exu @ X1099))&((X1099 @ (esk29_2 @ X1099 @ X1100))|((esk29_2 @ X1099 @ X1100)=(X1100))|(exu @ X1099)))&((((X1102)!=(X1103))|(((X1104)!=(X1105))|(~(in @ X1104 @ X1102)|(in @ X1105 @ X1103))))&(((~(in @ X1108 @ X1106)|(in @ X1109 @ X1107)|((X1108)!=(X1109))|((X1106)!=(X1107)))&(~(in @ X1109 @ X1107)|(in @ X1108 @ X1106)|((X1108)!=(X1109))|((X1106)!=(X1107))))&((~(exu @ X1110)|(~(X1110 @ X1111)|(~(X1110 @ X1112)|((X1111)=(X1112)))))&((((~(exu @ X1113)|(exu @ X1114)|((esk30_2 @ X1113 @ X1114)=(esk31_2 @ X1113 @ X1114)))&(~(exu @ X1114)|(exu @ X1113)|((esk30_2 @ X1113 @ X1114)=(esk31_2 @ X1113 @ X1114))))&(((~(exu @ X1113)|(exu @ X1114)|(~(X1113 @ (esk30_2 @ X1113 @ X1114))|~(X1114 @ (esk31_2 @ X1113 @ X1114))))&(~(exu @ X1114)|(exu @ X1113)|(~(X1113 @ (esk30_2 @ X1113 @ X1114))|~(X1114 @ (esk31_2 @ X1113 @ X1114)))))&((~(exu @ X1113)|(exu @ X1114)|((X1113 @ (esk30_2 @ X1113 @ X1114))|(X1114 @ (esk31_2 @ X1113 @ X1114))))&(~(exu @ X1114)|(exu @ X1113)|((X1113 @ (esk30_2 @ X1113 @ X1114))|(X1114 @ (esk31_2 @ X1113 @ X1114)))))))&(((emptyset)=(emptyset))&((((X1117)!=(X1118))|(((X1119)!=(X1120))|((setadjoin @ X1117 @ X1119)=(setadjoin @ X1118 @ X1120))))&((((X1121)!=(X1122))|((powerset @ X1121)=(powerset @ X1122)))&((((X1123)!=(X1124))|((setunion @ X1123)=(setunion @ X1124)))&(((omega)=(omega))&((~(exu @ X1125)|(~(X1125 @ X1126)|(~(X1125 @ X1127)|((X1126)=(X1127)))))&(((((esk32_2 @ X1128 @ X1129)=(esk33_2 @ X1128 @ X1129))|(~(exu @ X1128)|(~(exu @ X1129)|((descr @ X1128)=(descr @ X1129)))))&((~(X1128 @ (esk32_2 @ X1128 @ X1129))|~(X1129 @ (esk33_2 @ X1128 @ X1129))|(~(exu @ X1128)|(~(exu @ X1129)|((descr @ X1128)=(descr @ X1129)))))&((X1128 @ (esk32_2 @ X1128 @ X1129))|(X1129 @ (esk33_2 @ X1128 @ X1129))|(~(exu @ X1128)|(~(exu @ X1129)|((descr @ X1128)=(descr @ X1129)))))))&((((in @ (esk34_4 @ X1132 @ X1133 @ X1134 @ X1135) @ X1132)|((dsetconstr @ X1132 @ X1134)=(dsetconstr @ X1133 @ X1135))|((X1132)!=(X1133)))&(((in @ (esk35_4 @ X1132 @ X1133 @ X1134 @ X1135) @ X1133)|((dsetconstr @ X1132 @ X1134)=(dsetconstr @ X1133 @ X1135))|((X1132)!=(X1133)))&((((esk34_4 @ X1132 @ X1133 @ X1134 @ X1135)=(esk35_4 @ X1132 @ X1133 @ X1134 @ X1135))|((dsetconstr @ X1132 @ X1134)=(dsetconstr @ X1133 @ X1135))|((X1132)!=(X1133)))&((~(X1134 @ (esk34_4 @ X1132 @ X1133 @ X1134 @ X1135))|~(X1135 @ (esk35_4 @ X1132 @ X1133 @ X1134 @ X1135))|((dsetconstr @ X1132 @ X1134)=(dsetconstr @ X1133 @ X1135))|((X1132)!=(X1133)))&((X1134 @ (esk34_4 @ X1132 @ X1133 @ X1134 @ X1135))|(X1135 @ (esk35_4 @ X1132 @ X1133 @ X1134 @ X1135))|((dsetconstr @ X1132 @ X1134)=(dsetconstr @ X1133 @ X1135))|((X1132)!=(X1133)))))))&((((in @ (esk36_2 @ X1138 @ X1139) @ X1138)|(subset @ X1138 @ X1139))&(~(in @ (esk36_2 @ X1138 @ X1139) @ X1139)|(subset @ X1138 @ X1139)))&((((X1141)!=(X1142))|(subset @ X1142 @ X1141))&((((X1143)!=(X1144))|(subset @ X1143 @ X1144))&((((in @ (esk37_2 @ X1145 @ X1146) @ X1145)|(subset @ X1145 @ X1146))&(~(in @ (esk37_2 @ X1145 @ X1146) @ X1146)|(subset @ X1145 @ X1146)))&((subset @ emptyset @ X1148)&((~(subset @ X1149 @ X1150)|(~(in @ X1151 @ X1149)|(in @ X1151 @ X1150)))&((~(subset @ X1152 @ X1153)|((in @ X1154 @ X1153)|~(in @ X1154 @ X1152)))&((~(in @ X1157 @ X1155)|((in @ X1157 @ X1156)|~(subset @ X1155 @ X1156)))&(((subset @ X1158 @ X1159)|((X1158)!=(X1159)))&((~(in @ X1162 @ X1160)|((in @ X1162 @ X1161)|((X1160)!=(X1161))))&((subset @ X1163 @ X1163)&((~(subset @ X1164 @ X1165)|(~(subset @ X1165 @ X1166)|(subset @ X1164 @ X1166)))&((subset @ X1168 @ (setadjoin @ X1167 @ X1168))&((~(subset @ X1169 @ X1171)|(subset @ X1169 @ (setadjoin @ X1170 @ X1171)))&((~(subset @ X1172 @ X1173)|(in @ X1172 @ (powerset @ X1173)))&((~(subset @ X1174 @ X1175)|(~(subset @ X1175 @ X1174)|((X1174)=(X1175))))&((~(subset @ X1176 @ emptyset)|((X1176)=(emptyset)))&((~(subset @ X1178 @ X1177)|(in @ X1178 @ (powerset @ X1177)))&((~(in @ X1180 @ (powerset @ X1179))|(subset @ X1180 @ X1179))&((in @ X1181 @ (powerset @ X1181))&((~(subset @ X1182 @ X1183)|(subset @ (powerset @ X1182) @ (powerset @ X1183)))&((in @ (dsetconstr @ X1184 @ X1185) @ (powerset @ X1184))&((subset @ (dsetconstr @ X1186 @ X1187) @ X1186)&((~(in @ X1190 @ X1188)|(in @ X1190 @ (binunion @ X1188 @ X1189)))&((in @ X1192 @ (setadjoin @ X1191 @ (setadjoin @ X1192 @ emptyset)))&((~(in @ X1195 @ X1194)|(in @ X1195 @ (binunion @ X1193 @ X1194)))&(((((in @ X1198 @ X1197)|(X1199)|(in @ X1198 @ X1196)|~(in @ X1198 @ (binunion @ X1196 @ X1197)))&(~(X1199)|(X1199)|(in @ X1198 @ X1196)|~(in @ X1198 @ (binunion @ X1196 @ X1197))))&(((in @ X1198 @ X1197)|(X1199)|~(X1199)|~(in @ X1198 @ (binunion @ X1196 @ X1197)))&(~(X1199)|(X1199)|~(X1199)|~(in @ X1198 @ (binunion @ X1196 @ X1197)))))&((~(in @ X1202 @ (binunion @ X1200 @ X1201))|((in @ X1202 @ X1200)|(in @ X1202 @ X1201)))&((subset @ X1203 @ (binunion @ X1203 @ X1204))&((subset @ X1206 @ (binunion @ X1205 @ X1206))&((~(in @ X1209 @ X1207)|(~(in @ X1209 @ X1208)|(in @ X1209 @ (binintersect @ X1207 @ X1208))))&((~(subset @ X1212 @ X1210)|(~(subset @ X1212 @ X1211)|(subset @ X1212 @ (binintersect @ X1210 @ X1211))))&((~(in @ X1215 @ (binintersect @ X1213 @ X1214))|(in @ X1215 @ X1213))&((subset @ (binintersect @ X1216 @ X1217) @ X1216)&((~(subset @ X1218 @ X1219)|((binintersect @ X1218 @ X1219)=(X1218)))&((((binintersect @ X1220 @ X1221)!=(X1221))|(subset @ X1221 @ X1220))&((~(in @ X1224 @ (binintersect @ X1222 @ X1223))|(in @ X1224 @ X1223))&((((in @ (esk38_2 @ X1225 @ X1226) @ X1225)|((binintersect @ X1225 @ X1226)=(emptyset)))&((in @ (esk38_2 @ X1225 @ X1226) @ X1226)|((binintersect @ X1225 @ X1226)=(emptyset))))&((subset @ (binintersect @ X1228 @ X1229) @ X1229)&((~(subset @ X1231 @ X1230)|((binintersect @ X1230 @ X1231)=(X1231)))&((((binintersect @ X1232 @ X1233)!=(X1232))|(subset @ X1232 @ X1233))&(((binintersect @ X1234 @ (binunion @ X1235 @ X1236))=(binunion @ (binintersect @ X1234 @ X1235) @ (binintersect @ X1234 @ X1236)))&((~(in @ X1239 @ X1237)|((in @ X1239 @ X1238)|(in @ X1239 @ (setminus @ X1237 @ X1238))))&((~(in @ X1242 @ (setminus @ X1240 @ X1241))|(in @ X1242 @ X1240))&((~(in @ X1245 @ (setminus @ X1243 @ X1244))|~(in @ X1245 @ X1244))&((~(subset @ X1246 @ X1247)|((setminus @ X1246 @ X1247)=(emptyset)))&(((in @ X1250 @ (setminus @ X1248 @ X1249))|(~(in @ X1250 @ X1248)|(in @ X1250 @ X1249)))&(((in @ X1253 @ (setminus @ X1251 @ X1252))|((in @ X1253 @ X1252)|~(in @ X1253 @ X1251)))&(((in @ X1256 @ X1254)|~(in @ X1256 @ (setminus @ X1254 @ X1255)))&((~(in @ X1259 @ X1258)|~(in @ X1259 @ (setminus @ X1257 @ X1258)))&((subset @ (setminus @ X1260 @ X1261) @ X1260)&((((setminus @ X1262 @ X1263)!=(emptyset))|(subset @ X1262 @ X1263))&((((~(in @ X1266 @ X1264)|(X1267)|(in @ X1266 @ X1264)|~(in @ X1266 @ (symdiff @ X1264 @ X1265)))&(((in @ X1266 @ X1265)|(X1267)|(in @ X1266 @ X1264)|~(in @ X1266 @ (symdiff @ X1264 @ X1265)))&(~(X1267)|(X1267)|(in @ X1266 @ X1264)|~(in @ X1266 @ (symdiff @ X1264 @ X1265)))))&(((~(in @ X1266 @ X1264)|(X1267)|~(in @ X1266 @ X1265)|~(in @ X1266 @ (symdiff @ X1264 @ X1265)))&(((in @ X1266 @ X1265)|(X1267)|~(in @ X1266 @ X1265)|~(in @ X1266 @ (symdiff @ X1264 @ X1265)))&(~(X1267)|(X1267)|~(in @ X1266 @ X1265)|~(in @ X1266 @ (symdiff @ X1264 @ X1265)))))&((~(in @ X1266 @ X1264)|(X1267)|~(X1267)|~(in @ X1266 @ (symdiff @ X1264 @ X1265)))&(((in @ X1266 @ X1265)|(X1267)|~(X1267)|~(in @ X1266 @ (symdiff @ X1264 @ X1265)))&(~(X1267)|(X1267)|~(X1267)|~(in @ X1266 @ (symdiff @ X1264 @ X1265)))))))&((~(in @ X1270 @ X1268)|((in @ X1270 @ X1269)|(in @ X1270 @ (symdiff @ X1268 @ X1269))))&(((in @ X1273 @ X1271)|(~(in @ X1273 @ X1272)|(in @ X1273 @ (symdiff @ X1271 @ X1272))))&((~(in @ X1276 @ X1274)|(~(in @ X1276 @ X1275)|~(in @ X1276 @ (symdiff @ X1274 @ X1275))))&(((in @ X1279 @ X1277)|((in @ X1279 @ X1278)|~(in @ X1279 @ (symdiff @ X1277 @ X1278))))&((in @ X1281 @ (setadjoin @ X1280 @ (setadjoin @ X1281 @ emptyset)))&((in @ X1282 @ (setunion @ (setadjoin @ (setadjoin @ X1282 @ emptyset) @ (setadjoin @ (setadjoin @ X1282 @ (setadjoin @ X1283 @ emptyset)) @ emptyset))))&((in @ X1285 @ (setunion @ (setadjoin @ (setadjoin @ X1284 @ emptyset) @ (setadjoin @ (setadjoin @ X1284 @ (setadjoin @ X1285 @ emptyset)) @ emptyset))))&((iskpair @ (setadjoin @ (setadjoin @ X1286 @ emptyset) @ (setadjoin @ (setadjoin @ X1286 @ (setadjoin @ X1287 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X1288 @ X1289))&((~(in @ X1291 @ X1290)|(subset @ (setadjoin @ X1291 @ emptyset) @ X1290))&((~(in @ X1293 @ X1292)|(in @ (setadjoin @ X1293 @ emptyset) @ (powerset @ X1292)))&((~(in @ X1296 @ X1294)|(in @ (setadjoin @ X1296 @ emptyset) @ (powerset @ (binunion @ X1294 @ X1295))))&((~(in @ X1299 @ (setadjoin @ X1297 @ (setadjoin @ X1298 @ emptyset)))|(((X1299)=(X1297))|((X1299)=(X1298))))&((~(in @ X1302 @ X1300)|(~(in @ X1303 @ X1301)|(subset @ (setadjoin @ X1302 @ (setadjoin @ X1303 @ emptyset)) @ (binunion @ X1300 @ X1301))))&((~(in @ X1306 @ X1304)|(~(in @ X1307 @ X1305)|(in @ (setadjoin @ X1306 @ (setadjoin @ X1307 @ emptyset)) @ (powerset @ (binunion @ X1304 @ X1305)))))&((~(in @ X1310 @ X1308)|(~(in @ X1311 @ X1309)|(subset @ (setadjoin @ (setadjoin @ X1310 @ emptyset) @ (setadjoin @ (setadjoin @ X1310 @ (setadjoin @ X1311 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1308 @ X1309)))))&((~(in @ X1314 @ X1312)|(~(in @ X1315 @ X1313)|(in @ (setadjoin @ (setadjoin @ X1314 @ emptyset) @ (setadjoin @ (setadjoin @ X1314 @ (setadjoin @ X1315 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1312 @ X1313))))))&((~(in @ X1318 @ X1316)|(~(in @ X1319 @ X1317)|(in @ (kpair @ X1318 @ X1319) @ (powerset @ (powerset @ (binunion @ X1316 @ X1317))))))&((~(in @ X1322 @ X1320)|(~(in @ X1323 @ X1321)|(in @ (kpair @ X1322 @ X1323) @ (cartprod @ X1320 @ X1321))))&((((in @ (esk39_3 @ X1324 @ X1325 @ X1326) @ X1324)|~(in @ X1326 @ (cartprod @ X1324 @ X1325)))&(((in @ (esk40_3 @ X1324 @ X1325 @ X1326) @ X1325)|~(in @ X1326 @ (cartprod @ X1324 @ X1325)))&(((X1326)=(kpair @ (esk39_3 @ X1324 @ X1325 @ X1326) @ (esk40_3 @ X1324 @ X1325 @ X1326)))|~(in @ X1326 @ (cartprod @ X1324 @ X1325)))))&((~(in @ X1331 @ (cartprod @ X1329 @ X1330))|(iskpair @ X1331))&((((in @ (esk41_2 @ X1332 @ X1333) @ X1332)|~(in @ X1333 @ (setunion @ X1332)))&((in @ X1333 @ (esk41_2 @ X1332 @ X1333))|~(in @ X1333 @ (setunion @ X1332))))&((subset @ (setunion @ (setadjoin @ X1335 @ emptyset)) @ X1335)&((subset @ X1336 @ (setunion @ (setadjoin @ X1336 @ emptyset)))&(((setunion @ (setadjoin @ X1337 @ emptyset))=(X1337))&((((in @ (esk42_2 @ X1338 @ X1339) @ X1338)|(~(in @ X1342 @ X1338)|~(X1339 @ X1342)|(singleton @ (dsetconstr @ X1338 @ X1339))))&(((in @ (esk43_2 @ X1338 @ X1339) @ X1338)|(~(in @ X1342 @ X1338)|~(X1339 @ X1342)|(singleton @ (dsetconstr @ X1338 @ X1339))))&(((X1339 @ (esk42_2 @ X1338 @ X1339))|(~(in @ X1342 @ X1338)|~(X1339 @ X1342)|(singleton @ (dsetconstr @ X1338 @ X1339))))&(((X1339 @ (esk43_2 @ X1338 @ X1339))|(~(in @ X1342 @ X1338)|~(X1339 @ X1342)|(singleton @ (dsetconstr @ X1338 @ X1339))))&(((esk42_2 @ X1338 @ X1339)!=(esk43_2 @ X1338 @ X1339))|(~(in @ X1342 @ X1338)|~(X1339 @ X1342)|(singleton @ (dsetconstr @ X1338 @ X1339))))))))&((((in @ (esk44_2 @ X1343 @ X1344) @ X1343)|~(ex1 @ X1343 @ X1344))&((X1344 @ (esk44_2 @ X1343 @ X1344))|~(ex1 @ X1343 @ X1344)))&((((in @ (esk45_3 @ X1346 @ X1347 @ X1348) @ X1346)|(ex1 @ X1346 @ X1347)|~(X1347 @ X1348)|~(in @ X1348 @ X1346))&(((X1347 @ (esk45_3 @ X1346 @ X1347 @ X1348))|(ex1 @ X1346 @ X1347)|~(X1347 @ X1348)|~(in @ X1348 @ X1346))&(((esk45_3 @ X1346 @ X1347 @ X1348)!=(X1348))|(ex1 @ X1346 @ X1347)|~(X1347 @ X1348)|~(in @ X1348 @ X1346))))&((((in @ (esk46_2 @ X1350 @ X1351) @ X1350)|(~(in @ X1354 @ X1350)|~(X1351 @ X1354)|(ex1 @ X1350 @ X1351)))&(((in @ (esk47_2 @ X1350 @ X1351) @ X1350)|(~(in @ X1354 @ X1350)|~(X1351 @ X1354)|(ex1 @ X1350 @ X1351)))&(((X1351 @ (esk46_2 @ X1350 @ X1351))|(~(in @ X1354 @ X1350)|~(X1351 @ X1354)|(ex1 @ X1350 @ X1351)))&(((X1351 @ (esk47_2 @ X1350 @ X1351))|(~(in @ X1354 @ X1350)|~(X1351 @ X1354)|(ex1 @ X1350 @ X1351)))&(((esk46_2 @ X1350 @ X1351)!=(esk47_2 @ X1350 @ X1351))|(~(in @ X1354 @ X1350)|~(X1351 @ X1354)|(ex1 @ X1350 @ X1351)))))))&((((setadjoin @ X1355 @ emptyset)!=(setadjoin @ X1356 @ emptyset))|((X1355)=(X1356)))&((~(in @ (setadjoin @ X1359 @ emptyset) @ (setadjoin @ (setadjoin @ X1357 @ emptyset) @ (setadjoin @ (setadjoin @ X1357 @ (setadjoin @ X1358 @ emptyset)) @ emptyset)))|((X1357)=(X1359)))&((~(iskpair @ X1360)|(singleton @ (dsetconstr @ (setunion @ X1360) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1360))))))&((~(singleton @ X1361)|(in @ (setunion @ X1361) @ X1361))&(((kfst @ (kpair @ X1362 @ X1363))=(X1362))&((~(in @ X1366 @ (cartprod @ X1364 @ X1365))|(in @ (kfst @ X1366) @ X1364))&((((setadjoin @ (setadjoin @ X1367 @ emptyset) @ (setadjoin @ (setadjoin @ X1367 @ (setadjoin @ X1368 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1369 @ emptyset) @ (setadjoin @ (setadjoin @ X1369 @ (setadjoin @ X1370 @ emptyset)) @ emptyset)))|((X1367)=(X1369)))&((((kpair @ X1371 @ X1372)!=(kpair @ X1373 @ X1374))|((X1371)=(X1373)))&((((X1375)!=(X1376))|((setadjoin @ X1375 @ (setadjoin @ X1376 @ emptyset))=(setadjoin @ X1375 @ emptyset)))&((((X1377)!=(X1378))|((setadjoin @ (setadjoin @ X1377 @ emptyset) @ (setadjoin @ (setadjoin @ X1377 @ (setadjoin @ X1378 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1377 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1379 @ emptyset) @ (setadjoin @ (setadjoin @ X1379 @ (setadjoin @ X1380 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1381 @ emptyset) @ (setadjoin @ (setadjoin @ X1381 @ (setadjoin @ X1382 @ emptyset)) @ emptyset)))|(((X1381)!=(X1382))|((X1380)=(X1382))))&(((setadjoin @ esk48_0 @ (setadjoin @ esk49_0 @ emptyset))=(setadjoin @ esk50_0 @ emptyset))&((esk48_0)!=(esk49_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_196])])])])])])])). 0.90/180.05 thf(c_0_198, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_197])). 0.90/180.05 thf(c_0_199, negated_conjecture, ((setadjoin @ esk48_0 @ (setadjoin @ esk49_0 @ emptyset))=(setadjoin @ esk50_0 @ emptyset)), inference(split_conjunct,[status(thm)],[c_0_197])). 0.90/180.05 thf(c_0_200, negated_conjecture, ![X3:$i, X2:$i]:((((X2)=(X3))|~((in @ X3 @ (setadjoin @ X2 @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_197])). 0.90/180.05 thf(c_0_201, negated_conjecture, (in @ esk48_0 @ (setadjoin @ esk50_0 @ emptyset)), inference(spm,[status(thm)],[c_0_198, c_0_199])). 0.90/180.05 thf(c_0_202, negated_conjecture, ((esk50_0)=(esk48_0)), inference(spm,[status(thm)],[c_0_200, c_0_201])). 0.90/180.05 thf(c_0_203, negated_conjecture, ![X3:$i, X2:$i]:((in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_197])). 0.90/180.05 thf(c_0_204, negated_conjecture, ((setadjoin @ esk48_0 @ (setadjoin @ esk49_0 @ emptyset))=(setadjoin @ esk48_0 @ emptyset)), inference(rw,[status(thm)],[c_0_199, c_0_202])). 0.90/180.05 thf(c_0_205, negated_conjecture, (in @ esk49_0 @ (setadjoin @ esk48_0 @ emptyset)), inference(spm,[status(thm)],[c_0_203, c_0_204])). 0.90/180.05 thf(c_0_206, negated_conjecture, ((esk48_0)!=(esk49_0)), inference(split_conjunct,[status(thm)],[c_0_197])). 0.90/180.05 thf(c_0_207, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_200, c_0_205]), c_0_206]), ['proof']). 0.90/180.05 # SZS output end CNFRefutation 0.90/180.05 # Parsed axioms : 373 0.90/180.05 # Removed by relevancy pruning/SinE : 205 0.90/180.05 # Initial clauses : 265 0.90/180.05 # Removed in clause preprocessing : 25 0.90/180.05 # Initial clauses in saturation : 240 0.90/180.05 # Processed clauses : 349 0.90/180.05 # ...of these trivial : 7 0.90/180.05 # ...subsumed : 33 0.90/180.05 # ...remaining for further processing : 309 0.90/180.05 # Other redundant clauses eliminated : 16 0.90/180.05 # Clauses deleted for lack of memory : 0 0.90/180.05 # Backward-subsumed : 0 0.90/180.05 # Backward-rewritten : 5 0.90/180.05 # Generated clauses : 188 0.90/180.05 # ...of the previous two non-redundant : 140 0.90/180.05 # ...aggressively subsumed : 0 0.90/180.05 # Contextual simplify-reflections : 0 0.90/180.05 # Paramodulations : 171 0.90/180.05 # Factorizations : 0 0.90/180.05 # NegExts : 0 0.90/180.05 # Equation resolutions : 17 0.90/180.05 # Disequality decompositions : 0 0.90/180.05 # Total rewrite steps : 73 0.90/180.05 # ...of those cached : 45 0.90/180.05 # Propositional unsat checks : 0 0.90/180.05 # Propositional check models : 0 0.90/180.05 # Propositional check unsatisfiable : 0 0.90/180.05 # Propositional clauses : 0 0.90/180.05 # Propositional clauses after purity: 0 0.90/180.05 # Propositional unsat core size : 0 0.90/180.05 # Propositional preprocessing time : 0.000 0.90/180.05 # Propositional encoding time : 0.000 0.90/180.05 # Propositional solver time : 0.000 0.90/180.05 # Success case prop preproc time : 0.000 0.90/180.05 # Success case prop encoding time : 0.000 0.90/180.05 # Success case prop solver time : 0.000 0.90/180.05 # Current number of processed clauses : 87 0.90/180.05 # Positive orientable unit clauses : 40 0.90/180.05 # Positive unorientable unit clauses: 0 0.90/180.05 # Negative unit clauses : 6 0.90/180.05 # Non-unit-clauses : 41 0.90/180.05 # Current number of unprocessed clauses: 232 0.90/180.05 # ...number of literals in the above : 591 0.90/180.05 # Current number of archived formulas : 0 0.90/180.05 # Current number of archived clauses : 208 0.90/180.05 # Clause-clause subsumption calls (NU) : 5622 0.90/180.05 # Rec. Clause-clause subsumption calls : 3439 0.90/180.05 # Non-unit clause-clause subsumptions : 23 0.90/180.05 # Unit Clause-clause subsumption calls : 69 0.90/180.05 # Rewrite failures with RHS unbound : 0 0.90/180.05 # BW rewrite match attempts : 22 0.90/180.05 # BW rewrite match successes : 3 0.90/180.05 # Condensation attempts : 349 0.90/180.05 # Condensation successes : 4 0.90/180.05 # Termbank termtop insertions : 40933 0.90/180.05 # Search garbage collected termcells : 14888 0.90/180.05 0.90/180.05 # ------------------------------------------------- 0.90/180.05 # User time : 0.065 s 0.90/180.05 # System time : 0.010 s 0.90/180.05 # Total time : 0.074 s 0.90/180.05 # Maximum resident set size: 5500 pages 0.90/180.05 0.90/180.05 # ------------------------------------------------- 0.90/180.05 # User time : 0.072 s 0.90/180.05 # System time : 0.014 s 0.90/180.05 # Total time : 0.086 s 0.90/180.05 # Maximum resident set size: 2476 pages 0.90/180.05 % E---3.1 exiting 0.90/180.05 % E exiting 0.90/180.05 EOF