0.11/0.15 % Problem : Vampire---4.8_15175 : TPTP v0.0.0. Released v0.0.0. 0.11/0.16 % Command : run_E %s %d THM 0.15/0.36 % Computer : n025.cluster.edu 0.15/0.36 % Model : x86_64 x86_64 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.36 % Memory : 8042.1875MB 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.36 % CPULimit : 1440 0.15/0.37 % WCLimit : 180 0.15/0.37 % DateTime : Mon Jul 3 13:16:08 EDT 2023 0.15/0.37 % CPUTime : 0.21/0.52 Running higher-order theorem provingRunning: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175 0.21/0.52 # Version: 3.1pre001-ho 418.05/53.29 # Preprocessing class: HSLMSLSSLLLCHFA. 418.05/53.29 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 418.05/53.29 # Starting ehoh_best5 with 180s (1) cores 418.05/53.29 # Starting almost_fo_3_lam with 180s (1) cores 418.05/53.29 # Starting new_bool_5 with 180s (1) cores 418.05/53.29 # Starting pre_casc_3 with 180s (1) cores 418.05/53.29 # Starting ho_unfolding_8 with 180s (1) cores 418.05/53.29 # Starting new_ho_10_cnf2 with 180s (1) cores 418.05/53.29 # Starting new_bool_3 with 180s (1) cores 418.05/53.29 # Starting new_ho_5 with 180s (1) cores 418.05/53.29 # new_bool_5 with pid 15355 completed with status 0 418.05/53.29 # Result found by new_bool_5 418.05/53.29 # Preprocessing class: HSLMSLSSLLLCHFA. 418.05/53.29 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 418.05/53.29 # Starting ehoh_best5 with 180s (1) cores 418.05/53.29 # Starting almost_fo_3_lam with 180s (1) cores 418.05/53.29 # Starting new_bool_5 with 180s (1) cores 418.05/53.29 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 418.05/53.29 # Search class: HGHSM-FSLM31-MHFMMSBN 418.05/53.29 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 418.05/53.29 # Starting new_ho_10_cnf2 with 98s (1) cores 418.05/53.29 # new_ho_10_cnf2 with pid 15361 completed with status 0 418.05/53.29 # Result found by new_ho_10_cnf2 418.05/53.29 # Preprocessing class: HSLMSLSSLLLCHFA. 418.05/53.29 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 418.05/53.29 # Starting ehoh_best5 with 180s (1) cores 418.05/53.29 # Starting almost_fo_3_lam with 180s (1) cores 418.05/53.29 # Starting new_bool_5 with 180s (1) cores 418.05/53.29 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 418.05/53.29 # Search class: HGHSM-FSLM31-MHFMMSBN 418.05/53.29 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 418.05/53.29 # Starting new_ho_10_cnf2 with 98s (1) cores 418.05/53.29 # Preprocessing time : 0.005 s 418.05/53.29 # Presaturation interreduction done 418.05/53.29 418.05/53.29 # Proof found! 418.05/53.29 # SZS status Theorem 418.05/53.29 # SZS output start CNFRefutation 418.05/53.29 thf(decl_22, type, in: $i > $i > $o). 418.05/53.29 thf(decl_23, type, exu: ($i > $o) > $o). 418.05/53.29 thf(decl_24, type, setextAx: $o). 418.05/53.29 thf(decl_25, type, emptyset: $i). 418.05/53.29 thf(decl_26, type, emptysetAx: $o). 418.05/53.29 thf(decl_27, type, setadjoin: $i > $i > $i). 418.05/53.29 thf(decl_28, type, setadjoinAx: $o). 418.05/53.29 thf(decl_29, type, powerset: $i > $i). 418.05/53.29 thf(decl_30, type, powersetAx: $o). 418.05/53.29 thf(decl_31, type, setunion: $i > $i). 418.05/53.29 thf(decl_32, type, setunionAx: $o). 418.05/53.29 thf(decl_33, type, omega: $i). 418.05/53.29 thf(decl_34, type, omega0Ax: $o). 418.05/53.29 thf(decl_35, type, omegaSAx: $o). 418.05/53.29 thf(decl_36, type, omegaIndAx: $o). 418.05/53.29 thf(decl_37, type, replAx: $o). 418.05/53.29 thf(decl_38, type, foundationAx: $o). 418.05/53.29 thf(decl_39, type, wellorderingAx: $o). 418.05/53.29 thf(decl_40, type, descr: ($i > $o) > $i). 418.05/53.29 thf(decl_41, type, descrp: $o). 418.05/53.29 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 418.05/53.29 thf(decl_43, type, dsetconstrI: $o). 418.05/53.29 thf(decl_44, type, dsetconstrEL: $o). 418.05/53.29 thf(decl_45, type, dsetconstrER: $o). 418.05/53.29 thf(decl_46, type, exuE1: $o). 418.05/53.29 thf(decl_47, type, prop2set: $o > $i). 418.05/53.29 thf(decl_48, type, prop2setE: $o). 418.05/53.29 thf(decl_49, type, emptysetE: $o). 418.05/53.29 thf(decl_50, type, emptysetimpfalse: $o). 418.05/53.29 thf(decl_51, type, notinemptyset: $o). 418.05/53.29 thf(decl_52, type, exuE3e: $o). 418.05/53.29 thf(decl_53, type, setext: $o). 418.05/53.29 thf(decl_54, type, emptyI: $o). 418.05/53.29 thf(decl_55, type, noeltsimpempty: $o). 418.05/53.29 thf(decl_56, type, setbeta: $o). 418.05/53.29 thf(decl_57, type, nonempty: $i > $o). 418.05/53.29 thf(decl_58, type, nonemptyE1: $o). 418.05/53.29 thf(decl_59, type, nonemptyI: $o). 418.05/53.29 thf(decl_60, type, nonemptyI1: $o). 418.05/53.29 thf(decl_61, type, setadjoinIL: $o). 418.05/53.29 thf(decl_62, type, emptyinunitempty: $o). 418.05/53.29 thf(decl_63, type, setadjoinIR: $o). 418.05/53.29 thf(decl_64, type, setadjoinE: $o). 418.05/53.29 thf(decl_65, type, setadjoinOr: $o). 418.05/53.29 thf(decl_66, type, setoftrueEq: $o). 418.05/53.29 thf(decl_67, type, powersetI: $o). 418.05/53.29 thf(decl_68, type, emptyinPowerset: $o). 418.05/53.29 thf(decl_69, type, emptyInPowerset: $o). 418.05/53.29 thf(decl_70, type, powersetE: $o). 418.05/53.29 thf(decl_71, type, setunionI: $o). 418.05/53.29 thf(decl_72, type, setunionE: $o). 418.05/53.29 thf(decl_73, type, subPowSU: $o). 418.05/53.29 thf(decl_74, type, exuE2: $o). 418.05/53.29 thf(decl_75, type, nonemptyImpWitness: $o). 418.05/53.29 thf(decl_76, type, uniqinunit: $o). 418.05/53.29 thf(decl_77, type, notinsingleton: $o). 418.05/53.29 thf(decl_78, type, eqinunit: $o). 418.05/53.29 thf(decl_79, type, singletonsswitch: $o). 418.05/53.29 thf(decl_80, type, upairsetE: $o). 418.05/53.29 thf(decl_81, type, upairsetIL: $o). 418.05/53.29 thf(decl_82, type, upairsetIR: $o). 418.05/53.29 thf(decl_83, type, emptyE1: $o). 418.05/53.29 thf(decl_84, type, vacuousDall: $o). 418.05/53.29 thf(decl_85, type, quantDeMorgan1: $o). 418.05/53.29 thf(decl_86, type, quantDeMorgan2: $o). 418.05/53.29 thf(decl_87, type, quantDeMorgan3: $o). 418.05/53.29 thf(decl_88, type, quantDeMorgan4: $o). 418.05/53.29 thf(decl_89, type, prop2setI: $o). 418.05/53.29 thf(decl_91, type, prop2set2propI: $o). 418.05/53.29 thf(decl_92, type, notdexE: $o). 418.05/53.29 thf(decl_93, type, notdallE: $o). 418.05/53.29 thf(decl_94, type, exuI1: $o). 418.05/53.29 thf(decl_95, type, exuI3: $o). 418.05/53.29 thf(decl_96, type, exuI2: $o). 418.05/53.29 thf(decl_97, type, inCongP: $o). 418.05/53.29 thf(decl_98, type, in__Cong: $o). 418.05/53.29 thf(decl_99, type, exuE3u: $o). 418.05/53.29 thf(decl_100, type, exu__Cong: $o). 418.05/53.29 thf(decl_101, type, emptyset__Cong: $o). 418.05/53.29 thf(decl_102, type, setadjoin__Cong: $o). 418.05/53.29 thf(decl_103, type, powerset__Cong: $o). 418.05/53.29 thf(decl_104, type, setunion__Cong: $o). 418.05/53.29 thf(decl_105, type, omega__Cong: $o). 418.05/53.29 thf(decl_106, type, exuEu: $o). 418.05/53.29 thf(decl_107, type, descr__Cong: $o). 418.05/53.29 thf(decl_108, type, dsetconstr__Cong: $o). 418.05/53.29 thf(decl_109, type, subset: $i > $i > $o). 418.05/53.29 thf(decl_112, type, subsetI1: $o). 418.05/53.29 thf(decl_113, type, eqimpsubset2: $o). 418.05/53.29 thf(decl_114, type, eqimpsubset1: $o). 418.05/53.29 thf(decl_115, type, subsetI2: $o). 418.05/53.29 thf(decl_116, type, emptysetsubset: $o). 418.05/53.29 thf(decl_117, type, subsetE: $o). 418.05/53.29 thf(decl_118, type, subsetE2: $o). 418.05/53.29 thf(decl_119, type, notsubsetI: $o). 418.05/53.29 thf(decl_120, type, notequalI1: $o). 418.05/53.29 thf(decl_121, type, notequalI2: $o). 418.05/53.29 thf(decl_122, type, subsetRefl: $o). 418.05/53.29 thf(decl_123, type, subsetTrans: $o). 418.05/53.29 thf(decl_124, type, setadjoinSub: $o). 418.05/53.29 thf(decl_125, type, setadjoinSub2: $o). 418.05/53.29 thf(decl_126, type, subset2powerset: $o). 418.05/53.29 thf(decl_127, type, setextsub: $o). 418.05/53.29 thf(decl_128, type, subsetemptysetimpeq: $o). 418.05/53.29 thf(decl_129, type, powersetI1: $o). 418.05/53.29 thf(decl_130, type, powersetE1: $o). 418.05/53.29 thf(decl_131, type, inPowerset: $o). 418.05/53.29 thf(decl_132, type, powersetsubset: $o). 418.05/53.29 thf(decl_133, type, sepInPowerset: $o). 418.05/53.29 thf(decl_134, type, sepSubset: $o). 418.05/53.29 thf(decl_135, type, binunion: $i > $i > $i). 418.05/53.29 thf(decl_136, type, binunionIL: $o). 418.05/53.29 thf(decl_137, type, upairset2IR: $o). 418.05/53.29 thf(decl_138, type, binunionIR: $o). 418.05/53.29 thf(decl_139, type, binunionEcases: $o). 418.05/53.29 thf(decl_140, type, binunionE: $o). 418.05/53.29 thf(decl_141, type, binunionLsub: $o). 418.05/53.29 thf(decl_142, type, binunionRsub: $o). 418.05/53.29 thf(decl_143, type, binintersect: $i > $i > $i). 418.05/53.29 thf(decl_144, type, binintersectI: $o). 418.05/53.29 thf(decl_145, type, binintersectSubset5: $o). 418.05/53.29 thf(decl_146, type, binintersectEL: $o). 418.05/53.29 thf(decl_147, type, binintersectLsub: $o). 418.05/53.29 thf(decl_148, type, binintersectSubset2: $o). 418.05/53.29 thf(decl_149, type, binintersectSubset3: $o). 418.05/53.29 thf(decl_150, type, binintersectER: $o). 418.05/53.29 thf(decl_151, type, disjointsetsI1: $o). 418.05/53.29 thf(decl_152, type, binintersectRsub: $o). 418.05/53.29 thf(decl_153, type, binintersectSubset4: $o). 418.05/53.29 thf(decl_154, type, binintersectSubset1: $o). 418.05/53.29 thf(decl_155, type, bs114d: $o). 418.05/53.29 thf(decl_157, type, setminus: $i > $i > $i). 418.05/53.29 thf(decl_158, type, setminusI: $o). 418.05/53.29 thf(decl_159, type, setminusEL: $o). 418.05/53.29 thf(decl_160, type, setminusER: $o). 418.05/53.29 thf(decl_161, type, setminusSubset2: $o). 418.05/53.29 thf(decl_162, type, setminusERneg: $o). 418.05/53.29 thf(decl_163, type, setminusELneg: $o). 418.05/53.29 thf(decl_164, type, setminusILneg: $o). 418.05/53.29 thf(decl_165, type, setminusIRneg: $o). 418.05/53.29 thf(decl_166, type, setminusLsub: $o). 418.05/53.29 thf(decl_167, type, setminusSubset1: $o). 418.05/53.29 thf(decl_168, type, symdiff: $i > $i > $i). 418.05/53.29 thf(decl_169, type, symdiffE: $o). 418.05/53.29 thf(decl_170, type, symdiffI1: $o). 418.05/53.29 thf(decl_171, type, symdiffI2: $o). 418.05/53.29 thf(decl_172, type, symdiffIneg1: $o). 418.05/53.29 thf(decl_173, type, symdiffIneg2: $o). 418.05/53.29 thf(decl_174, type, iskpair: $i > $o). 418.05/53.29 thf(decl_175, type, secondinupair: $o). 418.05/53.29 thf(decl_176, type, setukpairIL: $o). 418.05/53.29 thf(decl_177, type, setukpairIR: $o). 418.05/53.29 thf(decl_178, type, kpairiskpair: $o). 418.05/53.29 thf(decl_179, type, kpair: $i > $i > $i). 418.05/53.29 thf(decl_180, type, kpairp: $o). 418.05/53.29 thf(decl_181, type, cartprod: $i > $i > $i). 418.05/53.29 thf(decl_182, type, singletonsubset: $o). 418.05/53.29 thf(decl_183, type, singletoninpowerset: $o). 418.05/53.29 thf(decl_184, type, singletoninpowunion: $o). 418.05/53.29 thf(decl_185, type, upairset2E: $o). 418.05/53.29 thf(decl_186, type, upairsubunion: $o). 418.05/53.29 thf(decl_187, type, upairinpowunion: $o). 418.05/53.29 thf(decl_188, type, ubforcartprodlem1: $o). 418.05/53.29 thf(decl_189, type, ubforcartprodlem2: $o). 418.05/53.29 thf(decl_190, type, ubforcartprodlem3: $o). 418.05/53.29 thf(decl_191, type, cartprodpairin: $o). 418.05/53.29 thf(decl_192, type, cartprodmempair1: $o). 418.05/53.29 thf(decl_193, type, cartprodmempair: $o). 418.05/53.29 thf(decl_194, type, setunionE2: $o). 418.05/53.29 thf(decl_195, type, setunionsingleton1: $o). 418.05/53.29 thf(decl_196, type, setunionsingleton2: $o). 418.05/53.29 thf(decl_197, type, setunionsingleton: $o). 418.05/53.29 thf(decl_198, type, singleton: $i > $o). 418.05/53.29 thf(decl_199, type, singletonprop: $o). 418.05/53.29 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 418.05/53.29 thf(decl_201, type, ex1E1: $o). 418.05/53.29 thf(decl_202, type, ex1I: $o). 418.05/53.29 thf(decl_203, type, ex1I2: $o). 418.05/53.29 thf(decl_204, type, singletonsuniq: $o). 418.05/53.29 thf(decl_209, type, setukpairinjL1: $o). 418.05/53.29 thf(decl_210, type, kfstsingleton: $o). 418.05/53.29 thf(decl_211, type, theprop: $o). 418.05/53.29 thf(decl_212, type, kfst: $i > $i). 418.05/53.29 thf(decl_213, type, kfstpairEq: $o). 418.05/53.29 thf(decl_214, type, epred1_0: $o). 418.05/53.29 thf(decl_215, type, esk1_2: $i > $i > $i). 418.05/53.29 thf(decl_216, type, esk2_2: $i > $i > $i). 418.05/53.29 thf(decl_217, type, esk3_2: $i > $i > $i). 418.05/53.29 thf(decl_218, type, esk4_1: $i > $i). 418.05/53.29 thf(decl_219, type, esk5_2: ($i > $i > $o) > $i > $i). 418.05/53.29 thf(decl_220, type, esk6_2: ($i > $i > $o) > $i > $i). 418.05/53.29 thf(decl_221, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 418.05/53.29 thf(decl_222, type, esk8_1: $i > $i). 418.05/53.29 thf(decl_223, type, esk9_1: ($i > $o) > $i). 418.05/53.29 thf(decl_224, type, esk10_1: ($i > $o) > $i). 418.05/53.29 thf(decl_225, type, esk11_2: $i > $i > $i). 418.05/53.29 thf(decl_226, type, esk12_2: $i > $i > $i). 418.05/53.29 thf(decl_227, type, esk13_1: $i > $i). 418.05/53.29 thf(decl_228, type, esk14_1: $i > $i). 418.05/53.29 thf(decl_229, type, esk15_1: $i > $i). 418.05/53.29 thf(decl_230, type, esk16_2: $i > $i > $i). 418.05/53.29 thf(decl_231, type, esk17_3: $i > $i > $o > $i). 418.05/53.29 thf(decl_232, type, esk18_1: ($i > $o) > $i). 418.05/53.29 thf(decl_233, type, esk19_1: $i > $i). 418.05/53.29 thf(decl_234, type, esk20_2: $i > ($i > $o) > $i). 418.05/53.29 thf(decl_235, type, esk21_2: $i > ($i > $o) > $i). 418.05/53.29 thf(decl_236, type, esk22_2: $i > ($i > $o) > $i). 418.05/53.29 thf(decl_237, type, esk23_2: $i > ($i > $o) > $i). 418.05/53.29 thf(decl_238, type, esk24_2: $i > ($i > $o) > $i). 418.05/53.29 thf(decl_239, type, esk25_2: $i > ($i > $o) > $i). 418.05/53.29 thf(decl_240, type, esk26_2: ($i > $o) > $i > $i). 418.05/53.29 thf(decl_241, type, esk27_1: ($i > $o) > $i). 418.05/53.29 thf(decl_242, type, esk28_1: ($i > $o) > $i). 418.05/53.29 thf(decl_243, type, esk29_2: ($i > $o) > $i > $i). 418.05/53.29 thf(decl_244, type, esk30_2: ($i > $o) > ($i > $o) > $i). 418.05/53.29 thf(decl_245, type, esk31_2: ($i > $o) > ($i > $o) > $i). 418.05/53.29 thf(decl_246, type, esk32_2: ($i > $o) > ($i > $o) > $i). 418.05/53.29 thf(decl_247, type, esk33_2: ($i > $o) > ($i > $o) > $i). 418.05/53.29 thf(decl_248, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i). 418.05/53.29 thf(decl_249, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i). 418.05/53.29 thf(decl_250, type, esk36_2: $i > $i > $i). 418.05/53.29 thf(decl_251, type, esk37_2: $i > $i > $i). 418.05/53.29 thf(decl_252, type, esk38_2: $i > $i > $i). 418.05/53.29 thf(decl_253, type, esk39_3: $i > $i > $i > $i). 418.05/53.29 thf(decl_254, type, esk40_3: $i > $i > $i > $i). 418.05/53.29 thf(decl_255, type, esk41_2: $i > $i > $i). 418.05/53.29 thf(decl_256, type, esk42_2: $i > ($i > $o) > $i). 418.05/53.29 thf(decl_257, type, esk43_2: $i > ($i > $o) > $i). 418.05/53.29 thf(decl_258, type, esk44_2: $i > ($i > $o) > $i). 418.05/53.29 thf(decl_259, type, esk45_3: $i > ($i > $o) > $i > $i). 418.05/53.29 thf(decl_260, type, esk46_2: $i > ($i > $o) > $i). 418.05/53.29 thf(decl_261, type, esk47_2: $i > ($i > $o) > $i). 418.05/53.29 thf(decl_262, type, esk48_0: $i). 418.05/53.29 thf(decl_263, type, esk49_0: $i). 418.05/53.29 thf(decl_264, type, esk50_0: $i). 418.05/53.29 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', dsetconstr__Cong)). 418.05/53.29 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', exuEu)). 418.05/53.29 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', exuE3u)). 418.05/53.29 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', exuI2)). 418.05/53.29 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', exuI1)). 418.05/53.29 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', exu__Cong)). 418.05/53.29 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', exuE2)). 418.05/53.29 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', descr__Cong)). 418.05/53.29 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setoftrueEq)). 418.05/53.29 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', nonemptyI)). 418.05/53.29 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', exuE3e)). 418.05/53.29 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', exuE1)). 418.05/53.29 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', dsetconstrEL)). 418.05/53.29 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', dsetconstrI)). 418.05/53.29 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', singletonprop)). 418.05/53.29 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', ex1E1)). 418.05/53.29 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', ex1I)). 418.05/53.29 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', ex1I2)). 418.05/53.29 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', kfstsingleton)). 418.05/53.29 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', sepSubset)). 418.05/53.29 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', sepInPowerset)). 418.05/53.29 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', exuI3)). 418.05/53.29 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', emptyE1)). 418.05/53.29 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setbeta)). 418.05/53.29 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', dsetconstrER)). 418.05/53.29 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', descrp)). 418.05/53.29 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', replAx)). 418.05/53.29 thf(cartprodfstin, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>(((((omegaSAx)=>(((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((((dsetconstrER)=>(((((emptysetimpfalse)=>((((setext)=>((((setbeta)=>((((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((((((((emptyInPowerset)=>((((setunionE)=>(((((uniqinunit)=>(((((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>(((prop2set2propI)=>((notdexE)=>((((exuI3)=>(((inCongP)=>(((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>(((((descr__Cong)=>((((eqimpsubset2)=>(((subsetI2)=>((emptysetsubset)=>(((subsetE2)=>((notsubsetI)=>((notequalI1)=>(((((setadjoinSub)=>(((subset2powerset)=>((((((inPowerset)=>((((((((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>(((binintersectSubset2)=>((binintersectSubset3)=>((((binintersectRsub)=>((((bs114d)=>(((setminusEL)=>((setminusER)=>(((setminusERneg)=>(((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>(((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>(((singletoninpowunion)=>(((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((((setunionE2)=>((((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>(((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>(![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))<=(kfstpairEq)))))<=(singletonsuniq)))))))<=(setunionsingleton2))<=(setunionsingleton1)))<=(cartprodmempair))<=(cartprodmempair1))))))))<=(upairset2E)))<=(singletoninpowerset)))))))))<=(symdiffIneg1)))))))))<=(setminusELneg)))<=(setminusSubset2))))<=(setminusI)))<=(binintersectSubset1))<=(binintersectSubset4)))<=(disjointsetsI1))<=(binintersectER))))<=(binintersectLsub)))))))))<=(binunionIR))<=(upairset2IR))<=(binunionIL))<=(sepSubset))<=(sepInPowerset))<=(powersetsubset)))<=(powersetE1))<=(powersetI1))<=(subsetemptysetimpeq))<=(setextsub)))<=(setadjoinSub2)))<=(subsetTrans))<=(subsetRefl))<=(notequalI2)))))<=(subsetE))))<=(eqimpsubset1)))<=(subsetI1))<=(dsetconstr__Cong)))<=(exuEu))<=(omega__Cong))<=(setunion__Cong)))))))<=(in__Cong)))<=(exuI2)))<=(exuI1))<=(notdallE))))<=(prop2setI)))))))))))<=(singletonsswitch))<=(eqinunit))<=(notinsingleton)))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU)))<=(setunionI))<=(powersetE)))<=(emptyinPowerset))<=(powersetI))<=(setoftrueEq))<=(setadjoinOr))<=(setadjoinE))<=(setadjoinIR)))))<=(nonemptyI))<=(nonemptyE1)))<=(noeltsimpempty))<=(emptyI)))<=(exuE3e))<=(notinemptyset)))<=(emptysetE))<=(prop2setE))<=(exuE1)))<=(dsetconstrEL))<=(dsetconstrI))))))<=(omegaIndAx)))<=(omega0Ax))<=(setunionAx))<=(powersetAx))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', cartprodfstin)). 418.05/53.29 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setadjoinOr)). 418.05/53.29 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', powersetAx)). 418.05/53.29 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', subsetI1)). 418.05/53.29 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', quantDeMorgan1)). 418.05/53.29 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', inCongP)). 418.05/53.29 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', omega__Cong)). 418.05/53.29 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setunion__Cong)). 418.05/53.29 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', in__Cong)). 418.05/53.29 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', notdallE)). 418.05/53.29 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', prop2setI)). 418.05/53.29 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', singletonsswitch)). 418.05/53.29 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', emptyset__Cong)). 418.05/53.29 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', eqinunit)). 418.05/53.29 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', notinsingleton)). 418.05/53.29 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setadjoin__Cong)). 418.05/53.29 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', nonemptyImpWitness)). 418.05/53.29 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', quantDeMorgan2)). 418.05/53.29 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', subPowSU)). 418.05/53.29 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setunionI)). 418.05/53.29 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', powerset__Cong)). 418.05/53.29 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', powersetE)). 418.05/53.29 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', emptyinPowerset)). 418.05/53.29 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', powersetI)). 418.05/53.29 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', binintersectEL)). 418.05/53.29 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', quantDeMorgan3)). 418.05/53.29 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setadjoinE)). 418.05/53.29 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setadjoinIR)). 418.05/53.29 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', eqimpsubset2)). 418.05/53.29 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', nonemptyE1)). 418.05/53.29 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', subsetI2)). 418.05/53.29 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', noeltsimpempty)). 418.05/53.29 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', emptyI)). 418.05/53.29 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', emptysetsubset)). 418.05/53.29 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', notinemptyset)). 418.05/53.29 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', emptysetE)). 418.05/53.29 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', subsetE2)). 418.05/53.29 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', prop2setE)). 418.05/53.29 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', notsubsetI)). 418.05/53.29 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', omegaIndAx)). 418.05/53.29 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', notequalI1)). 418.05/53.29 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', omega0Ax)). 418.05/53.29 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setunionAx)). 418.05/53.29 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setadjoinSub)). 418.05/53.29 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', subset2powerset)). 418.05/53.29 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', inPowerset)). 418.05/53.29 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', binunionEcases)). 418.05/53.29 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', binunionE)). 418.05/53.29 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', binunionLsub)). 418.05/53.29 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', binunionRsub)). 418.05/53.29 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', binintersectI)). 418.05/53.29 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', binintersectSubset5)). 418.05/53.29 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', binintersectSubset2)). 418.05/53.29 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', binintersectSubset3)). 418.05/53.29 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', binintersectRsub)). 418.05/53.29 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', bs114d)). 418.05/53.29 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setminusEL)). 418.05/53.29 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setminusER)). 418.05/53.29 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setminusERneg)). 418.05/53.29 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setminusILneg)). 418.05/53.29 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', quantDeMorgan4)). 418.05/53.29 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setminusIRneg)). 418.05/53.29 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', notdexE)). 418.05/53.29 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setminusLsub)). 418.05/53.29 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setminusSubset1)). 418.05/53.29 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', symdiffE)). 418.05/53.29 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', symdiffI1)). 418.05/53.29 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', symdiffI2)). 418.05/53.29 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', symdiffIneg2)). 418.05/53.29 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', secondinupair)). 418.05/53.29 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setukpairIL)). 418.05/53.29 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setukpairIR)). 418.05/53.29 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', kpairiskpair)). 418.05/53.29 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', kpairp)). 418.05/53.29 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', singletonsubset)). 418.05/53.29 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', singletoninpowunion)). 418.05/53.29 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', upairsubunion)). 418.05/53.29 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', upairinpowunion)). 418.05/53.29 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', ubforcartprodlem1)). 418.05/53.29 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', ubforcartprodlem2)). 418.05/53.29 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', ubforcartprodlem3)). 418.05/53.29 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', cartprodpairin)). 418.05/53.29 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setunionE2)). 418.05/53.29 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setunionsingleton)). 418.05/53.29 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setukpairinjL1)). 418.05/53.29 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', theprop)). 418.05/53.29 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', kfstpairEq)). 418.05/53.29 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', singletonsuniq)). 418.05/53.29 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setunionsingleton2)). 418.05/53.29 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setunionsingleton1)). 418.05/53.29 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', cartprodmempair)). 418.05/53.29 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', cartprodmempair1)). 418.05/53.29 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', upairset2E)). 418.05/53.29 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', singletoninpowerset)). 418.05/53.29 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', symdiffIneg1)). 418.05/53.29 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setminusELneg)). 418.05/53.29 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setminusSubset2)). 418.05/53.29 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setminusI)). 418.05/53.29 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', binintersectSubset1)). 418.05/53.29 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', binintersectSubset4)). 418.05/53.29 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', disjointsetsI1)). 418.05/53.29 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', binintersectER)). 418.05/53.29 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', binintersectLsub)). 418.05/53.29 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', binunionIR)). 418.05/53.29 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', upairset2IR)). 418.05/53.29 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', binunionIL)). 418.05/53.29 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', powersetsubset)). 418.05/53.29 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', powersetE1)). 418.05/53.29 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', powersetI1)). 418.05/53.29 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', subsetemptysetimpeq)). 418.05/53.29 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setextsub)). 418.05/53.29 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setadjoinSub2)). 418.05/53.29 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', subsetTrans)). 418.05/53.29 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', subsetRefl)). 418.05/53.29 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', notequalI2)). 418.05/53.29 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', subsetE)). 418.05/53.29 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', eqimpsubset1)). 418.05/53.29 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', vacuousDall)). 418.05/53.29 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', upairsetIR)). 418.05/53.29 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', upairsetIL)). 418.05/53.29 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', upairsetE)). 418.05/53.29 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', uniqinunit)). 418.05/53.29 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setunionE)). 418.05/53.29 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', emptyInPowerset)). 418.05/53.29 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', emptyinunitempty)). 418.05/53.29 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setadjoinIL)). 418.05/53.29 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', nonemptyI1)). 418.05/53.29 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setext)). 418.05/53.29 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', emptysetimpfalse)). 418.05/53.29 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', wellorderingAx)). 418.05/53.29 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', foundationAx)). 418.05/53.29 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', omegaSAx)). 418.05/53.29 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setadjoinAx)). 418.05/53.29 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', emptysetAx)). 418.05/53.29 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.Rg0zYIJiTq/Vampire---4.8_15175', setextAx)). 418.05/53.29 thf(c_0_162, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 418.05/53.29 thf(c_0_163, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 418.05/53.29 thf(c_0_164, 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])). 418.05/53.29 thf(c_0_165, 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])). 418.05/53.29 thf(c_0_166, 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])). 418.05/53.29 thf(c_0_167, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 418.05/53.29 thf(c_0_168, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 418.05/53.29 thf(c_0_169, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 418.05/53.29 thf(c_0_170, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 418.05/53.29 thf(c_0_171, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 418.05/53.29 thf(c_0_172, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 418.05/53.29 thf(c_0_173, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 418.05/53.29 thf(c_0_174, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 418.05/53.29 thf(c_0_175, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 418.05/53.29 thf(c_0_176, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 418.05/53.29 thf(c_0_177, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 418.05/53.29 thf(c_0_178, plain, ((ex1I)<=>![X4:$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])). 418.05/53.29 thf(c_0_179, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 418.05/53.29 thf(c_0_180, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 418.05/53.29 thf(c_0_181, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 418.05/53.29 thf(c_0_182, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 418.05/53.29 thf(c_0_183, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 418.05/53.29 thf(c_0_184, plain, ((emptyE1)<=>![X4:$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])). 418.05/53.29 thf(c_0_185, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 418.05/53.29 thf(c_0_186, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 418.05/53.29 thf(c_0_187, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 418.05/53.29 thf(c_0_188, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 418.05/53.29 thf(c_0_189, plain, ((epred1_0)<=>![X480:$i]:(?[X481:$i]:((((![X482:$i]:(((in @ X482 @ X481)=>![X483:$i]:(((in @ X483 @ X482)=>(in @ X483 @ X480)))))&![X484:$i, X485:$i]:((((in @ X484 @ X480)&(in @ X485 @ X480))=>(![X486:$i]:(((in @ X486 @ X481)=>((in @ X484 @ X486)<=>(in @ X485 @ X486))))=>((X484)=(X485))))))&![X487:$i, X488:$i]:((((in @ X487 @ X481)&(in @ X488 @ X481))=>(![X489:$i]:(((in @ X489 @ X487)=>(in @ X489 @ X488)))|![X490:$i]:(((in @ X490 @ X488)=>(in @ X490 @ X487)))))))&![X491:$i]:(((![X492:$i]:(((in @ X492 @ X491)=>(in @ X492 @ X480)))&?[X493:$i]:((in @ X493 @ X491)))=>?[X494:$i, X495:$i]:(((((in @ X494 @ X481)&(in @ X495 @ X491))&~(?[X496:$i]:(((in @ X496 @ X494)&(in @ X496 @ X491)))))&![X497:$i]:(((in @ X497 @ X481)=>(![X498:$i]:(((in @ X498 @ X497)=>(in @ X498 @ X494)))|(in @ X495 @ X497)))))))))))), introduced(definition)). 418.05/53.29 thf(c_0_190, negated_conjecture, ~((![X462:$i, X463:$i]:((![X464:$i]:(((in @ X464 @ X462)<=>(in @ X464 @ X463)))=>((X462)=(X463))))=>(![X465:$i]:(~(in @ X465 @ emptyset))=>(![X466:$i, X467:$i, X468:$i]:(((in @ X468 @ (setadjoin @ X466 @ X467))<=>(((X468)=(X466))|(in @ X468 @ X467))))=>(![X896:$i, X897:$i]:(((in @ X897 @ (powerset @ X896))<=>![X898:$i]:(((in @ X898 @ X897)=>(in @ X898 @ X896)))))=>(![X893:$i, X894:$i]:(((in @ X894 @ (setunion @ X893))<=>?[X895:$i]:(((in @ X894 @ X895)&(in @ X895 @ X893)))))=>((in @ emptyset @ omega)=>(![X469:$i]:(((in @ X469 @ omega)=>(in @ (setadjoin @ X469 @ X469) @ omega)))=>(![X890:$i]:((((in @ emptyset @ X890)&![X891:$i]:((((in @ X891 @ omega)&(in @ X891 @ X890))=>(in @ (setadjoin @ X891 @ X891) @ X890))))=>![X892:$i]:(((in @ X892 @ omega)=>(in @ X892 @ X890)))))=>(![X470:$i > $i > $o, X471:$i]:((![X472:$i]:(((in @ X472 @ X471)=>(exu @ (^[Z0/* 3 */:$i]:((X470 @ X472 @ Z0))))))=>?[X473:$i]:(![X474:$i]:(((in @ X474 @ X473)<=>?[X475:$i]:(((in @ X475 @ X471)&(X470 @ X475 @ X474))))))))=>(![X476:$i]:((?[X477:$i]:((in @ X477 @ X476))=>?[X478:$i]:(((in @ X478 @ X476)&~(?[X479:$i]:(((in @ X479 @ X478)&(in @ X479 @ X476))))))))=>((epred1_0)=>(![X499:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X499 @ Z0))))=>(X499 @ (descr @ (^[Z0/* 3 */:$i]:((X499 @ Z0)))))))=>(![X887:$i, X888:$i > $o, X889:$i]:(((in @ X889 @ X887)=>((X888 @ X889)=>(in @ X889 @ (dsetconstr @ X887 @ (^[Z0/* 3 */:$i]:((X888 @ Z0))))))))=>(![X884:$i, X885:$i > $o, X886:$i]:(((in @ X886 @ (dsetconstr @ X884 @ (^[Z0/* 3 */:$i]:((X885 @ Z0)))))=>(in @ X886 @ X884)))=>(![X500:$i, X501:$i > $o, X502:$i]:(((in @ X502 @ (dsetconstr @ X500 @ (^[Z0/* 3 */:$i]:((X501 @ Z0)))))=>(X501 @ X502)))=>(![X881:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X881 @ Z0))))=>?[X882:$i]:(((X881 @ X882)&![X883:$i]:(((X881 @ X883)=>((X882)=(X883))))))))=>(![X879:$o, X880:$i]:(((in @ X880 @ (prop2set @ ((X879))))=>(X879)))=>(![X877:$i]:(((in @ X877 @ emptyset)=>![X878:$o]:((X878))))=>(![X503:$i]:(~(in @ X503 @ emptyset))=>(![X876:$i]:(~(in @ X876 @ emptyset))=>(![X874:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X874 @ Z0))))=>?[X875:$i]:((X874 @ X875))))=>(![X504:$i, X505:$i]:((![X506:$i]:(((in @ X506 @ X504)=>(in @ X506 @ X505)))=>(![X507:$i]:(((in @ X507 @ X505)=>(in @ X507 @ X504)))=>((X504)=(X505)))))=>(![X872:$i]:((![X873:$i]:(~(in @ X873 @ X872))=>((X872)=(emptyset))))=>(![X870:$i]:((![X871:$i]:(~(in @ X871 @ X870))=>((X870)=(emptyset))))=>(![X508:$i, X509:$i > $o, X510:$i]:(((in @ X510 @ X508)=>((in @ X510 @ (dsetconstr @ X508 @ (^[Z0/* 3 */:$i]:((X509 @ Z0)))))<=>(X509 @ X510))))=>(![X868:$i]:(((nonempty @ X868)=>?[X869:$i]:((in @ X869 @ X868))))=>(![X865:$i, X866:$i > $o, X867:$i]:(((in @ X867 @ X865)=>((X866 @ X867)=>(nonempty @ (dsetconstr @ X865 @ (^[Z0/* 3 */:$i]:((X866 @ Z0))))))))=>(![X511:$i]:((?[X512:$i]:((in @ X512 @ X511))=>(nonempty @ X511)))=>(![X513:$i, X514:$i]:((in @ X513 @ (setadjoin @ X513 @ X514)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X862:$i, X863:$i, X864:$i]:(((in @ X864 @ X863)=>(in @ X864 @ (setadjoin @ X862 @ X863))))=>(![X858:$i, X859:$i, X860:$i]:(((in @ X860 @ (setadjoin @ X858 @ X859))=>![X861:$o]:(((((X860)=(X858))=>(X861))=>(((in @ X860 @ X859)=>(X861))=>(X861))))))=>(![X855:$i, X856:$i, X857:$i]:(((in @ X857 @ (setadjoin @ X855 @ X856))=>(((X857)=(X855))|(in @ X857 @ X856))))=>(![X854:$i]:(((dsetconstr @ X854 @ (^[Z0/* 3 */:$i]:(($true))))=(X854)))=>(![X851:$i, X852:$i]:((![X853:$i]:(((in @ X853 @ X852)=>(in @ X853 @ X851)))=>(in @ X852 @ (powerset @ X851))))=>(![X850:$i]:((in @ emptyset @ (powerset @ X850)))=>(![X515:$i]:((in @ emptyset @ (powerset @ X515)))=>(![X847:$i, X848:$i, X849:$i]:(((in @ X848 @ (powerset @ X847))=>((in @ X849 @ X848)=>(in @ X849 @ X847))))=>(![X844:$i, X845:$i, X846:$i]:(((in @ X845 @ X846)=>((in @ X846 @ X844)=>(in @ X845 @ (setunion @ X844)))))=>(![X516:$i, X517:$i]:(((in @ X517 @ (setunion @ X516))=>![X518:$o]:((![X519:$i]:(((in @ X517 @ X519)=>((in @ X519 @ X516)=>(X518))))=>(X518)))))=>(![X842:$i, X843:$i]:(((in @ X843 @ X842)=>(in @ X843 @ (powerset @ (setunion @ X842)))))=>(![X839:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X839 @ Z0))))=>?[X840:$i]:(![X841:$i]:(((X839 @ X841)<=>((X841)=(X840)))))))=>(![X837:$i]:(((nonempty @ X837)=>?[X838:$i]:((in @ X838 @ X837))))=>(![X520:$i, X521:$i]:(((in @ X520 @ (setadjoin @ X521 @ emptyset))=>((X520)=(X521))))=>(![X835:$i, X836:$i]:((((X835)!=(X836))=>~(in @ X836 @ (setadjoin @ X835 @ emptyset))))=>(![X833:$i, X834:$i]:((((X833)=(X834))=>(in @ X833 @ (setadjoin @ X834 @ emptyset))))=>(![X831:$i, X832:$i]:(((in @ X831 @ (setadjoin @ X832 @ emptyset))=>(in @ X832 @ (setadjoin @ X831 @ emptyset))))=>(![X522:$i, X523:$i, X524:$i]:(((in @ X524 @ (setadjoin @ X522 @ (setadjoin @ X523 @ emptyset)))=>(((X524)=(X522))|((X524)=(X523)))))=>(![X525:$i, X526:$i]:((in @ X525 @ (setadjoin @ X525 @ (setadjoin @ X526 @ emptyset))))=>(![X527:$i, X528:$i]:((in @ X528 @ (setadjoin @ X527 @ (setadjoin @ X528 @ emptyset))))=>(![X529:$i, X530:$i > $o]:((?[X531:$i]:(((in @ X531 @ X529)&(X530 @ X531)))=>((dsetconstr @ X529 @ (^[Z0/* 3 */:$i]:((X530 @ Z0))))!=(emptyset))))=>(![X532:$i > $o, X533:$i]:(((in @ X533 @ emptyset)=>(X532 @ X533)))=>(![X534:$i, X535:$i > $o]:((~(![X536:$i]:(((in @ X536 @ X534)=>(X535 @ X536))))=>?[X537:$i]:(((in @ X537 @ X534)&~(X535 @ X537)))))=>(![X538:$i, X539:$i > $o]:((![X540:$i]:(((in @ X540 @ X538)=>~(X539 @ X540)))=>~(?[X541:$i]:(((in @ X541 @ X538)&(X539 @ X541))))))=>(![X542:$i, X543:$i > $o]:((~(?[X544:$i]:(((in @ X544 @ X542)&(X543 @ X544))))=>![X545:$i]:(((in @ X545 @ X542)=>~(X543 @ X545)))))=>(![X546:$i, X547:$i > $o]:((?[X548:$i]:(((in @ X548 @ X546)&~(X547 @ X548)))=>~(![X549:$i]:(((in @ X549 @ X546)=>(X547 @ X549))))))=>(![X830:$o]:(((X830)=>(in @ emptyset @ (prop2set @ ((X830))))))=>((prop2set2propI)=>(![X550:$i, X551:$i > $o]:((~(?[X552:$i]:(((in @ X552 @ X550)&(X551 @ X552))))=>![X553:$i]:(((in @ X553 @ X550)=>~(X551 @ X553)))))=>(![X826:$i, X827:$i > $o]:((~(![X828:$i]:(((in @ X828 @ X826)=>(X827 @ X828))))=>?[X829:$i]:(((in @ X829 @ X826)&~(X827 @ X829)))))=>(![X823:$i > $o]:((?[X824:$i]:(((X823 @ X824)&![X825:$i]:(((X823 @ X825)=>((X824)=(X825))))))=>(exu @ (^[Z0/* 3 */:$i]:((X823 @ Z0))))))=>(![X554:$i > $o]:((?[X555:$i]:((X554 @ X555))=>(![X556:$i, X557:$i]:(((X554 @ X556)=>((X554 @ X557)=>((X556)=(X557)))))=>(exu @ (^[Z0/* 3 */:$i]:((X554 @ Z0)))))))=>(![X820:$i > $o]:((?[X821:$i]:(![X822:$i]:(((X820 @ X822)<=>((X822)=(X821)))))=>(exu @ (^[Z0/* 3 */:$i]:((X820 @ Z0))))))=>(![X558:$i, X559:$i]:((((X558)=(X559))=>![X560:$i, X561:$i]:((((X560)=(X561))=>((in @ X560 @ X558)=>(in @ X561 @ X559))))))=>(![X816:$i, X817:$i]:((((X816)=(X817))=>![X818:$i, X819:$i]:((((X818)=(X819))=>((in @ X818 @ X816)<=>(in @ X819 @ X817))))))=>(![X562:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X562 @ Z0))))=>![X563:$i, X564:$i]:(((X562 @ X563)=>((X562 @ X564)=>((X563)=(X564)))))))=>(![X565:$i > $o, X566:$i > $o]:((![X567:$i, 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setadjoinOr]), powersetAx]), subsetI1]), quantDeMorgan1]), c_0_162]), c_0_163]), inCongP]), omega__Cong]), setunion__Cong]), in__Cong]), c_0_164]), c_0_165]), c_0_166]), c_0_167]), notdallE]), prop2setI]), singletonsswitch]), emptyset__Cong]), eqinunit]), notinsingleton]), setadjoin__Cong]), nonemptyImpWitness]), c_0_168]), quantDeMorgan2]), subPowSU]), setunionI]), powerset__Cong]), powersetE]), emptyinPowerset]), c_0_169]), powersetI]), c_0_170]), binintersectEL]), quantDeMorgan3]), setadjoinE]), setadjoinIR]), eqimpsubset2]), c_0_171]), nonemptyE1]), subsetI2]), noeltsimpempty]), emptyI]), c_0_172]), emptysetsubset]), notinemptyset]), emptysetE]), subsetE2]), prop2setE]), c_0_173]), c_0_174]), notsubsetI]), c_0_175]), omegaIndAx]), notequalI1]), omega0Ax]), setunionAx]), setadjoinSub]), subset2powerset]), inPowerset]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), c_0_176]), c_0_177]), binintersectSubset2]), binintersectSubset3]), binintersectRsub]), bs114d]), setminusEL]), setminusER]), setminusERneg]), setminusILneg]), quantDeMorgan4]), setminusIRneg]), notdexE]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowunion]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), setunionE2]), setunionsingleton]), c_0_178]), c_0_179]), setukpairinjL1]), c_0_180]), theprop]), kfstpairEq]), singletonsuniq]), setunionsingleton2]), setunionsingleton1]), cartprodmempair]), cartprodmempair1]), upairset2E]), singletoninpowerset]), symdiffIneg1]), setminusELneg]), setminusSubset2]), setminusI]), binintersectSubset1]), binintersectSubset4]), disjointsetsI1]), binintersectER]), binintersectLsub]), binunionIR]), upairset2IR]), binunionIL]), c_0_181]), c_0_182]), powersetsubset]), powersetE1]), powersetI1]), subsetemptysetimpeq]), setextsub]), setadjoinSub2]), subsetTrans]), subsetRefl]), notequalI2]), c_0_183]), subsetE]), eqimpsubset1]), vacuousDall]), c_0_184]), upairsetIR]), upairsetIL]), upairsetE]), uniqinunit]), setunionE]), emptyInPowerset]), emptyinunitempty]), setadjoinIL]), nonemptyI1]), c_0_185]), setext]), emptysetimpfalse]), c_0_186]), c_0_187]), wellorderingAx]), foundationAx]), c_0_188]), omegaSAx]), setadjoinAx]), emptysetAx]), setextAx])]), c_0_189])). 418.05/53.29 thf(c_0_191, negated_conjecture, ![X899:$i, X900:$i, X902:$i, X903:$i, X904:$i, X905:$i, X906:$i, X907:$i, X908:$i, X909:$i, X910:$i, X912:$i, X913:$i, X915:$i, X916:$i, X917:$i, X918:$i, X919:$i, X921:$i, X922:$i > $i > $o, X923:$i, X926:$i, X928:$i, X929:$i, X930:$i, X931:$i, X933:$i, X934:$i > $o, X935:$i, X936:$i > $o, X937:$i, X938:$i, X939:$i > $o, X940:$i, X941:$i, X942:$i > $o, X943:$i, X944:$i > $o, X946:$i, X947:$o, X948:$i, X949:$i, X950:$o, X951:$i, X952:$i, X953:$i > $o, X955:$i, X956:$i, X959:$i, X961:$i, X963:$i, X964:$i > $o, X965:$i, X966:$i, X968:$i, X969:$i > $o, X970:$i, X971:$i, X972:$i, X973:$i, X974:$i, X975:$i, X976:$i, X977:$i, X978:$i, X979:$i, X980:$i, X981:$o, X982:$i, X983:$i, X984:$i, X985:$i, X986:$i, X987:$i, X989:$i, X990:$i, X991:$i, X992:$i, X993:$i, X994:$i, X995:$i, X996:$i, X997:$i, X998:$i, X999:$o, X1001:$i, X1002:$i, X1003:$i > $o, X1005:$i, X1006:$i, X1007:$i, X1009:$i, X1010:$i, X1011:$i, X1012:$i, X1013:$i, X1014:$i, X1015:$i, X1016:$i, X1017:$i, X1018:$i, X1019:$i, X1020:$i, X1021:$i, X1022:$i, X1023:$i, X1024:$i, X1025:$i > $o, X1026:$i, X1027:$i > $o, X1028:$i, X1029:$i, X1030:$i > $o, X1031:$i, X1033:$i, X1034:$i > $o, X1036:$i, X1037:$i, X1038:$i > $o, X1040:$i, X1041:$i, X1042:$i > $o, X1043:$i, X1045:$o, X1046:$i, X1047:$i > $o, X1049:$i, X1050:$i, X1051:$i > $o, X1052:$i, X1054:$i > $o, X1055:$i, X1057:$i > $o, X1058:$i, X1061:$i > $o, X1062:$i, X1064:$i, X1065:$i, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1070:$i, X1071:$i, X1072:$i > $o, X1073:$i, X1074:$i, X1075:$i > $o, X1076:$i > $o, X1079:$i, X1080:$i, X1081:$i, X1082:$i, X1083:$i, X1084:$i, X1085:$i, X1086:$i, X1087:$i > $o, X1088:$i, X1089:$i, X1090:$i > $o, X1091:$i > $o, X1094:$i, X1095:$i, X1096:$i > $o, X1097:$i > $o, X1100:$i, X1101:$i, X1103:$i, X1104:$i, X1105:$i, X1106:$i, X1107:$i, X1108:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1114:$i, X1115:$i, X1116:$i, X1117:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i, X1126:$i, X1127:$i, X1128:$i, X1129:$i, X1130:$i, X1131:$i, X1132:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1147:$i > $o, X1148:$i, X1149:$i > $o, X1150:$i, X1151:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$o, X1162:$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:$i, X1186:$i, X1187:$i, X1188:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i, X1198:$i, X1199:$i, 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:$i, X1227:$i, X1228:$i, X1229:$o, 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:$i, X1267:$i, 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:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i > $o, X1304:$i, X1305:$i, X1306:$i > $o, X1308:$i, X1309:$i > $o, X1310:$i, X1312:$i, X1313:$i > $o, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i]:((((~(in @ (esk1_2 @ X899 @ X900) @ X899)|~(in @ (esk1_2 @ X899 @ X900) @ X900)|((X899)=(X900)))&((in @ (esk1_2 @ X899 @ X900) @ X899)|(in @ (esk1_2 @ X899 @ X900) @ X900)|((X899)=(X900))))&(~(in @ X902 @ emptyset)&(((~(in @ X905 @ (setadjoin @ X903 @ X904))|(((X905)=(X903))|(in @ X905 @ X904)))&((((X905)!=(X903))|(in @ X905 @ (setadjoin @ X903 @ X904)))&(~(in @ X905 @ X904)|(in @ X905 @ (setadjoin @ X903 @ X904)))))&(((~(in @ X907 @ (powerset @ X906))|(~(in @ X908 @ X907)|(in @ X908 @ X906)))&(((in @ (esk2_2 @ X909 @ X910) @ X910)|(in @ X910 @ (powerset @ X909)))&(~(in @ (esk2_2 @ X909 @ X910) @ X909)|(in @ X910 @ (powerset @ X909)))))&(((((in @ X913 @ (esk3_2 @ X912 @ X913))|~(in @ X913 @ (setunion @ X912)))&((in @ (esk3_2 @ X912 @ X913) @ X912)|~(in @ X913 @ (setunion @ X912))))&(~(in @ X916 @ X917)|~(in @ X917 @ X915)|(in @ X916 @ (setunion @ X915))))&((in @ emptyset @ omega)&((~(in @ X918 @ omega)|(in @ (setadjoin @ X918 @ X918) @ omega))&(((((in @ (esk4_1 @ X919) @ omega)|~(in @ emptyset @ X919)|(~(in @ X921 @ omega)|(in @ X921 @ X919)))&((in @ (esk4_1 @ X919) @ X919)|~(in @ emptyset @ X919)|(~(in @ X921 @ omega)|(in @ X921 @ X919))))&(~(in @ (setadjoin @ (esk4_1 @ X919) @ (esk4_1 @ X919)) @ X919)|~(in @ emptyset @ X919)|(~(in @ X921 @ omega)|(in @ X921 @ X919))))&((((((in @ (esk7_3 @ X922 @ X923 @ X926) @ X923)|~(in @ X926 @ (esk6_2 @ X922 @ X923))|(in @ (esk5_2 @ X922 @ X923) @ X923))&((X922 @ (esk7_3 @ X922 @ X923 @ X926) @ X926)|~(in @ X926 @ (esk6_2 @ X922 @ X923))|(in @ (esk5_2 @ X922 @ X923) @ X923)))&(~(in @ X929 @ X923)|~(X922 @ X929 @ X928)|(in @ X928 @ (esk6_2 @ X922 @ X923))|(in @ (esk5_2 @ X922 @ X923) @ X923)))&((((in @ (esk7_3 @ X922 @ X923 @ X926) @ X923)|~(in @ X926 @ (esk6_2 @ X922 @ X923))|~(exu @ (^[Z0/* 3 */:$i]:((X922 @ (esk5_2 @ X922 @ X923) @ Z0)))))&((X922 @ (esk7_3 @ X922 @ X923 @ X926) @ X926)|~(in @ X926 @ (esk6_2 @ X922 @ X923))|~(exu @ (^[Z0/* 3 */:$i]:((X922 @ (esk5_2 @ X922 @ X923) @ Z0))))))&(~(in @ X929 @ X923)|~(X922 @ X929 @ X928)|(in @ X928 @ (esk6_2 @ X922 @ X923))|~(exu @ (^[Z0/* 3 */:$i]:((X922 @ (esk5_2 @ X922 @ X923) @ Z0)))))))&((((in @ (esk8_1 @ X930) @ X930)|~(in @ X931 @ X930))&(~(in @ X933 @ (esk8_1 @ X930))|~(in @ X933 @ X930)|~(in @ X931 @ X930)))&((epred1_0)&((~(exu @ (^[Z0/* 3 */:$i]:((X934 @ Z0))))|(X934 @ (descr @ (^[Z0/* 3 */:$i]:((X934 @ Z0))))))&((~(in @ X937 @ X935)|(~(X936 @ X937)|(in @ X937 @ (dsetconstr @ X935 @ (^[Z0/* 3 */:$i]:((X936 @ Z0)))))))&((~(in @ X940 @ (dsetconstr @ X938 @ (^[Z0/* 3 */:$i]:((X939 @ Z0)))))|(in @ X940 @ X938))&((~(in @ X943 @ (dsetconstr @ X941 @ (^[Z0/* 3 */:$i]:((X942 @ Z0)))))|(X942 @ X943))&((((X944 @ (esk9_1 @ X944))|~(exu @ (^[Z0/* 3 */:$i]:((X944 @ Z0)))))&(~(X944 @ X946)|((esk9_1 @ X944)=(X946))|~(exu @ (^[Z0/* 3 */:$i]:((X944 @ Z0))))))&((~(in @ X948 @ (prop2set @ ((X947))))|(X947))&((~(in @ X949 @ emptyset)|(X950))&(~(in @ X951 @ emptyset)&(~(in @ X952 @ emptyset)&((~(exu @ (^[Z0/* 3 */:$i]:((X953 @ Z0))))|(X953 @ (esk10_1 @ X953)))&(((((in @ (esk12_2 @ X955 @ X956) @ X956)|((X955)=(X956))|(in @ (esk11_2 @ X955 @ X956) @ X955))&(~(in @ (esk12_2 @ X955 @ X956) @ X955)|((X955)=(X956))|(in @ (esk11_2 @ X955 @ X956) @ X955)))&(((in @ (esk12_2 @ X955 @ X956) @ X956)|((X955)=(X956))|~(in @ (esk11_2 @ X955 @ X956) @ X956))&(~(in @ (esk12_2 @ X955 @ X956) @ X955)|((X955)=(X956))|~(in @ (esk11_2 @ X955 @ X956) @ X956))))&(((in @ (esk13_1 @ X959) @ X959)|((X959)=(emptyset)))&(((in @ (esk14_1 @ X961) @ X961)|((X961)=(emptyset)))&(((~(in @ X965 @ (dsetconstr @ X963 @ (^[Z0/* 3 */:$i]:((X964 @ 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@ X1283)|(in @ (kpair @ X1284 @ X1285) @ (cartprod @ X1282 @ X1283))))&((((in @ (esk39_3 @ X1286 @ X1287 @ X1288) @ X1286)|~(in @ X1288 @ (cartprod @ X1286 @ X1287)))&(((in @ (esk40_3 @ X1286 @ X1287 @ X1288) @ X1287)|~(in @ X1288 @ (cartprod @ X1286 @ X1287)))&(((X1288)=(kpair @ (esk39_3 @ X1286 @ X1287 @ X1288) @ (esk40_3 @ X1286 @ X1287 @ X1288)))|~(in @ X1288 @ (cartprod @ X1286 @ X1287)))))&((~(in @ X1293 @ (cartprod @ X1291 @ X1292))|(iskpair @ X1293))&((((in @ (esk41_2 @ X1294 @ X1295) @ X1294)|~(in @ X1295 @ (setunion @ X1294)))&((in @ X1295 @ (esk41_2 @ X1294 @ X1295))|~(in @ X1295 @ (setunion @ X1294))))&((subset @ (setunion @ (setadjoin @ X1297 @ emptyset)) @ X1297)&((subset @ X1298 @ (setunion @ (setadjoin @ X1298 @ emptyset)))&(((setunion @ (setadjoin @ X1299 @ emptyset))=(X1299))&((((in @ (esk42_2 @ X1300 @ X1301) @ X1300)|(~(in @ X1304 @ X1300)|~(X1301 @ X1304)|(singleton @ (dsetconstr @ X1300 @ (^[Z0/* 3 */:$i]:((X1301 @ Z0)))))))&(((in @ (esk43_2 @ X1300 @ X1301) @ X1300)|(~(in @ X1304 @ X1300)|~(X1301 @ X1304)|(singleton @ (dsetconstr @ X1300 @ (^[Z0/* 3 */:$i]:((X1301 @ Z0)))))))&(((X1301 @ (esk42_2 @ X1300 @ X1301))|(~(in @ X1304 @ X1300)|~(X1301 @ X1304)|(singleton @ (dsetconstr @ X1300 @ (^[Z0/* 3 */:$i]:((X1301 @ Z0)))))))&(((X1301 @ (esk43_2 @ X1300 @ X1301))|(~(in @ X1304 @ X1300)|~(X1301 @ X1304)|(singleton @ (dsetconstr @ X1300 @ (^[Z0/* 3 */:$i]:((X1301 @ Z0)))))))&(((esk42_2 @ X1300 @ X1301)!=(esk43_2 @ X1300 @ X1301))|(~(in @ X1304 @ X1300)|~(X1301 @ X1304)|(singleton @ (dsetconstr @ X1300 @ (^[Z0/* 3 */:$i]:((X1301 @ Z0)))))))))))&((((in @ (esk44_2 @ X1305 @ X1306) @ X1305)|~(ex1 @ X1305 @ (^[Z0/* 3 */:$i]:((X1306 @ Z0)))))&((X1306 @ (esk44_2 @ X1305 @ X1306))|~(ex1 @ X1305 @ (^[Z0/* 3 */:$i]:((X1306 @ Z0))))))&((((in @ (esk45_3 @ X1308 @ X1309 @ X1310) @ X1308)|(ex1 @ X1308 @ (^[Z0/* 3 */:$i]:((X1309 @ Z0))))|~(X1309 @ X1310)|~(in @ X1310 @ X1308))&(((X1309 @ (esk45_3 @ X1308 @ X1309 @ X1310))|(ex1 @ X1308 @ (^[Z0/* 3 */:$i]:((X1309 @ Z0))))|~(X1309 @ X1310)|~(in @ X1310 @ X1308))&(((esk45_3 @ X1308 @ X1309 @ X1310)!=(X1310))|(ex1 @ X1308 @ (^[Z0/* 3 */:$i]:((X1309 @ Z0))))|~(X1309 @ X1310)|~(in @ X1310 @ X1308))))&((((in @ (esk46_2 @ X1312 @ X1313) @ X1312)|(~(in @ X1316 @ X1312)|~(X1313 @ X1316)|(ex1 @ X1312 @ (^[Z0/* 3 */:$i]:((X1313 @ Z0))))))&(((in @ (esk47_2 @ X1312 @ X1313) @ X1312)|(~(in @ X1316 @ X1312)|~(X1313 @ X1316)|(ex1 @ X1312 @ (^[Z0/* 3 */:$i]:((X1313 @ Z0))))))&(((X1313 @ (esk46_2 @ X1312 @ X1313))|(~(in @ X1316 @ X1312)|~(X1313 @ X1316)|(ex1 @ X1312 @ (^[Z0/* 3 */:$i]:((X1313 @ Z0))))))&(((X1313 @ (esk47_2 @ X1312 @ X1313))|(~(in @ X1316 @ X1312)|~(X1313 @ X1316)|(ex1 @ X1312 @ (^[Z0/* 3 */:$i]:((X1313 @ Z0))))))&(((esk46_2 @ X1312 @ X1313)!=(esk47_2 @ X1312 @ X1313))|(~(in @ X1316 @ X1312)|~(X1313 @ X1316)|(ex1 @ X1312 @ (^[Z0/* 3 */:$i]:((X1313 @ Z0))))))))))&((((setadjoin @ X1317 @ emptyset)!=(setadjoin @ X1318 @ emptyset))|((X1317)=(X1318)))&((~(in @ (setadjoin @ X1321 @ emptyset) @ (setadjoin @ (setadjoin @ X1319 @ emptyset) @ (setadjoin @ (setadjoin @ X1319 @ (setadjoin @ X1320 @ emptyset)) @ emptyset)))|((X1319)=(X1321)))&((~(iskpair @ X1322)|(singleton @ (dsetconstr @ (setunion @ X1322) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1322))))))&((~(singleton @ X1323)|(in @ (setunion @ X1323) @ X1323))&(((kfst @ (kpair @ X1324 @ X1325))=(X1324))&((in @ esk50_0 @ (cartprod @ esk48_0 @ esk49_0))&~(in @ (kfst @ esk50_0) @ esk48_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_190])])])])])])). 418.05/53.29 thf(c_0_192, negated_conjecture, ![X3:$i, X2:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2))), inference(split_conjunct,[status(thm)],[c_0_191])). 418.05/53.29 thf(c_0_193, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((((X2)=(kpair @ (esk39_3 @ X3 @ X4 @ X2) @ (esk40_3 @ X3 @ X4 @ X2)))|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_191])). 418.05/53.29 thf(c_0_194, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ (esk39_3 @ X2 @ X3 @ X4) @ X2)|~((in @ X4 @ (cartprod @ X2 @ X3))))), inference(split_conjunct,[status(thm)],[c_0_191])). 418.05/53.29 thf(c_0_195, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:((((esk39_3 @ X2 @ X3 @ X4)=(kfst @ X4))|~((in @ X4 @ (cartprod @ X2 @ X3))))), inference(spm,[status(thm)],[c_0_192, c_0_193])). 418.05/53.29 thf(c_0_196, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ (kfst @ X2) @ X3)|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(spm,[status(thm)],[c_0_194, c_0_195])). 418.05/53.29 thf(c_0_197, negated_conjecture, (in @ esk50_0 @ (cartprod @ esk48_0 @ esk49_0)), inference(split_conjunct,[status(thm)],[c_0_191])). 418.05/53.29 thf(c_0_198, negated_conjecture, ~((in @ (kfst @ esk50_0) @ esk48_0)), inference(split_conjunct,[status(thm)],[c_0_191])). 418.05/53.29 thf(c_0_199, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_196, c_0_197]), c_0_198]), ['proof']). 418.05/53.29 # SZS output end CNFRefutation 418.05/53.29 # Parsed axioms : 361 418.05/53.29 # Removed by relevancy pruning/SinE : 199 418.05/53.29 # Initial clauses : 257 418.05/53.29 # Removed in clause preprocessing : 23 418.05/53.29 # Initial clauses in saturation : 234 418.05/53.29 # Processed clauses : 15439 418.05/53.29 # ...of these trivial : 828 418.05/53.29 # ...subsumed : 6869 418.05/53.29 # ...remaining for further processing : 7742 418.05/53.29 # Other redundant clauses eliminated : 151 418.05/53.29 # Clauses deleted for lack of memory : 101213 418.05/53.29 # Backward-subsumed : 516 418.05/53.29 # Backward-rewritten : 181 418.05/53.29 # Generated clauses : 2377443 418.05/53.29 # ...of the previous two non-redundant : 2340639 418.05/53.29 # ...aggressively subsumed : 0 418.05/53.29 # Contextual simplify-reflections : 19 418.05/53.29 # Paramodulations : 2377154 418.05/53.29 # Factorizations : 124 418.05/53.29 # NegExts : 0 418.05/53.29 # Equation resolutions : 152 418.05/53.29 # Total rewrite steps : 92903 418.05/53.29 # Propositional unsat checks : 0 418.05/53.29 # Propositional check models : 0 418.05/53.29 # Propositional check unsatisfiable : 0 418.05/53.29 # Propositional clauses : 0 418.05/53.29 # Propositional clauses after purity: 0 418.05/53.29 # Propositional unsat core size : 0 418.05/53.29 # Propositional preprocessing time : 0.000 418.05/53.29 # Propositional encoding time : 0.000 418.05/53.29 # Propositional solver time : 0.000 418.05/53.29 # Success case prop preproc time : 0.000 418.05/53.29 # Success case prop encoding time : 0.000 418.05/53.29 # Success case prop solver time : 0.000 418.05/53.29 # Current number of processed clauses : 6823 418.05/53.29 # Positive orientable unit clauses : 375 418.05/53.29 # Positive unorientable unit clauses: 0 418.05/53.29 # Negative unit clauses : 343 418.05/53.29 # Non-unit-clauses : 6105 418.05/53.29 # Current number of unprocessed clauses: 1334218 418.05/53.29 # ...number of literals in the above : 5199096 418.05/53.29 # Current number of archived formulas : 0 418.05/53.29 # Current number of archived clauses : 908 418.05/53.29 # Clause-clause subsumption calls (NU) : 2956617 418.05/53.29 # Rec. Clause-clause subsumption calls : 1440067 418.05/53.29 # Non-unit clause-clause subsumptions : 2732 418.05/53.29 # Unit Clause-clause subsumption calls : 157761 418.05/53.29 # Rewrite failures with RHS unbound : 0 418.05/53.29 # BW rewrite match attempts : 412 418.05/53.29 # BW rewrite match successes : 95 418.05/53.29 # Condensation attempts : 15439 418.05/53.29 # Condensation successes : 99 418.05/53.29 # Termbank termtop insertions : 58473559 418.05/53.29 418.05/53.29 # ------------------------------------------------- 418.05/53.29 # User time : 50.987 s 418.05/53.29 # System time : 1.100 s 418.05/53.29 # Total time : 52.087 s 418.05/53.29 # Maximum resident set size: 5252 pages 420.97/53.95 420.97/53.95 # ------------------------------------------------- 420.97/53.95 # User time : 50.997 s 420.97/53.95 # System time : 1.103 s 420.97/53.95 # Total time : 52.100 s 420.97/53.95 # Maximum resident set size: 2204 pages 420.97/53.95 % E---3.1 exiting 420.97/53.95 EOF