0.10/0.13 % Problem : Vampire---4.8_28428 : TPTP v0.0.0. Released v0.0.0. 0.10/0.14 % Command : run_E %s %d THM 0.12/0.34 % Computer : n024.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 1440 0.12/0.34 % WCLimit : 180 0.12/0.34 % DateTime : Mon Jul 3 12:51:53 EDT 2023 0.12/0.34 % CPUTime : 0.18/0.48 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.rlQ8fAdni1/Vampire---4.8_28428 0.18/0.48 # Version: 3.1pre001-ho 2.37/0.80 # Preprocessing class: HSLMSLSSLLLCHFA. 2.37/0.80 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 2.37/0.80 # Starting ehoh_best5 with 180s (1) cores 2.37/0.80 # Starting almost_fo_3_lam with 180s (1) cores 2.37/0.80 # Starting new_bool_5 with 180s (1) cores 2.37/0.80 # Starting pre_casc_3 with 180s (1) cores 2.37/0.80 # Starting ho_unfolding_8 with 180s (1) cores 2.37/0.80 # Starting new_ho_10_cnf2 with 180s (1) cores 2.37/0.80 # Starting new_bool_3 with 180s (1) cores 2.37/0.80 # Starting new_ho_5 with 180s (1) cores 2.37/0.80 # new_bool_3 with pid 28612 completed with status 0 2.37/0.80 # Result found by new_bool_3 2.37/0.80 # Preprocessing class: HSLMSLSSLLLCHFA. 2.37/0.80 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 2.37/0.80 # Starting ehoh_best5 with 180s (1) cores 2.37/0.80 # Starting almost_fo_3_lam with 180s (1) cores 2.37/0.80 # Starting new_bool_5 with 180s (1) cores 2.37/0.80 # Starting pre_casc_3 with 180s (1) cores 2.37/0.80 # Starting ho_unfolding_8 with 180s (1) cores 2.37/0.80 # Starting new_ho_10_cnf2 with 180s (1) cores 2.37/0.80 # Starting new_bool_3 with 180s (1) cores 2.37/0.80 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 2.37/0.80 # Search class: HGHSM-FSLM31-DHFMMSBN 2.37/0.80 # partial match(1): HGHSM-FSLM31-MHFMMSBN 2.37/0.80 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 2.37/0.80 # Starting new_ho_10_cnf2 with 98s (1) cores 2.37/0.80 # new_ho_10_cnf2 with pid 28616 completed with status 0 2.37/0.80 # Result found by new_ho_10_cnf2 2.37/0.80 # Preprocessing class: HSLMSLSSLLLCHFA. 2.37/0.80 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 2.37/0.80 # Starting ehoh_best5 with 180s (1) cores 2.37/0.80 # Starting almost_fo_3_lam with 180s (1) cores 2.37/0.80 # Starting new_bool_5 with 180s (1) cores 2.37/0.80 # Starting pre_casc_3 with 180s (1) cores 2.37/0.80 # Starting ho_unfolding_8 with 180s (1) cores 2.37/0.80 # Starting new_ho_10_cnf2 with 180s (1) cores 2.37/0.80 # Starting new_bool_3 with 180s (1) cores 2.37/0.80 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 2.37/0.80 # Search class: HGHSM-FSLM31-DHFMMSBN 2.37/0.80 # partial match(1): HGHSM-FSLM31-MHFMMSBN 2.37/0.80 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 2.37/0.80 # Starting new_ho_10_cnf2 with 98s (1) cores 2.37/0.80 # Preprocessing time : 0.005 s 2.37/0.80 # Presaturation interreduction done 2.37/0.80 2.37/0.80 # Proof found! 2.37/0.80 # SZS status Theorem 2.37/0.80 # SZS output start CNFRefutation 2.37/0.80 thf(decl_22, type, in: $i > $i > $o). 2.37/0.80 thf(decl_23, type, exu: ($i > $o) > $o). 2.37/0.80 thf(decl_24, type, setextAx: $o). 2.37/0.80 thf(decl_25, type, emptyset: $i). 2.37/0.80 thf(decl_26, type, emptysetAx: $o). 2.37/0.80 thf(decl_27, type, setadjoin: $i > $i > $i). 2.37/0.80 thf(decl_28, type, setadjoinAx: $o). 2.37/0.80 thf(decl_29, type, powerset: $i > $i). 2.37/0.80 thf(decl_30, type, powersetAx: $o). 2.37/0.80 thf(decl_31, type, setunion: $i > $i). 2.37/0.80 thf(decl_32, type, setunionAx: $o). 2.37/0.80 thf(decl_33, type, omega: $i). 2.37/0.80 thf(decl_34, type, omega0Ax: $o). 2.37/0.80 thf(decl_35, type, omegaSAx: $o). 2.37/0.80 thf(decl_36, type, omegaIndAx: $o). 2.37/0.80 thf(decl_37, type, replAx: $o). 2.37/0.80 thf(decl_38, type, foundationAx: $o). 2.37/0.80 thf(decl_39, type, wellorderingAx: $o). 2.37/0.80 thf(decl_40, type, descr: ($i > $o) > $i). 2.37/0.80 thf(decl_41, type, descrp: $o). 2.37/0.80 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 2.37/0.80 thf(decl_43, type, dsetconstrI: $o). 2.37/0.80 thf(decl_44, type, dsetconstrEL: $o). 2.37/0.80 thf(decl_45, type, dsetconstrER: $o). 2.37/0.80 thf(decl_46, type, exuE1: $o). 2.37/0.80 thf(decl_47, type, prop2set: $o > $i). 2.37/0.80 thf(decl_48, type, prop2setE: $o). 2.37/0.80 thf(decl_49, type, emptysetE: $o). 2.37/0.80 thf(decl_50, type, emptysetimpfalse: $o). 2.37/0.80 thf(decl_51, type, notinemptyset: $o). 2.37/0.80 thf(decl_52, type, exuE3e: $o). 2.37/0.80 thf(decl_53, type, setext: $o). 2.37/0.80 thf(decl_54, type, emptyI: $o). 2.37/0.80 thf(decl_55, type, noeltsimpempty: $o). 2.37/0.80 thf(decl_56, type, setbeta: $o). 2.37/0.80 thf(decl_57, type, nonempty: $i > $o). 2.37/0.80 thf(decl_58, type, nonemptyE1: $o). 2.37/0.80 thf(decl_59, type, nonemptyI: $o). 2.37/0.80 thf(decl_60, type, nonemptyI1: $o). 2.37/0.80 thf(decl_61, type, setadjoinIL: $o). 2.37/0.80 thf(decl_62, type, emptyinunitempty: $o). 2.37/0.80 thf(decl_63, type, setadjoinIR: $o). 2.37/0.80 thf(decl_64, type, setadjoinE: $o). 2.37/0.80 thf(decl_65, type, setadjoinOr: $o). 2.37/0.80 thf(decl_66, type, setoftrueEq: $o). 2.37/0.80 thf(decl_67, type, powersetI: $o). 2.37/0.80 thf(decl_68, type, emptyinPowerset: $o). 2.37/0.80 thf(decl_69, type, emptyInPowerset: $o). 2.37/0.80 thf(decl_70, type, powersetE: $o). 2.37/0.80 thf(decl_71, type, setunionI: $o). 2.37/0.80 thf(decl_72, type, setunionE: $o). 2.37/0.80 thf(decl_73, type, subPowSU: $o). 2.37/0.80 thf(decl_74, type, exuE2: $o). 2.37/0.80 thf(decl_75, type, nonemptyImpWitness: $o). 2.37/0.80 thf(decl_76, type, uniqinunit: $o). 2.37/0.80 thf(decl_77, type, notinsingleton: $o). 2.37/0.80 thf(decl_78, type, eqinunit: $o). 2.37/0.80 thf(decl_79, type, singletonsswitch: $o). 2.37/0.80 thf(decl_80, type, upairsetE: $o). 2.37/0.80 thf(decl_81, type, upairsetIL: $o). 2.37/0.80 thf(decl_82, type, upairsetIR: $o). 2.37/0.80 thf(decl_83, type, emptyE1: $o). 2.37/0.80 thf(decl_84, type, vacuousDall: $o). 2.37/0.80 thf(decl_85, type, quantDeMorgan1: $o). 2.37/0.80 thf(decl_86, type, quantDeMorgan2: $o). 2.37/0.80 thf(decl_87, type, quantDeMorgan3: $o). 2.37/0.80 thf(decl_88, type, quantDeMorgan4: $o). 2.37/0.80 thf(decl_89, type, prop2setI: $o). 2.37/0.80 thf(decl_91, type, prop2set2propI: $o). 2.37/0.80 thf(decl_92, type, notdexE: $o). 2.37/0.80 thf(decl_93, type, notdallE: $o). 2.37/0.80 thf(decl_94, type, exuI1: $o). 2.37/0.80 thf(decl_95, type, exuI3: $o). 2.37/0.80 thf(decl_96, type, exuI2: $o). 2.37/0.80 thf(decl_97, type, inCongP: $o). 2.37/0.80 thf(decl_98, type, in__Cong: $o). 2.37/0.80 thf(decl_99, type, exuE3u: $o). 2.37/0.80 thf(decl_100, type, exu__Cong: $o). 2.37/0.80 thf(decl_101, type, emptyset__Cong: $o). 2.37/0.80 thf(decl_102, type, setadjoin__Cong: $o). 2.37/0.80 thf(decl_103, type, powerset__Cong: $o). 2.37/0.80 thf(decl_104, type, setunion__Cong: $o). 2.37/0.80 thf(decl_105, type, omega__Cong: $o). 2.37/0.80 thf(decl_106, type, exuEu: $o). 2.37/0.80 thf(decl_107, type, descr__Cong: $o). 2.37/0.80 thf(decl_108, type, dsetconstr__Cong: $o). 2.37/0.80 thf(decl_109, type, subset: $i > $i > $o). 2.37/0.80 thf(decl_112, type, subsetI1: $o). 2.37/0.80 thf(decl_113, type, eqimpsubset2: $o). 2.37/0.80 thf(decl_114, type, eqimpsubset1: $o). 2.37/0.80 thf(decl_115, type, subsetI2: $o). 2.37/0.80 thf(decl_116, type, emptysetsubset: $o). 2.37/0.80 thf(decl_117, type, subsetE: $o). 2.37/0.80 thf(decl_118, type, subsetE2: $o). 2.37/0.80 thf(decl_119, type, notsubsetI: $o). 2.37/0.80 thf(decl_120, type, notequalI1: $o). 2.37/0.80 thf(decl_121, type, notequalI2: $o). 2.37/0.80 thf(decl_122, type, subsetRefl: $o). 2.37/0.80 thf(decl_123, type, subsetTrans: $o). 2.37/0.80 thf(decl_124, type, setadjoinSub: $o). 2.37/0.80 thf(decl_125, type, setadjoinSub2: $o). 2.37/0.80 thf(decl_126, type, subset2powerset: $o). 2.37/0.80 thf(decl_127, type, setextsub: $o). 2.37/0.80 thf(decl_128, type, subsetemptysetimpeq: $o). 2.37/0.80 thf(decl_129, type, powersetI1: $o). 2.37/0.80 thf(decl_130, type, powersetE1: $o). 2.37/0.80 thf(decl_131, type, inPowerset: $o). 2.37/0.80 thf(decl_132, type, powersetsubset: $o). 2.37/0.80 thf(decl_133, type, sepInPowerset: $o). 2.37/0.80 thf(decl_134, type, sepSubset: $o). 2.37/0.80 thf(decl_135, type, binunion: $i > $i > $i). 2.37/0.80 thf(decl_136, type, binunionIL: $o). 2.37/0.80 thf(decl_137, type, upairset2IR: $o). 2.37/0.80 thf(decl_138, type, binunionIR: $o). 2.37/0.80 thf(decl_139, type, binunionEcases: $o). 2.37/0.80 thf(decl_140, type, binunionE: $o). 2.37/0.80 thf(decl_141, type, binunionLsub: $o). 2.37/0.80 thf(decl_142, type, binunionRsub: $o). 2.37/0.80 thf(decl_143, type, binintersect: $i > $i > $i). 2.37/0.80 thf(decl_144, type, binintersectI: $o). 2.37/0.80 thf(decl_145, type, binintersectSubset5: $o). 2.37/0.80 thf(decl_146, type, binintersectEL: $o). 2.37/0.80 thf(decl_147, type, binintersectLsub: $o). 2.37/0.80 thf(decl_148, type, binintersectSubset2: $o). 2.37/0.80 thf(decl_149, type, binintersectSubset3: $o). 2.37/0.80 thf(decl_150, type, binintersectER: $o). 2.37/0.80 thf(decl_151, type, disjointsetsI1: $o). 2.37/0.80 thf(decl_152, type, binintersectRsub: $o). 2.37/0.80 thf(decl_153, type, binintersectSubset4: $o). 2.37/0.80 thf(decl_154, type, binintersectSubset1: $o). 2.37/0.80 thf(decl_155, type, bs114d: $o). 2.37/0.80 thf(decl_157, type, setminus: $i > $i > $i). 2.37/0.80 thf(decl_158, type, setminusI: $o). 2.37/0.80 thf(decl_159, type, setminusEL: $o). 2.37/0.80 thf(decl_160, type, setminusER: $o). 2.37/0.80 thf(decl_161, type, setminusSubset2: $o). 2.37/0.80 thf(decl_162, type, setminusERneg: $o). 2.37/0.80 thf(decl_163, type, setminusELneg: $o). 2.37/0.80 thf(decl_164, type, setminusILneg: $o). 2.37/0.80 thf(decl_165, type, setminusIRneg: $o). 2.37/0.80 thf(decl_166, type, setminusLsub: $o). 2.37/0.80 thf(decl_167, type, setminusSubset1: $o). 2.37/0.80 thf(decl_168, type, symdiff: $i > $i > $i). 2.37/0.80 thf(decl_169, type, symdiffE: $o). 2.37/0.80 thf(decl_170, type, symdiffI1: $o). 2.37/0.80 thf(decl_171, type, symdiffI2: $o). 2.37/0.80 thf(decl_172, type, symdiffIneg1: $o). 2.37/0.80 thf(decl_173, type, symdiffIneg2: $o). 2.37/0.80 thf(decl_174, type, iskpair: $i > $o). 2.37/0.80 thf(decl_175, type, secondinupair: $o). 2.37/0.80 thf(decl_176, type, setukpairIL: $o). 2.37/0.80 thf(decl_177, type, setukpairIR: $o). 2.37/0.80 thf(decl_178, type, kpairiskpair: $o). 2.37/0.80 thf(decl_179, type, kpair: $i > $i > $i). 2.37/0.80 thf(decl_180, type, kpairp: $o). 2.37/0.80 thf(decl_181, type, cartprod: $i > $i > $i). 2.37/0.80 thf(decl_182, type, singletonsubset: $o). 2.37/0.80 thf(decl_183, type, singletoninpowerset: $o). 2.37/0.80 thf(decl_184, type, singletoninpowunion: $o). 2.37/0.80 thf(decl_185, type, upairset2E: $o). 2.37/0.80 thf(decl_186, type, upairsubunion: $o). 2.37/0.80 thf(decl_187, type, upairinpowunion: $o). 2.37/0.80 thf(decl_188, type, ubforcartprodlem1: $o). 2.37/0.80 thf(decl_189, type, ubforcartprodlem2: $o). 2.37/0.80 thf(decl_190, type, ubforcartprodlem3: $o). 2.37/0.80 thf(decl_191, type, cartprodpairin: $o). 2.37/0.80 thf(decl_192, type, epred1_0: $o). 2.37/0.80 thf(decl_193, type, esk1_2: $i > $i > $i). 2.37/0.80 thf(decl_194, type, esk2_2: $i > $i > $i). 2.37/0.80 thf(decl_195, type, esk3_2: $i > $i > $i). 2.37/0.80 thf(decl_196, type, esk4_1: $i > $i). 2.37/0.80 thf(decl_197, type, esk5_2: ($i > $i > $o) > $i > $i). 2.37/0.80 thf(decl_198, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 2.37/0.80 thf(decl_199, type, esk7_2: ($i > $i > $o) > $i > $i). 2.37/0.80 thf(decl_200, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 2.37/0.80 thf(decl_201, type, esk9_1: $i > $i). 2.37/0.80 thf(decl_202, type, esk10_2: ($i > $o) > $i > $i). 2.37/0.80 thf(decl_203, type, esk11_2: ($i > $o) > $i > $i). 2.37/0.80 thf(decl_204, type, esk12_1: ($i > $o) > $i). 2.37/0.80 thf(decl_205, type, esk13_2: ($i > $o) > $i > $i). 2.37/0.80 thf(decl_206, type, esk14_1: ($i > $o) > $i). 2.37/0.80 thf(decl_207, type, esk15_2: $i > $i > $i). 2.37/0.80 thf(decl_208, type, esk16_2: $i > $i > $i). 2.37/0.80 thf(decl_209, type, esk17_1: $i > $i). 2.37/0.80 thf(decl_210, type, esk18_1: $i > $i). 2.37/0.80 thf(decl_211, type, esk19_1: $i > $i). 2.37/0.80 thf(decl_212, type, esk20_2: $i > $i > $i). 2.37/0.80 thf(decl_213, type, esk21_3: $i > $i > $o > $i). 2.37/0.80 thf(decl_214, type, esk22_2: ($i > $o) > $i > $i). 2.37/0.80 thf(decl_215, type, esk23_1: ($i > $o) > $i). 2.37/0.80 thf(decl_216, type, esk24_1: $i > $i). 2.37/0.80 thf(decl_217, type, esk25_2: $i > ($i > $o) > $i). 2.37/0.80 thf(decl_218, type, esk26_2: $i > ($i > $o) > $i). 2.37/0.80 thf(decl_219, type, esk27_2: $i > ($i > $o) > $i). 2.37/0.80 thf(decl_220, type, esk28_2: $i > ($i > $o) > $i). 2.37/0.80 thf(decl_221, type, esk29_2: $i > ($i > $o) > $i). 2.37/0.80 thf(decl_222, type, esk30_2: $i > ($i > $o) > $i). 2.37/0.80 thf(decl_223, type, esk31_2: ($i > $o) > $i > $i). 2.37/0.80 thf(decl_224, type, esk32_1: ($i > $o) > $i). 2.37/0.80 thf(decl_225, type, esk33_1: ($i > $o) > $i). 2.37/0.80 thf(decl_226, type, esk34_1: ($i > $o) > $i). 2.37/0.80 thf(decl_227, type, esk35_1: ($i > $o) > $i). 2.37/0.80 thf(decl_228, type, esk36_2: ($i > $o) > $i > $i). 2.37/0.80 thf(decl_229, type, esk37_1: ($i > $o) > $i). 2.37/0.80 thf(decl_230, type, esk38_2: ($i > $o) > $i > $i). 2.37/0.80 thf(decl_231, type, esk39_2: ($i > $o) > ($i > $o) > $i). 2.37/0.80 thf(decl_232, type, esk40_2: ($i > $o) > ($i > $o) > $i). 2.37/0.80 thf(decl_233, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 2.37/0.80 thf(decl_234, type, esk42_2: ($i > $o) > ($i > $o) > $i). 2.37/0.80 thf(decl_235, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 2.37/0.80 thf(decl_236, type, esk44_2: ($i > $o) > ($i > $o) > $i). 2.37/0.80 thf(decl_237, type, esk45_2: ($i > $o) > $i > $i). 2.37/0.80 thf(decl_238, type, esk46_2: ($i > $o) > ($i > $o) > $i). 2.37/0.80 thf(decl_239, type, esk47_2: ($i > $o) > ($i > $o) > $i). 2.37/0.80 thf(decl_240, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 2.37/0.80 thf(decl_241, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 2.37/0.80 thf(decl_242, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 2.37/0.80 thf(decl_243, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 2.37/0.80 thf(decl_244, type, esk52_2: $i > $i > $i). 2.37/0.80 thf(decl_245, type, esk53_2: $i > $i > $i). 2.37/0.80 thf(decl_246, type, esk54_2: $i > $i > $i). 2.37/0.80 thf(decl_247, type, esk55_2: $i > $i > $i). 2.37/0.80 thf(decl_248, type, esk56_2: $i > $i > $i). 2.37/0.80 thf(decl_249, type, esk57_2: $i > $i > $i). 2.37/0.80 thf(decl_250, type, esk58_2: $i > $i > $i). 2.37/0.80 thf(decl_251, type, esk59_0: $i). 2.37/0.80 thf(decl_252, type, esk60_0: $i). 2.37/0.80 thf(decl_253, type, esk61_0: $i). 2.37/0.80 thf(decl_259, type, esk67_0: $i). 2.37/0.80 thf(decl_260, type, esk68_0: $i). 2.37/0.80 thf(cartprod, axiom, ((cartprod)=(^[X4:$i, X5:$i]:(dsetconstr @ (powerset @ (powerset @ (binunion @ X4 @ X5))) @ (^[X2:$i]:(?[X3:$i]:(((in @ X3 @ X4)&?[X14:$i]:(((in @ X14 @ X5)&((X2)=(kpair @ X3 @ X14))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', cartprod)). 2.37/0.80 thf(kpair, axiom, ((kpair)=(^[X2:$i, X3:$i]:(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', kpair)). 2.37/0.80 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', nonempty)). 2.37/0.80 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', nonemptyI)). 2.37/0.80 thf(iskpair, axiom, ((iskpair)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ (setunion @ X4))&?[X3:$i]:(((in @ X3 @ (setunion @ X4))&((X4)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', iskpair)). 2.37/0.80 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', descr__Cong)). 2.37/0.80 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', exu)). 2.37/0.80 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', exuEu)). 2.37/0.80 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', exu__Cong)). 2.37/0.80 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', exuI2)). 2.37/0.80 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', exuI3)). 2.37/0.80 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', exuI1)). 2.37/0.80 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', exuE3u)). 2.37/0.80 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', exuE2)). 2.37/0.80 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', exuE3e)). 2.37/0.80 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', exuE1)). 2.37/0.80 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', descrp)). 2.37/0.80 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', replAx)). 2.37/0.80 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', sepSubset)). 2.37/0.80 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', nonemptyI1)). 2.37/0.80 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', nonemptyE1)). 2.37/0.80 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', dsetconstrEL)). 2.37/0.80 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', kpairiskpair)). 2.37/0.80 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', ubforcartprodlem3)). 2.37/0.80 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', cartprodpairin)). 2.37/0.80 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', kpairp)). 2.37/0.80 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', sepInPowerset)). 2.37/0.80 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', dsetconstr__Cong)). 2.37/0.80 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', emptyE1)). 2.37/0.80 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', nonemptyImpWitness)). 2.37/0.80 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setoftrueEq)). 2.37/0.80 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setbeta)). 2.37/0.80 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', dsetconstrER)). 2.37/0.80 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', dsetconstrI)). 2.37/0.80 thf(cartprodmempair1, conjecture, (((emptysetAx)=>((((setunionAx)=>(((omegaSAx)=>(((replAx)=>(((wellorderingAx)=>((descrp)=>((dsetconstrI)=>(((dsetconstrER)=>((exuE1)=>((prop2setE)=>((((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>(((setbeta)=>(((((setadjoinIL)=>((((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>(((((powersetE)=>(((setunionE)=>(((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>(((eqinunit)=>((((((emptyE1)=>(((quantDeMorgan1)=>(((((prop2setI)=>((prop2set2propI)=>(((notdallE)=>(((((((exuE3u)=>(((emptyset__Cong)=>((((setunion__Cong)=>((((((subsetI1)=>(((((emptysetsubset)=>((((((notequalI2)=>((((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((((powersetsubset)=>(((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>(((binunionE)=>(((binunionRsub)=>((((binintersectEL)=>((binintersectLsub)=>((((binintersectER)=>(((binintersectRsub)=>(((binintersectSubset1)=>((((setminusEL)=>((setminusER)=>(((((setminusILneg)=>((setminusIRneg)=>(((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>(((symdiffIneg1)=>(((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((((((upairset2E)=>((((((ubforcartprodlem3)=>((cartprodpairin)=>![X4:$i, X5:$i, X18:$i]:((?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))<=(in @ X18 @ (cartprod @ X4 @ X5))))))<=(ubforcartprodlem2))<=(ubforcartprodlem1))<=(upairinpowunion))<=(upairsubunion)))<=(singletoninpowunion))<=(singletoninpowerset))<=(singletonsubset))<=(kpairp))))))<=(symdiffIneg2)))<=(symdiffI2)))))<=(setminusLsub))))<=(setminusELneg))<=(setminusERneg))<=(setminusSubset2))))<=(setminusI))<=(bs114d)))<=(binintersectSubset4)))<=(disjointsetsI1)))<=(binintersectSubset3))<=(binintersectSubset2))))<=(binintersectSubset5))<=(binintersectI)))<=(binunionLsub)))<=(binunionEcases))))))<=(sepInPowerset)))<=(inPowerset))<=(powersetE1))))))))<=(subsetTrans))<=(subsetRefl)))<=(notequalI1))<=(notsubsetI))<=(subsetE2))<=(subsetE)))<=(subsetI2))<=(eqimpsubset1))<=(eqimpsubset2)))<=(dsetconstr__Cong))<=(descr__Cong))<=(exuEu))<=(omega__Cong)))<=(powerset__Cong))<=(setadjoin__Cong)))<=(exu__Cong)))<=(in__Cong))<=(inCongP))<=(exuI2))<=(exuI3))<=(exuI1)))<=(notdexE))))<=(quantDeMorgan4))<=(quantDeMorgan3))<=(quantDeMorgan2)))<=(vacuousDall)))<=(upairsetIR))<=(upairsetIL))<=(upairsetE))<=(singletonsswitch)))<=(notinsingleton)))))<=(subPowSU)))<=(setunionI)))<=(emptyInPowerset))<=(emptyinPowerset))<=(powersetI)))))<=(setadjoinIR))<=(emptyinunitempty)))<=(nonemptyI1))<=(nonemptyI))<=(nonemptyE1)))<=(noeltsimpempty))))))<=(emptysetimpfalse))<=(emptysetE)))))<=(dsetconstrEL)))))<=(foundationAx)))<=(omegaIndAx)))<=(omega0Ax)))<=(powersetAx))<=(setadjoinAx)))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', cartprodmempair1)). 2.37/0.80 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setextAx)). 2.37/0.80 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', notinsingleton)). 2.37/0.80 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', subset2powerset)). 2.37/0.80 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', subPowSU)). 2.37/0.80 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setunionI)). 2.37/0.80 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', emptyInPowerset)). 2.37/0.80 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', emptyinPowerset)). 2.37/0.80 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', binunionIL)). 2.37/0.80 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', powersetI)). 2.37/0.80 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setadjoinIR)). 2.37/0.80 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', upairset2IR)). 2.37/0.80 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', emptyinunitempty)). 2.37/0.80 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', binunionIR)). 2.37/0.80 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', noeltsimpempty)). 2.37/0.80 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', binunionE)). 2.37/0.80 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', emptysetimpfalse)). 2.37/0.80 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', emptysetE)). 2.37/0.80 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setextsub)). 2.37/0.80 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', foundationAx)). 2.37/0.80 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', binunionRsub)). 2.37/0.80 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', omegaIndAx)). 2.37/0.80 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', omega0Ax)). 2.37/0.80 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', binintersectEL)). 2.37/0.80 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', powersetAx)). 2.37/0.80 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setadjoinAx)). 2.37/0.80 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', subsetemptysetimpeq)). 2.37/0.80 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', binintersectLsub)). 2.37/0.80 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', binintersectER)). 2.37/0.80 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', binintersectRsub)). 2.37/0.80 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', binintersectSubset1)). 2.37/0.80 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setminusEL)). 2.37/0.80 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setminusER)). 2.37/0.80 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setminusILneg)). 2.37/0.80 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setminusIRneg)). 2.37/0.80 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setminusSubset1)). 2.37/0.80 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', symdiffE)). 2.37/0.80 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', symdiffI1)). 2.37/0.80 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', symdiffIneg1)). 2.37/0.80 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', secondinupair)). 2.37/0.80 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setukpairIL)). 2.37/0.80 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setukpairIR)). 2.37/0.80 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', notequalI1)). 2.37/0.80 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', notsubsetI)). 2.37/0.80 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', subsetE2)). 2.37/0.80 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', subsetE)). 2.37/0.80 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', upairset2E)). 2.37/0.80 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', ubforcartprodlem2)). 2.37/0.80 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', ubforcartprodlem1)). 2.37/0.80 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', upairinpowunion)). 2.37/0.80 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', powersetI1)). 2.37/0.80 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', upairsubunion)). 2.37/0.80 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', powersetsubset)). 2.37/0.80 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', singletoninpowunion)). 2.37/0.80 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', singletoninpowerset)). 2.37/0.80 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', singletonsubset)). 2.37/0.80 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', symdiffIneg2)). 2.37/0.80 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', symdiffI2)). 2.37/0.80 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setminusLsub)). 2.37/0.80 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setminusELneg)). 2.37/0.80 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setminusERneg)). 2.37/0.80 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setminusSubset2)). 2.37/0.80 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setminusI)). 2.37/0.80 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', bs114d)). 2.37/0.80 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', binintersectSubset4)). 2.37/0.80 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', disjointsetsI1)). 2.37/0.80 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', binintersectSubset3)). 2.37/0.80 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', binintersectSubset2)). 2.37/0.80 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', binintersectSubset5)). 2.37/0.80 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', binintersectI)). 2.37/0.80 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', binunionLsub)). 2.37/0.80 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', binunionEcases)). 2.37/0.80 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', inPowerset)). 2.37/0.80 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', powersetE1)). 2.37/0.80 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', subsetTrans)). 2.37/0.80 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', subsetRefl)). 2.37/0.80 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', subsetI2)). 2.37/0.80 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', eqimpsubset1)). 2.37/0.80 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', eqimpsubset2)). 2.37/0.80 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', omega__Cong)). 2.37/0.80 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', powerset__Cong)). 2.37/0.80 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setadjoin__Cong)). 2.37/0.80 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', in__Cong)). 2.37/0.80 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', inCongP)). 2.37/0.80 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', notdexE)). 2.37/0.80 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', quantDeMorgan4)). 2.37/0.80 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', quantDeMorgan3)). 2.37/0.80 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', quantDeMorgan2)). 2.37/0.80 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', vacuousDall)). 2.37/0.80 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', upairsetIR)). 2.37/0.80 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', upairsetIL)). 2.37/0.80 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', upairsetE)). 2.37/0.80 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', singletonsswitch)). 2.37/0.80 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setadjoinSub2)). 2.37/0.80 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setadjoinSub)). 2.37/0.80 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', notequalI2)). 2.37/0.80 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', emptysetsubset)). 2.37/0.80 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', subsetI1)). 2.37/0.80 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setunion__Cong)). 2.37/0.80 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', emptyset__Cong)). 2.37/0.80 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', notdallE)). 2.37/0.80 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', prop2setI)). 2.37/0.80 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', quantDeMorgan1)). 2.37/0.80 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', eqinunit)). 2.37/0.80 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', uniqinunit)). 2.37/0.80 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setunionE)). 2.37/0.80 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', powersetE)). 2.37/0.80 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setadjoinOr)). 2.37/0.80 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setadjoinE)). 2.37/0.80 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setadjoinIL)). 2.37/0.80 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', emptyI)). 2.37/0.80 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setext)). 2.37/0.80 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', notinemptyset)). 2.37/0.80 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', prop2setE)). 2.37/0.80 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', wellorderingAx)). 2.37/0.80 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', omegaSAx)). 2.37/0.80 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', setunionAx)). 2.37/0.80 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.rlQ8fAdni1/Vampire---4.8_28428', emptysetAx)). 2.37/0.80 thf(c_0_152, plain, ((cartprod)=(^[Z0/* 19 */:$i, Z1:$i]:(dsetconstr @ (powerset @ (powerset @ (binunion @ Z0 @ Z1))) @ (^[Z2/* 5 */:$i]:(?[X3:$i]:(((in @ X3 @ Z0)&?[X14:$i]:(((in @ X14 @ Z1)&((Z2)=(setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X14 @ emptyset)) @ emptyset)))))))))))), inference(fof_simplification,[status(thm)],[cartprod])). 2.37/0.80 thf(c_0_153, plain, ((kpair)=(^[Z0/* 19 */:$i, Z1:$i]:(setadjoin @ (setadjoin @ Z0 @ emptyset) @ (setadjoin @ (setadjoin @ Z0 @ (setadjoin @ Z1 @ emptyset)) @ emptyset)))), inference(fof_simplification,[status(thm)],[kpair])). 2.37/0.80 thf(c_0_154, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 2.37/0.80 thf(c_0_155, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 2.37/0.80 thf(c_0_156, plain, ((iskpair)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ (setunion @ Z0))&?[X3:$i]:(((in @ X3 @ (setunion @ Z0))&((Z0)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))), inference(fof_simplification,[status(thm)],[iskpair])). 2.37/0.80 thf(c_0_157, plain, ((cartprod)=(^[Z0/* 19 */:$i, Z1:$i]:(dsetconstr @ (powerset @ (powerset @ (binunion @ Z0 @ Z1))) @ (^[Z2/* 5 */:$i]:(?[X3:$i]:(((in @ X3 @ Z0)&?[X14:$i]:(((in @ X14 @ Z1)&((Z2)=(setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X14 @ emptyset)) @ emptyset)))))))))))), inference(apply_def,[status(thm)],[c_0_152, c_0_153])). 2.37/0.80 thf(c_0_158, plain, ((descr__Cong)<=>![X1:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 2.37/0.80 thf(c_0_159, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 2.37/0.80 thf(c_0_160, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 2.37/0.80 thf(c_0_161, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 2.37/0.80 thf(c_0_162, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 2.37/0.80 thf(c_0_163, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 2.37/0.80 thf(c_0_164, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 2.37/0.80 thf(c_0_165, 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])). 2.37/0.80 thf(c_0_166, 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])). 2.37/0.80 thf(c_0_167, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 2.37/0.80 thf(c_0_168, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 2.37/0.80 thf(c_0_169, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 2.37/0.80 thf(c_0_170, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 2.37/0.80 thf(c_0_171, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 2.37/0.80 thf(c_0_172, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_154])). 2.37/0.80 thf(c_0_173, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_155, c_0_154])). 2.37/0.80 thf(c_0_174, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_154])). 2.37/0.80 thf(c_0_175, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 2.37/0.80 thf(c_0_176, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X451:$i]:(((in @ X451 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&?[X452:$i]:(((in @ X452 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X451 @ emptyset) @ (setadjoin @ (setadjoin @ X451 @ (setadjoin @ X452 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_156])). 2.37/0.80 thf(c_0_177, axiom, ((ubforcartprodlem3)=(![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5)))))))))), inference(apply_def,[status(thm)],[ubforcartprodlem3, c_0_153])). 2.37/0.80 thf(c_0_178, axiom, ((cartprodpairin)=(![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (dsetconstr @ (powerset @ (powerset @ (binunion @ X4 @ X5))) @ (^[Z0/* 5 */:$i]:(?[X455:$i]:(((in @ X455 @ X4)&?[X456:$i]:(((in @ X456 @ X5)&((Z0)=(setadjoin @ (setadjoin @ X455 @ emptyset) @ (setadjoin @ (setadjoin @ X455 @ (setadjoin @ X456 @ emptyset)) @ emptyset))))))))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[cartprodpairin, c_0_153]), c_0_157])). 2.37/0.80 thf(c_0_179, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X453:$i]:(((in @ X453 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&?[X454:$i]:(((in @ X454 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X453 @ emptyset) @ (setadjoin @ (setadjoin @ X453 @ (setadjoin @ X454 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[kpairp, c_0_153]), c_0_156])). 2.37/0.80 thf(c_0_180, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 2.37/0.80 thf(c_0_181, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 2.37/0.80 thf(c_0_182, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X447:$i]:((((X1 @ X447))&![X448:$i]:((((X1 @ X448))=>((X447)=(X448)))))))=>((?[X449:$i]:((((X17 @ X449))&![X450:$i]:((((X17 @ X450))=>((X449)=(X450)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_158, c_0_159])). 2.37/0.80 thf(c_0_183, plain, ((exuEu)=(![X1:$i > $o]:(((?[X445:$i]:((((X1 @ X445))&![X446:$i]:((((X1 @ X446))=>((X445)=(X446)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_160, c_0_159])). 2.37/0.80 thf(c_0_184, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X441:$i]:((((X1 @ X441))&![X442:$i]:((((X1 @ X442))=>((X441)=(X442)))))))<=>(?[X443:$i]:((((X17 @ X443))&![X444:$i]:((((X17 @ X444))=>((X443)=(X444)))))))))))), inference(apply_def,[status(thm)],[c_0_161, c_0_159])). 2.37/0.80 thf(c_0_185, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X437:$i]:((((X1 @ X437))&![X438:$i]:((((X1 @ X438))=>((X437)=(X438))))))))))), inference(apply_def,[status(thm)],[c_0_162, c_0_159])). 2.37/0.80 thf(c_0_186, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X435:$i]:((((X1 @ X435))&![X436:$i]:((((X1 @ X436))=>((X435)=(X436)))))))))))), inference(apply_def,[status(thm)],[c_0_163, c_0_159])). 2.37/0.80 thf(c_0_187, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X433:$i]:((((X1 @ X433))&![X434:$i]:((((X1 @ X434))=>((X433)=(X434))))))))))), inference(apply_def,[status(thm)],[c_0_164, c_0_159])). 2.37/0.80 thf(c_0_188, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X439:$i]:((((X1 @ X439))&![X440:$i]:((((X1 @ X440))=>((X439)=(X440)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_165, c_0_159])). 2.37/0.80 thf(c_0_189, plain, ((emptyE1)<=>![X4:$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])). 2.37/0.80 thf(c_0_190, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_154])). 2.37/0.80 thf(c_0_191, plain, ((exuE2)=(![X1:$i > $o]:(((?[X431:$i]:((((X1 @ X431))&![X432:$i]:((((X1 @ X432))=>((X431)=(X432)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_166, c_0_159])). 2.37/0.80 thf(c_0_192, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 2.37/0.80 thf(c_0_193, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 2.37/0.80 thf(c_0_194, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X429:$i]:((((X1 @ X429))&![X430:$i]:((((X1 @ X430))=>((X429)=(X430)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_167, c_0_159])). 2.37/0.80 thf(c_0_195, plain, ((exuE1)=(![X1:$i > $o]:(((?[X427:$i]:((((X1 @ X427))&![X428:$i]:((((X1 @ X428))=>((X427)=(X428)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_168, c_0_159])). 2.37/0.80 thf(c_0_196, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 2.37/0.80 thf(c_0_197, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 2.37/0.80 thf(c_0_198, plain, ((descrp)=(![X1:$i > $o]:(((?[X425:$i]:((((X1 @ X425))&![X426:$i]:((((X1 @ X426))=>((X425)=(X426)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_169, c_0_159])). 2.37/0.80 thf(c_0_199, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X423:$i]:((((X6 @ X2 @ X423))&![X424:$i]:((((X6 @ X2 @ X424))=>((X423)=(X424)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_170, c_0_159])). 2.37/0.80 thf(c_0_200, plain, ((epred1_0)<=>![X470:$i]:(?[X471:$i]:((((![X472:$i]:(((in @ X472 @ X471)=>![X473:$i]:(((in @ X473 @ X472)=>(in @ X473 @ X470)))))&![X474:$i, X475:$i]:((((in @ X474 @ X470)&(in @ X475 @ X470))=>(![X476:$i]:(((in @ X476 @ X471)=>((in @ X474 @ X476)<=>(in @ X475 @ X476))))=>((X474)=(X475))))))&![X477:$i, X478:$i]:((((in @ X477 @ X471)&(in @ X478 @ X471))=>(![X479:$i]:(((in @ X479 @ X477)=>(in @ X479 @ X478)))|![X480:$i]:(((in @ X480 @ X478)=>(in @ X480 @ X477)))))))&![X481:$i]:(((![X482:$i]:(((in @ X482 @ X481)=>(in @ X482 @ X470)))&?[X483:$i]:((in @ X483 @ X481)))=>?[X484:$i, X485:$i]:(((((in @ X484 @ X471)&(in @ X485 @ X481))&~(?[X486:$i]:(((in @ X486 @ X484)&(in @ X486 @ X481)))))&![X487:$i]:(((in @ X487 @ X471)=>(![X488:$i]:(((in @ X488 @ X487)=>(in @ X488 @ X484)))|(in @ X485 @ X487)))))))))))), introduced(definition)). 2.37/0.80 thf(c_0_201, negated_conjecture, ~((![X887:$i, X888:$i]:((![X889:$i]:(((in @ X889 @ X887)<=>(in @ X889 @ X888)))=>((X887)=(X888))))=>(![X457:$i]:(~(in @ X457 @ emptyset))=>(![X884:$i, X885:$i, X886:$i]:(((in @ X886 @ (setadjoin @ X884 @ X885))<=>(((X886)=(X884))|(in @ X886 @ X885))))=>(![X881:$i, X882:$i]:(((in @ X882 @ (powerset @ X881))<=>![X883:$i]:(((in @ X883 @ X882)=>(in @ X883 @ X881)))))=>(![X458:$i, X459:$i]:(((in @ X459 @ (setunion @ X458))<=>?[X460:$i]:(((in @ X459 @ X460)&(in @ X460 @ X458)))))=>((in @ emptyset @ omega)=>(![X461:$i]:(((in @ X461 @ omega)=>(in @ (setadjoin @ X461 @ X461) @ omega)))=>(![X878:$i]:((((in @ emptyset @ X878)&![X879:$i]:((((in @ X879 @ omega)&(in @ X879 @ X878))=>(in @ (setadjoin @ X879 @ X879) @ X878))))=>![X880:$i]:(((in @ X880 @ omega)=>(in @ X880 @ X878)))))=>(![X462:$i > $i > $o, X463:$i]:((![X464:$i]:(((in @ X464 @ X463)=>?[X465:$i]:(((X462 @ X464 @ X465)&![X466:$i]:(((X462 @ X464 @ X466)=>((X465)=(X466))))))))=>?[X467:$i]:(![X468:$i]:(((in @ X468 @ X467)<=>?[X469:$i]:(((in @ X469 @ X463)&(X462 @ X469 @ X468))))))))=>(![X874:$i]:((?[X875:$i]:((in @ X875 @ X874))=>?[X876:$i]:(((in @ X876 @ X874)&~(?[X877:$i]:(((in @ X877 @ X876)&(in @ X877 @ X874))))))))=>((epred1_0)=>(![X489:$i > $o]:((?[X490:$i]:(((X489 @ X490)&![X491:$i]:(((X489 @ X491)=>((X490)=(X491))))))=>(X489 @ (descr @ (^[Z0/* 3 */:$i]:((X489 @ Z0)))))))=>(![X492:$i, X493:$i > $o, X494:$i]:(((in @ X494 @ X492)=>((X493 @ X494)=>(in @ X494 @ (dsetconstr @ X492 @ (^[Z0/* 3 */:$i]:((X493 @ Z0))))))))=>(![X871:$i, X872:$i > $o, X873:$i]:(((in @ X873 @ (dsetconstr @ X871 @ (^[Z0/* 3 */:$i]:((X872 @ Z0)))))=>(in @ X873 @ X871)))=>(![X495:$i, X496:$i > $o, X497:$i]:(((in @ X497 @ (dsetconstr @ X495 @ (^[Z0/* 3 */:$i]:((X496 @ Z0)))))=>(X496 @ X497)))=>(![X498:$i > $o]:((?[X499:$i]:(((X498 @ X499)&![X500:$i]:(((X498 @ X500)=>((X499)=(X500))))))=>?[X501:$i]:(((X498 @ X501)&![X502:$i]:(((X498 @ X502)=>((X501)=(X502))))))))=>(![X503:$o, X504:$i]:(((in @ X504 @ (prop2set @ ((X503))))=>(X503)))=>(![X869:$i]:(((in @ X869 @ emptyset)=>![X870:$o]:((X870))))=>(![X868:$i]:(~(in @ X868 @ emptyset))=>(![X505:$i]:(~(in @ X505 @ emptyset))=>(![X506:$i > $o]:((?[X507:$i]:(((X506 @ X507)&![X508:$i]:(((X506 @ X508)=>((X507)=(X508))))))=>?[X509:$i]:((X506 @ X509))))=>(![X510:$i, X511:$i]:((![X512:$i]:(((in @ X512 @ X510)=>(in @ X512 @ X511)))=>(![X513:$i]:(((in @ X513 @ X511)=>(in @ X513 @ X510)))=>((X510)=(X511)))))=>(![X514:$i]:((![X515:$i]:(~(in @ X515 @ X514))=>((X514)=(emptyset))))=>(![X866:$i]:((![X867:$i]:(~(in @ X867 @ X866))=>((X866)=(emptyset))))=>(![X516:$i, X517:$i > $o, X518:$i]:(((in @ X518 @ X516)=>((in @ X518 @ (dsetconstr @ X516 @ (^[Z0/* 3 */:$i]:((X517 @ Z0)))))<=>(X517 @ X518))))=>(![X864:$i]:((((X864)!=(emptyset))=>?[X865:$i]:((in @ X865 @ X864))))=>(![X861:$i, X862:$i > $o, X863:$i]:(((in @ X863 @ X861)=>((X862 @ X863)=>((dsetconstr @ X861 @ (^[Z0/* 3 */:$i]:((X862 @ Z0))))!=(emptyset)))))=>(![X859:$i]:((?[X860:$i]:((in @ X860 @ X859))=>((X859)!=(emptyset))))=>(![X519:$i, X520:$i]:((in @ X519 @ (setadjoin @ X519 @ X520)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X856:$i, X857:$i, X858:$i]:(((in @ X858 @ X857)=>(in @ X858 @ (setadjoin @ X856 @ X857))))=>(![X521:$i, X522:$i, X523:$i]:(((in @ X523 @ (setadjoin @ X521 @ X522))=>![X524:$o]:(((((X523)=(X521))=>(X524))=>(((in @ X523 @ X522)=>(X524))=>(X524))))))=>(![X525:$i, X526:$i, X527:$i]:(((in @ X527 @ (setadjoin @ X525 @ X526))=>(((X527)=(X525))|(in @ X527 @ X526))))=>(![X528:$i]:(((dsetconstr @ X528 @ (^[Z0/* 3 */:$i]:(($true))))=(X528)))=>(![X853:$i, X854:$i]:((![X855:$i]:(((in @ X855 @ X854)=>(in @ X855 @ X853)))=>(in @ X854 @ (powerset @ X853))))=>(![X852:$i]:((in @ emptyset @ (powerset @ X852)))=>(![X851:$i]:((in @ emptyset @ (powerset @ X851)))=>(![X529:$i, X530:$i, X531:$i]:(((in @ X530 @ (powerset @ X529))=>((in @ X531 @ X530)=>(in @ X531 @ X529))))=>(![X848:$i, X849:$i, X850:$i]:(((in @ X849 @ X850)=>((in @ X850 @ X848)=>(in @ X849 @ (setunion @ X848)))))=>(![X532:$i, X533:$i]:(((in @ X533 @ (setunion @ X532))=>![X534:$o]:((![X535:$i]:(((in @ X533 @ X535)=>((in @ X535 @ X532)=>(X534))))=>(X534)))))=>(![X846:$i, X847:$i]:(((in @ X847 @ X846)=>(in @ X847 @ (powerset @ (setunion @ X846)))))=>(![X536:$i > $o]:((?[X537:$i]:(((X536 @ X537)&![X538:$i]:(((X536 @ X538)=>((X537)=(X538))))))=>?[X539:$i]:(![X540:$i]:(((X536 @ X540)<=>((X540)=(X539)))))))=>(![X541:$i]:((((X541)!=(emptyset))=>?[X542:$i]:((in @ X542 @ X541))))=>(![X543:$i, X544:$i]:(((in @ X543 @ (setadjoin @ X544 @ emptyset))=>((X543)=(X544))))=>(![X844:$i, X845:$i]:((((X844)!=(X845))=>~(in @ X845 @ (setadjoin @ X844 @ emptyset))))=>(![X545:$i, X546:$i]:((((X545)=(X546))=>(in @ X545 @ (setadjoin @ X546 @ emptyset))))=>(![X842:$i, X843:$i]:(((in @ X842 @ (setadjoin @ X843 @ emptyset))=>(in @ X843 @ (setadjoin @ X842 @ emptyset))))=>(![X839:$i, X840:$i, X841:$i]:(((in @ X841 @ (setadjoin @ X839 @ (setadjoin @ X840 @ emptyset)))=>(((X841)=(X839))|((X841)=(X840)))))=>(![X837:$i, X838:$i]:((in @ X837 @ (setadjoin @ X837 @ (setadjoin @ X838 @ emptyset))))=>(![X835:$i, X836:$i]:((in @ X836 @ (setadjoin @ X835 @ (setadjoin @ X836 @ emptyset))))=>(![X547:$i, X548:$i > $o]:((?[X549:$i]:(((in @ X549 @ X547)&(X548 @ X549)))=>((dsetconstr @ X547 @ (^[Z0/* 3 */:$i]:((X548 @ Z0))))!=(emptyset))))=>(![X833:$i > $o, X834:$i]:(((in @ X834 @ emptyset)=>(X833 @ X834)))=>(![X550:$i, X551:$i > $o]:((~(![X552:$i]:(((in @ X552 @ X550)=>(X551 @ X552))))=>?[X553:$i]:(((in @ X553 @ X550)&~(X551 @ X553)))))=>(![X829:$i, X830:$i > $o]:((![X831:$i]:(((in @ X831 @ X829)=>~(X830 @ X831)))=>~(?[X832:$i]:(((in @ X832 @ X829)&(X830 @ X832))))))=>(![X825:$i, X826:$i > $o]:((~(?[X827:$i]:(((in @ X827 @ X825)&(X826 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inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[cartprodmempair1]), setextAx]), notinsingleton]), subset2powerset]), subPowSU]), c_0_171]), setunionI]), emptyInPowerset]), emptyinPowerset]), binunionIL]), powersetI]), setadjoinIR]), upairset2IR]), emptyinunitempty]), c_0_172]), c_0_173]), binunionIR]), c_0_174]), noeltsimpempty]), binunionE]), emptysetimpfalse]), emptysetE]), setextsub]), c_0_175]), foundationAx]), binunionRsub]), omegaIndAx]), omega0Ax]), binintersectEL]), powersetAx]), setadjoinAx]), c_0_176]), subsetemptysetimpeq]), binintersectLsub]), binintersectER]), binintersectRsub]), binintersectSubset1]), setminusEL]), setminusER]), setminusILneg]), setminusIRneg]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffIneg1]), secondinupair]), setukpairIL]), setukpairIR]), notequalI1]), notsubsetI]), subsetE2]), subsetE]), upairset2E]), c_0_177]), c_0_153]), c_0_178]), c_0_157]), ubforcartprodlem2]), ubforcartprodlem1]), upairinpowunion]), powersetI1]), upairsubunion]), powersetsubset]), singletoninpowunion]), singletoninpowerset]), singletonsubset]), c_0_179]), symdiffIneg2]), symdiffI2]), setminusLsub]), setminusELneg]), setminusERneg]), setminusSubset2]), setminusI]), bs114d]), binintersectSubset4]), disjointsetsI1]), binintersectSubset3]), binintersectSubset2]), binintersectSubset5]), binintersectI]), binunionLsub]), binunionEcases]), c_0_180]), inPowerset]), powersetE1]), subsetTrans]), subsetRefl]), subsetI2]), eqimpsubset1]), eqimpsubset2]), c_0_181]), c_0_182]), c_0_183]), omega__Cong]), powerset__Cong]), setadjoin__Cong]), c_0_184]), in__Cong]), inCongP]), c_0_185]), c_0_186]), c_0_187]), notdexE]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), vacuousDall]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), setadjoinSub2]), setadjoinSub]), notequalI2]), emptysetsubset]), subsetI1]), setunion__Cong]), emptyset__Cong]), c_0_188]), notdallE]), prop2setI]), quantDeMorgan1]), c_0_189]), eqinunit]), uniqinunit]), c_0_190]), c_0_191]), setunionE]), powersetE]), c_0_192]), setadjoinOr]), setadjoinE]), setadjoinIL]), c_0_193]), emptyI]), setext]), c_0_194]), notinemptyset]), prop2setE]), c_0_195]), c_0_196]), c_0_197]), c_0_198]), wellorderingAx]), c_0_199]), omegaSAx]), setunionAx]), emptysetAx])]), c_0_200])). 2.37/0.80 thf(c_0_202, negated_conjecture, ![X890:$i, X891:$i, X893:$i, X894:$i, X895:$i, X896:$i, X897:$i, X898:$i, X899:$i, X900:$i, X901:$i, X903:$i, X904:$i, X906:$i, X907:$i, X908:$i, X909:$i, X910:$i, X912:$i, X913:$i > $i > $o, X914:$i, X916:$i, X919:$i, X921:$i, X922:$i, X923:$i, X924:$i, X926:$i, X927:$i > $o, X928:$i, X930:$i, X931:$i > $o, X932:$i, X933:$i, X934:$i > $o, X935:$i, X936:$i, X937:$i > $o, X938:$i, X939:$i > $o, X940:$i, X943:$i, X944:$o, X945:$i, X946:$i, X947:$o, X948:$i, X949:$i, X950:$i > $o, X951:$i, X954:$i, X955:$i, X958:$i, X960:$i, X962:$i, X963:$i > $o, X964:$i, X965:$i, X967:$i, X968:$i > $o, X969:$i, X970:$i, X971:$i, X972:$i, X973:$i, X974:$i, X975:$i, X976:$i, X977:$i, X978:$i, X979:$i, X980:$o, X981:$i, X982:$i, X983:$i, X984:$i, X985:$i, X986:$i, X988:$i, X989:$i, X990:$i, X991:$i, X992:$i, X993:$i, X994:$i, X995:$i, X996:$i, X997:$i, X998:$o, X1000:$i, X1001:$i, X1002:$i > $o, X1003:$i, X1006:$i, X1007:$i, X1008:$i, X1010:$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:$i, X1026:$i > $o, X1027:$i, X1028:$i > $o, X1029:$i, X1030:$i, X1031:$i > $o, X1032:$i, X1034:$i, X1035:$i > $o, X1037:$i, X1038:$i, X1039:$i > $o, X1041:$i, X1042:$i, X1043:$i > $o, X1044:$i, X1046:$o, X1047:$i, X1048:$i > $o, X1050:$i, X1051:$i, X1052:$i > $o, X1053:$i, X1055:$i > $o, X1056:$i, X1059:$i, X1060:$i > $o, X1061:$i, X1065:$i, X1066:$i > $o, X1067:$i, X1070:$i, X1071:$i, X1072:$i, X1073:$i, X1074:$i, X1075:$i, X1076:$i, X1077:$i, X1078:$i, X1079:$i > $o, X1080:$i, X1082:$i, X1083:$i, X1084:$i > $o, X1085:$i > $o, X1088:$i, X1091:$i, X1092:$i, X1095:$i, X1096:$i, X1097:$i, X1098:$i, X1099:$i, X1100:$i, X1101:$i, X1102:$i, X1103:$i, X1104:$i > $o, X1105:$i, X1107:$i, X1108:$i, X1109:$i > $o, X1110:$i > $o, X1113:$i, X1115:$i, X1117:$i, X1118:$i, X1119:$i > $o, X1120:$i > $o, X1123:$i, X1124:$i, X1126:$i, X1127:$i, X1128:$i, X1129:$i, X1130:$i, X1131:$i, X1133:$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, 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 > $o, X1171:$i, X1172:$i > $o, X1173:$i, X1174:$i, X1175:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i, X1180:$i, X1181:$i, X1182:$i, X1183:$i, X1184:$o, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$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, 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:$i, X1230:$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:$i, X1252:$o, 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, X1275:$i, X1276:$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, X1316:$i, X1317:$i]:((((~(in @ (esk1_2 @ X890 @ X891) @ X890)|~(in @ (esk1_2 @ X890 @ X891) @ X891)|((X890)=(X891)))&((in @ (esk1_2 @ X890 @ X891) @ X890)|(in @ (esk1_2 @ X890 @ X891) @ X891)|((X890)=(X891))))&(~(in @ X893 @ emptyset)&(((~(in @ X896 @ (setadjoin @ X894 @ X895))|(((X896)=(X894))|(in @ X896 @ X895)))&((((X896)!=(X894))|(in @ X896 @ (setadjoin @ X894 @ X895)))&(~(in @ X896 @ X895)|(in @ X896 @ (setadjoin @ X894 @ X895)))))&(((~(in @ X898 @ (powerset @ X897))|(~(in @ X899 @ X898)|(in @ X899 @ X897)))&(((in @ (esk2_2 @ X900 @ X901) @ X901)|(in @ X901 @ (powerset @ X900)))&(~(in @ (esk2_2 @ X900 @ X901) @ X900)|(in @ X901 @ (powerset @ X900)))))&(((((in @ X904 @ (esk3_2 @ X903 @ X904))|~(in @ X904 @ (setunion @ X903)))&((in @ (esk3_2 @ X903 @ X904) @ X903)|~(in @ X904 @ (setunion @ X903))))&(~(in @ X907 @ X908)|~(in @ X908 @ X906)|(in @ X907 @ (setunion @ X906))))&((in @ emptyset @ omega)&((~(in @ X909 @ omega)|(in @ (setadjoin @ X909 @ X909) @ omega))&(((((in @ (esk4_1 @ X910) @ omega)|~(in @ emptyset @ X910)|(~(in @ X912 @ omega)|(in @ X912 @ X910)))&((in @ (esk4_1 @ X910) @ X910)|~(in @ emptyset @ X910)|(~(in @ X912 @ omega)|(in @ X912 @ X910))))&(~(in @ (setadjoin @ (esk4_1 @ X910) @ (esk4_1 @ X910)) @ X910)|~(in @ emptyset @ X910)|(~(in @ X912 @ omega)|(in @ X912 @ X910))))&((((((in @ (esk8_3 @ X913 @ X914 @ X919) @ X914)|~(in @ X919 @ (esk7_2 @ X913 @ X914))|(in @ (esk5_2 @ X913 @ X914) @ X914))&((X913 @ (esk8_3 @ X913 @ X914 @ X919) @ X919)|~(in @ X919 @ (esk7_2 @ X913 @ X914))|(in @ (esk5_2 @ X913 @ X914) @ X914)))&(~(in @ X922 @ X914)|~(X913 @ X922 @ X921)|(in @ X921 @ (esk7_2 @ X913 @ X914))|(in @ (esk5_2 @ X913 @ X914) @ X914)))&(((((in @ (esk8_3 @ X913 @ X914 @ X919) @ X914)|~(in @ X919 @ (esk7_2 @ X913 @ X914))|((X913 @ (esk5_2 @ X913 @ X914) @ (esk6_3 @ X913 @ X914 @ X916))|~(X913 @ (esk5_2 @ X913 @ X914) @ X916)))&((X913 @ (esk8_3 @ X913 @ X914 @ X919) @ X919)|~(in @ X919 @ (esk7_2 @ X913 @ X914))|((X913 @ (esk5_2 @ X913 @ X914) @ (esk6_3 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Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X1110 @ Z0)))))|(((X1113)!=(esk48_3 @ X1109 @ X1110 @ X1113))|~(X1109 @ X1113))|(~(X1109 @ (esk46_2 @ X1109 @ X1110))|~(X1110 @ (esk47_2 @ X1109 @ X1110))))&(((X1115)!=(esk49_3 @ X1109 @ X1110 @ X1115))|~(X1110 @ X1115)|((descr @ (^[Z0/* 3 */:$i]:((X1109 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X1110 @ Z0)))))|(((X1113)!=(esk48_3 @ X1109 @ X1110 @ X1113))|~(X1109 @ X1113))|(~(X1109 @ (esk46_2 @ X1109 @ X1110))|~(X1110 @ (esk47_2 @ X1109 @ X1110))))))&((((X1110 @ (esk49_3 @ X1109 @ X1110 @ X1115))|~(X1110 @ X1115)|((descr @ (^[Z0/* 3 */:$i]:((X1109 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X1110 @ Z0)))))|((X1109 @ (esk48_3 @ X1109 @ X1110 @ X1113))|~(X1109 @ X1113))|((X1109 @ (esk46_2 @ X1109 @ X1110))|(X1110 @ (esk47_2 @ X1109 @ X1110))))&(((X1115)!=(esk49_3 @ X1109 @ X1110 @ X1115))|~(X1110 @ X1115)|((descr @ (^[Z0/* 3 */:$i]:((X1109 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X1110 @ Z0)))))|((X1109 @ (esk48_3 @ X1109 @ X1110 @ X1113))|~(X1109 @ X1113))|((X1109 @ (esk46_2 @ X1109 @ X1110))|(X1110 @ (esk47_2 @ X1109 @ X1110)))))&(((X1110 @ (esk49_3 @ X1109 @ X1110 @ X1115))|~(X1110 @ X1115)|((descr @ (^[Z0/* 3 */:$i]:((X1109 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X1110 @ Z0)))))|(((X1113)!=(esk48_3 @ X1109 @ X1110 @ X1113))|~(X1109 @ X1113))|((X1109 @ (esk46_2 @ X1109 @ X1110))|(X1110 @ (esk47_2 @ X1109 @ X1110))))&(((X1115)!=(esk49_3 @ X1109 @ X1110 @ X1115))|~(X1110 @ X1115)|((descr @ (^[Z0/* 3 */:$i]:((X1109 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X1110 @ Z0)))))|(((X1113)!=(esk48_3 @ X1109 @ X1110 @ X1113))|~(X1109 @ X1113))|((X1109 @ (esk46_2 @ X1109 @ X1110))|(X1110 @ (esk47_2 @ X1109 @ X1110))))))))&((((in @ (esk50_4 @ X1117 @ X1118 @ X1119 @ X1120) @ X1117)|((dsetconstr @ X1117 @ (^[Z0/* 3 */:$i]:((X1119 @ Z0))))=(dsetconstr @ X1118 @ (^[Z0/* 3 */:$i]:((X1120 @ Z0)))))|((X1117)!=(X1118)))&(((in @ (esk51_4 @ X1117 @ X1118 @ X1119 @ X1120) @ X1118)|((dsetconstr @ X1117 @ (^[Z0/* 3 */:$i]:((X1119 @ Z0))))=(dsetconstr @ X1118 @ (^[Z0/* 3 */:$i]:((X1120 @ Z0)))))|((X1117)!=(X1118)))&((((esk50_4 @ X1117 @ X1118 @ X1119 @ X1120)=(esk51_4 @ X1117 @ X1118 @ X1119 @ X1120))|((dsetconstr @ X1117 @ (^[Z0/* 3 */:$i]:((X1119 @ Z0))))=(dsetconstr @ X1118 @ (^[Z0/* 3 */:$i]:((X1120 @ Z0)))))|((X1117)!=(X1118)))&((~(X1119 @ (esk50_4 @ X1117 @ X1118 @ X1119 @ X1120))|~(X1120 @ (esk51_4 @ X1117 @ X1118 @ X1119 @ X1120))|((dsetconstr @ X1117 @ (^[Z0/* 3 */:$i]:((X1119 @ Z0))))=(dsetconstr @ X1118 @ (^[Z0/* 3 */:$i]:((X1120 @ Z0)))))|((X1117)!=(X1118)))&((X1119 @ (esk50_4 @ X1117 @ X1118 @ X1119 @ X1120))|(X1120 @ (esk51_4 @ X1117 @ X1118 @ X1119 @ X1120))|((dsetconstr @ X1117 @ (^[Z0/* 3 */:$i]:((X1119 @ Z0))))=(dsetconstr @ X1118 @ (^[Z0/* 3 */:$i]:((X1120 @ Z0)))))|((X1117)!=(X1118)))))))&((((in @ (esk52_2 @ X1123 @ X1124) @ X1123)|(subset @ X1123 @ X1124))&(~(in @ (esk52_2 @ X1123 @ X1124) @ X1124)|(subset @ X1123 @ X1124)))&((((X1126)!=(X1127))|(subset @ X1127 @ X1126))&((((X1128)!=(X1129))|(subset @ X1128 @ X1129))&((((in @ (esk53_2 @ X1130 @ X1131) @ X1130)|(subset @ X1130 @ X1131))&(~(in @ (esk53_2 @ X1130 @ X1131) @ X1131)|(subset @ X1130 @ X1131)))&((subset @ emptyset @ X1133)&((~(subset @ X1134 @ X1135)|(~(in @ X1136 @ X1134)|(in @ X1136 @ X1135)))&((~(subset @ X1137 @ X1138)|((in @ X1139 @ X1138)|~(in @ X1139 @ X1137)))&((~(in @ X1142 @ X1140)|((in @ X1142 @ X1141)|~(subset @ X1140 @ X1141)))&(((subset @ X1143 @ X1144)|((X1143)!=(X1144)))&((~(in @ X1147 @ X1145)|((in @ X1147 @ X1146)|((X1145)!=(X1146))))&((subset @ X1148 @ X1148)&((~(subset @ X1149 @ X1150)|(~(subset @ X1150 @ X1151)|(subset @ X1149 @ X1151)))&((subset @ X1153 @ (setadjoin @ X1152 @ X1153))&((~(subset @ X1154 @ X1156)|(subset @ X1154 @ (setadjoin @ X1155 @ X1156)))&((~(subset @ X1157 @ X1158)|(in @ X1157 @ (powerset @ X1158)))&((~(subset @ X1159 @ X1160)|(~(subset @ X1160 @ X1159)|((X1159)=(X1160))))&((~(subset @ X1161 @ emptyset)|((X1161)=(emptyset)))&((~(subset @ X1163 @ X1162)|(in @ X1163 @ (powerset @ X1162)))&((~(in @ X1165 @ (powerset @ X1164))|(subset @ X1165 @ X1164))&((in @ X1166 @ (powerset @ X1166))&((~(subset @ X1167 @ X1168)|(subset @ (powerset @ X1167) @ (powerset @ X1168)))&((in @ (dsetconstr @ X1169 @ (^[Z0/* 3 */:$i]:((X1170 @ Z0)))) @ (powerset @ X1169))&((subset @ (dsetconstr @ X1171 @ (^[Z0/* 3 */:$i]:((X1172 @ Z0)))) @ X1171)&((~(in @ X1175 @ X1173)|(in @ X1175 @ (binunion @ X1173 @ X1174)))&((in @ X1177 @ (setadjoin @ X1176 @ (setadjoin @ X1177 @ emptyset)))&((~(in @ X1180 @ X1179)|(in @ X1180 @ (binunion @ X1178 @ X1179)))&(((((in @ X1183 @ X1182)|(X1184)|(in @ X1183 @ X1181)|~(in @ X1183 @ (binunion @ X1181 @ X1182)))&(~(X1184)|(X1184)|(in @ X1183 @ X1181)|~(in @ X1183 @ (binunion @ X1181 @ X1182))))&(((in @ X1183 @ X1182)|(X1184)|~(X1184)|~(in @ X1183 @ (binunion @ X1181 @ X1182)))&(~(X1184)|(X1184)|~(X1184)|~(in @ X1183 @ (binunion @ X1181 @ X1182)))))&((~(in @ X1187 @ (binunion @ X1185 @ X1186))|((in @ X1187 @ X1185)|(in @ X1187 @ X1186)))&((subset @ X1188 @ (binunion @ X1188 @ X1189))&((subset @ X1191 @ (binunion @ X1190 @ X1191))&((~(in @ X1194 @ X1192)|(~(in @ X1194 @ X1193)|(in @ X1194 @ (binintersect @ X1192 @ X1193))))&((~(subset @ X1197 @ X1195)|(~(subset @ X1197 @ X1196)|(subset @ X1197 @ (binintersect @ X1195 @ X1196))))&((~(in @ X1200 @ (binintersect @ X1198 @ X1199))|(in @ X1200 @ X1198))&((subset @ (binintersect @ X1201 @ X1202) @ X1201)&((~(subset @ X1203 @ X1204)|((binintersect @ X1203 @ X1204)=(X1203)))&((((binintersect @ X1205 @ X1206)!=(X1206))|(subset @ X1206 @ X1205))&((~(in @ X1209 @ (binintersect @ X1207 @ X1208))|(in @ X1209 @ X1208))&((((in @ (esk54_2 @ X1210 @ X1211) @ X1210)|((binintersect @ X1210 @ X1211)=(emptyset)))&((in @ (esk54_2 @ X1210 @ X1211) @ X1211)|((binintersect @ X1210 @ X1211)=(emptyset))))&((subset @ (binintersect @ X1213 @ X1214) @ X1214)&((~(subset @ X1216 @ X1215)|((binintersect @ X1215 @ X1216)=(X1216)))&((((binintersect @ X1217 @ X1218)!=(X1217))|(subset @ X1217 @ X1218))&(((binintersect @ X1219 @ (binunion @ X1220 @ X1221))=(binunion @ (binintersect @ X1219 @ X1220) @ (binintersect @ X1219 @ X1221)))&((~(in @ X1224 @ X1222)|((in @ X1224 @ X1223)|(in @ X1224 @ (setminus @ X1222 @ X1223))))&((~(in @ X1227 @ (setminus @ X1225 @ X1226))|(in @ X1227 @ X1225))&((~(in @ X1230 @ (setminus @ X1228 @ X1229))|~(in @ X1230 @ X1229))&((~(subset @ X1231 @ X1232)|((setminus @ X1231 @ X1232)=(emptyset)))&(((in @ X1235 @ (setminus @ X1233 @ X1234))|(~(in @ X1235 @ X1233)|(in @ X1235 @ X1234)))&(((in @ X1238 @ (setminus @ X1236 @ X1237))|((in @ X1238 @ X1237)|~(in @ X1238 @ X1236)))&(((in @ X1241 @ X1239)|~(in @ X1241 @ (setminus @ X1239 @ X1240)))&((~(in @ X1244 @ X1243)|~(in @ X1244 @ (setminus @ X1242 @ X1243)))&((subset @ (setminus @ X1245 @ X1246) @ X1245)&((((setminus @ X1247 @ X1248)!=(emptyset))|(subset @ X1247 @ X1248))&((((~(in @ X1251 @ X1249)|(X1252)|(in @ X1251 @ X1249)|~(in @ X1251 @ (symdiff @ X1249 @ X1250)))&(((in @ X1251 @ X1250)|(X1252)|(in @ X1251 @ X1249)|~(in @ X1251 @ (symdiff @ X1249 @ X1250)))&(~(X1252)|(X1252)|(in @ X1251 @ X1249)|~(in @ X1251 @ (symdiff @ X1249 @ X1250)))))&(((~(in @ X1251 @ X1249)|(X1252)|~(in @ X1251 @ X1250)|~(in @ X1251 @ (symdiff @ X1249 @ X1250)))&(((in @ X1251 @ X1250)|(X1252)|~(in @ X1251 @ X1250)|~(in @ X1251 @ (symdiff @ X1249 @ X1250)))&(~(X1252)|(X1252)|~(in @ X1251 @ X1250)|~(in @ X1251 @ (symdiff @ X1249 @ X1250)))))&((~(in @ X1251 @ X1249)|(X1252)|~(X1252)|~(in @ X1251 @ (symdiff @ X1249 @ X1250)))&(((in @ X1251 @ X1250)|(X1252)|~(X1252)|~(in @ X1251 @ (symdiff @ X1249 @ X1250)))&(~(X1252)|(X1252)|~(X1252)|~(in @ X1251 @ (symdiff @ X1249 @ X1250)))))))&((~(in @ X1255 @ X1253)|((in @ X1255 @ X1254)|(in @ X1255 @ (symdiff @ X1253 @ X1254))))&(((in @ X1258 @ X1256)|(~(in @ X1258 @ X1257)|(in @ X1258 @ (symdiff @ X1256 @ X1257))))&((~(in @ X1261 @ X1259)|(~(in @ X1261 @ X1260)|~(in @ X1261 @ (symdiff @ X1259 @ X1260))))&(((in @ X1264 @ X1262)|((in @ X1264 @ X1263)|~(in @ X1264 @ (symdiff @ X1262 @ X1263))))&((in @ X1266 @ (setadjoin @ X1265 @ (setadjoin @ X1266 @ emptyset)))&((in @ X1267 @ (setunion @ (setadjoin @ (setadjoin @ X1267 @ emptyset) @ (setadjoin @ (setadjoin @ X1267 @ (setadjoin @ X1268 @ emptyset)) @ emptyset))))&((in @ X1270 @ (setunion @ (setadjoin @ (setadjoin @ X1269 @ emptyset) @ (setadjoin @ (setadjoin @ X1269 @ (setadjoin @ X1270 @ emptyset)) @ emptyset))))&(((in @ (esk55_2 @ X1271 @ X1272) @ (setunion @ (setadjoin @ (setadjoin @ X1271 @ emptyset) @ (setadjoin @ (setadjoin @ X1271 @ (setadjoin @ X1272 @ emptyset)) @ emptyset))))&((in @ (esk56_2 @ X1271 @ X1272) @ (setunion @ (setadjoin @ (setadjoin @ X1271 @ emptyset) @ (setadjoin @ (setadjoin @ X1271 @ (setadjoin @ X1272 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1271 @ emptyset) @ (setadjoin @ (setadjoin @ X1271 @ (setadjoin @ X1272 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk55_2 @ X1271 @ X1272) @ emptyset) @ (setadjoin @ (setadjoin @ (esk55_2 @ X1271 @ X1272) @ (setadjoin @ (esk56_2 @ X1271 @ X1272) @ emptyset)) @ emptyset)))))&(((in @ (esk57_2 @ X1275 @ X1276) @ (setunion @ (setadjoin @ (setadjoin @ X1275 @ emptyset) @ (setadjoin @ (setadjoin @ X1275 @ (setadjoin @ X1276 @ emptyset)) @ emptyset))))&((in @ (esk58_2 @ X1275 @ X1276) @ (setunion @ (setadjoin @ (setadjoin @ X1275 @ emptyset) @ (setadjoin @ (setadjoin @ X1275 @ (setadjoin @ X1276 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1275 @ emptyset) @ (setadjoin @ (setadjoin @ X1275 @ (setadjoin @ X1276 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk57_2 @ X1275 @ X1276) @ emptyset) @ (setadjoin @ (setadjoin @ (esk57_2 @ X1275 @ X1276) @ (setadjoin @ (esk58_2 @ X1275 @ X1276) @ emptyset)) @ emptyset)))))&((~(in @ X1280 @ X1279)|(subset @ (setadjoin @ X1280 @ emptyset) @ X1279))&((~(in @ X1282 @ X1281)|(in @ (setadjoin @ X1282 @ emptyset) @ (powerset @ X1281)))&((~(in @ X1285 @ X1283)|(in @ (setadjoin @ X1285 @ emptyset) @ (powerset @ (binunion @ X1283 @ X1284))))&((~(in @ X1288 @ (setadjoin @ X1286 @ (setadjoin @ X1287 @ emptyset)))|(((X1288)=(X1286))|((X1288)=(X1287))))&((~(in @ X1291 @ X1289)|(~(in @ X1292 @ X1290)|(subset @ (setadjoin @ X1291 @ (setadjoin @ X1292 @ emptyset)) @ (binunion @ X1289 @ X1290))))&((~(in @ X1295 @ X1293)|(~(in @ X1296 @ X1294)|(in @ (setadjoin @ X1295 @ (setadjoin @ X1296 @ emptyset)) @ (powerset @ (binunion @ X1293 @ X1294)))))&((~(in @ X1299 @ X1297)|(~(in @ X1300 @ X1298)|(subset @ (setadjoin @ (setadjoin @ X1299 @ emptyset) @ (setadjoin @ (setadjoin @ X1299 @ (setadjoin @ X1300 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1297 @ X1298)))))&((~(in @ X1303 @ X1301)|(~(in @ X1304 @ X1302)|(in @ (setadjoin @ (setadjoin @ X1303 @ emptyset) @ (setadjoin @ (setadjoin @ X1303 @ (setadjoin @ X1304 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1301 @ X1302))))))&((~(in @ X1307 @ X1305)|(~(in @ X1308 @ X1306)|(in @ (setadjoin @ (setadjoin @ X1307 @ emptyset) @ (setadjoin @ (setadjoin @ X1307 @ (setadjoin @ X1308 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1305 @ X1306))))))&((~(in @ X1311 @ X1309)|(~(in @ X1312 @ X1310)|(in @ (setadjoin @ (setadjoin @ X1311 @ emptyset) @ (setadjoin @ (setadjoin @ X1311 @ (setadjoin @ X1312 @ emptyset)) @ emptyset)) @ (dsetconstr @ (powerset @ (powerset @ (binunion @ X1309 @ X1310))) @ (^[Z0/* 5 */:$i]:(?[X659:$i]:(((in @ X659 @ X1309)&?[X660:$i]:(((in @ X660 @ X1310)&((Z0)=(setadjoin @ (setadjoin @ X659 @ emptyset) @ (setadjoin @ (setadjoin @ X659 @ (setadjoin @ X660 @ emptyset)) @ emptyset)))))))))))))&((in @ esk61_0 @ (dsetconstr @ (powerset @ (powerset @ (binunion @ esk59_0 @ esk60_0))) @ (^[Z0/* 5 */:$i]:(?[X661:$i]:(((in @ X661 @ esk59_0)&?[X662:$i]:(((in @ X662 @ esk60_0)&((Z0)=(setadjoin @ (setadjoin @ X661 @ emptyset) @ (setadjoin @ (setadjoin @ X661 @ (setadjoin @ X662 @ emptyset)) @ emptyset)))))))))))&(~(in @ X1316 @ esk59_0)|(~(in @ X1317 @ esk60_0)|((esk61_0)!=(setadjoin @ (setadjoin @ X1316 @ emptyset) @ (setadjoin @ (setadjoin @ X1316 @ (setadjoin @ X1317 @ emptyset)) @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_201])])])])])])). 2.37/0.80 thf(c_0_203, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((X1 @ X2)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_202])). 2.37/0.80 thf(c_0_204, negated_conjecture, (in @ esk61_0 @ (dsetconstr @ (powerset @ (powerset @ (binunion @ esk59_0 @ esk60_0))) @ (^[Z0/* 5 */:$i]:(?[X1341:$i]:(((in @ X1341 @ esk59_0)&?[X1342:$i]:(((in @ X1342 @ esk60_0)&((Z0)=(setadjoin @ (setadjoin @ X1341 @ emptyset) @ (setadjoin @ (setadjoin @ X1341 @ (setadjoin @ X1342 @ emptyset)) @ emptyset))))))))))), inference(split_conjunct,[status(thm)],[c_0_202])). 2.37/0.80 thf(c_0_205, negated_conjecture, ?[X1343:$i]:(((in @ X1343 @ esk59_0)&?[X1344:$i]:(((in @ X1344 @ esk60_0)&((esk61_0)=(setadjoin @ (setadjoin @ X1343 @ emptyset) @ (setadjoin @ (setadjoin @ X1343 @ (setadjoin @ X1344 @ emptyset)) @ emptyset))))))), inference(spm,[status(thm)],[c_0_203, c_0_204])). 2.37/0.80 thf(c_0_206, negated_conjecture, ![X2:$i, X3:$i]:((~((in @ X2 @ esk59_0))|~((in @ X3 @ esk60_0))|((esk61_0)!=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_202])). 2.37/0.80 thf(c_0_207, negated_conjecture, ((setadjoin @ (setadjoin @ esk67_0 @ emptyset) @ (setadjoin @ (setadjoin @ esk67_0 @ (setadjoin @ esk68_0 @ emptyset)) @ emptyset))=(esk61_0)), inference(dynamic_cnf,[status(thm)],[c_0_205])). 2.37/0.80 thf(c_0_208, negated_conjecture, (in @ esk68_0 @ esk60_0), inference(dynamic_cnf,[status(thm)],[c_0_205])). 2.37/0.80 thf(c_0_209, negated_conjecture, (in @ esk67_0 @ esk59_0), inference(dynamic_cnf,[status(thm)],[c_0_205])). 2.37/0.80 thf(c_0_210, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206, c_0_207]), c_0_208]), c_0_209])]), ['proof']). 2.37/0.80 # SZS output end CNFRefutation 2.37/0.80 # Parsed axioms : 323 2.37/0.80 # Removed by relevancy pruning/SinE : 171 2.37/0.80 # Initial clauses : 274 2.37/0.80 # Removed in clause preprocessing : 23 2.37/0.80 # Initial clauses in saturation : 251 2.37/0.80 # Processed clauses : 884 2.37/0.80 # ...of these trivial : 17 2.37/0.80 # ...subsumed : 201 2.37/0.80 # ...remaining for further processing : 666 2.37/0.80 # Other redundant clauses eliminated : 20 2.37/0.80 # Clauses deleted for lack of memory : 0 2.37/0.80 # Backward-subsumed : 3 2.37/0.80 # Backward-rewritten : 4 2.37/0.80 # Generated clauses : 10188 2.37/0.80 # ...of the previous two non-redundant : 9951 2.37/0.80 # ...aggressively subsumed : 0 2.37/0.80 # Contextual simplify-reflections : 0 2.37/0.80 # Paramodulations : 10163 2.37/0.80 # Factorizations : 2 2.37/0.80 # NegExts : 0 2.37/0.80 # Equation resolutions : 20 2.37/0.80 # Total rewrite steps : 343 2.37/0.80 # Propositional unsat checks : 0 2.37/0.80 # Propositional check models : 0 2.37/0.80 # Propositional check unsatisfiable : 0 2.37/0.80 # Propositional clauses : 0 2.37/0.80 # Propositional clauses after purity: 0 2.37/0.80 # Propositional unsat core size : 0 2.37/0.80 # Propositional preprocessing time : 0.000 2.37/0.80 # Propositional encoding time : 0.000 2.37/0.80 # Propositional solver time : 0.000 2.37/0.80 # Success case prop preproc time : 0.000 2.37/0.80 # Success case prop encoding time : 0.000 2.37/0.80 # Success case prop solver time : 0.000 2.37/0.80 # Current number of processed clauses : 430 2.37/0.80 # Positive orientable unit clauses : 52 2.37/0.80 # Positive unorientable unit clauses: 0 2.37/0.80 # Negative unit clauses : 2 2.37/0.80 # Non-unit-clauses : 376 2.37/0.80 # Current number of unprocessed clauses: 9486 2.37/0.80 # ...number of literals in the above : 36534 2.37/0.80 # Current number of archived formulas : 0 2.37/0.80 # Current number of archived clauses : 223 2.37/0.80 # Clause-clause subsumption calls (NU) : 21287 2.37/0.80 # Rec. Clause-clause subsumption calls : 10586 2.37/0.80 # Non-unit clause-clause subsumptions : 128 2.37/0.80 # Unit Clause-clause subsumption calls : 183 2.37/0.80 # Rewrite failures with RHS unbound : 0 2.37/0.80 # BW rewrite match attempts : 18 2.37/0.80 # BW rewrite match successes : 4 2.37/0.80 # Condensation attempts : 884 2.37/0.80 # Condensation successes : 4 2.37/0.80 # Termbank termtop insertions : 231781 2.37/0.80 2.37/0.80 # ------------------------------------------------- 2.37/0.80 # User time : 0.300 s 2.37/0.80 # System time : 0.017 s 2.37/0.80 # Total time : 0.317 s 2.37/0.80 # Maximum resident set size: 5248 pages 2.37/0.82 2.37/0.82 # ------------------------------------------------- 2.37/0.82 # User time : 0.307 s 2.37/0.82 # System time : 0.020 s 2.37/0.82 # Total time : 0.327 s 2.37/0.82 # Maximum resident set size: 2100 pages 2.37/0.82 % E---3.1 exiting 2.37/0.82 EOF